  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.
