Isospectral and square root Cholesky photonic lattices
arXiv:2005.10069 · doi:10.1103/PhysRevA.102.043521
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.
arXiv comment15 pages, 4 figures
References in corpus (22)
- Supersymmetry and Quantum Mechanics
- Supersymmetric Optical Structures
- Supersymmetric mode converters
- Supersymmetric Laser Arrays
- Invisibility in non-Hermitian tight-binding lattices
- Symmetry-protected zero-mode laser with a tunable spatial profile
- SUSY-inspired one-dimensional transformation optics
- Universal sign-control of coupling in tight-binding lattices
- Supersymetric laser arrays
- Supersymmetric microring laser arrays
- Non-Hermitian engineering of single mode two dimensional laser arrays
- Observation of supersymmetric scattering in photonic lattices
- Supersymmetric transparent optical intersections
- Jacobi photonic lattices and their SUSY partners
- An intensity-dependent quantum Rabi model: Spectrum, SUSY partner and optical simulation
- Symmetry in optics and photonics: a group theory approach
- Supersymmetry-guided method for mode selection and optimization in coupled systems
- Supercharge optical arrays
- Supersymmetric Bragg gratings
- Symmetric supermodes in cyclic multicore fibers
- Parity anomaly laser
- Lasing in para-Fermi class-B microring resonator arrays