Third-order Nonlinear Effects Research Articles

三阶非线性色散异向介质中的调制不稳定性

On the basis of the extended nonlinear propagation equation without normalization in metamaterials with the first-order to third-order nonlinear dispersion effects,the dispersion relation and gain spectra of modulation instability were deduced by adopting the linear stability analysis and the Drude electromagnetic model.Variations of the equation coefficients and gain spectra with the normalized angular frequencies were calculated and discussed in real units in both the positive and negative refractive-index regions in cases of self-focusing and self-defocusing.The results show that,the third-order nonlinear dispersion coefficients are all along positive in both the positive and negative refractive-index regions.In the negative refractive-index region,with increase of normalized angular frequencies,the spectral widths of the gain spectra increase before become zero and the peak gains increase before decrease and then become zero in the selffocusing case.While in the case of self-defocusing,modulation instability can only occur near the forbidden band and both the spectral widths and peak gains decrease monotonically.In the positive refractive-index region,modulation instability can only occur in the self-focusing case.And the spectral widths increase monotonically and the peak gains decrease before increase with the normalized angular frequencies.Generally,the third-order nonlinear dispersion is detrimental to modulation instability generation.

Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides

In this paper, we derive the couple-mode equations for third-order nonlinear effects in photonic crystal waveguides by employing the modal theory. These nonlinear interactions include self-phase modulation, cross-phase modulation and degenerate four-wave mixing. The equations similar to that in nonlinear fiber optics could be expanded and applied for third-order nonlinear processes in other periodic waveguides. Based on the equations, we systematically analyze the group-velocity dispersion, optical propagation loss, effective interaction area, slow light enhanced factor and phase mismatch for a slow light engineered silicon photonic crystal waveguide. Considering the two-photon and free-carrier absorptions, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slow light enhanced multiple four-wave-mixing process on the conversion efficiency.

Wavelength conversion, time demultiplexing and multicasting based on cross-phase modulation and four-wave mixing in dispersion-flattened highly nonlinear photonic crystal fiber **The work was supported in part by the CAS/SAFEA International Partnership Program for Creative Research Teams.

We propose the use of cross-phase modulation (XPM) and four-wave mixing (FWM) in dispersion-flattened highly nonlinear photonic crystal fibers (HNL-PCFs) to implement the functionalities of wavelength conversion, simultaneous time demultiplexing and wavelength multicasting in optical time-division multiplexing (OTDM) systems. The experiments on wavelength conversion at 80 Gbit s−1and OTDM demultiplexing from 80 to 10 Gbit s−1 with wavelength multicasting of two channels are successfully demonstrated to validate the proposed scheme, which are carried out by using two segments of dispersion-flattened HNL-PCFs with lengths of 100 and 50 m, respectively. Moreover, the bit error rate (BER) performance is also measured. The results show that our designed system can achieve a power penalty of less than 4.6 dB for two multicasting channels with a 24 nm wavelength span at the BER of 10−9 when compared with the 10 Gbit/s back-to-back measurement. The proposed system is transparent to bit rate since only an ultrafast third-order nonlinear effect is used. The resulting configuration is compact, robust and reliable, benefiting from the use of dispersion-flattened HNL-PCFs with short lengths. This also makes the proposed system more flexible in the operational wavelengths than those based on dispersion-shifted fibers and traditional highly nonlinear fibers.

Investigation of self-focusing effects in wurtzite InGaN/GaN quantum dots

The third-order nonlinear optical properties in wurtzite InGaN/GaN pyramid and truncated-pyramid quantum dots are studied, and the oscillator strength, third-order nonlinear optical susceptibility and self-focusing effects are analyzed theoretically taken into account the strong built-in electric field effect due to the piezoelectric and spontaneous polarization in nitride materials. The numerical results clearly show that the quantum dot (QD) size of InGaN/GaN have a significant influence on the nonlinear optical properties of wurtzite InGaN/GaN quantum dots. Furthermore, the self-focusing effect increases with decrease in size of QDs.

Resonant cascaded down-conversion

We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\ensuremath{\chi}}^{(2)}$-level oscillation thresholds that are therefore much lower than for a ${\ensuremath{\chi}}^{(3)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\ensuremath{\chi}}^{(2)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-$P$ representation and undertake an analysis of steady-state and dynamical properties of this system.

Silicon-on-insulator photonic crystal miniature devices with slow light enhanced third-order nonlinearities

The effects of the slow-down factor on third-order nonlinear effects in silicon-on-insulator photonic crystal channel waveguides were investigated. In the slow light regime, with a group index equal to 99, these nonlinear effects are enhanced but the enhancement produced depends on the input peak power level. Simulations indicate the possibility of soliton-like propagation of 1 ps pulses at an input peak power level of 50 mW inside such a photonic crystal waveguide. The increase in the induced phase shift produced by lower group velocities can be used to decrease the size and power requirements needed to operate devices such as optical switches, logic gates, and wavelength translators.

Monolithic Photonics Using Second-Order Optical Nonlinearities in Multilayer-Core Bragg Reflection Waveguides

Recent advancements in phase-matching second-order nonlinear processes by using matching-layer-enhanced Bragg reflection waveguides (ML-BRWs) in Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> As material system are discussed. The limitations on the choice of the Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> As layers for applications that require high pump power operation are highlighted. Multilayer-core ML-BRWs are proposed as a new waveguide design with relaxed constraints over the choice of the Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> As layers composition. The tradeoffs associated with material bandgap on the efficiency of second-order nonlinear processes are examined by using this novel structure. The interplay among the various factors, including the nonlinear overlap factor, the effective second-order nonlinearity, and the third-order nonlinear effects result in the presence of an optimum detuning of the core bandgap from the operating wavelength for maximum conversion efficiency. Two different wafer structures are examined by using second-harmonic generation to elucidate these tradeoffs. The conversion efficiency is examined by using 30-ps, 2-ps, and 250-fs pulses at various pump average power levels.

Role of entropy perturbations in third-order nonlinear acoustic tomography problems

The effect of the entropy perturbations on the acoustic pressure, which arises due to third-order nonlinear interaction, has been considered. The contribution to entropy perturbation due to the presence of viscosity and thermal conductivity (by means of the general equation of heat transfer) and also due to the nonlinearity of the considered medium has been estimated. It has been shown that when all possible factors responsible for the change in entropy are taken into account, the third-order contribution to the acoustic pressure due to density perturbations in primary waves strongly exceeds that due to entropy perturbations. It has been concluded that an isoentropic mathematical description of third-order nonlinear effects in nonlinear acoustic tomography problems is appropriate.

Enhancement of the nonlinear effects in composite plasmonic nanoparticles

Features of the second- and third-order nonlinear effects in composite plasmonic core/shell nanoparticles placed into a polymer matrix are investigated. Resonant enhancement of the effective third-order susceptibility is observed, as well as the appearance of a coherent magnetization-induced component of the second harmonic.

Bright soliton solution to a generalized Burgers–KdV equation with time-dependent coefficients

We consider a generalized Burgers–KdV type equation with time-dependent coefficients incorporating a generalized evolution term, the effects of third-order dispersion, dissipation, nonlinearity, nonlinear diffusion and reaction. The exact bright soliton solution for the considered model is obtained by using a solitary wave ansatz in the form of sech s function. The physical parameters in the soliton solution are obtained as functions of the time varying coefficients and the dependent exponents. The dependent exponents and the temporal variations of the model coefficients satisfy certain parametric conditions as shown by the obtained soliton solution. This solution may be useful to explain some physical phenomena in genuinely nonlinear dynamical systems that are described by Burgers–KdV type models.

Degenerate Two-Beam Phase Conjugation in One-Dimensional ZnS–YF$_{3}$ Photonic Crystal With Central Defect Mode

This letter presents the experimental demonstration of degenerate two-beam phase conjugation (2BPC) by using a one-dimensional ZnS-YF3 photonic crystal (PhC) with central defect mode. The effective third-order nonlinearity of the PhC sample is (2.3 ± 0.1) × 10-9 esu which is almost four orders of magnitude larger in comparison with bulk ZnS (?ZnS (3) = 3.1 × 10-13 esu). This large nonlinearity enhancement is attributed to the high density of mode and the electric field localization around the central defect layer near the defect mode wavelength. The realization of 2BPC utilizing defect mode in a simple PhC structure will greatly reduce the complexity to achieve compact and low-power nonlinear optical devices.

Type-II quasi phase matching in periodically intermixed semiconductor superlattice waveguides

Second-harmonic generation using the type-II polarization configuration is demonstrated in quasi-phase-matched GaAs radicalAlGaAs superlattice waveguides. Phase-matching wavelengths and conversion efficiencies were determined for several quasi-phase-matching periods using 1.9 ps pulses. Saturation effects at high input power were concluded to be the result of third-order nonlinear effects.

Synthesis and Optical Nonlinearities of a 2-Amino-1,2,3-triazolquinone Derivative

We report on the synthesis and nonlinear optical characterization of a novel 2-amino-1,2,3-triazolquinone derivative, namely, 2-(yliminopropylphenyl-N,N′-dimethylamino)naphto-1,2,3-triazole-4,9-dione (ATZQ). The second-order nonlinear optical properties in solution were characterized using the hyper-Rayleigh scattering (HRS) technique, while the third-order nonlinearities of ATZQ-doped polymer films were measured through the use of the THG-Maker fringes technique. These experiments showed that this compound exhibits large second- and third-order nonlinear effects at the molecular level, with a first hyperpolarizability constant of β∼834 × 10−30 esu at 1064 nm and a second hyperpolarizability constant of γ∼3.5 × 10−33 esu at the telecommunication wavelength range of 1200–1700 nm.

Strong reduction of laser power noise by means of a Kerr nonlinear cavity

We demonstrated the power noise reduction of a continuous-wave laser field by means of an effective third-order Kerr nonlinear cavity. In contrast to conventional noise reduction schemes relying on linear cavities, a strong noise suppression at Fourier frequencies below the linewidth of the nonlinear cavity was possible. The laser light was reflected off a Kerr nonlinear cavity that had a half width half maximum linewidth of 4.5 MHz. The cavity was operated slightly off-resonance at approximately half of the maximum power buildup, close to its so-called critical state; a power noise reduction of up to 32 dB at Fourier frequencies below 1 MHz was observed after reflection. The effective third-order nonlinearity was a so-called cascaded second-order nonlinearity of $\text{MgO}:{\text{LiNbO}}_{3}$. The laser had a power of 0.75 W at the wavelength of 1064 nm.

Numerical and physical modeling of the tomography process based on third-order nonlinear acoustic effects

The possibility of employing the nonlinear effect of generation of third-order combination waves for the purposes of medical diagnostics is analyzed. This effect can be used to reconstruct the spatial distribution of acoustic nonlinear parameters in the framework of the wave approach. Contributions of third-order nonlinear scattering itself and of the double second-order scattering are evaluated. These two competing processes evolve simultaneously and produce similar observed effects, which can nevertheless be separated. A two-dimensional experimental scheme that contains only three transmitters and one receiver, uses two primary wideband modulated waves and an introduced third monochromatic wave, is proposed. Results of the numerical and physical model experiments are provided.

Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect

We experimentally studied enhancement of the third-order nonlinear optical phenomena, i.e., self-phase modulation due to optical Kerr effect and two-photon absorption (TPA) in a small group-velocity (V(g)) line-defect guided-mode of AlGaAs-based photonic-crystal slab waveguide. We found that the phase shift Deltaphi or nominal Kerr constant n'(2) and TPA coefficient beta were strikingly enhanced due to small V(g) as the band edge was approached, such that they were proportional to (V(g))(-2); the nonlinear refractive index n(2) is enhanced proportional to V(g)(-1). We also observed that owing to this enhancement as well as an extremely small cross-section area, the energy required for inducing pi-phase shift was very small, being of an order of a few pJ for 5 ps optical pulse and for a 0.5-mm long sample. Based on those results, we discuss the possibility of developing ultra-fast and ultra-small all-optical switches that operate due to cross-phase modulation.

On nonlinear wave groups and crest statistics

We present a second-order stochastic model of weakly nonlinear waves and develop theoretical expressions for the expected shape of large surface displacements. The model also leads to an exact theoretical expression for the statistical distribution of large wave crests in a form that generalizes the Tayfun distribution (Tayfun, J. Geophys. Res., vol. 85, 1980, p. 1548). The generalized distribution depends on a steepness parameter given by μ = λ3/3, where λ3 represents the skewness coefficient of surface displacements. It converges to the Tayfun distribution in narrowband waves, where both distributions describe the crests of all waves well. In broadband waves, the generalized distribution represents the crests of large waves just as well whereas the Tayfun distribution appears as an upper bound and tends to overestimate them. However, the theoretical nature of the generalized distribution presents practical difficulties in oceanic applications. We circumvent these by adopting an appropriate approximation for the steepness parameter. Comparisons with wind-wave measurements from the North Sea suggest that this approximation allows both distributions to assume an identical form with which we can describe the distribution of large wave crests fairly accurately. The same comparisons also show that third-order nonlinear effects do not appear to have any discernable effect on the statistics of large surface displacements or wave crests.

Determinations of the transient thermal lensing effect in metal cluster Polymer {WS 4Cu 4I 2(bpe) 3} n solution by the use of the Z-scan

The nonlinear optical (NLO) properties of a novel cluster Polymer {WS 4Cu 4I 2(bpe) 3} n solution are studied by using Z-scan technique with laser pulses of 4.5 ns pulse-width at a wavelength of 532 nm. The results show that the cluster solution possesses strong nonlinear absorption and refraction. Nonlinear refraction of the cluster is composed of third-order nonlinear refraction and transient thermal effect. The thermal effect is mainly due to the strong nonlinear absorption. Numerical simulations obtained by solving simultaneously photo-acoustic and electromagnetic wave equations, agrees basically with experimental results.

Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 µm

We study free-carrier nonlinearities in crystalline silicon at 1.064 microm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n(2eff) and nonlinear absorption coefficient beta(eff) are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density sigma(r) and the total carrier absorption cross section sigma(ab) from the dependence of n(2eff) and beta(eff) on the pulse width, respectively. In this work we had sigma(r) =-1.0 x 10(-21) cm(3) and sigma(ab)=8.4 x 10(-18) cm(2), which agree well with previous data. We also observed the decrease in the magnitude of n(2eff) and beta(eff) at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.

Large Third-Order Optical Nonlinear Effects of Gold Nanoparticles with Unusual Fluorescence Enhancement

The third-order nonlinear optical properties of two solutions of gold nanoparticles protected by carbazolyldiacetylene derivatives were investigated using the Z-scan technique. Both gold nanoparticle colloid solutions in toluene show unusual fluorescent enhancement and large third-order nonlinear optical properties including nonlinear absorption and refractive effects. When extending the pi-conjugated length of the ligands, the third-order nonlinear properties of composite materials based on gold nanoparticles were enhanced accordingly.