Light propagation in nonlinear waveguide and classical two-dimensional oscillator

Physica A: Statistical Mechanics and its Applications

Volumn 256, Issue 3-4, 1998, Pages 485-498

  Angelow, A ^a  

^a INSTITUTE OF SOLID STATE PHYSICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; LIGHT TRANSMISSION; OPTICAL WAVEGUIDES; OSCILLATORS (ELECTRONIC);

TWO DIMENSIONAL NONSTATIONARY OSCILLATOR;

QUANTUM OPTICS;

EID: 0032141285     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00198-8     Document Type: Article

References (43)

1. G.S. Agarwal, S.A. Kumar, Phys. Rev. Lett. 67 (26) (1991) 3665-3668.
2. L.S. Brown, Phys. Rev. Lett. 66 (5) (1991) 527-529.
3. W. Paul, Rev. Mod. Phys. 62 (3) (1990) 531-540.
4. F.L. Li, Phys. Lett. A 168 (1992) 400.
5. S.J. Wang, F.L. Li, A. Weiguni, Phys. Lett. A 180 (1993) 189-196.
6. F.L. Li, S.J. Wang, A. Weiguny, D.L. Lin, J. Phys. A 27 (1994) 985-992.
7. A.L. de Brito, A.N. Chaba, B. Baseia, Phys. Rev. A 52 (2) (1995) 1518-1524.
8. J.-Y. Ji, J.K. Kim, S.P. Kim, Phys. Rev. A 51 (5) (1995) 4268-4271; H.-C. Kim, M.-H. Lee, J.-Y. Ji, J.K. Kim, Phys. Rev. A 53 (6) (1996) 3767-3772.
9. J.-Y. Ji, J.K. Kim, S.P. Kim, Phys. Rev. A 51 (5) (1995) 4268-4271; H.-C. Kim, M.-H. Lee, J.-Y. Ji, J.K. Kim, Phys. Rev. A 53 (6) (1996) 3767-3772.
10. A.N. Seleznyova, Phys. Rev. A 51 (2) (1995) 950-959.
11. A.F.R. de Toledo Piza, Phys. Rev. A 51 (2) (1995) 1612-1616. The second pair variables in this work relevant to ours are: {Q = σ,P = Π}.
12. Y.-Z. Lai, J.-Q. Liang, H.J.W. Müler-Kirtsten, J.-G. Zhou, Phys. Rev. A 53 (5) (1996) 3691-3693.
13. N.J. Gunther, P.G. Leach, J. Math. Phys. 18 (4) (1977) 572; A.K. Rajagopal, J. Marshal, Phys. Rev. A 26 (1982) 2977; J. Hartley, H. Ray, Phys. Rev. D 25 (1982) 382; X. Jing-Bo, Q.T. Zheng, G.X. Chun, Europhys. Lett. 15 (2) (1991) 119; J.B. Xu, T.Z. Quang, X.C. Gao, Phys. Lett. A 159 (1991) 113.
14. N.J. Gunther, P.G. Leach, J. Math. Phys. 18 (4) (1977) 572; A.K. Rajagopal, J. Marshal, Phys. Rev. A 26 (1982) 2977; J. Hartley, H. Ray, Phys. Rev. D 25 (1982) 382; X. Jing-Bo, Q.T. Zheng, G.X. Chun, Europhys. Lett. 15 (2) (1991) 119; J.B. Xu, T.Z. Quang, X.C. Gao, Phys. Lett. A 159 (1991) 113.
15. N.J. Gunther, P.G. Leach, J. Math. Phys. 18 (4) (1977) 572; A.K. Rajagopal, J. Marshal, Phys. Rev. A 26 (1982) 2977; J. Hartley, H. Ray, Phys. Rev. D 25 (1982) 382; X. Jing-Bo, Q.T. Zheng, G.X. Chun, Europhys. Lett. 15 (2) (1991) 119; J.B. Xu, T.Z. Quang, X.C. Gao, Phys. Lett. A 159 (1991) 113.
16. N.J. Gunther, P.G. Leach, J. Math. Phys. 18 (4) (1977) 572; A.K. Rajagopal, J. Marshal, Phys. Rev. A 26 (1982) 2977; J. Hartley, H. Ray, Phys. Rev. D 25 (1982) 382; X. Jing-Bo, Q.T. Zheng, G.X. Chun, Europhys. Lett. 15 (2) (1991) 119; J.B. Xu, T.Z. Quang, X.C. Gao, Phys. Lett. A 159 (1991) 113.
17. N.J. Gunther, P.G. Leach, J. Math. Phys. 18 (4) (1977) 572; A.K. Rajagopal, J. Marshal, Phys. Rev. A 26 (1982) 2977; J. Hartley, H. Ray, Phys. Rev. D 25 (1982) 382; X. Jing-Bo, Q.T. Zheng, G.X. Chun, Europhys. Lett. 15 (2) (1991) 119; J.B. Xu, T.Z. Quang, X.C. Gao, Phys. Lett. A 159 (1991) 113.
18. I.A. Malkin, V.I. Manko, D.A. Trifonov, J. Math. Phys. 14 (5) (1973) 576; I.A. Malkin, V.I. Manko, D.A. Trifonov, Phys. Rev. D 2 (8) (1970) 1371-1385; I.A. Malkin, V.I. Manko, D.A. Trifonov, Nuovo Cimento A4 (1971) 773.
19. I.A. Malkin, V.I. Manko, D.A. Trifonov, J. Math. Phys. 14 (5) (1973) 576; I.A. Malkin, V.I. Manko, D.A. Trifonov, Phys. Rev. D 2 (8) (1970) 1371-1385; I.A. Malkin, V.I. Manko, D.A. Trifonov, Nuovo Cimento A4 (1971) 773.
20. I.A. Malkin, V.I. Manko, D.A. Trifonov, J. Math. Phys. 14 (5) (1973) 576; I.A. Malkin, V.I. Manko, D.A. Trifonov, Phys. Rev. D 2 (8) (1970) 1371-1385; I.A. Malkin, V.I. Manko, D.A. Trifonov, Nuovo Cimento A4 (1971) 773.
21. A. Holz, Nuovo Cimento Lett. A 4 (1970) 1319.
22. D.A. Trifonov, Coherent states and uncertainty relation, Phys. Lett. A 48 (3) (1974) 165-166.
23. 2 should be replaced in their expressions in formulas (18) in the first reference (respectively in (15) in the second reference). Note that the difference between these formulas and the first two expressions in (24) in our article is due to the different definitions of the Hamiltonian's coefficients.
24. 2 should be replaced in their expressions in formulas (18) in the first reference (respectively in (15) in the second reference). Note that the difference between these formulas and the first two expressions in (24) in our article is due to the different definitions of the Hamiltonian's coefficients.
25. A. Angelow, D.A. Trifonov, Schrodinger Covariance States in Anisotropic Waveguide, Preprint ICTP, IC/95/44 Trieste, Italy, 1995.
26. I. Zlatev, A. Nikolov, Theoretical Mechanics, 1 N.I., Sofia, 1981.
27. C.F. Lo, Nuovo Cimento B 105 (5) (1990) 497-506; C.F. Lo, J. Phys. A 23 (1990) 1155; C.F. Lo, Nuovo Cimento D 13 (1991) 1279; C.F. Lo, Europhys. Lett. 24 (1993) 319; C.F. Lo, Nuovo Cimento Ser 2 (9) (1995) 1015.
28. C.F. Lo, Nuovo Cimento B 105 (5) (1990) 497-506; C.F. Lo, J. Phys. A 23 (1990) 1155; C.F. Lo, Nuovo Cimento D 13 (1991) 1279; C.F. Lo, Europhys. Lett. 24 (1993) 319; C.F. Lo, Nuovo Cimento Ser 2 (9) (1995) 1015.
29. C.F. Lo, Nuovo Cimento B 105 (5) (1990) 497-506; C.F. Lo, J. Phys. A 23 (1990) 1155; C.F. Lo, Nuovo Cimento D 13 (1991) 1279; C.F. Lo, Europhys. Lett. 24 (1993) 319; C.F. Lo, Nuovo Cimento Ser 2 (9) (1995) 1015.
30. C.F. Lo, Nuovo Cimento B 105 (5) (1990) 497-506; C.F. Lo, J. Phys. A 23 (1990) 1155; C.F. Lo, Nuovo Cimento D 13 (1991) 1279; C.F. Lo, Europhys. Lett. 24 (1993) 319; C.F. Lo, Nuovo Cimento Ser 2 (9) (1995) 1015.
31. C.F. Lo, Nuovo Cimento B 105 (5) (1990) 497-506; C.F. Lo, J. Phys. A 23 (1990) 1155; C.F. Lo, Nuovo Cimento D 13 (1991) 1279; C.F. Lo, Europhys. Lett. 24 (1993) 319; C.F. Lo, Nuovo Cimento Ser 2 (9) (1995) 1015.
32. H.R. Lewis, W.B. Risenfeld, J. Math. Phys. 10 (1969) 1458.
33. C.F. Lo, Phys. Rev. A 43 (1) (1991) 404-409.
34. Cofluctuant (or Covariance) states with a non-zero cofluctuation are a sub-class of Schrödinger minimum uncertainty states, generalized squeezed states, two-photon coherent states e.c. Equivalence between them has been proved for first time in: D.A. Trifonov (Ed.), On the stable evolution of squeezed and correlated states, J. Sov. Laser Res. 12 (5) (1991) 414-420.
35. M.D. Levenson, R.M. Shelby, A. Aspect, M. Reid, D.F. Walls, Phys. Rev. A 32 (3) (1985) 1550-1562.
36. P.D. Drummond, S.J. Carter, J.O.S.A. 4 (10) (1987) 1565-1573; P.D. Drummond, Phys. Rev. A 42 (11) (1990) 6845-6857.
37. P.D. Drummond, S.J. Carter, J.O.S.A. 4 (10) (1987) 1565-1573; P.D. Drummond, Phys. Rev. A 42 (11) (1990) 6845-6857.
38. A. Yariv, Quantum Electronics, 3rd ed., Wiley, New York, 1988; J. Perina, Quantum Statistic of Linear and Nonlinear Optical Phenomena, D. Reidel Publishing Company, Boston, 1984.
39. A. Yariv, Quantum Electronics, 3rd ed., Wiley, New York, 1988; J. Perina, Quantum Statistic of Linear and Nonlinear Optical Phenomena, D. Reidel Publishing Company, Boston, 1984.
40. H.W. Lee, Phys. Lett. A 153 (4,5) (1991) 219-223.
41. C.M. Cheng, P.C. Fung, J. Phys. A 21 (22) (1988) 4115-4131.
42. E. Schrödinger, Um Heisenbergschen unscharfeprinzip, Sonderausgabe aus den sitzungsberichten der preussischen akademie der wissenschaften, Phys. Math. Klasse XIX (1930) 348-356.
43. E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen, Gewöhnliche differentialgleichungen, vol. I., Leipzig, Akademische Verlagsgesellschaft, 1959.