Nonlinear photonic crystals: II. Interaction classification for quadratic nonlinearities

Waves Random Media

Volumn 12, Issue 4, 2002, Pages

  Babin, Anatoli ^a   Figotin, Alexander ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BRILLOUIN SCATTERING; DIELECTRIC MATERIALS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE PROPAGATION; MAXWELL EQUATIONS; PHOTONS; SECOND HARMONIC GENERATION;

GROUP VELOCITY MATCHING CONDITION; NONLINEAR PHOTONIC CRYSTALS; WAVEPACKETS;

NONLINEAR OPTICS;

EID: 0036805259     PISSN: 09597174     EISSN: None     Source Type: Journal    
DOI: 10.1088/0959-7174/12/4/202     Document Type: Review

References (65)

1. 2000 Optical gap solitons: past, present, and future; theory and experiments Chaos 9 584-9
2. Agrawal G 1995 Nonlinear Fiber Optics (New York: Academic)
3. Aközbek N and John S 1998 Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures Phys. Rev. E 57 2287-319
4. Atai J and Mahomed B A 2000 Bragg-grating solitons in a semilinear dual-core system Phys. Rev. E 60 8713-18
5. Arnold V I Methods of Classical Mechanics (Springer Graduate Texts in Mathematics vol 60) (New York: Springer)
6. Arnold V I, Gusein-Zade S M and Varchenko A N 1985 Singularities of Differentiable Mappings (Monographs in Mathematics vol 82) vol 1 (Basle: Birkhauser)
7. Arnold V I, Gusein-Zade S M and Varchenko A N 1988 Singularities of Differentiable Mappings (Monographs in Mathematics vol 83) vol 2 (Basle: Birkhauser)
8. Arraf A and de Sterke C M 1998 Coupled-mode equations for quadratically nonlinear deep gratings Phys. Rev. E 58 7951-8
9. 2 nonlinearity: analysis and solutions Opt. Fiber Technol. 5 223-34
10. Arraf A, de Sterke C M and He H 2001 Bright stationary solitary waves in deep gratings with a quadratic nonlinearity Phys. Rev. E 63 026611
11. Ashcroft N and Mermin N 1976 Solid State Physics (New York: Holt, Rinehart and Winston)
12. Babin A and Figotin A 2001 Nonlinear photonic crystals: I. Quadratic nonlinearity Waves Random Media 11 R31-102
13. Belyakov V 1992 Diffraction Optics of Complex-Structured Periodic Medium (Berlin: Springer)
14. Berger V 1998 Nonlinear photonic crystals Phys. Rev. Lett. 81 4136-9
15. Broderck N G R, Ross G W, Offerhous H L, Richardson D J and Hanna D C 2000 Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal Phys. Rev. Lett. 84 4345-8
16. Butcher P and Cotter D 1990 The Elements of Nonlinear Optics (Cambridge: Cambridge University Press)
17. Boyd R 1992 Nonlinear Optics (New York: Academic)
18. Centini M, D'Aguanno G, Scalora M, Sibilia C, Bertolotti M, Bloemer M J and Bowden C M 2001 Simultaneously phase-matched enhanced second and third harmonic generation Phys. Rev. E 64 046606
19. Carrasco S, Torres J P, Artigas D and Torner L 2000 Generation of multicolor spatial solitons with pulsed light Opt. Commun. 192 347-55
20. Cojocaru C, Martorell J, Vilaseca R, Trull J and Fazio E 1999 Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity Appl. Phys. Lett. 74 504-6
21. Cojocaru C, Vilaseca R, Martorell J, Carvajal J, Massons J and Diaz F 2001 Actively induced transmission via a quadratic nonlinear optical interaction in a postassium titanyl phosphate microcavity Appl. Phys. Lett. 79 4479-81
22. Conti C, Trillo S and Assanto G 1997 Bloch function approach for parametric gap solitons Opt. Lett. 22 445-7
23. Dumeige Y, Vidakovic P, Sauvage S, Sagnes I, Levenson J A, Sibilia C, Centini M, D'Aguanno G and Scalora M 2001 Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap Appl. Phys. Lett. 78 3021-3
24. Eggleton B J, de Sterke C M and Slusher R E 1997 Nonlinear pulse propagation in Bragg gratings J. Opt. Soc. Am. B 14 2980-93
25. Eggleton B J, Slusher R E, de Sterke C M, Krug P A and Sipe J E 1996 Bragg grating solitons Phys. Rev. Lett. 76 1627-30
26. Estrada R and Kanwal R 1994 Asymptotic Analysis: A Distributional Approach (Basle: Birkhäuser)
27. Fedorjuk M V 1987 Asimptotika Integraly i Rjady (Moskow: Nauka)
28. Fedorjuk M V 1962 The method of stationary phase for multiple integrals J. Commun. Math. Math. Phys. 2 145-50
29. Fedorjuk M V 1977 The Saddle-Point Method (Moscow: Nauka)
30. Fejer M M, Magel G A, Jundt D H and Byer R L 1992 Quasi-phase-matched second harmonic generation: tuning and tolerances IEEE J. Quantum. Electron. 28 2631-54
31. Figotin A and Vitebsky I 2001 Nonreciprocal magnetic photonic crystals Phys. Rev. E 63 1-17
32. Felsen L and Marcuvits N 1994 Radiation and Scattering of Waves (Oxford: Oxford University Press)
33. 3:Y:Fe Phys. Rev. Lett. 86 4021-4
34. Haus J, Viswanathan, Scalora M, Kalocsai A, Cole J and Theimer J 1998 Enhanced second-harmonic generation in media with a weak periodicity Phys. Rev. A 57 2120-8
35. He H and Drummond P D 1997 Ideal soliton environment using parametric band gaps Phys. Rev. Lett. 78 4311-15
36. He H and Drummond P D 1998 Theory of multidimensional parametric band-gap simultons Phys. Rev. E 58 5025-46
37. Iizuka T and de Sterke C M 2000 Corrections to coupled mode theory for deep gratings Phys. Rev. E 61 4491-9
38. Kappeler T 1988 Multiplicities of the eigenvalues of the Schrödinger equation in any dimension J. Funct. Anal. 77 346-51
39. Kato T 1995 Perturbation Theory for Linear Operators (Berlin: Springer)
40. Kumasako J, Matsumoto M and Waiyapot S 2000 Linear stability analysis of dispersion-managed solitons controlled by filters J. Lightwave Technol. 18 1064-8
41. Martorell J, Vilaseca R and Corbalan R 1997 Second harmonic generation in a photonic crystal Appl. Phys. Lett. 70 702-4
42. Mills D 1991 Nonlinear Optics (Berlin: Springer)
43. Mihalache D, Mazilu D, Crasovan L-C, Torner L, Malomed B and Lederer F 2000 Three-dimensional walking spatiotemporal solitons in quadratic media Phys. Rev. E 62 7340-7
44. Mou S, Lin C-F and Chou H-F 2001 Quasi-3-D beam-propagation method for modeling nonlinear wavelength conversion J. Lightwave Technol. 19 772-9
45. Nijhof J H B, Forysiak W and Doran N J 2000 The averaging method for finding exactly periodic dispersion-managed solitons IEEE J. Sel. Top. Quantum. Electron. 6 330-6
46. Schiff L 1968 Quantum Mechanics (New York: McGraw-Hill)
47. Saleh B and Teich M 1991 Fundamentals of Photonics (New York: Wiley)
48. Scalora M, Bloomer M J, Manka A S, Dowling J P, Bowden C M, Viswanathan R and Haus J W 1997 Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures Phys. Rev. A 56 3166-74
49. Simonneau C, Debray J P, Harmand J C, Vidakovic P, Lovering D J and Levenson J A 1997 Second-harmonic generation in a doubly resonant semiconductor microcavity Opt. Lett. 22 1775-7
50. Steel M J and de Sterke C M 1996 Parametric amplification of short pulses in optical fiber Bragg gratings Phys. Rev. E 54 4271-84
51. Stein E 1993 Harmonic Analysis. Real-Variable Methods, Orthogonality, and Oscillatory Integrals (Princeton, NJ: Princeton University Press)
52. de Sterke C M, Salinas D G and Sipe J E 1996 Coupled-mode theory for light propagation through deep nonlinear gratings Phys. Rev. E 54 1969-89
53. de Sterke C M, Eggleton B J and Krug P A 1997 High-intensity pulse propagation in uniform gratings and grating superstructures J. Lightwave Technol. 15 1494-502
54. Reed M and Simon B 1978 Analysis of Operators vol 4 (New York: Academic)
55. Tarasishin A, Zheltikov A and Magnitskii S 1999 Matched second-harmonic generation of ultrasoft laser pulses in photonic crystals JETP Lett. 70 819-25
56. Teytel M 1999 How rare are multiple eigenvalues? Commun. Pure Appl. Math. 52 917-34
57. Di Trapani P, Caironi D, Valiulis G, Dubietis A, Danielius R and Piskarskas A 1998 Observation of temporal solitons in second-harmonic generation with tilted pulses Phys. Rev. Lett. 81 570-3
58. Trull J, Vilaseca R, Martorell J and Corbalan R 1995 Second-harmonic generation in local modes of a truncated periodic structure Opt. Lett. 20 1746-8
59. Uhlenbeck K 1976 Genetic properties of eigenfunctions Am. J. Math. 98 1059-78
60. Weiner A M, Kan'an A M and Leaird D E 1998 High-efficiency blue generation by frequency doubling of femtosecond pulses in a thick nonlinear crystal Opt. Lett. 23 1441-3
61. Whitham G 1984 Linear and Nonlinear Waves (New York: Wiley)
62. Yariv A. and Yeh P. 1984 Optical Waves in Crystals (New York: Wiley)
63. Yasui T and Kosiba M 2001 Three-dimensional vector beam-propagation method for second harmonic generation analysis J. Lightwave Technol. 19 780-5
64. Hheng Z and Weiner A M 2001 Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms Chem. Phys. 267 161-71
65. Zhu Y and Ming N 1999 Dielectric superlattices for nonlinear optical effects Opt. Quantum. Electron. 31 1093-128