一维亚波长光栅等效折射率描述光栅光谱特性的有效性研究

Study on Validity of Effective Refractive Indices of One-Dimensional Subwavelength Gratings on Grating Spectral Properties

运用有效媒质、薄膜干涉及耦合波理论,结合数值寻优算法,采用不同形式的等效折射率来描述一维亚波长光栅的光谱特性。借助光谱误差函数及耦合波折射率,分别针对TE和TM模,对其他等效折射率在描述亚波长光栅时的有效性加以分析比对。研究结果表明:在光栅结构参数已确定的情况下,当归一化光栅周期Λ/λ<0.30时,TE模的二级近似折射率和精确近似折射率能够对其光谱特性给出高精度的描述;而对于TM模,由于光栅层中高级次谐波影响效应的显著性,导致用相应等效折射率描述其光谱特性时精度下降。此外,在采用不同形式的等效折射率计算亚波长光栅光谱特性随光栅深度变化关系时,除TE模情形的二级近似折射率以及精确近似折射率外,其他情形采用等效折射率计算得到的光谱均可能与实际光谱产生较大偏差。

By using the effective medium theory,thin film theory,rigorous coupled-wave analysis,and elaborated root finding method,the spectral properties of one-dimensional subwavelength gratings are investigated by using different expressions of the effective refractive index.By using the defined error function of the spectra,the validation of other effective refractive indices is evaluated by using the rigorous refractive index in both cases of TE and TM modes.For the given grating parameters,it is shown that the second order effective refractive index and the exact effective refractive index can provide solid results in estimating the spectral properties of one-dimensional subwavelength gratings for TE mode when the normalized grating period Λ/λ is less than 0.30.For TM mode,the effective refractive indices cannot give solid estimations because more evanescent waves are excited in this case.In addition,it cannot provide solid estimations by using the effective refractive indices in calculating the spectrum as a function of the grating thickness except the second order effective refractive index and the exact effective refractive index for TE mode.