Polarization coupling and pattern selection in a type-II optical parametric oscillator

Gonzalo Izús; Maxi San Miguel; Daniel Walgraef

doi:10.1103/PhysRevE.66.036228

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Polarization coupling and pattern selection in a type-II optical parametric oscillator

Gonzalo Izús^*, Maxi San Miguel, and Daniel Walgraef^†,‡

Instituto Mediterráneo de Estudios Avanzados, IMEDEA (CSIC-UIB), Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain

^*Permanent address: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata y CONICET, Funes 3350 (7600) Mar del Plata, Argentina. Electronic address: izus@mdp.edu.ar
^†Permanent address: Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Blvd. du Triomphe B.P 231, 1050 Bruxelles, Belgium.
^‡URL: http://www.imedea.uib.es/PhysDept

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Phys. Rev. E 66, 036228 – Published 30 September, 2002

DOI: https://doi.org/10.1103/PhysRevE.66.036228

Abstract

We study the role of a direct intracavity polarization coupling in the dynamics of transverse pattern formation in type-II optical parametric oscillators. Transverse intensity patterns are predicted from a stability analysis, numerically observed, and described in terms of amplitude equations. Standing wave intensity patterns for the two polarization components of the field arise from the nonlinear competition between two concentric rings of unstable modes in the far field. Close to threshold a wavelength is selected leading to standing waves with the same wavelength for the two polarization components. Far from threshold the competition stabilizes patterns in which two different wavelengths coexist.

References (36)

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D. Walgraef, Spatio-Temporal Pattern Formation (Springer-Verlag, New York, 1996).
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F.T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
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R. Zambrini, S.M. Barnett, M. San Miguel, and P. Colet, Phys. Rev. A 65, 023813 (2002).
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Equations (1) have been integrated using the algorithm described in Ref. [35]. We use a grid of $256 \times 256$ samples with grid space $Δ x = Δ y = 0.3125$ and time step $Δ t = 0.01.$ For all cases we use a flat-top super-Gaussian pump beam $E_{0} (x, y) .$
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[c1] M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).

[c2] D. Walgraef, Spatio-Temporal Pattern Formation (Springer-Verlag, New York, 1996).

[c3] G. J. Valcárcel, E. Roldan, and R. Vilaseca, in Proceedings of the Euroconference: Patterns in Nonlinear Optical Systems, Alicante, Spain, 1998, special issue of J. Opt. B: Quantum Semiclassical Opt. 1, 1 (1999).

[c4] F.T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).

[c5] L. Lugiato, A. Gatti, and H. Wiedemann, in Quantum Fluctuations and Nonlinear Optical Patterns, Proceedings of the Les Houches Summer School, Session 63, edited by S. Reynaud, E. Giacobino, and J. Zinn-Justin (Elsevier Science, Amsterdam, 1995).

[c6] G.L. Oppo, M. Brambilla, and L.A. Lugiato, Phys. Rev. A 49, 2028 (1994).

[c7] G.C. de Valcarcel, K. Staliunas, E. Roldan, and V.J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).

[c8] S. Longhi, Phys. Rev. A 53, 4488 (1996); ibid.S. Longhi and A. Geraci 54, 4581 (1996).

[c9] H. Ward, M.N. Ouarzazi, M. Taki, and P. Glorieux, Eur. Phys. J. D 3, 275 (1998).

[c10] P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. Lett. 85, 4506 (2000).

[c11] M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 3843 (1998).

[c12] S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).

[c13] S. Longhi, Phys. Scr. 56, 611 (1997).

[c14] M. Santagiustina, P. Colet, M. San Miguel, and D. Walgaef, Opt. Lett. 23, 1167 (1998).

[c15] K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998).

[c16] G.L. Oppo, A.J. Scroggie, and W.J. Firth, J. Opt. B: Quantum Semiclassical Opt. 1, 133 (1999); Phys. Rev. E 63, 066209 (2001).

[c17] M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B: Quantum Semiclassical Opt. 1, 153 (1999).

[c18] M. Santagiustina, E. Hernández-García, M. San Miguel, A.J. Scroggie, and G.L. Oppo, Phys. Rev. E 65, 036610 (2002).

[c19] L.A. Lugiato and F. Castelli, Phys. Rev. Lett. 68, 3284 (1992).

[c20] A. Gatti et al., Phys. Rev. A 56, 877 (1997).

[c21] R. Zambrini, S.M. Barnett, M. San Miguel, and P. Colet, Phys. Rev. A 65, 023813 (2002).

[c22] M. Vaupel, A. Maître, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999); S. Ducci, N. Trêps, A. Maître, and C. Fabre, Phys. Rev. A 64, 023803 (2001).

[c23] E.J. Mason and N.C. Wong, Opt. Lett. 23, 1733 (1998).

[c24] C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999).

[c25] S. Longhi, Phys. Rev. A 53, 4488 (1996).

[c26] G. Izús, M. Santagiustina, M. San Miguel, and P. Colet, J. Opt. Soc. Am. B 16, 1592 (1999).

[c27] G. Izús, M. San Miguel, and M. Santagiustina, Opt. Lett. 25, 1454 (2000).

[c28] G. Izús, M. San Miguel, and M. Santagiustina, Phys. Rev. E 64, 056231 (2001).

[c29] J. Falk, IEEE J. Quantum Electron. 7, 230 (1971).

[c30] R. Eckardt, C.D. Nabors, W.J. Kozlowsky, and R.L. Byer, J. Opt. Soc. Am. B 8, 646 (1991).

[c31] T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).

[c32] H. Kimble, in Quantum Fluctuations in Quantum Optics–Squeezing and Related Phenomena, Proceedings of the Les Houches Summer School, Session 53, edited by J. Dalibard, J. Raimond, and J. Zinn-Justin (Elsevier Science, Amsterdam, 1992).

[c33] H. Ward, M. Ouarzazi, M. Taki, and P. Glorieux, Phys. Rev. E 63, 016604 (2001).

[c34] Equations (1) have been integrated using the algorithm described in Ref. [35]. We use a grid of $256 \times 256$ samples with grid space $Δ x = Δ y = 0.3125$ and time step $Δ t = 0.01.$ For all cases we use a flat-top super-Gaussian pump beam $E_{0} (x, y) .$

[c35] R. Montagne, E. Hernández-García, A. Amengal, and M. San Miguel, Phys. Rev. E 56, 151 (1997).

[c36] A. Amengual, D. Walgraef, M. San Miguel, and E. Hernández-García, Phys. Rev. Lett. 76, 1956 (1996).

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Polarization coupling and pattern selection in a type-II optical parametric oscillator

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