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In this article we show that in a three dimensional (3D) optical field there can exist two types of hidden singularities, one is spin density (SD) phase singularity and the other is SD vector singularity, which are both unique to 3D fields. The nature of these SD singularities is discussed and their connection with traditional optical singularities is also examined. Especially it is shown that in a 3D field with purely transverse spin density (`photonic wheels), these two types of singularities exhibit very interesting behaviors: they are exactly mapped to each other regardless of their different physical meanings and different topological structures. Our work supplies a fundamental theory for the SD singularities and may provide a new way for further exploration of 3D optical fields.
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Chiral optical effects are generally quantified along some specific incident directions of exciting waves (especially for extrinsic chiralities of achiral structures) or defined as direction-independent properties by averaging the responses among all structure orientations. Though of great significance for various applications, chirality extremization (maximized or minimized) with respect to incident directions or structure orientations have not been explored, especially in a systematic manner. In this study we examine the chiral responses of open photonic structures from perspectives of quasi-normal modes and polarization singularities of their far-field radiations. The nontrivial topology of the momentum sphere secures the existence of singularity directions along which mode radiations are either circularly or linearly polarized. When plane waves are incident along those directions, the reciprocity ensures ideal maximization and minimization of optical chiralities, for corresponding mode radiations of circular and linear polarizations respectively. For directions of general elliptical polarizations, we have unveiled the subtle equality of a Stokes parameter and the circular dichroism, showing that an intrinsically chiral structure can unexpectedly exhibit no chirality at all or even chiralities of opposite handedness for different incident directions. The framework we establish can be applied to not only finite scattering bodies but also infinite periodic structures, encompassing both intrinsic and extrinsic optical chiralities. We have effectively merged two vibrant disciplines of chiral and singular optics, which can potentially trigger more optical chirality-singularity related interdisciplinary studies.
Polarization singularities of vectorial electromagnetic fields locate at the positions (such as points, lines, or surfaces) where properties of polarization ellipses are not defined. They are manifested as circular and linear polarization, for which respectively the semi-major axes and normal vectors of polarization ellipses become indefinite. First observed in conical diffraction in the 1830s, the field of polarization singularities has been systematically reshaped and deepened by many pioneers of wave optics. Together with other exotic phenomena such as non-Hermiticity and topology, polarization singularities have been introduced into the vibrant field of nanophotonics, rendering unprecedented flexibilities for manipulations of light-matter interactions at the nanoscale. Here we review the recent results on the generation and observation of polarization singularities in metaphotonics. We start with the discussion of polarization singularities in the Mie theory, where both electric and magnetic multipoles are explored from perspectives of local and global polarization properties. We then proceed with the discussion of various photonic-crystal structures, for which both near- and far-field patterns manifest diverse polarization singularities characterized by the integer Poincare or more general half-integer Hopf indices (topological charges). Next, we review the most recent studies of
Electromagnetic plane waves, solutions to Maxwells equations, are said to be `transverse in vacuum. Namely, the waves oscillatory electric and magnetic fields are confined within a plane transverse to the waves propagation direction. Under tight-focusing conditions however, the field can exhibit longitudinal electric or magnetic components, transverse spin angular momentum, or non-trivial topologies such as Mobius strips. Here, we show that when a suitably spatially structured beam is tightly focused, a 3-dimensional polarization topology in the form of a ribbon with two full twists appears in the focal volume. We study experimentally the stability and dynamics of the observed polarization ribbon by exploring its topological structure for various radii upon focusing and for different propagation planes.
We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded
profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co- ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an invisible disc and multipole lenses.
Spatially inhomogeneous fields of electromagnetic guided modes exhibit a complex of extraordinary dynamical properties such as the polarization-dependent transverse momentum, helicity-independent transverse spin, spin-associated non-reciprocity and unidirectional propagation, etc. Recently, the remarkable relationship has been established between the spin and propagation features of such fields, expressed through the spin-momentum equations [Proc. Natl. Acad. Sci. 118 (2021) e2018816118] connecting the wave spin with the curl of momentum. Here, the meaning, limitations and specific forms of this correspondence are further investigated, involving the physically transparent and consistent examples of paraxial light fields, plane-wave superpositions and evanescent waves. The conclusion is inferred that the spin-momentum equation is an attribute of guided waves with well defined direction of propagation, and it unites the helicity-independent extraordinary transverse spin with the spatially-inhomogeneous longitudinal field momentum (energy flow) density. Physical analogies with the layered hydrodynamic flows and possible generalizations for other wave fields are discussed. The results can be useful in optical trapping, manipulation and the data processing techniques.
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