Analytic theory of coupled waveguide transformation under randomly perturbations

TL;DR

This paper develops an analytical framework to quantify how random fabrication-induced perturbations affect the optical transformation accuracy in coupled waveguides, emphasizing the role of perturbation statistics and correlation scales.

Contribution

It introduces analytical equations linking perturbation statistics to transformation uncertainty, advancing understanding of fabrication imperfections in coupled waveguide systems.

Findings

Uncertainty depends on perturbation intensity and correlation scale.

Interaction length for power distribution is influenced by random process parameters.

Analytical models predict how fabrication imperfections impact optical transformations.

Abstract

Coupled waveguides are convenient at implementing useful optical transformations. In this letter, we investigate the uncertainty of transformation by two coupled waveguides that stems from the perturbations of waveguide's mode indices~--- the effect that may be imposed by a non-ideal fabrication process, in particular, those of femtosecond direct laser writing. In our analysis, the perturbations are assumed to be samples of a stationary random process, characterized by an intensity and a correlation scale parameter. We have derived analytical equations that link these parameters with relevant statistical characteristics and applied them to analyse how the uncertainty evolves with field propagation length. We have shown that the interaction length over which the expectation value of power becomes evenly distributed among the waveguides is crucially dependent on the random process correlation scale and perturbation intensity.