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Register a new userCreating Complex Optical Longitudinal Polarization Structures
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In this paper we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon non-paraxially propagating a tightly focused sub-wavelength beam. Remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.
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Random light fields -- commonly known as speckles -- demonstrate Rayleigh intensity statistics and only possess local correlations: which occur within the individual speckle grains. In this work, we develop an experimental method for customizing the intensity probability density function (PDF) of speckle patterns while simultaneously introducing non-local spatial correlations among the speckle grains. The various families of tailored speckle patterns -- created by our method -- can exhibit radically different topologies, statistics, and variable degrees of spatial order. Irrespective of their distinct statistical properties, however, all of these speckles are created by appropriately encoding high-order correlations into the phase front of a monochromatic laser beam with a spatial light modulator. In addition to our experimental demonstration, we explore both the theoretical and practical limitations on the extent to which the intensity PDF and the spatial intensity correlations can be manipulated concurrently in a speckle pattern. This work provides a versatile methodology for creating complex light fields and controlling their statistical properties with varied applications in microscopy, imaging, and optical manipulation.
A classical way of describing a dielectric function employs sums of contributions from damped harmonic oscillators. Each term leads to a maximum in the imaginary part of the dielectric function at the transversal optical (TO) resonance frequency of the corresponding oscillator. In contrast, the peak maxima of the negative imaginary part of the inverse dielectric function are attributed to the so-called longitudinal optical (LO) oscillator frequencies. The shapes of the corresponding bands resemble those of the imaginary part of the dielectric function. Therefore, it seems natural to also employ sums of the contributions of damped harmonic oscillators to describe the imaginary part of the inverse dielectric function. In this contribution, we derive the corresponding dispersion relations to investigate and establish the relationship between the transversal and longitudinal optical oscillator strength, which can differ, according to experimental results, by up to three orders of magnitude. So far, these differences are not understood and prevent the longitudinal optical oscillator strengths from proper interpretation. We demonstrate that transversal and longitudinal oscillator strengths should be identical for a single oscillator and that the experimental differences are in this case due to the introduction of a dielectric background in the dispersion formula. For this effect we derive an exact correction. Based on this correction we further derive a modified Kramers-Kronig sum rule for the isotropic case as well as for the components of the inverse dielectric function tensor. For systems with more than one oscillator, our model for the isotropic case can be extended to yield oscillator strengths and LO resonance wavenumber for uncoupled LO modes with or without dielectric background...
We show that non-linear optical structures involving a balanced gain-loss profile, can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T), with optical nonlinear effects. This novel unidirectional dynamics is specifically demonstrated for the case of an integrable PT-symmetric nonlinear system.
Birefringent materials or nanostructures that introduce phase differences between two linear polarizations underpin the operation of wave plates for polarization control of light. Here we develop metasurfaces realizing a distinct class of complex-birefringent wave plates, which combine polarization transformation with a judiciously tailored polarization-dependent phase retardance and amplitude filtering via diffraction. We prove that the presence of loss enables the mapping from any chosen generally non-orthogonal pair of polarizations to any other pair at the output. We establish an optimal theoretical design-framework based on pairwise nanoresonator structures and experimentally demonstrate unique properties of metasurfaces in the amplification of small polarization differences and polarization coupling with unconventional phase control. Furthermore, we reveal that these metasurfaces can perform arbitrary transformations of biphoton polarization-encoded quantum states, including the modification of the degree of entanglement. Thereby, such flat devices can facilitate novel types of multi-functional polarization optics for classical and quantum applications.
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.
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