Photonic Devices for Telecommunications

I Photonic Waveguide Structures.- 1 Mode solvers and related methods.- 1.1 MoL mode solver using enhanced line algorithm.- 1.1.1 Theoretical foundation of the algorithm.- 1.1.2 Determination of matrices.- 1.1.3 Numerical results.- 1.2 Film-mode matching with relation to BEP and MoL.- 1.2.1 Reference model geometry.- 1.2.2 Theory.- 1.2.3 Numerical considerations.- 1.2.4 Discussion.- 1.2.5 Conclusion.- 1.3 Free space radiation mode method.- 1.3.1 Polarised and vectorial modal analysis of buried waveguides.- 1.3.2 Waveguide facet reflectivities.- 1.3.3 Propagation in 3D structures.- References.- 2 Beam propagation methods.- 2.1 Finite difference beam propagation method basic formulae and improvements.- 2.1.1 Finite difference BPM equations in 2D.- 2.1.2 Applicability.- 2.1.3 Applications.- 2.2 Beam propagation method based on the method of lines.- 2.2.1 Theory.- 2.2.2 Special case: very thin layers.- 2.3 Bi-directional eigenmode expansion and propagation method.- 2.4 Method of backward calculation.- 2.4.1 Description of the method.- 2.4.2 Application to distributed Bragg reflectors.- References.- 3 Benchmark tests and modelling tasks.- 3.1 BPM benchmark tests.- 3.1.1 Tilted waveguides.- 3.1.2 Square meander coupler.- 3.1.3 Gain-loss waveguide benchmark test.- 3.1.4 Directional coupler benchmark test.- 3.2 Wave propagation in a waveguide with a balance of gain and loss.- 3.2.1 Quasi-analytic solution.- 3.2.2 Wave growth in the gain-loss waveguide with lossless eigenmodes.- 3.3 Waveguide tapers.- 3.3.1 Modelling task and reciprocity test.- 3.3.2 Numerical results.- 3.3.3 Discussion.- 3.3.4 Conclusion.- 3.4 Electro-optic modulator based on surface plasmons.- 3.4.1 Problem definition.- 3.4.2 About the computational methods.- 3.4.3 Results and discussion.- 3.4.4 Conclusions.- 3.5 Waveguide Bragg grating filter.- 3.5.1 Formulation of the problem.- 3.5.2 Outline of computational methods applied.- 3.5.3 Numerical results.- 3.5.4 Conclusions.- References.- 4 Methods for waveguide characterization.- 4.1 FP resonator method for loss and group index measurement.- 4.1.1 Waveguide loss determination.- 4.1.2 Group effective index determination.- 4.2 Optical low coherence reflectometry for group index, chromatic dispersion and loss measurements.- 4.2.1 Theory.- 4.2.2 OLCR experimental set-up.- 4.2.3 Calibration and performance of the system.- 4.2.4 Experimental results on simple lOCs.- 4.2.5 Experimental results on more complex lOCs.- 4.3 Near field imaging for mode profile measurement.- 4.3.1 Near field determination by imaging detectors.- 4.3.2 Near field determination by scanning a single-element detector.- 4.3.3 Practical aspects of near field imaging in the 1.3-1.55 ?m range.- 4.4 Transverse offset method for mode profile measurement.- 4.5 Spectral transmission method for cut-off wavelength measurements.- 4.5.1 Experimental set-up.- 4.5.2 Typical response.- 4.5.3 Conclusion.- References.- 5 Comparison of experimental results.- 5.1 Loss measurements.- 5.1.1 Loss measurements on rib waveguides.- 5.1.2 Loss measurements on diffused waveguides.- 5.2 Group index measurements.- 5.3 Mode profile measurements.- 5.4 Cut-off wavelength measurements.- References.- II Semiconductor Distributed Feedback Laser Diodes.- 6 Introductory physics.- 6.1 Historical background.- 6.2 Description of DFB and DBR laser diodes.- 6.2.1 Geometric structure.- 6.2.2 Threshold condition.- 6.2.3 Distributed reflections.- 6.3 Introduction to DFB laser characteristics.- 6.3.1 The P-I characteristic.- 6.3.2 The V-I characteristic.- 6.3.3 The optical spectrum.- 6.3.4 The modulation responses.- 6.3.5 The FM- and intensity noise spectra, the linewidth.- 6.4 Problems in modelling and measuring DFB laser diodes.- 6.5 General approximations used in laser diode modeling.- 6.6 Standardisation of laser parameters166.- 6.6.1 Derivation of an ASCII equivalent of a symbol.- 6.6.2 Optical output definitions.- 6.6.3 Cavity dimensions.- 6.6.4 Symbols used to describe internal variables.- 6.6.5 Optical waveguide parameters.- 6.6.6 Waveguide gratings.- 6.6.7 Stimulated emission parameters.- 6.6.8 Spontaneous recombination parameters.- 6.6.9 Current injection parameters.- References.- 7 Modelling of DFB laser diodes.- 7.1 Overview of laser models.- 7.1.1 Desirable characteristics of laser models.- 7.1.2 Single-mode rate equation laser models.- 7.1.3 Multi-mode rate equation laser models.- 7.1.4 Travelling-wave rate equation laser models.- 7.1.5 Transfer-matrix models.- 7.1.6 Fully time-domain models.- 7.1.7 Other numerical models.- 7.2 Numerical case studies.- 7.2.1 Introduction.- 7.2.2 AR-coated, A/4-shifted DFB lasers.- 7.2.3 DFB lasers with cleaved facets.- 7.2.4 Large signal dynamic behaviour of a A/4-shifted laser.- 7.2.5 Self pulsations of a multi-electrode laser.- References.- 8 Measurements on DFB lasers.- 8.1 Basic measurements.- 8.2 Emission linewidth and other more specific measurements.- 8.3 Measurement of dynamic characteristics.- 8.3.1 Aim of this work.- 8.3.2 Devices and measurements description.- 8.3.3 Measurement results: device “A”.- 8.3.4 Measurement results: device “B”.- 8.3.5 Parameter extraction from high frequency measurements.- References.- 9 Parameter extraction.- 9.1 General remarks on laser parameter extraction.- 9.2 Extraction from the ASE spectrum.- 9.2.1 Measurement of the ASE spectrum.- 9.2.2 Theoretical formula for ASE spectrum.- 9.2.3 Fitting technique.- 9.2.4 Comparative experimental results.- 9.3 Extraction from the RIN spectrum.- 9.3.1 Measurement of RIN.- 9.3.2 Theoretical formula for RIN.- 9.3.3 Parameter extraction example.- 9.4 Extraction from modulation response measurements.- 9.4.1 Measurement of modulation response.- 9.4.2 Theoretical formula for modulation response.- 9.4.3 Fitting procedure and extraction example.- 9.4.4 The concept of the three bandwidth limits.- 9.5 Other methods and the role of facet properties.- 9.5.1 Cross-check of extracted parameters by different methods.- 9.5.2 The role of facet properties.- References.- III Nonlinear Effects in Semiconductor Optical Amplifiers: Four-Wave Mixing.- 10 Why and how to study four-wave mixing?.- 10.1 Applications of semiconductor optical amplifiers.- 10.2 Principle of four-wave mixing.- 10.3 Efficiency and signal-to-background ratio.- References.- 11 Theory of four-wave mixing.- 11.1 Rate equations.- 11.2 Time-domain description.- 11.2.1 Derivation of the integral equation.- 11.2.2 Four-wave mixing between CW beams.- 11.3 Coupled mode theory.- 11.3.1 Fundamental equations.- 11.3.2 General assumptions.- 11.3.3 Saturation of the single-pass gain.- 11.3.4 Gain-cube theory.- 11.3.5 Inclusion of saturation effects.- 11.3.6 Inclusion of gain dispersion effects.- 11.3.7 Comparison with a numerical model.- 11.4 Noise analysis.- 11.4.1 Calculation of the ASE spectral density.- 11.4.2 Uniform inversion parameter.- 11.4.3 Nonuniform inversion parameter.- 11.4.4 Effect of gain dispersion.- 11.4.5 Comparison with measurements.- 11.4.6 Signal-to-background ratio.- 11.4.7 Noise figure.- References.- 12 Measurement techniques and results.- 12.1 Set-up.- 12.1.1 Sources.- 12.1.2 Tested device.- 12.1.3 Detection and filtering.- 12.1.4 Set-up examples.- 12.2 General results.- 12.2.1 FWM performance vs. optical input power.- 12.2.2 FWM performance vs. driving current.- 12.2.3 FWM performance vs. detuning.- 12.3 Round robin results.- 12.3.1 Device description.- 12.3.2 Comparison of the round robin results.- References.- 13 Related topics.- 13.1 Parameter extraction.- 13.1.1 Parameter extraction: first approach.- 13.1.2 Parameter extraction: second approach.- 13.1.3 Interpretation of the results.- 13.2 Cross gain modulation measurements.- 13.3 Nearly degenerated FWM measurements.- 13.3.1 Measurement set-up.- 13.3.2 Results.- 13.4 Effect of birefringence on four-wave mixing.- 13.4.1 Experimental set-up.- 13.4.2 Impact of birefringence on the conversion efficiency and the signal-to-background ratio.- 13.4.3 Polarisation resolved ASE measurements.- 13.5 Four-wave mixing experiments with picosecond optical pulses.- 13.5.1 Experimental set-up.- 13.5.2 Short pulse amplification in SOAs.- 13.5.3 Comparison of CW and pulsed FWM measurements.- References.- Appendix. An optical data interchange format.- Symbols.