# Transient behavior of surface plasmon polaritons scattered at a subwavelength groove

## TL;DR

This paper combines numerical simulations and analytical modeling to understand how surface plasmon polaritons behave transiently near subwavelength grooves in silver, aiding the design of photonic circuits.

## Contribution

It introduces a semi-analytical model that accurately describes transient surface waves and SPPs near grooves, independent of groove shape, enhancing photonic device design.

## Key findings

- The diffracted field is equivalent to an oscillating dipolar line source.
- The analytical model reproduces asymptotic SPP and near-zone transient waves.
- The model aids in designing photonic circuits with controlled surface wave behavior.

## Abstract

We present a numerical study and analytical model of the optical near-field diffracted in the vicinity of subwavelength grooves milled in silver surfaces. The Green's tensor approach permits computation of the phase and amplitude dependence of the diffracted wave as a function of the groove geometry. It is shown that the field diffracted along the interface by the groove is equivalent to replacing the groove by an oscillating dipolar line source. An analytic expression is derived from the Green's function formalism, that reproduces well the asymptotic surface plasmon polariton (SPP) wave as well as the transient surface wave in the near-zone close to the groove. The agreement between this model and the full simulation is very good, showing that the transient "near-zone" regime does not depend on the precise shape of the groove. Finally, it is shown that a composite diffractive evanescent wave model that includes the asymptotic SPP can describe the wavelength evolution in this transient near-zone. Such a semi-analytical model may be useful for the design and optimization of more elaborate photonic circuits whose behavior in large part will be controlled by surface waves.