(2D+1) pendulum beams: non-diffracting optical spatial wavepackets that simulate quantum pendulum dynamics

Thao P. Nguyen; Valeria Rodríguez-Fajardo; Enrique J. Galvez

doi:10.1117/12.2627732

2 March 2022 (2D+1) pendulum beams: non-diffracting optical spatial wavepackets that simulate quantum pendulum dynamics

Thao P. Nguyen, Valeria Rodríguez-Fajardo, Enrique J. Galvez

Proceedings Volume 12017, Complex Light and Optical Forces XVI; 1201704 (2022) https://doi.org/10.1117/12.2627732
Event: SPIE OPTO, 2022, San Francisco, California, United States

Abstract

The similarity between the 2D Helmholtz equation in elliptical coordinates and the Schr¨odinger equation for the simple mechanical pendulum inspires us to use light to mimic this quantum system. When optical beams are prepared in Mathieu modes, their intensity in the Fourier plane is proportional to the quantum mechanical probability for the pendulum. Previous works have produced a two-dimensional pendulum beam that oscillates as a function of time through the superpositions of Mathieu modes with phases proportional to pendulum energies. Here we create a three-dimensional pendulum wavepacket made of a superposition of Helical Mathieu-Gaussian modes, prepared in such a way that the components of the wave-vectors along the propagation direction are proportional to the pendulum energies. The resulting pattern oscillates or rotates as it propagates, in 3D, with the propagation coordinate playing the role of time. We obtained several different propagating beam patterns for the unbound-rotor and the bound-swinging pendulum cases. We measured the beam intensity as a function of the propagation distance. The integrated beam intensity along elliptical angles plays the role of quantum pendulum probabilities. Our measurements are in excellent agreement with numerical simulations.

Conference Presentation

Citation Download Citation

Thao P. Nguyen, Valeria Rodríguez-Fajardo, and Enrique J. Galvez "(2D+1) pendulum beams: non-diffracting optical spatial wavepackets that simulate quantum pendulum dynamics", Proc. SPIE 12017, Complex Light and Optical Forces XVI, 1201704 (2 March 2022); https://doi.org/10.1117/12.2627732

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