Photonic Band Gap Material Topological Design at Specified Target Frequency

Abstract

To achieve any specified band gap structure around target frequency, a new photonic crystals (PhC) topological design strategy is proposed. In the design optimization model, a band gap index that measures the minimal signed distances between the specified frequency and any two adjacent orders of frequencies is proposed, and the topology of PhC unit cell is represented with a low number of design variables through the material‐field series‐expansion. Then the sequential Kriging‐based algorithm is adopted for solving the multi‐peak and nondifferentiable optimization problems. Based on the numerical implementation of the proposed optimization method, the PhC unit cells are designed to provide band gaps precisely matching any specified central frequency value. The optimized unit cell designs are easily assembled to achieve a PhC device with the large relative band gap.

A Precisely‐Controlled Multichannel Phononic Crystal Resonant Cavity

“…The gap measure Δ m can be also be expressed as Δ m = min(d up , d down ) ∕𝜔 * with two distances d up and d down shown in Figure 1. As the band gap order of the PnC unit cell may switch during the optimization process, the target band gap index for Stage 1 is defined by the maximum gap between the specified frequency 𝜔 * and all the adjacent orders of bands as, [34] f…”

“…Therefore, it is very important to implement various functional PnC designs for unit cells with a certain size. Maximizing the spatial decay of evanescent waves [33] and the minimal distances between two adjacent bands to specified frequencies, [34] with TO methods are both effective manners to open complete and multiple band gaps at specified frequencies. In design of the precisely-controlled PnC resonant cavity, it is reasonable to involve a narrow defect band into a sufficiently wide band gap, whereas the narrow defect band can be realized by introducing a supercell where a specific-shaped "defect" cell is surrounded by several "perfect" unit cells possessing a wide band gap.…”

Optimal Designs of Phononic Crystal Microstructures Considering Point and Line Defects

“…The compositions of PnC microstructures, including the material properties, the shapes of the scatterers, and the filling ratio, significantly affect the band gap characteristics of PnCs. It is meaningful to optimize the PnC microstructures systematically to broaden the application prospects of PnCs [8][9][10][11][12].…”

A Gradient-Free Topology Optimization Strategy for Continuum Structures with Design-Dependent Boundary Loads

“…In gradient-free topology optimization, researchers have conducted a lot of work, including the genetic algorithm [24,25], the kriging-assisted level-set method (KG-LSM) [26], the teaching-learning-based optimization (TLBO) approach [27][28][29], and the Kriging-based material-field series expansion (KG-MFSE) method [30][31][32][33][34][35]. In this study, a general gradientfree topology optimization framework that combines the material-field series-expansion (MFSE) model [36][37][38] and an adaptive body-fitted finite element mesh is proposed.…”