Topologically Robust Transport of Photons in a Synthetic Gauge Field

Electronic transport is localized in low-dimensional disordered media. The addition of gauge fields to disordered media leads to fundamental changes in the transport properties. We implement a synthetic gauge field for photons using silicon-on-insulator technology. By determining the distribution of transport properties, we confirm that waves are localized in the bulk and localization is suppressed in edge states. Our system provides a new platform for investigating the transport properties of photons in the presence of synthetic gauge fields.

Figure 1

(a) SEM image of a 2D lattice with the measurement setup. Light is coupled into the lattice or chain at input port exciting a counterclockwise rotating mode. The output at the drop port is measured using an optical vector network analyzer (OVA). An erbium-doped fiber amplifier (EDFA) and variable optical attenuator (VOA) are used to control input power along with a polarization controller. (b) SEM image of a 1D device with 10 main rings. Main rings are coupled using link rings similar to 2D devices. (c) Simulated edge state intensity and (d) bulk states intensity for an $8\times 8$ lattice averaged over 50 realizations. The edge states span the long edge of the lattice, whereas the bulk states are localized near the input port. (e),(f) Simulated intensity images for edge and bulk states in a $15\times 15$ lattice. The long-edge wave function still extends across the lattice edge, but the bulk state is again localized with localization extent independent of lattice size.

Figure 2

(a) Measured transmission and (b) delay-time spectra for eight $8\times 8$ lattice size devices. The spectra have been normalized and shifted along the $x$ axis to superpose them [22]. Two regions with reduced variance in transmission and delay are indicated (shaded red and green). The noisy bulk states region is shown in blue. (c),(d) Simulated transmission and delay with the average (solid blue line) and 95% confidence band (gray shaded area) determined from the standard deviation across devices. (e),(f) Measured and simulated delay statistics for edge and bulk states. The delay distribution for edge states is Gaussian, indicating diffusive transport. For bulk states the distribution is asymmetric, showing localized transport. Data is taken across 8 devices. The delays are normalized to the average (rms) and the overall delay distribution is normalized to the in-band average and the delay distribution is normalized such that the area under the curve is unity.

Figure 3

(a) Transmission and (b) delay-time scaling for 2D and 1D devices. Solid markers with error bars are the measured average and standard deviation (65% confidence band) values. Solid lines with shaded areas are the simulated average and standard deviation. Also shown is the transmission when there is no disorder in the system. For 2D data, we measured (7,8,9,8,8) the number of chips for ($6\times 6$, $8\times 8$, $10\times 10$, $15\times 15$, $18\times 18$ ring) sized devices, respectively. For the 1D data, we measured (11,15,11,12,6) number of chips for (2,10,20,30,50) ring devices. (c) Delay statistics for the long edge of $15\times 15$ lattice sized devices, midband, and band ends of 30-ring 1D devices. The long edge and midband of 1D devices show diffusive transport. The band ends in 1D devices, however, show localization.