Introducing Berry phase gradients along the optical path via propagation-dependent polarization transformations

Ahmed H Dorrah,Aun Zaidi,Michele Tamagnone,Noah A Rubin,Federico Capasso

doi:10.1515/nanoph-2021-0560

Abstract

Abstract As a classical or quantum system undergoes a cyclic evolution governed by slow change in its parameter space, it acquires a topological phase factor known as the geometric or Berry phase. One popular manifestation of this phenomenon is the Gouy phase which arises when the radius of curvature of the wavefront changes adiabatically in a cyclic manner, for e.g., when focused by a lens. Here, we report on a new manifestation of the Berry phase in 3D structured light which arises when its polarization state adiabatically evolves along the optical path. We show that such a peculiar evolution of angular momentum, which occurs under free space propagation, is accompanied by an accumulated phase shift that elegantly coincides with Berry’s prediction. Unlike the conventional dynamic phase, which accumulates monotonically with propagation, the Berry phase observed here can be engineered on demand, thereby enabling new possibilities; such as spin-dependent spatial frequency shifts, and modified phase matching in resonators and nonlinear interactions. Our findings expand the laws of wave propagation and can be applied in optics and beyond.

Highlights

One of the many wonders of the quantum world manifests when a charged particle passes around a long solenoid; the magnetic field is negligible in the region through which the particle passes and the particle’s wavefunction is negligible inside the solenoid, the particle’s wavefunction still experiences a phase shift as a result of the enclosed magnetic field [1]
The output beam was detected by a CCD after passing through a combination of polarization optics which analyze for x, ŷ, 45◦, and circular polarization states, to measure the output polarization state via Stokes polarimetry [59]
We examined a new class of polarization meta-optics which implements a superposition of Bessel beams with different cone angles, each weighted by a different Jones matrix, allowing the spin angular momentum of the ensemble to be tailored at-will along the optical path

Summary

Introduction

One of the many wonders of the quantum world manifests when a charged particle passes around a long solenoid; the magnetic field is negligible in the region through which the particle passes (outside the solenoid) and the particle’s wavefunction is negligible inside the solenoid, the particle’s wavefunction still experiences a phase shift as a result of the enclosed magnetic field [1] This mysterious interaction—confirmed by various experimental setups [2,3,4,5,6,7,8,9,10]—is known as the Aharonov–Bohm effect and highlights the role of electromagnetic potentials, φ and A, which were often debated as mere mathematical constructs, in enforcing the principle of locality [11]. This additional phase factor is referred-to today as the geometric or Berry phase

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Conclusion