Supersymmetric (SUSY) transformations that originated in quantum physics and were recently adapted to photonics, offer a robust, physics-based approach to designing photonic structures such as optical filters, gratings, and lasers. On the other hand, second-order supersymmetry (2-SUSY) facilitates the engineering of quantum wells in order to optimize second-order nonlinear interactions. In this talk, we discuss a number of linear and nonlinear photonic structures designed using the 2-SUSY. In particular, we demonstrate the design of strongly enhanced second-order nonlinear optical susceptibilities in quantum wells that are being fabricated using digitally graded alloys.
The rapid development of optical technologies, such as optical manipulation and trapping, data processing, optical sensing and metrology, enhanced imaging and microscopy, as well as classical and quantum communications necessitates fundamental studies of the new degrees of freedom for sculpting optical beams in space and time beyond conventionally used amplitude, phase, and polarization. Topological structured optical fields have emerged as one of the most promising candidates for such degrees of freedom. We will discuss our theoretical and experimental studies of “structured light and darkness” generation, detection, and linear and nonlinear light-matter interactions of optical links and knots in complex media such as optical metasurfaces and highly scattering media.
In contrast to the conventional Gaussian beams or plane waves, the interaction of structured lights with matter and meta-matter can pave the way toward novel optical effects such as exciting higher order multipolar moments or enabling nonradiating anapole states. In this work, Laguerre-Gaussian (LG) beams with various orbital angular momentum are used to excite and control the spectral location of the magnetic quadrupole modes within the all-dielectric meta-atoms. To experimentally validate this phenomenon, silicon-based meta-atoms are fabricated and illuminated by various LG beams. The experimental results are in good agreement with the theoretical predictions.
Supersymmetry (SUSY) enables tuning of certain eigenvalues of quantum well without changing other states. We leverage second-order SUSY to tune the intermediate state of asymmetric coupled quantum well states. A family of such quantum wells can be used for upconversion of two bands of frequencies into a single frequency. We investigate the total nonlinear conversion of light in a metallic coupled quantum well system. We obtain non-uniform refractive index distributions required to tune the frequency of the intermediate state while leaving the ground and excited state unchanged. We repeat SUSY transformations to tune the eigenvalues required for third-order susceptibility.
In electromagnetics, a medium moving at non-relativistic velocities is equivalent to a bianisotropic refractive index, produces the same effect for light as vector potential for charged particles. We investigate Mie scattering from the cylinder made of magneto-electric material. We find Poynting vector singularities in the near field distribution. A high k-vector region around the singularity may find applications in the near field superresolution imaging. We predict an additional phase change in the far-field for the magneto-electric cylinder compared to conventional Mie scattering. The magneto-electric coefficient can control the angular position of the phase change in the far-field and the position of the Poynting vector singularities.
In this talk we theoretically and experimentally investigate an interesting family of null solutions to Helmholtz equation in 3D free space - optical vortices, or zero lines of complex amplitude in a propagating light field, that are knotted or linked in a certain way. We design all-dielectric optical metasurfaces – nanostructures enabling unprecedented control over the amplitude, polarization and phase of optical fields, for generation of optical knots, and study their stability and evolution in engineered colloidal suspensions with saturable Kerr-like nonlinearity. These studies are further generalized to characterization of knot evolution in turbid linear and nonlinear media, such as clouds, fog, biological media, and undersea environments. Knotted electromagnetic fields may find applications in three-dimensional optical manipulations or could be considered as candidates for new information carriers in classical and quantum communication systems.
Structured light carrying spin and orbital angular momentum brings about new light-matter interactions in optical nanostructures. We demonstrate the possibility of using structured light beams carrying orbital angular momentum (OAM) to access resonant modes of all-dielectric meta-atoms that cannot be excited by the conventional Gaussian beam or by a plane wave. We use multipole decomposition approach to match extinction resonances with high-order multipole excitation. These results can find applications in sensing, spectroscopy, and enable new regimes of nonlinear optical interactions.
Supersymmetric (SUSY) design is an intuitive procedure for the inverse design of structures from known spectral features. We design one-dimensional corrugated waveguides using SUSY for the desired spectral response. Due to the finite length of the grating, inserted states have a finite lifetime. We obtain a bound state in the continuum by the interference of two states at the same frequency decaying in the same waveguide. The transmission coefficient has no imaginary part at the BIC point, leading to an infinite lifetime. For a finite structure, the phase changes abruptly by 2pi without changing the density of states.
To date, the supersymmetric (SUSY) formalism in optics has been used to engineer the spatial distributions of refractive indices. Here, we use SUSY formalism to engineer the shape of the corrugated dielectric waveguide instead of its refractive index profile to enable the insertion of an arbitrary number of transmission peaks in the stopband. These peaks can be used to make low-power intensity-dependent optical switches. Moreover, at microwave frequencies, the embedded states can be used to design leaky wave antennas, capable of scanning continuously from forward to the backward direction through broadside without degradation in beam quality.
The growing demand for high-capacity optical-transmission technologies sparked the growth of integrated and silicon photonics. Efficient on-chip manipulation of optical signals requires development of high-fidelity Y-junctions, photonic lanterns, mode filters and multiplexers, and interferometers.
The concept of supersymmetry (SUSY) originated in the fields of particle physics and enabled treatment for bosons and fermions on equal footing. Supersymmetry has expanded to quantum mechanics, and optics where it can be used, for instance, to design (de)multiplexing arrays of waveguides. To date, the majority of optical applications employed the unbroken SUSY that relates partners supporting the same set of eigenstates with the exception of the fundamental state.
We propose a design of a mode sorter made of fully iso-spectral permittivity profiles related by a continuous SUSY transformation in the broken regime. This ensures that the propagation constants of the all the modes to be sorted are preserved along the length of the device. As a result of this global matching of the propagation constants, the SUSY design allows for reduction of the modal cross-talk by two orders of magnitude compared with a standard asymmetric Y-splitter. Moreover, the SUSY mode sorter operates for both transverse-electric and transverse-magnetic light polarization, and it shows low losses and modal cross-talk over a broad wavelength range (1300-1700 nm). Compared with the previous SUSY based modes sorters, our design offers similar performance with an order of magnitude smaller sorter length and can separate modes without losing energy via radiative modes.
Traditionally, geometrical factors have not played an important role in determining the distribution of current across conducting boundaries. Typically, the classical skin depth expression is used to estimate currents within the volume. We have developed a novel geometry-based framework which describes current distributions within the volume of structures which allows us to engineer skin depth using boundary shapes. A more accurate knowledge of current densities is an important degree of freedom to design and analyze meta-structures and their interactions. Our approach is grounded in a rigorous analysis of electromagnetic wave scattering from shell structures for which the importance of geometrical parameters in the expressions for skin depth to accurately describe interactions has been confirmed. Starting from Maxwell’s equations, we have analyzed the temporal dynamics of electromagnetic interactions with meta-structures and their relationship to vector potentials. Individual wavelength or subwavelength sized meta-structures can be designed to localize the incident electromagnetic radiation and create a change in the local constitutive relations. Having an accurate determination of the current distribution within the volume of scattering structures plays an important role in designing and determining the effective constitutive parameters of 2D and 3D metamaterials. Combinations of materials with custom geometries suggest that this kind of skin depth engineering can lead to new families of linear and non-linear meta-atoms impacting imaging, harmonic generation, and the design of antennas and their shielding.
We discuss the design of two complimentary media for analog detection of sources placed at subwavelength separation using time reversal of observed signals. We have used two metasurfaces composed of bianisotropic structures to code and decode the evanescent fields of the sources to propagating waves. In order to reduce losses and create a perfect focus, resonances are avoided to achieve negative index. We have studied various shapes such as, split ring resonators to determine the least lossy structure for time reversal. We have used simulations to study the behavior of permittivity and permeability values of these structures at various frequencies. Shape parameters such as size of the gap and thickness is being optimized to achieve refractive index of ± 1 at the same frequency and minimize losses in the metasurfaces.
Observations of anomalous far-field scattering patterns from non-perfectly conducting cylindrical shells have lead to an analysis including surface currents and waves. The concept of skin depth is analyzed for wavelength-scale scattering structures when the permeability of the material is low in terms of the magnetic vector potential. Conditions under which interactions between the incident field and material properties below the skin depth affect the far field scattering pattern are illustrated and explained. The possibility of exploiting this to better characterize material properties of meso and nanoscale structures at optical frequencies is presented.
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