7 X 11 Long.P65

Cambridge University Press 978-0-521-89542-2 - Fundamentals of Micro-Optics Hans Zappe Index More information

Index

Abbe anti-reflection coating, 154, 315, 356 diagram, 83 ants number, 70–71, 84, 85, 245 fried, 213 number, diffractive lens, 304 aperture, 221, 239 Abbe, Ernst, 10, 70 circular, 278–283 aberrations, lens, see lenses diffraction from, 266–270 absorption, 77–81, 86 dual slit, 274–275 coefficient, 77–79, 399, 437, 457 multiple slits, 275–276 in waveguides, 361–363 rectangular, 277–278 of photons, 395 single slit, 270–273 spectroscopy, 455–459 waveguide, 361 achromatic lenses, 245–246, 307–308, 512 aplanatic lenses, 237 adaptive optics, xii, 189–193 apochromatic lenses, 245 afocal, 230, 234 apodization, 274 Ag APS, see photodetectors for metamaterials, 557 AR, see anti-reflection coating for plasmonics, 553, 556 Arago, Dominique Francois, 8 for reflection, 171–172 arrayed waveguide grating, 368, 383, 384 air aspheric lenses, 237, 251, 258, 480, 484 refractive index, 26, 164 assembly, optical, 489–496 Airy active alignment, 490–491 disk, 188, 219, 220, 281–283 flip-chip, 492–494 Airy, George, 8, 10, 188 passive alignment, 491 Al Si optical bench, 493–496 for plasmonics, 553 V-grooves, 491–492, 494 for reflection, 170–171 astigmatism, 45, 240–241 mole fraction, 90 in laser diodes, 420 Al2O3, 157, 413 in microlenses, 472 AlGaAs, 90–92, 351, 360, 404, 412 waveguide far field, 361 AlGaInP, 90, 404, 406 athermal lenses, 305–307 laser characteristics, 416 attenuation AlGaN, 413 in waveguides, 361–363 Alhazen (Ibn-al-Haitham), 4, 7, 9 optical, 77–82, 399 alignment Au active, 490–491 for contacts, 493 passive, 491 for electroplating, 480 aluminum, see Al for plasmonics, 553, 556 Ampère’s law, 20 for reflection, 172 Ampère, André Marie, 20 avalanche photodiodes, 429 amplification AWG, see arrayed waveguide grating optical, 396–397 anamorphic optics, 316, 361, 420 BaF2, 372 angular frequency, 25 back focal length, 226, 257

606 Index

Bacon, Roger, 9 candela ball lenses, 224, 256–257, 494 definition, 408 Balmer, Johann, 6 carrots band tails, 80, 362 novel uses, 449 bandgap energy, 87, 90–92 CCD, see photodetectors values, 92 CD, 452–455, 480 bandpass filter, 163 CdSe, 411 bandwidth, 431 chalcogenides, 83, 372 barium borate, 77 charge density, 19 Bartholinus, Erasmus, 8 chirp Bayer filter, 436 in gratings, 295 BD, see Blu-ray disc in modulators, 440 beam chocolate expander, 234–235 optical properties, 523 optical, see optical beam chromatic aberration, 244–248 shaping, 310 axial, 244 Beer’s law, 78, 396, 457 correction, 245–248 Beer, August, 78 diffractive lenses, 304 Bessel function, 187, 279, 373 lateral, 244 recurrence relation, 280 circle of least confusion, 240, 244 Bessel, Friedrich Wilhelm, 187 circular polarization, see polarization Bi3Fe5O12, 448 Clausius, Rudolf, 67 biaxial materials, 73 Clausius–Mossotti equation, 67 binary compound semiconductor, 90 CMOS, 194, 384, 436 binary optics, 12, 303, 475–478 coherence, 126–128 Biot, Jean-Baptist, 20 definition, 126 birefringence, 8, 72–75, 85, 95 length, 126, 142 BK7, see glass time, 126 blazed gratings, 11, 297–299 collimation, 42, 51, 210, 233 Blu-ray disc, 283, 308, 452–455, 515 coma, 238–239, 242 Bohr, Niels, 6, 60 in microlenses, 472 Boltzmann, Ludwig, 394 compound semiconductors, 89–93, 403 Bordeaux, 258 concave Bragg definition, 175, 208 filters, see filters lens behavior, 210 for photonic crystals, 540–543 conductivity, 58 mirrors, see mirrors confusion, maximum, 240 stack, 311 conjugates, 214, 260 Bragg, William Henry, 161 convex Bragg, William Lawrence, 161 definition, 175, 208 bread lens behavior, 210 with butter, 228 coupled mode analysis Brewster in photonic crystals, 540–543 angle, 111, 116 coupling window, 111 efficiency, 356 Brewster, David, 8, 111, 258 waveguides, 355–359 Brillouin scattering, 82 critical angle, 115–116, 327, 330 Brillouin, Léon, 82 crown glass, 71 broad-area laser, see lasers cryolite, 155 Bunsen, Robert, 6 cutoff butt coupling in a waveguide, 325 waveguides, 356 CVD, 465

CaCO3, 73 DBR laser, see lasers CaF2, 83, 85, 256 decibel, 79 camera on a chip, 436 depth of ﬁeld, see depth of focus

Index 607

depth of focus, 48, 51, 230 ruled, 294 Descartes, René, 5, 7, 27 stray light, 293 detectors, see photodetectors surface emission, 426 DFB laser, see lasers tunable, 516–519 diamond, 85 VCSELs, 420–423 dielectric Wood’s anomalies, 294 constant, 19, 57 kinoform, 308, 472, 475 films, 93 limit, 219, 265, 282 dielectrophoresis, 504, 507 microlenses, 250 diffraction near-field, 267 apertures orders, 284 circular, 278–283 diffractive lenses, see diffraction dual slit, 274–275 diffractive optical elements, see diffraction multiple slits, 275–276 Digital Micromirror Device, see DMD rectangular, 277–278 diopter, 210, 505 single slit, 270–273 dipole moment, 63 binary optics, 12, 303, 475–478 Dirac, Paul, 6, 395 definition, 265 direct-bandgap semiconductor, 87, 88 diffractive lenses, 299–308 dispersion aberrations, 304–305 diffractive microlenses, 303 achromatic, 307–308 fiber, 376–379 athermal, 305–307 grating, 290, 299 binary optics, 12, 303, 475–478 material, 68, 71, 244 hybrids, 305–308 displays kinoforms, 308, 472, 475 optofluidic, 532–533 diffractive optical elements, 308–310, 472 distortion, 242 applications, 310 distributed feedback lasers, see lasers beam shaping, 310 DMD, 14–15, 193–196 design, 309–310 DOE, see diffractive optical elements fan-outs, 310 DOF, see depth of focus efficiency, 286 Dollond, John, 10 far field, 267, 269 Doppler shift, 127 Fraunhofer regime, 267, 269 Drude model, 65 Fresnel Drude, Paul, 65 regime, 267, 300 Ducasse, Alain, 56 zone plates, 303–304, 476 DVD, 283, 308, 452–455, 480 Fresnel–Kirchhoff formula, 268–270 gratings, 11, 283–299 e-beam, 473, 543 blazed, 11, 295, 297–299 echelette gratings, see blazed gratings chirped, 295 Edison, Thomas, 10 coupled-mode analysis, 540–543 effective couplers for waveguides, 358 focal length, 226, 257 Dammann, 311 index, 312, 331–332 DBR/DFB lasers, 418–420 eigenvalue equation, 46, 119, 337 diffraction pattern, 288 Einstein, Albert, 6 dispersion, 290, 299 elastomers, 224, 483, 485 efficiency, 293 electric fabrication, 478–480 field, 18 free spectral range, 291–293 flux density, 18, 72 ghosts, 293 electro-optic effects, 75, 438–441, 520 grating equation, 284, 288, 298 electroabsorption, 439 holographic, 295, 315, 478–480 electroactive polymers, 516 lamellar, 294 electromagnetic Littrow mount, 298–299 field profiles, 294–295 energy density, 32 resolution, 316 power density, 33

608 Index

model for waveguides, 337–349 PDMS, 483, 485, 508, 509 waves, 30–36 photonic crystals, 543–545 boundary conditions, 106–107, 150–152 photoresist reflow, 12, 466–470 one-dimensional, 27 Pyrex, 85, 135, 197, 221, 465, 506, 508 polarization, 36–40, 107 replication, 480–485 spectrum, 34–36 self-assembly, 466–472, 543–545, 550 three-dimensional, 41 semiconductor processes, 464–466 transverse, 27–28 Si optical bench, 493–496 electrorefraction, 438 soft lithography, 470, 526, 528 electrowetting, 502–508 sol-gels, 484–485, 551 displays, 532–533 SU-8, 192, 484, 509 on dielectrics, 504 UV casting, 483 opto-electrowetting, 507 V-grooves, 491–492, 494 elliptical polarization, see polarization Fabry, Georges, 145 end-fire coupling Fabry–Pérot waveguides, 357 etalon, 145 energy interferometer, see interferometers bands, 87–88, 540–543 laser, see lasers conversion to wavelength, 35 resonances in electromagnetic fields, 32–34 for waveguide loss measurement, 363 epitaxial crystal growth, 91 laser, 398–401 erbium-doped fiber amplifiers, 427 parasitic, 357 etalon, see Fabry–Pérot fan-outs, 310 Euclid, 4, 7 far field Euler, Leonhard, 147 broad-area lasers, 417 evanescent field, 119–122, 342–344 diffraction, 267, 269 external cavity laser, see lasers edge-emitting lasers, 420 external incidence, 109, 111, 114 mirror, 186 extraordinary axis, 73 VCSELs, 423 waveguide, 360–361 f-number, see lenses Faraday effect, 97, 447 fabrication Faraday’s law, 21 binary optics, 475–478 Faraday, Michael, 5, 21 continuous-profile optics, 472–475 Fermat’s principle, 102–103, 204, 206 direct-write lithography, 472–473 Fermat, Pierre de, 5, 7, 102 e-beam, 473, 543 Fermi, Enrico, 395 electroplating, 480 Fermi–Dirac distribution, 395 embossing, 259, 482–483 fiber, optical, 13, 369–379 etching, 465 attenuation, 374–376 flip-chip, 492–494 Bragg gratings (FBG), 390, 516 glass molding, 484 dispersion, 376–379 gray-scale lithography, 473–475 dispersion-flattened, 379 hybrid integration, 489–490 dispersion-shifted, 379 injection molding, 259, 481–482 field distribution, 373–374 interference lithography, 12, 294, 295, 478–480, graded-index, 370 545 gyroscope, 144 ion exchange, 487–489 hollow-core, 371, 551 layer deposition, 465 modes, 374 LIGA, 481 multimode, 370 lithography, 12, 465, 472–480 photonic crystal, 371, 551 microcontact printing, 252, 470–472 plastic, 372, 385 MOEMS, 485–487 polarization-maintaining, 371 monolithic integration, 489–490 single-mode, 370 nano-imprint lithography, 483, 526 Fick, Adolf Eugen, 10 near-field holography, 480 field optical assembly, 489–496 curvature, 241

Index 609

fill factor, 253 gain in, 397 filters heterostructures, 412 Bragg, 163, 517–519 Gabor, Dennis, 11 optofluidic, 531–532 gain tunable, 163, 517–519 optical, 397–398 finesse, 148 Galilean telescope, 229 Fizeau interferometer, see interferometers Galilei, Galileo, 9, 229 Fizeau, Armand Hippolyte, 8, 140 gallium arsenide, see GaAs flint glass, 71 GaN, 90, 404, 413, 414 flip-chip, 492–494 GaP, 406, 548 focal length, 207, 209–211, 224 GaSb, 316 thick lenses, 226 Gauss’s law, 19 focal plane, 215 Gauss, Johann Carl Friedrich, 10, 19 FOG, see gyroscope Gaussian beam, 46–52, 211 Foucault, Jean, 8 collimation, 233 Fourier transform, 127, 186, 270, 273–274, 279, definition, 47 287, 309 depth of focus, 48, 51, 230 Fourier, Jean Baptiste Joseph, 5, 127 expansion, 234–235 Franklin, Benjamin, 10 focusing, 232–233 Franz, Walter, 439 from fiber, 373 Franz–Keldysh effect, 439, 441, 444 intensity, 50 Fraunhofer magnification, 231 diffraction, 186, 267 radius of curvature, 47, 48 doublet, 245, 248, 308, 512 through lenses, 230–235 lines, 71, 244, 248 waist, 48, 49 regime, 269 width, 47, 230 Fraunhofer, Joseph von, 6, 8, 11, 186, 283 Gaussian lens formula, 211, 227 free spectral range Ge Fabry–Pérot interferometer, 148 for photodetectors, 429 grating, 291–293 geometric optics free-electron absorption, 81 definition, 203 free-space optics, 321 GGG (gadolinium gallium garnet), 97, 448 Freiburg im Breisgau, 82, 141 ghosts, 293 frequency gimbals (for micromirrors), 182, 198 conversion to wavelength, 35 glass, 73, 82–86 doubling, see second harmonic generation BK7, 71, 84, 109, 110, 113, 116, 121, 154, 155, Fresnel 157, 246, 256, 342, 348, 351, 358, 465, 468, diffraction, 267, 300 477 equations, 107–109 chalcogenide, 83, 372 lenses, 12, 257–260, 300–303, 472, 475 crown, 71, 245 fabrication, 481, 483 flint, 71, 245 tunable, 515, 520 fluorozirconate, 372 reflection, 107–109, 406 for optical fiber, 372 zone plates, 12, 303–304, 476, 515, 520 halide, 83 Fresnel, Jean Augustin, 5, 8, 108, 258 HEBS, 474 Fresnel–Kirchhoff formula, 268–270 optical absorption, 79, 374 fringe Pyrex, 85, 135, 197, 220, 221, 465, 506 definition, 134, 138 SF11, 307 fused silica, 465 SF59, 448 SF6, 84, 358 GaAs, 56, 87, 90, 115, 387 sputtered, 85 bandgap, 88 thermal expansion, 85, 86 electro-optic effect, 76, 439–441 ULE, 86 for lasers, 402, 414, 421 Zerodur, 86 for LEDs, 404, 406 gold, see Au for photodetectors, 429 Goos, Fritz, 347

610 Index

Gouy phase shift, 47, 48 for photodetectors, 429 Gouy, Louis Georges, 47 InGaAsP, 404, 413, 414, 419, 426, 449, 547 Granger, Hermione, 557 InGaN, 90, 404, 413 grating InP, 76, 90, 381, 383, 384, 413 coupling integrated optics, 13 waveguides, 358 applications, 379 light valve, 311 definition, 321, 379 gratings, see diffraction for sensors, 386–390 Green, Alfred, 139 for telecommunications, 385 Grimaldi, Francesco Maria, 5, 7 intensity GRIN lenses, 254–256, 488–489, 515 modulation, see modulators group velocity, 30, 348 optical, 77 gyroscope interference, 128–135 integrated optical, 387 constructive, 131 optical fiber (FOG), 144 destructive, 131 filters, 160–163 Hänchen, Hilda (Lindberg-), 347 intensities, 131–134 half-wave plate, 74 lithography, 478–480, 545 Hall, Chester Moor, 10 path length difference, 133–134 handedness, see polarization superposition of fields, 129–130 Hartmann, Johannes, 191 visibility, 134 HEBS glass, 474 wavelength difference, 132 Helmholtz equation, 46, 119, 337 interferometers, 135–149 paraxial, 47 Fabry–Pérot, 145, 149, 398–401, 550 Helmholtz, Hermann von, 6, 46 Fizeau, 140 Hertz, Heinrich, 6, 25 Mach–Zehnder, 141–143, 252, 381, heterostructure, 413, 429, 434 389, 444 HgCdTe, 90, 431 Michelson, 137–139, 387 holograms, 12, 308, 311, 451, 478 Sagnac, 143–145, 200, 387 holography, 11 Twyman–Green, 139, 252 near-field, 480 Young, 136–137, 389 Hook, Robert, 5, 7, 9 internal incidence, 114–122 Huygens’ principle, 266–268 inverse centimeters, 35 Huygens, Christiaan, 5, 8, 9, 266 ion-exchange waveguide, 353 hydrogels, 520 isolator optical, 97, 381, 446–449 IBM, 465 isotropic materials, 72 II-VI semiconductors, 90, 414, 429 ITO, 410, 411 III-V semiconductors, 89–93, 464 bandgap, 90–92, 403 Jones matrices, 39 cleaving, 149 Jones, R. Clark, 39 for optical telecommunications, 381, 384, 489 for waveguides, 351 kaleidoscope, 8 light emission, 403 KDP (KH2PO4), 73, 76, 77, 441 monolithic integration, 489 Keats, John, 7 image Keldysh, Leonid Veniaminovich, 439 real, 173, 180, 213 Kepler, Johannes, 7, 9, 229 virtual, 173, 180, 213 Keplerian telescope, 229 immersion optics, 224 Kerr effect, 76, 438, 439 impedance, 32, 108, 151 Kerr, John, 76 for optical multilayers, 159–163 kinoform, 12, 308, 472, 475 implanted waveguide, 353 Kirchhoff, Gustav, 6, 269 incoherent light sources, 126 KNbO3, 441 indirect bandgap semiconductor, 88, 403 Kramers, Hendrik Anthony, 60 indium tin oxide, see ITO, 506, 507, 515 Kramers–Kronig relation, 60, 68, 440 InGaAs, 90, 384 Kronecker, Leopold, 43

Index 611

Kronig, Ralph, 60 LCD, see liquid crystals, displays KTP (KTiOPO4), 414, 441 LEDs, 56, 178, 403–411 as a point source, 42 Lambert, Johann Heinrich, 78 Burrus structure, 406 lamellar gratings, 294 emission efficiency, 406–407 Laplace, Pierre-Simon, 5 emission from substrate, 116 lasers materials, 403 active region, 412 OLEDs, 409–411 Ar, 36, 478 power emission, 408 broad-area, 417 quantum dots, 411, 536 characteristics of resonant cavity, 409 DFB, 419 spectrum, 407–408 Fabry–Pérot, 416 structures, 404–406 VCSEL, 422 superluminescent (SLED), 409 DBR, 311, 382, 387, 418–420 using photonic crystals, 547 DFB, 312, 376, 381, 418–420, 425, 458, 521, using plasmons, 555 527–530 Leeuwenhoek, Anton van, 9 diode, 12, 33, 56, 90, 93, 233, 238, 314, 316, lenses 411–426 aberrations, 235–248 disk, 425–426, 536 astigmatism, 240–241 distributed feedback, 417–420 chromatic, 244–248 dye, 525–530 coma, 238–239, 242 external cavity, 314–316 diffractive, 304–305 VCSEL, 423 distortion, 242 Fabry–Pérot, 381, 414–417, 525, 527 field curvature, 241 fiber, 424 spherical, 237–238 HeCd, 51, 473, 478 achromatic, 245–246, 307–308, 512 HeNe, 26, 75, 111, 128, 132, 154, 155, 188, 267, aperture, 221 289, 332, 389 aplanatic, 237 lead-salt, 458 apochromatic, 245 materials, 403 aspheric, 237, 251, 258, 480, 484 mode hops, 312 athermal, 305–307 monomode emission, 418, 526 ball, 224, 256–257, 494 multimode emission, 416 chromatic aberration, 244–248, 304 Nd:YAG, 77, 97, 310, 479, 521, 526, 545 combinations of, 228–230 optofluidic, 525–530 concave, 204, 208, 210 pointers, 414 convex, 204, 208, 210 principles of, 394–403 diffraction limited, 219, 265 quantum cascade, 424–425 diffractive, 299–308 Raman, 427 aberrations, 304–305 resonance, 398–403 achromatic, 307–308 ring, 144 athermal, 305–307 Si, 427 binary optics, 12, 303, 475–478 single mode, 312 hybrids, 305–308 spaser, 555 kinoforms, 308, 472, 475 threshold, 399 diopter, 210 threshold current, 416 elliptical, 205 tunable, 420, 520 f/#, 224–225, 233 VCSEL, 163, 313–314, 420–423, 457 focal length, 207, 209–211, 224 polarization control, 422 Fresnel lenses, 257–260, 481, 483 tunable, 423 Fresnel zone plates, 303–304, 476 using photonic crystals, 548 Fresnel-like lenses, 300–303, 472, 475 LaSFN9, 256 Gaussian beams, 230–235 lateral GRIN lenses, 254–256, 488–489, 515 definition, 352 hyperbolic, 205 lattice constant, 90–92 liquid, 502–508, 520, 530–531

612 Index

liquid crystal, 451, 514–515 LSF, see line spread function magnification, 217–218 lumen membrane, 508–514 definition, 408 microlenses, 248–254 arrays, 252 Mach, Ludwig, 141 profile measurement, 139 Mach–Zehnder interferometer, see interferometers scaling, 250 magnetic sizes, 251 field, 18 modulation transfer function, 220 flux density, 18 multiple, 228–230 magneto-optics, 97, 447–449 numerical aperture, 223–224 data storage, 453 principal planes, 225, 228 magnification resolution, 220 Gaussian beam, 231 Seidel aberrations, 235–244 lenses, 217–218 sign conventions, 207–209 mirrors, 179 spherical, 205 Maiman, Theodore, 10 spot diagram, 219 Malus, Etienne Louis, 8 Strehl ratio, 219, 282 marginal rays, 238 thick, 225–228 mass and spring model, 62 thin, 209–212 material usage, 55–56 tunable materials liquid, 502–508, 520, 530–531 ceramics, 491 liquid crystal, 514–515 compound semiconductors, 89–93 membrane, 508–514 dielectrics, 93, 465 zoom, 228 elastomers, 470 lensmaker’s formula, 209 electroactive polymers, 516 LiF, 83 glasses, 82–86, 465, 487, 525 liftoff, 465 hydrogels, 520 LIGA, 481 LiNbO3, 97, 487 light bulb, 33 liquid crystals, 449–451, 514–515 light-emitting diode, see LEDs metals, 465 light guide, 322 PDMS, 252, 483, 485, 508, 509, 526 LiNbO3, 56, 73, 76, 97, 351, 381, 441, 520 polymers, 94–96, 481 line spread function, 219 Pyrex, 85, 135, 197, 221, 465, 506, 508 linear polarization, see polarization semiconductors, 86, 93 linewidth, 127, 397 silicon, 89, 464, 486, 491–496 Lippersley, Hans, 9 sol-gels, 96, 484–485 Lippmann, Gabriel, 503 SU-8, 192, 484, 509, 525, 545 liquid crystals, 449–451 Teflon, 505 displays, 451 Maxwell’s equations, 19–23 lenses, 451, 514–515 Maxwell, James Clerk, 5, 17, 23 nematic, 449 Maxwell–Boltzmann distribution, 394 on silicon, 451 mean square value, 432 switching, 451 measurement liquid lenses, 502–508, 520, 530–531 displacement, 139 Lister, Joseph Jackson, 10 refractive index, 139, 142 LiTaO3, 441, 520 surface deformation, 139 lithium niobate, see LiNbO3 MEH-PPV, 409 lithium triborate, 77 membrane lenses, 508–514 lithography, see fabrication MEMS, xi, 13, 14, 145, 163, 182, 198, 252, 314, Littrow mount, 298–299 463, 485–487 Littrow, Joseph Johannn von, 298 fabrication, 464–466 loss MOEMS, 13, 485–487 optical, see absorption tunable lenses, 505–508 love songs, 295 meridional plane, 240 LPCVD, 465 metals

Index 613

for laser diodes, 415 plasma effect, 440 for mirrors, 170–172 Pockels effect, 438 reflectivity, 66 quantum well, 440 metamaterials, 556–557 quantum-confined Stark effect, 440, 444 MgAl2O4, 413 MOEMS, see MEMS MgF2, 83, 154–157, 171, 557 monomode emission, lasers, 418, 526 Michelson interferometer, see interferometers Morley, Edward, 6 Michelson, Albert, 6, 8, 11, 137, 283 Mossotti, Ottaviano-Fabrizio, 67 micro-electromechanical systems, see MEMS MSM photodetector, 430 micro-total-analysis systems (µTAS), 523 MTF, see modulation transfer function microcontact printing, 252, 470–472 Mulhouse, 78 microlenses, see lenses multilayers micromirrors, see mirrors dual-layer, 156–158 microsystems, xi–xii half-wave, 154, 160 Mie scattering, 82 impedance, 159–163 Mie, Gustav, 82 materials, 155 mirrors mirrors, 160–163 Bragg, 160–163, 417–423, 517–519 optical, 150–163 cleaning, 170 quarter-wave, 153–154, 159–160 imaging, 179–181 multimode emission, lasers, 416 magnification, 179 multimode interference coupler, 368, 384 metals for, 170–172 multiple-lens systems, 228–230 micromirrors, 181–189 adaptive, 189–193 NA, see numerical aperture aperture, 186 Na3AlF6, 155 applications, 193–199 nano-optics deformable, 191–193 definition, 535 diffraction from, 186–189 metamaterials, 556–557 optical properties, 185–189 photonic crystals, 537–551 parabolic, 176 plasmonics, 552–556 planarity, 185 subwavelength optics, 484, 535, 536, pneumatic, 513 552, 556 resolution, 189 nanophotonics, 535–537 roughness, 185 nanorods, 422, 553 scanning, 182–185 nanoshells, 556 structure, 181–182 nanospheres, 551, 553, 555 mirror equation, 177, 178 nanotubes, 537 nonplanar, 175–181 nanowires, 537, 554–555 parabolic, 175–176 near field planar, 172–175 diffraction, 267, 300 imaging, 173 holography, 480 rotating, 173–175 optics, 536 spherical, 176–181 waveguide, 359–360 surfaces, 170 Newton, Isaac, 5, 7, 10 tunable, 163 NiGeAu, 415 MMI, see multimode interference coupler noise-equivalent power, 432 modulation transfer function, 220–221, 510 nonlinear materials, 75–77, 438–441 modulators, 76, 437–446 notation, 17 bulk, 442–444 numerical aperture, 223–224 chirp, 440 in a waveguide or fiber, 358 electro-optic, 143, 438–441 numerical simulation Franz–Keldysh effect, 439, 441, 444 ZEMAX, 220–221, 242–243, 246–248 integrated optical, 444–446 intensity, 438 OCT, see optical, coherence tomography Kerr effect, 439 OEIC, see optoelectronic integrated circuits phase, 438 OLED, see LEDs

614 Index

olives paraboloidal wavefront, see wavefront may have pits, 449 parametric amplification, 76 on-axis rays, 237 paraxial, 46, 177 opals, 539 approximation, 207, 215, 235 OPD, see optical, path difference wave equation, 254 OPL, see optical, path length Passard, Alain, 55 optical PDMS, 252, 483, 485, 508, 509, 543 amplification, 396–397 PDOT, 410 assembly, 489–496 PECVD, 465 coherence tomography, 495 PEDOT, 410 cross-connect, 198–199, 487 permeability, 18 crossbars, 198 negative, 556 data storage, 452–455 permittivity, 18, 57 fiber, see fiber, optical direction dependence, 72–75 isolator, 97, 381, 446–449 negative, 556 multilayers, see multilayers of free space, 18 path difference, 219 Petzval, Józeph Miksa, 241 path length, 102, 206, 219 PFPE, 530 resolution, 282–283 phase modulation, see modulators sensors, 386–390, 455–459, 516 phase shift switching, 198–199, 311, 487 total internal reflection, 117–119, 328 telecommunications, xi, 143, 372, 385, 537 upon reflection, 110–111 thickness, 74 phase velocity, 30 transitions, 394–398 photodetectors, 428–434 tweezers, 534 APS, 436–437 optical beam arrays, 434–437 collimated, 42, 51, 210 avalanche photodiodes, 429 definition of, 42, 49 CCD, 435–436 expander, 234–235 dark current, 431 Gaussian, 46–52, 211 efficiency, 430–431 marginal rays, 238 materials, 93 on-axis, 237 MSM, 430 principal rays, 238 noise, 431–433 skew rays, 219, 237, 240 noise-equivalent power, 432 optoelectronic integrated circuits, 379 organic, 433–434 opto-thermal expansion coefficient, 306 photodiodes, 428–433 opto-electrowetting, 507 quantum dot, 434 optofluidics, 523–534 responsivity, 430 applications, 524 signal-to-noise ratio, 432 displays, 532–533 photon filters, 531–532 origin of name, 6 lasers, 525–530 photonic crystals, 537–551 microlenses, 502–514, 530–531 band structure, 540–543 microscopy, 533–534 coupled-mode analysis, 540–543 photonic crystals, 533 fabrication, 479, 543–545 waveguides, 524–525 fiber, 371, 551 ordinary axis, 73 for improving LED efficiency, ormocer, 96 406, 547 overlap integral, 356 optofluidic, 533 OXC, see optical, cross-connect structures, 537–539 tunable, 519, 533, 550–551 p-i-n junction waveguides, 354, 546–547 in a photodiode, 428 woodpile structures, 545 Pérot, Alfred, 145 photonic integrated circuits, 379 paper photonics electronic, 532–533 definition, 321, 379

Index 615

nanophotonics, 535–537 population inversion, 397, 402 silicon, 354, 383–384, 427–428, 489, 494 position-sensitive detector, 197, 430 photoresist Potter, Harry, 557 reflow lenses, 466–470 power refractive index, 221, 252, 468 density, 33 PIC, see photonic integrated circuits optical, 32, 77 pigeons reflection and transmission, 113–114 roasted, 52 Poynting vector, 32, 150 pitch Gaussian beam, 50 of a GRIN lens, 255 time average, 33 planar lightwave circuits, 383–384, 489, 494 Poynting, John Henry, 32 planar wavefront, see wavefront PPV, 409 Planck, Max, 6, 35 primary aberrations, 235–244 plasma principle effect, 440 of least time, 102 frequency, 66, 171 planes, 225, 228 plasmonics, 552–556 rays, 238 for lasers, 422 propagation constant, 26, 437 light sources, 555 complex, 58–59, 437 plasmons, 552–553 in a medium, 31 sensors, 555–556 relation to wavevector, 26 waveguides, 553–555 propagation vector, see wavevector plastic optical fiber, see fiber, optical PSF, see point spread function PLC, see planar lightwave circuits Ptolemy, 7 PLZT, 520 PVC, 94, 342, 348, 358, 481 PMMA, 94, 121, 227, 259, 351, 372, 473, 481, 543 Pyrex, 85, 135, 197, 221, 465, pneumatic micro-optics, 508–514 506, 508 Pockels effect, 76, 438 Pockels, Friedrich, 76 Q (quality factor), 369, 549 POF, see fiber, optical, plastic QCL, see lasers, quantum cascade Poincaré sphere, 39 quantum dots, 411, 427, 434, 536, 537 Poincaré, Jules Henri, 6, 39 quantum well, 413, 427, 440 point source, 42, 266, 268 intermixing, 383 point spread function, 219 quantum-confined Stark effect, 440, 444 polarizability, 18, 57, 63, 66, 72 quarter wave polarization, 36–40 film, 153–154 angle, 111, 113, 116 plate, 74 circular, 37, 39, 74 quartz, 73, 83 ellipse, 38 quaternary compound semiconductor, 90 elliptical, 37 handedness, 37, 39 Rømer, Ole, 8 linear, 36, 39, 74 Raman retarder, 74 laser, 427 rotation, 74, 447–448 scattering, 82, 556 poly (methyl methacrylate), see PMMA Raman, Chandrasekhara Venkata, 82 polycarbonate, 94, 351, 481 ray tracing polyimide, 351, 450 by hand, 213–218 polymers, 94–96 numerically, 218–221, 242, 246 for LEDs, 409–411 ray-optic model for waveguides, 322–336 for optical fiber, 372 Rayleigh for photodetectors, 433–434 limit, 219, 282 for replication, 480–483 range, 48 for waveguides, 351 scattering, 81, 82, 86, 375 polysilicon, 192 Rayleigh, Lord, 11, 48 polystyrene, 94, 481 real image, see image polyvinyl chloride, see PVC reciprocal optical systems, 359

616 Index

reflectance, 113 Sagnac interferometer, see interferometers multilayer, 153 Sagnac, Georges, 143 normal incidence, 114 salad reflection, 103–104, 169–172 tossed, 417 external incidence, 109, 111, 114 sapphire, 85, 256, 413 internal incidence, 114–122 Savart, Felix, 20 normal incidence, 114 sawtooth gratings, see blazed gratings specular, 172, 285 scattering, 81–82 total internal, 116–119 Schottky, Walter, 429 reflectivity, 109 second harmonic generation, 76–77 metals, 66, 170–172 Seidel aberrations, 235–244 multilayer, 152–153 Seidel, Philipp Ludwig von, 236 phase shift, 110–111 Sellmeier formula, 68–70 refraction, 104–106 Sellmeier, W., 69 at a curved surface, 204–205 semiconductor at a spherical surface, 205–209 absorption, 80 negative, 556–557 gain, 397–398 refractive index, 56–77 materials, 86–93 complex, 59–60, 399 optical amplifier, 382 definition, 31, 57 optical transitions, 393–398 direction dependence, 72–75 organic, 409 extraordinary, 73, 97, 449 photon absorption, 395 measurement of, 139 photon emission, 395 negative, 556 sensors of air, 26, 164 µTAS, 523 of photoresist, 221, 252, 468 absorption spectroscopy, 455–459 of water, 110, 165 chemical, 142, 388–389, 524 ordinary, 73, 97, 449 displacement, 387 temperature variation, 72, 440 fiber, 389, 516 values, 92 integrated optical, 386–390 wavelength variation, 68–69 nanophotonic, 537 replication, see fabrication rotation, 144, 387 resolution surface plasmon resonance, 389, 524, 552 grating, 316 TDLAS, 455–459 lens, 220 torque, 386 optical, definition of, 282–283 Young interferometer, 137, 389 spectrometer, 316–317 SERS, see surface-enhanced Raman spectroscopy resonance SF11, see glass atomic, 64 SF6, see glass laser, 398–403 Shack, Ronald, 191 whispering gallery, 426 Shack–Hartmann sensor, 191 responsivity, 430 sharks Reynolds number, 524 hungry, 371 Reynolds, Osborne, 524 SHG, see second harmonic generation rhodamine, 526 Si, 56, 73, 89, 464 rib waveguide, 352 amorphous, 517 RIBE, 465 as lens substrate, 468 ridge waveguide, 352 bandgap, 88, 403 RIE, 465 electro-optic effect, 76, 441 ring resonator, 368, 383, 386, 389, 425–426, 531, for photodetectors, 429, 434 536 for waveguides, 350 Rittenhouse, David, 11 laser, 427 Rowland, Henry Augustus, 11 light emission, 427–428 optical bench, 384, 493–496 sag height, 251 photonics, 354, 383–384, 427–428, sagittal plane, 240 489, 494

Index 617

plasma effect, 440 stop-band, 163, 517 thermo-optic effect, 440 in VCSELs, 421 Si2O3, 171 stops, 239 Si3N4, 517 stray light, 293 waveguide, 332, 333, 335, 340, 342, 344, 350 Strehl ratio, 219, 282 SiC, 413 Strehl, Karl, 219 side-mode suppression ratio, 419 strip-loaded waveguide, 352 SiGe, 427 Strutt, John William, 11, 48 sign conventions, 29 SU-8, 192, 484, 509, 525, 545 signal-to-noise ratio, 432 subwavelength optics, see nano-optics silica supercontinuum spectrum, 536, 551 fused, 465 surface plasmon resonance, 389, 524, 552–553 silicon, see Si surface-enhanced Raman spectroscopy, 556 silicon dioxide, see SiO2 susceptibility, 61–67 silver, see Ag atomic, 62–64 SiN, 192 definition, 57 sinc function, 271 electronic, 65–66 SiO2, 73, 83, 155, 426, 449, 465, 505, 507, 517 nonlinear, 75–77 absorption, 79, 374 plot, 67 dispersion, 68, 70 waveguide, 332, 333, 335, 340, 342, 344, 350 Ta2O5, 155, 389, 449 SiOB, see Si, optical bench tangential plane, 218, 240 skew rays, 219, 237, 240 TDLAS, see sensors SLED, see LEDs TE polarization, 74, 107 Snell’s law, 105, 204, 254 Teflon, 505 Snell, Willebrord, 7, 105 telescope, 229–230 SOA, see semiconductor, optical amplifier TEM, see transverse electromagnetic SOI (silicon on insulator), 350, 543 ternary compound semiconductor, 90 sol-gels, 96, 484–485 thermal effects spaser, 555 athermal lenses, 305–307 speckles, 135 in glass, 72 spectrometers, 316–318 thermal coefficient of expansion, 72, 85, 86, 305, Fourier transform, 494 306 resolution, 316–317 thermo-optic effect in glass, 72 spectrum thermo-optic effect in Si, 440, 518 electromagnetic, 34–36 thick lenses, 225–228 supercontinuum, 536, 551 thin lens approximation, 209–212 width (FWHM), 149 threshold current, for lasers, 416 specular reflection, 172, 285 TiO2, 155 speed of light TiPtAu, 415 from Maxwell’s equations, 5, 25 TM polarization, 74, 107, 294 historical, 6, 8–9 total internal reflection, 116–119, 260 in a medium, 31, 102 in a waveguide, 327, 347 spherical in an LED, 406 aberration, 237–238 phase shift, 117–119, 328 in microlenses, 472 transmittance, 113, 273 wavefront, see wavefront normal incidence, 114 spin-on glass, 96 transmittivity, 109 spinel, 413 transverse spontaneous emission, 395 definition, 352 spot diagram, 219 electromagnetic, 27 SPR, see surface plasmon resonance tunable micro-optics Stark, Johannes, 440 diffractive optics, 516 Steinheil achromatic doublet, 245 electrowetting, 502–508 step function, 273 Fresnel lenses, 515, 520 stimulated emission, 395 gratings, 516–519

618 Index

liquid crystal, 514–515 waveguides liquid lenses, 502–508, 520, 530–531 arrayed waveguide grating, 368 membrane lenses, 508–514 asymmetric, 329–330, 335–336 photonic crystals, 519, 550–551 channel, 349–354 pneumatic, 508–514 implanted, 353 Twyman, Frank, 139 ion-exchange, 353 Twyman–Green interferometer, see interferometers rib, 352 ridge, 352 ULE glass, 86 strip-loaded, 352 uniaxial materials, 73, 74, 449 characteristic equation, 325, 327–330, 345–346 unit vector, 18 characterization, 354–363 Urbach tails, 80, 362 cladding, 326, 327 confinement factor, 344–345 V-grooves, 491–492, 494, 505 core, 326, 327 variable optical attenuator, 383, 487 coupling light in and out, 355–359 VCL, see VCSEL butt coupling, 356 VCSEL, see lasers end-fire coupling, 357 vector, 17 grating coupling, 358 velocity curves, 364, 547 group, 30, 348 cutoff, 325 modal, in a waveguide, 333, 348–349 dielectric, 326–336 phase, 30 dimensions, 354 Verdet, Émile, 448 discrete propagation in, 325–326 vertical-cavity lasers, see VCSEL effective index, 312, 331–332, 335 virtual image, see image electric field, 339–345 visibility electromagnetic model, 337–349 interference, 134 evanescent field, 342–344, 347 visible wavelength range, 34, 292 far-field, 360 VOA, see variable optical attenuator fluidic, 524–525 Goos–Hänchen shift, 347–348 water III-V, 351 refractive index, 110, 165 isolators, 448–449 wave light guide, 322 equation, 23–25 losses, 361–363 cylindrical coordinates, 373 in nanowires, 554 eigenvalue form, 46, 119, 337 in photonic crystal, 547 general solution, 25, 58 in plasmonic, 553 in a waveguide, 337–338 measurement, 362–363 one-dimensional, 27 mirror, 323–326 paraxial, 254 mode number, 324, 330 three-dimensional, 24 mode velocity, 333, 348–349 vector, 25, 87 modeling, 354–355 in a medium, 31 modulators, 444–446 in a waveguide, 323 multimode interference coupler, 368 relation to propagation constant, 26 near-field, 359–361 velocity photonic crystal, 354, 546–547 from Maxwell’s equations, 25 plasmonic, 553–555 in a medium, 30–31, 102 polymer, 351 wavefront, 40–45, 103 propagating and decaying solutions, 338–339 correction, 190–193 propagation constant, 330–331, 335, 340 definition, 41 proximity couplers, 366–368 Huygens’ principle, 266–267 PVC/BK7, 342, 348, 358 in a waveguide, 323 ray-optic model, 322–336 paraboloidal, 47 ring resonator, 368, 383, 386, 389, 531, 536 planar, 41, 47, 49 Si3N4/BK7, 335 spherical, 42, 47, 49 SiO2/Si3N4, 332, 333, 335, 340, 342, 344, 350

Index 619

slab, 323, 326, 337, 539 YAG (yttrium aluminum garnet), 97, 408 slot, 354 YIG (yttrium iron garnet), 97, 448 solving, 332–336 Young stripe, 350 double-slit experiment, 274 symmetric, 328–329 equation, 502 Y-junctions, 365–366 interferometer, see interferometers wavelength, 26 Young, Thomas, 5, 8, 136, 274, 502 YVO (yttrium aluminum vanadate), 414 conversion to frequency, 35 4 in a medium, 31 Zehnder, Ludwig, 141 visible range, 34, 292 ZEMAX, 220–221, 242–243, 246–248 wavelength-division multiplexing, 379, 381 Zernike polynomials, 43–45, 191, 472 WDM, see wavelength-division multiplexing Zernike, Frits, 43 whispering gallery modes, 426 Zerodur, 86 Witelo, 7 zig-zags, 331, 349 Wollaston, William, 6 ZnS, 411 Wood’s anomalies, 294 ZnSe, 90 Wood, Robert W., 11, 294 zone plates, see Fresnel zone plates ZrF4, 372 X-rays, 34, 141, 170, 303, 481 Zurich, 242, 429