Wavelength conversion and parametric amplification of optical pulses via quasi-phase-matched four-wave mixing in long-period Bragg silicon waveguides.

We present a theoretical analysis supported by comprehensive numerical simulations of quasi-phase-matched four-wave mixing (FWM) of ultrashort optical pulses that propagate in weakly width-modulated silicon photonic nanowire gratings. Our study reveals that, by properly designing the optical waveguide such that the interacting pulses copropagate with the same group velocity, a conversion efficiency enhancement of more than 15 dB, as compared to a uniform waveguide, can readily be achieved. We also analyze the dependence of the conversion efficiency and FWM gain on the pulse width, time delay, walk-off parameter, and grating modulation depth.

Nonlinear superchiral meta-surfaces: tuning chirality and disentangling non-reciprocity at the nanoscale.

Circularly polarized light is incident on a nanostructured chiral meta-surface. In the nanostructured unit cells whose chirality matches that of light, superchiral light is forming and strong optical second harmonic generation can be observed.

Nonlinear surface-plasmon whispering-gallery modes in metallic nanowire cavities.

We demonstrate that the surface second-harmonic generation can lead to the formation of nonlinear plasmonic whispering-gallery modes (WGMs) in microcavities made of metallic nanowires. Since these WGMs are excited by induced surface nonlinear dipoles, they can be generated even when they are not coupled to the radiation continuum. Consequently, the quality factor of these nonlinear modes can be as large as the theoretical limit imposed by the optical losses in the metal. Remarkably, our theoretical analysis shows that nonlinear plasmonic WGMs are characterized by fractional azimuthal modal numbers. This suggests that the plasmonic cavities investigated here can be used to generate multicolor optical fields with fractional angular momentum. Applications to plasmonic sensors are also discussed.

Fano resonance resulting from a tunable interaction between molecular vibrational modes and a double continuum of a plasmonic metamolecule.

Coupling between tunable broadband modes of an array of plasmonic metamolecules and a vibrational mode of carbonyl bond of poly(methyl methacrylate) is shown experimentally to produce a Fano resonance, which can be tuned in situ by varying the polarization of incident light. The interaction between the plasmon modes and the molecular resonance is investigated using both rigorous electromagnetic calculations and a quantum mechanical model describing the quantum interference between a discrete state and two continua. The predictions of the quantum mechanical model are in good agreement with the experimental data and provide an intuitive interpretation, at the quantum level, of the plasmon-molecule coupling.

Subwavelength plasmonic lattice solitons in arrays of metallic nanowires.

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies.

We present the first observations of zero-n[over ] band gaps in photonic crystal superlattices consisting of alternating stacks of negative-index photonic crystals and positive-index dielectric materials in the near-infrared range. Guided by ab initio three-dimensional numerical simulations, the fabricated nanostructured superlattices demonstrate the presence of zeroth-order gaps in remarkable agreement with theoretical predictions across a range of different superlattice periods and unit cell variations. These volume-averaged zero-index superlattice structures present a new type of photonic band gap, with the potential for complete wave front control for arbitrary phase delay lines and open cavity resonances.

Nonlinear-optical phase modification in dispersion-engineered Si photonic wires.

The strong dispersion and large third-order nonlinearity in Si photonic wires are intimately linked in the optical physics needed for the optical control of phase. By carefully choosing the waveguide dimensions, both linear and nonlinear optical properties of Si wires can be engineered. In this paper we provide a review of the control of phase using nonlinear-optical effects such as self-phase and cross-phase modulation in dispersion-engineered Si wires. The low threshold powers for phase-changing effects in Si-wires make them potential candidates for functional nonlinear optical devices of just a few millimeters in length.

Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range.

We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure of merit [-Re(n)/Im(n)] of at least 380, approximately 125x improvement over recent efforts in the near-infrared range, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47lambda, clearly smaller than the diffraction limit of 0.61lambda. Importantly, we show this subdiffraction imaging is due to the resonant excitation of surface slab modes.

Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks.

Numerical simulations of a near-infrared negative-index metamaterial (NIM) slab consisting of multiple layers of perforated metal-dielectric stacks exhibiting a small imaginary part of the index over the wavelength range for negative refraction are presented. A consistent effective index is obtained using both scattering matrix and modal analysis approaches. Backward phase propagation is verified by calculation of fields inside the metamaterial. The NIM figure of merit, [ -Re(n)/Im(n) ], for these structures is improved by ~ 10x compared with previous reports, establishing a new approach to thick, low-loss metamaterials at infrared and optical frequencies.

Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array.

By extending GaAs dielectric posts with a large second-order nonlinear susceptibility through the holes of a subwavelength metallic hole array coupled to the metal surface-plasma wave, strong second harmonic (SH) signal is observed. The SH signal is strengthened as a result of the enhanced electromagnetic fields inside the hole apertures.

Experimental demonstration of near-infrared negative-index metamaterials.

Metal-based negative refractive-index materials have been extensively studied in the microwave region. However, negative-index metamaterials have not been realized at near-IR or visible frequencies due to difficulties of fabrication and to the generally poor optical properties of metals at these wavelengths. In this Letter, we report the first fabrication and experimental verification of a transversely structured metal-dielectric-metal multilayer exhibiting a negative refractive index around 2 microm. Both the amplitude and the phase of the transmission and reflection were measured experimentally, and are in good agreement with a rigorous coupled wave analysis.

Parametric light bullets supported by quasi-phase-matched quadratically nonlinear crystals.

We present a comprehensive analysis of the dynamics of three-dimensional spatiotemporal nonspinning and spinning solitons in quasi-phased-matched (QPM) gratings. By employing an averaging approach based on perturbation theory, we show that the soliton's stability is strongly affected by the QPM-induced third-order nonlinearity (which is always of a mixed type, with opposite signs in front of the corresponding self-phase and cross-phase modulation terms). We study the dependence of the stability of the spatiotemporal soliton (STS) on its energy, spin, the wave-vector mismatch between the fundamental and second harmonics, and the relative strength of the intrinsic quadratic and QPM-induced cubic nonlinearities. In particular, all the spinning solitons are unstable against fragmentation, while zero-spin STS's have their stability regions on the system's parameter space.

Near-infrared double negative metamaterials.

We numerically demonstrate a metamaterial with both negative epsilon and negative mu over an overlapping near-infrared wavelength range resulting in a low loss negative-index material. Parametric studies optimizing this negative index are presented. This structure can be easily fabricated with standard semiconductor processing techniques.

Two-dimensional solitons in quasi-phase-matched quadratic crystals.

We study the existence and dynamics of two-dimensional spatial solitons in crystals that exhibit a periodic modulation of both the refractive index and the second-order susceptibility for achieving quasi-phase-matching. Far from resonances between the domain length of the periodic crystal and the diffraction length of the beams, it is demonstrated that the properties of the solitons in this quasi-phase-matched geometry are strongly influenced by the induced third-order nonlinearities. The stability properties of the two-dimensional solitons are analyzed as a function of the total power, the effective wave-vector mismatch between the first and second harmonics, and the relative strength between the induced third-order nonlinearity and the effective second-order nonlinearity. Finally, the formation of two-dimensional solitons from a Gaussian beam excitation is investigated numerically.

Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials.

We study numerically the influence of the frequency dispersion of the dielectric function of metals on the physical properties of negative-refractive-index metamaterials. A numerical analysis is performed using the transfer matrix formalism in conjunction with the finite-difference time-domain method. We analyze the dependence of the transmission and absorption properties of a slab of split-ring-type resonators on the parameters characterizing the frequency dispersion of the metallic dielectric function: plasma frequency and damping frequency. Then, using these transmission and reflection coefficients, we show that the refractive index remains negative near the resonant frequency of the rings, despite the presence of frequency dispersion. We also determine the dependence of the position and width of the band gaps of a slab of such a metamaterial on the material dispersion. Finally, we also discuss the influence of the shape of the split-ring resonators on the transmission and reflection coefficients. The calculations are performed for both two- and three-dimensional structures.

Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects.

The nonlinear optical effects induced by a one-dimensional (1D) line defect, made of Kerr material, in a 2D photonic crystal are studied. Comprehensive ab initio numerical simulations based on the finite-difference time-domain method show efficient third-harmonic generation in a photonic crystal waveguide consisting of the 1D defect line. The relationship between the third harmonic generation process and the nonlinear modal properties of the waveguide is discussed. We investigate optical limiting in such a device, that is, control of the transmitted power as a function of the Kerr-induced variation of the refractive index. Power dependent spectral changes in such a device and its use as a frequency selector are also examined.

Spatial solitons in type II quasiphase-matched slab waveguides.

The existence and dynamics of one-dimensional spatial solitons formed upon propagation in quasiphase-matched gratings, through three-wave parametric interaction, is analyzed. We study the general case in which the grating exhibits a periodic modulation of both the refractive index and the second-order susceptibility. It is demonstrated that for negative effective wave vector mismatch the induced third-order nonlinearities increase the domain of soliton instability. Finally, the dependence of the efficiency of the second harmonic generation process in the soliton regime, on the parameters of the grating, is discussed.

Limits for interchannel frequency separation in a soliton wavelength-division multiplexing system.

We identify the required interchannel frequency separation of the input field for a soliton wavelength-division multiplexing (WDM) system. It is found that the critical frequency separation above which WDM with solitons is feasible increases with the number of transmission channels. Moreover, it is shown that a combination of time- and wavelength-division multiplexing yields the largest transmission capacity. Finally, the structure of the soliton spectra which correspond to the frequency separation smaller than the critical frequency is discussed.

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry.

The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.