Transverse Spin and Transverse Momentum in Structured Optical Fields

Abstract

It has been recently recognized that in addition to the conventional longitudinal angular momentum, structured (inhomogeneous) optical fields exhibit helicity‐independent transverse spin angular momentum (SAM) and an unusual spin (circular polarization)‐dependent transverse momentum, the so‐called Belinfante's spin momentum. Such highly nontrivial structure of the momentum and the spin densities in the structured optical fields (e.g. evanescent fields) has led to a number of fundamentally interesting and intricate phenomena, e.g. the quantum spin Hall effect of light and the optical spin‐momentum locking in surface optical modes similar to that observed for electrons in topological insulators. In this article, we introduce the basic concepts and look into the genesis of transverse SAM and transverse spin–momentum in structured light. We then discuss few illustrative examples of micro‐ and nano‐optical systems where these illusive entities can be observed. The studied systems include planar and spherical micro‐ and nanostructures. We also investigate the ways and means of enhancing the elusive extraordinary spin. In particular, we show that dispersion management leading to avoided crossing along with perfect absorption mediated by recently discovered coherent perfect absorption can positively influence the resonant enhancement of the transverse spin and spin momentum. The role of mode mixing and interference of neighboring transverse electric and transverse magnetic scattering modes of diverse micro‐ and nano‐optical systems are illustrated with the selected examples. The results demonstrate possibilities for the enhancement of not only the magnitudes but also the spatial extent of transverse SAM and the transverse momentum components, which opens up interesting avenues for experimental detection of these illusive fundamental entities and may enhance the ensuing spin‐based photonic applications.

Structured Light: Ideas and Concepts

“…It is tempting to call it "momentum spin, " as a reciprocal to the "spin momentum" of Equation (29), but this may be confusing, and therefore, the term "extraordinary spin" will be used. Existence of extraordinary spin and momentum with directions different from the wave propagation is a characteristic feature of structured light and is attracting much attention [74]; their specific examples and possible applications are discussed below in the Evanescent Waves: Extraordinary Spin and Momentum section, Surface Plasmon-Polaritons section and the Applications of Structured Light section. The latter Equation (39) discloses an interesting relation between the s E and the vorticity [9,20] (curl) of the OM.…”

Extraordinary transverse spin: hidden vorticity of the energy flow and momentum distributions in propagating light fields

“…, regardless of how is it divided between the polarization components). This spin appears due to the field vector rotation in the longitudinal plane and its analogues were recently discovered in a series of structured optical fields [6,[10][11][12][13][14][15][16] as well as in structured fields of other physical natures [17][18][19]. By comparison with Eqs.…”

“…In particular, a complex structure of electromagnetic momentum has been revealed: it consists of the orbital (canonical) and spin (virtual) contributions, reflecting the roles of spatial (orbital) and polarization (spin) degrees of freedom [6,5,10]; likewise, the electromagnetic spin can also be decomposed into physically meaningful parts, differently related to the field polarization. It is found that the polarization-dependent "spin momentum" (SM) p S shows an "extraordinary" behavior: it can be directed orthogonally to the predominant direction of light propagation [11][12][13][14][15][16]. Quite similarly, the "transverse" orientation is typical for the helicityindependent "extraordinary spin" (ES) s E associated with the rotation of the field vectors in the longitudinal plane [12][13][14][15].…”

Spectral singularity enhances transverse spin

“…In recent years there has been a great deal of interest in the angular momentum carried by light [1][2][3]. It is now well understood that in addition to usual longitudinal angular momentum structured light can possess an extraordinary transverse spin angular momentum (SAM) [4][5][6][7][8][9][10][11]. While the transverse SAM is helicity independent, the transverse momentum can be sensitive to the helicity, opening up new possibilities for spin optics [4][5][6].…”

“…The rotating tip of the field vector in time in the plane of incidence results on transverse spin. All these features have been discussed at great length in several recent reviews [3,11,22,23]. One of the major directions that emerge is how to enhance the tiny Belinfante momentum.…”