Poles of the scattering matrix: an inverse method for designing photonic resonators.

We develop and implement a new inverse computational framework for designing photonic elements with one or more high-Q scattering resonances. The approach relies on solving for the poles of the scattering matrix, which mathematically amounts to minimizing the determinant of the matrix representing the Fredholm integral operator of the electric field with respect to the permittivity profile of the scattering element. We apply the method to design subwavelength gradient-permittivity structures with multiple scattering resonances and quality factors as high as 800. We also find the spectral scattering cross sections are consistent with Fano lineshapes. The compact form and computational efficiency of our formalism suggest it can be an effective tool for designing Fano-resonant structures with multiple high-Q resonances for applications such as frequency mixing and conversion.

Indium phosphide metasurface with enhanced nonlinear absorption.

We solve the nonlinear Maxwell equations in an InP-based dielectric metamaterial, considering both two-photon absorption and photo-induced free-carrier absorption. We obtain the intensity-dependent reflection, absorption, and effective permittivity and permeability of the metamaterial. Our results show that nonlinear absorption dampens both the electric and magnetic Mie resonance, although the magnetic resonance is more affected because it occurs at longer wavelengths where the free-carrier absorption cross section is larger. Owing to field concentration in the metamaterial at resonance, the threshold intensity for nonlinear absorption is reduced by a factor of about 30 compared to a homogeneous layer of the same thickness. Our results have implications on the use of dielectric metamaterials for nonlinear applications such as higher harmonic generation, optical limiting, and ultrafast modulation.

Transfer matrix method for four-flux radiative transfer.

We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.

Metasurface polarization splitter.

Polarization beam splitters, devices that separate the two orthogonal polarizations of light into different propagation directions, are among the most ubiquitous optical elements. However, traditionally polarization splitters rely on bulky optical materials, while emerging optoelectronic and photonic circuits require compact, chip-scale polarization splitters. Here, we show that a rectangular lattice of cylindrical silicon Mie resonators functions as a polarization splitter, efficiently reflecting one polarization while transmitting the other. We show that the polarization splitting arises from the anisotropic permittivity and permeability of the metasurface due to the twofold rotational symmetry of the rectangular unit cell. The high polarization efficiency, low loss and low profile make these metasurface polarization splitters ideally suited for monolithic integration with optoelectronic and photonic circuits.This article is part of the themed issue 'New horizons for nanophotonics'.

Infrared antenna measurement of the spatial coherence function.

The degree of coherence of a partially coherent monochromatic optical field is measured with a dual-dipole phased-array antenna coupled to a metal-oxide-metal tunnel diode detector. For a two-element phased-array, the degree of coherence is a measure of the correlation of electric fields received by the antennas as a function of the element separation. To extract the coherence function from the measured antenna response, a calibration method is developed to remove propagation loss and device nonuniformity. Measurements at 10.6 µm are substantiated by electromagnetic simulations and compared to the result derived from the Van Cittert-Zernike theorem.

Directional control of infrared antenna-coupled tunnel diodes.

Directional control of received infrared radiation is demonstrated with a phased-array antenna connected by a coplanar strip transmission line to a metal-oxide-metal (MOM) tunnel diode. We implement a MOM diode to ensure that the measured response originates from the interference of infrared antenna currents at specific locations in the array. The reception angle of the antenna is altered by shifting the diode position along the transmission line connecting the antenna elements. By fabricating the devices on a quarter wave dielectric layer above a ground plane, narrow beam widths of 35° FWHM in power and reception angles of ± 50° are achieved with minimal side lobe contributions. Measured radiation patterns at 10.6 µm are substantiated by electromagnetic simulations as well as an analytic interference model.

Influence of substrate configuration on the angular response pattern of infrared antennas.

The far-field angular response pattern for dipole antenna-coupled infrared detectors is investigated. These devices utilize an asymmetric metal-oxide-metal diode that is capable of rectifying infrared-frequency antenna currents without applied bias. Devices are fabricated on both planar and hemispherical lens substrates. Measurements indicate that the angular response can be tailored by the thickness of the electrical isolation standoff layer on which the detector is fabricated and/or the inclusion of a ground plane. Electromagnetic simulations and analytical expressions show excellent agreement with the measured results.

Wavelength-dependent diffraction patterns from a liquid crystal display.

Liquid crystal displays (LCDs) are invaluable for a variety of optical applications, including the encoding of programmable diffractive optical elements. The pixel structure in these devices produces a set of diffracted orders of which the central order is the strongest. In most devices that we have examined, the intensity distribution of the diffraction pattern is independent of the wavelength of the illuminating light. Recently we have been examining the performance of LCDs having very small pixel sizes. We compare results for two devices from the same manufacturer. One of them exhibits the normal behavior. For the other, we find surprisingly strong wavelength dependence. The diffraction pattern varies from having most of the energy in the zero order for long wavelengths to having the energy distributed among 50-60 orders as the wavelength decreases. We attribute this behavior to a phase structure over each pixel. We analyze this behavior using a simple two-dimensional model that qualitatively explains the phenomenon. These results can be viewed in two ways--on the positive side this behavior might lead to optical logic or fan-out applications. On the negative side, there is less intensity available in the normally used zero order.

High diffraction efficiency from one- and two-dimensional Nyquist frequency binary-phase gratings.

We examine the diffraction properties of one- and two-dimensional binary-phase gratings encoded onto pixelated liquid crystal displays (LCDs). We find that the first-order diffracted intensity from these binary-phase patterns can reach 100% of the zero-order intensity when the period of the grating approaches the Nyquist limit of the LCD. Experimental results show excellent agreement with theoretical predictions. This is a surprising result that has a number of implications for the encoding of diffractive optical elements.