• Open Access

Transverse Spin and Momentum in Two-Wave Interference

Aleksandr Y. Bekshaev, Konstantin Y. Bliokh, and Franco Nori
Phys. Rev. X 5, 011039 – Published 30 March 2015
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Abstract

We analyze the interference field formed by two electromagnetic plane waves (with the same frequency but different wave vectors), and find that such a field reveals a rich and highly nontrivial structure of the local momentum and spin densities. Despite the seemingly planar and extensively studied character of the two-wave system, we find that it possesses a transverse (out-of-plane) helicity-independent spin density and also a transverse polarization-dependent momentum density with unusual physical properties. The polarization-dependent transverse momentum represents the so-called Belinfante spin momentum, which does not exert the usual optical pressure and is considered as “virtual” in field theory. We perform analytical estimations and exact numerical simulations of the interaction of the two-wave field with probe Mie particles. The results of these calculations clearly indicate the straightforward detectability of the unusual spin and momentum properties in the two-wave field and strongly motivate their future experimental verifications.

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  • Received 15 September 2014

DOI:https://doi.org/10.1103/PhysRevX.5.011039

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Aleksandr Y. Bekshaev1,2, Konstantin Y. Bliokh1,3, and Franco Nori1,4

  • 1Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan
  • 2I. I. Mechnikov National University, Dvorianska 2, Odessa, 65082, Ukraine
  • 3iTHES Research Group, RIKEN, Wako-shi, Saitama 351-0198, Japan
  • 4Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

Popular Summary

The interference between two plane waves has always provided an important model for understanding the basic features of wave fields; it is difficult to find a simpler and more thoroughly studied system in wave physics. We show that such a basic system still exhibits unexpected and unusual features.

We analyze the interference field of two electromagnetic plane waves, with the same frequency but different directions of propagation, and find that such a field reveals a rich and nontrivial structure of the local momentum and spin angular-momentum densities. Despite the seemingly planar character of the two-wave system, it possesses transverse (out-of-plane) momentum and spin densities with extraordinary physical properties. In contrast to the usual longitudinal momentum and spin of a plane wave, the transverse momentum is strongly polarization dependent, and the transverse spin is independent of the polarization helicity and appears even for linearly polarized waves. These findings have only been shown previously for evanescent waves, which are more difficult to produce in the laboratory. We perform analytical estimations and exact numerical simulations of the interaction of the two-wave field with a spherical Mie particle. The results of these calculations indicate the straightforward detectability of the unusual transverse momentum and spin, which push and twirl the probe particle.

Our findings offer a new vision for the fundamental properties of propagating optical fields and pave the way for novel optical manipulations of small particles. We suggest that these theoretical results be followed up with experimental verification.

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Vol. 5, Iss. 1 — January - March 2015

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