Goos-Hänchen shift for an Airyprime beam

Area of Science:

• Optics
• Quantum Optics
• Photonics

Background:

• The Goos-Hänchen (GH) effect describes the transverse spatial shift of a light beam upon reflection.
• Airy beams and their modified versions (Airyprime beams) exhibit unique propagation dynamics.
• Understanding GH shifts is crucial for optical sensing and manipulation.

Purpose of the Study:

• To develop a comprehensive theory for analyzing the Goos-Hänchen (GH) shift of arbitrarily polarized Airyprime beams.
• To establish the relationship between the GH shift of Airyprime beams and standard Airy beams.
• To investigate novel optical phenomena associated with Airyprime beam reflection.

Main Methods:

• Derivation of general expressions for spatial and angular GH shifts for Airyprime beams.
• Analysis of beam polarization effects on the GH shift.
• Investigation of reflection phenomena near Brewster's angle.

Main Results:

• General formulas for spatial and angular GH shifts of Airyprime beams were derived.
• A direct relationship between the GH shifts of Airyprime and Airy beams was established.
• A significantly enhanced spatial GH shift and a near-zero angular GH shift were predicted for horizontally polarized Airyprime beams near Brewster's angle.

Conclusions:

• The proposed theory provides a robust framework for analyzing GH shifts of Airyprime beams.
• The findings reveal unique optical behaviors of Airyprime beams, particularly near Brewster's angle.
• This research contributes to the understanding of light-matter interactions and potential applications in optical devices.