Observation of a Topological Transition in the Bulk of a Non-Hermitian System

We present the first experimental observation of a topological transition in a non-Hermitian system. In contrast to standard methods for examining topological properties, which involve probing edge (or surface) states, we monitor the topological transition by employing bulk dynamics only. The system is composed of a lattice of evanescently coupled optical waveguides, and non-Hermitian behavior is engineered by inducing bending loss by spatially “wiggling” every second waveguide.

Figure 1

(a) Schematic diagram of the waveguide array. The $B$ sites oscillate in the vertical direction with a period $Z=1\mathrm{mm}$, causing bending or radiation losses to continuum modes. (b) Sketch of the input facet labeling the unit cell index $m$ and the sublattices $A$ (nonlossy) and $B$ (lossy).

Figure 2

Mean displacement $⟨\mathrm{\Delta }m⟩$ plotted as a function of $\mathrm{\Delta }d$. The blue curve depicts the result when light is input in the $A$ site, and the red curve corresponds to input at the $B$ site. The insets show the absolute value of the wave function as a function of $z$ (ascending) in the waveguide array (note the presence of the long-lived dark state on the right inset).

Figure 3

Experimental and simulation results showing the mean displacement $⟨\mathrm{\Delta }m⟩$ vs $\mathrm{\Delta }d$. The insets represent experimentally achieved fluorescence images. Blue shades correspond to injection on a nonlossy site, red shades on a lossy site.

Figure 4

Experimental results showing the total integrated power in all waveguides in the last 2.5 cm of propagation through the array, as a function of $\mathrm{\Delta }d$.