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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St, John's Road, Tyler's Green High Wycombe. Bucks, England HP10 8HR 78-5888 McMANAMON, Paul Francis, 1946- AN INVESTIGATION OF FLASHLAMP PUMPED DYE LASERS. The Ohio State University, Ph.D., 1977 Physics, optics
University Microfilms International, Ann Arbor, Michigan 48106
@ 1977
PAUL FRANCIS McMANAMON
ALL RIGHTS RESERVED AN INVESTIGATION OF FLASHLAMP PUMPED
DYE LASERS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Paul Francis McManamon, B.S., M.S.
*****
The Ohio State University
1977
Reading Committee: Approved By
Prof. Clifford V. Heer Prof. K. Narahari Rao Prof. Frederick P. Dickey Adviser Department of Physics VITA
July 1, 1946 Born - Cleveland, Ohio
1968 . . . . B.S. Physics, John Carroll University, Cleveland, Ohio
1968-1970 . Physicist, Electronic Warfare Wright-Patterson AFB, Dayton, Ohio
1970-1972 . Electronics Engineer, Electronic Warfare Wright-Patterson AFB, Dayton, Ohio
1973 . . . . M.S. Physics, The Ohio State University Columbus, Ohio
1973-1976 . Electronics Engineer, Avionics Engineering Wright-Patterson AFB, Dayton, Ohio
1976-1977 . Electronics Engineer, Laser Development Wright-Patterson AFB, Dayton, Ohio
PUBLICATIONS
"Wavefront Correction with Photon Echoes," Optics Communications, to be published, by Prof. Clifford V. Heer and Paul F. McManamon.
"Analysis of Candidate Electro-Optical Countermeasure Systems." Twenty-First Annual Joint Electronic Warfare Planning Conference, May, 1976.
"Homing Accuracy Requirements for Deployment of Expendable Jammers (U)." August, 1970, ASD-TR-70-12.
In addition twenty-one technical memorandums on various subjects have been written.
FIELDS OF STUDY
Major Field: Physics
Studies in Laser Physics. Professor Clifford V. Heer
ii TABLE OF CONTENTS
Page VITA ...... ii
LIST OF TABLES ...... '...... v
LIST OF FIGURES...... vii
Chapter
I. INTRODUCTION ...... 1
II. THE IDEAL DYE L A S E R ...... 3
A; Rate Equation Development...... 3 B. Dye Characteristics...... 9 C." A Simplified Set of Rate Equations ...... 12 D. A CW Solution of the Rate Equations...... 14 E. A Digital Solution of the Transient Rate Equations ...... 23
III. THE COMMERCIAL FLASHLAMF PUMPED DYE LASER...... 26
A. Introduction ...... 26 B. . The Coaxial Flashlamp...... 26 1. Blackbody Temperature...... 28 2. Distribution of Absorbed Pump Photon Density ...... 31 3. Distribution of Local Heating...... 37 4. Shockwave Effects...... 41 C. Beam Divergence...... 48 D. Steady State Optical Distortion Due to the Dye M e d i u m ...... 52 1. Distortion of a Transmitted HeNe Beam. . 52 2. Auto-Collimator Results...... 57 3. Twyman Green Results ...... 58 4. Light Focusing Experiments ...... 62 E. Discussion of the Laser Pulse Shape...... 65
iii TABLE OF CONTENTS (continued)
Chapter Page
IV POTENTIAL IMPROVEMENTS ...... 81
A. Resonator Considerations ...... 81 1. Introduction ...... 81 2. A Discussion of the Influence of Optical Distortion on Resonator Q ...... 83 3. Beam Divergence Measurement Theory .... 89 4. A Discussion of Candidate Resonators . . . 95 5. Beam Divergence Measurements ...... 102 6 . Cavity Loss Measurements ...... 107 B. Use of Triplet Quenchers ...... 118 C. Cavity Dumping ...... 1^9 1. Switching Mechanisms ...... 129 2. Experimental Results ...... 1^8 3. Anticipated Optimal Configuration...... 151 D. Q Switching a Dye Laser...... 155 E. Alternate Dye Cell Configurations...... 162 F. Double Laser Configurations...... 168
V CONCLUSIONS...... 174
APPENDICES
A The DY2 Computer Program ...... 177
B PUMP Computer Program...... 182
C BOUNCE Computer Program ...... 188
D Selection of an Electro-Optical Crystal for S w i t c h i n g ...... 195
BIBLIOGRAPHY ...... 214
iv LIST OF TABLES
Page
1 Simple Cross Section Values ...... 12
2 Values of 1/A and A, Found in the Literature . . . 18 ca be 3 FT/Fn vs and J ...... 22 J u 4 Commercial Flashlamp Pumped Dye Laser ...... 27
5 Blackbody Temperature of a Coaxial Lamp ...... 30
6 Average Number of Photons Per Mode 31
7 Pump F l u x ...... 31
8 E vs r for C = 10 ^ Molar RD6 G ...... 40 P 9 Percent Volume Reached by Pressure Wave from Light Absorbed at the Dye Boundary ...... 41
10 Transmission Through a Pinhole...... 64
11 Parameters of a Flashlamp Pumped Dye Laser...... 6 6
12 The Exponential Gain Region ...... 6 8
13 Energy per Pulse vs Concentration ...... 6 8
14 Output Energy with 85% T Mirror ...... 74
15 Percent Loss vs Average Distortion...... 8 8
16 Characteristics of the Fundamental Mode of Various Resonators...... 100
17 "Half Confocal" Resonator Performance ...... 106
18 The Effect of a Variable Aperture ...... 115
19 Allowed Configurations...... 131
20 FTIR Crystal Separation for a Given Reflection. . . . 134
21 FTIR Switching Performance...... 135 v LIST OF TABLES (continued)
Page
22 Cavity Loss Mechanisms ...... 151
23 Stored Energy...... 160
24 Initial Gain Per Pass vs Concentration ...... 161
25 Liquid Considered to Fill Diffuse Reflecting Cell. 166
26 A Partial List of PUMP Variables ...... 182
27 A Listing of the PUMP Program...... 183 -4 28 PUMP Output for C = 10 M ...... 184
29 PUMP Output for C = 5 x 10 ^ M ...... 185
30 PUMP Output for C = 2.5 x 10~ 5 M ...... 186 -5 31 PUMP Output for C = 10 M ...... 187
32 A Listing of the BOUNCE Computer Program ...... 190
33 Sample Output of the BOUNCE Program...... 192
34 Summary of BOUNCE Computer Runs...... 194
35 Candidate E-0 Modulator Crystals ...... 196
vi LIST OF FIGURES
Figure Page
1 Energy Level Diagram...... 4
2 Rodamine 6 G in Ethanol...... 10
3 Rodamine 6 G in Water'...... 11
4 Computer Generated Plot ...... 25
5 Projection onto the Base of the Cylinder...... 33
6 Full View of the Coaxial Geometry ...... 33
7 ,Densitometer Traces ...... 35
8 Pump Absorption Profiles...... 36
9 Laser Set-up...... 43
10 Pulse Shape Results with Off-center Apertures . . . 45
11 Experimental Set-up ...... ;...... 46
12 Transmission of a HeNe Beam Through a Dye Cell Filled with Ethanol ...... 47
13 Output Mirror Reflectivity...... 49
14 Normalized Dye Laser Output Energy as a Function of Half—Angle Divergence for Different Concentration of Rd 6 G Solutions...... 50
15 Triangle Mode ...... 51
16 Shot to Shot Peripheral Distortion...... 55
17 Shot to Shot Central Distortion ...... 55
18 Shot to Shot Distortion Using a 1-pm Flow Filter. . 56
19 Shot to Shot Distortion Without a Flow Filter . . . 56
vii LIST OF FIGURES (continued)
Twyraan Green Geometry ...... 59
Flowing Coaxial Dye Cell ...... 59
22 Clear Aperture ...... 59
23 A Pattern With a Stationary Dye ...... 60
24 Pattern Generated by Stretched Handi-Wrap ...... 60
25 Coaxial Dye Cell...... 63
26 Clear Aperture...... 63
27 Stored Energy vs Time ...... 69
28 Stored Energy vs Time ...... 70
29 Stored Energy vs Time ...... 71
30 Stored Energy vs Time ...... 72
31 Stored Energy vs Time ...... 73
32 Flashlamp Pulse Shape ...... 74
33 Pulse Shapes for a 144 cm Flat/Flat Cavity...... 75
34 Pulse Shapes for a 3 m "Half Confocal" Cavity . . . 75
35 Laser Pulse Shape With a Max R Output Mirror. . . . 76
36 Laser Pulse Shape With a 20% R Output Mirror. . . . 77
37 Resonator Distortion...... 86
38 Assumed Phase Distortion...... 89
39 Beam Expanding Telescope...... 90
40 Beam Expanding Telescope...... 94
41 Cavity Designs...... 96
viii LIST OF FIGURES (continued)
Figure Page
42 Unstable Resonator ...... 103
43 Beam Pattern From an Unstable Resonator...... 103
44 Experimental Beam Expander Set-up ...... 103
45 Beam Pattern From a Long Flat/Flat Resonator . . . 105
46 Microdensitometer Scans for Three Shots of the Laser Under Identical Conditions ...... 108
47 Beam P a t t e r n ...... 109
48 Experimental Set-up...... H I
49 Pulse Detected Around Laser End Mirror . '...... H I
50 Beam Spreading Measurement Geometry...... 112
51 Cavity Configuration...... 115
52 Pulse Shape Measurements ...... 117
5 3 .Laser C a v i t y ...... 118
54 The Influence of CHT on Laser Performance...... 120
55 The Effect of 0^ on the Laser Pulse...... 121
56 The Effect of Og on the Laser Pulse...... 122
57 Spectral Output of a Cerium Doped Quartz Coaxial Flashlamp...... 123
58 Influence of COT on a Low Q Cavity ...... 124
59 Influence of COT on a High Q Cavity...... 124
60 Influence of CHT on a Laser Pulse With a Max R "Output" Mirror...... 126
61 Influence of CHT on a Laser Pulse With a 20% R Output Mirror...... 126
62 The Influence of COT on Laser Performance for a Max R "Output" Mirror (Cerium Doped Lamp)...... 127
ix LIST OF FIGURES (continued)
Page
The Influence of COT on Laser Performance for a 20% R Output Mirror (Cerium Doped Lamp)...... 127
Influence of COT on KRS Laser Performance for a Max R "Output" Mirror (Cerium Doped Lamp)...... 128
65 Influence of COT on KRS Laser Performance for a 20% R Output Mirror (Cerium Doped Lamp)...... 128
66 Light Through a Right Triangular Crystal ...... 133
67 Initial Polarization ...... 137
68 Rotated Polarization ...... 137
69 Electro-Optical Switch ...... 137
70 Laser Cavities Using Electro-Optical Switching . . . 139
71 A Glan-Foucault Prism ...... 141
72 Reflection Loss Due to Two Internal Surfaces . . . . 142
73 Modified Gian Prism...... 144 147 74 Voltage Conversion Circuit ......
75 Cavity Dumping Configuration ...... 148
76 Stored Energy vs Time...... 148
77 Cavity Dumped Energy ...... 150
78 Cavity Dumped Pulse Shape...... 150
79 Optimum Cavity Dumping Configuration ...... 153
80 Voltage Pulse...... 154
Cross Section of Ru (bibyr)^ Cl2 ...... 157
Rate Constants and Energy Level Diagram for Ru (bipyr) 3 Cl2 ...... 159
Q Switching Arrangement...... 160
x LIST OF FIGURES (continued)
Figure Page
84 Diffuse Reflecting Dye Cell ...... 164
85 Diffuse Reflectance of Eastman White Reflectance C o a t i n g ...... 165
8 6 Transverse Dye Cell ...... 169
87 Dye Laser Pumped by a Flashlamp Pumped Dye Laser. . 170
8 8 Experimental Set-up for a Laser-Pumped Laser .... 172
89 Optical Distortion Results...... 173
90 Rotation Geometry ...... 206
xi CHAPTER I
INTRODUCTION
Dye lasers are divided into two types, those excited with radiation from another laser and those excited directly by a flash- lainp. Flashlamp pumped dye lasers hold promise of higher efficiency, but are not as well developed. They still have many technical deficiencies when compared to laser pumped dye lasers. For example, flashlamp pumped dye lasers have a very wide beamwidth^ and poor dye 2 lifetime. In addition, commercially available flashlamp pumped dye 3 lasers have pulse widths from 200 nsec to 1.5 psec whereas laser pumped dye lasers are available at other pulse widths and CW. T.astly, commercially available flashlamp pumped dye lasers are restricted to 4 advertised repetition rates below 50 hz, with practical use of most commercially available flashlamp pumped dye laser limited to no more than a few hertz.
In this effort flashlamp pumped dye lasers were investigated.
Both limitations and growth potential of these devices were specified.
Areas of particular interest were beam divergence, pulse height, and
^Theodore F. Ewanizky, Beam Quality of Pulsed Organic Dye Lasers. ECOM-4163 (October 1973), p. 16. 2 Discussion with Captain Sid Johnson, U.S. Air Force, AFAL/DHO-1.
Frances M. Lussier, "Selecting a Tunable Dye Laser," Laser Focus, Volume 13, No. 2, February, 1977, p. 48.
^Lussier, "Selecting a Tunable Dye Laser," p. 48.
1 pulse rise time. Theoretical calculations concerning the performance possible with an ideal dye laser were performed followed by both experimental and theoretical investigations of real flashlamp pumped dye lasers. The influence of a number of effects on flashlamp pumped dye laser performance was quantified. In addition, since the technique available to sharpen pulse rise time and to increase laser pulse height (without increasing the power input to the laser) involve switching the laser cavity Q, various switching techniques were investigated for applicability to flashlamp pumped dye lasers. CHAPTER II
THE IDEAL DYE LASER
Calculations concerning the performance of an ideal dye laser are performed in this chapter. Basic rate equations are developed. Then dye characteristics are specified and discussed. It is shown in the following discussion that the dye laser can potentially pass through three gain regions during a pulse. Initially, exponential gain occurs. Then a first level of saturation is reached in which linear gain occurs, and finally complete saturation (where power in the cavity is no longer increasing). Complete saturation occurs when the input power provided by the pump is balanced by losses in the laser cavity.
A. Rate Equation Development
Figure 1 shows an energy level diagram for a dye laser. Using this figure a relatively general set of rate equations can be developed. In this figure states a, a 1, b, b', and d represent singlet states; c, c', and e represent triplet states, and therefore have slightly lower energy levels than their corresponding singlet states.
Ideally pumping would occur from a to b' followed by rapid decay from b' to b, lasing from b to a1, and rapid decay from a* to a. In fact the pump used for flashlamp pumped dye lasers has a high density of photons at energy levels larger than from a to b 1 (unless a UV DYE LASER ENERGY DIAGRAM
Singlet States Triplet States
T-T absorption
;vj 300 nsec ...... > I intrasystem / crossing / pumping
lasing / 250 nsec
Times quoted are for Rd 6G in ethanol.
Figure 1. Energy Level Diagram filter Is used to eliminate this light). Level d is used in the above
diagram to represent the excited states to which pumping can occur.
Pumping does, of course, occur also to the desired energy states, b ’.
Those molecules, pumped up to state d then can fall to b' or a ’ or
could cross to state e. Due to the rapid decay rate from d to b
it is assumed however that molecules pumped up to state d fall back to
state b ’, from which they fall to b. Molecules in state b can then
lase, spontaneously, decay to state a', or cross to cr, the lowest
triplet state. Crossing to c' is undesirable because: a) molecules
can tend to accumulate in state c, thus removing them from laser action, and b) absorption from c to e can be a direct loss at the laser wavelength.' Fortunately, other molecules, called triplet quenchers, can be added to the dye solution to collide with dye molecules in the triplet state and cause them to return to the ground state. The natural decay rates from c to a* or a are very low since this is- a forbidden transition.
The rate equations used to describe populations in each of the states are given in Eq. (1).
dN (la)
dM (lb)
5 F. P. Schafer, "Principles of Dye Laser Operation," Dye Lasers Topics in Allied Physics, Vol. 1, ed. F. P. Schafer (New York: Springer-Verlag, 1973), p. 28.
B. B. Snavely, "Continuous Wave Dye Lasers," Dye Lasers, Topics in Allied Physics, Vol. 1, ed. F. P. Schafer (New York: Springer-Verlag, 1973), p. 87. 6
dNh ~6t = 'b^b1 " £ Wk,b+afNb " ^a^b " ^c^b " £ Wk,b-dNb (lc) dll, - = -A, ,, N. , + + )W . , ,N (Id) dt b b d b ’ d £ k,a-+bf a
dN - ~ = A , N , - A ,N - I W, N + A N (le) dt c c c ca' c “ k,c-*-e c ec e k
dN , ~ = ~ = A, ,N. - A , N , + A ,N (If) dt be b c'c c ec e dN, . = I W. ,N - A,, ,N, + I W, , ,K, (Ig) dt £ k,a-*-d a db d £ k,b-d b dN = I W. N-AN-A.N (lh) dt “ k,c->e c ec e ec e k where
N. is the number of molecules in state i i A^j is the rate of transition from state i to state j
W, . .is the rate of stimulated emission from state i to state j ’ 3 by mode k Additional equations of use are:
N = N + N f + N, + N, , + N + N t + N j + N (2) 0 a a' b b' c c a e
dN - [W ■ i + W A N (3) at P|3 “b p)3 —d 3
d % ■•■ft = [W£,b-a' - W ,.b-a] Nb - Vc-eNc <« where
Np is the number of pump photons in the cavity in mode p
N^ is the number of laser photons in the cavity in mode £ Next, the rate equations given above will be divided by volume, using the substitution
- Ik (5) n i V
Also transition rates can be expressed in terms of cross section,
Wk,a'->b = Fk V b <6) a^,^, and photon flux, F^, using Eq (6). Photon flux, F^, is the number of photons per second in mode k which cross a given area, whereas cross section, a ,, , is the effective area’of a molecule ’ a'b presented to radiation in mode k. Also, it will be assumed that n£ = ne , = 0. With these simplifications and substitutions, in addition to using two average pump flux values, an<^
Eq (1) becomes Eq (7). an^ are avera6e flux values over the an<3 ° a(j average cross section values.
dn -dT “ Aa'ana- ' (Fab'°ab- + Fad°ad] "a <7a)
dn , = J F na.n, - A , n , + A fn + A, ,n, (7b) dt J H b a ’a a' ca' c T>a' d Xi
dnb d T “ V b V - j V n nb - Aba'nb - Abc'nb " J V s nb (7c) dv “ d T = ‘ V b V + Adb'"d + Fab’aab'"a (7d>
dn *-r~ = A, n, - A ,n (7e) dt d c b ca' c where it was also assumed A^, = 0 , and
a = absorption cross section at the laser wavelength for absorption from b to d
a = average absorption cross section for absorption from a to b*
a ^ = average absorption cross section for absorption from a to d
F = flux of laser photons in mode £ X*
F k» = Punip photons at a wavelength suitable for a to b 1
F ^ = flux of pump photons at a wavelength suitable for a to d
Also, Eq (3) becomes Eq (8 ) and Eq (4) becomes Eq (9).
dn , = [F , ,o , + F ,o ] n (8 ) dt ab ab ad ad a
dn
■dr'V(°i-“s)nb - V c 1 <9)
Next, Eq (9) can be converted to Eq (10) using the definition of n^ and F , where F^ is taken in the z direction and 3 is loss per unit length (a distributed loss).
dIV ~dT = pit[(0i as)nb - °cenc - (10)
To further simplify these equations it will be necessary to consider the typical values of quantities in the rate equations. B. Dye Characteristics
The absorption of Rd 6 G as a function of wavelength is given in
7 8 Figs. 2 and 3 for solvents of ethanol and water , respectively.
Figure 2 is given in units of molar extinction coefficient, the
extinction coefficient for light of a given wavelength travelling
through a one molar solution of the dye. Figure 3 is given as cross sectional area of a dye molecule. Figure 3 has units of square meters.
Equation (11) gives the relationship' between extinction coefficient and molecular cross section.
a = a n (1 1 ) a where
a = extinction coefficient
a = molecular cross section 23 In addition, however, it must be known that there are 6.6x10 molecules per liter in a one molar solution. This is the well known 26 Avogadro's number. Therefore, there are 6.6x10 molecules per cubic meter in a one molar solution and Eq (12) gives the extinction coefficient as a function of dye concentration, C, given in molarity.
a o 6 . 6 x 10 2 6 a C (12)
^K. H. Drexhage, "Structure and Properties of Laser Dyes," Dye Lasers, Topics In Applied Physics, Vol. 1, ed. F. P. Schafer (New York: Springer-Verlag, 1973), p. 168.
8 * F. P. Schafer, "Principles of Dye Laser Operation," Dye Lasers, Topics in Applied Physics, Vol. 1, ed. F. P. Schafer (New York: Springer-Verlag, 1973), p. 89. Figure 2. Rhodamine Rhodamine 2. Figure
a x 10 (mole 10 0 300 200 molar decadic extinction coefficient); coefficient); extinction decadic molar pcrmo fursec (rirr units). (arbitrary fluorescence of spectrum 6 G in ethanol. ethanol. in G 400 aeegh (nra) Wavelength 500 --- 600 asrto pcrm (and spectrum absorption 700 --- quantum 10 Figure 3, Spectrophotoinetric Spectrophotoinetric 3, Figure cr(A) and E(A) 0.4 0.8 1.6 2.0 2.8 C F X CF X moy O a omril ufcat Te triplet- The surfactant. commercial a LO, Ammonyx omlzd o ht EAd * .2 te measured the =* 0.92, /E(A)d that so normalized un (93 wt n tao slto. h de con dye The solution. and ethanol an Morrow with by (1973) obtained Quinn o^.CA), was spectrum, state etain nal ae a 1“* . () a been has E(A) * M. 10“ was cases all in centration obtained from a solution of the dye in water plus plus water in dye were the E(A), of solution emission, a and from (A), o obtained absorption, singlet unu il fr fluorescence. for yield quantum 10 aeegh (ran) Wavelength 4 50 2 60 700 660 620 580 540 data a (A) 10 x for the 22 dye rhodamine rhodamine dye 10 -1 6
. The G.
2
%
11 Comparing Figures 2 and 3 one can see that peak cross section in 7 Figure 2 converts to a molar extinction coefficient of 1.78 x 10 7 1/mole 1/m as compared to 1.17 x 10 1/mole 1/m in Figure 3. Also, the ratio between absorption cross section and emission cross section is higher for Rd 6 G in water (Fig. 3) than for Rd 6 G in ethanol (Fig. 2).
This tends to produce a more efficient laser in an ethanol solvent.
Since ethanol was used as a solvent in most cases, the data of
Fig. 2 was employed in later theoretical calculations. For simplicity three average cross section values were defined and are shown in
Table 1. Values in this table are given in the mks system of units.
Table 1
AVERAGE CROSS SECTIONS
Wavelength Molar Extinction Cross Section Symbol 7 -20 2 507 nm to 545 rim 10 1 /mole 1/m 1.5 x 10 m o ab — 91 210 nm to 250 nm 3.5 x 10 1/mole 1/m 5.3 x 10 a ad 6 —20 2 Laser Emission 8 x 10 1/mole 1/m 1.2 x 10 m a.
These are averages of the peak values of cross section and would be of interest for flashlamp pumped dye lasers. Laser pumped dye lasers use cross section at the pump laser wavelength as well as the emission cross section.
C. A Simplified Set of Rate Equations
Now that characteristics of a typical dye are known reasonable pump levels were assumed and the rate equations simplified. 13
Equation (13) gives an expression for n^, derived from Eq (7f) under
steady state conditions.
F j ct j n. = v 3' " <13> d Adb’ -21 12 Then one can use cr , = 5.3 x 1 0 and A ,, , = 1 0 .along with a ad db reasonable value for F , to obtain an estimate of the size of n, ad d 9 relative to n . Assuming a usable pump photon density of approximately 3 9 2 28 10 watts per m at 0.5 pm one has F ^ as 5.05 x 10 photons per
square meter. Equation (14) then gives the estimated relationship
between n , and n . d a
i n, = 2.7 x 10 ^ n (14) d a
Therefore n^ will be neglected. Since n^ is proportional to a
high enough pump flux density could invalidate this approximation,
however, that should not occur for either flashlamp pumped dye lasers
or most laser pumped dye lasers. Some high power pulsed lasers (such
as doubled NdYag), if focussed to a small spot, would invalidate this
approximation. In a similar manner na , and n^, can be neglected,
allowing Eq (7) to reduce to Eq (15).
dn | V i " b + Acanc + ^ " b • [Fab°ab + Fad0ad] “a (15a>
dnb ~dtT = ^Fabaab + Fadaad^ na " ? F£a£nb “ ^ a 1^ " ^c^b ^15b^
Q F. P. Schafer, "Principles of Dye Laser Operation," Dye Lasers, Topics in Applied Physics, Vol. 1, ed. F. P. Schafer (New York: Springer-Verlag, 1973), p. 28. dn ■df - - Acanc U5C)
where it was assumed F ^ = F an^ 0 ^ = CTat>»*
Equation (10), the gain equation, can then be used with Eq (15)
and Eq (16) to determine the shape of the laser pulse.
n_ = n + n, + n (16) 0 a d c
D. A CW Solution to the Rate Equations
Assuming a steady state approximation, Eqs (10), (15) and (16)
were solved analytically. For steady state Eq (15) becomes Eq (17).
0 = I V A + Acanc + Aba11b ' [Iab°ab + Fad°ad] na <17a)
0 = lFab°ab + Fab°ad ^ na “ I V*"b " ^"b ' *bA <17b)
0 “ - Acan c (17c) And from Eq (17c) it can be seen that
_ (18) nc - A ~ % ca Also, from Eq (17b) one has:
(19) I V + Ab, where Then, using Eqs (18), (19) and (16) one has Eqs (21) and (22).
n 0 n = 0 (21) a Fa / A + A. x + P P I ca *b £ F A ° A + ^ a + ' A ca ■) A
n n------(2 2 ) I'b ' TvlA F a F a A P P P P ca
Equation (22) is an important equation since if Eq (10) and
Eq (18) are combined, it becomes obvious that laser gain is heavily
dependent on n^. This is shown in Eq (23)
dF ' A, . TT " °ca> % - B1 <23> ca
Then, in order to obtain an indication of how laser flux x^ill build up, the loss term, 8 , was set equal to zero and Eq (22) for n^ was substituted into Eq (23). It was assumed all laser flux was in a single
mode and Eqs (24), (25), and (26) resulted. Equation (24) can then be integrated to obtain Eq (27).
—Ld F P = - -V S (24) dz F £B + 1 where . _ ^bc . _ „ A s A ca A pn0 on where d = distance travelled through the gain medium. Equation (27) can then be converted to Eq (28).
F Ad - B(F - F ) -S. = e 1 (28) F £0 1 Unfortunately this is a transcendental equation and is therefore impossible to solve explicitly for F^. One can however see the initial exponential gain characteristic in Eq (28). Also, one can see that if saturation is approached, then linear gain as given by Eq (29) occurs.
f* - fao= t d <29)
Since Eq (28) is transcendental, however, it was advantageous to break the evaluation of Eq (23) into two regions as given by Eqs (30) and (31). These equations are just special cases of Eq (22).
1. For £ F£ct£ <<: + ^bc^ * unsaturated SL
n 0 ° - (30) A, + A, A, oa be . - , d c + 1 + F a A . p p cd
2. For I F£a& » (A^ + A^), saturated a 17
Initially one has the unsaturated condition, but as laser flux grows a transition into the saturated region takes place. For the unsaturated condition n^ is a constant, therefore Eq (23) can be integrated to yield Eq (32).
[(oA - °s - A 2*1 ace> " b - S,,r (1 - a) (32) FAn+l F £n where
a = loss per pass
d = length of dye cell
F„Jin = laser flux after n passes F, ,, = laser flux after n+1 passes Jln+1
It should be noted that Eq (32) contains two loss terras, a distributed loss, 0, and a loss per pass, a. The distributed loss term, 0 , reduces laser gain in a similar manner to triplet-triplet absorption or singlet absorption. In this initial region however a dye laser has very high gain and neither loss is expected to be very significant.
Before proceeding, the influence of triplet-triplet loss and singlet-singlet loss will be considered. For singlet-singlet loss, it was assumed that a < o . For triplet-triplet loss a rather S A* extensive literature search was conducted concerning the relative values of A^c and Aca In order to determine how severe a problem would be posed by triplet-triplet absorption. Table 2 gives various values found in the literature for (A ) and A^c (referred to in the literature as K ). Due to its recent nature, method of measurement, o JL 18
Table 2
VALUES OF 1/A AND A,_ FOUND IN THE LITERATURE ca l>c
(A )_ 1 A, Solvent ca g - 1 A, /A (if mentioned)______(nsec)______10 sec______d c cd_____ Footnote o +
+1.3 0.85 1 0 ethanol 250 1 3.4 methanol 105 ±15 1 1 o • ethylene glycol 125 + 2 0 6.4 00 1 2 ethanol 250 13 } 1 . 0 ethanol 4.0 14 50 28 1.4 15 • 1 0 0 16 140 2 0 2 . 8 17 16 18
1 0 J.P. Webb, W.C. McColgin, and O.G., Peterson, "Intersystem Cro! Rate and Triplet State Lifetime for a Lasing Dye," IEEE Journal of Chemical Physics, Vol. 53, 11 (1 Dec 1970), p. 4227.
1 :LIbid. 12 O. Teschke, A. Dienes, and Gary Holton, "Measurement of Triplet Lifetime in a Jet Stream CW Dye Laser," Optics Communications, Vol. 13, No. 3 (Mar 1975), p. 318. 13 A.V. Aristov and Yu. S. Maslyukov, "Gain and Induced Absorption of Organic Lurainophors as a Function of Their Structural Properties," Opt. Spectrosc., Vol. 41, No. 2 (Aug 1976), p. 141.
^A.V. Aristov and Yu. S. Maslyukov, "Amplification and Induced Absorption in Solutions of Organic Luminophors," Opt. Ipektrosk, Vol. 35, No. 6 (Dec 1973), p. 660. 15 Benjamin B. Snavely, "Flashlamp-Excited Organic-Dye Lasers," Proc. IEEE, Vol. 57 (Aug 1969), pp. 1374-1390. 1 £ B.B. Snavely and F.P. Schafer, "Feasibility of CW Operation of Dye- Lasers," Physics Letters, Vol. 28A, No. 1.1 (10 Mar 1969), p. 728.
■^F.P. Schafer, "Principles of Dye Laser Operation," p. 58.
1 8 B.B. Snavely, "Continuous Dye Lasers," p. 90. 19 and good correlation with other recent measurements the values given in Webb et al. were chosen as probably the most accurate with ethanol as a solvent. Some of the earlier estimates would cause problems in building CW dye lasers — which have been built. Combining a A. /A value of 0.85 with cross section values given in Fig. 3 DC ca one can see that:
A, a 9 ^ 0.095 at 580 nm (33) ca aJt
This ratio becomes even lower at slightly shorter wavelengths, whereas it climbs to about 0.25 at 600 nm. Laser action will however occur near 580 nm since this is the peak of the gain spectrum. Therefore, triplet state absorption will only decrease gain by about 1 0 % for a steady state situation.
To determine how many passes take place with exponential gain one must evaluate Eq (35) in order to determine initial gain per pass. That combined with an evaluation of the spontaneous emission present due to the level of excited n^ states gives an estimate of how many passes are required to reach the region where
J >> (A^a + A^c) . In this second region then linear gain takes place since the amount of power added to the laser energy is directly dependent on the input pump power. The initial level of spontaneous emission from which exponential gain occurs is given by Eq (34) since this gives the spontaneous emission in a given solid angle.
F - (&-) (34) n a. \ 4 tt / I 20
Once saturation occurs Eq (31) for is applicable instead of
Eq (30). Then, combining Eq (31) with Eq (23), Eq (35) results
dF* <[«* - r* - 6 V dz <35> ca &
It can be seen from Eq (35) that complete saturation occurs when
Eq (36) is satisfied.
F Amax = *°£ “ °bd “ A ^ ^ B e . ca *
Often, however, it is more convenient to deal with loss per pass, a,
instead of a distributed loss term, B. Changing differentials to differences and including lumped loss, a, one can obtain Eq (37) from Eq (35),
F*,J+1 " F*,J(1 -«) + («*- r * v-p--p~ f - (37) ? ca Jt where d is the length of the dye cell and it has been assumed that the distributed loss, B, has been included in loss per pass, a. Based on Eq (37), max laser flux is given by Eq (38).
F a n_d a. - t—Abc a - a A, max Si A „ ce s V V °- ... <38> ca
The triplet state effect therefore lowers the peak attainable laser flux by about 10% for Rd 6 G. Also, it can be seen that the peak laser flux is inversely proportional to loss per pass through the cavity. For any given case this maximum should be checked against the limits placed on previous approximations. Also, it can be seen 21
that the singlet state cross section, a , directly lowers maximum s laser flux.
To calculate the rate of flux increase in the linear region, while including lumped loss per pass, a, one starts by rewriting
Eq (37) as in Eq (39), where a term, F q , has been implicitly defined.
FS,J+1 " F*,J - “> + Fo <39>
Equation (40) then follows, and can be converted to Eq (41) by 19 appropriate substitution.
• ' * . j ■ Fo " “),n W0) Xm = 0 a
F1,J = ^ [1 - a - a)J ] (41)
As can be seen growth in this region is basically linear (an amount of flux F q is added each time to the existing flux in a mode),
It is, however, modified by the loss term such that as flux develops loss per pass, which is a percentage of the flux in the cavity, eventually equals the new flux added per pass and final saturation, as in Eq (38), occurs. It should be noted that J in Eq (41) only refers to the number of passes occurring after the linear gain region has been reached.
19 Mathematical Tables from Handbook of Chemistry and Physics (Chemical Rubber Co., 1959), p. 317. 22
If loss per pass In each laser mode is equal then Eq (41) could be converted to total laser flux as in Eq (42).
F 0 J Fj = [1 - (1 " ot) ] (42)
Equation (42) was then used to generate Table 3 which gives F^/F q as a function of loss per pass and number of passes. Since steady state has been assumed it means that change is relatively slow. As can be seen in a low loss per pass cavity flux generated on many passes can be stored in the laser cavity. For high loss per pass saturation occurs quickly. To store energy in the laser cavity it is therefore necessary to minimize loss per pass through the dye
Cregardless of laser gain).
Table 3
Fj /Fq vs a and J
Ct/J 1 5 1 0 2 0 30 60 ca
1 % 1 . 4.9 9.6 18 26 65 1 0 0 GO r-*
3% 1 4.7 • 15.3 2 0 28 33.3
1 0 % 1 4.1 6.5 8 . 8 9.6 1 0 1 0 o 25% 1 3.0 3.76 4.0 .e* ■ 4.0 4 CO o 1 1.25 1.25 1.25 1.25 1.25 1.25
Once flux, Fj, is determined energy stored in the laser cavity can be found from Eq (43).
e j = hvA ( t ) f j <43> where h is Planck's constant V is the laser frequency L is the distance light travels between passes through the dye cell 23
A is area of the dye cell c is the speed of light
For a linear format laser L is the length of the cavity and for
a ring laser it is the length around the ring, The factor of two is
necessary since flux is travelling in both directions.
A new expression for E^, can be generated by combining Eq (42)
and Eq (43), forming Eqs (44) and (45). Then, since Eq (44) is the same in form as Eq (42) , Table 3 can be used to find Ej as a function of J and a.
g Ej = “ [1 - (1 - a)J ] (44) where 2hAL P , n„d ^ c (45) " “—A • o ce> (■ ca
In a conventional dye laser, however, one is more concerned about emitted energy than stored energy. Equation (46) gives energy emitted by a laser with pulse width T and output mirror reflectivity, R.
Emitted - TT (£) - R> <46>
E, A Digital Solution of the Transient Rate Equations
Equations (15), (16), and (10) are the rate equations applicable for a dye laser with reasonable rate constants. Some steady state approximations were used to derive these equations, -but these were only employed to neglect the population in states that were calculated to have very small populations. For digital solutions Eqs (15), (16), and (1 0 ) were treated as difference equations and modelled on a digital 24 computer. It was assumed initially that n& = n^, - nc = 0, and F^ had a very small value. Then various conditions were modelled on the computer. Appendix A gives a listing of the computer model used. Figure 4 gives a sample computer-generated plot. The pump curve is normalized to peak at 1 . 0 and is presented for comparison against the stored laser energy in the cavity. Energy (mJoules) 20.0 30.0 40.0 10.0 50.0 Length Length TT1G » 250,0 nsec 250,0 » TT1G percent 80,0 Loss SAE= . x.+7 photons xl.E+27 1.7 = PSCALE TS1T1 Energy = 693.7 mJoules 693.7 = Energy SIGL = 1.2 x l.E-20 SQ M SQ l.E-20 x 1.2 = SIGL =50,0 =2,5 200 iue . optr eeae Plot Generated Computer 4. Figure meters nsec ie (nsec) Time 600 800 pump □ 0 pulse 1000 25 CHAPTER III
THE COMMERCIAL FLASHLAMP PUMPED DYE LASER
A. Introduction
The flashlamp pumped dye laser available for this experiment was
a Phase^R Model DL-1100 laser. It uses a coaxial flashlamp with a
flowing dye system and is typical of commercially available flashlamp 20 pumped dye laser systems. A recent article summarizes the
characteristics of commercial flashlamp pumped dye lasers. Table 4 is
taken from that article. Most of the commercial flashlamp pumped dye
lasers are pumped with a coaxial flashlamp. Some (e.g., by Electro
Photonics, Ltd.) are pumped with a linear flashlamp. Lasers with linear
flashlamps have somewhat longer pulsewidth as can be seen from Table 4.
Since a coaxial flashlamp pumped dye laser was available for the
experiment more detail concerning the characteristics of this type of
laser is given below. The coaxial flashlamp is discussed in detail
along with the beam divergence, optical quality of the laser cavity,
and the resulting pulse shape. Later potential improvements to this
type of laser will be discussed.
B. The Coaxial Flashlamp
A coaxial flashlamp is cylindrical in shape. The discharge occurs between an outer cylinder and an inner cylinder. It is therefore possible to flow dye through the inner cylinder and obtain a high
20 Lussier, Frances M., "Selecting a Tunable Dye Laser," Laser Focus, Vol. 13, No. 2 (Feb 1977), pp. 48-52. 26 Table 4 COMMERCIAL FLASHLAMP PUMPED DYE LASERS (as of Feb., 1977)______
degree ojj coupling between the lamp and .the dye medium. The alternate
types of flashlamps are called linear lamps and vortex stabilized
lamps. Blackbody temperature of these other two types of lamps will
not be estimated here.
1. Blackbody Temperature
The flashlamp which was used experimentally was a coaxial flash-
larap approximately one centimeter in diameter (I.D.) by 12 cm long.
The dye cell through the middle of the flashlamp is however 20-cra
long since dye flow connections are required on each end. References
in the literature refer to this type' of lamp as a near blackbody 21 radiator with an effective temperature in the 20000 to 30000°K range.
In order to confirm this temperature range a calculation of lamp
blackbody temperature was made as shown below. This calculation could
then also be used to determine the influence of firing voltage and
other parameters on lamp blackbody temperature. 22 The power per unit area emitted from a blackbody is given by
Eq (47)
PT = oT4 (47)
__ S. Blit and U. Ganiel, "Distribution of Absorbed Pump Power in Flashlarap-Pumped Dye Lasers," Optical and Quantum Electronics, Vol. 7 (1975) pp. 87-93: H. Furomoto and II.L. Ceccon, "Optical Pump for Organic Dye Lasers," Applied Optics, Vol. 8 , No. 8 (August 1969), pp. 1613-1623: C.M. Farrar, "Simple, High Intensity Short Pulse Flash- laraps," The Review of Scientific Instruments, Vol. 40, No. 11 (Nov. 1969), pp. 1436-1438. 22 RCA, Electro-Optics Handbook, Technical Series EOH-11 (1974), p. 36: Heer, C.V., Statistical Mechanics, Kinetic Theory and Stochastic Processes (New York: Academic. Press., 1972), p. 44. 29
r-8 where o i,s the Stefan~Boltzmann constant and is equal to 5,67 x 10
The energy dumped into the laser during pulsewidth, t, is simply the energy in the storage capacitor and is given by Eq (48),
E = ~ CV 2 (48) where E = stored energy
C = capacitance
V = laser firing voltage (across capacitor)
Then, assuming a lamp efficiency, K, which includes the fact that the lamp is not a perfect radiator, it can be seen that the power per unit area emitted from the flashlamp is given by Eq (49).
P = KCvl ( 4 9 ) T 2tA K } where A = radiating surface area of the lamp.
The two expressions for P^, can then be equated and an effective temperature of the lamp found as in Eq (50).
4 _ KCV 2 , . T 2tAo <50)
The laser used in experiments had C = 0.3 pf and t = 750 nsec.
Also, only one side of the cylinder was allowed to radiate (the other surface was covered with a reflecting metal foil that acted as a ground). — 3 2 Therefore the radiating area of the lamp was 3.77 x 10 m . Table 5 gives the calculated blackbody temperature as a function of lamp efficiency and laser firing voltage. 30 Table 5
BLACKBODY TEMPERATURE OF A COAXIAL LAMP
Efficiency/ Voltage 18 kv 22 kv 25% 16 600°K 18 300 50% 19 700°K 21 800 75% 21 800°K 24 100
Furumoto and Ceccon measured spectral brightness of a similar lamp
and concluded that in the visible region the lamp acted as a 21 000°K
23 o o blackbody. In the UV region from 2500 A to 3000 A it acted as a
24 000° blackbody. Below that level they did not take measurements.
For simplicity a 21 000°K blackbody lamp will be assumed In future
calculations.
Now that the effective blackbody temperature of the lamp has been
determined it can be used to find the # of photons per unit area per
second transmitted into the dye as a function of A and a A (see Eq (51))•
The term in parentheses in Eq (51) Is the average number of thermal
quanta per mode.
§ of photons per c AX unit area per second (51) for a given A and a A h c kTA - 1 23 H. Furumoto and H.L. Ceccon, Appl. Opt., Vol. 8 , No. 8 (1969) pp. 1613-1623. 24 RCA, Electro-Optical Handbook, E0H-11 (1974), p. 36: This can also be obtained from Eq 2.35 in Heer, C.V., Statistical Mechanics, Kinetic Theory and Stochastic Processes (New York, Academic Press, 1974), p. 51 31
This terra is given in Table 6 for the same wavelengths as specified in Table 1. The number of photons per unit area per second is given in Table 7 for two values of A and . One for absorption in the .21
^ m to . 2 5 Am band (Fa(j) and one for absorption in the 0 . 5 0 7 5 >*ni to
0.5^5 /W band (Fab). For a given term(e.g. Faa)the difference between
the wavelengths (e.g. . 2 5 - .2 1 /tm) was taken as^A, with the average
taken as X. Table 7 then gives these values at the surface of the
dye cell, the following section then determines photon density as
a function of position in the dye cell.
Table 6
Average Number of Photons Per Mode
0 . 2 1 yin .0 4 0.25 ym .0696 0.5075 ym .352 0.545 ym ■ «4
Table 7
# of Photons per Unit Area per Second 26 2 F ,, 3.5 x 10 photons/m Pab- 27 2 F ^ 1.4 x 10 photons/m
2. Distribution of Absorbed Pump Photon Density
Figures 5 and 6 show two views of the path taken by a photon which
is emitted along the surface of a cylinder and travels through a volume 32
Figure 5. Projection Onto the Base of the Cylinder
\
- r i u *
s.
Figure 6 . Full View of the Coaxial Geometry 33 dV* Tills is a simplified model of a coaxial flashlamp pumped dye laser cell, where the cylinder would be filled with an absorbing medium
(the dye). The major simplication used is that the glass envelope between the dye medium and tiie lamp discharge is ignored.
The rate equation governing absorption of pump photons is given by
Eq (52).
^ b n (52) dt £ak,ab Fk •a k
The term in brackets in Eq (52) will decay as a function of radius inside of the coaxial dye cylinder. Molecules inside the dye cylinder will therefore have a lower transition rate than molecules at the dye surface. For constant cross section, ground state population, and direction this term has an exponential decay. The exponential decay however only holds for a given light ray as it travels a distance r in a given direction. The photon density inside the dye cell is the sum of photons reaching that volume from the entire flashlamp. Summing over a small solid angle one has:
7 F. dS = F„ dfi, cosQ dS, e~aX (53) Ak where
dSfa is a differential surface at the outside of the dye cylinder
df^ is the solid angle projected from dS, to a differential surface in the dye cylinder, dS^
a is the attenuation coefficient
F q I s the flux at the surface of the dye cylinder
6 and r are defined by Figure 6 . 34 dS dS, cosO d b Since dft, = tz and dn = --- zz— Eq (53) can then be converted b r 2 a r to yield Eq (54).
y F - F 0 dna e-“ r (54) Ak Then, since dft = sin0 d0 d<|>, one can see that the transition rate
of a molecule inside of the dye cylinder will be proportional to G(a)» where G(a) is given by Eq (55).
Tt 2 tt
G(a) = J J* sin0 dO dt|> e ar (55)
0 0 0 <|>
For low absorption (a^ << 1) this expression correctly reduces to a
uniform distribution (since the focusing affect due to having a cylinder 25 with an index of refraction greater than one has been neglected ).
In order to evaluate Eq (55) one must find an expression for r.
Based on Fig. 5 one can use the cosine law to find Eq (56)
2 2 2 b = a + p - 2a p c o s (tt- c}>) (56)
where p is the projection of r onto a two-dimensional slice of the
cylinder. This equation can then be solved for p, yielding Eq (57).
/ 2 2 2 p = -a cos
Then by evaluating p(u) and p(0) it can be seen that the + sign in
Eq (57) should be chosen to conform with the geometry In Fig. 5. Eq (57)
and Fig. 6 can then be used to find r, as in Eq (58).
— a coscb +•h l/b/ 2 - a 2 sin • 2 cf> sca\ r = ------x — f-r------(58) sin0 25 G.E. Devlin, J. McKenna, A.D. May and A.L. Schawlow, "Composite Rod Optical Masers," Applied Optics. Vol. 1, No. 1 (Jan 1962), pp. 11-15; J. McKenna, "The Focusing of Light by a Dielectric Rod," Applied Optics, Vol. 2, No. 3 (Mar 1963), pp. 303-310. 35 Then it is possible to evaluate Eq (55), using Eq (58) to provide
a value for r. This is however a complicated integral and was therefore
performed digitally using the PUMP computer program listed in Appendix B.
Figure 8 shows photon density versus radius, a, for a constant lamp
inner radius, b, and various values of dye concentration. An examina
tion of Fig. 8 shows that flux can be roughly approximated by a simple exponential decay law with change in radius, as given in Eq (59). -onn (b-a)C Ga(b) ' e U (59) where a = absorption cross section
n^ = number of molecules per cubic meter in a one molar solution
C = concentration in molarity 26 Figure 7 shows some profiles measured across a 2-cm cylinder of Rd6G.
These profiles are taken from a densitometer reading of a photograph and are not calibrated.
C- 1.5 x 10 *M -5, '"N c= 1.5 x 10 M
C= .5 x 10"5M
Figure 7. Densitometer traces (redrawn) of the fluorescence pattern over the cross section of a 2 -cm diameter cell containing an aqueous solution of Rhodamine 6 G for different concentrations
Michael H. Gassman and Horst Weber, "Flashlamp-Pumped High Gain Laser Dye Amplifiers," Opto-Electronics, Vol. 3 (1971), pp. 174-184. Arbitrary Units 30 20 10 5 0 M 10 x 5 m C M 10 » C C = 2.5 x 10 x 2.5 = C C = 1 x 10 x 1 = C
5 - M 5 " Figure Figure M
8 . Pump Absorption Profiles Absorption Pump . ais (mm) radius 37
The reason for the difference between measured curves In Fig. 7 and calculated curves in Fig. 8 is that glass between the dye and the lamp discharge was ignored in the analytic development. A focusing effect in dielectric cylinders, referred to earlier, causes a somewhat different flux profile if the discharge is modelled as separated from the dye cylinder by a substance with a lower index of refraction than the dye solvent.
,A simplification that will be used later is to model the effective area of the dye cylinder as:
(60)
This is done to obtain an approximation of that part of the cylinder which is actually obtaining a population Inversion. As dye concen tration becomes higher eventually only the outer surface of the dye cylinder has population inversion.
3. Distribution of Local Heating
In the previous section pump flux as a function of radial distance was calculated. This was done for the absorption cross section of Rd6 G in the 5075 A to 5450 X region. Some of this light will be re-emitted as laser energy, but much of it will go into heating the dye. In addition absorption at other wavelengths, both in the dye and in the solvent will cause heating. Those wavelengths (in the UV and infrared) which are absorbed by the solvent will be discussed later. Those wavelengths which are absorbed by the dye will be absorbed with varying flux distributions, depending on absorption 38
cross section-and dye concentration. For Rd6 G the wavelength region O O from 5075 A to 5450 A will be absorbed closer to the cell walls than other wavelengths. For each cross section and concentration it is, however, possible to use the PUMP computer program to find a flux
density distribution in the cell. This flux density distribution can
then be converted to a level of absorption. Absorption causes the dye
to become a convex lens since more heat is absorbed at the surface
than at the center — causing a larger decrease in index of refraction at the surface. The index change occurs since heating the dye causes a pressure difference, which in turn causes a change in the density of the liquid and therefore a change in its index of refraction. In order to determine how significant this heating effect is, dye absorption was divided into regions, 0.21 to 0.25 pm, and 0.5075 to
0.545 pm. From Fig. 2 it was estimated earlier that cross section -21 2 -20 2 in these two areas is 5.3 x 10 m and 1.5 x 10 m , respectively. 27 Also, pump flux at the surface of the dye is 1.4 x 10 photons per 26 square meter in the UV and 3.4 x 10 photons per square meter in 8 2 the visible. This converts to 1.27 x 10 watts/m in the visible g and 1.23 x 10 watts/square meter in the UV. Since the lamp has -3 2 5 3.7 x 10 m of area, 4.8 x 10 watts are incident on the dye in the visible area and 4 . 6 x 1 0 ^ watts are incident in the ultraviolet.
Over the duration of a 750 nsec flashlamp pulse this results in
3.45 joules of heat in the ultraviolet and 0.36 joules in the visible.
The item of interost is not whether the dye is heated, but whether it is heated non-uniformly. It is therefore of interest to note that since UV light has an absorption cross section only, one third that of
the visible light it will have a flux intensity distribution char
acteristic of one third the dye concentration in visible light. -5 Therefore, if a dye concentration of 5 x 10 molar is used the UV
flux will have a rather uniform distribution and will not cause a -4 significant amount of uneven heating. For a concentration of 10 M
the UV light will have a distribution characteristic of visible light -5 with a concentration of about 3.5 x'10 M, and will have a somewhat
uneven flux distribution.
Given these factors it was assumed a resonable heating problem would be modeled by assuming the 0.36 joules of energy in the visible
and 3.45 joules of energy in the UV are absorbed according to
Eq (61). This was done since the PUMP program indicated that exponential
decay from the dye cell wall was a reasonable model of the flashlamp
pump distribution.
-a , n Ar -o ,n Ar Ep(r) = 0.36 e 3b & + 3.45 e a (61)
Ep (r) gives the energy which passes through a given slab of thickness
Ar in the assumed 750 nanosecond flashlamp pump duration. Table 8
gives Ep vs r. Also the change in temperature which would be caused by absorption of the amount of absorbed energy going from one radius
to the next is calculated. This is calculated using Eq (62). 40
Table 8 -4 E vs r for C = 10 molar Rd 6 G P
r E AT . An P 5 mm 3.81 j 1 . 2 x 1 0 ~ 4 4 mm 2.57 j 0.091 1 . 2 x 1 0 " 4 3 mm 1.76 j 0.077 1.04 x 10- 4 2 mm 1.23 j 0.07 0.95 x 10~ 4 1 mm 0 . 8 6 3 0.082 1 . 1 1 x 10**4 0 nun 0 . 6 j 0.17 2.3 x 10" 4
A change in temperature of the solvent then causes a change in pressure which in turn changes the density (and therefore the index of refraction) of the solvent. Equation (63) gives the change in index caused by a given change in temperature.
An = n a AT (63)
Table 8 also gives the change in index which would occur in ethanol for a temperature change as large as is given in the table. For -3 ethanol a = 10 and n = 1.36. These values are taken from
References 27 and 28, respectively.
27CRT Handbook, p. 2248.
2^Aldrich Chemical Company, Inc., The 1975-1976 Aldrich Catalog/ Handbook of Organic and Biochemicals, 1974. 41
4. Shock Wave Effects
A number of references conclude that flashlamp pumped dye laser 29 pulses are terminated by a shockwave propagating inward. This wave is created at the surface of the dye where the solvent absorbs infrared (and possible UV) radiation from the flashlamp. The wave 30 then propagates inward at 1.6 mm/psec. Due to the high density of solvent molecules the penetration depth of light absorbed by the solvent is very shallow (for reasonable absorption cross sections).
Therefore the shock wave originates at the surface of the dye. For a 5-mm radius dye cell Table 9 gives percentage of the dye cylinder reached by the' shock wave as a function of time.
Table 9
PERCENT VOLUME REACHED BY PRESSURE WAVE FROM LIGHT ABSORBED AT THE DYE BOUNDARY
Time (nsec) Percent Volume
0 0 5-mm radius dye 100 6.3 cell 1 . 6 mm/psec 200 12.4 wave velocity 300 18.3 400 24.0 500 29.4 600 34.7 700 39.8 800 44.6 . 900 49.3 1000 53.8
29 T.F. Ewanizky, R.H. Wright, Jr., and H.H. Therssing, "Shock wave Termination of Laser Action in Coaxial Flashlamp Dye Lasers," Appl. Phys. Lett. J22, p. 520 (1973); S. Blit, A. Fisher and U. Ganiel, "Early Termination of Flashlamp Pumped Dye Laser Pulses by Shock Wave Formation," Applied Optics, Vol. 13, No. 2, p. 335. February 1974. ■an S. Blit, A. Fisher and U. Ganiel, "Early Termination of Flash lamp Pumped Dye Laser Pulses by Shock Wave Formation," Applied Optics, Vol. 13, No. 2, p. 335, February 1974. Table 9,- of course, only Indicates the area covered by some
level of shock wave. Since the flashlamp pulse gradually grows in
intensity, so does the shock wave eminating from the dye surface.
At a little over 3 psec from flashlamp initiation the whole dye
cylinder will contain a shock wave at some level. The literature
articles which refer to shock wave as the cause of laser pulse ter mination have a longer pulsewidth than the 350 nsec of a DL-1100.
Therefore it is reasonable that shock wave effects will have a
substantially lower influence on the DL-1100 (and most other commercial
flashlamp pumped lasers) than indicated in these articles. There
simply is not enough time for the shock wave to strongly influence a laser that has a 500 nsec or even a 1 psec pulsewidth.
Two experiments were conducted to determine the influence of a
shock wave on.DL-1100 laser. In one of the experiments a non-standard resonator design was used since this design was used for many other
tests in this investigation. Also, this resonator design results in a substantially longer laser pulse than the resonator standard design.
Therefore, if shock wave effects are present they will be more apparent using this resonator design than if the standard design were used.
Experiment One: One method which was used to determine the possible influence of a shock wave travelling in from the edge of the dye cell was to look at laser pulses generated using only a small aperture of the dye cell. This aperture was taken both In the center of the dye cell and displaced by various amounts. If the shock wave 43
travels inward fast enough to have an influence on laser action in
this laser then the laser pulse generated when the aperture is taken at the center of the dye cell should be longest and the pulse generated when the aperture has maximum displacement from the center should be shortest. This is because the shock wave will reach those parts of the dye cell near the flashlamp wall first, while it will take a significant
time for it to reach the center of the dye cell. Pictures of the pulse detected using a 4-mm aperture near the dye cell were taken.
Displacements of approximately 0, 1-mm, 2-mm, and 3-mm, were used.
This was done by simply moving the laser head sideways, leaving the aperture and all-but the "output mirror" in place. The "output mirror" was a flat mirror with 99.9% reflectivity. The laser pulse was viewed through this mirror. Figure 9 shows the laser setup.
\ V.
N N aperture s \ HeNe
Figure 9. Laser Setup Cavity length was 2.5 meters. The detector used was an EG&G 580
Series detector. For each condition one pulse was used to measure
energy and the other pulse was used to take a picture of the pulse
shape. A 150 MHz, 50 £2 Hewlett Packard amplifier was used to amplify
the pulse between the detector head and the oscilloscope so that
sufficient voltage would be available on the oscilloscope to compete
against the noise that was fed through the trigger (which came off of
the sync output of the DL-1100 laser). For each of the pictures taken
the scope settings were 0.5 volts/cm and 0.2 ysec/cm. Figure 10 shows
the results. Due to noise it was, however, still difficult to obtain
data. The pulse shapes in Fig. 10 are approximate averages after
visually eliminating noise. Viewing Fig. 10 it does appear that
pulses with the aperture near the outside of the dye cell are shortened
Most of the laser action is, however, over by the time any significant
influence of the shock wave is felt. This is consistent with
previously discussed calculations since the shock wave will travel
inward at 1 . 6 mm/psec and laser action will terminate within one nsec.
It also should be pointed out that the shortening effect which does
take place would be more significant in this case than with other
resonators since this resonator configuration, using maximum reflector
mirrors and a very stable configuration, produces a longer laser pulse
than other resonator configurations. This allows more time for the
shock wave to travel inward and influence the laser pulse. The
commercially available resonator, using flat/flat mirrors and a 2 0 %
reflecting output mirror has a.0.3 to 0.4 psec pulse. 45
0 iran offset
._____.______.______-^*=.-- 1 .2 .4 .6 .8 1.0
1 mm offset
4-----1 .2 .4 .6 .8 1.0
2 nun offset
.2 .4 .6 .8 1 . 0
3 mm offset
I,., . ..J .2 .4 .6 .8 1.0 Time (nsec)
Figure 10. Pulse Shape Results with Off-Center Aperture 46
Experiment Two: Another experiment whin), was conducted to deter
mine the influence of a shock wave on the optical quality of the dye
medium consisted of simultaneously monitoring the flashlamp pulse and
a HeNe beam which was being transmitted through the dye cell at various
displacements from the center of the cell. This was done both for a
dye cell filled with pure ethanol and for a dye cell filled with a
- 5 solution of 5 x 10 M Rd6 G in ethanol. Figure 12 shows the results
for a cell filled with ethanol. The experimental setup is shown in
Fig. 11.
Det 1
Dye Cell HeNe
6328A Filter
et 2
Figure 11. Experimental Setup
In order, to avoid detecting the flashlamp with the detector that was supposed to detect the HeNe beam this detector was placed about
O O 4 meters from the flashlamp and a 30 A wide filter at 6328 A was placed in front of the detector. Even with these precautions the
first 1.5 psec or so after triggering the laser could.not be
detected becuase of either noise or detection of the flashlamp. reference pump pulse
■ ‘ 1 2 3 4 5
0 offset
1.5 mm offset
3 mm offset
1 2 3 4 5 Time (ysec)
Figure 12. Transmission of a HeNe Beam Through a Dye Cell Figure l*2a shows the flashlamp pulse detected by detector 1 (as shown in Fig. 11). Figures 12b through d then show the signal detected by detector 2 as a function of the displacement of the HeNe beam from the center of the dye cell. It can be seen that as the HeNe beam is offset from the center of the dye cell it is more quickly obscured. The center region of the dye cell is not obscured until
3-4 psec after triggering the laser while areas close to the wall are obscured earlier. It appears based on these results that the influence of this shock wave will be felt primarily after the laser pulse has ended. Some influence near the dye wall will, however, occur in the time frame of the laser pulse.
C. Beam Divergence
The standard DL-1100 laser uses a 35-50 cm long resonator formed by flat mirrors. Mirror reflectivity is approximately 99.9% for one mirror and 20% for the other, output mirror. Output mirror reflectivity was measured on the CARY and is given vs wavelength in
Fig. 13. The dye cell, consisting of a coaxial flashlamp with dye flowing through it and AR coated windows, is situated approximately in the middle of the resonator. Measurements of the beam divergence of this laser were made. In addition, measurements taken from the literature were reviewed. > Tt -U o 0) rH 10 a)
i______1_____ i ___I 6000 6500 7000 7500 O Wavelength (A)
Figure 13. Output Mirror Reflectivity
Figure 14 shows normalized energy contained within a given half angle for a coaxial flashlamp pumped dye laser with flat resonator mirrors. This figure was taken from the article referred
to by Footnote 31. As can be seen dye concentration has a significant influence on beam divergence. Also, it is apparent that the beam consists of basically two parts, a central core plus a rapidly diverging disk. Figure 15 shows a "triangle mode" which explains the division 32 into two energy groups. At high dye concentration this triangle mode is pumped more strongly since it is closer to the dye surface than a mode through the middle of the resonator.
31 Ewanizky, Theodore, F., Beam Quality of Pulsed Organic Dye Lasers, ECOM-4163 (October 1973), p. 16. 32 Ibid., p. 18. 50
A - 5 X io-5 molar concentration I
o B - 2 X !—1 mo ] a r concentration 1 o r-* 0 u 1
0 X concentration
P(Q) E.
2 4 6 - 8 10 12 14 15 "Iff t o — rf 0 (lialf-angle divergence in milliradians)
Figure 14. Normalized dye iaser output energy as a function of lialf-angle divergence for different concentration rliodamlne CG solutions. 51
Laser Cavity
*
Figure 15. Triangle Mode
Beam divergence measured by taking a burn pattern at the focal point of a one-meter lens was 6 mrad for a dye concentration of -A 2 x 10 M. The formula to convert spot size at the focal point of a lens to beam divergence will be derived later. Other measurements of beamwidth taken just by measuring the rate at which the beam is expanding seem to indicate a significantly larger beam divergence.
For a concentration of 10 molar and a cavity length of 38.5 cm the beam expanded from 1-cm diameter at 29 cm from the output mirror to
1.3 cm at 120 cm from the output mirror. This indicates a beam divergence of 33 milliradians, except that this is only in the near field so it is not entirely accurate to extrapolate these measure ments to determine far field beam divergence. Considering however that the near field contains the beam waist it seems reasonable that the beam divergence should be larger than this measured value. Based on these measurements and observation of the beam pattern at about
7 meters, the beam emitted by the standard laser is made up of about a 6 -mrad central portion plus about a 40-mrad ring caused by the "diamond mode" discussed earlier. 52
In the standard configuration 410 mj output was achieved at a firing voltage of 18 kv and 690 mj at a firing voltage of 22 kv. These -5 measurements were made with a concentration of 5 x 10 M. At a -4 concentration of 2 x 10 M 355 mj was achieved at a voltage of 18 kv and 685 mj at 22 kv. Using an energy into the flashlamp of
E. = 1/2 CV 2 (64) in where C = capacitance = 0.3 yf these measurements can be translated -5 into efficiences of 0.84% and 0.94% at a concentration of 5 x 10 M -5 and 0.95 % at concentration of 2 x 10 M
D. Steady State Optical Distortion Due to the Dye Medium
There were a number of experiments performed which give an indication of the optical quality of the dye medium. Each of these experiments will be discussed below.
1. Distortion of a Transmitted HeNe Beam
The laser was usually aligned using a HeNe beam. Distortion of the beam passing through the dye cell could therefore be taken as an indication of poor optical quality. Enlargement of the beam could be caused either by a lens effect in the medium or by forward scattering.
In an attempt to determine the amount of distortion normally introduced when a beam passes through the dye medium a HeNe pattern was observed about 8 meters after passing through the dye cell. The pattern obtained with the dye cell removed was compared with the pattern obtained for a beam which traversed the dye cell. In both 53 cases a 1.5 cm diameter spot was obtained. Also, when the beam was passed through a l/64th-inch pinhole prior to the dye cell a 1.3-cm diameter circle was observed at the 8 -meter distance with the first ring having an outer diameter of 2.5 cm and the second ring not quite visible all the way around. These patterns occurred whether the
HeNe beam passed through a flowing dye cell or not (the cell was filled flowing with ethanol). When the beam passed through a flowing dye cell, however, the basic pattern was filled with motion. It was apparent that the dye medium was having a varying influence on the
HeNe beam. If the dye pump was turned off the 1.5-cm diameter circle obtained for a HeNe beam became an oblong shape approximately 2.5 cm high by 1.3 cm wide. The dye was not left off long enough for the pattern to return to normal. It had been noted while using the HeNe alignment laser that the distortion caused when the dye flow was turned off gradually faded if the flow was left off long enough.
The HeNe beam used above was 4-mm in diameter as it passed through the dye cell. In addition it was not collimated. Therefore the HeNe beam was expanded to 10 mm and collimated. The beam was then either viewed on a wall about 2 meters from the cell or used to expose film at about 1.5 meters from the cell. The pattern observed contained substantial motion. In addition it was enlarged substantially over the 10-mni collimated diameter. It was therefore concluded that either scattering was taking place or that a portion of the dye cell was being distorted (causing most of the light to pass through with minor distortion while.some of the light is deflected by up to about 10 mrad). Pictures of the exposed beam were taken on two 54 different occasions. The first time a 10 pm pore size flow filter was used. Figure 16 shows three exposures with neutral density (N.D.) =
0, ASA 50-speed film, and an exposure time of l/30th of a second. The density of a filter is the common logarithm of the attenuation due to that filter. A neutral density filter is one that has constant density vs wavelength. A change in the pattern from picture to picture can be observed. Figure 17 shows the pattern obtained under identical conditions except N.D. = 1.3. The fringe patterns observed in the intense portion of the beam do not appear to vary as much as the peripheral fringe pattern.
The second time this experiment was set up one objective was to determine the influence that forward scattering had on the pattern observed. Figure 18 shows the pattern observed 1.5 meters beyond the dye cell with.the dye flowing through a filter that had a 1 pm pore size. Film for these shots was ASA 400 and the exposure was for l/125th of a second. Figure 18a had a N.D. of 0 and 18b had a N.D. of 1.0.
Figure 19 was then taken without any flow filter. Again, Fig. 19a was with a N.D. of 0 and Fig. 19b had a N.D. of 1.0. Based on these measurements it was concluded that the varying pattern observed was not due to 1 pm or larger particles or bubbles in the dye. If forward scattering is causing the effect, smaller particles would have to be the cause. Figure 16. Shot to Shot Peripheral Distortion
(a) (b)
Figure 17, Shot to Shot Central Distortion 56
(a) (b)
Figure 18. Shot to Shot Distortion Using a 1 pm Flow Filter
(a) (b)
Figure 19. Shot to Shot Distortion Without a Flow Filter 57
2. Auto-Collimator Results
Another experiment which was conducted to determine the steady
state optical quality of the dye medium was to look through the dye
cell with an auto-collimator. With the dye flowing it was possible to
obtain a weak return in the auto-collimator. When the dye cell was
not in its path the auto-collimator displayed a sharp, bright set of
crosshairs caused by the flat mirror being viewed. Then the dye cell was moved into place and the crosshairs caused by the flat mirror
became weak and fuzzy. In fact, they were weaker than the return cross
hairs caused by the AR coated window on the near side of the dye cell.
A return from the AR coated window on the opposite end of the dye
cell could not be obtained. Even if a one-centimeter diameter
aperture was placed in front of the mirror being viewed the return
crosshairs were sharp and bright until the dye cell or some other
object of low optical quality was introduced. For example, the
return caused by using a one-centimeter aperture with a stretched piece of Handi-wrap in the path was about the same quality as the return caused by having the dye cell in the path (when the dye cell was filled with flowing ethanol). When the dye flow was stopped the return crosshairs would disappear completely. Then after about five minutes they would gradually begin to fade in. The dye was left
stationary for a maximum of about 15 minutes and during this period
the optical quality of the dye medium did not reach the same level
as it had with the dye flowing. When the flow was turned on approximately the same optical quality as had been previously obtained was quickly achieved. 58
3. Twyman-Green Results
One standard method of judging optical quality is to use a
Twyman-Green interferometer. Figure 20 shows a diagram of the Twyman- 33 Green test setup. As can be seen it is basically a Michelson interferometer. The item to be tested is placed in one of the arms of the interferometer and any path difference caused by the tested item becomes apparent by a change in the fringe pattern. This testing method was employed for the coaxial flashlamp used in my dye laser. Figure 21 was taken with a flowing coaxial dye cell as the test item. The number of fringes in the pattern was chosen arbitrarily by adjusting the interferometer. Deviation of these fringes from a straight line indicates distortion. Figure 22 is shown for comparison. In it a clear aperture of about 10-mm diameter was the "test item." As can be seen this does produce straight fringes. These pictures were taken with ASA 400 film at an exposure time of 0.4 psec. Figure 23 then shows the pattern obtained looking through the coaxial dye cell ten minutes after dye flow has been turned off. Figure 24 shows the pattern obtained when the stretched piece of Handi-wrap mentioned with the auto-collimator test was used as a test item.
To better evaluate these results a portion of the theory associated with Twyman-Green testing was developed. The intensity
2 3 Briers, J.D., "Interferometric Testing of Optical Systems and Components: A Review," Optics and Laser Technology, Vol. 4, No. 1 ■ (Feb. 1972, Guilford), pp. 1-56. 59
} flat mirror sample beamsplitter pinhole
flat mirror source
condenser collimatin lens focusing lens
viewing area
Figure 20, Twyman-Green Geometry
Figure 21. Flowing Coaxial Dye Cell Figure 23. A Pattern With a Stationary Dye
Figure 24. Pattern Generated by Stretched Handi»-wrap 61 patterns recorded above are generated by the absolute value of the
square of the field at a given point. The field is here given by
the sum of two terms. One term is a reference wave and the other is identical to the reference wave except for distortion in the test object. Therefore Eq (65) gives intensity across the pattern.
K*.y) = {e±kz + e±tkz y)1} " 2 (65) 1 O
Therefore intensity will appear to vary as in Eq (6 6 ). ,
— = 1 + cos [t|> (x,y) ] (6 6 ) o
A tilt of the test object will therefore result in straight fringes, whereas a distortion will result in either curved fringes, or unequal separation between fringes, depending on the orientation of the distortion. Also, a distortion which is small in the x,y plane would result in a light spot within a dark fringe or a dark spot within a light fringe. Therefore any "fuzziness" to the fringes is also a sign of poor quality optics.
The test data above was then re-evaluated. It appears optical quality through the coaxial cell cannot be perfect or the auto collimator results for the obviously distorted Handi-wrap (see
Fig. 24) would not be similar to the results for the dye cell. Much of the similarity could be due to physically small distortions in the dye cell which would only show up in the Twyman-Green experiments as small light or dark areas in an otherwise straight fringe. This would 62 be difficult to detect due to the fact that grain qualities of the film can produce a similar effect.
To further define the optical quality of the coaxial cell two additional Twyman-Green patterns were taken. One through a coaxial dye cell with ethanol flowing and the other through a clear aperture.
This time P/N 55 film with ASA 50 was used so a negative would be available. Also, exposure time was 1 second and the image size was smaller since to the slower film speed requires more light. Figure 25 shows the picture for a coaxial dye cell and Figure 26 the picture for a clear aperture. The aperture was unfortunately somewhat larger than the dye cell. On these pictures there does appear to be a difference in contrast level between the clear aperture and the dye cell. This difference in contrast can be caused by motion of the fringes through the dye cell or by physically small phase distortions in the dye cell.
A. Light Focusing Experiment
In an attempt to measure the loss per pass due to either scattering or distortion the collimated light from a HeNe beam was focused through a pinhole, both after the beam passed through the dye cell and without passing the beam through the dye cell. It was felt that any distortion or scattering would prevent focusing and reduce the amount of light passing through the pinhole. Table 10 gives the results. As can be seen the wavefront does not deteriorate completely on passing through the dye medium. It is however degraded enough that a sub stantial change in resonator mode could occur. Figure 25. Coaxial Dye Cell 64
Table 10
TRANSMISSION THROUGH A PINHOLE
Lens Focal Pinhole Dye Flow Percent Length______Diameter______Cell Filter______Transmission
1 0 0 cm theoretical 1 0 0 % 400 nm no — 95% yes no 84% yes yes 79%
2 0 cm theoretical 1 0 0 % 50 ym no — 95%*
yes no 6 8 %
1 0 0 cm theoretical 60% . 50 pm no — 77%^ yes no 51%^ yes yes 57%t
Assumed value, used as a reference for those values below. j* Each of these values quoted is the best value of a series of measure ments in which much variation occurred. The best value was chosen since it was assumed that variation was due to misalignment of the small pinhole with respect to the small focus that was to pass through the pinhole. The adjustment mechanism was fairly crude.
The transmission values when no dye cell is present are reference values and should not deviate substantially from theoretical values for a perfect plane wave. Theoretical values were calculated from
Eq (67) and Eq (6 8 ). Eq (67) Is derived later and Eq (6 fl) is taken from Reference 34.
Siegman, A.E., An Introduction to Lasers and Masers (1971, McGraw-Hill), p. 312. 65
w = --- (67) O W -
- 2 (a/wQ )
= 1 = e (68)
In this experiment is 5 mm.
E. Discussion of Laser Pulse Shape
In the first chapter dye laser theory was developed. In this section that theory is applied to a coaxial flashlamp pumped dye laser and compared against experimentally measured results. It is then concluded that the commercial coaxial flashlamp pumped dye laser used in these experiments must have high loss per pass to account for its pulse shape compared to its pump pulse shape.
Both an analytical continuous wave approximation theory and the computer model approach were used for a coaxial flashlamp pumped dye laser. Table 11 gives necessary specific laser parameters to use in the Chapter One theory. The computer model, however, takes actual pump pulse shape.
Initially laser flux level is the noise level, [as given by
Eq (34)]. Then, since laser flux is low, exponential gain occurs
[according to Eq (32)]. In this region n^ is given by Eq (30).
These factors are combined in Table 12, where a number of characteristics of the exponential gain region are given as a function of concentration.
As can be seen this theory indicates that at a concentration of 10 ^ M 66
Table 11
PARAMETERS OF A FLASHLAMP PUMPED DYE LASER
Parameter Symbol Parameter Value
A cell area 7.85 x 10~ 5 m 2 d cell length 0.12 m 26 2 F pump flux a-»-b 3.5 x 10 photons/m ab (see Table 8 ) 27 2 pump flux a->d 1.4 x 1 0 photons/m Pad (see Table 8 ) a loss per pass variable 3 loss per length of dye variable 0 beam divergence variable (half angle)
X wavelength 0.59 ym (Rd6 G) L cavity length variable T pump pulsewidth 750 nsec (assumed)
laser cross section 1 . 2 x 1 0 ” 2 0 m 2 a * (see Table 1) (Rd6 G) - c . „-20 2 cross section a-+b 1.5 x 10 m aab (see Table 1) (Rd6 G) -21 2 cross section a->-d 5.3 x 10 A m °ad (see Table 1) (Rd6 G) 8 —1 rate from b->a 2 . 5 x 1 0 sec ^ a (Ref. 6 ) (Rd6 G)
rate from b-vc 3.4 x 10 6 1/sec (see Table 2) (Rd6G) A rate from c-*a 4 x 10 sec ca (see Table 2) (Rd6 G) dye concentration variable
6 . 6 x 1 0 2 6 C 0 -20 2 triplet-triplet 0.3 x 10 U in ce cross section (Rd6G) 67 gain does not even occur with a 20% R output mirror. Experimentally gain does, however, occur in this situation, but it is marginal.
Then, once saturation occurs Eq (31) for n^ is applicable instead of Eq (31). Equation (45) for Eq can then be used along with either Eq (44) for stored energy or Eq (46) for output energy
(Eq (46) is only applicable for low Q resonators). Table 13 gives
Eq, emitted energy, and stored energy as a function of dye concen tration. These calculations assume as increment of laser energy Eq is added to the cavity once a pass after the threshold is reached.-
Stored energy is given for a 3% loss per pass and emitted energy is given for an 80% output coupling mirror (only 20% reflectivity). As can be seen the emitted energy obtained with a 2 0 % reflecting output mirror drops off much faster than the stored energy (3% loss per pass) as concentration drops.
A digital solution to the rate equations was also used. Figures 27 to .31 show summarized results of the model for various concentrations of Rd6 G and for various mirror reflectivities. These graphs show stored energy as a function of time. Energy values given in these figures do however assume a uniform pump illumination throughout the -4 dye cell and especially at a concentration of 1 0 M this approximation breaks down. In reality the smaller area given by Eq (60) is available.
In Table 14 for output energy an adjusted energy value which takes this area difference into account is given. 68 Table 12
THE EXPONENTIAL GAIN REGION
g N M °b n -4 21 23 10 3.3 x 10 4.2 x 10 116 45,000 2.25 2.7 -5 21 23 5 x 10 1.67 x 10 2 . 1 x 1 0 10.8 90,000 4.8 7.2 23 2.5.5 x 10~ 5 0.83 x 102 1 1.04 x 10 3.3 180,000 10 31 v- 5 21 23 10 0.33 x 10 0.42 x 10 1 . 6 450,000 28
Assumptions: Terms: 0 - 1.5 mrad g — gain per pass through the dye d = 0 . 1 2 m G = gain required to reach the linear gain region 6 = 0 N = number of passes through the dye to reach the linear gain region if loss per pass is zero M = number of passes through the dye to reach the gain region if a 20% R output mirror is used and other losses are zero
Table 13
ENERGY PER PULSE VS CONCENTRATION
T, pulsewldth = 750 nsec L, cavity length = 3 m d, dye cell length = 0 . 1 2 m
E* emitted _____
10“ 4 2.85 x 10- 5 m 2 1.49 mj 215 443 mj
5 x 10“ 5 5 x 10“ 5 m 2 1.3 mj 169 382 mj
2.5 x 10“ 5 7.6 x 10“ 5 m 2 9.9 mj 87 284 mj
10“ 5 7.85 x 10” 5 m 2 4.1 mj 0 104 mj 69
3 000 10 M Concentration
0 37. loss [3 « 25% loss
100 __
Energy (mj )
200 600 800 1000 . Time (nseo)
Figure 27. Stored Energy vs Time 70
1000__ 3 x 10 ** H Concentration 0 = 3% loss = 25% loss □ = 85% loss
100__
Energy (m j)
-10
200 • 600 800 . 1000
Figure 28. Stored Energy vs Time 71 1000 5 x 10 ** M Concent rut loti 0=3% loss o = 25% loss 0 *= 85% loss
100
Energy (n>j)
10 __
200 400 600 BOO 1000
Figure 29. Stored Energy vs Time 72
1000 10 ^ M Concentration Q » 3% loss
0 - 25% l o BS Q ° 85% loss
o o © O
100 p □ p p
Energy __ (mj)
10 ..—
200 800600 1000
Figure 30. Stored Energy vs Time _5 5 x 10 M Concentration 1000__ PSCAI.E “ 0.35 Q = 3% loss o « 25% loss □ = 85% loss i
O O 100_
Energy (mj)
10—
200 600 BOO 1000
Figure 31. Stored Energy vs Time 74
Table 14
OUTPUT MIRROR WITH 85% T MIRROR
c______E______Adjusted E
10“ 4 M 1280 mj 461 mj
5 x 10" 5 M 353 mj 226 mj
3 x 10“ 5 M 59 mj 50 mj
1 x 10" 5 M 0 0
Figure 31 has slightly higher energy values than Fig. 29 due to a higher pump energy which includes the ultraviolet pump.
Experimentally, the measured pulse shape appears to depend on loss factors ignored in the theory developed above. For example, the shape of resonator mirrors and the type of dye flow filter have an influence on stored energy. This can be seen by examining Figs. 33 through 36. Figure 32 shows the flashlamp pulse shape for comparison.
0 . 2 ysec/cm
Figure 32. Flashlamp Pulse Shape,
Figure 33 shows the pulse shapes detected through the end mirror . of a 144-cm long laser cavity formed by two flat mirrors. Figure 33a shows the pulse detected with a 20% R mirror and Fig. 33b shows the 75
0 . 1 psec/cm (a)
0 . 1 psec/cm (b)
Figure 3 3 . Pulse Shapes For a 144-cm Flat/Flat Cavity
2 volts/cm, 0 . 2 sec/cm (a) (2 0 % R output)
5 volts/cra, 0 . 2 sec/cm (b) (max R output)
Figure 34. Pulse Shapes for a 3-m "Half Confocal" Cavity 76
no filter (a)
5 pm filter (b)
2 Vm filter -(c)
■ 1 pm filter (d)
, .— ^ — 0 . 6 pm filter (e)
0 . 5 volt/cm, 0 . 2 psec/cm
Figure 3 5 ^ Laser Pulse Shape with a Max R Output Mirror 77
no filter (a)
5 pm filter (b)
2 pm filter (c)
1 ytn filter (d)
0 . 6 pm filter (e)
0 . 2 volt/cm, 0 . 2 psec/ cm
Figure 36. Laser Pulse with a 20% R Output Mirror 78
pulse detected with a 99.9% output mirror. As can be seen from
Fig. 33b even with a maximum reflector "output" mirror this cavity
configuration has very large loss (this is obvious both by the
height of the pulse and rapid decay). Figures 33a and 33b have the
same vertical scale, therefore it can be seen that peak power in the
cavity does not increase substantially when an 80% transmitting output
mirror is replaced by a 0.1% transmitting output mirror. This
cavity must therefore have high loss even without a high loss output
mirror.
In Fig. 34 the pulse shapes detected for a 3-meter long cavity
formed by a 6 -m mirror and a flat mirror. Dye concentration with -4 10 M of Rd 6G in ethanol and the flashlamp used was doped with Cerium,
therefore it cut off UV pumping. It can be seen that peak stored
energy with a 99.9% R "output" mirror is about two times as high as with a 20% R output mirror. Also, laser action does occur longer with the maximum reflector "output" mirror. Still, there must be a very large inherent loss in the laser or else a much larger difference between the two pulse heights and shapes would be noted.
Figures 35 and 36 show the influence of a flow filter on stored energy in the laser cavity. The resonator used was a 2.5-m resonator formed by a 5-meter mirror and a flat mirror. Figure 35 shows the energy in the cavity vs time for a 99.9% R "output" mirror while
Fig. 36 shows the energy stored in the cavity vs time for a 20% R output mirror. Note that the vertical scale in Fig. 35 is 2.5 times as large as the vertical scale in Fig. 36. This means that for smail 79 pore size flow filters peak energy is about seven times as high with the max R mirror as the 20% R mirror. For no flow filter this ratio is only about 2.5. Therefore filtering the flowing dye has a very significant influence on cavity loss. Figure 32, the flashlamp pulse shape, should also be compared to Fig. 35 since this indicates that the laser pulse for low loss situations approaches the flashlamp pulse shape.
Figures 34 and 35 were taken with a dye concentration of
5 x lb M Rd 6G in ethanol. Also the one 5-m radius end mirror was a 2-inch diameter mirror. The conditions shown with small pore size filters were the best cavity energy storage obtained. Comparing these figures against Fig. 29 seems to indicate that even in this case a loss on the order of 20% per pass is probable. Most of the situations tested (such as the "no filter" case shown in Figs. 35 and 36) have an intrinsic loss on the order of 50 to 80% — as indicated by the lack of energy storage obtained when a maximum reflector mirror is substituted for a 20% R mirror.
The results shown in Figs. 35 and 36 are highly significant since they indicate that a change in the optical quality of the flowing medium can cause a significant reduction in cavity loss. Introducing flow filters can change optical quality either by eliminating bubbles in the dye or by changing flow velocity and therefore influencing the optical properties of the dye cell. An alternate explanation for the effect would be that the flow filter is eliminating impurities in the dye. This is however considered unlikely since the dye has been filtered in preparation. Impurities would therefore have had to come either from the solvent or the dye flow system. It Is therefore anticipated that further increase In dye laser energy storage (in the laser cavity) could result from careful attention to dye optical quality. CHAPTER IV
POTENTIAL IMPROVEMENTS
The worth of a number of possible changes to the commercially available dye laser was considered in this section. First resonator design was considered. Then the use of triplet quenchers. Other changes considered were: cavity dumping, Q-switching, alternate dye cell configurations, and double laser configurations.
A. Resonator Design Considerations
1. Introduction
Improved beam divergence and reduced cavity loss are two goals of this resonator investigation. These must be accomplished despite the fact that flashlamp pumped dye lasers have very high gain, a large aperture, and a flowing liquid gain medium (which can cause optical distortions). The reduced cavity loss goal was chosen in order to make consideration of cavity dumping (to be discussed later) reasonable, while improving beam divergence was chosen simply to increase far field beam intensity. Also, these goals must be obtained while maintaining high mode volume in order to maintain laser efficiency.
As stated previously commercially available flashlamp pumped 35 dye lasers have a beam divergence of 10 to 40 mrad. For a 10-mm
35 Ewanizky, Beam Quality of Pulsed Organic Dye Lasers, EC0M-4163 (Oct. 1973), p. 16. exit aperture this is 70 to 280 times the diffraction limit (1=0.6 pm). 36 The diffraction limit for a circular exit aperture is given by:
0 = -2---4-4A (69) a where
6 = angular beam diameter to the. first zeros either side of the peak intensity (full angle beam divergence)
X = laser wavelength
d = diameter of exit aperture
A goal of this resonator investigation was to reduce beam divergence to about 1 0 times the diffraction limit.
If cavity dumping is to be considered a high Q resonator cavity must be constructed. Commercially available coaxial flashlamp pumped dye lasers have a very low Q cavity which is about 40-cm long and has a 20% reflectivity output mirror. Energy is therefore stored in the cavity for less than a single pass. Average storage time is on the order of 0.27 nsec while storage times on the order of hundreds of nanoseconds are required in order to make cavity dumping efficient.
Therefore a substantial increase in cavity Q was also set as a goal of the resonator investigation.
This resonator discussion is divided into: 1) a discussion of the influence of optical distortion on resonator Q, 2 ) beam divergence measurement theory, 3) a discussion of candidate resonators, 4) beam divergence measurements, and 5) cavity loss measurements.
36 Joseph W. Goodman, Introduction to Fourier Optics (New York: McGraw-Hill, 1968), p. 65. 2. Discussion of the Influence of Optical Distortion on Resonator Q
One method by which loss of laser light in the cavity can occur
is through optical distortion in the dye cell or by having mirror
imperfections. To be a large loss however this distortion does not
need to be so large that it causes a significant deflection of light
travelling through the dye cell. If the distortion simply causes a
change of mode from low order, low loss modes to high order, high
loss • modes a high cavity loss can be created. To approach the
solution of this problem a general level of theory will be considered
followed by a relatively simple approximate solution . The theory necessary starts with Eq (70), Kirchoff's solution to the scalar 37 Helmholtz equation (which gives the wave at x, y, z in terms of
the wave at xQ, yQ , zQ).
ikr
Then the approximations listed in Eqs (71), (72), and (73) are used to simplify Eq (70).
cos(it,r01) = 1 (71)
r^ = z in the denominator (72) and
37 Joseph W. Goodwin, Introduction to Fourier Optics (New York: McGraw-Hill, 1968), p. 58. 84
X + (73) r 0 1 z i ( = 0 ’ * K ^ r )
In the numerator.
A more accurate approximation for the Fresnel approximation, is used in the numerator since Eq (70) is much more sensitive to the r0i value in the numerator than in the denominator. Using these approximations one has Eq (74).
ielkz f f f!r(x-x 0 ) 2 + (y-y0)2] U(x,y,Z) = - n — J j dx0 dyQ U(xo ,yo0) e (74) — CO —00
This equation can be used to determine the field at any x, y, and z and a given x^, y^ plane-
In a resonator Eq (74) can be used to drive a field back and forth over the resonator. A transverse mode of a resonator is defined as a pattern which repeats itself again and again (except for applitude) at every given z value of the resonator. Also, Hermite
Gaussian polynomials of the form given in Eq (75) form a complete 38 set of orthonormal modes for any given resonator.
U (x,y,z) = ' 2 nm nri-n , , 2 minlTT /■ 2 . 2. (75) -i /JL\ (x +y ) e X q(z) e~i[kz + ‘ (n+nrt-1 ) i^(z)]
38 Kogelnik, H. and T. Li, "Laser Beams and Resonators," Proc. IEEE, Vol. 54 (Oct. 1966), pp. 1312-1329. 85 where
Hn (x) = n. T (-1)" ; (76) m=0
w (z) = wU 0 V 1 + T 1 ~ 2 (77) W 0 2 iirw q (z) = — T + z (78)
ifj(z) = arc tan ( ^ "2 ' (79)
Since the modes are orthonormal Eq (80) follows.
J 1 Dnm(x>y>2) Vm’ The first approximate method for considering the influence of optical distortion on resonator modes in a dye laser is based on the distortion produced by passing a plane wave through a medium which has an inhomogeneous index of refraction. The loss occurring in this plane wave due to distortion then gives an upper limit for the loss which would occur in a resonator containing the same index inhomogeneity. Figure 37 can be used to understand the approximation. If distortion is placed near the plane mirror in Fig. 37 the resonator modes of the original cavity (before distortion) would be plane waves at the location of the distortion. If the distortion changes some percentage of the laser energy from plane waves to some other wave shape this 86 energy will have been removed from the original laser modes. It can therefore be argued that it will no longer return again and again to the same positions and will therefore constitute a cavity loss. Distortion Figure 37. Resonator Distortion The reason, however, why this approximation is only claimed to give an upper limit on loss is because of the possibility that a different mode pattern, including the distortion, could be set up. For example at the other end of the resonator in Fig. 37 a curved mirror can be considered as a phase distortion plus a plane mirror. The curved mirror, however, does not cause a cavity loss. It merely causes a change in the mode structure. Therefore distortion caused loss from a given mode can merely be treated as an upper limit on loss from that mode. If a plane wave in mode ^nm(X0 »y0 »O) passes through a distorted medium a phase shift, ^(x^y^) will occur. Therefore Eq (81) gives U ( x Q , y Q ) 0 ) . i‘>(x0 ’y0 ) u (x0 ,y0 ,0 ) = e u„m < V yo>0) (81> 87 Actually, however, what is of interest is the loss caused in a given mode by the phase shift, tCx^y^). To find this loss it is necessary to separate U(Xg,yQ,0 ) into modes, Un ,m ,(x^y^, 0 ) as is done by Eq (82). u (x0,yo>°) = I .^n'm' + iBn'mT) (x0 ’y0 ’0) (82) n'nr Then the two expressions for U(Xg,yg,0) can be equated and one can make use of the orthogonal nature of unn/ xo*yo*8^ t 0 0^ ta:i-n EtI (83). , i*(x0.y0) A + iB = \ [U (x ,y ,0)]“ e dxn dy (83) nm nm J nm' 0 0 0 0 Then Eqs (84) and (85) follow from Eq (83). Anm “J■ J (Unm(x0’y0’0)]2 cosI+(x0’y0)1 dx0dy0 (84) Bnm = J[Unm(Vy0>0>]2 sirl['l’(x0-y0) 1 dx0dy0 (85) Since is the integral of an odd function it will average to zero for random phase shift around L = (1 - A ) 2 (8 6 ) nm nm' - ' 7 One can then approximate this by Eq (87) L nm= [ j [Ui m for this approximation. As can be seen loss begins to be significant with a l/1 0 th wave or larger distortion. Table 15 PERCENT LOSS VS AVERAGE DISTORTION Distortion Loss 1/40th wave 0.015% l/2 0 th wave 0.-24% l/1 0 th wave- 3.9% l/5th wave -62% A more accurate method of calculating loss would be to actually solve the problem of a resonator with a phase distortion inside. This problem could either be treated in terms of new laser modes developed in a distorted cavity or in terms of the standard modes. In terms of the. standard modes a given mode suffers loss to other modes (which is taken into account by the previous model), but it also gains energy by scattering from other modes into it. Another loss mechanism obviously is the loss that occurs at an aperture stop, although that loss is only significant for higher order modes. In terms of new modes created for this cavity the only loss in a given mode is the loss due to an aperture stop. A second estimating procedure was considered to obtain an indication of the loss per pass experienced by a given mode. If one assumes a phase distortion that occurs in a slit pattern as shown in Fig. 38, then one can calculate a far field beam divergence. While 89 this is strictly not applicable in a resonator since one is still in ' the near field it is easy to see that a distortion which is small in one dimension can cause a wave to spread enough that it will miss the opposite end mirror. This spreading essentially constitutes scattering of the beam into higher order modes. Figure 38. Assumed Phase Distortion 3. Beam Divergence Calculation and Measurement The beamwidth of a laser system is determined by the exit aperture and how close the laser beam used is to the diffraction limit for its wavelength (i.e., ten times diffraction limited). This section develops the optical theory necessary to determine the 90 far field beam divergence of a laser system once the laser used is characterized in terms of how close it is to the diffraction limit. In addition, a method of measuring far field beam divergence is developed. Consider the situation shown in Figure 39. Figure 39. Beam Expanding Telescope A laser is emitting a beam which has a waist radius w^ through an aperture D. The higher the mode of the emitted light the larger the aperture required to pass a beam with a basic Guassian radius w^ since the real beam radius increases with about the square root of the mode number as indicated in Eq (8 8 ). Wx = / n ' (8 8 ) where = full beam radius w - beam radius for a fundamental mode of the emitting laser cavity n = mode number in one dimension 91 Then, in order to calculate the beam waist as a function of 39 distance after the beam passes through a lens one uses Eq (89). (89) where X is the wavelength is the fundamental beam waist at point i W q is the fundamental beam waist at the focal point z is the distance between point i and the focal point and letting z = F^, one can calculate wfi by Eq (90). 4 p F 2 1 2 1± f1 - w 4 (90) &J Then if 2 2 4X F 1 » 2 g (91) IT W ^ one has Eq (92) w_ = —A F 1- (92) 0 TTW, 39 A.E. Siegman, An Introduction to Lasers and Masers (New York: McGraw-Hill, 1971), p. 309. Therefore the beam waist at the focal point is linearly proportional to the focal length. Combining Eq (89) and Eq (93) one can now solve for the beam waist at lens 2 . XF 1 « — o (93) W 0 For the case in which Eq (90) can be approximated as in Eq (94). XF2 Combining this with Eq (92) one has Eq (95). w 2 " » 1 <95) The beam waist is therefore expanded in direct ratio to the lens focal lengths. The maximum F^/F^ ratio allowed is that value which expands to the point that it fills without having appreciable loss. Equation (96) shows the expansion in terms of the beamwidth of a given mode, not just the fundamental. W 2 = ^ U 1 ■ <96> After lens //2 the beam expansion is given by Eq (97) 93 This equation-is essentially the same as Eq (89), since after lens #2 a new beam waist has been formed, from which the beam then expands. l2 In the far field one has 1 < AZ w = (98) TTW, The beam size of a higher order mode beam is therefore given by Eq (99), where n is the highest order mode of the beam. AZ W = / n (99) TTW, Then, setting W (100) 1/2 z one has __ A^n 0 (101) 1/2 TTW0 Using Eq (94) this can be converted to Eq (102). w Jti n W„ o 6 (102) 1/2 2 2 Therefore it can be seen that higher order modes have a linearly larger beam divergence, assuming a fixed exit aperture and good design. It is obvious that if F, = F„, the beam is returned to the J. / • same width beam it had originally. Therefore, to measure beamwidth out of the laser one can measure the beam waist at the focal point of a lens and divide that by the focal length of that lens. One 94 must, however', convert ■ Eq (100) to be in terms of beam radius of the laser modes, W q , instead of beam radius of the fundamental, W q . The development to this point assumed parallel beams entering lens //l. If beams that are not parallel enter the lens they will not focus at the central focal point. Instead they will focus a small distance off to the side of the focal point as shown in Fig. 40. It is obvious that the effect of Ay will be to reduce by a factor of P^/F^ V7hen compared to since Ay is farther away from the large lens by that factor. ~ r / “ 1 1 / Figure 40. Beam Expanding Telescope Therefore beam divergence attainable will be inversely propor tional to exit aperture size as it was in the previous development. This can also be concluded from basic telescope optics in which it is known that the magnification is equal to the ratio of lens focal 95 lengths. Obviously the reason an object appears to be nearer after its image passes through a telescope is because of a change in the angle at which light rays enter the eye. In regard to whether the beam waist at the focal point can be used to measure far field beam divergence (for non-parallel rays entering lens #1 , a simple geometric approximation was used). ei / 2 " <103> This is essentially the same as Eq (102). If rays that are significantly different than parallel enter lens //l, then the resulting beam divergence is limited by geometric optics to the value given by Eq (103) and this would show up as a minimum spot radius of Ax. 4. Discussion of Candidate Resonators Many different mirror configurations were considered as possible methods of obtaining acceptable beam divergence and energy storage from an efficient flashlamp pumped dye laser. Figure 41 shows a number of resonators which were considered. Comments concerning each of the resonator configurations considered are as follows: (a) The Plane Parallel Configuration. This is a marginally stable configuration so accurate beam alignment and virtually zero perturba tions in the laser medium are required in order to store energy. With a high transmission output mirroi* and a relatively short cavity this 96 (a) The Plane Parallel Configuration Dyc‘ Switch (b) The Simple Concave Configuration ( Dye Switch (c) The Unstable Center/Plane Configuration Dye Switcl Cd) Convex/Concave Configuration In yel S w t f.p -h ) (e) Simple Concave with Magnification < > <----- f, f. Dv a Switch I ( r The concave mirror has a radius of curvature slightly longer than the convex mirror. Figure 41. Cavity Designs 97 configuration does, however, provide high efficiency. This is the commercially available cavity configuration. It suffers from a very large beamwidth. (b) Simple Concave Configuration. This is a stable configuration which will, therefore, alleviate the alignment problems associated with option (a). Also the beam is forced to mix radially in this configuration so even if dye concentration is high, the output will not form a doughnut as readily as in the plane parallel configuration. (c) The Unstable Center/Concave Configuration. This configuration has been proposed as a method of providing a large mode 40 volume in a stable resonator configuration. The problem is that if a coaxial flashlamp is used the center of the laser beam can only be expanded a limited amount or else too much radiation will be inter cepted by the lamp, which is a limiting aperture immediately surrounding the gain medium. (d) Convex/Concave Configuration. This configuration also holds 41 promise of large mode volume in a stable resonator. Since the convex mirror is, however, chosen to almost balance the concave mirror this configuration is not that much different than option (a), the plane parallel configuration. Like option (a) it suffers from problems of alignment and any instabilities in the dye medium would prevent energy storage. ^M. Lax, "Large-Mode-Volume Stable Resonators," J. Opt. Soc. of America, Vol. 65, No. 6 (June 1975) p. 642. 41 R.B. Cliesler and D. Maydan, "Convex-Concave Resonators for TEM Operation of Solid-State Ion Lasers," Journal of Applied Physics, Vol. 43, No. 5 (May 1972), p. 2254. 98 (e) Concave with Magnification. The purpose of this configura tion is to expand the fundamental mode as it travels through the dye cell and therefore obtain good mode volume. A pinhole at the focal 42 point of the lenses can be added to obtain more mode control. One condition which it is necessary to avoid no matter which exact 43 resonator condition is chosen is a diamond mode as shown in Fig. 15. This mode is part of the reason for the exceptionally poor beamwidth of commercial flashlamp pumped dye lasers. If the dye cell is offset from the center of the laser cavity, this mode can be eliminated and ' a substantial reduction in beam divergence occurs. Therefore the dye cell was offset from the center of the cavity in all resonator configurations which were considered. In considering which resonator type to choose it is useful to keep in mind the relative advantages of resonator stability vs large mode volume. In general the more stable a resonator is the smaller 44 the fundamental mode. Lax has shown that it is desirable to fill the gain medium with the fundamental mode and capture the gain as a method of suppressing higher order modes. However, with the high gain of a coaxially pumped dye laser (especially near the walls) and the — J.G. Shinner and J.E. Geusic, "A Diffraction Limited Oscillator," Quantum Electronics, Proceedings of the Third International Congress (New York: Columbia University Press, 1964), pp. 1437-1444. 4 3 Theodore F. Ewanizky, "Beam Quality of Pulsed Organic Dye Lasers," ECOM-4163 (October 1973), p. 18. 44 Melvin Lax, "Mode Competition in High-Power Homogeneously Broadened Lasers," Journal of Applied Physics 43 (7 July 1972), pp. 3136-3141. 99 increased loss at the walls resulting from a larger- fundamental mode this does not appear to be desirable in this case. Also, a stable resonator should be able to function better with a medium that contains index of refraction inhomogeneities. With the above constraints in mind each resonator configuration was examined. Strong emphasis, was placed on resonator stability in the sense that the resonator design needs to prevent an aperture in the resonator from causing a loss. Also, in order to gain more information about candidate designs a computer program which is based on geometric optics was written. In this program a paraxial ray 45 approximation was made and ray transfer matrices were then utilized to bounce a ray back and forth within various resonator designs. The distance from the resonator axis was recorded at a given mirror for each bounce and after 1 0 0 bounces these distances formed a radial distribution representative of the energy distribution within that cavity. Appendix C gives a copy of the computer program, some sample outputs, and a table of data summarizing various runs which have been made. Comparing W^ values calculated by the computer program and w^ values for a fundamental mode of a Gaussian beam reaonable correlation was found (see Table 16). Also, it was attempted to use the computer program to evaluate unusual mirror configurations which are difficult to evaluate in physical optics and to use it for misaligned mirrors, 45 H. Kogelnik and T. Li, "Laser Beams and Resonators," Proceedings of IEEE, 54 (October 1966), pp. 1312-1329; A.E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill: New York, 1971), pp. 294-300. 100 Table 16 CHARACTERISTICS OF THE FUNDAMENTAL MODE OF VARIOUS RESONATORS L R 1 R 2 W 1 w i jn) (m) Cm) (mm) (mm 6 - 3 1.5 2.5 - 6 3 0.75 0.4 1 0 - 3 1.64 1 . 6 - 1 0 3 1.14 1.3 1 0 1 0 3 1.05 1.4 1 0 • - 1 1 3 3.03 2 . 1 •11 1 0 3 1.67 1 . 6 6 6 3 0.87 1.4 6 5 3 0.75 1.5 5 6 3 0.94 1 . 6 5 1 0 3 1.17 1.7 1 0 5 3 0.67 1.3 1 0 3 1.5 0.54 1.3 13 1 0 1.5 0.92 1 . 8 101 For misalignment it turned out that this geometric computer program was not applicable because, as has been stated earlier, mode shifts in the resonator can result in a large loss. Geometric optics do not consider laser modes and therefore could not take into account a loss mechanism resulting from mode changes. This computer program was useful in evaluating the cavity design shown in Fig. 41c. It was determined from program results that a convex portion in the center of a concave mirror would expand the beam to the point that an unacceptable loss would result at the dye cell aperture. Based on both analytic and digital results the resonator configuration which appeared most promising was a "half confocal" resonator in which = 2L and R£ is a flat. This is the configuration used in many previous examples since it turned out to be a promising resonator. A half confocal resonator is as stable as a resonator it (5 can be since g^g2 = 0 .5 . Seigraan defines the stability condition in terms of g parameters as shown in Eq (104). (104) where L = length of the resonator R^ = radius of curvature of mirror //I Rg ~ radius of curvature of mirror it2 46 Siegman, A.E., An Introduction to Lasers and Masers (McGraw- Hill: New York, 1971), p. 322. 102 5. Beam-Divergence Measurements Many of the resonators discussed previously were tested to determine their beam divergence and efficiency. In addition an unstable resonator configuration was tested and a number of variations of the "half confocal" resonator were tested. 47 The unstable resonator which was set up is shown in Fig. 42. -5 For a 5 x 10 M concentration of Rd 6 G in ethanol 150 mj was emitted with a beam divergence of 2.3 mrad (full angle), or 240 mj with a full angle beam divergence of 3 mrad. The higher energy emission occurred by slightly decreasing the distance.specified in Fig. 42. Beamwidths were measured at the focal point of a one-meter lens. One other measurement taken with this same configuration was a picture of the beam at a distance of 15.7 meters, Fig. 43. This beam is 3.6-cm in diameter. Assuming an initial beam diameter of 1-cm, this seems to indicate a 1.7 mrad beam divergence. Since this is in the near field, it is however once again not a very reliable measurement. As would be expected, however, this is somewhat less than the 2.3 mrad measured by measuring the diameter of a spot at the focal point of a one-meter lens. The beam expander option shown in Fig. 41e was also tried. Very small beamwidths could be achieved b'ut at the price of having very small output energies. A 0.7 mrad beam divergence was achieved with the configuration in Fig. 44 at a pulse energy of 7 mjoule. Then the 47 This configuration was first prepared by Theodore F. Ewanlzky, A High Radiance Flashlamp Pumped Dye Laser (EC0M-4260, September 1974). 103 -51.. 5— cm. / 50 cm D y e 1 0 0 cm radius radius mirror / mirror Figure 42. Unstable Resonator Figure 43. Beam Pattern from an Unstable Resonator -3fl cra_ 32 cm 32 era Dye HeNe 0 o Figure 44. Experimental Beam Expander Set-Up lenses were removed and a simple 154-cnv long cavity, with flat mirrors was tried and yielded 89 mj with a 2-mrad beamwidth. Again this -5 was for a 5 x 10 M concentration of Rd6G in ethanol and beam widths were measured at the focal point of a 1-meter lens. Figure 45 shows the beam pattern at 15.7 meters from the 154-cm long flat/flat cavity using a concentration of 5 x 10 M Rd6G in ethanol. Using the expansion of the beam from 1 cm at the output mirror to about 2.6 cm at 15.7 meters would indicate a beam divergence of 1 mrad. This again contains the beam waist and is smaller than the far field measurement of 2 mrad taken at the focal point of a 1-meter lens. "Half confocal" cavities with three different lengths and three different dye concentrations were tried. In addition, placement of the gain medium in the dye cell was varied. Table 17 shows the results which were attained. In all of these cases the standard 20% reflecting output mirror was used. As can be seen from Table 17 the best efficiency was obtained with a 1.5-meter "half confocal" cavity that had the gain medium near to flat mirror. Efficiency almost as great was however attained with a 3-m "half confocal" cavity, and beamwidth for this cavity was substantially better than for the 1.5-m cavity. Also, It can be observed that beamwidth Improves if the gain medium is placed nearer the curved mirror, but this improvement comes at the price of efficiency. This is consistent with previous theoretical results. It is believed that the 3-ra "half confocal" results which yield 0.87% efficiency with a 2.5-mrad beamwidth are state-of-the-art results (exit aperture was about 8 mm for a beamwidth x aperture product of 20 m x mrad). ' 105 Figure 45. Beam Pattern From a Long Flat/Flat Resonator Table 17 "HALF CONFOCAL" RESONATOR PERFORMANCE Distance from Mirror Cavity Dye Cell to Beam Energy Radius Length Flat Mirror width Laser - Out Efficiency meters meters Meters mrad Voltage Molarity i oules % 3 1.5 1.2 2.2 18.0 kv 4 x 10-5 230.5 0.47 3 1.5 1.2 2.2 20.4 5 x 10“5 393.5 0.63 3 1.5 1.5 2.2 21.1 5 x 10~5 490.5 0.67 3 1.5 0.1 6.0 18.0 5 x 10~5 370.0 0.76 3 1.5 0.1 6.0 20.3 5 x 10_5 540.0 0.87 3 1.5 0.1 6.0 21.8 5 x 10~5 672.0 0.94 10 4.74 0.1 1.9 18.0 5 x 10“5 225.0 0.46 10 5.03 0.1 1.5 18.0 5 x 10"5 156.0 0.32 6 3.0 0.1 2.5 18.0 5 x 10"5 363.0 0.75 6 3.0 0.1 2.5 22.0 5 x 10-5 600.0 0.83 6 3.0 0.1 2.5 18.0 lO-4 359.0 0.74 ( 6 . 3.0 0.1 2.5 22.0 i—1 o 633.0 0.87 6 3.0 0.1 2.8 18.0 2 x 10"4 273.0 0.56 -4 6 3.0 0.1 2.8 22.0 2 x 10 467.0 0.64 6 3.0 0.9 2.5 22.0 10’4 415.0 0.57 o cr> 107 To investigate beam shape more accurately photographs of the beam waist at the focal point of a 1-meter lens were taken for the 3-meter "half confocal" cavity. Kodak SO-243 (ASA 1.6) film was used with a neutral density (ND) filter of 5.6 in front. The laser was pulsed thus exposing the film. These negatives were then developed and scanned with a microdensitometer. Figure 46 shows three scans with the microdensitometer for three laser shots under identical conditions. These scans are enlarged 50 times from the spot size on the film negative. As can be seen the beamwidth is reasonably consistent in shape from pulse to pulse. Also it is a beam which deposits its energy in a fairly uniform manner over its beamwidth and then abruptly falls toward zero. Figure 47 is a 40 times enlargement of one of the spots scanned in Fig. 46 by the microdensitometer. It is included to allow an examination of both dimensions of the spot since the microdensitometer only scans in a single dimension. The small dots in the picture are dust particles on the negative. 6. Cavity Loss Measurements The loss per pass that a given resonator has is another important characteristic. This loss results either from the inherent loss of various modes within the resonator or from scattering out of the resonator. Also, as has been stated, index inhomogeneities can * scatter light from a low loss mode to a higher loss mode. A few methods of measurement were used to obtain an indication of the loss per pass that was occurring with "half confocal" cavities. Figure 46. Microdensitometer Scans for Three Shots of the Laser Under Identical Conditions 108 i Figure 47. Beam Pattern 110 The first attempt at measuring cavity loss due to beam spreading was by a maximum reflector end mirror which was only dielectrically coated in the center 1.7 cm. Light could therefore pass around the coated portion of the mirror and be detected. Figure 48 shows the cavity configuration. A KORAD photodetector large enough to intercept the light passing around the 3-ni mirror was used. Figure 49a shows a trace of the pulse detected on an oscilloscope when the laser was fired. Then the KORAD detector was moved to the other end of the laser, a neutral density of 1.3 was used and the output through an 80% transmitting mirror was detected. Figure 49b shows the result Time scale on these pulses is 200 nanosecond per centimeter. As can be seen the loss around the maximum reflecting end mirror that passes through the clear area is about 5% of the loss through an 80% transmitting mirror. I then observed the laser "splash" which occurred around the three-meter mirror and discovered that the majority of the lost energy was not passing through the clear section, but was hitting the mirror mount at a still larger radius. X also observed significant amounts of "splash" at both ends of the pockels cell. Visually comparing the intensity and area of the "splash" that passed through the uncoated area of the 3-m mirror to splash at other areas I estimated that the total loss to "splash" at the 3-m mirror was 15% and X had 5% loss at each end of the pockels cell. These were, of course, rough estimates. The only "splash" which was accurately measured was the approximately 5% that passed Ill Dye Cell Polarizer Pockels Cell Detector Figure 48. Experimental Setup (a) (b) Figure 49. Pulse Detected Around Laser End Mirror 112 through the uricoated portion of the 3-meter mirror. This however gave an estimated loss per pass of 25% due to beam expansion. A more quantitative method of measuring loss due to beam spreading was then developed. Figure 50 shows the cavity configuration which was used. A 2-in. diameter mirror with a 4-mm hole in the center was used as a limiting aperture in the laser cavity. In this manner if the beam spread beyond a 4-mm radius that portion of the beam beyond 4-mm would be reflected off the aperture mirror to a detector. Det 2 5-m mirror Det 1 Dye ’'output1' aperture mirror mirror Figure 50. Beam Spreading Measurement Geometry Measurements were taken with the detector in each of the three positions shown in Fig. 50. With an 80% transmitting output mirror the loss at the aperture could be calculated by Eq (105), % Loss (105) where Det 2 = the energy measured by the EG&G detector at position two, Det 1 = energy measured at position 1, and 0.8 is the reflectivity of the output mirror. This loss was measured at 9.6% on one day and 6.5% on another. When, however, the output mirror,is replaced by a maximum reflector the percentage loss by beam expansion could rise due to the fact that the average path length in the laser increases with the possible result that smaller angle deflections become more significant. Referring to measurements with the output mirror in the cavity as (a) measurements and those with the maximum reflector in the cavity as (b) measurements, Eq (106) yields the percent loss with a maximum reflector in the cavity. Det 2b 0.8 % Loss b = -r— — i— X 1 — (106) Det la Det 3b Det 3a Using this formula a loss of 13.3% was calculated for the day that a 9.6% loss had been calculated with the output mirror in the cavity. On that day a storage ratio, given by Eq (107), of 5.5 and an apparent storage ratio, given by Eq (108), of 7.7 were calculated. 114 Storage Ratio = ^ (107) Apparent Storage Ratio = (108) On the previous day, when a loss of 6.5% was measured for the case with the output mirror in the cavity an apparent storage ratio of 27 was measured. Unfortunately, insufficient data was taken to measure the other quantities. One other interesting item is that on the first day, when lower loss was achieved, I measured the output at position 1 even with a max R mirror at that position. When I removed the 4*-mm aperture from the laser the measured value at Detector one actually decreased slightly in spite of the fact that substantially more mode volume would be available. Therefore, much better storage must have been achieved with the limiting aperture than was achieved without that aperture. There is therefore probably a definite advantage in trying to limit laser oscillation to fundamental modes. This was however only one anamolous measurement, and the conditions could not be repeated. Another experiment which was conducted was that of placing a variable aperture in the laser cavity and measuring the laser energy per pulse and pulse shape resulting from various aperture sizes. Figure 51 shows the cavity configuration. Table 18 shows the aperture sizes, measured energy and the figure number for that condition. The EG&G detector was used with its aperture multiplier = -9 100, coul mult = 10 for all energy measurements, except one, and that reading was adjusted as though it had been done with apert mult = 100. 115 5-m mirror aperture EGG Dye flat flat mirror mirror Figure 51. Cavity Configuration Table 18 THE EFFECT OF A VARIABLE APERTURE Aperture Size Energy Figure 4 cm 4.4 52a 3 cm 4.3 — 2 cm 4.4 52b 1 cm 3.9 52c 0.8 cm 2.8 52d 0.5 cm 0.7 52e 0.3 cm 0.057 52f 116 The aperture multiplier used for various figures is given with Fig. 52. Pulse shape measurements were taken with 0.2 volt/cm and 0.2 psec/cm. Also, the dye cell aperture was 1-cm in diameter. B. The Effect of Triplet-Triplet Absorption For a time, prior to finding recent measurements of triplet state constants, it seemed triplet-triplet absorption might be a major cause of loss in the flashlamp pumped dye laser. If this was true a definite advantage would be obtained by using a triplet quencher. This led to a rather thorough investigation of triplet quenching and its influence on flashlamp pumped dye lasers. Oxygen, cyclooc.tratraene (COT), and cycloheptatriene (CHT) were used as triplet quenchers in both RdGG and Kiton-Red-S (KRS). Also, these same triplet quenchers were used in conjunction with a flashlamp that eliminated much of the UV radiation by employing a cerium-doped flashlamp envelope to absorb UV before it reaches the dye. The UV filter was used since COT and CHT are more effective triplet quenchers if UV radiation is removed.^ In virtually all cases that triplet quenching was attempted it had either a negative influence on laser energy or no influence at all. Even when nitrogen was bubbled through the dye to remove all oxygen (which is a triplet quencher), and no triplet quencher was added to the dye, there was no negative influence on energy per pulse 48 R. Pappalardo, H. Samuelson, and A. Lempicki, "Long Pulse Laser Emission from Rhodamine 6G Using CyclooctatraeneApplied Physics Letters, Vol. 16, No. 7 (1 Apr 1970), pp. 267-269. Charles Brecher, R. Pappalardo, H. Samuelson, "Liquid Laser Containing Cycloheptatriene," United States Patent #3,677,959 (July 18, 1972). 117 (a) 4-cm aperture apert mult = 100 (b) 2-cm aperture , apert mult = 100 (c) 1-cm aperture apert mult = 100 (d) 0.8 cm aperture apert mult =*100 i (e) 0.5-cra aperture apert mult = 30 (f) 0.3-cm aperture apert mult = 3 Figure 52. Pulse Shape Measurements 118 from the laser. It was concluded from this plus analytical considera tions that triplet state population did not cause a significant loss. The triplet quenchers used should have decreased the population of the triplet state — but their negative effects on lasing had more influence than the positive influence resulting from a decreased triplet population. Therefore, while there may be some triplet- triplet absorption it must not be an extremely large loss. This corresponds with results achieved by digital solution of the rate 49 equations and with results given in a recent article. Computer results indicated less than 2% loss from triplet-triplet absorption if realistic rate constants were used. The first triplet-triplet experiment to be discussed in detail is one in which I added CHT to a 5 x 10 "* M solution of Rd6G in ethanol. The laser cavity used was as shown in Fig. 53, Mirror Detector Dye. Prism Pockels 6-m Cell Mirror Figure 53. Laser Cavity 49 Wang, II.H.L., C.H, Taji, "The Negative Effect of Cyclooctatraene on Small Coaxial Flashlamp Pumped Dye Lasers," IEEE J. Quantum Electronics, Vol. QE-13, No. 3 (Mar 1977), p. 85. 119 The cavity was 2.46 meters long. With a 99.8% R maximum reflecting "output” mirror Fig. 54a- was the pulse response measured at the detector with a KORAD detector using a neutral density (ND) of 0. Then Fig. 54b through 54e show the pulse response obtained under identical conditions except with various concentrations of CHT added to the solution. Characteristics of CHT are:^ molecular weight = 92.14 and density = 0.888. As can be seen CHT has a negative influence on laser performance. There were a number of different items in which 0^ was bubbled through the dye to determine its influence on the laser pulse. One time the laser intensity actually grew brighter (see Fig. 55). In other experiments, however, the laser pulse was disturbed but with no significant overall affect on pulse energy. For example, in Fig. 56 it can be seen that bubbling oxygen resulted in a more variable pulse intensity with a small overall decrease in laser energy. Both of these conditions were with 5 x 10”^ M Rd6G in ethanol and a 2.5-m laser cavity using a 6-m mirror at one end and a flat mirror at the other end. Again the KORAD detector was used with N.D. = 0. The laser was fired at 18 kv. It is assumed that in Fig. 56 the variable pulse intensity is due to bubbles that have made it into the dye cell occasionally and cause an increase in laser loss. 50 Aldrich Chemical Company, Inc., The 1975-1976 Aldrich Catalog/ Handbook of Organic and Biochemicals, 1974, p. 203. 120 (a) 0 CHT -3 (b) 0.22 x 10 M CHT -3 (c) 0.43 x 10 M CHT -3 (d) 0.86 x 10 M CHT -3 (e> 1.72 x 10 M CHT Figure 54. The Influence of CHT on Laser Performance 121 Before Bubbling 0^ After Bubbling 0^ Figure 55. The Effect of 0 ^ on the Laser Pulse 122 (a) Before Bubbling (b) While Bubbling with 0, (c) While Bubbling with 0, (d) While Bubbling with 0^ Figure 56. The Effect of 0^ on the Laser Pulse 123 Also, a number of experiments using COT were performed. In one -5 of those experiments a nitrogen saturated solution of 5 x 10 M Rd6G _3 in ethanol was used. A 5.3 x 10 M concentration of COT was added to the solution and a comparison made with the unchanged solution. Figure 59' gives the result with a maximum reflecting mirror on both ends of the laser cavity and Fig. 58 gives the result with a 20% reflecting output mirror on one end. As can be seen the COT has a negative affect in both cases. However, the influence on a low Q cavity is more substantial than the influence on a high Q (or a least higher Q) cavity is not as great. This can be explained since COT has a negative influence on laser gain. The drop in gain is not as significant in a high Q cavity. Then a cerium-doped flashlamp was used in order to eliminate UV light from the flashlamp. Figure 57 shows the spectral output of a 51 cerium-doped lamp vs a standard lamp. 0.4 0.3 Wavelength (pm) Figure 57. Spectral Output of a Cerium-Doped Ouartz Coaxial Flashlamp ■*^ILC, Cerium-Doped Fused Quartz Envelope Flashlamp, Eng. Note //19 (May 1973), p. 5. 124 0. COT 5.3 x 10“ 3 M COT Figure 58. Influence of COT on a Low Q Cavity i 0. COT 5.3 x 10 M COT Figure 59. influence of COT on a iiigh Q Cavity I 125 Figure 60 then shows the influence of CHT on the laser pulse generated using this flashlamp, a 2.28-cin long cavity formed by a flat 99.8% mirror and a 6-m radius max reflector, and a 5 x 10 M solution of Rd6G in ethanol. Figure 61 then shows the influence of CHT for identical conditions except that the flat mirror is replaced by a 20% reflecting mirror. As can be seen from both figures the addition of a UV filter does not prevent the CHT from causing a degradation to laser action. It also should be noted that for relatively standard laser conditions (a 20% reflecting output mirror, a 303-cm long cavity formed by a flat mirror near the dye cell and a 6-m mirror at the other end) the laser using a cerium-doped lamp emitted about 70% as much energy as one using a regular quartz lamp. Actual average energies were 252.4 mj with the cerium-doped lamp and 362 mj with the standard quartz lamp. Then I tried COT with the UV filtering, cerium doped, lamp. Figures 62 and 63 give the results for cavities with a max R "output mirror" and a 20% R output mirror. As can be seen COT also still has a negative influence on laser action. Then, finally it should be mentioned that COT was used as a triplet quencher with Kiton-Red-S (KRS) in ethanol. Figures 64 and 65 give the results. Again the addition of COT produced a negative effect, A cerium-doped flashlamp was used for these tests. 0 CUT 5.8 x 10" 3 M CHT Figure 60. Influence of CHT on a Laser Pulse With Max R "Output" Mirror Figure 61. Influence of CHT on a Laser Pulse With a 20% R "Output" Mirror 127 0 COT 5.3 x 10“3 M COT Figure 62. Influence of COT on Laser Performance for a Max R "Output Mirror" (cerium doped lamp) Figure 63. Influence of COT on Laser Performance for a 20% R "Output Mirror" (cerium doped lamp) 5 volts/cm 1 volt/cm 0 COT 5.3 x 10-3 M COT Figure 64. Influence of COT on KRS Laser Performance for a ■ Max R "Output Mirror" (cerium doped lamp) 2 volts/cm 0.5 volt/cm 0 COT -3 5.3 x 10 M COT Figure 65. Influence of COT on KRS Laser Performance for a 20% R "Output Mirror" (cerium doped lamp) 129 C. Cavity Dumping la a previous section it was experimentally shown that under the right conditions a peak intra-cavity power seven times as great as the peak intra-cavity power of a commercial dye laser can be obtained. Also, if losses in the laser cavity can be limited, theory indicates that peak power ratios much higher than this could be achieved. Therefore, it appears that cavity dumping a flashlamp pumped dye laser is one method of increasing peak power, although it is not yet possible to tell whether the increase will be large enough to be useful. In addition pulse rise time can be held to very short times, depending on switching time and cavity length. Areas concerning cavity dumping discussed below are: 1) Switching Mechanisms, 2) Major Loss Mechanisms in the Laser Cavity, 3) Experi mental Cavity Dumping Results, and 4) Potential Cavity Dumping Results. 1. Switching Mechanisms Three switching methods were considered. They are: a) acousto- optical switching, b) frustrated internal reflection (FTIR), and c) an electro-optical switching device. The three devices considered will be discussed in the order given above. An electro-optical switch (pockels cell) was chosen as the only method available that has the required switching times for high energy pulses. For low energy pulses an acousto-optical device can also have fast switching times (on the * order of 10 nsec). Detailed electro-optical theory is discussed in Appendix D. a. Acousto-Optical Switching. An Acousto-Optical Switch (Spectra Physics Model 365) has been used to cavity dump a low energy per pulse 130 52 (CMX-4) flashlamp pumped dye laser. Output energy was 0.1 mj per pulse. The output coupler focuses the beam down to a 40-pm diameter 53 spot in order to obtain fast response. This is done in optical 2 54 quality quartz which has a damage threshold of 2.4 GW/cm or , 2 55 14.5 GW/cm depending on the reference source, for a Q-switched laser pulse. Simple calculations indicate that for the experiment with a CMX-4 dye laser (which had a 2.5 meter cavity)^ a power density of 0.95 GW/cm resulted at the focal point of the coupler. Therefore, stored energy cannot be substantially increased without modifying the output coupler. Power density at the focal point of the coupler can be decreased either by lengthening the laser cavity or by focusing to a larger diameter spot. Either of these changes does, however, tend to reduce the coupler's response time. The output coupler functions by allowing the acoustic wave to set up a diffraction grating. Therefore, dumping time is limited first by the time it takes an acoustic wave to travel across the spot and set up the grating, and then by the time it takes light stored in the cavity to pass — — F.E. Lytle and J.M. Harris, "Nanosecond Pulse Shaping of a Flashlamp Pumped Dye Laser," Applied Spectroscopy 30 (1976), p. 633. 53 F.E. Lytle and M.S. Kelsey, "Cavity Dumped Argon-Ion Laser as an Excitation Source in Time Resolved Flourimetry," Analytical Chemistry 46 (June 1974), p. 855. 54 John F. Ready, Effects of High Power Laser Radiation (New York:' Academic Press, 1971), p. 289. 55Ibid., p. 292. 56 Discussion with F.E. Lytle, Purdue University, Indiana, November 1976. 131 through the coupler often enough that it will be deflected by the , 2 grating. Assuming a maximum allowed power density of 1 GW/cm , and a peak stored energy of 100 mj, one can calculate allowed combinations of cavity length and spot size. These in turn correspond to a given cavity time, the time it takes for light to travel the length of the cavity, and spot time, the time it takes sound to travel the diameter of the spot. Table 19 gives some ; representative values. Table 19 ALLOWED CONFIGURATIONS Cavity Cavity Spot Spot Time Length Diameter Time 8.3 nsec 2.5 m 1265 pm 210 n: 16.7 5.0 894 149 33,0 10.0 632 105 67.0 20.0 447 74.5 100.0 30.0 365 61 The shortest total switching time would occur around a 20-meter cavity length, when the cavity length and spot diameter contribute about equally to the delay. Possibly a cavity somewhat shorter than 20 meters would however be ideal since not all energy is coupled out 57 5 This assumes a velocity of sound in quartz of 6 x 10 cm/sec, which was obtained from the following article. D. Maydan, "Fast Modulator for Extraction of Internal Laser Power," Journal of Applied Physics 41 (4 March 1970), pp. 1552-1559. 132 in a given pass through the modulator, so some energy will make more than one trip across the length of the cavity before being coupled out. Regardless, it appears unreasonable to design for an acousto- optical coupler with less than about a 100 nsec response time for high energy per pulse lasers (100 mj or more). b. Frustrated Internal Reflection Device (FTIR). An FTIR is a device which consists of two crystals, each in a right triangular shape, made of the same material, and cut such that total internal reflection occurs when light which entered one of the perpendicular faces is incident on the face of the crystal which is cut at an angle. When the two crystals are placed with their angle cut faces almost touching, this total internal reflection is frustrated and light is transmitted through the crystals. If, however, the crystals are suddenly moved apart, light will then be reflected by the device. Alternately, a device can be constructed in which the two crystals were normally separated and then they were quickly pushed close together. The mechanism used for moving the crystals is that one crystal has been cemented to a piezo-electric crystal which can expand or contract when a voltage is applied. To understand FTIR devices somewhat better Eqs (109) and (110) , 58 were used. 58 Dale R. Corson and Paul Lorrain, Introduction to Electromagnetic Fields and Waves (San Francisco: W.H. Freeman and Company, 1962), pp. 372-378. 133 0 > arc sin (?) (109) where 0^ is an angle of Incidence for which total internal reflection takes place; n ^ is the index of refraction In media 2; n^ is the index of refraction in media 1 and n ^ < (110) where 5 is the depth of penetration of the electromagnetic field z into media 2 (e.g., A=Aq exp(-z/6z); is the wavelength in media 2. Then for a right triangular crystal of length, L, and width, d, the angle of incidence that occurs when a beam of light (which has entered through one of the legs of the triangle) attempts to exit the crystal is 0^ = arc tan(L/d). Figure 66 shows this situation. Table 20 is then given to show how close two right triangles of a given length, width, and index of refraction have to be in order to cause a given amount of reflection. L d Figure 66. Light Through a Right Triangular Crystal 134 Table 20 FTIR CRYSTAL SEPARATION FOR A GIVEN REFLECTION n 6 0% 20% 80% 99% 99.5% 7 d 0i z 1 45° 1.42 6.6 pm 0 pm 1.47 pm 10.6 pm 30.3 pm 35 pm 1 45° 1. 7 0.899 0 0.2 1.45 4.1 4.7 2 63.4° 1.42 0. 76 0 0.17 1.2 3.5 4.0 2 63.4° 1.7 0.52 0 0.12 0.84 2.4 2.75 A 2 = 0-6 pm assumed Indices of refraction of 1.42, representative of quartz or calcium fluoride, and 1.7, representative of sapphire, were used in 59 the table. Also L/d ratios of 1 and 2 were used. These conditions appear to bound the practical cases in which an FTIR can be set up. It was also assumed that ^ - 1 is the index of refraction between the two triangular crystals. As can be seen from Table 21 a minimum motion of 0.84 gin is required to change reflection from 0% up to 80%. To change from 99.5% down to 20% would, however, take a motion of 2.63 pm. At first glance it would therefore appear best to operate from 0 up to 80% instead of the other way (since it would take less motion and therefore less time). Unfortunately, the two triangles cannot come into contact or they will freeze together. The minimum adjustable distance yields about 10% reflection (or else the crystals freeze together). Therefore 59 Optical Design. Military Standardization Handbook MIL-HDBK.-141 (5 October 1962), pp. 20-15. 135 the switch must be operated from reflecting to some transmittance if it is desired to have a quescent mode which is almost either totally transmitting or totally reflecting. Experimental Section of FTIR Discussion An FTIR was purchased from Erickson Laser Products. This unit was modified compared to the normal unit supplied since it operated from almost completely reflecting to partially transmitting. A HeNe beam was then transmitted through the device and illuminated a photodetector, whose output was viewed on a Tektronix 475 oscilloscope. The device was set at various initial separations (corresponding to a quiescent transmission level), and switching time and level of change In transmission were measured. Table 21 gives the result. As can be seen the device does not appear to be very promising for rapid cavity dumping. Table 21 FTIR SWITCHING PERFORMANCE Quiescent Minimum Maximum Opening Transmittance Transmittance Transmittance Time 30% 0% 80% 170 17% 0% 55% 140 7% 0% 41% 100 5-6% 0% 39% 90 4% 0% 30% 80 2% 0% 21% 65 1% 0% 17% 60 0.5% 0% 15% 50 136 The problem associated with using an FTIR for cavity dumping is that for a given piezo-electric driver crystal there is a certain maximum motion. The thicker the crystal the larger the allowed maximum motion, but crystal response time decreases. Then, for a fixed motion one can see from Table 20 that if very good initial reflection is desired, the switch will not cause much of a change in transmission. Table 21 shows that if 0.5% initial transmittance is allowed, only a 15% transmission occurs after switching. This means that about six laser cavity round trips would be required to dump the stored energy in the cavity. That fact, plus the 50 nsec switching time make FTIR's a low priority switch for cavity dumping. c. Electro-Optical Switching. When a voltage is applied across an electro-optical crystal one polarization is delayed with respect to the other. An electro-optical crystal is used by sending linearly polarized light into the crystal at a 45° angle with the crystal's axes (see Fig. 67). If the y axis polarization shown in Fig. 67 is delayed by 90° with respect to the x axis polarization, then the output of the crystal is circular polarization. If the y axis is delayed by 180° with respect to the x axis then the 0 output is linearly polarized as shown in Fig. 68. The y component is now negative when the x component is positive. One can therefore see that if an electro-optical crystal is placed between two polarizers, as shown in Fig. 69, a switch results. If the two polarizers are both of the same polarization then the switch shown in Fig. 69 is open when zero voltage is applied to the crystal. Then if the crystal's half wave voltage is applied it 137 y Figure 67. Initial Polarization y Figure 68. Rotated Polarization Polarizer E-0 Crystal Polarizer Figure 69. Electro-Optical Switch 138 rotates the linear polarization going through it by 90° and the light cannot pass through the other polarizer. Figure 70 shows a number of possible laser cavity configurations which use electro-optical switching for cavity dumping. The electro-optical crystals are referred to as pockels cells. In each of the configurations given in Fig. 70 the switching mechanisms of Fig. 69 are re-created by a single polarizer, a pockels cell which is used with its quarter wave voltage, and a mirror. Since light reflected off the mirror travels through the pockels cell and the polarizer a second time, this is essentially the same as the switch shown in Fig. 69. Also, the polarizer shown in Fig. 70 Is a Gian Foucault Prism, which will be discussed later. Figures 70a and 70b only allow a single polarization to develop in the cavity while Figs. 70c and 70d allow oscillation on both polarizations. The configuration shown in Fig. 70d was eliminated since dye lasers have a large beam diameter and it would therefore be difficult to physically separate beams of two different polarizations. Either a large walk-off angle or a very long bi-refringent crystal would have to be used. Equation (111) gives the angle, iji, of the extraordinary ray in a bi-refringent crystal with respect to the optical axis. (111) where 0 = angle of the ordinary ray with respect to the optical axis; ne = index of refraction along the extraordinary ray of polarization; n„ = index of refraction along the ordinary ray of polarization. The 139 Clan Prism Pockels Cell (a) J Output Pockels Cell V Gian Pri3m "Dye" (b) N. 'X Output Pockels Cell Dye (c) Clan Prism Pockels Cell Output , ^ Dye' h - E ’ockels Cell (d) Output Figure 70. Laser Cavities Using Electro-Optical Switching 140 walk off angle is therefore ^0, and the distance S, separating the two beams after passing through a bi-refringent crystal with length, b, is S = b (112) If I then assume 0 = 45°, which is near the maximum walk off, one can see that to obtain a 1.5-cm separation requires a value of nQ/ne 1.228 for a 7.5-cm long crystal. This is obviously an unrealistic crystal size and level of bi-refringence. Calcite, which is very bi-refringent has indices*^ of n^ = 1.658 and ng = 1.486, a ratio of 1.115. A 1.5-cm separation can only be obtained in calcite if a 13.8-cm long crystal is used. For a 1.1-cm separation a 10.11-cm crystal could be used. Elimination of the configuration given in Fig. 70d leaves three configurations, each using a Glan-Foucault Prism. Figure 70a shows the simplest and easiest to align configuration. Figure 70b shows a somewhat more difficult configuration to work with, although it will be shown later that this configuration has potentially less loss than the configuration shown in Fig. 70a. Finally, Fig. 70c shows a combination of 70a and 70b which is therefore more complicated, but has the advantage of allowing oscillation on both polarizations. American Institute of Physics Handbook, Coordinating Editor, Dwight E. Gray, Section Editor, Bruce H. Billings (McGraw-Hill: New York, 1963), 6-98 and 6-18. 141 A Gian Foucault prism, which is used as the polarizer in each of the proposed designs, makes use of a set of bi-refringent crystals cut so total internal reflection occurs on one of the polarizations, but not on the other. A second crystal is required, after an air space, so the transmitted ray exits the Gian prism parallel to its entry direction. Figure 71 shows a Glan-Foucault prism. The crystal is cut so reflection occurs off a surface at angle 0. For a rectangular crystal the reflected ray approaches the exit interface at angle <}>^, and is bent to angle (J^, resulting in a total angle between the input and reflected exit ray of the angle y. The transmitted ray is translated somewhat at the interface, whereas the reflected ray is totally internally reflected. Figure 72 shows reflection loss suffered by the transmitted ray for a LilO^ Gian Foucault prism.^ The angles in this figure are referenced to the angle at which the INRAD 703 Prism polarizer is cut. As can be seen, depending on angular adjustment, a significant transmission loss can occur. The graph stops on the low loss end when the crystal begins to transmit both polarizations. Figure 71. A Glan-Foucault Prism 61 INRAD data sheet on "703 Series High Power IR Prism Polarizers." 142 -1° 0 1° 2° 3 0, 0, Angle from Entrance Face Normal -2 -3 Figure 72. Reflection Loss Due to Two Internal Surfaces -4 20 30 70 80 90 10 40 60 .50 100 SSO'T UOTIDSTIS'W 143 Therefore if Che configuration shown in Fig. 70a is used the Glan-Foucault prism will cause a minimum loss on the order of 2% per pass while the laser energy is being built up in the cavity. This minimum loss could be slightly reduced by operating where the other polarization is not totally reflected, but is reflected at a greater than 50% level (this increases dumping time since multiple passes through the crystal are required in order to output all of the stored energy). One of the major drawbacks to the resonator configuration shown in Fig. 70a is that dispersion plays a role in cavity alignment. From Fig. 71 it can be seen that Eq (113) follows y = 90° - arc sin[n sin where = 9 0 ° “ 20 For either calcite or LilO^* the two materials used for Glan-Foucault prisms, the index, n, depends on wavelength. Therefore, mirror position and alignment become wavelength sensitive. One way to remedy that problem is to make a Glan-Foucault prism as shown in Fig. 73. With this configuration all dispersion would be eliminated due to having entrance and exit windows parallel to the wave front. The only cavity loss in the prism prior to dumping would be caused by reflection off the AR coated entrance and exit apertures. This could even be minimized by aligning the system so these reflections stayed in the laser cavity. Therefore the configuration given in Fig. 70b can be a very low loss resonator. 144 \ Figure 73. Modified Gian Prism The configuration given in Fig. 70c allows buildup on both polarizations. If it turned out that significantly lower output energy was available lasing on a single polarization, then this would be the preferred cavity. In Appendix D selection of an electro-optical crystal is discussed. A number of materials were considered, finally settling * on KD P, which has a very high damage threshold and a half-wave O voltage of about 3500 volts at 5900 A. Switching times for this 6 2 voltage level are as low as about 0.1 nsec. This is even faster than the required switching time. A pulse generator which has a rise time of 10 nsec was purchased and used to switch KD P. The KD P was enclosed by two windows and an index matching liquid. For minimum loss all of these surfaces should be aligned so that reflections which occur can be kept within the laser cavity. Otherwise reflection loss as high as about 4% will occur in the cavity / 9 Laser Focus, March 1977, Vol. 13, No. 3, p. 81. 145 A due to a KD P pockels cell. My cell was not aligned this well, so I did have an estimated Insertion loss of 4%. The pulse generator which was purchased was an Interactive Radiation Model 2-015 Switch Driver, with modified delay settings. Specifications for this unit are: Switched Voltage 1 to 8 kv Switching Time 10 nanosec Recovery Time 3 millisec (RC with 100 pf load) Repetition Time single pulse to 40 pps Trigger Input ±0*2 to 3 volts (50 ft input) Delay, Input to Output 100 nanosec typ, 200 ns max Additional, variable delay 10 nanosec to 1.6 nsec Delay Resolution 7 nanosec, nominal Delay Jitter 1 nanosec When the Model 2-015 is turned on it places a DC voltage, at the level which is set, across the pockels cell. When the pulse generator Is triggered a Krytron is used to quickly (10 nanosec or less) drop the voltage across the pockels cell to zero. Then during the recovery time the DC voltage across the pockels cell is restored. This voltage variation is ideal for laser Q switching, or for use in an optical switch as shown in Fig. 69. In order to use this type of voltage variation for cavity dumping however an additional optical element, a quarter wave plate, is required. For cavity dumping It is preferred if zero voltage is initially applied across the pockels cell and then the quarter wave voltage Is suddenly placed across the cell, dumping the laser cavity. Therefore a voltage conversion box was constructed which would take the output 146 of the Model 2^015 Q-swltch driver and convert it to the desired voltage output. Figure 74 shows the circuit which was employed. A DC voltage, V, applied by the Q-swtich driver results in a voltage, V, across the capacitor. Both sides of the pockels cell are floating at the voltage, V, resulting in zero voltage across the cell. When the Q-switch driver is triggered it becomes a short circuit and one side of the pockels cell is then directly connected to ground. The charge on capacitor, C, is then split between C and the pockels cell resulting in a voltage drop across the pockels cell (until the charge can leak off through resistor, R). Experimentally, a 300 pf, 6000 volt capacitor was used for C and it appeared to take a Q-switch driver setting of about 2200 volts with the converter circuit in, as compared to about 1600 volts without the circuit in order to obtain the quarter wave setting. This would seem to indicate that the pockels cell has a capacitance of about 112 pf. 2. Cavity Dumping Experimental Results Figure 75 shows the cavity configuration used for cavity dumping. Stored energy can be monitored through the end mirrors. Figure 76 shows the energy stored in the laser cavity as a function of time both with switching and without. As can be seen if switching occurs the energy in the cavity does drop. It does not, however, drop to zero. Apparently enough feedback is still present to maintain laser oscillation. It is possible then if exactly the quarter wave voltage for the laser wavelength were used this would not happen. It is 147 Pockels Cell (a capacitive la Q-switch driver C Figure 74, Voltage Conversion Circuit 148 curved ml rror/ 'detector \ q ------/ D- flat mirror flat dye Gian pockels mirror prism cell Figure 75. Cavity Dumping Configuration without switching with switching at T = 250 nsec Figure 76. Stored Energy vs Time 149 more probable however that due to the bandwidth and high gain of this laser it would be impossible to obtain a high enough output percentage to stop the laser action. Figure 77 shows an output pulse measured at the position a detector is shown in Fig. 76. As can be seen a high initial output occurs due to a level of energy storage followed by output from the sustained laser action. The energy measured at this position using a Quantronix energy meter was 93 mj. It is estimated from the shape of Fig. 77 that 20 or 30 mj of this output is stored energy. On another day that cavity dumping was performed Fig. 78 gives the cavity dumped pulse shape. It also gives the pulse which occurred for switching at zero delay (before the flashlamp initiates). As can be seen there is enough feedback to initiate and maintain a laser pulse even after switching. With switching at 250 nanosec I measured 81 mj and with switching at 0 nanoseconds I measured 24 mj. Therefore the stored energy portion of the pulse shown In Fig. 78 is 57 mj. This compares against a laser output of about 350 mj for VT = 18 kv Li for a standard 300-500 nanosecond laser pulse from the dye laser. Also, at the time this measurement was taken the peak power in the laser cavity while using a max R "output" mirror was only a factor of 2.5-3 above the peak power achieved using a 20% R output mirror. As has been stated a condition was found later in which this ratio was increased to a factor of 7. This would significantly increase short pulse laser power output. This better condition was not tested, however, since the Gian prism of the switch had been damaged at the time when better storage was attained. Figure 77. Cavity Dumped Energy Figure 78. Cavity Dumped Pulse Shape 3. Anticipated Optimal Configuration In order to produce the highest peak power possible from a cavity dumped dye laser it is necessary to reduce cavity losses to an absolute minimum. Table 22 lists possible cavity loss mechanisms. Many of these mechanisms have been discussed before and are related strictly to dye cell design. As stated previously the best experi mental results concerning a low loss situation were to achieve a factor of seven times higher intracavity power using a 99.9% R "output" mirror than was achieved using a 20% R "output" mirror. For this case, however, no switching mechanism was placed in the cavity so only dye cell related losses plus mirror related losses were involved. The Gian prism and pockels cell used for switching can introduce loss. Table 22 CAVITY LOSS MECHANISMS 1 Reflection off of Non-aligned Surfaces 2 Transmission through Maximum Reflecting Mirrors 3 Diffraction Loss (mode dependent) 4 Triplet-Triplet Absorption 5 Singlet-Singlet Absorption 6 Shock Wave Effects 7 Local Heating 8 Scattering In minimizing losses each type of loss will be considered. As shown earlier, triplet quenchers do not have a favorable influence on short pulse (1 ysec or less) coaxial flashlamp pumped dye lasers. 152 Therefore triplet-triplet absorption is a given value which must be tolerated (probably a low value and not that significant). Also, singlet-slnglet absorption cannot be changed except by either tuning the laser wavelength away from the absorption region or choosing a new dye which has a large separation between absorption and emission spectra (such as a coumarin dye). Again, I do not believe this will have a large influence. As far as shock wave effects are concerned, a cell will be discussed later which removes much of the influence of shock waves, but it was shown earlier that for a pulse as short as the ones considered here shock waves do not have a significant influence. Also, it was shown earlier that local heating should not be very influential. Lastly, it is believed that transmission through max R mirrors is totally negligible at this wavelength since it can easily be down to less than 0.1%. This leaves three loss areas which have not been minimized: 1) reflection off of non-aligned surfaces, 2) diffraction loss, and 3) scattering. It is believed that the major loss mechanism remaining in the dye laser is one of scattering from low order, low loss laser modes to high order, high loss modes. Also, it is believed that if maximum performance of a cavity dumped flashlamp pumped dye laser is desired careful attention must be paid to reflections occurring in the switching mechanism. To reduce scattering from one mode to another it is believed that an optimum laser configuration would be one in which careful attention has been given to fluid flow characteristics. This would be done in order to assure that the dye cell have excellent optical quality. 153 The exact design of an optimum dye cell has not been considered, however, it has been determined that for the laser used a 1-pm pore size fluid filter improved laser performance so it is anticipated that an optimum design would include a fluid flow filter. It is also probable that an optimum design would have a transverse flow cavity as a method of minimizing optical distortion. Figure 79 shows an optimum cavity dumping configuration. The dye cell has two AR coated windows that each have their sides parallel to within one arc second. These windows can then be aligned so a single return occurs off of all four surfaces. The laser cavity uses the Gian prism in a reflective mode since total internal reflection occurs at the inside surface. Each of the three exit apertures of the Gian prism are AR coated, and the angle of the two surfaces inside the laser cavity is such that if a beam enters perpendicular to one surface and reflects off of the polarizing surface it will exit perpendicular to the other surface. This allows even the reflections off of these AR coated windows to stay in the cavity. Pockels Cell Gian Prism Figure 79. Optimum Cavity Dumping Configuration Output I 154 The pockels cell recommended for an optimum cavity must be such that all surfaces in the pockels cell are parallel. For a KD P pockels cell this includes the two surfaces to the KD*P plus a total of four surfaces for the optical windows used to protect the KD P from moisture. Ideally this would be a rigid structure with all six surfaces aligned. Alternately so long as the sides of each window >j|^ and the KD P are parallel adjustment mechanisms could be used on the windows to align them. For a LiNO^ crystal protective windows are not required so the alignment problem would not be as severe. A Absorptive loss in LiNO^ would also be slightly lower than in KD P, but the difference is probably negligible. The pulse generator used to drive the pockels cell should be capable of generating a pulse with the format shown in Fig. 80. Before applying the pulse the generator should generate zero voltage. V Voltage 0 Time Figure 80. Voltage Pulse The pulse should then have a 3-nsec or less rise time up to a voltage between 1 and 8 kv. The pulse should then last anywhere from 155 10 to 300 nsec and then fall to zero with a fall time of 3 nsec or less. Pulse position should be adjustable in approximately 10 nsec increments from 150 nsec delay after triggering to 1500 nsec delay. A pulse generator with these characteristics will allow rapid dumping of stored laser energy at whenever the optimum time occurs. Also since pulse termination is included it will be possible to cut off the pulse if desired. One final characteristic of an optimum configuration is that the dye cell used would have a clear aperture greater than the aperture of the gain region. In addition all other apertures in the cavity would be greater than the gain region aperture. If this could be accomplished then diffraction loss for the highest order modes that could be supported by the size of the gain media aperture would be reduced. The difficulty, however, is that the dye would probably have to be enclosed with an index matched glass of some type and an index matching solvent cannot be picked without degrading laser efficiency. For - 5 example, when a 5 x 10 M solution of Rd6G was used in 50% benzl alcohol (n = 1.54) and 50% ethanol (n = l,36) only about 50 mj was emitted while with identical conditions except for a solvent of 100% ethanol 350 mj were emitted. D . A Dye Laser That Can be Q Switched? In the introduction it was mentioned that in order to Q switch a dye laser it would be necessary to develop a phosphorescent dye laser. A phosphorescent dye laser would lase from the triplet state, T, down to the ground state (see Fig. 1). Since this is a forbidden transition 156 the upper state lifetime would be long enough to store energy for the duration of a flashlamp pulse. Problems associated with potential development of phosphorescent dye lasers are: 1) many dye molecules have 3uch a weak phosphorescence that it would be difficult to have high enough dye concentration to develop gain, and 2) triplet-triplet absorption is not forbidden. Therefore, on an average the absorptive transition up to higher triplet states will have a cross section which is orders of magnitude higher than the forbidden cross section 6 3 down to the ground. Therefore the lasing action must take place at a wavelength which does not have triplet-triplet absorption. The need for extremely high concentration can be alleviated if a dye with a relatively short phosphorescent lifetime is found. This also increases the probability of successful lasing due to the fact that a dye of this type has a higher laser cross section and is therefore more likely to compete successfully at some wavelength against the triplet-trlplet absorption cross section. One series of dyes which has a relatively short triplet state radiative decay time is made up of dyes containing a second-row transition element such 64 as ruthenium or osmium. figure 81 indicates the absorption cross section and the laser cross section of RuCbipyr^C^. This figure was derived from absorbance 63 F.P. Schafer, "Principles of Dye Laser Operation," Dye Lasers, Topics in Applied Physics, Vol. 1, ed. F.P. Schafer (New York: Springer-Verlag, 1973), p. 33. 64 Fred E. Lytle and David M. Hercules, "The Luminescence of Tris(2,2'-bipyridine) ruthenium (II) Dichloride," J. American Chem. Society, Vol. 91 (1969), p. 253. 157 -21 -22 10 3000 4000 5000 6000 7000 Figure 81. Cross Section of Ru(bipyr) 158 65 measurements. Converting from absorbance to cross section per square meter was accomplished using Eq (114). A b In 10 ,., , x ° = — 24“ (114) C 6.6 x 10 where Is absorbance;C is concentration. Figure 82 shows an energy level diagram and rate constants for RuCbipyr)^^* This dye has very favorable properties for flashlamp pumping since it has high absorption in the UV and short wavelength -22 2 visible regions. Laser cross section was approximated as 4 x 10 m and absorption cross section in the visible was also approximated as — 22 2 4 x 10 m . Since pump cross section is about three orders of magnitude lower than the pump cross section of Rd6G the necessary laser dye concentration should be approximately two orders of magnitude greater than with Rd6C. Therefore a dye concentration -3 -2 between 5 x 10 M and 10 M should be used. Table 23 gives energy storage capability as a function of concentration, assuming a dye 6 cell volume of 5 x 10 cubic meters (a cylinder 0.13-m long and 1-cm in diameter) that one photon of wavelength = 0.6 pm can be stored per dye molecule. 6 5 Ibid. 159 A 3 2 m m O o 1 0 •v S inglets Trip]eta Figure 82. Rate Constanta and Energy Level Diagram for Ru(bipyr) 160 Table 23 STORED ENERGY Concentration Stored Energy 3 x 10-2 30 j 10~2 10 j 3 x 10~3 3 j 10"3 1 j As can be seen these concentrations are easily high enough to store the required level of energy. In order to Q-switch a phosphorescent dye laser a standard Q switching arrangement such as shown in Fig. 83 would be used (if a phosphorescent dye laser could be built in the first place). Dye output Prism Pockels mirror Cell Mirror Figure 83. Q-Switching Arrangement A quarter wave voltage is placed on the pockels cell until after complete laser buildup then the voltage is switched to zero — thus allowing a return from the end mirror. Once switching takes place rapid exponential buildup of laser action can occur. If triplet- triplet absorption were no problem the gain per pass would be given 161 _2 by Eq (33) such that for a concentration of 10 M and a gain length 24 of 0.12 m one would have an initial gain per pass of 50 (n « 6.6x 10 , -24 = 4x10 » d = 0.12), assuming the flashlamp excites all of the molecules. Equations (115) and (33) are required to estimate the initial gain of the laser for firing without Q switching. n n = (115) c ca + 1 F a P P 5 27 From Fig. 76, A „ = 3 x 10 . Also it is estimated that F = 10 , ° ca p therefore initial gain per pass vs concentration is given in Table 24. As can be seen a concentration if there is sufficient gain at any concentration if triplet-triplet absorption does not overshadow the stimulated emission. Table 24 INITIAL GAIN PER PASS VS CONCENTRATION (100% mirrors) Concentration Gain 99 i o "1 > ioyy 99 3 x 10~2 > ioyy i to i—1 o 4 x 10 23 3 x 10 3 3.8 x 10iJ io" 3 7.3 x 107 162 Experimental Results Three attempts at laser action were made. They were with concentrations of 3 x 10 ^ M, 9 x 10 ^ M and 6 x 10 ^ M, All were in ethylene glycol since the dye available had been mixed in ethylene glycol. Unfortunately, the optical quality of the medium, judging from the HeNe pattern transmitted through the dye cell, was very poor. None of these attempts at laser action were successful even though a very short cavity was used to try and minimize the influence of poor dye medium optical quality. It is therefore probable that triplet- triplet absorption is dominating over stimulated emission and preventing laser action. If the dye were cooled it is possible that wavelengths with lower triplet-triplet absorption could be found and that wave length selective lasing would occur. This was not, however, attempted. E. Alternate Dye Cell Configuration The dye cell configuration used in the Phaser DL-1100 laser, which was tested, is a coaxial flashlamp with dye flowing through the middle. Two alternate configurations were given consideration. These alter natives will be referred to as the "Diffuse Reflector" alternative and the "Transverse Flow" alternative. The "Diffuse Reflector" alternative was considered analytically and was constructed. The major reason for constructing this cell was to eliminate shock wave effects from the laser performance. As has been stated, however, it was determined by tests with a HeNe beam that even in the standard cell shock waves arrive after most of the laser 163 action has already occurred. Figure 84 shows two views of the new laser cell. The large inside tube contained the flashlamp while the 10-mm ID tube contained the flowing dye. The outside surfaces of the large cylinder were coated with Eastman White Reflectance Coating, which has very high diffuse reflectance properties*^ as shown in Fig. 85. This coating was placed on the outside of the cell in order to protect it from the liquid which filled the inside of the cell. Various liquids were considered for the inside of the cell based on both UV absorption characteristics and their index of refraction. Table 25 gives properties of a number of liquids which were considered 6 7 as index matching/UV absorbing liquid for the inside of this cell. In this cell the coaxial flashlamp used is inverted and light flashes outward from the lamp into the rest of the cell. It is transmitted through the glass and reflected off the diffuse reflecting coating. In this manner most of the flashlamp energy should be retained inside the cell until it is absorbed either by the dye or by the blackbody flashlamp. Initially a quartz cell was constructed. This cell was,however, difficult for the glassblower to construct and had some white silicon monoxide film in a number of places. Before the cell could be used it was accidentally shattered. After one more attempt at constructing 66 KODAK "Eastman White Reflectance Coating," Kodak Publication No. JJ-32. 67 Aldrich Chemical Company, The 1975-1976 Aldrich Catalog/Handbook of Organic and Biochemicals, 1974, pp. 146-147, 127, 5, 653, 676-677, 74-75, 294-295, 306, 521, 346, 476, 253-254, 324, 204, 408. TOP VIEW 164 10 mmID 1/2" 5" END VIEW Figure 84. Diffuse Reflecting Dye Cell Absolute Reflectance 0.85 0.90 0.95 1.00 Figure Diffuse 85. Reflectance of Kastinan White 300 Hufleetance Coating Kastman WhiteReflectance Coating 400 Absolute Reflectance versus Wavelength UavelcngLh (am) Magnesium Oxide 500 600 165 166 Table 25 LIQUID CONSIDERED TO FILL DIFFUSE REFLECTING CELL Wavelength of Index of Liquid UV Cutoff Refraction Carbon Disulfide 385 pm — Bromotrichloromethane 350 ym 1.5 Acetone 330 pm 1.36 Methyl Ethyl Ketone 330 pm — Tetrachloroethylene 290 pm 1.5 Toulene 285 pm 1.5 Benzene 280 pm 1.5 N ,N“Ditne thy lace t amide 270 pm 1.4375 N,N-Dimethylformanide 270 pm 1.4305 Methyl Sulfoxide 261.5 pm 1.48 Ethyl Acetate 255 pm 1.37 2-Methoxyethanol 245 pm 1.4 Diclboromethane 232 pm 1.42 P-Dioxane 215 pm 1.42 Cyclohexane 205 pm 1.42 Hexane 195 pm 1.375 167 this cell out of quartz a pyrex version was constructed. Since pyrex cuts off most of the UV light anyway the liquids chosen in Table 25 for UV absorption characteristics were therefore not useful. Instead ethanol was used to fill the cell simply because it would absorb all the same wavelengths as the ethanol solvent and therefore any shock wave which was formed should be initiated at the wall of the cell rather than at the dye tube wall. The pyrex cell which was constructed was coated with diffuse reflecting paint and an inverted coaxial flashlamp from Phase — R was placed inside the cell. This flashlamp was identical to a standard DL-llOO laser flashlamp except the electrical ground was along the inside of the lamp and the flash occurred toward the outside. When an attempt to lase this configuration was made it was, however, found that only a slight laser action occurred, and then only with high reflectance mirrors. With a 20% R output mirror no laser action occurred. Obviously therefore the pump energy in the dye Is much lower in this configuration than in the coaxial configuration. Low pump flux in the cavity is attributed to the many loss regions in the cavity (holes on the top and bottom as well as the holes for and the dye and flashlamp); and probable lower reflectance due to absorption in the infrared and less than ideal painting technique. Some evidence suggests that the white enamel painted over the diffuse reflecting paint to protect it may have gotten under the diffuse reflecting paint and lowered reflectivity.. This was not repeated however due to 168 lack of time and the fact that earlier tests showed the shock wave to be a relatively minor influence on a laser having this pulsewidth. A flashlamp pumped, transverse flow, dye cell was not constructed. However it does appear to have the potential for improving the optical quality of the dye cell and therefore decreasing loss. Figure 86 68 shows a transverse dye cell that appeared in a recent publication. If a 1-pm flow filter was used in conjunction with a dye cell such as this one I believe that reduced optical distortion would result and it would be possible to obtain better energy storage in the laser cavity (for use with cavity dumping). F, Double Laser Configurations One other method of decreasing cavity loss would be to use the flashlamp pumped dye laser to pump a laser pumped dye laser. The laser pumped dye medium could then either be a relatively narrow trans verse flow dye cell or a dye imbedded in plastic. These options should allow for the possibility of having very good optical quality in the medium. Also, this pumping method allows one to have a gain medium with a smaller diameter than the clear aperture containing the gain medium, and the size of the gain region can be controlled simply by focusing the pump light. Therefore the laser pumped dye laser can be operated in a lower order mode. The potential advantage of pumping a dye laser with another dye laser as compared to some other laser is that the pump laser is tunable. 68 Herbert W. Friedman and Richard G. Morton, "Transverse Flow Flashlamp Pumped Dye Laser," Applied Optics, Vol. 15, No. 6 (June 1976) pp. 1494-1498. 169 Cusped flow diverted Quartz (Pyrex) Side Window Thermal Insulation Axial Water Flashlamp Reflector Flow Flashlamp Transverse Inlet Manifold Dye Flow Figure 8 6 . Transverse Dye Cell 170 Figure 87 shows a possible configuration in which a dye laser could be pumped by a flashlamp pumped dye laser. A lens placed between the flashlamp pumped dye laser and the dye cell allows the illuminating spot size to be adjusted. Assuming a 500 mj pump pulse lasting 500 nsec one would have a pump power of 1 Mw. It will be assumed that this power distributed over a spot 2-mm in diameter. This size was chosen since even a flashlamp pumped dye laser of doubtful beam quality can be focused to this spot size. Also for a 3-meter long laser cavity this spot would be slightly smaller than the 11 2 fundamental Gaussian mode. Power density is therefore 3 x 10 watts/m 30 incident on the dye cell. Therefore F ^ = 1.9x10 pump photons per square meter. Dye output Prism Pockels mirror Cell Mirror Figure 87. Dye Laser Pumped by a Flashlamp Pumped Dye Laser The optimum dye concentration will be assumed to yield a 20% 69 transmission of pump radiation through the dye cell. Using Eq (116) 69 Arnold Bloom, "CW Pumped Dye Lasers," Optical Engineering, Vol. 11, No. 1 (Jan/Feb 1972), p. 6. 171 with p(d) =■ 0.2 and d = 6.3 mm one calculates an optimum dye concen- — S — 20 2 tration of 3.2 x 10 M (assuming a ^ = 1.2 x 10 m ). -a Kn„dc p(d) = e ab U (116) where d = thickness of the dye cell a - absorption cross section c = molar concentration Oq = number of molecules in a cubic meter of a one molar solution p(d) = transmission of the dye cell For a simple one-way transmission of the pump beam through the dye cell an exponential decay of pump flux through the dye cell occurs. If a mirror on the other side of the dye cell is added the light transmitted through the dye can be reflected back, resulting in a distribution that is the sum of two exponentials. Gain of the laser medium again depends on the population of state b. Therefore, using Eq (30) and previously used values of con- —9 stants in the equation (A^a = 1/4,45 x 10 sec, A ^ / A ^ = 0.85, A^c = 3.4 x 10^) one can calculate the initial value of n^ as 54% of nQ at the front surface of the dye cell and 53% of n^ at the back surface. The gain over and back through the dye cell is therefore only a factor of 4.2 A single pass only has a gain factor of two. If, however, the flashlamp pumped dye laser is not right on an absorption peak of the dye used in the laser pumped dye laser a higher concentration can be used (and still only absorb 80% of the pump radiation). 172 When a dye laser pumped dye laser was tested two different dye combinations were attempted. The setup shown In Fig. 88 was used. The experiment was, however, not done carefully enough to obtain lasing with the laser pumped dye laser. Dye HeNe cm lens \ " Dye HeNe r Figure 88. Experimental Setup for a Laser Pumped Laser Figure 89 shows the result of a Twyman-Green measurement of the optical quality of the transverse flow dye cell that was constructed for this test. As is obvious the optical quality is poor. Therefore to run a good test a new dye cell for the laser pumped laser would be required. An experiment was conducted, however, in which a flash lamp pumped R6G laser was used to try and pump Kiton-Red-S (lases at 6250 A) and to try and pump Ozanine 170 (lases at 7200 X). Neither experiment yielded laser action from the laser pumped laser. 173 Figure 89. Optical Distortion Results If a dye is embedded in plastic it is possible to keep index of refraction gradients down^ to less than 5 x 10 Also* since the reference which was quoted is old, current capability should yield even more uniform index of refraction. In addition, it is possible to design a transverse dye cell with much better optical quality than the one constructed. It therefore seems reasonable that one or the other of these two approaches could, with care, yield a laser with good mode qualities. Due to the double laser aspect, however, efficiency would be lower than a flashlamp pumped laser. ^Stockman, David L. and Raymond A. Shirk, "On the Preparation and Properties of an Optically Isotropic Polymer," Applied Optics, Vol. 5, No. 5 (May 1966), p. 863. CHAPTER V CONCLUSIONS An ln-depth investigation of flashlamp pumped dye lasers has been performed and the feasibility of developing short pulse flash lamp pumped dye laser evaluated. Specific results of this investigation are; 1. The primary loss mechanism in flashlamp pumped dye laser cavities has been identified. It is the poor optical quality of the dye medium and the beam spreading that results from its inhomogeneous nature. 2. It has been determined that triplet stage effects In the dye medium are not a significant loss mechanism for coaxial flashlamp pumped dye lasers. This verifies recently published results which show the negative influence of triplet quenchers on flashlamp pumped dye lasers with pulsewidths on the order used in this investigation (less than 1 psec). 3. Shock wave effects resulting either directly from the flashlamp or from absorption by the solvent are not a significant loss mechanism in the flashlamp pumped dye laser with pulsewidths as used in this study. For longer pulsewidths shock waves would be of significance and these effects are well documented In the literature. 174 175 4. State-of-the-art efficiency (0.87%) has been achieved for a flashlamp pumped dye laser that has reasonable beam divergence (2.5 mrad with an 8-mm exit aperture). 5. An analytic solution to the rate equations for a flashlamp pumped dye laser has been developed. In addition, a digital solution to these equations has been formulated and used. 6. Cavity dumping of 57 mj has been measured. This exceeds by a factor of 570 the previous level of energy cavity dumped from a flashlamp pumped dye laser (0.1 mj). 7. The possibility of Q switching dye lasers has been briefly investigated. The dye which was used in an attempt to develop a phosphorescent dye laser (which would have the required upper state lifetime) did not however yield laser action. 8. A pump energy density profile in the dye cell was developed through digital solution of the absorption equations. 9. A unique analytic treatment of index inhomogeneities in a laser resonator has allowed analysis of cavity loss resulting from scattering out of lower order, low loss modes into higher order, high loss laser modes. 10. Cavity loss in a flashlamp pumped dye laser has been reduced to the point that if a 99.9% reflective "output" mirror is used peak intra-cavity power seven times as high as is obtained with a 20% reflective output mirror occurs. This provides promise that cavity dumping will be useful to at least increase the initial pulse power; although with this level of storage it would be inefficient to wait until the end of the normal laser pulse time before dumping. A pulse with high initial peak power and then finishing with standard powers may be realistic. Appendix A THE DYE 2 COMPUTER PROGRAM This is a computer program to calculate the pulse shape out of a dye laser. It uses rate equations derived in Chapter II, The program generates both a tabular output and a graphical output showing energy stored as a function of time. The graph is on linear paper and is done for a single set of conditions. Each graph also has the shape of the pump pulse included. These graphs were not used in the body of the text since it was necessary to combine a number of conditions on one graph to clarify the results. 177 178 PROGRAM DYE?( INPUT.OUTPUT) COMMON/AAA/PSCALE, TSCALE DIMENSION YPOS(500 > iY FP (50 0) ...... REAL NG*NSt,NT1*MOL»LFNGTH,INDEX,N0»LAMDA DATA PI *DCL«C,AVIG»DIAM/3. 14159,,11,3.E + B,6.02E*26,,01/. .. DATA SIGPfSIGl.,T51G,SIGT,LAMf)A/1.5E-20tl.?E-20»6.E-9, X • 3E-20 *.6E-6/ | CALL PLOT(0.,0.,-3) I.NDEX=l,36 .______R=DIAM/2. s CONTINUE .. PRINT 60 1 ' 601. FORMAT ( 1H1 ) . j READ 500,MOL,TSCALE,LFNGTH,TEND.Y,PSCAL£»TTlG,TS)Tl ! ..TEND^l ,4«TSCALE ...... ! PRINT 500, MOL,TSCALE*LENGTH,TENO,Y»PSCALt,TT1G,TS1T1 IF (MOL.LT.O. )G0 TO 100 . ^______500 FORMAT(8F10.5) CALL SYMBOL t,S,B.25,.|,7HPSCALE=,0, ,71 ...... CALL NUMBER( 9 9 9 . , 9 9 9 . 1 ,PSCALE,0. , 1 ) ..call 5YMROL(999( , 9 9 9 , f , l 17Hfl].E + 27.*.0*.» 7 )_____!______. CALL SYMBOL <999. ,9 9 9 . W 8H PHOTONS, 0 H1 PSCALE = PSCALE CALL SYMBOL<.5,0.7,.1,7H LOSS=,0.,7> CALL NUMBER(9 9 9 .* 9 9 9 .« .1 * 10fl.°Y»Q .»1) CALL SYMBOL( 9 9 9 . , 9 9 9 . , . 1 ,HH PERCENT* 0 . « 0) CALL SYMBOL(.S,H.5 5 ..1 ,7H TS1T1=,0.,7) CALL NUMBER(999.,999...1,I.E«9»TS1T],0..1> ...... CALL SYMBOL(999.,999...1,bh NSEC.0.,5) CALL SYMBOL< . 5 . 8 , 4 . . 1 , 7H T Tlfi=,0.»7) CALL NUMBER !9 9 9 t .9 9 9 . . . 1 . 1 ,t * 9 * T T ] G. 0. , ] .)______CALL SYMBOL(999..999...1,5H NSEC.O..5) t CALL SYMBOL<.5,«.l,.l,7H SIGL=.0..71 CALL NUMBER (999. *999. 1 ,SIGL«) .E*'20*0. , 1 ) ...... CALL SYMBOL (999. ,9 9 9 . , . 1 , 7H<»] .E -2 0 , ft. , 7 > ..CAUL. SYMBOL. <999 , ,9.99, , t \ ,5H SO M , JJ , , 5 ) ______ CALL SYMBOL( , 5 * 7 . 7 . . 1 *7H PULSE , 0 . , 7 ) . . CALL SYMBOL(999..999...1.2.0..-1) CALL SYMBOL( . 5 . 7 . S 5 . . 1 . 7H PUMP , 0 . , 7 ) ’ CALL .SYMBOL (999, ,9 9 9 , , 9\ ,5 , 0, t.r\)______ CALL PLOT ( 0 . , 0 . , 3 >______CONTINUE CALL PUMP ( T » FP 1...... FNS1=NS1♦OT 0 (NG«SI6P»FP-NS1«(1./TS1G+1./TS1TI+SIGL*FL.)) FN.T1=NTJ .D T M -N T 1 /T J )G *N S 1 /T S ] T1 ) .______FFL = FL*DT» (NS1*>SIGL~NT1*SIGT)*C«FL f n g =n o -f n t i -fnsi ______NT1=FNTI NSI=FNS1 ______NG=FNG ' F L = FFL ______T = T ♦ D T TT = TT*f)T PL = FL»6.6E-34 »C«*PI * (01 AM/2. ) "«2/LAM0A ELC=PL»TTT ____ £L = EL + PL*»Yl*DT Tl=T*l,F*9 ______IFiTT.LT.TTTJGO TO 30 IT=IT*1 _ „ FL=FL«(1.-Y) PRINT 600 »T1.ELC.FL.PL.NG.NS1, NT J.FP ______YPOS(IT)=ELC IF PUMP COMPUTER PROGRAM A partial list of variables used in the computer program is given in Table 26. Table 26 A PARTIAL LIST OF PUMP VARIABLES SIGP Pump cross section FNO Number of dye molecules in a one cubic meter one molar solution FM Concentration (molarity) B Radius of the dye cylinder ALPHA Extinction coefficient THETA, PHI Angular coordinates used PUMP A variable which is proportional to the absorption of energy at a given radius and concentra tion Table 27 then gives a listing of the PUMP program and Tables 28 through 3 i give, output for four different concentrations. When a = 0 was used the flux obtained (column 2) was 0.37687. This can be used for normalization. 182 Table 27. A Listing of the PUMP Program 183 PROGRAM PSPH(INPUT,OUTPUT) DIMENSION FI(21> PI=3.14159 SIGP=1•5E-20 FN0=6•6E♦26 1 CONTINUE PRINT 601 READ 500 * FM * H 500 FORMAT t 2F10.2) PRINT 500*FM*B IF(FM.LT.O.)GO TO 1000 B = P ° *001______PRINT 60 1 601 FORMAT I 1H0) PRINT 603 603 FORMAT(1H0 * 15X ,6HRADI US *9X ,4NFLUX*11X*4HPUMP) ALPHA=SIGP*FN0*FM...... 00 5 1-1*21 FI (I > — 0 . “ ...... 5 CONTINUE DO 100 1=1*21 A=FLOAT CI-1»*B*.05 H-n...... t h e t a =-p i /?. DTHETA=Pl/50...... PHI=0• DPHl=PI/50...... — 1 0 CONTINUE FK = SIN < THETA ) .... FK = AflS(FK ) IF(FK.LT..0001)FK=.O001 P=-A»C0S PUMP Output for C - 10 RADIUS FLUX PUMP 0 . 0 0 0 0 0 .00127 .00127 .250 00 .00142 .00142 .50000 .00167 .00167 .75000 .00203 .00203 1 .00000 .00254 .00254 1.25000 .00321 .00321 1 .50000 .00412 .00412 1.75000 .00532 .00532 2.00000 .00691 .00691 2.25000 .00902 .00902 2.50000 .01181 .01181 2.75000 .01551 .01551 3.00000 .02044 .02044 3.25000 .02703 .02703 3.50000 .03590 .03590 3.75000 .04792 .04792 4.00000 • 06437 .06437 4.25000 .08719 .08719 4.50000 .11958 .11958 4.75000 .16751 .16751 5.00000 .25151 .25151 Table 29 -5 PUMP Oupput for C = 5 « 10 M HADIUS FLUX PUMP 0 . 0 0 0 0 0 .01887 .00943 * 25000 .01991 .00995 .50000 .02130 .01065' .75000 .02308 .01154 1.00000 .02529 .01264 1.25000 .02797 .01398 1.50000 .03118 .01559 1 .75000 .03500 .01750 2.00000 .03952 .01976 2.25000 .04485 .02243 2*50000 .05114 .02557 2.75000 .05853 .02927 3.00000 .06726 .03363 3.25000 .07756 .03878 3.50000 .08977 • 04489 3.75000 .10433 .05217 4.00000 .12181 .06090 4.25000 .14303 .07151 4.50000 .16925 .08462 4.75000 .20280 ,10140 5.00000 .25249 .12625 186 Table 30 PUMP Output for C = 2.5 x 10~5 M RADIUS FLUX PUMP 0.00000 .07778 .01944 .25000 .07987 .01997 .50000 •08236 .02059 .75000 .08528 .02132 1 . 0 0 0 0 0 •0 8865 .02216 1.25000 .09249 .02312 1.50000 .09683 .02421 1.75000 .10172 .02543 2.00000 .10719 .02680 2.25000 .11329 .02832 2.50000 .12010 .03002.... 2.75000 .12767 .03192 3.00000 .13609 • 03402 3.25000 . 14S4B .03637 3.50000 .15597 .03899 3.75000 .16771 .04193 4.00000 .18095 .04524 4.25000 .19600 • 04900 4.50000 .21337 .05334 4.75000 .23405 .05851 5.00000 .26235 .06559 187 Table 31 -5 PUMP Output for C = 10 M RADIUS FLUX PUMP 0 . 0 0 0 0 0 .19212 .01921 .25000 . 1 ^ 4 2 4 .01942 .50000 .14659 .01966 .75000 .19917 .01992 1 .00000 .20198 .02020 1 .25000 .20503 .02050 1.50000 .20833 .02083 1.75000 .21189 .02119 2.00000 .21573 .02157 2.25000 .21986 .02199 2.50000 .22429 .02243 2.75000 .22906 .02291 3.00000 .23418 .02342 3.25000 .23969 .02397 3.50000 .24563 .02456 3.75000 .25206 .02521 A .00000 .25907 .02591 A ,25000 .26675 .02668 A.50000 .27532 ,02753 A.75000 .28517 .02852 5.00000 .29830 .02983 Appendix C BOUNCE COMPUTER PROGRAM This appendix gives a listing of the two subroutines which comprise the Bounce Computer Program. It also contains output data for a number of conditions. This program is a geometric approximation to what would happen inside a resonator cavity. Beams are initially started at various radii away from the center of the cavity and are allowed to bounce back and forth while the computer tabulates how far from the origin the light beam hits one of the mirrors. This creates a distribution which is printed in the data output. This computer program uses ray matrices. Changes in displacement, r, and slope, r', of a ray as it passes through an optical element can be summarized a s ^ (117) where (118) and A B M = (119) C D Therefore Eq (117) could be split into: Slegman, A.E., An Introduction to Lasers and Masers, (McGraw- Hill; New York, 1971), p. 294. 189 r2 = Arx + Br j (120) (121) r * 2 = Crl + D r { The M matrix for a straight section of length L is 1 L M = (122) 0 1 ” 72^ and for a curved mirror is 1 0 M = (123) Bouncing a ray back and forth in a laser cavity is therefore just a simple process of matrix multiplication. A listing of the BOUNCE Computer Program is given in Table 32. This program allows mirror number 1 to have two different radii of curvatures, R3 from the center of the mirror out to a radius A and Rl beyond that radius. This allowed evaluation of some complicated resonator structures. Also, one of the end mirrors may be misaligned by inputting a non-zero value for the term ALN. Table 33 shows a sample output for a case of interest. Input conditions for this run were A = 0, R^ = °°, = 6 meters, FL = cavity length = 3 meters, and ALN = mirror misalignment =0.0 radians. These input values are printed across the top of the output with the addition of the parameter = °° which is not needed for this case since 72 Ibid., p. 294 Table 32 190 A Listing of the BOUNCE Computer Program PROGRAM BOUNCE Table 33 Sample Output of the BOUNCE Program 6.0000»<»*<* t NO 1 END 2 RADIUS PERCENT DENSITY PERCENT DENSITY .onos .9439 50.0000 . 4 4 ft 9 4 9 1 .0 0 0 0 . 0 0 1 0 .0328 3 3.0000 .3920 16.6667 .do 15 . 7? 1 7 1 9 . ft 0 o 0 .3367 10.0000 .0020 .6105 14. 1429 .2006 7.1429 . 0025 .4994 1 1 .0000 .2245 5 .5 5 5 6 .0030 . 3003 9.0000 . 1 604 4 .5455 .0015 .27 72 7.6 154 .11? 2 3.0 4 6 2 .0040 . 1 661 6.6000 . 0561 3. 3333 .0045 .0550 5 .5 2 3 5 0.0000 2 .9 4 1 ? .0050 0.0000 2 .5 7H9 0.0000 o 0 00 0 .0055 0.0000 0 . (1 0 0 0 0.0000 o o 6 6 o .0060 0.0000 0.000 0 ft . 0 0 0 0 o.oooo . 0065 0.0000 0 . 0 0 0 0 0.0000 0.0000 .0070 0.0000 0.0000 0.0000 0000 .0075 0.0000 0.0000 0.0000 0000 . 0 0 tt 0 0.0000 0.0000 0.0000 000.0 , .0005 0.0000 0.0000 0 . 0 0 ft 0 0000 .0090 0.00 0 0 0.0000 0.0000 0000 .0095 0.0000 0.0000 0.00 0 0 0.0000 . 0 1 00 0.0000 0.0000 0.0000 0.0000 193 A = 0. Then a table Is generated which gives the percent of bounces beyond a given radius at each end of the cavity. Also, a relative density of bounces at that radius is generated. To summarize data from a number of computer runs the radius at which the 50% point is reached is noted. These are called W-^ and respectively. For the case included in Table 33 and Wg were estimated to be 2.2 mm and 5.0 ram, respectively. Also, the percent over 5 mm is noted for each mirror. These are referred to as and Tn Table 33 and P^ are 0 and 50%, respectively. Table 34 summarizes the data from many different computer runs. R R R3 R2 R1 A (mm) OOOOOOOOOOOWWtotoOOOOOOO o o ooooooooo 5 5 10 5 6 5 ____ -11 m (m) (m) 010 10 05 10 10 10 10 10 o o D C D C J O 6 O C 10 3 5 6 5 6 6 6 3 0 D C 0 0 O C cx> o o o o 5 O C o o O C o o o c -11 12 12 10 12 12 10 10 10 12 12 O O O C 6 3 3 6 6 6 6 3 3 3 6 6 SUMMARY Ol’ liOUNGE COMPUTER RUNS Ol’ liOUNGE COMPUTER SUMMARY ____ (m) 1.6 2.1 0 1.5 0 3 3 0 3 1.7 0 0 3 0 3 3 3 3 3 3 6 34 Table 0 3 0 3 3 0.1 6 6 0 6 3 0 3 3 3 3 0.4 1.5 1.5 3 6 6 0.4 0 3 0.5 3 1.5 1.5 1.5 (m) ALN L (tnraci) 1.8 1.3 0 0 0 0 0 0 0.2 0.8 0.4 . 1.5 0.8 0.1 0.2 1.6 1.6 0.2 2.5 0 . 1.5 1.6 0 121.9 - 1.2 W1 ,W 1.5 1.4 1.6 1.4 1.3 1.4 2.5 5.0 2.2 0.7 1.8 0.4 1.6 1.5 1.2 0.7 0.4 1.2 0.4 . 2.3 0.4 2.2 0.7 0.4 (mm) - 10.0 1.3 0.8 0 1.7 0 1.4 4.3 1.6 1.6 1.3 2.1 1.3 2.3 . 3.4 1.8 1.4 1.5 1.6 1.9 . 21 1.6 5.0 2.3 2 W . 0 2.2 . 0 2.4 2.5 . 0 5.0 2.2 1.8 0.4 . 0 0 2.3 2.3 2.3 2.2 2.5 (nun) - - - 13 076 50 23 2 P 1 P (%) 0 0 1.7 6.5 0 0 2.6 7.2 2.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 194 12.6 18 17 50 11.2 50 11.2 11.2 (%) 0.8 0 0 3.5 1.6 0 3.8 2.5 2.8 2.8 5.6 0 5.6 0 0 5.6 2.8 Appendix D SELECTION OF AN ELECTRO-OPTICAL CRYSTAL FOR SWITCHING 1. Introduction to Electro-Optical Crystal Selection Crystals that can be used as electro-optical modulators were screened on the basis of 1) damage threshold, 2) loss through the crystal, and 3) half wave voltage. In addition, electro-optical theory is discussed in this appendix. A number of crystals were reviewed and Table 35 gives capsule comments on each crystal. If it is assumed that the desired pulse output is 0.5 joules in 20 nsec, therefore one has a 25 Mw power output. Assuming this is 2 over a 1 cm beam and assuming hot spots which have ten times the power density this results in a need to have a crystal which will 2 withstand 250 Mw/cm • Most of the crystals listed in Table 35 will be damaged by these power densities. Of those crystals that can withstand high power, the most interesting ones are KD*P, LiTaO^* ifc and LiNbO^. KD P has the highest damage threshold, which has been 73 2 7 A reported to be about 1 GW/cm . Next comes LiTaO^ at about 2 7 5 400 mW/cm , and slightly below LiTaO^ comes LiNbO^ which however must be heated to obtain a good damage threshold. LiTaO^ and LiNbO^ 73 John Ragazzo, INRAD, phone conversation held in February 1976. 74 Bob Carleson, Crystal Technology, phone conversation held in February 1976. 75 Ibid. 195 196 Table 35 CANDIDATE E-0 MODULATOR CRYSTALS BaNaNbO^ Insufficient information was available concerning damage threshold and crystal availability. This crystal does however have desirable half wave voltage characteristics. KTN This crystal has a very promising half wave voltage, but was eliminated due to lack of information — especially concerning damage effects. KD*P This crystal has good damage characteristics, reasonable half wave voltage, and transmits over an acceptable band. Since it is hygroscopic it does however require placement in a liquid bath and therefore incurs the additional loss of having a window and liquid on both sides of the crystal. Prousite Only transmits down to 0.6 pm. KDP Similar to KD*P, but has a lower damage threshold and higher loss. CD*A and CDA Crystals with an excellent damage threshold, but not as readily available as KD*P. These crystals are also hygroscopic and offer no substantial advantage over KD*P, A ADA Has a higher half-wave voltage than KD P and a lower damage threshold. It is also hygroscopic. LiTaO^ An excellent crystal with low half-wave voltage, excellent transmission characteristics and good damage properties. KD P does however have better resistance to damage. Crystal Technology Inc. claims to have used 400 Mw/cm without damage. LlNb03 Similar to LlTa03 , except it would require heating and has a somewhat lower damage threshold. ADA This crystal is transparent in the region of interest, but it has a high half-wave voltage and damage data was not readily available. LiI03 A hygroscopic crystal with a lower damage threshold than K D D P . 197 have very low Internal loss and do not need protection from moisture, whereas KD*P has somewhat higher loss and requires JL protective windows and an index matching fluid. Since KD P requires protective windows it is very important to align all surfaces in the assembly if absolutely minimum cavity loss is to be maintained. If these surfaces are aligned then reflections off of them can be contained in the cavity. Otherwise this is a loss mechanism. Before making a decision on the EO modulator material the three most promising crystals, KD P, LlTaO^ and LiNbO^* were considered in more detail. Specific orientations were picked and the necessary voltage required for a half wave shift was then calculated. Also, problems concerning undesirable output coupling prior to voltage application were addressed. Theory for this analysis was developed in two parts: 1) a simple theory applicable when the electro-optical crystal being considered has zero non-diagonal matrix elements, and 2) a more general theory which is partially developed here, but is 7fi given in more detail by Dr. Clifford V. Heer's notes. 77 The simply theory begins with Eqs (124) and (125). E b = ^ Ba b Da <124> Bab < “ > = Ba b ° k > + rabc Ec <125) C.V. Heer, "Notes for Nonlinear Optics," notes used in a non linear optics course given by the Physics Department of The Ohio State University in 1975. 7 7 Ibid. 198 Optical activity and photoeleasticity are assumed to be negligible. The term r , is then usually contracted such that abc r , = r, = r , where Table 36 shows a correspondence between ab,cba,cu,c u values and values of a and b. In addition for u = l,2, or 3 B cah u be related to the more commonly known term, index of refraction by Eq (126). B =(“-(t) “ ) (126) Table 36 u a ,b 1 1,1 2 2,2 3 3,3 4 2,3 or 3,2 5 1,3 or 3,1 6 1,2 or 2,1 For simple situations this fact can be used to calculate the change in the index of refraction as given in Eqs (127) through (129) .2 Bq + AB = — 1— 2 s fir) t1 “IT1 ]> or (127> (n0 +4- An) \ n0/ n0 AB = - , or (128) n0 4B„ 3 An = - — ^--- (129) Using Eq (126) one can then obtain Eq (130). 199 3 -r E uc cn o An (130) u 2 So long as An^ = 0 or u = 4,5, or 6 then Eq (130) is all that is needed to calculate the change in index of refraction caused by applying a given electric field. If, however, An ^ 0 for u = 4, 5, or 6 then coordinates must be rotated such that the matrix is diagonal prior 78 to calculation of the effective An. While many books, use an index ellipsoid for this rotation, it is the author's opinion that the most straightforward, general approach is the one described in the next section of this appendix. 2. General Electro-Optical Theory For the situation in which J = p = 0 , Maxwell's equations in mks units are given by Eq (131): c) V . B = 0 (131) d) V • D = 0 Expanding these equations using Eq (132), one obtains Eq (133). E(r, t) = Eei ^k ‘r + C.C (132) d) k x E - c) k • B = 0 (133) b) It x 3 = -(jD d) k . 3 = 0 In addition, one has Eq (134) 78 Amnon, Yariv, Introduction to Optical Electronics, "Holt, Rinehart and Winston Series in Electrical Engineering, Electronics, and Systems" (New York, Holt, Rinehart and Winston, Inc., 1971), p. 223. 2 0 0 a) B = MqH d> Bab “be = 6ac . 2 k 2c2 b) Da = £0KabEb e) n - — 7T~ (134) hi B abu D bk c) E = f) B a ab Then, using Eqs (132) and (133) one has Eq (135); 1 it x i (135) U)|J This can be converted to Eq (136) -> 7^ -V 2 -> kxkxE + ua) D = 0 (136) o Then, using the identity given in Eq (137), Eq (138) becomes obvious. X X (B X c) = B(X X c) - (t X B)c (137) k 2 [k (k E ) ] - k 2E + m oi2D = 0 (138) a b b a o a k is a unit vector in Eq (138). Using Eq (133) and Eq (138) one then 3 has Eq (139). n [k (k,B D ) - B ,D, ] + D = 0 (139) a d be c ab b a B ^ Is a real symmetric tensor so it is always possible to find a (140) holds B 0 0 XX B 0 B 0 (140) ab yy 0 - 0 B zz 201 To find the normal modes It is noted that D is transverse to a —y the direction of propagation k. Therefore, the normal modes will occur in a reference frame which has one axis along k. In order to accomplish this a rotation t is performed about the z axis followed by a rotation 0 about the y' axis. Then the only possible other rotation necessary in order to find the reference frame in which*]! is diagonal is a rotation, ip, about the zM axis (z" is along the direction of propagation given by k). In the desired reference frame it is known that along the axes Eq (141) holds B _ (141) 2 Sn n where n = x R and £ = x R xn x£ In addition, just after rotation by Bak has been partially dlagonalized. It is of the form given by Eq (142). 0 B11 B12 0 (142) Bab = B,'l2 B22 0 0 B 33_ The rotations necessary can be represented by Eq (143): x' cos X cosG 0 -sinB x' 0 1 0 (b) sin© 0 cos9 2 0 2 and cos ijj -sin if, 0 sin ifj cos if, 0 (c) (143) 0 0 1 Then, if A is used to represent a transformation matrix, each of the above equations is of the form given by Eq (145). E(r') = A E(r) (145) To see how transforms into the new system one starts with Eq (134c) and multiplies each side by resulting in Eq (146) -1 A B . A A Bab Db ab AE = A D. a eo (146) or, ^ I I B abw Du b 0 -1 where B ab^ = A B abu E = A E a D, b “ ADb Then, in order to find the angle, tfi, the constraint given by Eq (141) will be used. Also, notation will be changed such that B qq = Bi2 = ® 0tf>’ = B22* tBen a^Cer some work shown here Eq (147) follows. 2 2 B = B cos tp - Brt, simp cosip - B nrt costp simp + B sin ip nn 00 r 0 therefore, ^ sin2ip + cos2ip = 0 t herefore, 2B, = tan2ip (147) B00 ~ B«p But one does not need to explicitly use ip in determining An, 79 The expressions given in Eqs (148) and (149) can be used. 79 C.V. Heer, "Notes for Nonlinear Optics," 1975. 204 B00 " BXX cos^ B« “ Bxx sln2'1' + byy cos2* - bxy sln2,1, (b) B8d* ” T^BYY ~ Bxx) sin2‘j| cos0 + bxy cos2lt> cose (148) (c) - B^ 2 costj) sin0 + B ^ sin “ H e B q ^ = B^.y cos0 + B ^ c o s <{> sinQ + si11*!1 si.ii0 (d) _ T>tt <{.0 and 1/2 (a 7 2 = i (Bee + V + < i (B8 e - V 2 + ( B e*>2 + % >2 \ (a) (149) 1 = k(Kaa + b aj 2 2 ' 00 - (i(B68 - V2 + (,v2 + BS*>2} 1/2 (b) n2 Then one can obtain a value for An by using Eq (153), developed below. L e t : ^ = x + Ax (a) and — ~ = x - Ax (b) (150) 2 “““ 2 nl n 2 Then, ni= (a) and n2= t z t t t x (b) (151> therefore &n ° "2 - nl ° 7x - to - 7x 1 Ax - %2 <152> X and Eq (153) follows 205 1/2 O o o - Bw > 2 + (b m )2 + Be*>2)' An = ^ ^ ^ ------(153) 3/2 ^B0O + B Alternately, it is possible to express An in terms of Boa, B,., B ' , yo (p(p o (p and ip. 3. Crystal Selection Summarizing previously developed theory for zero non-diagonal elements one can use Eq (154), -A Bn 3 An = --- (154) whereas in general Eqs (148) and (153) must be used, where 2 BX X = H M (a) e y Byy -(—-(-y I 1 (155) ^zz =-cy (c> and and are shown in Fig. 90. In order to reach the reference frame in which B ^ is diagonal first a rotation of <}) about z would be performed, then a rotation by 0 would be performed about y 1 , and then a rotation of ipwould be performed about z" (the k direction). X Figure 90. Rotation Geometry Now that the necessary background theory has been discussed, the specific candidate crystals, LiNbOg, LiTaOg and KD*P, will be considered. KD*P is a 4.2m crystal. Therefore ABu for KD*P i3 given by Eq (156). where r^-g = 25x10 m/V, r ^ = 8.8x10 ^ m/V, and at A = 0.6234 pm, nQ = 1.5044 and nfi = 1.4656. For LiTaOg, the crystal structure is not the only limit. LiTaOg has a 3 m crystal structure but some of its coefficients are zero. Therefore for LiTaOg one uses Eq (157). 207 0 0 ABi\ 13 r13E3 \ 0 0 iB2 13 r13E 3 0 0 AB3 *33 r33E3 (157) AB. 0 0 0 0 a b 5 0 0 0 0 AB, ) 0 0 0 0 where = 30.3x10 12 m/V, - 7.0x10 ^2 m/V and at 0.6 pm n = 2.1834 and n = 2.1878. LiNbO- Is also a 3 m crystal. All of o e J its coefficients are however non-zero. Therefore Eq (158) gives AB. for LiNbOn. / / / 0 r E, \ / -E„r__ + 13 f 2 22 3 13 r22 1 \ i 0 r E \ f E^r__ + r22 13 2 I / 2 22 3 13 0 0 r 33 E 3 ' E3r33 0 0 (l58> r42 " E 2r42 0 0 r42 \, E lr42 U 1 CM CM 0 0 \ -E,r „ \ 1 22 .-12 .-12 8.6 x 10"*12 m/V, m/V, 33 13 22 .-12 and r^ 2 = 30x10 m/V. Also, at 0,6 pm nQ = 2.2083, and ng = 2.3002, As can be seen, the simple theory can be applied for LiTaOg, while the more complex theory is necessary for LiNbO^ and KD*P. Therefore LiTaOg will be analyzed first. One can see from Eq (157) that for LiTaOg if propagation occurs along the z axis there is no resultant phase change, A0, between the two components of E, E^ and E^. Both n^ and change by the same 208 amount. Also, propagation along x or y results in the same phase change. Picking propagation along the y axis with initial polarization such that E = z one has Eqs (159) and (160). ton i(oit - — ^ z) c e (159) i(ait - — - z) E y “ -if*- e “ (160) Therefore the phase difference, , is given by Eq (161): A* = f A(n3 - nx) = (n3 - r^) (161) where I is the length of the crystal. Substituting in values for n^ and n^ one has Eq (162). A* = ^ [ne ' n ! + X (no3r13 " V S s * ] (162) The first concern to evaluate is the expected phase shift that will occur at E^ = 0. Any constant component of phase shift can be zeroed out by setting the basic voltage on the crystal at an appropriate level, or by methods using two crystals. Changes in phase due to variations in crystal length across the surface of the crystal can however not be zeroed. Necessary crystal flatness therefore needs to be calculated. If no more than 0.5% of the Incoming radiation is to be shifted in polarization, that implies a phase shift of no more than 0.286 degrees. The allowed roughness is given by Eq (163). r = V2tt (n ---- n. 7) <163> e 1 209 For LiTaOg this results in r - 0.18 X at 0.6 pm. While this does constitute a highly polished surface that is within reason. In order to cause a change in linear polarization by 90° a 180° phaee shift is required. Output polarization will then be of the form E = x - z. From Eq (164) it can be seen when a phase shift of tt occurs. V l/2 " ---- 3--- ~ --- 3---- (164) ^ e r33 " "o r 13) where d = the diameter of the electro-optical crystal and a voltage, V, is applied across that diameter. Assuming d = A and X = 0.6 pm the necessary half wave voltage is 2455 volts. For LiTaOg the desirable method of keeping phase shift to zero prior to application of a voltage pulse is to use two crystals. Applying a DC voltage to zero phase shift results in a lower damage threshold for LiTaOg. Analyzing KD*P requires a rotation of coordinates. Therefore the more complicated analysis scheme will be used. Also, since rco OJ is about three times as great as a minimum half wave voltage is required if the crystal is oriented to use r ^ (with a voltage along the z axis). This results in changes in and ng. In addition if propagation occurs along z no problem with respect to unwanted polari zation shifts prior to cavity dumping will occur. Prior to rotation, one has B = (1/n )^, B = (1/n )^, B = (1/n )^, B = r,.E , B =0, xx o * yy o * zz e * xy 63 3* yz * and B =0. Using these as inputs, and 0 = 0, one has Eq (165). Au V * " 0 Also, tan2tjj = cot2 Indicates a value of An. A _ r63E3______3 , , . An 3^2 no r6 3 ^ 3 (166) ^ C 2 ) i— o The phase difference which develops in a single pass through the crystal is given by Eq (167): 2vi 3 2v 3 „ A(j) = — -— r,, n E = — r,_ n V (167) r A 63 o 3 A 63 o v and the half wave voltage (Acf> = tr) , is 3524 volts at A = 0.6 pm. LiNbO^ has greater bi-refringence than LiTaOg. It also has a slightly lower damage threshold. Therefore the only condition under which LiNbO^ might be more desirable than LiTaOg for this application would be for propagation along z (the optical axis). For LiTaOg there was no phase difference developed between the two polarizations by the electro-optical effect when propagation occurred along the z axis. For LiNbO^, however, there are additional non-zero electro-optical coefficients. When propagation is along the z axis, the and E2 polarizations are along the x and y axis. Therefore the condition to be Investigated is a condition which creates substantially different An^ and An£ terms. From Eq (160) it can be seen that this can occur with either voltage across E^ or E^ (remember An^ is influenced directly by AB^ and indirectly by Ab^ and ABg. An£ is influenced directly by AB£ and indirectly by AB^ and AB^). For E = E ^ , one has the B values given in Eq (168) and for E = one has the B values given in Eq (169). B / (1/no) XX3 B1\ B B2 1 (1/ne) 3yy (1/n ) B, B3 e zz (168) 0 B B4 3yz B V« xz3 BS 1 B B6 \ " Elr22 xy B B] (1/no ) ~ E2r22 XX3 B, B (1/no> + E 2r42 yy1 B. Cl/ne )2 B zz2 (169) B b ; E2r42 yz B, 0 B 3xz B, 0 B xy, For propagation along the optical axis 0 = 0 and <{> can be chosen at any convenient angle. For E = E^ and B 00 -to B H - t o (170) 212 Then, using Eq (170) and an equation similar to Eq (163),AiJ> = 2tt£ (An/x), one has Eq (171) 2nZ V,r„„n B » xi- - - — (171) for a phase difference of it, one has Eq (172) vi/2 - — (172> 2* r22no Therefore for voltage across the x axis, propagation along the z axis, a wavelength of 0.6 pm, and d = £,-one has a half wave voltage, of 4643 volts. For propagation along the optical axis (0= 0), voltage applied along the y axis, and $ = 45 degrees one has Eq (173). 2 B00 ■ © * (173) B o'(|) 2^2E2r42* E 2r42 An = E„r.0 n 2 42 o Equation (174) therefore results and v i /2 ■ — -—r (174) 21 r,. n 42 o for X = 0.6 pm, and & = d, one has = 929 volts, 213 Based on the above results, the Interesting crystal orientations ar e : 1) KD P with propagation along the z axis and voltage along the z axis. KD*P needs a half wave voltage of 3524 volts, has a high 2 damage threshold (1 Gw/cm or more), and no leakage phase shift. 2) LiTaO^ with propagation along either the x or y axes and voltage applied along the z axis. Because of leakage phase shift this crystal should be used in pairs with a quarter wave voltage of 1228 volts applied to each crystal. Crystal surface flatness and matching crystal lengths is very important if leakage phase shift is to be kept to a minimum. Damage threshold is lower than KD*P 2 (anticipate a damage threshold of 400 Mw/cm ). 3) LiNbO^ can be employed with propagation along z to eliminate leakage phase shift. With voltage applied to the y axis it has a half wave voltage of 929 volts, and has very low absorption. This crystal may, however, have too low a damage threshold. It will definitely need a crystal oven in order to heat the crystal and therefore increase the damage threshold. “ft For initial demonstration purposes KD P was chosen due to the high damage threshold. BIBLIOGRAPHY Aldrich Chemical Company, Inc., The 1975-1976 Aldrich Catalog/Handbook of Organic and Biochemicals, 1974. American Institute of Physics Handbook. Co. Ed. Dwight E. Gray, Section Ed. Bruce H. Billings. New York: McGraw-Hill (1963) Section 6. Aristov, A.V. and Yu. S. Maslyukov, "Amplification and Induced Absorption in Solutions of Organic Luminophors." Opt. Spectrosk. Vol. 35, No. 6 (December 1973), pp. 660-661. Aristov, A.V. and Yu. S. 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