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

Explore the theory and applications of mutually injected semiconductor lasers, examining coupling principles, numerical results, and conclusions from ESLW 2016. Discover how laser modes combine and form super modes, the benefits of photonic integration, and the self-consistent treatment needed for strong coupling processes.

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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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