Localized light waves: Paraxial and exact solutions of the wave equation (a review)

Optics and Spectroscopy (English translation of Optika i Spektroskopiya)

Volumn 102, Issue 4, 2007, Pages 603-622

  Kiselev, A P ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC ANALYSIS; GAUSSIAN BEAMS; LIGHT POLARIZATION; WAVE PACKETS; WAVELET ANALYSIS;

BATEMAN FINDINGS; GAUSSIAN LOCALIZATION; LEONTOVICH-FOCK PARABOLIC EQUATION; OPTICAL RADIATION;

WAVE EQUATIONS;

EID: 34248403590     PISSN: 0030400X     EISSN: 15626911     Source Type: Journal    
DOI: 10.1134/S0030400X07040200     Document Type: Article

References (123)

1. T. Brabec and F. Krausz, Rev. Mod. Phys. 72 (2), 545 (2000).
2. J. N. Brittingham, J. Appl. Phys. 54 (3), 1179 (1983).
3. A. P. Kiselev, Radiophys. Quantum Electron. 26 (5), 1014 (1983).
4. R. W. Zhiolkowski, Phys. Rev. A 39 (4), 2005 (1989).
5. P. L. Overfelt, Phys. Rev. A 44 (6), 3941 (1991).
6. A. P. Kiselev and M. V. Perel, J. Math. Phys. 42 (4), 1934 (2000).
7. H. E. Moses and R. N. Prosser, SIAM J. Appl. Math. 50 (5), 1325 (1990).
8. H. Bateman, Proc. London Math. Soc., No. 7, 70 (1909).
9. H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell's Equations (Dover, New York, 1955; Nauka, Moscow, 1958).
10. R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962; Gostekhizdat, Moscow, 1941).
11. V. S. Vladimirov, Equations of Mathematical Physics (2nd ed., Nauka, Moscow, 1971; Dekker, New York, 1971).
12. M. A. Leontovich, Izv. Akad. Nauk SSSR, Ser. Fiz. 8 (10), 16 (1944).
13. M. A. Leontovich and V. A. Fock, J. Phys. USSR 10, 13 (1946).
14. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Nauka, Moscow, 1970; Pergamon, Oxford, 1965).
15. L. A. Vainshtein, Open Resonators and Open Waveguides (Sov. Radio, Moscow, 1966; Colem, Boulder, 1970).
16. H. Kogelnik and T. Li, Proc. IEEE 54 (10), 1312 (1966).
17. H. Kogelnik and T. Li, Appl. Opt. 5 (10), 1550 (1966).
18. V. M. Babič and V. S. Buldyrev, Short-Wavelength Diffraction Theory (Nauka, Moscow, 1972; Springer, New York, 1991).
19. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarsky, Introduction to Statistical Radio Physics (Nauka, Moscow, 1978), Part 2 [in Russian];
20. Principles of Statistical Radiophysics (Springer, Berlin, 1978), Part 4.
21. S. N. Vlasov and V. I. Talanov, Radiophys. Quantum Electron. 38 (1-2), 1 (1995).
22. S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves (Nizhni Novgorod, 1997) [in Russian].
23. V. É. Grikurov and A. P. Kiselev, Radiophys. Quantum Electron. 29 (3), 233 (1986).
24. A. V. Popov and S. A. Khozioskij, USSR Comput. Math. Math. Phys. 17 (2), 238 (1978).
25. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11 (4), 1365 (1975).
26. A. P. Kiselev, Pis'ma Zh. Tekh. Fiz. 10 (22), 1377 (1984)
27. [Sov. Tech. Phys. Lett. 10 (11), 581 (1984)].
28. J. F. Nye and M. V. Berry, Proc. Roy. Soc. (London) A 336, 165 (974).
29. M. Soskin and M. Vasnetsov, Progress in Optics 42, 219 (2001).
30. A. V. Volyar, Ukr. J. Phys. Opt. 3 (2), 69 (2002).
31. J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6 (2004).
32. E. G. Abramochkin and V. G. Volostnikov, Usp. Fiz. Nauk 174 (12), 1273 (2004)
33. [Phys. Usp. 47, (12), 1177 (2004)].
34. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Progress in Optics 47, 291 (2005).
35. A. P. Kiselev, Opt. Spektrosk. 96 (4), 533 (2004)
36. [Opt. Spectrosc. 96 (4), 479 (2004)].
37. A. Wünsche, J. Opt. Soc. Am. 6 (9), 1320 (1989).
38. V. M. Babich and Yu. P. Danilov, Semin. Math., V.A. Steklov. Math. Inst. 15, 23 (1969).
39. A. E. Siegman, Lasers (University Science, Mill Valley, 1986).
40. A. Wünsche, J. Phys. A 33 (8), 1603 (2000).
41. E. G. Abramochkin and V. G. Volostikov, J. Opt. A 6 (5), 157 (2004).
42. F. Gori, C. Guattari, and C. Padovani, Opt. Commun. 64 (6), 491 (1986).
43. J. Durnin and J. Micelli, Phys. Rev. Lett. 58, 1499 (1987).
44. P. V. Adamson, Quantum Electron. (Moscow) 30 (4), 365 (2000).
45. C. J. R. Sheppard, J. Opt. Soc. Am. A 18 (10), 2594 (2001).
46. L. N. Pyatnitskii, Rlasma Phys. Rep. 27 (9), 799 (2001).
47. C. J. R. Sheppard, Proc. IEEE Microwaves Opt. Acoust. 2 (5), 163 (1978).
48. B. W. Shore and P. L. Knight, Laser Phys. 15 (10), 1448 (2005).
49. Yu. A. Anan'ev, Opt. Spektrosk. 64 (6), 1211 (1988)
50. [Opt. Spectrosc. 64 (6), 722 (1988)].
51. J. C. Gutiérrez-Vega and M. A. Bandres, J. Opt. Soc. Am. A 22 (2), 289 (2005).
52. M. A. Bandres, Opt. Lett. 30 (16), 2155 (2005).
53. M. A. Porras, Phys. Rev. E 59 (1), 1088 (1998).
54. M. A. Porras, R. Borghi, and M. Santarsiero, Phys. Rev. E 62 (4), 5729 (2000).
55. J. Lekner, J. Opt. A 6 (1), 146 (2004).
56. P. Hillion, Acta Appl. Math. 30 (1), 35 (1993).
57. A. P. Kiselev, J. Math. Sci. 117 (2), 3945 (2003).
58. A. P. Kiselev, Math. Notes 79 (4), 587 (2006).
59. P. A. Bélanger, J. Opt. Soc. Am. A 1 (7), 723 (1984).
60. A. Sezginer, J. Appl. Phys. 57 (3), 678 (1986).
61. A. P. Kiselev and M. V. Perel, in Proceedings of the International Seminar "Day on Diffraction'97", Ed. by V. M. Babich (S.-Peterb. Gos. Univ., St. Petersburg, 1997), pp. 86-90.
62. A. P. Kiselev and M. V. Perel', Opt. Spektrosk. 86 (3), 357 (1999)
63. [Opt. Spectrosc. 86 (3), 307 (1999)].
64. A. P. Kiselev and M. V. Perel, J. Math. Sci. 96 (4), 3355 (1999).
65. A. P. Kiselev, J. Phys. A 36 (23), L345 (2003).
66. A. P. Kiselev, Wave Motion 29 (2), 111 (1989).
67. V. V. Borisov, Eur. Phys. J. B 6 (2), 163 (1998).
68. V. V. Borisov and A. B. Utkin, Eur. Phys. J. B 21 (4), 477 (2001).
69. A. P. Kiselev, J. Electromagn. Waves Appl. 17 (1), 115 (2003).
70. I. M. Besieris, A. M. Shaarawi, and A. M. Attia, Progress in Electromagnetic Research 48, 201 (2004).
71. A. P. Kiselev, J. Sov. Math. 11 (3), 444 (1979).
72. A. P. Kiselev, J. Sov. Math. 11 (5), 744 (1979).
73. M. V. Fedoryuk, The Steepest Descent Method (Nauka, Moscow, 1977) [in Russian].
74. P. Hillion, Opt. Commun. 227 (1-3), 57 (2003).
75. P. D. Lax and R. S. Phillips, Scattering Theory (Academic, New York, 1967; Mir, Moscow, 1971).
76. A. S. Blagoveshchenskiǐ, in Proceedings of the V All-Union Symposium on Diffraction and Wave Propagation (Nauka, Leningrad, 1971), pp. 29-35 [in Russian].
77. A. S. Blagovestchenskii and A. A. Novitskaya, in Proceedings of the Day on Diffraction Millenium Workshop (S.-Peterb. Gos. Univ., St. Petersburg, 2000), pp. 34-39.
78. A. S. Blagovestchenskii, in Abstracts of the Day on Diffraction'01 International Seminar (S.-Peterb. Gos. Univ., St. Petersburg, 2001), p. 16.
79. A. A. Izmest'ev, Radiophys. Quantum Electron. 13 (9), 1062 (1970).
80. G. A. Deschamps, Electron. Lett. 7 (23), 684 (1971).
81. L. B. Felsen, J. Opt. Soc. Am. 66 (8), 751 (1976).
82. S. I. Shin and L. B. Felsen, J. Opt. Soc. Am. 67 (5), 699 (1977).
83. R. W. Ziolkowski, J. Math. Phys. 26 (4), 861 (1985).
84. G. Kaiser, J. Phys. A 36 (30), R291 (2003).
85. G. Rodrfguez-Moralez, Opt. Lett. 29 (5), 430 (2004).
86. E. Heyman and L. B. Felsen, J. Opt. Soc. Am. A18 (7), 1588 (2001).
87. J. Y. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 39 (1), 19 (1992).
88. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62 (3), 4261 (2000).
89. V. V. Borisov and A. P. Kiselev, Appl. Math. Lett. 13 (1), 83 (2000).
90. V. V. Borisov, J. Phys. A 34 (34 P), 6565 (2001).
91. P. Hillion, Eur. Phys. J. B 30 (4), 527 (2002).
92. E. Recami, M. Zamboni-Rached, K. Z. Nobrega, et al., IEEE J. Select. Topics Quant. Electron 9 (1), 59 (2003).
93. P. Saari, Atti Della Fondazione Giorgio Ronci 58 (6), 729 (2003).
94. P. Saari and K. Reivelt, Phys. Rev. E 69 (3), 036612 (2004).
95. A. Ciattoni, C. Conti, and P. Di Porto, Phys. Rev. E 69 (3), 036608 (2004).
96. B. G. Klevitskiǐ and I. P. Korshunov, J. Commun. Technol. Electr. 47 (4), 347 (2002).
97. N. N. Rozanov, Usp. Fiz. Nauk 175 (2), 181 (2005)
98. [Phys. Usp. 42, 167 (2005)].
99. I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 72, 056612 (2005).
100. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th English ed. (Nauka, Moscow, 1973; Pergamon Press, Oxford, 1987).
101. Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Nauka, Moscow, 1980) [in Russian].
102. V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation in Quantum Mechanics (Nauka, Moscow, 1976; Reidel, Dordrecht, 1981).
103. V. M. Babich and V. V. Ulin, J. Sov. Math. 20 (1), 1749 (1982).
104. V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, Spatiotemporal Ray Method (Leningr. Gos. Univ., Leningrad, 1985) [in Russian].
105. V. M. Babich and V. V. Ulin, J. Sov. Math. 24 (3), 269 (1984).
106. J. Ralston, MAA Studies in Mathematics 23, 206 (1982).
107. J. S. B. de Freitas and M. M. Popov, J. Math. Sci. 138 (2), 5590 (2006).
108. M. M. Popov, Ray Theory and Gaussian Beams for Geophysics (EDUFBA, Salvador-Bahia, 2002).
109. V. P. Maslov, The Complex WKB Method for Nonlinear Equations: I. Linear Theory (Nauka, Moscow, 1977; Birkhäuser, Basel, 1994).
110. A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, J. Math. Phys. 31 (10), 2511 (1990).
111. I. M. Besieris, A. M. Shaarawi, and L. P. Ligthart, J. Electromagn. Waves Appl. 14 (5), 593 (2000).
112. A. B. Shvartsburg, Usp. Fiz. Nauk 175 (8), 833 (2005)
113. [Phys. Usp. 48 (8), 797 (2005)].
114. M. V. Perel' and I. V. Fialkovsky, J. Math. Sci. 117 (2), 3994 (2003).
115. A. P. Kiselev and M. V. Perel', Diff. Eqs. 38 (8), 1206 (2002).
116. G. B. Witham, Linear and Nonlinear Waves (Wiley, New York, 1974; Mir, Moscow, 1977).
117. M. V. Perel and I. V. Fialkovsky, in Nonlinear Acoustics in the Beginning of the 21st Century, Ed. by O. V. Rudenko and O. A. Sapozhnikov (Mosk. Gos. Univ., Moscow, 2002), pp. 113-116.
118. V. M. Babich and M. M. Popov, Radiophys. Quantum Electron. 32 (12), 1063 (1989).
119. F. Gori, Opt. Commun. 107 (5-6), 335 (1994).
120. R. A. Egorchenkov and Yu. A. Kravtsov, Radiophys. Quantum Electron. 43 (10), 798 (2000).
121. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992).
122. M. V. Perel and M. S. Sidorenko, in Proceedings of the 6th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, 2003, Ed. by G. C. Cohen et al. (Springer, Berlin, 2003), pp. 794-798.
123. M. V. Perel and M. S. Sidorenko, http://arxiv.org/abs/math-ph/0701051.