Deterministic access of broadband frequency combs in microresonators using cnoidal waves in the soliton crystal limit.

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si3N4 microresonators with small or intermediate dimensions and an SiO2 microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

Ultra-broadband, polarization-independent, wide-angle absorption in impedance-matched metamaterials with anti-reflective moth-eye surfaces.

We computationally study periodic impedance-matched metal-dielectric metamaterials and the advantage of imprinting moth-eye surfaces on them. Impedance-matched metamaterials are known to act as strong, polarization-independent, broadband absorbers. However, in the infrared region far from the metal's plasma frequency, the reflection from metal layers dominates over the absorption. Using anti-reflective moth-eye surfaces we show that it is possible to obtain absorption independent of polarization or incidence angle, over an exceptionally broad frequency range from 400 nm to 6 µm.

Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal.

We study second harmonic generation in a 2-D photonic crystal with the pump field tuned at the Dirac point of the structure. The simultaneous generation of both forward and backward phase-matched second harmonic is achieved by exploiting a peculiar regime in which the interacting waves have zero phase velocity in the lattice. This regime can be attained even when strong material dispersion is present and therefore lends itself well to be implemented in semiconductor-based frequency conversion devices. A comparison between this method and the quasi-phase-matching technique is also presented.

All-optical bistability and switching near the Dirac point of a 2-D photonic crystal.

We investigate all-optical switching at the guided mode resonances originating near the Dirac point of a finite, 2-D photonic crystal consisting of a square lattice of dielectric columns possessing a cubic nonlinearity. The peculiar field localization properties of these Dirac-point guided mode resonances conspire to yield extremely low switching threshold at near-to-normal incidence for remarkably low filling factors of the nonlinear material.

Nonlinear plasmonic cloaks to realize giant all-optical scattering switching.

Here we extend the reach of Fano resonant coupling by combining this concept with cloaking and plasmonic resonances in a single nonlinear nanoparticle, in order to realize giant all-optical scattering nanoswitches controlled by moderate pumping intensities. We show that a core-shell nonlinear plasmonic particle may be designed to abruptly switch from being completely cloaked to being strongly resonant, with up to a 40 dB cross-sectional difference. Self-tunable optical cloaks and resonant scatterers are envisioned for use as efficient all-optical switches and nanomemories.

Long range plasmon assisted all-optical switching at telecommunication wavelengths.

We exploit the properties of ultranarrow, Fano-like resonances generated by the coupling of long range surface plasmons with ultrathin (~10 nm), metallic, subwavelength gratings embedded in a nonlinear, cubic material to obtain all-optical switching at telecommunication wavelengths for extremely low input power. We provide an example of a silver metallic grating embedded in a chalcogenide glass (As2S3), and we show the concrete possibility to achieve all-optical switching at local field intensities compatible with the photo-darkening threshold of the material.

Ultraviolet surface-enhanced Raman scattering at the plasmonic band edge of a metallic grating.

Surface-enhanced Raman Scattering (SERS) is studied in sub-wavelength metallic gratings on a substrate using a rigorous electromagnetic approach. In the ultraviolet SERS is limited by the metallic dampening, yet enhancements as large as 10(5) are predicted. It is shown that these enhancements are directly linked to the spectral position of the plasmonic band edge of the metal/substrate surface plasmon. A simple methodology is presented for selecting the grating pitch to produce optimal enhancement for a given laser frequency.

Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings.

Extraordinary optical transmission through metallic gratings is a well established effect based on the collective resonance of corrugated screens. Being based on plasmonic resonances, its bandwidth is inherently narrow, in particular, for thick screens and narrow apertures. We introduce here a different mechanism to achieve total transmission through an otherwise opaque screen, based on an ultrabroadband tunneling that can span from dc to the visible range at a given incidence angle. This phenomenon effectively represents the equivalent of Brewster transmission for plasmonic and opaque screens.

Second harmonic generation from metallo-dielectric multilayered structures in the plasmonic regime.

We present a theoretical study on second harmonic generation from metallo-dielectric multilayered structures in the plasmonic regime. In particular we analyze the behavior of structures made of Ag (silver) and MgF2 (magnesium-fluoride) due to the straightforward procedure to grow these materials with standard sputtering or thermal evaporation techniques. A systematic study is performed which analyzes four different kinds of elementary cells--namely (Ag/MgF2)N, (MgF2/Ag)N, (Ag/MgF2/Ag)N and (MgF2/Ag/MgF2)N--as function of the number of periods (N) and the thickness of the layers. We predict the conversion efficiency to be up to three orders of magnitude greater than the conversion efficiency found in the non-plasmonic regime and we point out the best geometries to achieve these conversion efficiencies. We also underline the role played by the short-range/long-range plasmons and leaky waves in the generation process. We perform a statistical study to demonstrate the robustness of the SH process in the plasmonic regime against the inevitable variations in the thickness of the layers. Finally, we show that a proper choice of the output medium can further improve the conversion efficiency reaching an enhancement of almost five orders of magnitude with respect to the non plasmonic regime.

Energy considerations for a superlens based on metal/dielectric multilayers.

We investigate the resolution and absorption losses of a Ag/GaP multilayer superlens. For a fixed source to image distance the resolution is independent of the position of the lens but the losses depend strongly on the lens placement. The absorption losses associated with the evanescent waves can be significantly larger than losses associated with the propagating waves especially when the superlens is close to the source. The interpretation of transmittance values greater than unity for evanescent waves is clarified with respect to the associated absorption losses.

Gap solitons in a nonlinear quadratic negative-index cavity.

We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton.

Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks.

We numerically demonstrate negative refraction of the Poynting vector and sub-wavelength focusing in the visible part of the spectrum using a transparent multilayer, metallo-dielectric photonic band gap structure. Our results reveal that in the wavelength regime of interest evanescent waves are not transmitted by the structure, and that the main underlying physical mechanisms for sub-wavelength focusing are resonance tunneling, field localization, and propagation effects. These structures offer several advantages: tunability and high transmittance (50% or better) across the visible and near IR ranges; large object-image distances, with image planes located beyond the range where the evanescent waves have decayed. From a practical point of view, our findings point to a simpler way to fabricate a material that exhibits negative refraction and maintains high transparency across a broad wavelength range. Transparent metallo-dielectric stacks also provide an opportunity to expand the exploration of wave propagation phenomena in metals, both in the linear and nonlinear regimes.

Second-harmonic generation at angular incidence in a negative-positive index photonic band-gap structure.

In the spectral region where the refractive index of the negative index material is approximately zero, at oblique incidence, the linear transmission of a finite structure composed of alternating layers of negative and positive index materials manifests the formation of a new type of band gap with exceptionally narrow band-edge resonances. In particular, for TM-polarized (transverse magnetic) incident waves, field values that can be achieved at the band edge may be much higher compared to field values achievable in standard photonic band-gap structures. We exploit the unique properties of these band-edge resonances for applications to nonlinear frequency conversion, second-harmonic generation, in particular. The simultaneous availability of high field localization and phase matching conditions may be exploited to achieve second-harmonic conversion efficiencies far better than those achievable in conventional photonic band-gap structures. Moreover, we study the role played by absorption within the negative index material, and find that the process remains efficient even for relatively high values of the absorption coefficient.

Accessing quadratic nonlinearities of metals through metallodielectric photonic-band-gap structures.

We study second harmonic generation in a metallodielectric photonic-band-gap structure made of alternating layers of silver and a generic, dispersive, linear, dielectric material. We find that under ideal conditions the conversion efficiency can be more than two orders of magnitude greater than the maximum conversion efficiency achievable in a single layer of silver. We interpret this enhancement in terms of the simultaneous availability of phase matching conditions over the structure and good field penetration into the metal layers. We also give a realistic example of a nine-period, Si3/N4Ag stack, where the backward conversion efficiency is enhanced by a factor of 50 compared to a single layer of silver.

Radiation pressure of light pulses and conservation of linear momentum in dispersive media.

We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed 10(10) m/s(2) for a mass of 10(-5) g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media.

Large enhancement of interface second-harmonic generation near the zero-n(-) gap of a negative-index Bragg grating.

We predict a large enhancement of interface second-harmonic generation near the zero-n(-) gap of a Bragg grating made of alternating layers of negative- and positive-index materials. Field localization and coherent oscillations of the nonlinear dipoles located at the structure's interfaces conspire to yield conversion efficiencies at least an order of magnitude greater than those achievable in the same length of nonlinear, phase-matched bulk material. These findings thus point to a new class of second-harmonic-generation devices made of standard centrosymmetric materials.

Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: ultrawide bandwidth optical limiting.

We numerically study the nonlinear optical properties of metal-dielectric photonic band gap structures in the pulsed regime. We exploit the high chi3 of copper metal to induce nonlinear effects such as broadband optical limiting, self-phase modulation, and unusual spectral narrowing of high intensity pulses. We show that in a single pass through a typical, chirped multilayer stack nonlinear transmittance and peak powers can be reduced by nearly two orders of magnitude compared to low light intensity levels across the entire visible range. Chirping dielectric layer thickness dramatically improves the linear transmittance through the stack and achieves large fields inside the copper to access the large nonlinearity. At the same time, the linear properties of the stack block most of the remaining electromagnetic spectrum.

Dynamics of short pulses and phase matched second harmonic generation in negative index materials.

We study pulsed second harmonic generation in metamaterials under conditions of significant absorption. Tuning the pump in the negative index range, a second harmonic signal is generated in the positive index region, such that the respective indices of refraction have the same magnitudes but opposite signs. This insures that a forward-propagating pump is exactly phase matched to the backward-propagating second harmonic signal. Using peak intensities of ~500 MW/cm(2), assuming chi((2))~80pm/V, we predict conversion efficiencies of 12% and 0.2% for attenuation lengths of 50 and 5microm, respectively.

Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials.

A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.

Dispersion-free pulse propagation in a negative-index material.

The possibility of controlling the spectral position of the zero group-velocity dispersion point of a negative-index material can be exploited by varying the ratio between the electric and the magnetic plasma frequency to obtain dispersion-free propagation in spectral regions otherwise inaccessible using conventional positive-index materials. Our predictions are confirmed by pulse propagation simulations where all the orders of the complex dispersion of the material are taken into account.