Distributed feedback semiconductor lasers

Transcription

1 Distributed feedback semiconductor lasers John Carroll, James Whiteaway & Dick Plumb The Institution of Electrical Engineers SPIE Optical Engineering Press

2 1 Preface Acknowledgments Principal abbreviations Principal notation xiii xv xvii xix 1 The semiconductor-diode laser Background l 1.2 Early developments The first semiconductor lasers Fabry-Perot gain and phase requirements Some characteristics of diode lasers Improvements to reduce operating currents Heterojunctions: carrier confinement Heterojunctions: photon confinement Structures for'horizontal'confinement Degree of confinement the confinement factor Variations on conventional Fabry-Perot laser design High-low reflective facets External cavities Externalgrating System requirements for single-frequency lasers Introduction to lasers based on Bragg gratings Introduction to Bragg gratings Fabrication of gratings inside lasers Some principal forms of grating laser The distributed Bragg reflector laser The distributed feedback (DFB) laser More complex grating-based lasers Summary Bibliography Semiconductor lasers Optical communication systems References 32

3 vi 2 Gain, loss and spontaneous emission Introduction Electronic processes in semiconductors Energy states Occupation probabilities Radiative recombination and absorption Transitions and transition rates Auger recombination Absorption, emission rates and spectra Absorption, stimulated and spontaneous emission in a semiconductor Stimulated-gain spectra in semiconductors Homogenous and inhomogeneous broadening Spontaneous-emission spectra from semiconductors Semiconductor interactions with the lasing mode Spontaneous-coupling factor Petermann's '^factor' Gain saturation in semiconductors Spectral hole burning and carrier heating Scattering losses Free-carrier absorption Henry's a factor (or linewidth enhancement factor) Temperature-induced variations in semiconductor lasers Properties of quantum-well-laser active regions Introduction to quantum wells Gain saturation and the need for multiple quantum wells Strained quantum wells Carrier transport Summary Bibliography References 73 3 Principles of modelling guided waves Introduction Vertical and horizontal guiding Index and gain guiding Effective area and confinement factor The slab guide ТЕ and TM guided waves Multilayer slab guides Wave equations for the ТЕ and TM guided waves Solving multislab guides Effective refractive index Reflection coefficient calculation Gain-guiding example 89

4 vii 3.5 Scaling Horizontal guiding: effective-index method Orthogonality o$ fields Far fields Waveguiding with quantum-well materials Summary and conclusions References 96 4 Optical energy exchange in guides The classic rate equations Introduction Rate of change of photon density Rate of change of electron density Some basic results from rate-equation analysis Simplifying the rate equations Steady-state results Dynamic analysis Problems of particle balance Field equations and rate equations Introduction Wave propagation Decoupling of frequency and propagation coefficient Field equations with a grating The periodic permittivity Phase matching Second-order gratings Shape of grating Summary References Basic principles of lasers with distributed feedback Introduction Coupled-mode equations for distributed feedback Physical derivation of the coupling process Complex gratings Coupled-mode solutions and stopbands Eigenmodes The dispersion relationship and stopbands Matrix solution of coupled-mode equations for uniform grating laser The field input-output relationships Reflections and the observed stopband DFB lasers with phase shifts Phase shifts Insertion of phase shifts: the transfer-matrix method 142

5 viii 5.6 Longitudinal-mode spatial-hole burning The phenomena The stopband diagram Influence of KL product on spatial-hole burning Influence of phase shifts on spatial-hole burning Spectrum and spatial-hole burning Influence of series resistance Simulating the static performance of DFB lasers Light/current characteristics Simulation of emission spectrum Summary References More advanced distributed feedback laser design Introduction Linewidth General Calculation of linewidth under static conditions Linewidth enhancement Effective linewidth enhancement Effective dynamic linewidth enhancement Linewidth rebroadening Influence of reflections from facets and external sources Reflections and stability Facet reflectivity and spectral measurements Influence of facet reflectivity on SMSR for DFB lasers Complex grating-coupling coefficients General Techniques for introducing complex grating-coupling coefficients Influence of complex grating-coupling coefficient on static performance Influence of complex grating-coupling coefficient on dynamic performance Influence of facet reflectivity High-power lasers with distributed feedback General Techniques for obtaining high front-to-back emission ratios Laser-amplifier structures with distributed feedback Dynamic modelling of DFB lasers Uniform-grating DFB laser with reflective rear facet Large signal performance of 2 x A /8 DFB lasers with strong and weak carrier-transport effects Summary 202

6 ix 6.8 References 202 Numerical modelling for DFB lasers Introduction Ordinary differential equations A first-order equation Accuracy First-order wave equations Introduction Step lengths in space and time central-difference method Numerical stability Gain and phase Coupled reflections Kappa coupling but no gain or phase changes Matrix formulation Phase jumps replacing scattering Fourier checks A uniform Bragg laser: finite difference in time and space Full coupled-wave equations MATLAB code Analytic against numeric solutions Spontaneous emission and random fields Spontaneous noise and travelling fields Null correlation for different times, positions and directions Spontaneous magnitude Tutorial programs Physical effects of discretisation in the frequency domain Discretisation process integrals to sums Fast Fourier transform (FFT) Finite-element strategies for a spectral filter Lorentzian filter Numerical implementation Application of the filter theory to gain filtering General Filtering the gain in the travelling-wave equations Numerical implementation Basic DFB laser excited by spontaneous emission Introduction and normalisation Field equations Charge-carrier rate equation Numerical programs Summary References 249

7 x 8 Future devices, modelling and systems analysis Introduction Systems analysis Introduction Component modelling System modelling Gbit/s power amplification Direct modulation: recapitulation Simulation of integrated DFB laser and electroabsorption modulator Cross-gain and four-wave-mixing wavelength conversion in an SOA Simulation of cross-phase wavelength conversion in a Mach-Zehnder interferometer incorporating two SOAs The push-pull laser Introduction: push-pull electronics Symmetrical push-pull DFB laser Asymmetry and the push-pull DFB laser Speed of response for a push-pull DFB laser Tunable lasers with distributed feedback Introduction Simple multicontact tunable lasers Wide-tuning-range lasers with nonuniform gratings Other tunable-laser structures Tunable-laser linewidth and modulation Modelling tunable semiconductor lasers Multiple DFB lasers with optical couplers for WDM Surface-emitting lasers Introduction to surface-emitting lasers Operating parameters of VCSELs compared with edge emitters Construction of VCSELs Additional features of VCSELs Summary References 295 Appendix 1 Maxwell, plane waves and reflections ^ 304 Al.l The wave equation 304 Al.2 Linearly polarised plane waves (in a uniform 'infinite' material) 304 A1.3 Snell's law and total internal reflection 305 Al.4 Reflection amplitudes at surfaces: ТЕ fields 308 Al.5 ТЕ reflection amplitudes: three special cases 309 Al.6 Reflection amplitudes at surfaces: TM fields 309

8 xi Al.7 TM reflection amplitudes at surfaces: four special cases 310 Al.8 Reflection for waveguide modes at facets 311 Al.9 References 312 Appendix 2 Algorithms for the multilayer slab guide 313 A2.1 ТЕ slab modes 313 A2.2 TM slab modes 317 A2.3 Far fields 319 A2.4 Slab waveguide prog*>am 322 A2.5 References 323 Appendix 3 Group refractive index of laser waveguides 324 A3.1 References 328 Appendix 4 Small-signal analysis of single-mode laser 329 A4.1 Rate equations: steady-state and small-signal 329 A4.2 Carrier-transport effects 334 A4.3 Small-signal FM response of single-mode laser 336 A4.4 Small-signal FM response and carrier transport 337 A4.5 Photonic and electronic equations for large-signal analysis 339 A4.6 Reference 340 Appendix 5 Electromagnetic energy exchange 341 A5.1 Dielectric polarisation and energy exchange 341 A5.2 Electromagnetic-energy exchange and rate equations reconciled 344 A5.3 Electromagnetic-energy exchange and guided waves: field equations 348 A5.4 References 351 Appendix 6 Pauli equations 352 A6.1 Reference 356 Appendix 7 Kramers-Krönig relationships 357 A7.1 Causality 357 A7.2 Cauchy contours and stability 359 A7.3 A proper physical basis builds in causality 360 A7.4 Refractive index of transparent quaternary alloys 362 A7.5 References 364 Appendix 8 Relative-intensity noise (RIN) 366 A8.1 References 371 Appendix 9 Thermal, quantum and numerical noise 372 A9.1 Introduction 372 A9.2 Thermal and quantum noise 373

9 xii A9.3 Ideal amplification 374 A9.4 The attenuator 377 A9.5 Einstein treatment: mode counting 378 A9.6 Aperture theory 379 A9.7 Numerical modelling of spontaneous noise 380 A9.8 Higher-order noise statistics 384 A9.9 References 385 Appendix 10 Laser packaging 386 Al 0.1 Introduction 386 A10.2 Electrical interfaces and circuits 386 Al0.3 Thermal considerations 388 Al 0.4 Laser monitoring 388 A10.5 Package-related backreflections and fibre coupling 389 A10.6 References 391 Appendix 11 Tables of device parameters and simulated performance for DFB laser structures 392 Appendix 12 About MATLAB programs 396 Al 2.1 Instructions for access 396 Al2.2 Introduction to the programs 398 Index 405