Abstract
The fundamental property of photonic crystals is the band gap effect, which arises from the periodic dielectric modulation of electromagnetic waves and plays an indispensable role in manipulating light. Ever since the first photonic-bandgap structure was discovered, the ability to tune its bandgap across a wide wavelength range has been highly desirable. Therefore, obtaining photonic crystals possessing large on-demand bandgaps has been an ever-attractive study but has remained a challenge. Here we present an analytical design method for achieving high-order two-dimensional photonic crystals with tunable photonic band gaps on-demand. Based on the Bloch mode analysis for periodic structures, we are able to determine the geometric structure of the unit cell that will realize a nearly optimal photonic band gap for one polarization between the appointed adjacent bands. More importantly, this method generates a complete bandgap for all polarizations, with frequencies tuned by the number of photonic bands below the gap. The lowest dielectric contrast needed to generate a photonic band gap, as well as conditions for generating complete bandgaps, are investigated. Our work first highlights the systematic approach to complete photonic band gaps design based on Bloch mode analysis. The physical principles behind our work are then generalized to other photonic lattices.
Highlights
Structures with periodic dielectric distributions, such as photonic crystals (PhCs), can achieve unique dispersion properties for controlling electromagnetic waves
With gap positions controlled by N1 and N2, our work in this paper provides an analytical method for the design of PhC structures with the maximum transverse electric (TE)-Photonic band gaps (PBG), transverse magnetic (TM)-PBG and
The results indicate that the analytical design method is capable to achieve large PBGs for any number of N, validating the generality of the proposed method
Summary
Structures with periodic dielectric distributions, such as photonic crystals (PhCs), can achieve unique dispersion properties for controlling electromagnetic waves. This way, the method is able to design structures with nearly optimal PBG sizes between arbitrarily appointed adjacent photonic bands for both TM and TE polarizations without any iterative calculations. This method allows one to analytically design PhCs with tunable CPBGs, the position of which is controlled by the number of photonic bands below the gap. With this method, we are able to realize nearly optimal PhC structures composed of two arbitrary materials with dielectric constants ε1 and ε2. Two conditions are necessarily satisfied to obtain the structure that supports a large CPBG: 1) the ability to support both TE and TM
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