高Q共振与光子晶体脊波导上的连续态束缚

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"这篇论文研究了在硅片波导表面设置单个硅质脊结构对导引导模产生的衍射效应。通过使用非周期性严格的耦合波分析进行数值模拟，作者发现，在倾斜入射的横向电（TE）极化导模式与脊结构相互作用时，反射率和透射率光谱中存在尖锐的共振特性以及存在于连续介质中的束缚态（BICs）现象。" 这篇论文深入探讨了光子学领域的一个关键问题——如何在集成光子学结构中实现高品质因数（Q因子）的共振器。在光学系统中，高Q因子意味着共振频率的窄线宽，这在许多应用中都是至关重要的，例如光滤波、光存储和传感器设计。"束缚态在连续介质中"（Bound States in the Continuum, BICs）是光学中的一种特殊现象，它描述的是能量状态虽然理论上应该扩散到无限空间，但实际上由于特定的几何或拓扑条件，这些状态被有效地限制在一个有限的区域。在本研究中，研究者们选择了一个简单的硅片波导模型，其上有一个硅质脊结构。硅片波导是一种常见的光子学平台，用于传输和操纵光信号。脊结构的引入可以改变波导的传播特性，创造出新的光学模式和共振行为。当TE极化的导模式以倾斜角度入射到脊结构上时，产生了显著的共振特征，这表明脊结构可以作为设计高Q因子共振器的有效手段。非周期性的严格耦合波分析（Rigorous Coupled-Wave Analysis, RCWA）是一种广泛应用于光栅和复杂结构的光谱分析方法，它可以精确计算出复杂的光与结构相互作用的过程。在这项工作中，RCWA被用来验证并解析BICs和共振峰的出现，为理解和优化这种结构提供了理论基础。论文的结果不仅揭示了脊结构对波导模式的影响，还为未来设计新型光子器件提供了新的思路。例如，通过调整脊结构的尺寸、形状和位置，可以控制和调谐这些共振特性，从而在微纳尺度上实现更高效的光操控。此外，这种结构可能在量子光学、光通信和光电子学等领域找到潜在的应用。这项研究强调了微结构对光波导性能的深刻影响，并展示了如何利用这种影响来创建高性能的光学共振器。通过对倾斜入射TE模式与脊结构相互作用的深入分析，研究人员成功地观察到了BICs现象，这为进一步优化集成光子学器件的设计提供了新的视角和方法。

Bound states in the continuum and high-Q

resonances supported by a dielectric ridge

on a slab waveguide

EVGENI A. BEZUS,

1,2,

*DMITRY A. BYKOV,

1,2

AND LEONID L. DOSKOLOVICH

1,2

Image Processing Systems Institute—Branch of the Federal Scientific Research Centre “ Crystallography and Photonics” of the Russian Academy

of Sciences, 151 Molodogvardeyskaya St., Samara 443001, Russia

Samara National Research University, 34 Moskovskoe Shosse, Samara 443086, Russia

*Corresponding author: evgeni.bezus@gmail.com

Received 5 July 2018; revised 4 September 2018; accepted 20 September 2018; posted 20 September 2018 (Doc. ID 337954);

published 1 November 2018

We investigate the diffraction of the guided modes of a dielectric slab waveguide on a simple integrated structure

consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic

rigorous coupled-wave analysis demonstr ate the existence of sharp resonant features and bound states in the

continuum (BICs) in the reflectance and transmittance spectra occurring at the oblique incidence of a transverse-

electric (TE)-polarized guided mode on the ridge. Using the effective index method, we explain the resonances

by the excitation of cross-polarized modes of the ridge. Formation of the BICs are confirmed using a theoretical

model based on coupled-wave theory. The model suggests that the BICs occur due to the coupling of quasi-TE

and quasi-transverse-magnetic modes of the structure. Simple analytical expressions for the angle of incidence and

the ridge width predicting the location of the BICs are obtained. The existence of high-Q resonances and BICs

enables using the considered integrated structure for sensing, transformation of optical signals, and enhancing

nonlinear light–matter interactions. Due to the Lorentzian line shape of the resonances near the BICs, the struc-

ture is also promising for filtering applications.

https://doi.org/10.1364/PRJ.6.001084

1. INTRODUCTION

In a wide class of planar (integrated) optoelectronic systems,

processing of the optical signal is performed in a slab wave-

guide [1– 11]. Such a geometry corresponds to the “insulator-

on-insulator” platform and is suitable for the creation of fully

integrated optical devices. In this case, the processed signal cor-

responds to a superposition of slab waveguide modes having

different propagation directions (in the case of spatial process-

ing) or different frequencies (in the case of spectral processing).

In this regard, the design of integrated resonant photonic struc-

tures is of great interest [12,13].

In the last few years, much attention has been paid to the

investigation of so-called bound states in the continuum (BICs)

in resonant photonic structures (see the recent review [14] and

references therein). BICs are eigenmodes that have an infinite

lifetime (and an infinitely high quality factor), although they

are supported by a structure having open scattering channels.

The mode leakage of these channels is canceled either due to

symmetry reasons or by means of par ameter tuning [14]. In

photonics, BICs were studied in periodic structures (diffraction

gratings, photonic crystal slabs, and infinite arrays of dielectric

rods or spheres) [15–23], defects and interfaces of photonic

crystals [24–26], arrays of optical waveguides [27–29], and

leaky optical waveguides [30], among others [14]. The struc-

tures supporting BICs can be used as “unconventional” narrow-

band waveguides [30]. A slight deviation from the BIC

condition enables obtaining very high-Q resonators, which

leads to various potential applications including lasers, sensors,

and filters.

In this work, we investigate the resonant optical properties

of a very simple structure consisting of a single subwavelength

or near-wavelength ridge on the surface of a single-mode dielec-

tric slab waveguide. We analytically and numerically demon-

strate that, in the case of diffraction of a transverse-electric

(TE)-polarized mode of the waveguide, the studied structure

exhibits BICs and high-Q resonances associated with the exci-

tation of cross-polarized modes of the ridge. Comparing to

Ref. [30], we present a theoretical model that accurately

describes the optical properties of the studied structure. In par-

ticular, we prove the existence of robust BICs and obtain simple

closed-form expressions predicting their locations. The discov-

ered high-Q resonances and BICs supported by the presented

1084

Vol. 6, No. 11 / November 2018 / Photonics Research

Research Article

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高Q共振与光子晶体脊波导上的连续态束缚

Bound states in the continuum and Fano resonances in the strong mode coupling regime

Waves stranded at sea: bound states in the continuum in a strong coupling regime

c=[-10,-9]; A=[6 5;10 20;1 0]; b=[60;150;8]; vlb=zeros(2,1); Aeq=[]; beq=[]; vub=[]; [x,fval]=linprog(c,A,b,Aeq,beq,vlb,vub);

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