Abstract
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
Highlights
Topology, the study of those properties of geometric objects that remain invariant under continuous transformations such as bending or stretching, has recently entered optics in several guises
The physical platform we examine is an array of parallel waveguides with nearest-neighbor-only evanescent coupling[20], and we investigate the optical statistics when coherent light excites a single site[21,22,23,24,25,26,27]; but the results can be readily extended to other photonic realizations
We have found that topology plays an unexpected role in determining the thermalization statistics of light propagating in a disordered lattice of coupled waveguides
Summary
The study of those properties of geometric objects that remain invariant under continuous transformations such as bending or stretching (homeomorphisms[1] in general), has recently entered optics in several guises. In an altogether different vein, topological features of the three-dimensional distribution of the optical field in physical space have been investigated, such as the knottedness of scalar wavefronts[10,11,12,13] and the emergence of non-trivial topological structure in tightly focused vector fields[14]. A lesser-studied impact of topology on optics, is that resulting from the interaction of light with a photonic structure that itself features non-trivial topology. In the case of the disordered ring lattices examined here, the delineation of the field into real and imaginary quadratures occupying alternating sites as a result of chiral symmetry brings about a new self-consistency condition: the complete braiding of the two strands representing the field quadratures. We show that all these scenarios are spanned by light emerging from disordered 1D lattices in different topologies that support chiral-symmetric mode pairs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
