  Implementation of topology on photonics has opened new functionalities of
photonic systems such as topologically protected boundary modes. We present
polarization-dependent topological properties in 2D Su-Schrieffer-Heeger
lattice by using a metallic nanoparticle array and considering the polarization
degree of freedom. We demonstrate that when eigenmodes are polarized parallel
to the plane of the 2D lattice, it supports isolated longitudinal edge modes
and transverse modes that are hidden from the projected bulk states. Also, the
in-plane polarized modes support a second-order topological phase under an open
boundary condition by breaking the four-fold rotational symmetry. This work
will offer polarization-based multifunctionality in compact photonic systems
that have topological features.
