# Direct calculation of the strong Goos-H\"{a}nchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configuration

## TL;DR

This paper theoretically investigates how surface plasmon excitation influences the lateral shift of a Gaussian light beam in the Otto configuration, revealing sensitive dependence on layer thickness, beam width, and incident angle, with large shifts near plasmon resonance.

## Contribution

It provides a detailed theoretical analysis of the strong Goos-H"{a}nchen effect caused by surface plasmon polaritons in a dielectric-metal bilayer, highlighting the dependence on various parameters and beam deformation.

## Key findings

- Lateral shift varies from negative to positive near plasmon resonance.
- Maximal shifts can reach several hundred wavelengths for wide beams.
- Reflected beam often splits into two parts, with transmitted shift always positive.

## Abstract

We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends sensitively on the thickness of the metal layer and the width of the incident beam, as well as on the incident angle. Near the incident angle at which surface plasmons are excited, the lateral shift changes from large negative values to large positive values as the thickness of the metal layer increases through a critical value. For wide incident beams, the maximal forward and backward lateral shifts can be as large as several hundred times of the wavelength. As the width of the incident Gaussian beam decreases, the magnitude of the lateral shift decreases rapidly, but the ratio of the width of the reflected beam to that of the incident beam, which measures the degree of the deformation of the reflected beam profile, increases. In all cases considered, we find that the reflected beam is split into two parts. We also find that the lateral shift of the transmitted beam is always positive and very weak.