# Probing topological phases in waveguide superlattices

## TL;DR

This paper introduces a general bulk probing method for topological invariants in waveguide superlattices using spatial beam displacement, enabling the detection of topological edge states without relying on Wannier functions.

## Contribution

It proposes a novel bulk probing technique for topological properties in superlattices, applicable beyond simple dimeric systems, and introduces a simplified method for quadrimeric superlattices.

## Key findings

- Bulk probing method accurately measures topological invariants.
- Method distinguishes topological edge states from non-topological states.
- Applicable to complex superlattice structures.

## Abstract

One-dimensional superlattices with modulated coupling constants show rich topological properties and tunable edge states. Beyond the dimeric case, probing the topological properties of superlattices is a challenge. Here we suggest a rather general method of bulk probing topological invariants in waveguide superlattices based on spatial displacement of discretized beams. A judiciously tailored initial beam excitation of the lattice, corresponding to superposition of Wannier functions, provides a direct measure of the band gap topological numbers. For a quadrimeric superlattice, a simple bulk probing method, which avoids Wannier states, is proposed to discriminate the existence of zero-energy topological edge states from non-topological ones