发表机构
Landau Institute for Theoretical Physics RAS（朗道理论物理研究所俄罗斯科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究理论分析球形布拉格谐振腔中光波的弱非线性径向隧穿，构建描述中心模与壳层模相互作用的哈密顿系统，揭示隧穿耦合不对称参数对非线性动力学行为的调控规律。
AI 中文摘要
本文从理论上研究了球形介质布拉格谐振腔中光波的弱非线性径向隧穿机制，该谐振腔包含一组具有不同方位角数$l\geq 1$的“壳层”本征模（包括TE和TM模），这些模式集中在布拉格结构的缺陷附近，与原点相隔若干层。谐振腔中心存在一个$l=1$的单一径向模式，可为TM或TE模。在主近似下，克尔型非线性仅对中心模起作用，而所有壳层模式均处于线性区域。隧穿发生在中心模与具有相同对称性的$l=1$壳层模之间。光场动力学的非平凡部分由一个关于复矢量${\bf C}_{1}(t)$和${\bf C}_{2}(t)$的常微分方程哈密顿系统描述，这两个复矢量分别决定了中心和壳层处波结构的幅值与空间取向。根据隧穿耦合的“不对称参数”的不同，该系统会表现出不同形式的非线性行为。
英文摘要
A weakly nonlinear regime of radial tunneling is theoretically considered for a light wave in a spherical dielectric Bragg resonator containing a set of ``shell'' eigenmodes (both TE and TM) with different azimuthal numbers $l\geqslant 1$, which are concentrated near a defect of the Bragg structure, several layers away from the origin. Also, a single mixed radial mode with $l=1$ is located near the resonator center, either TM or TE. Nonlinearity of Kerr type in the main approximation is actual for the central mode only, while all the shell modes remain in the linear regime. The tunneling occurs between the central mode and the shell $l=1$ mode of the same symmetry. Nontrivial part of the dynamics of optical field is described by a Hamiltonian system of ordinary differential equations for complex vectors ${\bf C}_{1}(t)$ and ${\bf C}_{2}(t)$, which determine the magnitude and spatial orientation of the wave structures at the center and at the shell, respectively. Depending on ``asymmetry parameter'' of tunnel coupling, the system demonstrates different variants of nonlinear behavior.
Comments6 pages, 7 figures, more explanations added
