Achieving Large Band Gaps in 2D Symmetric and Asymmetric Photonic Crystals

This paper systematically studies the influence of symmetry on photonic band gaps (PBGs) of two-dimensional photonic crystals (PhCs) by using the finite-element analysis and topology optimization methods. Optimal designs of symmetric and asymmetric PhCs of square and hexagonal lattices with PBGs of both transverse electric (TE) and transverse magnetic (TM) modes are designed and analyzed. The results show that the band gap sizes of asymmetric designs are larger than those of symmetric ones. More importantly, we found that the largest TM band gap of the square lattice PhCs is comparable to that of the hexagonal lattice PhCs, which extends the state-of-the-art understanding. Physically, forming orthogonal patterns of electric or magnetic fields is critical for maximizing TE or TM band gaps. Our unique design method opens new possibility of generating novel PhCs with properties on demand.