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Self-consistent Rate-Equation Theory of Coupling in Mutually Injected Semiconductor Lasers

Self-consistent Rate-Equation Theory of Coupling in Mutually Injected Semiconductor Lasers. Daan Lenstra Photonic Integration Group Gravitation. ESLW 2016. Outline. Longitudinally Coupled FP-Lasers Principle of Coupling : Conventional or Interference-Based

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Self-consistent Rate-Equation Theory of Coupling in Mutually Injected Semiconductor Lasers

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  1. Self-consistent Rate-Equation Theory of Coupling in Mutually Injected Semiconductor Lasers DaanLenstra Photonic Integration Group Gravitation ESLW 2016

  2. Outline • LongitudinallyCoupled FP-Lasers • Principle of Coupling: Conventional or Interference-Based • General Rate-Equations Model for Coupled Lasers • Steady State andStability • Intermezzo: Simple Considerations • Numerical Results: • Output IntensityandOperationFrequencyvsDetuningandLocking Range • Dependence on Coupling Phase, Pumping and • Output Intensities: Experiment vs. Theory (Anti-phase MMI coupler) • Conclusions ESLW 2016 p.1

  3. Coupled-CavityFP-Lasers • Can combine mode selectivity with wide wavelength tunability based on Vernier effect • Application in optical communication and sensing • Conventional coupling difficult due to demanding coupling phase control • Photonic integration technology allows use of MMI-based couplers • MMI Anti-Phase Reflector allows easy phase-difference control • In all cases, strong coupling is non-linear process; needs self-consistent treatment • How and when do two individual laser modes combine to form one super mode? ESLW 2016 p.2

  4. Principle of Coupling: Transmission/Reflection ConventionalCoupler Laser 2 Laser 1 Transmissive: Glassplate Air gap etc Multiple reflections i.e. fringeformation MM-Interference-BasedCoupler Reflective: 2-port MMI-reflector No fringes ESLW 2016 p.3

  5. ConventionalvsInterference-BasedCoupling t r • Conventional transmission/reflection: • no loss, i.e. non-favourable • stronglywavelength dependent, i.e. difficult to control • MMI-imaging based transmission/reflection: • Well-defined coupling phase canbedesigned; f.i. • no multiple reflectionfringessothatwavelength independent, hence easyto control Preferable for coupled lasers; phase relation betweenand fixed by design ESLW 2016 p.4

  6. IntegratedTunable CCL with MMI-basedcoupler D’Agostino et al., OpticsLett. 40, 653 (2014) (1550 nm) D’Agostino et al., Proc. IPR 2015, JT5A.1 (2000 nm) 2-port reflective MMI couplerbased on 3x3 MMI device. ESLW 2016 p.5

  7. General Model for Coupled Lasers Laser 1, length Laser 2, length Rate equations: (referencefrequency to bechosenconveniently; -): ; . ; effectivecouplinginversiondependent selfconsistency! inversionscouplingdependent ESLW 2016 p.6

  8. Steady-state analysis (photon number,phase in laser j; ; ; . , . () (functions of , given in [1]) Stable mutual locking: [1] D. Lenstra: IJET 8 (2016) pp. 14-23 ESLW 2016 p.7

  9. Intermezzo: Simple Consideration t r laser 1 laser 2 } } Optimum effectivereflectivitiesif, henceeither, or When, non-optimalcompromiseor no stablecw=operation. ESLW 2016 p.8

  10. Numerical Results • Choosing such that. • Details of self-consistent numerical procedure in: D. Lenstra: IJET 8 (2016) pp. 14-23 ESLW 2016 p.9

  11. Output Intensity, Frequency and Locking Range Detuning rad/s Locking range ESLW 2016 p.10

  12. Optimal CouplingLocking Range, Pumping and 1 2 Asymmetric pumping and large up to ~30 hardlyinfluence the locking range ESLW 2016 p.11

  13. Lockingvscouplingphase(mod ); I1 &I2 No locking for ESLW 2016 p.12

  14. SymmetricPumping (OptimizedDetuning) ESLW 2016 p.13

  15. P-I curves (compared); output power laser 1 Measured (Optimized detuning) D’Agostino et al., OpticsLett. 40, 653 (2014) Theory (Optimized Detuning) ESLW 2016 p.14

  16. Conclusions • General rate-equationtheoryadequatelydescribes single-mode CW operation of CCL with MMI anti-phasecoupler • Self-consistent numerical iteration methoddemonstratesstablefrequency and phaselockingunderflexibleconditions • Sizeabledetuning interval for locking ~ 6 GHz allows easy fine tuning (as was observed in the experiment) • Duetocoupling, inversionsclamp at lowervaluesthan without coupling • Operationfrequencysubstantiallylower (~3.5 GHz) than in uncoupledsituationdue to (linewidthenhancement) parameter ~2.5 • Thankyou! ESLW 2016 p.15

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