Isospectral and square root Cholesky photonic lattices

TL;DR

This paper introduces a method to design photonic lattices using Cholesky factorization, creating isospectral and square root arrays with potential applications in telecommunications, supported by theoretical and experimental analysis.

Contribution

It presents a novel application of Cholesky decomposition to photonic lattices, enabling the construction of isospectral and square root arrays with experimental validation.

Findings

Successful construction of isospectral and square root photonic lattices

Good agreement between finite element models and analytical predictions

Demonstration of supersymmetric-like properties in photonic systems

Abstract

Cholesky factorization provides photonic lattices that are the isospectral partners or the square root of other arrays of coupled waveguides. The procedure is similar to that used in supersymmetric quantum mechanics. However, Cholesky decomposition requires initial positive definite mode coupling matrices and the resulting supersymmetry is always broken. That is, the isospectral partner has the same range than the initial mode coupling matrix. It is possible to force a decomposition where the range of the partner is reduced but the characteristic supersymmetric intertwining is lost. As an example, we construct the Cholesky isospectral partner and the square root of a waveguide necklace with cyclic symmetry. We use experimental parameters from telecommunication C-band to construct a finite element model of these Cholesky photonics lattices to good agreement with our analytic prediction.