Anomalous spatial modifications of beams diffracted by two-dimensional periodic media

Area of Science:

• Electromagnetics and Optics
• Wave Propagation
• Materials Science

Background:

• Understanding wave interactions with periodic structures is crucial for optical and electromagnetic applications.
• Previous studies primarily focused on one-dimensional (1D) periodic surfaces, limiting the understanding of complex two-dimensional (2D) interactions.
• Gaussian beam analysis provides a more realistic model for incident radiation compared to plane waves.

Purpose of the Study:

• To rigorously examine the spatial modifications of diffracted beams from a 2D periodic structure illuminated by a Gaussian beam.
• To quantify the effects of spectral variations on beam profiles and compare them to simpler geometric predictions.
• To develop analytical models for these modifications and explore their dependence on incidence conditions and grating resonances.

Main Methods:

• Utilizing a plane-wave representation for rigorous analysis of diffracted fields.
• Initially determining a geometric profile by neglecting plane-wave spectrum amplitude variations.
• Incorporating spectral variations to reveal 2D lateral displacements, focal shifts, angular deviations, and beam-width alterations.
• Employing Padé approximants for accurate analytical expressions of spatial modifications.

Main Results:

• Diffracted beams from 2D periodic structures exhibit significant spatial modifications beyond simple geometric predictions.
• These modifications, including lateral shifts and focal changes, are amplified under conditions favoring grating resonances.
• The analysis reveals 2D effects with greater complexity and novel features compared to 1D periodic surface interactions.
• A canonical grating model with sinusoidal impedance variation was used for illustration.

Conclusions:

• Gaussian beam incidence on 2D periodic structures leads to complex spatial beam modifications.
• Accurate analytical expressions using Padé approximants capture these intricate 2D effects.
• The findings provide a deeper understanding of wave phenomena in 2D periodic systems, relevant for advanced optical and electromagnetic device design.