  Second-order photonic topological insulators that host highly localized
corner states resilient to defects, are opening new routes towards developing
fascinating photonic devices. However, the existing works on second-order
photonic topological insulators have mainly focused on either transverse
magnetic or transverse electric modes. In this paper, we propose a
dual-polarization topological photonic crystal structure for both transverse
magnetic and transverse electric modes through topology optimization. Simple
tight-binding lattice models are constructed to reveal the topological features
of the optimized photonic crystal structure in a transparent way. The optimized
dual-polarization second-order photonic topological insulator hosts four groups
of corner states with different profiles and eigenfrequencies for both the
transverse magnetic and transverse electric modes. Moreover, the robustness of
theses corner states against defects is explicitly demonstrated. Our results
offer opportunities for developing polarization-independent topological
photonic devices.
