Photonic topological insulators are special materials in whose structural topology fully disallows the energy transport into their interior. Instead, they keep energy circulating along their surfaces. In contrast to ordinary surface wave systems, the prominence of photonic topological insulators lies on the fact that the surface transport occurs in unidirectional fashion, irrespective of whether the system exhibits disorder or contains random imperfections.
Thus far, such insulators have been mainly employed to topologically protect the transport of fully coherent (nonrandom) light. However, all practical light sources are partially coherent and, as a result, the generated light always exhibits random fluctuations that may be small, as in many lasers, or large, as in light generated by thermal sources.
The research group leaded by Prof. Armando Perez-Leija from Max-Born-Institut has investigated the interplay of topological protection and the degree of spatial coherence of classical light propagating in disordered photonic topological insulators. The research results are published in Photonics Research, Volume 10, No. 5, 2022 (Konrad Tschernig, Gabriel Martinez-Niconoff, Kurt Busch, Miguel A. Bandres, Armando Perez-Leija. Topological protection of partially coherent light[J]. Photonics Research, 2022, 10(5): 05001223).
In a fully coherent scenario, topologically protected edge-states have their energy well separated from bulk states. Consequently, edge-states cannot interact with bulk states thereby preventing energy flow from the surface into the bulk of the system. For partially coherent light, however, the allowed light states are mixtures of edge and bulk states, and these mixed states can readily exchange energy with one another. At first sight, this seems to imply that partially coherent light is intrinsically excluded from topological protection. This statement is only partly true.
In the above investigation, the authors demonstrated that partially coherent light can be structured to possess relatively high topological immunity. Specifically, in the universe of allowed partially coherent states there exists combinations of topological edge states with certain degree of coherence and whose energy lies on an elliptical region localized in the center of the energy spectrum. With decreasing the degree of coherence, this ellipse unavoidably extends to overlap with the bulk-bulk and edge-bulk regions causing rapid deterioration of the associated wave packets, thereby loosing topological protection (see Fig. (1)) and allowing flow of energy into the bulk of the system.
Hence, the key to optimize topological protection for partially coherent light is to minimize the interaction induced by disorder of the initial energy spectrum with the edge-bulk and bulk-bulk spectral regions. This optimization can be achieved by noting that for every instance of disorder, there exists a window in the energy spectrum within which light states enjoy topological protection.
To deduce the topological window of protection, one can perform a numerical simulation of the propagation of spatially narrow fully coherent light fields through an ensemble of many disordered photonic topological insulators and determine the spectral region where the spectral intensities and coherences survive the impact of disorder. This window is the spectral window of topological protection, and it shrinks with increasing levels of disorder.
In short, to guarantee topological protection of partially coherent light, we must keep the spectral coherence maps of the initial light fields at the center of the topological window of protection.
Fig.1 Top: fully coherent light with spectral coherence distribution inside the topological window of protection. After evolution through disorder the state emerges intact. Bottom: for partially coherent light, whose spectral coherence distribution lies outside the window, the disorder prevents its clean transport.