Using nonlinear coupled mode equations, the spectral properties of long-period fiber grating are studied analytically taking into account the Kerr type optical nonlinearity in the medium. The nonlinear coupled-mode equations were solved for co-propagating core and cladding mode amplitudes and expressions for transmittivity and phase factor at high excitation intensity are obtained. It is observed that the resonance wavelength of grating shifts towards higher wavelength side with increasing excitation intensity. Also, the minimum transmittivity of the grating shows oscillating behavior with increasing grating length, whereas the phase of the transmitted wave increases monotonically with length at high input intensities.

中文翻译：

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用于光波通信应用的长周期光纤光栅的强度相关光谱特性

利用非线性耦合模式方程，考虑到介质中的克尔型光学非线性，分析研究了长周期光纤光栅的光谱特性。求解了共传播纤芯和包层模幅值的非线性耦合模方程，得到了高激发强度下透射率和相位因子的表达式。可以观察到，随着激发强度的增加，光栅的共振波长向更高波长侧移动。此外，光栅的最小透射率随着光栅长度的增加表现出振荡行为，而在高输入强度下，透射波的相位随长度单调增加。