We propose and theoretically and numerically investigate narrowband integrated filters consisting of identical resonant dielectric ridges on the surface of a single-mode dielectric slab waveguide. The proposed composite structures operate near a bound state in the continuum (BIC) and enable spectral filtering of transverse-electric-polarized guided modes propagating in the waveguide. We demonstrate that by proper choice of the distances between the ridges, flat-top reflectance profiles with steep slopes and virtually no sidelobes can be obtained using just a few ridges. In particular, the structure consisting of two ridges can optically implement the second-order Butterworth filter, whereas at a larger number of ridges, excellent approximations to higher-order Butterworth filters can be achieved. Owing to the BIC supported by the ridges constituting the composite structure, the flat-top reflection band can be made arbitrarily narrow without increasing the structure size. In addition to the filtering properties, the investigated structures support another type of BICs - Fabry-Perot BICs arising when the distances between the adjacent ridges meet the Fabry-Perot resonance condition. In the vicinity of the Fabry-Perot BICs, an effect similar to the electromagnetically induced transparency is observed, namely, sharp transmittance peaks against the background of a wide transmittance dip.

中文翻译：

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集成平顶反射滤波器在连续介质中的束缚态附近运行

我们提出并从理论上和数值上研究了窄带集成滤波器，该滤波器由单模介质平板波导表面上的相同谐振介质脊组成。所提出的复合结构在连续介质 (BIC) 中的束缚态附近运行，并且能够对在波导中传播的横向极化导模进行光谱滤波。我们证明，通过正确选择脊之间的距离，可以只使用几个脊获得具有陡坡的平顶反射率和几乎没有侧链。特别是，由两个脊组成的结构可以在光学上实现二阶巴特沃斯滤波器，而在更多的脊处，可以实现对高阶巴特沃斯滤波器的极好近似。由于BIC由构成复合结构的脊支撑，可以在不增加结构尺寸的情况下使平顶反射带任意窄。除了过滤特性之外，所研究的结构还支持另一种类型的 BIC——当相邻脊之间的距离满足 Fabry-Perot 共振条件时产生的 Fabry-Perot BIC。在法布里-珀罗 BIC 附近，观察到类似于电磁感应透明的效果，即在宽透射率下降的背景下出现尖锐的透射率峰值。研究的结构支持另一种类型的 BIC - 当相邻脊之间的距离满足 Fabry-Perot 共振条件时出现的 Fabry-Perot BIC。在法布里-珀罗 BIC 附近，观察到类似于电磁感应透明的效果，即在宽透射率下降的背景下出现尖锐的透射率峰值。研究的结构支持另一种类型的 BIC - 当相邻脊之间的距离满足 Fabry-Perot 共振条件时出现的 Fabry-Perot BIC。在法布里-珀罗 BIC 附近，观察到类似于电磁感应透明的效果，即在宽透射率下降的背景下出现尖锐的透射率峰值。