Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones.

A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.

Lasing threshold control in two-dimensional photonic crystals with gain.

We demonstrate how the lasing threshold of a two dimensional photonic crystal containing a four-level gain medium is modified, as a result of the interplay between the group velocity and the modal reflectivity at the interface between the cavity and the exterior. Depending on their relative strength and the optical density of states, we show how the lasing threshold may be dramatically altered inside a band or, most importantly, close to the band edge. The idea is realized via self-consistent calculations based on a finite-difference time-domain method. The simulations are in good agreement with theoretical predictions.

Finite element simulation of microphotonic lasing system.

We present a method for performing time domain simulations of a microphotonic system containing a four level gain medium based on the finite element method. This method includes an approximation that involves expanding the pump and probe electromagnetic fields around their respective carrier frequencies, providing a dramatic speedup of the time evolution. Finally, we present a two dimensional example of this model, simulating a cylindrical spaser array consisting of a four level gain medium inside of a metal shell.

Complex k band diagrams of 3D metamaterial/photonic crystals.

A finite element method (FEM) for solving a complex valued k(ω) vs. ω dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue method [Opt. Express 15, 9681 (2007)]. This method is particularly convenient for analyzing periodic systems containing dispersive (e.g., plasmonic) materials, for computing isofrequency surfaces in the k-space, and for calculating the decay length of the evanescent waves. Two specific examples are considered: a photonic crystal comprised of dielectric spheres and a plasmonic fishnet structure. Hybridization and avoided crossings between Mie resonances and propagating modes are numerically demonstrated. Negative index propagation of four electromagnetic modes distinguished by their symmetry is predicted for the plasmonic fishnets. By calculating the isofrequency contours, we also demonstrate that the fishnet structure is a hyperbolic medium.

Measurements of the negative refractive index of sub-diffraction waves propagating in an indefinite permittivity medium.

An indefinite permittivity medium (IPM) has been fabricated and optically characterized in mid-infrared spectral range (10.7 µm-11.3 µm). Phase and amplitude transmission measurements reveal two remarkable properties of IPMs: (i) transmission of sub-diffraction waves (as short as λ/4) can exceed those of diffraction-limited ones, and (ii) sub-diffraction waves can propagate with negative refractive index. We describe a novel double-detector optical technique relying on the interference between sub-diffraction and diffraction-limited waves for accurate measurement of the transmission amplitude and phase of the former.

Interferometric characterization of a sub-wavelength near-infrared negative index metamaterial.

Negative phase advance through a single layer of near-IR negative index metamaterial (NIM) is identified through interferometric measurements. The NIM unit cell, sub-wavelength in both the lateral and light propagation directions, is comprised of a pair of Au strips separated by two dielectric and one Au film. Numerical simulations show that the negative phase advance through the single-layer sample is consistent with the negative index exhibited by a bulk material comprised of multiple layers of the same structure. We also numerically demonstrate that the negative index band persists in the lossless limit.

Critically coupled surface phonon-polariton excitation in silicon carbide.

We observe critical coupling to surface phonon-polaritons in silicon carbide by attenuated total reflection of mid-IR radiation. Reflectance measurements demonstrate critical coupling by a double scan of wavelength and incidence angle. Critical coupling occurs when prism coupling loss is equal to losses in silicon carbide and the substrate, resulting in maximal electric field enhancement.

Polarization conversion in a silica microsphere.

We experimentally demonstrate controlled polarization-selective phenomena in a whispering gallery mode resonator. We observed efficient ( approximately 75%) polarization conversion of light in a silica microsphere coupled to a tapered optical fiber with proper optimization of the polarization of the propagating light. A simple model treating the microsphere as a ring resonator provides a good fit to the observed behavior.

Nonlinear polarization conversion using microring resonators.

We present a design of a polarization converter between linear, circular, and elliptic accomplished with an on-chip high-Q dielectric microring resonator. Nonlinear polarization switching can be accomplished at modest input intensities because of the high-intensity compression in the ring. We predict an optical bistability effect making the polarization of the transmitted light dependent on its spectral or intensity history.

Simultaneous fast and slow light in microring resonators.

Two orthogonal light polarizations in a waveguide overcoupled to microring resonators can propagate as fast and slow light. Which polarization is fast (slow) is determined by input polarization and the number of resonators.

Whispering gallery mode microresonators as polarization converters.

A ring resonator coupled to a waveguide can be used as a highly efficient polarization converter when the input is properly polarized. We model this phenomenon and verify the predictions with a demonstration of very efficient polarization conversion (>90%) on a silica microsphere coupled to a tapered optical fiber.