Doskolovich Leonid L, Golovastikov Nikita V, Bykov Dmitry A, Bezus Evgeni A
Opt Express. 2019 Sep 16;27(19):26786-26798. doi: 10.1364/OE.27.026786.
Resonant properties of composite structures consisting of several identical resonant structures (e.g. multilayer thin-film structures or guided-mode resonance gratings) separated by phase-shift layers are investigated theoretically. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses of the phase-shift layers, the composite structures comprising two or four resonant diffractive structures with a Lorentzian transmittance profile optically implement the Butterworth filters of the order two or three, respectively, and enable achieving flat-top transmission spectra with steep slopes and low sidebands. In addition, we show that the composite structures consisting of three or four second-order Butterworth filters can accurately approximate the fourth- or fifth-order Butterworth filters, respectively. The presented theoretical results are confirmed by rigorous numerical simulations of composite structures consisting of the so-called W-structures (simple three-layer resonant structures comprising a high-index core layer and two low-index cladding layers in a high-index dielectric environment). The simulation results confirm the formation of flat-top transmittance peaks, the shape of which fully agrees with the derived theoretical description. Moreover, we demonstrate an exceptionally simple mechanism of controlling the transmittance peak width, which consists in changing the thicknesses of the cladding layers of the initial W-structure and enables generating flat-top transmission peaks with a significantly subnanometer width.
从理论上研究了由几个相同的谐振结构（例如多层薄膜结构或导模共振光栅）组成、被相移层隔开的复合结构的谐振特性。使用散射矩阵形式，我们通过分析证明，在适当选择相移层的厚度时，由具有洛伦兹透射率分布的两个或四个谐振衍射结构组成的复合结构分别光学实现了二阶或三阶巴特沃斯滤波器，并能够实现具有陡峭斜率和低边带的平顶透射光谱。此外，我们表明由三个或四个二阶巴特沃斯滤波器组成的复合结构可以分别精确逼近四阶或五阶巴特沃斯滤波器。由所谓的W结构（在高折射率介电环境中由一个高折射率芯层和两个低折射率包层组成的简单三层谐振结构）组成的复合结构的严格数值模拟证实了所呈现的理论结果。模拟结果证实了平顶透射峰的形成，其形状与推导的理论描述完全一致。此外，我们展示了一种控制透射峰宽度的极其简单的机制，该机制在于改变初始W结构包层的厚度，并能够生成宽度明显小于纳米的平顶透射峰。
