On-Demand Design of Tunable Complete Photonic Band Gaps based on Bloch Mode Analysis

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.