High-efficiency Electro-Optic Lens for radio frequency beam wavefront modulation for mode mismatch sensing

TL;DR

This paper introduces a highly efficient electro-optic lens for RF beam wavefront modulation, enabling improved mode mismatch sensing in optical cavity experiments like gravitational wave detectors.

Contribution

It presents a novel RF beam wavefront curvature modulation scheme using an electro-optic lens and mode converting telescope, with detailed analysis for optimizing modulation efficiency.

Findings

Demonstrated second-order mode generation as a function of beam waist and crystal size.

Provided design guidance for beam profile optimization to enhance EOL modulation.

Analyzed effects of Gaussian beam evolution and phase mismatch cancellation.

Abstract

Active mode mismatch sensing and control can facilitate optimal coupling in optical cavity experiments such as interferometric gravitational wave detectors. In this paper, we demonstrate a radio-frequency (RF) beam wavefront curvature modulation-based mode mismatch sensing scheme inspired by the previously proposed RF beam jitter alignment sensing scheme. The proposed mode mismatch sensing scheme uses an electro-optic lens (EOL) device that is designed to provide the required beam wavefront curvature actuation, as well as a mode converting telescope that rephases the RF second-order modes and generates a non-vanishing mode mismatch sensing signal. We carefully investigate the total second-order mode generation from the wavefront actuation both analytically and numerically, taking the effects of Gaussian beam size evolution and the second-order mode phase mismatch cancellation into consideration. We demonstrate the second-order mode generation as a function of the incident beam waist size and the electro-optic crystal size, which along with a ``trade-off'' consideration of the beam size at the edges of the crystal and the clipping loss, provides us with guidance for designing the beam profile that interacts with the crystal to improve the EOL modulation efficiency.