We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures

Two-dimensional transition-metal dichalcogenides (TMDCs) with intrinsically broken crystal inversion symmetry and large second-order nonlinear responses have shown great promise for future nonlinear light sources. However, the sub-nanometer monolayer thickness of such materials limits the length of their nonlinear interaction with light. Here, we experimentally demonstrate the enhancement of the second-harmonic generation from monolayer MoSe2 by its integration onto a 220-nm-thick silicon waveguide. Such on-chip integration allows for a marked increase in the interaction length between the MoSe2 and the waveguide mode, further enabling phase matching of the nonlinear process. The demonstrated TMDC–silicon photonic hybrid integration opens the door to second-order nonlinear effects within the silicon photonic platform, including efficient frequency conversion, parametric amplification and the generation of entangled photon pairs.

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.

We experimentally demonstrate efficient third harmonic generation from an indium tin oxide (ITO) nanofilm (λ/42 thick) on a glass substrate for a pump wavelength of 1.4 µm.A conversion efficiency of 3.3x10 -6 is achieved by exploiting the field enhancement properties of the epsilon-near-zero (ENZ) mode with an enhancement factor of 200. This nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.

We present a detailed analysis of the optical properties of one-dimensional arrays of slits in metal films. Although enhanced transmission windows are dominated by Fabry-Perot cavity modes localized inside the slits, the periodicity introduces surface modes that can either enhance or inhibit light transmission. We thus illustrate the interaction between cavity modes and surface modes in both finite and infinite arrays of slits. In particular we study a grating that clearly separates surface plasmon effects from Wood-Rayleigh anomalies. The periodicity of the grating induces a strong plasmonic band gap that inhibits coupling to the cavity modes for frequencies near the center of the band gap, thereby reducing the transmission of the grating. Strong field localization at the high energy plasmonic band edge enhances coupling to the cavity modes while field localization at the low energy band edge leads to weak cavity coupling and reduced transmission

We show an alternative path to efficient second-and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layers of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF 2 is excited at 21 μm, where ε ∼ 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the ε ∼ 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.

The present investigation is concerned with the study of pulsed second-harmonic generation under conditions of phase and group velocity mismatch, and generally low conversion efficiencies and pump intensities. In positive-index, nonmetallic materials, we generally find qualitative agreement with previous reports regarding the presence of a double-peaked second harmonic signal, which comprises a pulse that walks off and propagates at the nominal group velocity one expects at the second-harmonic frequency, and a second pulse that is "captured" and propagates under the pump pulse. We find that the origin of the double-peaked structure resides in a phase-locking mechanism that characterizes not only second-harmonic generation, but also chi((3)) processes and third-harmonic generation. The phase-locking mechanism that we describe occurs for arbitrarily small pump intensities, and so it is not a soliton effect, which usually relies on a threshold mechanism, although multicolor solitons display similar phase locking characteristics. Thus, in second harmonic generation a phase-matched component is always generated, even under conditions of material phase mismatch: This component is anomalous, because the material does not allow energy exchange between the pump and the second-harmonic beam. On the other hand, if the material is phase matched, phase locking and phase matching are indistinguishable, and the conversion process becomes efficient. We also report a similar phase-locking phenomenon in negative index materials. A spectral analysis of the pump and the generated signals reveals that the phase-locking phenomenon causes the forward moving, phase-locked second-harmonic pulse to experience the same negative index as the pump pulse, even though the index of refraction at the second-harmonic frequency is positive. Our analysis further shows that the reflected second-harmonic pulse generated at the interface and the forward-moving, phase-locked pulse appear to be part of the same pulse initially generated at the surface, part of which is immediately back-reflected, while the rest becomes trapped and dragged along by the pump pulse. These pulses thus constitute twin pulses generated at the interface, having the same negative wave vector, but propagating in opposite directions. Almost any break of the longitudinal symmetry, even an exceedingly small chi((2)) discontinuity, releases the trapped pulse which then propagates in the backward direction. These dynamics are indicative of very rich and intricate interactions that characterize ultrashort pulse propagation phenomena

Abstract:We have conducted a theoretical study of harmonic generation from a silver grating having slits filled with GaAs. By working in the enhanced transmission regime, and by exploiting phase-locking between the pump and its harmonics, we guarantee strong field localization and enhanced harmonic generation under conditions of high absorption at visible and UV wavelengths. Silver is treated using the hydrodynamic model, which includes Coulomb and Lorentz forces, convection, electron gas pressure, plus bulk χ (3) contributions. For GaAs we use nonlinear Lorentz oscillators, with characteristic χ (2) and χ (3) and nonlinear sources that arise from symmetry breaking and Lorentz forces. We find that: (i) electron pressure in the metal contributes to linear and nonlinear processes by shifting/reshaping the band structure; (ii) TE-and TM-polarized harmonics can be generated efficiently; (iii) the χ (2) tensor of GaAs couples TE-and TM-polarized harmonics that create phase-locked pump photons having polarization orthogonal compared to incident pump photons; (iv) FabryPerot resonances yield more efficient harmonic generation compared to plasmonic transmission peaks, where most of the light propagates along external metal surfaces with little penetration inside its volume. We predict conversion efficiencies that range from 10 6 for second harmonic generation to 10 3 for the third harmonic signal, when pump power is 2GW/cm 2 . 606-622 (1962). 30. W. Glenn, "Second-harmonic generation by picosecond optical pulses," IEEE J. Quantum Electron. 5(6), 284-290 (1969). 31. J. T. Manassah, and O. R. Cockings, "Induced phase modulation of a generated second-harmonic signal," Opt. ©2011 Optical Society of AmericaLett. 12(12), 1005-1007 (1987). 32. S. L. Shapiro, "Second harmonic generation in LiNbO3 by picosecond pulses," Appl. Phys. Lett.