Topology optimization of photonic crystals with exotic properties resulting from Dirac-like cones

The Dirac-like cones underlie many unique properties of photonic crystals (PhCs). This paper aims to design fabrication-friendly PhCs with Dirac-like cones for transverse magnetic (TM) modes and transverse electric (TE) modes at different specific frequencies. By maximizing the minimum of a collection of the local density of states corresponding to different judiciously selected sources, this paper demonstrates that Dirac-like cones formed by the degeneracy of a doubly degenerate mode and a single mode at different desired frequencies are successfully obtained. The exotic wave manipulation properties associated with Dirac-like cones, such as cloaking, wavefront shaping and tunneling through bent channels, are exhibited based on the optimized structures. This paper also demonstrates that the proposed method could be used for the design of PhCs with one Dirac-like cone at ω , and one monopolar band at 2 ω at the Γ point, and PhCs with third order Dirac-like cones, which have potential applications in nonlinear optics. All topological patterns of the optimized PhCs are reported and have regular and smooth features, meaning they can be readily fabricated.