A quantum analysis of structured classical light beams

Structured light refers to beams endowed with spatially and possibly temporally varying amplitude, phase, or polarization profiles—or all three. A light beam with orbital angular momentum (OAM), for example, has a donut-shaped intensity profile and a helical phase pattern and will twist like a corkscrew as it propagates (see the article by Miles Padgett, Johannes Courtial, and Les Allen, Physics Today, May 2004, page 35 ). A structured beam with inhomogeneous polarization is known as a vector beam, because describing it requires a full vector treatment of Maxwell’s equations. Such a beam could be radially or azimuthally polarized, both of which have cylindrical symmetry about the propagation direction.

Techniques for generating and characterizing structured light are multiplying, and structured light is finding increasing application in areas including optical trapping, metrology , and communication. For both classical and quantum communication—whether through the atmosphere, underwater, or in optical fibers or other media—propagation losses are a central concern. Atmospheric turbulence, for example, doesn’t disturb the polarization of an optical beam but rapidly scatters the spatial components, which results in information loss.

For vector beams, however, the polarization and spatial components are inherently linked through quantumlike correlations. As Andrew Forbes and his group at South Africa’s University of the Witwatersrand now show, that nonseparability lends itself to a quantum mechanics–inspired analysis of propagation losses, even for classical light.

Vector beams can be represented as superpositions of components that each combine a spatial mode with a polarization state. For example, a cylindrical-vector-vortex (CVV) beam that combines OAM ±l modes with right (R) or left (L) circular polarization can be written symbolically as |ψ_l〉 = a|l〉|R〉 + b|−l〉|L〉. Mathematically, the form resembles that of an entangled two-particle quantum system. The figure shows the radial polarization profile that results for l = 1.

As a vector beam travels through a noisy medium, its degree of nonseparability or entanglement—the “vectorness"—decays. Exploiting a concept known as channel–state duality from quantum information theory, Forbes’s PhD student Isaac Nape with collaborators from India show theoretically and experimentally that the decay of any OAM vector beam can be purely determined by that of a single CVV beam—or any other beam that’s maximally nonseparable. The approach offers a fast, easy probe for characterizing information loss, both classical and quantum, in noisy channels. (I. Nape et al., Phys. Rev. Appl. 15, 034030, 2021 .)