Abstract

The Schmidt decomposition is exploited to study the spatial entanglement of laser transverse modes analogous to quantum Lissajous states. Based on the inverse Fourier transform, the stationary Lissajous state can be analytically derived as a coherent superposition of degenerate Hermite–Gaussian eigenmodes. With the derived stationary state, the Schmidt modes and the participation number ${N}$ can be employed to evaluate the spatial localization and the quantum entanglement. The larger the participation number, the more localized is the stationary coherent state on the Lissajous figure. Moreover, the larger the participation number, the higher is the spatial entanglement.

© 2021 Optical Society of America

Quantum entanglement by a beam splitter analogous to laser mode transformation by a cylindrical lens

Y. F. Chen, M. X. Hsieh, H. T. Ke, Y. T. Yu, H. C. Liang, and K. F. Huang
Opt. Lett. 46(20) 5129-5132 (2021)

Characterizing propagation-dependent spatial entanglement for structured laser beams generated by an astigmatic mode converter

Y. T. Yu, M. X. Hsieh, H. C. Liang, and Y. F. Chen
Opt. Lett. 47(13) 3223-3226 (2022)

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes

Y. F. Chen, W. C. Chung, X. L. Zheng, M. X. Hsieh, J. C. Tung, and H. C. Liang
Opt. Lett. 48(7) 1818-1821 (2023)

Generalized wave-packet formulation with ray-wave connections for geometric modes in degenerate astigmatic laser resonators

Y. F. Chen, J. C. Tung, M. X. Hsieh, Y. H. Hsieh, H. C. Liang, and K. F. Huang
Opt. Lett. 44(21) 5366-5369 (2019)

High-power structured laser modes: manifestation of quantum Green’s function

Y. F. Chen, Y. C. Tseng, H. T. Ke, M. X. Hsieh, J. C. Tung, Y. H. Hsieh, H. C. Liang, and K. F. Huang
Opt. Lett. 45(16) 4579-4582 (2020)