448 absorption coefficient, 181 in a two-level system, 168, 169 infrared, 109 of power in photodetectors, 242 spectrum, 243 ultraviolet, 109 acceptance angle, see critical angle active region, 173, 176 in a VCSEL, 173 air mass, 369 amplifier gain, 206 amplifier, erbium-doped fibre (EDFA), 209 13 typical characteristics, 213, 215 amplifier, semiconductor (SOA) Fabry-Perot (FPA), 223 travelling-wave (TWA), 223, 227 antireflection (AR) coating, 50 1, 205 half-wave layer, 53 quarter-wave layer, 53 array waveguide grating (AWG), 318 asymmetry parameter, 67 attenuation, see loss band gap, 243 in solar cells, 376 bandwidth 3-dB, 207 of a photodetector, 247 of an NRZ signal, 144 of an optical amplifier, 207 of an RZ signal, 143 of gain, 206, 224 Bessel functions modified, 113, 114, 129, 132, 133 ordinary, 113, 129, 131, 132 bit error rate (BER), 240, 252 7, 259, 336 bit-pattern independency, 242 bit-rate transparency, 241 boundary conditions absorbing (ABC) in 1D, 272 5 absorbing (ABC) in 2D, 277 9 for a magnetic field, 37 8 for an electric field, 36 7 Mur s first order, 272 3 Bragg mirror, 53, 54, 62 reflectivity spectrum, 57, 62 Brewster s angle, 49 50 C-band, see transmission bands carrier generation rate, 182 leakage rate, 183 lifetime, 184 recombination rate, 183 chirping, 192 3 cloaking, 398 9 coefficient of finesse, 29 coordinate transformation, 398 Courant-Friedrichs-Levy (CFL) stability condition, 270 Crank-Nicolson scheme, 301, 302 critical angle, 18, 30, 64, 106 cross-gain modulation (XGM), 234 5 cross-phase modulation (XPM), 233, 235 current bias, 144 dark, 246 forward diode, 372 injection, 143 leakage, 182 photocurrent, 242, 245, 371, 374 reverse saturation, 374 short-circuit, 369 threshold, 143 current density, 35 cutoff wavelength in optical fibres, 122 3, 128 in photodiodes, 245 Debye medium, 280 depletion region, 370 detection coherent, 240 incoherent (direct), 240 diffraction, 396 dispersion equation of the waveguide, 66 group velocity (GVD), 106, 124 in free space, 24 material, 124 8, 136, 280
449 modal, 124 multipath, 108 numerical, 269, 270, 283 of a 1D wave, 21 of a Debye medium, 280 of a Lorentz medium, 280 of a pulse in optical fibre, 127 8 waveguide, 124 127 distributed Bragg reflector (DBR), 173, 174 Drude relation, 389 dynamic range, 241 E-band, see transmission bands effective index method, 89 92 effective medium, 391, 394 effective thickness of a slab waveguide, 77 EH modes, 116, 117, 119 electric boundary conditions, 36 37 field intensity, 35 flux, 35 electron, see carrier emission amplified spontaneous (ASE), 215, 248, 255 spontaneous, 168, 169, 208 stimulated, 168, 169 equivalent circuit, 193 for bulk laser, 194 6 for PIN photodetector, 245, 250 for solar cell, 373 6, 380 error function, 231 Euler differentiation method, 429 31 Euler s rule (integration method), 436 Euler-Cromer differentiation method, 431 evanescent waves, 396 excited state, 168 external modulator, 6, 193 eye diagram, 337 Fabry-Perot (FP) interferometer, 29 30 resonance conditions, 171 resonant modes, 171, 172 resonator, 170 Faraday rotator, 323 Fast Fourier transform (FFT), 443 4 Fermi golden rule, 180 Fermi level, 176 fibre Bragg grating, 318 filter function, 258 finite difference method, 425 9 backward differences, 426 central differences, 426 forward differences, 426 finite-difference (FD) approximation, 297 9 focal length, 19, 20 plane, 19, 20 point, 19 four-wave mixing (FWM), 233, 352 Fourier series, 438 9 change of interval, 439 40 of a square wave, 440 1 Fourier transform, 441 2 of a chirped Gaussian pulse, 142 of a Gaussian pulse, 141 of a rectangular pulse, 139, 140, 158 of an electric field, 146 Fresnel coefficients and phases for TE polarization, 44 7 coefficients and phases for TM polarization, 47 8 reflection, 45, 47 Fresnel approximation, 290 gain approximate formula, 206 differential, 178 in an EDFA, 213 in semiconductors, 177 81 peak, 178, 180 ripple, 227, 237 saturation, 190, 207, 216, 234 spectrum of semiconductor laser, 172 Gaussian probability density function (pdf), 255 generation of carriers in laser didoes, 183 in PIN photodiodes, 244 in solar cells, 371 geometrical optics, 17 21 Goos-Hänchen (G-H) shift, 58 9, 397 graded index, 20, 107 grid, see mesh GRIN system, 20 1 group delay, 124 5, 148 velocity, 32 guides modes in optical fibres, 114 in slab waveguides, 65 6 HE modes, 116, 117, 119 Helmholtz equation, 288, 289, 292, 299 hole, see carrier hybrid modes, 116, 119 impedance, 41 interference in dielectric films, 26 7 intersymbol (ISI), 255 multiple, 27 9 invisibility cloak, see cloaking
450 L-band, see transmission bands large-signal analysis (in laser diodes), 192 laser diode distributed feedback laser (DFB), 173, 174 in-plane laser, 172 vertical cavity surface-emitting laser (VCSEL), 172, 173 leap-frog differentiation method, 431 left-handed materials (LHM), see negative index materials (NIM) lens perfect, 396 thin, 19 linear system, 338 linewidth enhancement factor (Henry factor), 228 Lorentz medium, 280 loss extrinsic, 110 in optical fibres, 108, 129 intrinsic, 109 10 LP modes, 119 20 Mach-Zehnder interferometer (MZI), 235 magic time step, 270 magnetic boundary conditions, 37 8 field intensity, 35 flux, 35 Maxwell s equations, 262 differential form, 35 in cylindrical coordinates, 111 12 integral form, 36 source-free, 69, 388 mesh 1D generation algorithm, 102 staggered grid, 266 Yeegridin1D,266, 267 Yeegridin2D,276 mid-point differentiation method, 431 mode number azimuthal, 116 radial, 116 modulation format non-return-to-zero (NRZ), 143 5 return-to-zero (RZ), 143 5 modulation of semiconductor lasers, 143, 144 modulation response function, 188, 190 2 Muller s method, 100, 422 5 negative index materials (NIM), 385, 386 Newton s method, 420 1 noise Gaussian, 255 7 in optical amplifiers, 208 9 in photodetectors, 248 9 shot, 249 thermal (Johnson), 249 50 nonlinear Schrödinger equation, 353 7 normalized guide index, 67, 94 Numerical aperture (NA), 65, 106 7 O-band, see transmission bands optical black holes, 399 400 optical cavity, 168 Fabry-Perot, 170 optical communication system, 331 3 optical coupler, 319 22 optical fibre bit-rate, 108 extrinsic loss, 110 intrinsic loss, 109 10 modes, 116 17 single-mode, 122 3 optical isolator, 322 3 optical splitter, 319 20 p-n junction double heterostructure, 176 7 homogeneous (homojunction), 175 6 multijunction, 376 7 paraxial approximation, 288 92 permeability, 35 negative, 386, 391 5 permittivity, 35 negative, 387, 389 91, 395 plasmon-like, 386 photocurrent, 245 in photodiodes, 242 in solar cells, 370, 371, 374 photodiode avalanche (APD), 242, 248, 258 metal-semiconductor-metal (MSM), 246 PIN, 242, 244 power, 252 sensitivity, 241, 257 photon density, 183 lifetime, 183, 184, 187 Planck s radiation law, 169 plane wave, 40 1 plasma, 390 frequency, 390, 391 Poisson distribution, 249, 252, 253 polarization circular, 42 3 elliptical, 42 3 linear, 42 transverse electric (TE), 44 transverse electric (TM), 47 polarization of dielectric medium, 148 population inversion, 167, 204, 208 power budget, 333 4 Poynting vector, 59 60
451 propagation constant, 41, 42 in slab waveguides, 66, 95 pulse broadening, 12, 151 in optical fibres, 106 pulse half-width, 142 pulse type chirped Gaussian, 141 2, 159 Gaussian, 139 40, 159, 163, 164, 281 6 rectangular, 138 9, 157, 340 2, 344 Super-Gaussian, 140 1, 159, 162 pulse wave, see waveform pumping, 167, 168 quantum efficiency, 247 quantum well, 173, 232 quasi-fermi level, 175, 176 rate equations in EDFA, 211 rate equations in laser diodes for an electric field, 184 7 for carriers, 182 3 for photons, 183 parameters, 184 ray optics, 17 in metamaterials, 389 in slab waveguides, 64 9 Rayleigh scattering, 110 receiver, 331, 343 recombination of carriers, 183 reflection at a plane interface, 17, 18 coefficient, 17, 45, 46, 48 external, 48, 49 internal, 48 of TE polarized waves, 44 7, 61 of TM polarized waves, 48, 61 total internal, see critical angle refractive index, 17 in GRIN structures, 20 negative, 384 numerical values for popular materials, 18 relative difference, 65 relaxation-oscillation frequency, 189 Resonant cavity, see optical cavity rise time, 144 rise time budget, 333 6 Runge-Kutta method fourth order, 433 second order, 432 S-band, see transmission bands Sellmeier equation, 31, 125 6, 135 signal-to-noise ratio (SNR), 208, 248, 336 Simpson s rule (integration method), 437 8 slowly varying envelope approximation (SVEA), 150, 296 7 small-signal analysis (in laser diodes) with linear gain, 188 9 with non-linear gain, 189 92 Snell s law, 18 soliton interactions, 363 period, 362 spectral intensity of solar energy, 368, 369 responsivity, 247 split-ring resonator (SRR), 391 4 split-step Fourier method, 357 60 steady-state analysis in a laser diode, 187 in an EDFA, 211 12 step index, 107 Stokes relations, 24 6 susceptibility, 186 TE modes in optical fibres, 116 18 in slab waveguides, 71 2 three-level system, 210 threshold carrier density, 178, 182 current, 143 time constant in photodetectors, 246, 247 time division multiplexing (TDM), 11 time-harmonic field, 39 41 TM modes in optical fibres, 116 18 in slab waveguides, 71 2 train of pulses, see waveform transatlantic telecommunications cable (TAT), 6 transfer function, 339 transfer matrix approach for antireflection (AR) coatings, 51 3 for Bragg mirrors, 54 7 for slab waveguides, 79 85 transitions in a two-level system, 169 70 in semiconductors, 174 5 transmission bands, 10 transmittance of Fabry-Perot interferometer, 29, 33 transmitter, 331, 342 transparency density, 178 transparent boundary conditions, 304 6 transverse resonance condition, 66 7 normalized form, 67 9 trapezoidal rule (integration method), 437 two-level system (TLS), 167, 169 U-band, see transmission bands velocity group, 23 4, 124, 126 phase, 21 3, 32 Verlet differentiation method, 432
452 wave equation, 38 9 for TE modes, 72 for TM modes, 72 in cylindrical coordinates, 112 in metamaterials, 388 waveform, 145, 160 waveguide 2D, 88 92 asymmetric slab (planar), 75 9, 95 cylindrical (optical fibre), 110 23 lossy, 86 symmetric slab (planar), 72 5 wavevector, see propagation constant weakly guiding approximation (wga), 118 19 wire medium, 395 Y-junction, 14, 325, 327 Yee algorithm lossless in 1D, 266 8, 282 lossless in 2D, 275 7, 285 lossy in 1D, 271 2