Second harmonic generation: The solution for an amplitude-modulated initial pulse

Optics Communications

Volumn 150, Issue 1-6, 1998, Pages 363-371

  Steudel, H ^a   De Morisson Faria, Carla Figueira ^b   Paris, M G A ^c   Kamchatnov, A M ^d   Steuernagel, O ^e  

^a HUMBOLDT UNIVERSITY   (Germany)

^b MAX BORN INSTITUT   (Germany)

^c UNIVERSITY OF PAVIA   (Italy)

^d INSTITUTE OF SPECTROSCOPY   (Russian Federation)

^e PRINCETON UNIVERSITY   (United States)

Author keywords

Analytical solutions; Liouville equation; Second harmonic generation; Ultrashort optical pulses

Indexed keywords

APPROXIMATION THEORY; INTEGRATION; LASER PULSES; LIGHT MODULATION; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

AMPLITUDE MODULATED FUNDAMENTAL WAVES; AMPLITUDE MODULATED INITIAL PULSES; INITIAL VALUE PROBLEMS; LIOUVILLE EQUATION; SCHRODINGER EQUATION; ULTRASHORT OPTICAL PULSES;

SECOND HARMONIC GENERATION;

EID: 0032069878     PISSN: 00304018     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0030-4018(98)00100-X     Document Type: Article

References (30)

1. P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett. 7 (1961) 118.
2. R.W. Terhune, P.D. Maker, C.M. Savage, Appl. Phys. Lett. 2 (1963) 54.
3. J.A. Armstrong, N. Bloembergen, J. Ducuing, P.S. Pershan, Phys. Rev. 127 (1962) 1918.
4. E. Sidick, A. Knoesen, A. Dienes, J. Opt. Soc. Am. B 12 (1995) 1704.
5. V. Krylov, A. Rebane, A.G. Kalintsev, H. Schwoerer, U.P. Wild, Optics Lett. 20 (1995) 198.
6. J. Liouville, J. Math. Pure Appl. 18 (1853) 71.
7. F.G. Bass, V.G. Sinitsyn, Ukrain. Fis. Shourn. 17 (1972) 124, in Russian.
8. W.H. Glenn, IEEE J. Quantum Electron. QE-5 (1969) 284.
9. A.L. Aleksandrovskii, S.A. Akhmanov, V.A. D'yakov, N.I. Zheludev, V.I. Pryalkin, Sov. J. Quantum Electron. 15 (1985) 885.
10. T.R. Zhang, H. Ro Choo, M.C. Downer, Appl. Optics 29 (1990) 3927.
11. S.H. Ashworth, M. Joschko, M. Wörner, E. Riedle, T. Elsässer, Optics Lett. 20 (1995) 2120.
12. S. Szatmari, P. Simon, M. Feuerhake, Optics Lett. 21 (1996) 1150.
13. S.A. Akhmanov, A.S. Chirkin, K.N. Drabovich, A.I. Kovrigin, R.V. Khokhlov, A.P. Sukhorukov, IEEE J. Quantum Electron. QE-4 (1968) 598; see also Y.R. Shen, The Principles of Nonlinear Optics, section 7.6, Wiley, New York, 1984.
14. S.A. Akhmanov, A.S. Chirkin, K.N. Drabovich, A.I. Kovrigin, R.V. Khokhlov, A.P. Sukhorukov, IEEE J. Quantum Electron. QE-4 (1968) 598; see also Y.R. Shen, The Principles of Nonlinear Optics, section 7.6, Wiley, New York, 1984.
15. S.A. Akhmanov, V.A. Vysloukh, A.S. Chirkin, Optics of Femtosecond Laser Pulses, American Institute of Physics, New York, 1992, and references therein.
16. D.J. Kaup, Stud. Appl. Math. 59 (1978) 25.
17. K. Khusnutdinova, H. Steudel, to be published in J. Math. Phys.
18. See e.g. G.I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Optics Lett. 18 (1993) 13; M.M. Fejer, Phys. Today 47 (1994) 25, and references therein; E. Sidick, A. Dienes, A. Knoesen, J. Opt. Soc. Am. B 12 (1995) 1713; A. Otomo, G.I. Stegeman, W.H.G. Horsthuis, G.R. Möhlman, Appl. Phys. Lett. 68 (1996) 3683;
19. See e.g. G.I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Optics Lett. 18 (1993) 13; M.M. Fejer, Phys. Today 47 (1994) 25, and references therein; E. Sidick, A. Dienes, A. Knoesen, J. Opt. Soc. Am. B 12 (1995) 1713; A. Otomo, G.I. Stegeman, W.H.G. Horsthuis, G.R. Möhlman, Appl. Phys. Lett. 68 (1996) 3683;
20. See e.g. G.I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Optics Lett. 18 (1993) 13; M.M. Fejer, Phys. Today 47 (1994) 25, and references therein; E. Sidick, A. Dienes, A. Knoesen, J. Opt. Soc. Am. B 12 (1995) 1713; A. Otomo, G.I. Stegeman, W.H.G. Horsthuis, G.R. Möhlman, Appl. Phys. Lett. 68 (1996) 3683;
21. See e.g. G.I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Optics Lett. 18 (1993) 13; M.M. Fejer, Phys. Today 47 (1994) 25, and references therein; E. Sidick, A. Dienes, A. Knoesen, J. Opt. Soc. Am. B 12 (1995) 1713; A. Otomo, G.I. Stegeman, W.H.G. Horsthuis, G.R. Möhlman, Appl. Phys. Lett. 68 (1996) 3683;
22. M.A. Arbore, O. Marco, M.M. Fejer, Optics Lett. 22 (1997) 865.
23. F. Calogero, in: V.E. Zakharov (Ed.), What is integrability, Springer, Berlin, 1991, p. 1.
24. I. Drevensek, R. Torre, M. Copic, Molec. Cryst. 251 (1994) 101; G. Assanto, I. Torelli, Optics Comm. 119 (1995) 143.
25. I. Drevensek, R. Torre, M. Copic, Molec. Cryst. 251 (1994) 101; G. Assanto, I. Torelli, Optics Comm. 119 (1995) 143.
26. E. Hille, Ordinary Differential Equations in the Complex Plane, Wiley, New York, 1976, p. 1.
27. This type of equation was first investigated in connection with the theory of lunar motion by G.W. Hill, Acta Math. 8 (1886) 1; it is also well known in the quantum theory of metals and semiconductors, see, e.g., L.W. Casperson, Phys. Rev. A 30 (1984) 2749; S.M. Wu, C.C. Shih, Phys. Rev. A 32 (1985) 3736; K. Takayama, Phys. Rev. A 34 (1986) 4408.
28. This type of equation was first investigated in connection with the theory of lunar motion by G.W. Hill, Acta Math. 8 (1886) 1; it is also well known in the quantum theory of metals and semiconductors, see, e.g., L.W. Casperson, Phys. Rev. A 30 (1984) 2749; S.M. Wu, C.C. Shih, Phys. Rev. A 32 (1985) 3736; K. Takayama, Phys. Rev. A 34 (1986) 4408.
29. This type of equation was first investigated in connection with the theory of lunar motion by G.W. Hill, Acta Math. 8 (1886) 1; it is also well known in the quantum theory of metals and semiconductors, see, e.g., L.W. Casperson, Phys. Rev. A 30 (1984) 2749; S.M. Wu, C.C. Shih, Phys. Rev. A 32 (1985) 3736; K. Takayama, Phys. Rev. A 34 (1986) 4408.
30. This type of equation was first investigated in connection with the theory of lunar motion by G.W. Hill, Acta Math. 8 (1886) 1; it is also well known in the quantum theory of metals and semiconductors, see, e.g., L.W. Casperson, Phys. Rev. A 30 (1984) 2749; S.M. Wu, C.C. Shih, Phys. Rev. A 32 (1985) 3736; K. Takayama, Phys. Rev. A 34 (1986) 4408.