M. A. Tapia-Valerdi | Searcharxiv

arXiv2025

Waveguide arrays interaction to second neighbors: Exact solution

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which makes for a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems.

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arXiv2024

Some non-algebraic forms of $\exp(A+B)$

We present examples where expressions for $\exp(\hat{A}+\hat{B})$ can be derived even though the operators (or superoperators) $\hat{A}$ and $\hat{B}$ do not commute in a manner that leads to known factorizations. We apply our factorization to the case of a Lindblad operator modeling single photon decay and to a binary Glauber-Fock photonic lattice.

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