# Guided Modes in the Plane Array of Optical Waveguides

## TL;DR

This paper demonstrates that an infinite array of dielectric waveguides can support guided modes below the cutoff frequency of an isolated waveguide, with the mode quality improving as the array size increases.

## Contribution

It reveals the existence of sub-cutoff guided modes in periodic waveguide arrays and provides a quantitative relation between array size and mode quality factor.

## Key findings

- Guided modes exist below the cutoff frequency in infinite arrays.
- Mode quality factor scales as N^3 with the number of waveguides.
- Numerical and analytical methods confirm the results.

## Abstract

It is known that for an isolated dielectric cylinder waveguide there exists the cutoff frequency $\omega_\ast$ below which there is no guided mode. It is shown in the paper that the infinite plane periodic array of such waveguides possesses the guided modes in the frequency domain which is below the frequency $\omega_\ast$. In the case of a finite array, the modes in this frequency domain are weakly radiating ones, but their quality factor $Q$ increases with the number of waveguides $N$ as $Q(N)\sim N^3$. This dependence is obtained both numerically, using the multiple scattering formalism, and is justified with a simple analytical model.