# Phase induced transparency mediated structured beam generation in a closed-loop tripod configuration

## TL;DR

This paper introduces a phase induced transparency method in a closed-loop atomic system to generate and control structured optical beams with petal-like patterns, enhanced contrast, and rotation effects, applicable in strong and weak field regimes.

## Contribution

It presents a novel scheme combining phase structured beams and magnetic fields to produce and manipulate structured light in a four-level atomic system, extending previous work with new control mechanisms.

## Key findings

- Structured beams with petal-like patterns are generated through phase-dependent absorption.
- Contrast of the structured beams can be enhanced by adjusting magnetic field and probe intensity.
- Strong fields induce nonlinear magneto-optical rotation affecting beam orientation.

## Abstract

We present a phase induced transparency based scheme to generate structured beam patterns in a closed four level atomic system. We employ phase structured probe beam and a transverse magnetic field (TMF) to create phase dependent medium susceptibility. We show that such phase dependent modulation of absorption holds the key to formation of a structured beam. We use a full density matrix formalism to explain the experiments of Radwell et al. [Phys. Rev. Lett. 114,123603 (2015)] at weak probe limits. Our numerical results on beam propagation confirms that the phase information present in the absorption profile gets encoded on the spatial probe envelope which creates petal-like structures even in the strong field limit. The contrast of the formed structured beam can be enhanced by changing the strength of TMF as well as of the probe intensity. In weak field limits an absorption profile is solely responsible for creating a structured beam, whereas in the strong probe regime, both dispersion and absorption profiles facilitate the generation of high contrast structured beam. Furthermore we find the rotation of structured beams owing to strong field induced nonlinear magneto-optical rotation (NMOR).