Photonic Device and System Laboratories Department of Electrical and Computer Engineering
Tunable semiconductor lasers
Thesis qualifying exam presentation by
Chuan Peng
B.S. Optoelectronics, Sichuan University(1994) M.S. Physics, University of Houston(2001)
Thesis adviser: Dr. Han Le
Submitted to the Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the Doctor of Philosophy At the University of Houston Oct. 2003 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Outline
1. Introduction and motivation 2. Semiconductor laser physics 3. Tunable laser fundamentals 4. Technologies for tunable lasers 5. Summary and Conclusion Photonic Device and System Laboratories Department of Electrical and Computer Engineering Introduction: Laser History
Milestones: • 1917 Origin of laser can be traced back to Einstein's treatment of stimulated emission and Planck’s description of the quantum. • 1951 Development of the maser by C.H. Townes. • 1958 Laser was proposed by C.H. Townes and A.L. Schawlow • 1960 T.H. Maiman at Hughes Laboratories reports the first laser: the pulsed ruby laser. • 1961 The first continuous wave laser was reported (the helium neon laser). • 1962 First semiconductor laser Photonic Device and System Laboratories Department of Electrical and Computer Engineering Introduction: Laser types and applications
Compact disk Basic Scientific Research Laser printer Spectroscopy Free Electron laser (FEL) Scientific Optical disc drives Nuclear Fusion Applications Optical computerLead-salt Sb CoolingAs AtomsN Bar code scanner Short Pulses Common Daily Holograms againstSemiconductor forgery lasers ApplicationsGas Lasers Fiber optic communications Ti-Sphire Free space communications Ruby X-ray lasers Laser shows Surgery:Nd:YAG Liquid Lasers Holograms Alexandrite•Eyes Kinetic sculptures •GeneralOrganic Dye •DentistryAg (Gold) vapor Medical Solid Lasers •DermatologyCu vapor Applications Diagnostic fluorescence Laser range-finder Soft lasers Ar+ Military Target designation Special Lasers Kr+ Applications Laser weapons N2 Laser FIRblinding lasers CO 2 HF He-Ne He-Ne He-Cd Far infaredInfared Measurements Visible Ultraviolet Soft x-rays Energy Transport Straight Lines Industrial Special Laser Gyroscope Material Processing Applications Applications Fiber Lasers30 µµµm 10 µµµm 3µµµmSpectral 1µµµm Analysis300nm 100nm 30nm 10nm λλλ Energy Photonic Device and System Laboratories Department of Electrical and Computer Engineering Introduction: Semiconductor Laser
What made the semiconductor lasers the most popular light sources ? • Small physical size • Electrical pumping • High efficiency in converting electric power to light • High speed direct modulation (high-data-rate optical communication systems) • Possibility of monolithic integration with electronic and optical components to form OEICs (optoelectronic integrated circuits) • Optical fiber compatibility • Mass production using the mature semiconductor-based manufacturing technology. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Motivations Application interests in tunable mid-IR semiconductor lasers: • Spectroscopy - Single frequency mode, tunable • Environmental sensing and pollution monitoring - Lidar - Requires Ruggedness, Correct Wavelength • Industrial Process Monitoring - Requirements similar to Environmental Monitoring • Medical Diagnostics - Breath analysis; Non-invasive Glucose monitoring, Cancer Detection, etc. • Military and law enforcement • Optical communication A key requirement: Broad, continuous wavelength tunability Photonic Device and System Laboratories Department of Electrical and Computer Engineering Outline
1. Introduction and motivation 2. Semiconductor laser physics 3. Tunable laser fundamentals 4. Technologies of tunable lasers 5. Conclusion Photonic Device and System Laboratories Department of Electrical and Computer Engineering Laser physics
Mirror Active medium
R1 R2 Laser output
α G, i Oscillation condition is reached when ~ 2/1 2i β L Partially (R R ) e =1 transmitting 1 2 L mirror ~ β = µk − iα 2/ Loop ν = µ Gain 0 gain m mc 2/ L curve µ ∆ν∆ν∆ν =c/2nL=c/2 gL GL 1 1 g = α + ln | | th i 2L R R Real part: Threshold condition Laser 1 2 −α threshold (R R ) 2/1 e( g i )L =1 ννν 1 2 o Laser Longitudinal µ = π == output 2 k0 L 2m , (m 3,2,1 ,..) power modes Imaginary part: wavelength condition Linewidth
ννν ννν ννν ννν ννν m-2 m-1 m+1 m+2 Frequency (v) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor laser physics
• Threshold: carrier density, cavity loss • Wavelength: bandgap physics, or intraband energy level (QC) • Tunability: gain bandwidth: for interband D.H. and quantum well laser: Fermi Distribution for quantum cascade laser: energy level linewidth • Power and efficiency • Operating temperature Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor laser band diagram
(a) Equilibrium band structure Probability of occupancy ∆∆∆ 3 Ec E c ρ (E) 2 c n(E) N-GaAlAs p-GaAs P-AlGaAs 1 E F E Ef v 0 f(E) p(E) ρ Energy (eV) Energy -1 v (E)
-2 0.0E+00 1.0E+21 2.0E+21 3.0E+21 4.0E+21 (b) Forward biased -3 -1 Efc ∆∆∆Ec Density (cm eV ) EcEc Carrier concentration in each band: N-GaAlAs P-AlGaAs ρ c (Ec ) Ev n = dE ∫ − + c Efv exp[( Ec EFC /) KT ] 1 ρ (E ) p = v v dE ∫ − + v Energy band diagrams for a double hetero- exp[( Ev EFV /) KT ] 1 structure laser (a) unbiased, (b) forward biased Photonic Device and System Laboratories Department of Electrical and Computer Engineering Threshold current density
∂n J Carrier density rate equation: = D(∇2n) + − R(n) ∂t qd ∂n At steady state, = 0 ∂t Anr nonradiative process 2 J Bn spontaneous radiative rate So: R(n) = 3 qd Cn nonradiative Auger recombination R stimulated recombination that leads = + 2 + 3 + st R(n) Anr n Bn Cn Rst N ph to emission of light and it is proportional
to the photon density N ph . n Below or near threshold: R(n) = τ e (n) qdn So, the threshold current density is J = th th τ e (nth ) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Power and efficiency of semiconductor lasers
If the current is above threshold, this leads to stimulated emission = + J Jth qdv g gth N ph
Optical output power P out vs. injection current is determined by hν α P = v α VN hν = η m (I − I ) out g m ph i α +α th q m i
External quantum efficiency is defined as: dP / dI α η = out = m η = η ln( /1 R) e hω α +α i i α + / q m i i L ln( /1 R) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum Well lasers
Intersubband transition QC Energy eigenvalues for a particle confined in the quantum well are: h2 = + 2 + 2 E(n,kx ,k y ) En * (kx k y ) 2mn Inerband transition
Density of states :
>>> ρ = mci ci πh2 Lz
Quantum wells are important in semiconductor lasers because they allow some degree of freedom in the design of the emitted wavelength through Compare with Heterostructure: 2m adjustment of the energy levels within the well by ρ (E) = 4π ( c ) 2/3 E 2/1 careful consideration of the well width. c h2 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum cascade lasers
Advantages: • It doesn’t depends on material hω = E − E system bandgap making it easy to 3 2 make long wavelength lasers. • In a QCL, each electron can take participate in stimulated emission many times. • QC lasers in mid-IR region have Quantum cascade laser is unipolar intersubband now been demonstrated with CW device operations at room temperature. • It could be used as THz sources.
The QC laser relies on only one type of carrier, making electronic transition between conduction band states arising from size quantization. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Outline
1. Introduction and motivation 2. Semiconductor laser physics 3. Tunable laser fundamentals 4. Technologies of tunable lasers 5. Conclusion Photonic Device and System Laboratories Department of Electrical and Computer Engineering Existing Tunable Laser technologies
•Distributed Feedback Bragg Grating (DFB)
•Sampled grating Distributed Bragg Reflectors (DBR)
•MEM-VCSEL
•Grating coupled external cavity (ECLD) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Existing Tunable Laser Structures (DFB)
Wavelength (um) Cross section Intensity Intensity
4.420 4.440 4.460 4.480 4.500 4.520 wavelength (um) Intensity Intensity
4.420 4.440 4.460 4.480 4.500 4.520 wavelength (um) DFB laser structure. The grating is etched onto one of the cladding layers. Grating period is determined by ΛΛΛ=m λλλ/2. λλλ is the wavelength inside the medium.
DFB MEMs tilt Wire Laser Array mirror bond stripes
Optical fiber QDI Fujitsu Santur Tunable DFB laser arrays (a) Serial (b) Parallel (c) Mem mirror Photonic Device and System Laboratories Department of Electrical and Computer Engineering Existing Tunable Laser Structures (DBR)
SG-DBR laser
EAM Amplifier Front mirror Gain Phase Rear mirror
Light output
Q waveguide MQW active region Agility λ RFP ( ) Longitudinal modes λ
λ R1( ) Front mirror Fabry-Perot cavity : λ λ • Modes with FP spacing B R (λ) Rear mirror 2 Sampled Bragg Reflectors : • Spectra with wider spacing and broader profile λ • Filters out 1 Bragg mode R( λ) λ • Increasing I dbr shifts filter profile to shorter Lasing mode λ Phase Section: Fine tuning Photonic Device and System Laboratories Department of Electrical and Computer Engineering Existing Tunable Laser Structures (Mem(Mem--VCSEL)VCSEL)
Top curved• MEM-VCSELmirror Output Membrane post
Active region
Bottom mirror Substrate Pump injection Coretek
Schematic of micromechanically tunable VCSEL from Coretek / Nortel Networks.The upper membrane is moved electrostically to modify the cavity length and tune the lasing wavelength of the vertical cavity laser. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Existing Tunable Laser Structures (ECLD)
Schematic representations of the Littman Cavities.
Photograph and schematic of Iolon’s MEMs based external cavity laser configuration. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Grating coupled external cavity tunable laser fundamentals
Example
Collimating lens Blazed grating λλλ 1 Output λλλ λλλ λλλ λλλ λλλ 1 2 3 2 θθθ d Laser chip .. λλλ 3
1st order Grating equation: Feed back 2dsin θθθ = m λλλ Zeroth order output
Grating coupled external cavity tunable laser structure. Photonic Device and System Laboratories Department of Electrical and Computer Engineering External cavity laser modeling
r r r r r r 1m 1p 1p − 2m 2 p 2 p t − ik sem l t 1p e 0 2 p t t t2m t2m S1 = 1m 1m S2 = S3 = −ik l r 1 r1m 1 sem − 2m − 0 e t2m t2m t1m t1m
(-) (+) − S = 2n = n 1 4 t m r λλλ1 + p S1S2S3 n 1 n +1 S5 n λλλ2 1− n 2 Laser S6 = = λλλ3 rm t chip n +1 p n +1 1st order Feed back
r r r t − Gm Gp Gp eik air L 0 Gp t t closs 0 = S5 = Gm Gm = 1 S4 − S6 ik air L rGm 1 0 0 e − closs tGm tGm Photonic Device and System Laboratories Department of Electrical and Computer Engineering Grating coupled external cavity tunable Laser
An example: Cavity mode loss curve with longitudinal modes. 25 )
-1 20
15 Laser oscillation condition 10 −α β 1 e(gth i )le2il sem = 5 refft r1p Cavity modemode Cavity Cavity lossloss(cm (cm = iφ reff | reff | e Frequency (THz) =α +1 1 gth ln | | l reff r1p β +φ = π 2l sem 2m Photonic Device and System Laboratories Department of Electrical and Computer Engineering Current tunable laser development
Laser Power Tuning CompaniesDBRMEMExternalDFB VCSEL cavity lasers Advantages: type range Advantages:Advantages: WideLow• Widecost tuning tuning range range • Cost comparable to fixed lasers DBR 30 mW* > 40 nm Agility*(SGDBR),FastLow• Highpowerswitching output consumption speed powerBookham(Marconi)(DSDBR) , NTT/NEL(SSGDBR),Good•• High High sidemode power spectral mode stability suppression purity Multiplex, Intel(Sparkolor), (Altitun(GCSRDBR)),ModerateWide•• Wavelength Low tuning RINoutput range stability power DFB 40 mW* < 5 nm Fujitsu*,LowWafer•• Proven powerContinuous level Santur, technology consumptiontesting tuningQDI , Princeton Lightwave, Excelight,IntegratedDisadvantages: Alcatel, functions Intel, (Modulators, Nortel,Triquint(Agere), optical per λ •Disadvantages: Plug-in module for different wavelength JDSU,amplifiers)LowDisadvantages: output, etc. power • Limited tuning range (5nm per laser) Disadvantages:Slow• Highswitching cost Bandwith9*, Novalux, Beamexpress, (Coretek) VCSEL <2 mW* ~ 40 nm Yield1550•• Slow Bulky nm tuning technology speed still(~ few in development ms) Wavelength•• Reproducibility Slow switching stability in manufacturing Relatively• Shock/vibration broad linewidth sensitivity Intel(new focus)*, Iolon, Blue Sky Research, External 30 mW* >100 nm Complex software Princeton Optronics, cavity Power
Companies in brackets no longer exist, but honorable Photonic Device and System Laboratories Department of Electrical and Computer Engineering Outline
1. Introduction and motivation 2. Semiconductor laser physics 3. Tunable laser fundamentals 4. Technologies of tunable lasers 5. Proposed research and summary Photonic Device and System Laboratories Department of Electrical and Computer Engineering Key points of the Proposed Research
Theoretical calculations and modeling in order to get single mode and continuous long tuning range Design and construct the E.C. laser testing apparatus and programs Perform testing to qualify lasers for more in depth testing
Laser spectroscopy of some real samples Design compact and robust EC laser source Photonic Device and System Laboratories Department of Electrical and Computer Engineering Recent performance of tunable MidMid--IRIR lasers
- For basic research, breadboard systems - Study of basic properties: thermo-optic behavior, gain property, power, efficiency, noise model developed - Overcome challenges: λλλ-scaling issue, facet coating problem, non-optimum optics - Single -mode or nearly so (pulse operation), 7-12-dB side mode suppression ratio - Linewidth dominated by thermo-optics (~500 MHz; theoretical model projects near transform-limited for < 20-ns pulse) - Wavelength bands: 4.6, 5.2, 7.1, 9 µµµm - Tuning range ~ 2-2.5% of center wavelength, limited by the gain band - Power ~1 – 40 mW peak (up to 5% d.c.) - Turn-key, high stability Photonic Device and System Laboratories Department of Electrical and Computer Engineering Thermal fine phase control of tunable laser
Use the coupled- cavity effect to advantage
- Substantial thermal-induced phase tuning and grating tuning provide continuous and broad tuning even without AR coating Peng et al., Appl. Optics (8/20/03) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Tuning performance of tunable MidMid--IRIR lasers
Peng et al., Appl. Optics (8/20/03) Ammonia Photonic Device and System Laboratories Department of Electrical and Computer Engineering Approach for miniature tunable module
Phase tuning is needed: 2-segment laser • Use only thermo-optic effect • No need of specialized phase-segment in monolithic device • A key test of the miniature module design
100 I =800mA, 600mA, 400mA, 300mA, 200mA 0.5 phase Phase: 0.4 Gain 50ns: 10 0.3 Variable ∆∆∆t Thermal decay time ~ 3 µs 0.2
Iphase f (GHz) 1 ∆ ∆ 0.1 ∆ ∆ Current (A) Current T=1 µµµs 0
-0.1 0.1 0 1000 2000 3000 4000 0 2 4 6 8 10 12 14 16 18 20 Time (ns) Delay ( µµµs) Photonic Device and System Laboratories Department of Electrical and Computer Engineering CO gas absorption spectroscopy
1.0 0.8 0.6
0.4 288 GHz 0.2
0.0 4.86 4.87 4.88 4.89 4.90 Wavelength ( µµµm) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Summary and Conclusion
• Various types of semiconductor lasers were investigated and studied. • Most common used tunable laser structures were introduced and evaluated. One example of tuning principle was explained. • Dissertation research topics will be novel mid-IR tunable semiconductor laser concept and demonstration. • Research strategy and recent results were presented. Photonic Device and System Laboratories Department of Electrical and Computer Engineering
Thank you ! Photonic Device and System Laboratories Department of Electrical and Computer Engineering
Additional readings Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser Physics: Density of states calculation
dN dN dk L dk = = ( )3 ×π × k 2 dE dk dE π dE
Where
1 dN 4πk 2 dk k 2 dk ρ(E) = = 2 = L3 dE 2( π )3 dE π 2 dE 1 L 4 N = 2× ×( )3 × ×π × k 3 8 π 3 4πk 2 dk 1 2m ρ = )2( = ( c ) 2/3 E 2/1 c 2( π )3 dE π 2 h2 1 2m ρ = ( v ) 2/3 E 2/1 v π 2 h2 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser Physics: Occupation factors for both bands
Occupation factor for each band by Fermi-Dirac distribution function
1 f = c E − E 1+ exp( c FC ) KT 1 f = v E − E 1+ exp( v FV ) KT
Probability of occupancy versus energy of the Fermi-Dirac, the Bose-Einstein and the Maxwell-Boltzmann distribution Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser Physics: Carrier concentration calculation
ρ (E ) n = c c dE ∫ − + c Electron concentration n and hole exp[( Ec Fc /) KT ] 1 ρ (E ) concentration p are given by p = v v dE ∫ − + v exp[( Ev Fv /) KT ] 1 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser Physics: Fermi energy and occupation factor calculation
ρ (E ) ρ (E ) n = c c dE , p = v v dE ∫ − + c ∫ − + v exp[( Ec Fc /) KT ] 1 exp[( Ev Fv /) KT ] 1
Fermi energy, occupation probability can be approximately derived from above equations, which is often referred as Boltzmann approximation.
For conduction band: For valence band: = n p EFC KT ln( ) E = KT ln( ) N FV C NV n − E p − E f (E) ≅ exp( ) f (E) ≅ exp( ) c N KT v C NV KT
= π 2 2/3 where NC 2(2 mc KT / h ) Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser Physics: Stimulated emission rate and gain calculation
Net stimulated emission rate per unit volume per unit energy interval at photon energy hννν: +∞ ρ R (hν ) = P(hν ) B (E ,hν )Vρ (E )ρ (E − hν )( f − f )( 1+ v )−1 dE stim ∫ 21 c c c v c c v ρ c −∞ c Gain per unit length can be derived as µ Γµ +∞ ρ g(hν ) = R g Γ = ( g ) B(E )Vρ (E )ρ (E − hν )( f − f )( 1+ v )−1 dE stim ∫ c c c v c c v ρ c c c −∞ c Bernard and Duraffourg condition for stimulated emission E − hν − E E − E exp( c FV ) > exp( c FC ) Or E − E > hν kT kT FC FV Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum well lasers
Another innovation, now nearly ubiquitous, was the use of a Quantum Well (QW) active region where the gain region thickness is reduced until V the electronic states are quantised in one dimension. The quantisation allows the density of states to be engineered, and the tiny active volume reduces greatly the injection current 0 L required to achieve transparency. z z Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum well lasers: Energy levels calculations by Schrodinger equation
Along the x, y direction, the energy levels form a continuum of states given by h2 V E = (k 2 + k 2 ) 2m x y The energy levels in z direction can be solved by Schrodinger equation for one 0 Lz dimensional potential well: z h2 d 2ψ Eψ = − inside the well 2 (0
Boundary conditions are that ψ and d ψ/dz are continuum
at z=0 and z=L z, The solution is:
Aexp( k z) z ≤ 0 2m(V − E) 1 k = [ ] 2/1 ψ = +δ ≤ ≤ 1 h2 Bsin( k2 z ) 0 z Lz where − ≥ 2mE 2/1 C exp( k1z) z Lz k = ( ) 2 h2
The eigenvalue equation is: = tan( k2 Lz ) k1 / k2 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum well lasers: Energy quantization in quantum well
Energy eigenvalues for a particle Conduction confined in the quantum well are: band 2 E h 3c = + 2 + 2 E(n,kx ,k y ) En * (kx k y ) ∆∆∆E c 2mn E2c
E1c En is the nth confined particle energy level for carrier motion normal to the ωωω E well and m* is the effective mass for g ωωω=E +E +E g 1c 1hh this level.
E1hh E 1lh The confined energy levels E n are E2hh ∆∆∆E E E v denoted by E 1c , E 2c , E 3c , for 3hh 2lh electrons, … heavy holes and light Valence holes. They can be calculated by the Lz band solution above. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum well lasers: Density of sates calculation Density of states : The number of electron states per unit area in the x-y plane for the i th subband, within an energy interval dE is given by: d 2k h2k 2 D (E)dE = 2 , E = i π 2 2( ) 2mci m >>> D = ci i πh2
Density of states per unit volume:
>>> ρ = Di = mci ci πh2 Lz Lz
2m Compare with Heterostructure: ρ (E) = 4π ( c ) 2/3 E 2/1 c h2 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Quantum well lasers Carrier concentration calculation
Calculated number of electrons in the conduction band
∞ = 1 n = ρ f (E )dE where fc (Ei ) ∑ ∫ ci c i i 1+ exp[( E − E /) k T ] i i fc B Eio
It is easy to obtain
E − E E = ρ + fc io = fc n kBT ∑ ci ln[ 1 exp( )] Nc exp( ) i kBT kBT = ρ where Nc ci kBT
Similar solutions hold for holes in the valence band. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Electrical properties of semiconductor lasers Carrier density derivation from photoluminance
The light spectrum taken from facet is the amplified spontaneous emission, L hω L (hω) = hω wdR spon (hω)eGn ( ) zdz F ∫ z=0 10 6 120K 5 hω 10 140K Gn ( )L e −1 10 4 160K spon 180K = hωR (hω)[ ]wd 3 hω 10 200K Gn ( ) 10 2 220K 240K 10 1
where G (hω ) = Γg − α is net gain. 10 0 n i Intensity 10 -1 10 -2 CO Absorption 10 -3 2 10 -4 By fitting the gain curve of the device, 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 the carrier density can be derived at Energy (eV) different current. The threshold carrier Threshold photoluminescence spectra at density will increase with increasing different temperatures. Experimental data are temperature. shown in square symbols. Solid lines show the calculations. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Temperature dependence of electrical properties of semiconductor lasers = • Temperature dependence of threshold current Ith I0 exp( T /T0 )
T0 is characteristic temperature. A lower T 0 value implies that the threshold current increases more rapidly with increasing temperature. • Temperature dependence of carrier lifetime = τ Jth qdn th / th It decreases with increasing temperature.
• Temperature dependence of optical gain It increases with increasing temperature. • Temperature dependence of differential quantum efficiency It decreases with increasing temperature.
• Leakage current
Caused by diffusion and drift It is higher at higher temperature of electrons and holes from It increases when the barrier height decreases. the edges of the active region It increases with the decreases in cladding layer to the cladding layers. doping. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Optical properties of semiconductor lasers: Gaussian beam profile
The expression for a real laser beam’s electric field is given by:
exp[ −ikz − iψ (z)] x2 + y 2 x2 + y 2 E(x, y, z) ∝ exp[ − − ik ] w(z) w2 (z) 2R(z) Expression for spot size, radius of curvature, and phase shift:
= + 2 w(z) w0 1 (z / zR ) Where Z R is the Rayleigh The beam divergence Range, it is given by = + 2 half angle is given by R(z) z zR / z = π 2 λ w(z) w z w λ ψ (z) = arctan( z / z ) zR w0 / θ = = 0 = 0 = R /1 e π z zR z zR w0 Photonic Device and System Laboratories Department of Electrical and Computer Engineering Optical properties of semiconductor lasers: Astigmatism
w θθθ w λλλ /lw λλλ/wL L>w θθθ θθθ L< w lW θθθ wL L
L
λ θ = An edge emitting laser has w πw astigmatism, the divergent λ θ = angles are: L πL Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser gain dynamics
Consider two coupled aspects. We therefore consider two simple “rate equations” – first order differential equations that are coupled to one another. Number of carriers added per dN η I N unit volume per unit time = i − − v gN τ g p Number of undesired carrier recombination dt eV gain per unit volume per unit time dN N Number of stimulated carrier recombination p = Γv gN − p per unit volume per unit time g p τ dt p At steady state, the carrier and photon Number of photons added per density are stable, so unit cavity volume per unit time η I N 0 = i 0 − 0 − v gN τ g p0 Number of photons lost from eV gain the cavity per unit cavity volume N 0 = Γv g N − po per unit time g 0 po τ p Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser gain dynamics
Suppose there is small variation at steady condition. dδN η δI δN δN = i − − p − v aN δN τ Γτ g po dt eV gain p dδN p = Γv aN δN dt g po Solving them: d 2δN 1 dδN v aN η dδI + ( + v aN ) + ( g po )δN = i 2 τ g po τ dt dt p eV gain dt
vg aN po Relaxation oscillation frequency: ω = R τ p Photonic Device and System Laboratories Department of Electrical and Computer Engineering Semiconductor Laser gain dynamics
δP(ω) 1 General form of the frequency response = δP )0( ω 2 ω 1 1− + i ( +ω τ ) ω 2 ω ω τ R p R R R
Note that 1. there is an intrinsic limit to the modulation speed 2. the modulation speed tend to rise with the square root of the differential gain, 3. the modulation speed tends Frequency response of the output power to rise as the square root of modulation of a laser diode as the frequency the laser output power. of electrical drive is increased. Photonic Device and System Laboratories Department of Electrical and Computer Engineering Noise properties of semiconductor lasers
Noise arises from the spontaneous emission process and carrier- generation-recombination process, can be modeled by adding Langevin noise source.
Modified rate equations with added noise
• = −γ + + P (G )P Rsp Fp (t) F and F φ are from spontaneous • p emission, F has its origin in the discrete N = I / q −γ N − GP + F (t) N e N nature of carrier generation and • 1 recombination processes (shot noise) φ = −(ω −ω ) + β (G −γ ) + Fφ (t) 0 th 2 c Photonic Device and System Laboratories Department of Electrical and Computer Engineering Electrical and optical properties of semiconductor lasers
Intensity noise, RIN P3 RIN decreases with increasing power P2 (P 3>P 2>P 1). It shows maximum at the relaxation-oscillation peak.
P1
Phase noise RINRINRINRIN(dB/Hz) (dB/Hz) (dB/Hz) (dB/Hz)
Phase fluctuation comes from spontaneous emission, change in optical gain and refractive index induced by carrier population, linewidth Frequancy (GHz) enhancement factor (huge for semiconductor laser). R δν = sp 1( + β 2 ) 4πP c