A phase-matched third-harmonic (TH) generation from multilayered metamaterials (MMs) with a third-order nonlinearity is numerically investigated in the ultrashort pulse regime. To overcome the phase-mismatch problem due to natural material dispersion, we propose a solution based on engineered dispersion provided by MMs with hyperbolic dispersion, i.e., with anisotropic materials possessing a positive and negative dielectric permittivity. We analyzed selected material choices and demonstrated quasibirefringent phase-matched conditions for TH conversion, which could be achieved by optimizing the fill-factor of metamaterials. We study the conversion efficiencies of transmitted and reflected TH pulses as a function of incident angles and input fundamental-frequency intensity; the maximum efficiencies are obtained for optimal incident angles.
In this research, a third-harmonic generation (THG) in a tunable nonlinear hyperbolic metamaterial (TNHM) has been investigated numerically. The TNHM is consisted of periodically arranging of multilayered graphene layers system for controlled optical properties purpose, and ordinary nonlinear dielectric layer. The possibility of TNHM permittivity dispersion controlled by number of graphene layers and external bias voltage to graphene layers was satisfied, then the structure has created the nearly perfect phase-matching scheme based on epsilon-near-zero (ENZ) behavior of the nonlinear medium. Finally, the optimal designed TNHM structure with sufficient bias voltage have given the forwardand backward-direction TH pulses, which the backward-forward TH intensity ratio is closely unity. The THG conversion efficiencies have been maximized after increasing the pumping level to 800 MW/cm<sup>2</sup> . From this study, the optimal designed TNHM can be applied as a bi-directional nonlinear frequency converters in nanophotonic systems.
Multilayered hyperbolic metamaterials (MHM) is proposed to create phase matching of fundamental-frequency (FF) and third-harmonic (TH) field components with a unique dispersion provided by the engineered MHM structure for third-harmonic generation in ultra-short pulse regime. In this work, we analytically study the ensuing possibilities and demonstrate that a birefringent phase-matching can be alternatively achieved with a wide range of involved material parameters and optimal engineering of MHM structure. When the phase-matched conditions is satisfied by birefringent phase-matching method, the growth rate of the TH intensity generating as a function of the nonlinear-optical interaction length to be obviously increased. This method opens new ways of improving the conversion efficiency of frequency tripling regardless of the coherence length in the bulk of a nonlinear material.
In this paper, a second-order nonlinear interaction, difference-frequency generation, based on three-wave mixing process
in nonlinear multilayered metmaterial has been investigated numerically. The nonlinear multilayered metmaterial is
composed of two periodically alternating metallic and dielectric layers, which their layer thicknesses are reduced into
deep-subwavelength size for creating some nonlinear optical effect enhancement mechanism. The optimal engineered
structure gives a dispersion relation having near zero permittivity at some frequencies and can be called epsilon-nearzero
point. When a pump frequency (ω<sub>1</sub>) is determined at this point, the epsilon-near-zero phase matched condition and
field intensity enhancement are easily achieved and then a strong idler wave at difference-frequency ω<sub>3</sub> = ω<sub>1</sub> − ω<sub>2</sub>,
corresponding to DFG effect can be generated efficiently. According to this parametric interaction, the nonlinear
multilayered metamaterial can be applied as nonlinear frequency converters in various nanophotonic systems.
In this article, we have numerically investigated an intense terahertz (THz) pulses generation in gaseous plasma based on the third-order nonlinear effect, four-wave mixing rectification (FWMR). We have proposed that the fundamental fields and second-harmonic field of ultra-short pulse lasers are combined and focused into a very small gas chamber to induce a gaseous plasma, which intense THz pulse is produced. To understand the THz generation process, the first-order multiple-scale perturbation method (MSPM) has been utilized to derive a set of nonlinear coupled-mode equations for interacting fields such as two fundamental fields, a second-harmonic field, and a THz field. Then, we have simulate the intense THz-pulse generation by using split step-beam propagation method (SS-BPM) and calculated output THz intensities. Finally, the output THz intensities generated from induced air, nitrogen, and argon plasma have been compared.
In this research, the nonlinear frequency conversion effect based on four-wave mixing (FWM) principle in a onedimensional graphene-based photonics crystal (1D-GPC) has been investigated numerically. The 1D-GPC structure is composed of two periodically alternating material layers, which are graphene-silicon dioxide bilayer system and silicon membrane. Since, the third-order nonlinear susceptibility χ<sup>(3)</sup> of bilayer system is hundred time higher than pure silicon dioxide layer, so the enhancement of FWM response can be achieved inside the structure with optimizing photon energy being much higher than a chemical potential level (μ) of graphene sheet. In addition, the conversion efficiencies of 1DGPC structure are compared with chalcogenide based photonic structure for showing that 1D-GPC structure can enhance nonlinear effect by a factor of 100 above the chalcogenide based structure with the same structure length.
In this paper, the enhancement of third-harmonic generation in one-dimensional periodic grating structure with lowindex
contrast, which is produced by holographic illuminated liquid crystal droplets and called polymer-dispersed liquid
crystal grating, with near-infrared pumping has been demonstrated. The observed enhancement process is theoretically
explained and modeled with a multi-scale perturbation analysis and split-step Fourier transform technique, respectively.
We show that the third-harmonic generation has been enhanced by setting the fundamental frequency wavelength to the
long-wavelength band-edge of the first photonic band-gap of this periodic structure and satisfying band-edge phasematched
condition. The numerical results show that a dramatic enhancement of the third-harmonic field is observed near
the long-wavelength band-edge of the second photonic band-gap. Furthermore, the conversion efficiency of thirdharmonic
field of forward-propagating direction is more than of backward-propagating direction by a factor of 600.
Enhanced third-harmonic generation in a one-dimensional photonic crystal doped with third-order nonlinear medium was numerically investigated using the multiple-scale method and the split-step Fourier transform. The optimal fundamental frequency for third-harmonic wave generation was determined from the transmission spectrum. The third-harmonic pulse intensities grow, depending on the structure thickness and the fundamental-frequency detuning parameter, which determines the band-edge phase matching condition. Furthermore, the total energy output of third-harmonic pulses, depending on the fundamental-frequency pulse width, may be more than 1000 times the energy produced by a phase-matched bulk medium. A narrow pulse with bandwidth less than the band-edge transmission peak enables high conversion efficiency. The maximum conversion efficiency of the forward component may be 12 to 13 orders of magnitude greater than that of the backward component.
In this paper, we have solved nonlinear coupled-mode equations valid for light propagation in a one-dimensional photonic crystal by using numerical expression. Moreover, the medium in this problem has been considered as a nonlinear <i>x</i> <sup>(3)</sup> material. The numerical results have been used to calculate the conversion efficiency in nondepleted-pump limit. The results have been shown us that the maximum conversion efficiency of third-harmonic generation could be occurred when the fundamental field has been tuned near the lower band-edge of photonic band-gap that band-edge phase matched condition has been satisfied.
In this paper we have numerically investigated the parametric down conversion process in one dimensional-photonic
band gap (1D-PBG) structure, which is composed of linear and nonlinear dielectric layers, under four wave mixing
phenomena. The nonlinear dielectric layer is material with third-order nonlinear susceptibility χ<sup>(3)</sup>. First, we used
coupled-mode theory and slowly varying amplitude approximation to derive a complete set of nonlinear coupled mode
equations (NLCMEs) for the FWM phenomena. Then, we have solved these NLCMEs by using undepleted pump
approximation. We have got the solution for amplitude of signal and idler waves. Finally, we have used these solutions
to calculate the down-converted frequency conversion efficiency. We found that the conversion efficiency can be
enhanced by increasing the number of periodic layers and χ<sup>(3)</sup> value. Meanwhile, the conversion efficiency is decreased
by increasing of phase mismatch (▵k).