Excitability and Elliptically Polarized Standing Waves in the Vector Complex Ginzburg Landau Equation for a Birefrigent Cavity

M. San Miguel, A. Amenqual, D. Walgraef, E. Hernández‐García
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Abstract

Transverse pattern formation in dcgenerate optical parametric oscillation (DOPO) is a subject of' present interest [ I ] . In this work we carry out an analytical study of pattern formation i n DOPO and degenerate lour-wave mixing (DFWM), which is complemented by numerical integration of the microscopic cquations of both systems. In the limit of small pump and signal detunings both systems are described by the real SwiftHohenberg equation (SHE). This broadens the range of similarities existing between DOPO and DFWM, which comprise both temporal instabilities and quantum properties. On the other hand the derivation of the SHE gives support io the already observed leading role of rolls in DOPO 111. l'he predictions about the stability of these patterns given by the SHE are in good agreement with numerical simulations. Moreover. i t has been recently shown that the SHE contains stable hexagons with an additional zero-mode [ 2 ] . which have been also found by numerical simulation. Contrarily, for small signal and large pump detunings the SHE is modified by the appearance of additional nonlinear tenns, which signals the existence of a nonlinear resonance (NLR). These additional ternis are however different iii DOPO and DFWM, limiting the similarities existing between both systems.
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双冷腔矢量复金兹堡-朗道方程中的激发态和椭圆极化驻波
在退化光学参量振荡(DOPO)中横向图样的形成是一个“当前感兴趣”的主题[1]。在这项工作中,我们对DOPO和简并低波混频(DFWM)的模式形成进行了分析研究,并对这两个系统的微观方程进行了数值积分。在小泵浦和信号失谐的极限下,这两个系统都用真实的SwiftHohenberg方程(SHE)来描述。这扩大了DOPO和DFWM之间存在的相似性范围,包括时间不稳定性和量子特性。另一方面,SHE的推导支持了在dopo111中已经观察到的卷的主导作用。SHE给出的关于这些模式稳定性的预测与数值模拟很好地吻合。此外。最近已经证明,SHE包含具有附加零模的稳定六边形[2]。数值模拟也发现了这一点。相反,对于小信号和大泵浦失谐,SHE被附加非线性张力的出现所修正,这表明存在非线性共振(NLR)。然而,DOPO和DFWM的这些附加条件是不同的,限制了这两个系统之间存在的相似性。
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