A study of mode-locking in a ruby laser operating near 77⁰K Item Type text; Thesis-Reproduction (electronic) Authors Osmundsen, James Frederick, 1944- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 27/09/2021 16:34:02 Link to Item http://hdl.handle.net/10150/554791 A STUDY OF MODE-LOCKING IN A RUBY LASER OPERATING NEAR 77°K ; by James Frederick Osmundseii A Thesis Submitted to the Faculty of the COMMITTEE ON OPTICAL SCIENCES (GRADUATE) In Partial Fulfillment of the Requirements • For the Degree of MASTER OF SCIENCE In the Graduate College • THE UNIVERSITY OF ARIZONA 1 9 7 f , STATEMENT BY AUTHOR This thesis has been submitted in partial fulfill­ ment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowl­ edgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the inter­ ests of scholarship. In all other instances, however, permission must be obtained from the author. APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: FREDERIC A. HOPy Dat< Assistant Professor of Optical Sciences ACKNOWLEDGMENTS This thesis is dedicated to Pat for her unfailing encouragement and understanding. iii TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ............. V ABSTRACT ............. vi CHAPTER 1, INTRODUCTION ......... 1 2. COMPLETE MODE-LOCKING IN A LASER WITH A SATURABLE ABSORBER ............. 5 The Letokhov Model 11 Conditions Required for Complete Mode- Locking in a Laser with a Saturable A b s o r b e r .................... 17 Theory for Experimental Determination of the Parameter A ............ 27 3. THE EXPERIMENT ..................................... 31 The Alignment Procedure ......... 36 Mode-Locking the Laser ............. 39 Measurement of the Lasing Linewidth .... 46 Determination of the Parameter A and the Degree of Mode-tLocking . ...... 60 4, CONCLUSION..................... 72 LIST OF REFERENCES „ . 75 iv LIST OF ILLUSTRATIONS Figure Page 1. Shape of a Pulse for Large N „ 8 2. Relationship Between N and p for Complete Mode^Locking ...... 26 3. The Laser Components and Their Relative Positions in the Laser ............ 32 4. Flashlamp Power Supply ................ ..... 35 5. An Output Pulse Train Recorded with the H.P. 183A Oscilloscope ........... 42 6. Mode-Locked Pulse Trains from a Ruby Laser Operating Near 77°K . , ....... 45 7. The Fabry Perot Interferometer . ........ 47 8. Some Interference Rings ............ 49 9. Schematic Diagram of Interference Rings. .... 51 10. Plot of Pumping Energy and Population Inversion Versus Saturable Absorber Absorbence . 63 11. Relationship Between t^ and A . 65 12. Plot of In KtdA/dt^) Versus t^ , 66 V ABSTRACT This thesis describes an experiment demonstrating passive mode-locking in a ruby laser operating near 77°K. First, the theory is reviewed and the Letokhov model is used to define the conditions required for complete passive mode-locking to occur in a laser using a saturable absorber„ Also included is a review of the theory required for experimental determination of the laser parameters which determine the conditions for passive mode-locking with a saturable absorber. Next, a description of the actual experiment is given. The laser and the procedure for its proper alignment are described, Then a description is given of the actual procedure that was followed to produce mode- locking, to measure the lasing linewidth, and to determine the degree of mode-locking. vi CHAPTER 1 INTRODUCTION Mode-locking in ruby lasers at room temperature has been observed by a number of investigators (Mocker and Collins 1965; Sacchi, Sancini, and Svelto 1967; Mack 1968; Bradley, Morrow, and Petty 1970)„ At room temperature the linewidt'h of the ruby R^-line is about 360 GHz. (Schawlow 1961), and mode-locked ruby pulses as short as 2 ps. have been observed (Mack 1968) . As the temperature of a ruby gain medium is reduced from room temperature, the characteristics of the R^-line are seen to change. The homogeneously broadened line is t seen to narrow down to about 20 GHz. at 100QK« Below this temperature the single line is seen to split into a doublet with a 12 GHz. separation; and at 77°K the components of the doublet are completely inhomogeneously broadened and completely resolved, each having a linewidth of about 3 GHz. in a high quality single crystal ruby. This splitting is just the crystal field splitting of the ruby ground state into two doubly degenerate levels which are unresolved at room temperature because the width of the R^-line is so large. 2 The positions of the energy levels of ruby are also strongly temperature-dependent„ Between 300°K and 7?°K the R^-line is displaced from 6943 A to 6934 A, Also, with the large reduction of the linewidth with decreasing tempera­ ture, a very large increase in the gain at line center is seen to occur„ Because of these changes in the R^-line, it is of interest to see if they would lead to any fundamental changes in the mode-locking process in a ruby laser operated at 77°K. One change is an observed increase in the minimum pulse duration because of the decreased linewidth of the lasing transition. And one theory (Letokhov 1969) indi­ cates that this reduced linewidth and the reduced number of oscillating modes should make mode-locking more difficult to achieve. However, according to the analysis presented by Kuznetsova (197 0) , the narrower linewidth and fewer oscillating modes should instead make mode locking easier to achieve. Another effect of the reduced linewidth is enhanced frequency pulling of the lasing modes. At room temperature this effect is negligible in a ruby laser; but at 77°K the frequency pulling effect, in the linear approximation, is as large as 4% (Slegman 1971, p. 408), The modes should be pulled toward the center of the line; the separation between modes should be reduced; and the actual lasing linewidth should be at least 4% less than that expected neglecting frequency pulling. In addition, there should be a small nonlinear frequency pulling effect because of the inhomogeneous groadening (Maitland and Dunn 1969, p. 246). This nonlinear frequency pulling should prevent the lasing modes from being equidistant in frequency and might have an effect upon the quality of the mode-locking if it is large enough. Another change that also should be looked for results from the inhomogeneous broadening of the R^-line, This is a possible increase in the pulse duration toward the end of the pulse train (Kafri, Kimel, and Shamir 1972), This results because in an inhomogeneously broadened medium the population inversion is frequency dependent. Thus, over the duration of a pulse train the inversion responsible for the modes in the wings of the line is depleted sooner than that at the center of the line, and the lasing linewidth gets narrower as the outer modes cease oscillating. Finally, it is reasonable to expect, since the Fe­ line splits into a doublet, that lasing and mode—locking might actually occur simultaneously at two different wave­ lengths, Evidence to support this possibility will be shown. Chapter 2 discusses the theory of complete mode- locking in a laser with a saturable absorber. The Letokhov model is used to determine the conditions required in the laser for complete mode-locking to occur„ Then the theory for experimental determination of the degree of mode- locking in a given laser is discussed. Chapter 3 describes the actual mode-locking of a ruby laser operating near 77°K and applies the theory to actual experimental determination of the degree of mode- locking in this laser. CHAPTER 2 COMPLETE MODE-LOCKING IN A LASER WITH A SATURABLE ABSORBER The output spectrum of a free running ruby laser can be described as a superposition of contributions from all of the oscillating resonant cavity modes. If the laser is considered to be a linear device in which the oscillating modes are viewed to be completely independent, it is possible to describe the field inside a resonator of length L in terms of a superposition of the separate oscillating modes. The simplest case is when only the axial modes of the resonator are favored; and the nth mode has the form E (x, t) = e sin [ (m+n) ^-] sin [ (w tnm) t+(f> ] . (1) ii i_j cj n The number m is an arbitrary integer such that m+n = 2L/A. The frequency w is the frequency separation between modes and is equal to ttc/L , , the frequency at line center, is equal to m ttc/L. The amplitude of the nth mode is en , which is determined by the line shape; and cf>n is the phase of the nth mode. If the number of lasing modes is N , then the total field is 6 At some arbitrary point in space, for example at the output mirror, the total electric field as a function of time for a free-running laser can be written as E (t) = £ enexp{i [ (a)o+na)) t+(}>n] } . (3) N Note that if the phases ^ are fixed and the modes are equally spaced in frequency, then (3) is periodic in the period T = 2tt/u) = 2L/c, which is the round-trip transit time of the resonator.