# Abnormal Angle-Dependent Multi-Channel Filtering in Photonic Crystals Containing Hyperbolic Metamaterials

## TL;DR

This paper explores how photonic crystals with hyperbolic metamaterials can create filters with unusual angle-dependent behavior for optical devices.

## Contribution

The study introduces photonic crystal structures with angle-dependent tunneling modes that can exhibit blue, red, or zero shifts based on material interactions.

## Key findings

- Tunneling modes in photonic crystals with hyperbolic metamaterials can show blue, red, or zero shifts depending on phase changes.
- Composed structures can support multiple tunneling modes with different angle dependencies.
- These structures are applicable in optical devices requiring specific angle-dependence behaviors.

## Abstract

Tunneling modes in all-dielectric one-dimensional photonic crystals can be utilized for multi-channel filtering. However, these tunneling modes generally blue shift upon increasing the incident angle. When hyperbolic metamaterials are introduced into one-dimensional photonic crystals, the competition between the propagation phase shifts in the dielectric materials and hyperbolic metamaterials can result in different angle dependencies, including blue shift, abnormal zero shift, and abnormal red shift. When the reduction in the propagation phase in the dielectric layer exceeds the increment in the propagation phase in the hyperbolic metamaterial, the tunneling modes are blue-shifted; conversely, when the phase increment in the hyperbolic metamaterial exceeds the phase reduction in the dielectric layer, the tunneling modes are abnormally red-shifted. When the phase changes in the two materials are the same, the tunneling modes are angle independent. In this study, we investigated the multiple filtering effects of one-dimensional photonic structures composed of hyperbolic metamaterials. These composed structures exhibited multiple tunneling modes based on one-, two-, or three-angle dependencies and can be applied in novel optical devices with different angle-dependence requirements.