Fifth-order Nonlinearity Research Articles

Temporally two-dimensional overtone vibrational dephasing spectroscopy in liquids

A temporally two-dimensional overtone vibrational dephasing spectroscopy, which is based on the fifth-order nonlinearity, is proposed to investigate correlation between fluctuations of different vibrational frequencies in liquids. The experiment is done for the C--D stretching of neat ${\mathrm{CDCl}}_{3}$ liquid. We found that a signal decay as a function of the second-pulse interval gets faster as the first-pulse interval increases.

Effective non-linear coefficients of optical waveguides

Using the weakly guiding approximation, and with the assumption that the non-linearities are sufficiently weak so as not to change the transverse mode profile, perturbation theory is used to derive simple expressions for evaluating the modal, or effective, non-linear coefficients of optical waveguide structures based on the non-linear coefficients of the constituent materials. In particular, the third-order and fifth-order optical non-linearities of refraction and absorption are discussed. The expressions are used to estimate the effective modal non-linear refraction coefficients for various types of slab waveguides, focusing primarily on femtosecond refractive non-linearities in semiconductor amplifiers, including quantum-well structures. The results are of particular relevance to the design of all-optical switches based on these effects.

Bright and dark solitary wave propagation and bistability in the anomalous dispersion region of optical waveguides with third- and fifth-order nonlinearities

A unified analysis of all existing solitary wave solutions - bright, black and gray - of the cubic-quintic nonlinear Schrödinger equation (CQNLSE) is made concretely, considering a monomode step-index optical fibre with third- and fifth-order nonlinearities in the anomalous dispersion frequency region. Different aspects of the effect of the fifth-order nonlinearity, such as the existence of bright and gray solitary waves in the same parameter range and dark solitary wave bistability are considered. The influence of the distributions modified by the nonlinearity radial fields on the quintic dispersion coefficient in the CQNLSE is calculated. The results obtained are applicable to the cases of spatial solitons and optical beam self-action in highly nonlinear media.

Overtone vibrational dephasing in liquids studied by femtosecond fifth-order nonlinear spectroscopy.

We have directly observed vibrational dephasing of the first overtone bands in liquids by femtosecond fifth-order nonlinear spectroscopy for the first time to our knowledge. The overtone and fundamental dephasing processes have been studied for the C-D stretching of CDC${\mathrm{l}}_{3}$ and the sym-methyl stretching of C${\mathrm{D}}_{3}$I in neat liquid and in its binary mixture with CHC${\mathrm{l}}_{3}$. Simulations based on simple stochastic theory or perturbation theory for a harmonic oscillator do not explain both the overtone and fundamental dephasing simultaneously.

Third- and fifth-order optical nonlinearities in organic materials

We measure the nonlinear optical properties of solutions of a bisbenzethiozole-substituted thiophene compound (BBTDOT) and didecyloxy substituted polyphenyl (DDOS) using the Z-scan technique with 532 nm picosecond pulses. Both compounds exhibit two-photon absorption (2PA) and excited-state absorption (ESA) from the 2PA generated excited states. We measure the magnitude and sign of the real (refractive) and imaginary (2PA) parts of the third-order hyperpolarizability, and the excited-state absorptive and refractive cross sections. We observe third-order self-focusing in BBTDOT and self-defocusing in DDOS while both show excited-state defocusing. All these effects were previously observed and modeled in semiconductors giving insight into the nonlinearities occurring in these organic materials.

Applying the controlled aliasing technique for fast prediction of the output response of nonlinear circuits driven by composite signals

It is assumed that the transfer characteristic of a nonlinear circuit in its severe form is represented by a power series with six terms (fifth-order nonlinearity) and that the circuit is injected by a composite signal (arbitrary shape of excitation). An analysis based on the controlled aliasing technique is carried out to determine the amplitude of each output harmonic. Results show that this technique is an accurate CAD tool for analysis of any order of nonlinearity for any form of input, with no limitations. CPU-time investigations show that the choice of the sampling window for both speed of solution and minimisation of algebraic effort is the critical parameter. A typical CPU time for analysis of this severe nonlinearity is 4 min.

Nonresonant fifth-order nonlinearities induced by ultrashort intense pulses

We demonstrate the existence of χ(5) nonlinearities induced in a transparent glass by intense femtosecond pulses at 620 nm. Polarization selectivity associated with a transient-grating technique allows us to discriminate this contribution from the electronic third-order one. A value of 5 is measured for the ratio between symmetric and nonsymmetric elements for this fifth-order susceptibility. This value corresponds to the expected value deduced from the anharmonic model presented and is definitely attributed to a direct six-wave mixing process.

Analysis of Modulational Instability in Monomode Optical Fibres with High-order Nonlinearity

Abstract The modulational instability (MI) in monomode optical fibres with fifth-order nonlinearity, fibre loss, higher-order dispersion, and the temporal variation of third-order nonlinearity is studied theoretically. The conditions for the existence of the MI and the maximal modulational growth are given and discussed in detail. The results obtained show that the key factor dominating the producing condition of the MI is the power P of the continuous wave initially launched into the optical fibres. If P falls into 3/10<P/P 0 <1/2 where P 0 is defined as characteristic power, the MI can be produced in the range of not only anomalous group velocity dispersion but also the normal in which the final evolution state of the modulated wave is dark soliton.

Phase measurements of the fifth-order susceptibility of Cd(S, Se)-doped glasses

We present what are to our knowledge the first measurements of the phase of the fifth-order nonlinearity, χ 5. A method is introduced and applied to determine the phase of χ 5 in Cd(S, Se)-doped glasses.

Effective dielectric response of nonlinear composites.

A perturbative approach is developed to compute the local field for the case of a nonlinear inclusion embedded in a nonlinear host. The result is applied to nonlinear composites. General formulas for calculating the effective nonlinear susceptibility up to the case of fifth-order nonlinearity are given. The formulation is applied to problems in two dimensions (2D) and in three dimensions (3D). For 2D problems, the cases of cylindrical inclusions and concentric cylindrical inclusions are studied. By invoking an exact mapping, the problem of the concentric cylinder can be mapped onto the problem of an elliptic cylinder. A general expression of the effective nonlinear susceptibility for a dilute composite of randomly oriented elliptic cylinders embedded in a linear host is derived. For 3D problems, the cases of spherical inclusions and coated spherical inclusion are studied. General expressions for the effective nonlinear susceptibility are given in the dilute limit up to the case of fifth-order nonlinearity. For composites consisting of spherical inclusions coated by a nonlinear material and embedded in linear host, it is possible to enhance the nonlinear response of the composite by tuning material parameters such as the linear dielectric constants of the host, coating and core materials, and by adjusting the thickness of the coating.

Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe

We extend the application of the Z-scan experimental technique to determine free-carrier nonlinearities in the presence of bound electronic refraction and two-photon absorption. We employ this method, using picosecond pulses in CdTe, GaAs, and ZnTe at 1.06 μm and in ZnSe at 1.06 and 0.53 μm, to measure the refractive-index change induced by two-photon-excited free carriers (coefficient σr,), the two-photon absorption coefficient β, and the bound electronic nonlinear refractive index n2. The real and imaginary parts of the third-order susceptibility (i.e., n2 and β, respectively) are determined by Z scans with low inputs, and the refraction from carriers generated by two-photon absorption (an effecitve fifth-order nonlinearity) is determined from Z scans with higher input energies. We compare our experimental results with theoretical models and deduce that the three measured parameters are well predicted by simple two-band models. n2 changes from positive to negative as the photon energy approaches the band edge, in accordance with a recent theory of the dispersion of n2 in solids based on Kramers–Kronig transformations [ Phys. Rev. Lett.65, 96 ( 1990); IEEE J. Quantum Electron.27, 1296 ( 1991)]. We find that the values of σr are in agreement with simple band-filling models.

Formation and propagation of steady-state laser pulses in media under the combined action of third- and fifth-order nonlinearities

A family of steady-state solutions is obtained for the propagation of high-power laser pulses in nonlinear media under the combined influence of third- and fifth-order nonlinearities. The stability of these solutions is analyzed and the conditions for the formation of suitable pulses are determined for arbitrary initial conditions.

Femtosecond soliton attractors in fibres

It is shown that the attraction of femtosecond solitons in fibres is possible. Soliton attraction is calculated numerically, taking into account the fifth-order non-linearity in the refractive index of the fibre for the varying initial conditions. The role of the non-linear and dispersion higher-order effects and self-frequency shift in soliton attraction is also considered.

Interaction of baseband and envelope solitary wave solutions of the nonlinear Klein-Gordon equation with dispersion

The interaction of solitary wave solutions of the nonlinear Klein-Gordon equation for baseband and envelope propagation is numerically studied by introducing them from linear nondispersive semi-infinite regions into a finite nonlinear dispersive region which can be modeled by a cubically nonlinear Klein-Gordon equation. In both baseband and envelope cases the solitary wave solutions are unstable upon mutual interaction. Envelope propagation has less distortion after interaction, but instability in baseband case can be easily removed by incorporating a small amount of a fifth-order saturating nonlinearity in the system.

Second-harmonic generation from quantum noise owing to fifth-order nonlinearity

Simple quantum theory of second-harmonic generation from quantum noise owing to the fifth-order nonlinear optical interaction in centrosymmetric media is presented. This theory explains the rise of initial second-harmonic seeding radiation in optical fibers.

General formalism for the study of nonlinear pulse propagation in optical fibres

A general formalism for the study of nonlinear pulse propagation in optical fibres is presented. It is then applied to study the time evolution of a Gaussian laser pulse in a fibre with cubic and fifth-order nonlinearity in the index of refraction. The results are presented and discussed.

Reflection and collision of solitary wave solutions of the nonlinear Klein-Gordon equation

The reflection of solitary wave solutions of the cubically nonlinear Klein-Gordon equation from rigid and nonrigid boundaries, and their mutual interaction are studied using finite-difference numerical techniques. The instability of these solutions is shown to be removed by incorporating a small amount of a fifth-order saturating nonlinearity in the system.

Effect of fifth-order nonlinearity in refractive index on Gaussian pulse propagation in lossy optical fibers

The effect of fifth-order nonlinearity in refractive index on Gaussian pulse propagation in lossy optical fibers is considered. It is shown that fifth-order nonlinearity considerably modifies the pulse propagation, as a result of which the frequency at which the reshaping of the pulse should be done to have a distortionless propagation is reduced significantly (by a factor of about 3 compared with the case of cubic nonlinearity). The peak power for which fifth-order nonlinearity becomes significant is of the same order of magnitude that is required for cubic nonlinearity.

Optical hysteresis and bistability in phase conjugation by degenerate six-photon mixing

The exact solution of the nonlinear phase-conjugation equations in the case of fifth-order nonlinearity is presented. The theoretical dependence of the backward-wave intensity on that of the interacting waves with Gaussian time shape exhibit well-pronounced hysteresis that is in agreement with experimental results performed on CdS crystals (nanosecond laser pulses). The physical nature of the phenomenon is discussed using the concept of scattering diagrams in terms of dynamic holography.

Induced autoionization-like resonances in nonlinear third- and fifth-order susceptibilities of sodium vapor

A study was made of the influence of autoionization-like resonances in the continuum, induced by strong optical radiation, on the nonlinear susceptibilities governing third harmonic generation and the optical activity of sodium vapor. It was demonstrated experimentally for the first time that it should be possible to study high-lying states of atoms and molecules by the method of nonlinear polarization spectroscopy of the fifth-order optical nonlinearity. The experimental results were compared with the theory. An analysis was made of the feasibility of using this effect for spectroscopy of the states in the continuum and for generation of short-wavelength radiation in gaseous media.