## Christina Jörg

*TU Kaiserslautern*

Since June 2015: PhD student in the group for Optical Technologies and Photonics (Georg von Freymann), department of physics, TU KaiserslauternJanuary 2013 – July 2013: Exchange semester at Universidade de Santiago de Compostela (Spain)October 2009 – May 2015: Diploma in physics at TU Kaiserslautern (equivalent to the Masters degree)

We study the transition between bulk states and an edge state in the topologically nontrivial Su-Schrieffer-Heeger (SSH) system, in which the edge state is driven by a local AC-field. Theory is verified by experiments in evanescently coupled dielectric waveguide systems.

Introduction:

The SSH model consists of a linear chain of sites, where each two sites are connected via a strong bond and a weak bond alternately. We introduce an "edge" by putting a defect with two weak bonds at either side into the chain (at site 0). That creates an edge state that is exponentially localized around site 0, as the topological invariant in the left side of the chain differs from that in the right side.

Now we drive site 0 periodically by modulating its position in the y-direction sinusoidally with frequency ω. This makes the coupling from site 0 to its neighbors time-dependent. Also, the on-site potential at site 0 differs from that of the other sites due to the curvature. If we solve the time-dependent Schrödinger equation with the system's Hamiltonian, we see that Floquet replicas [1] of the edge state appear, spaced with ω around zero energy.

Whenever the driving frequency ω is such that the replicas hit the bulk bands the edge state couples to the bulk states, i.e. the light delocalizes from site 0. For the cases where the replicas lie outside the bands no Floquet replica can couple to bulk states and the light stays localized around site 0.

Methods:

Experiments were conducted in arrays of 3D printed dielectric evanescently coupled waveguides [2].

Results and Discussion:

The experiments confirm the effect predicted by theory. Light is localized around the defect except for frequencies resonant with the bulk bands. By selecting the frequency we can also control the angle under which the light spreads into the bulk.

Our setup serves to control the localization and steering of light via an external parameter. It also gives insight into Floquet mechanisms.

[1] S. A. Reyes *et al.*, New J. Phys. **19**, 043029 (2017).

[2] C. Jörg *et al.*, New J. Phys. **19**, 083003 (2017).