Fitio Volodymyr, Yaremchuk Iryna, Bendziak Andriy, Marchewka Michal, Bobitski Yaroslav
Department of Photonics, Lviv Polytechnic National University, S. Bandera Str., 12, 79013 Lviv, Ukraine.
College of Natural Sciences, Institute of Physics, University of Rzeszow, 1 Pigonia St., 35-959 Rzeszow, Poland.
Materials (Basel). 2021 Apr 27;14(9):2252. doi: 10.3390/ma14092252.
In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.
在这项工作中，对高斯光束在体相位光栅上的衍射进行了理论和数值研究。所提出的方法基于严格耦合波分析（RCWA）和傅里叶变换。利用傅里叶变换将高斯光束分解为平面波。根据采样定理确定平面波的数量。对每个RCWA平面波计算复反射和透射振幅。利用逆傅里叶变换确定反射波和透射波沿光栅的场分布。基于这些分布确定反射波和透射波的功率。我们的方法表明，相位光栅满足能量守恒定律。也就是说，入射高斯光束的功率等于反射光束和透射光束功率之和。这证明了我们方法的正确性。众多研究表明，在共振条件下，反射光束和透射光束的空间形状与高斯光束不同。此外，光栅中还会出现波导模式。在无共振情况下，反射光束和透射光束的空间形式为高斯分布。发现高斯光束的共振曲线宽度比平面波的宽。然而，光谱和角度灵敏度与平面波相同。平面波和高斯光束的共振波长略有不同。利用所提出的方法对光栅介质的四个折射率调制系数进行了数值计算。共振曲线的宽度随折射率调制的增加而减小。此外，反射系数也增加。
