Normalization of the wavefunction obtained from perturbation theory based on a matrix method

TL;DR

This paper derives a normalization constant for a perturbation matrix method and demonstrates its effectiveness on a binary waveguide array, achieving third-order accuracy matching exact solutions.

Contribution

It introduces a normalization procedure for the perturbation matrix method and validates it against an exact solution in waveguide arrays.

Findings

Normalized matrix method matches exact solutions to third order.

The derived normalization constant improves the accuracy of the perturbation approach.

The method is validated on a binary waveguide array problem.

Abstract

We present the derivation of the normalization constant for the perturbation matrix method recently proposed. The method is tested on the problem of a binary waveguide array for which an exact and an approximate solution are known. In our analysis, we show that to third order the normalized matrix method approximate solution gives results coinciding with the exact known solution.