Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators

Physica D: Nonlinear Phenomena

Volumn 206, Issue 1-2, 2005, Pages 62-81

  Moore, Richard O ^a   Promislow, Keith ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Nonlinear Schr dinger equation; Optical parametric oscillator; Renormalization group

Indexed keywords

ABSORPTION; COMPUTER SIMULATION; HEATING; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; REFRACTIVE INDEX; THERMAL LOAD;

ENVELOPE EQUATIONS; NONLINEAR SCHRÖDINGER EQUATION; OPTICAL PARAMETRIC OSCILLATOR; RENORMALIZATION GROUP;

PARAMETRIC OSCILLATORS;

EID: 19944370883     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.04.015     Document Type: Article

References (26)

1. N.V. Alexeeva, I.V. Barashenkov, and D.E. Pelinovsky Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability Nonlinearity 12 1999 103 140
2. G. Arisholm, E. Lippert, G. Rustad, and K. Stenersen Efficient conversion from 1 to 2 μ m by a KTP-based ring optical parametric oscillator Opt. Lett. 27 15 2002 1336 1338
3. I.V. Barashenkov, M.M. Bogdan, and V.I. Korobov Stability diagram of the phase-locked solitons in the parametrically driven, damped nonlinear Schrödinger equation Europhys. Lett. 15 2 1991 113 118
4. I.V. Barashenkov, and E.V. Zemlyanaya Traveling solitons in the damped-driven nonlinear Schrödinger equation SIAM J. Appl. Math. 64 3 2004 800 818
5. I.V. Barashenkov, E.V. Zemlyanaya, and M. Bär Traveling solitons in the parametrically driven nonlinear Schrödinger equation Phys. Rev. E 64 2001 016603
6. I. Barashenkov, and E. Zamlyanaya Stable complexes of parametrically driven, damped nonlinear Schrödinger solitons Phys. Rev. Lett. 83 1999 2568 2571
7. P.A.C.-Y. Chang, Modulational stability of oscillatory pulse solutions of the parametrically forced nonlinear Schrödinger equation, Ph.D. thesis, Simon Fraser University, December 2003.
8. L.Y. Chen, N. Goldenfeld, and Y. Oono Renormalization-group theory and variational calculations for propagating fronts Phys. Rev. E 49 5 1994 4502 4511
9. L.Y. Chen, N. Goldenfeld, and Y. Oono Renormalization group and singular perturbations: multiple scales, boundary layers, and reductive perturbation theory Phys. Rev. E 54 1 1996 376 394
10. R.E. Lee Deville, A. Harkin, K. Josic, T. Kaper, Asymptotic normal form theory for nonautonomous equations and its connection with a renormalization group method, SIAM J. Appl. Dyn. Syst., September 2004, submitted for publication.
11. M. Ebrahinzadeh Parametric light generation Philos. Trans. Roy. Soc. Lond. A 361 1813 2003 2731 2750
12. S.I. Ei, K. Fujii, and T. Kunihiro Renormalization-group method for reduction of evolution equations; invariant manifolds and envelopes Ann. Phys. 280 2 2000 236 298
13. D. Henry Geometric theory of semilinear parabolic equations, volume 840 of Lecture Notes in Mathematics, Springer-Verlag, New York, 1981.
14. D.H. Jundt Temperature-dependent Sellmeier equation for the index of refraction, n (e), in congruent lithium niobate Opt. Lett. 22 20 1997 1553 1555
15. T. Kapitula, and B. Sandstede Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. Physica D 124 1-3 1998 58
16. T.J. Kulp, S.E. Bisson, R.P. Bambha, T.A. Reichardt, U.B. Goers, K.W. Aniolek, D.A.V. Kliner, B.A. Richman, K.M. Armstrong, R. Sommers, R. Schmitt, P.E. Powers, O. Levi, T. Pinguet, M. Fejer, J.P. Koplow, L. Goldberg, and T.G. McRae The application of quasi-phase-matched parametric light sources to practical infrared chemical sensing systems Appl. Phys. B 75 2-3 2002 317 327
17. R.O. Moore, A study of optical devices with parametric gain, Ph.D thesis, Northwestern University, Engineering Sciences and Applied Mathematics, 2001.
18. R.O. Moore, G. Biondini, and W.L. Kath Self-induced thermal effects and modal competition in continuous-wave optical parametric oscillators J. Opt. Soc. Am. B 19 4 2002 802 811
19. K. Promislow A renormalization method for modulational stability of quasi-steady patterns in dispersive systems SIAM J. Anal. Math. Anal. 33 6 2002 1455 1482
20. K. Promislow, and J.N. Kutz Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator Nonlinearity 13 3 2000 675 698
21. A. Sanchez, and A.R. Bishop Collective coordinates and length-scale competition in spatially inhomogeneous soliton-bearing equations SIAM Rev. 40 3 1998 579 615
22. B. Sandstede Stability of multiple-pulse solutions Trans. Amer. Math. Soc. 350 2 1998 429 472
23. B. Sandstede, and A. Scheel Defects in oscillatory media: toward a classification SIAM J. Appl. Dyn. Sys. 3 1 2004 1 68
24. J.M. Song, R. Jagannathan, D.L. Stokes, P.M. Kasili, M. Panjehpour, M.N. Phan, B.F. Overholt, R.C. DeNovo, X.G. Pan, R.J. Lee, and V.D. Tuan Development of a fluorescence detection system using optical parametric oscillator (OPO) laser excitation for in vivo diagnosis Tech. Cancer Res. Treat. 2 6 2003 515 523
25. M.M.J.W. van Herpen, S.E. Bisson, and F.J.M. Harren Continuous-wave operation of a single-frequency optical parametric oscillator at 4-5 μ m based on periodically poled LiNbO3 Opt. Lett. 28 24 2003 2497 2499
26. M. Ziane On a certain renormalization group method J. Math. Phys. 41 5 2000 3290 3299