Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Summary

Disordered structures offer new mechanisms for forming photonic bandgaps and unprecedented freedom in functional-defect designs. To circumvent the computational challenges of disordered systems, we construct modular macroscopic samples of the new class of PBG materials and use microwaves to characterize their scale-invariant photonic properties, in an easy and inexpensive manner.

Abstract

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction.

Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

Introduction

The existence of a bandgap for photons has been the focus of many scientific works, starting from the earlier studies done by Lord Rayleigh on the one-dimensional stop-band, a range of frequencies that are forbidden from propagation through a periodic medium¹. Research into electromagnetic wave (EM) propagation in periodic structures has really flourished in the last two decades after the seminal publications of E. Yablonovitch^2,3 and S. John⁴. The term “photonic crystal” was coined by Yablonovitch to describe the periodic dielectric structures that possessed a photonic bandgap (PBG).  

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Protocol

1. Design a 2D Hyperuniform Disordered Dielectric Structure¹¹

1. Chose a subclass of 2D hyperuniform disorder point pattern (blue circles in Figure 2) and partition it (blue lines in Figure 2) using Delaunay tessellation. A 2D Delaunay tessellation is a triangulation that maximizes the minimum angle for each triangle formed and guarantees there are no other points inside the circumcircle of each triangle¹¹.
2. Locate the centroids of each triangle (solid black circles in Figure 2); these centroids are the locations of the dielectric rods of radius r¹¹.
3. Connect....

Results

We have achieved the first confirmation ever of an isotropic complete PBG present in hyperuniform disorder dielectric structures. Here, we present our HD structure results and compare them to that of a periodic square lattice photonic crystal.

Figure 5 shows a semi-log plot of TE polarization transmission (dB) vs. frequency (GHz) for a hyperuniform disorder structure at one incident angle. This plot shows that the stop band region is located approximately between 8.5 and 9.5 G.......

Discussion

Starting from a hyperuniform disordered point pattern, 2D HD structures consisting rods and/or wall network can be designed to obtain a complete PBG for all polarization¹¹. Based on the design, we constructed a template with holes and slots for assembling 2D Alumina rods and walls structures at cm-scale which could be tested with microwaves. We chose to work with microwaves, because cm-scale building blocks, such as Alumina rods and walls, are inexpensive, and easily handled. We have experimentally demonstrate.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Stereolithography machine	3D Systems	SLA-7000
Resin for base	3D Systems	Accura 60
Alumina rods			r=2.5 mm, cut to 10.0 cm height
Alumina sheets			Thickness 0.38 mm, various width: from 1.0 mm to 5.3 mm with 0.2 mm increments
Microwave generator	Agilent/HP	83651B
S-Parameter test set	Agilent/HP	8517B
Microwave Vector Network Analyzer	Agilent/HP	8510C