Fifth-order Nonlinearity Research Articles

THE THIRD- AND FIFTH-ORDER NONLINEAR REFRACTION IN THE SINGLE- AND DOUBLE-SIDED TMAF/PSS ELECTROSTATIC SELF-ASSEMBLY FILMS

The nonlinear refraction in the single- and double-sided 40-bilayer TMAF/PSS electrostatic self-assembly films were measured by closed-aperture Z-scan technique with picosecond laser pulses (with duration of 40 ps at 532 nm). The materials contain a positively charged material trifluoroacetic acid (TFA) salt of amino-substitute methanofullerene derivative monoadduct fullerene (TMAF) and a negatively charged material ploy (sodium 4-styrenesulfon ate) (PSS). The experimental results show that under the conditions of the peak intensity I0 = 7.0 GW/cm2, both the single- and double-sided films demonstrate third- and fifth-order non-linearities, and the fifth-order non-linearity has greater contribution to the nonlinear refraction than the third-order nonlinearity. The theoretical fittings also prove that the nonlinear refraction coefficients both γ and η are almost the same for the same materials no matter what the measurements are from the single- or the double-sided films.

High-efficiency diffraction from thin and volume dynamic holograms in linear absorbers

The possibilities of improving the efficiency of light-field transformation by dynamic holograms using schemes of frequency-nondegenerate multiwave mixing in linearly absorbing liquids have been analyzed. The conditions are determined and the mechanism of the fifth-order nonlinearity related to the nonlinearity of the thermo-optical coefficient and the temperature dependence of the solvent density and specific heat is established.

Two-photon-induced excited-state nonlinearities

We report a theoretical investigation of laser-pulse-duration dependence of excited-state nonlinearities induced by two-photon absorption (2PA). We investigate the spatiotemporal characteristics of the transmitted pulses caused by 2PA-induced excited-state absorption, which strongly depends on laser pulse duration. By taking into account 2PA cross-section, excited-state photophysical properties, as well as laser pulse duration, we quantitatively determine the effective fifth-order nonlinearities caused by excited-state absorption and refraction. The results are capable of predicting the magnitude of 2PA-induced excited-state nonlinearities on the time scales where laser pulse duration is less than or comparable to the lifetime of 2PA-induced excited states. We also develop Z-scan theories for quickly yet unambiguously estimation of 2PA coefficient, third-order nonlinear refraction index, and excited-state absorption and refraction cross-sections.

Ninth-order effective responses of nonlinear composites in external DC and AC electric fields

The perturbation expansion method, including the third-order potential, is employed to compute the high-order effective nonlinear coefficients of weakly nonlinear dielectric composites. We derive the general formulae for effective nonlinear coefficients up to the ninth order, which include the fifth-order nonlinearity for both DC and AC responses. In addition, the general transformation relations from the effective DC response to effective AC responses up to the ninth harmonic are originally presented in this article. These newly derived formulae are consistent with previously reported work, but are more generally applicable and likely to yield more accurate AC and DC response predictions yet do not require prior knowledge of the fourth-order potential.

Enabling Low-Distortion Varactors for Adaptive Transmitters

A varactor diode configuration is presented for the implementation of low-distortion tunable matching networks, phase shifters, and filters. The configuration is based on varactors with an "exponential" C(V) relation in antiseries configuration with specific control voltage harmonic loading conditions. The resulting network combines a high capacitance tuning range with relatively low control voltages and excellent linearity. The linearity is independent of the applied control voltage and does not degrade at low tone spacing, which is ideal for the realization of adaptive transmitters and modulators. A specific N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> x-2 varactor doping profile is required for exact third-order intermodulation (IM3) cancellation. The remaining distortion is dominated by the much smaller fifth-order nonlinearities. The required impedance levels of the harmonic terminations are studied in terms of the maximum modulation bandwidth for which the proposed configuration remains linear. The doping profile optimization for quality factor, tuning range, and breakdown voltage is discussed. For experimental verification, the proposed varactor configuration has been implemented using a silicon-on-glass technology. The measurements demonstrate IM3 cancellation and indicate a superior linearity for modulated signals up to 10-MHz bandwidth.

Fifth-order nonlinearity and 3-qubit phase gate in a five-level tripod atomic system

We first investigate the nonlinear optical response of a five-level tripod atomic system in electromagnetically induced transparency and then propose a 3-qubit phase gate protocol based on the fifth-order nonlinearity. The cross-phase modulation among the three weak fields induced by the fifth-order nonlinearity in electromagnetically induced transparency can produce the phase shift of order π, which can be used to realize the 3-qubit polarization phase gate. This protocol should have potential applications in quantum information processing.

用变分法研究高阶色散和五阶非线性对高斯脉冲在光纤中传输特性的影响

用变分法研究高阶色散和五阶非线性对高斯脉冲在光纤中传输特性的影响

Application of the differential transformation method to the free vibrations of strongly non-linear oscillators

This paper adopts the differential transformation method to obtain the free vibration behavior of an oscillator with fifth-order non-linearities. The principle of differential transformation is briefly introduced, and is then applied in the derivation of a set of difference equations for the free vibration oscillator problem. The solutions are subsequently solved by a process of inverse transformation. The time responses of the oscillator are presented under different parameter conditions, and the current results are then compared with those derived from the established Runge–Kutta method in order to verify the accuracy of the proposed method. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the proposed differential transformation method is a powerful and efficient tool for solving non-linear problems.

Influence of pulsed and cw pumping on optical nonlinear parameters of laser dyes probed by a closed-aperture Z-scan technique

Two dye pairs suitable for energy transfer along with a photostable dye have been studied by using the closed-aperture (CA) Z-scan technique under pulsed and cw pumping. Here we use a theoretical model to elucidate the refractive and absorptive nonlinearity present simultaneously in the CA Z-scan profile. A separate open-aperture (OA) Z-scan study has been carried out to compare the nonlinear absorption parameters obtained from the CA Z-scan technique. At a fixed pumping wavelength, values of optical nonlinear parameters increase with the absorbance of dyes. It is found that the sign of refractive nonlinearity is dependent on the irradiance and the pulse width of the pump beam. In addition to the contribution of the third-order optical nonlinearity, various other mechanisms such as fifth-order nonlinearity, population relaxation to triplet states, and thermal effects are discussed here.

Nonlinear Dynamical Model for Hysteresis Based on Nonconvex Potential Energy

A model for hysteretic dynamics is proposed in the current paper. Hysteresis is treated as an input-output relation for a dynamic system. The Lagrangian of the dynamic system is constructed on the basis of a nonconvex potential energy and governing equations of the system dynamics are obtained using the Lagrangian equation. Bifurcations will be induced in the nonlinear dynamics due to the nonconvexity of the potential energy. It is shown that when the coefficients are chosen appropriately, the bifurcation diagram will lead to hysteretic behavior. Both the third- and fifth-order nonlinear terms are investigated and it is shown that the fifth-order nonlinearity is able to give a perfect prediction of experimental hysteretic behaviors. Hysteretic damping force of a magneto-rheological fluid damper and polarization hysteresis in piezoelectric materials are modeled successfully using the current model. The parameter identification for the model is also presented.

Formation of the nonlinear dynamic hologram in clear organic fluids

The recording of dynamic holograms during multiwave interactions in clear organic fluids (ethanol, acetone, dioxan, etc.) is investigated. It is shown that the fifth-order nonlinearities and higher become activated along with the cubical nonlinearity under the intense laser excitation (∼100 MW cm−2) in the near-IR spectral range, which allows visualization of the IR images using different orders of diffraction.

Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system

We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. We show that the enhanced completely cross fifth-order nonlinearity generated in such a system can be used to produce efficient three-way entanglement and to realize a three-qubit quantum phase gate. We demonstrate that such phase gate can be transferred to an all-optical Toffoli gate, facilitating practical applications in quantum information and computation.

Enhanced linear dynamic range of asymmetric Fabry-Pe/spl acute/rot modulator/detector

An InGaAsP multiple-quantum-well asymmetric Fabry-Pe/spl acute/rot modulator/detector has been developed for radio-over-fiber systems. The measured bandwidth is more than 6 GHz and the total insertion loss is 7.1 dB. The property of nonlinearity and spurious-free dynamic range (SFDR) has been studied theoretically. By optimizing the operation optical wavelength and bias voltage based on the numerical simulation, fifth-order nonlinearity dominates the intermodulation distortion and an SFDR of 101 dB/spl middot/Hz/sup 4/5/ has been achieved experimentally.

Enhanced linear dynamic range of asymmetric Fabry-Pe/spl acute/rot modulator/detector

An InGaAsP multiple-quantum-well asymmetric Fabry-Pe/spl acute/rot modulator/detector has been developed for radio-over-fiber systems. The measured bandwidth is more than 6 GHz and the total insertion loss is 7.1 dB. The property of nonlinearity and spurious-free dynamic range (SFDR) has been studied theoretically. By optimizing the operation optical wavelength and bias voltage based on the numerical simulation, fifth-order nonlinearity dominates the intermodulation distortion and an SFDR of 101 dB/spl middot/Hz/sup 4/5/ has been achieved experimentally.

Switching mirror in the CdTe-based photonic crystal

Theoretical investigations, modeling and design of a Bragg mirror (photonic crystal structure) in the CdTe-based material system are presented. It is shown that, in addition to the third-order nonlinearity (Kerr-like effect), the two-photon absorption and the resulting free-carrier refraction have to be included in the analysis and design. Inclusion of changes in the refractive index with the square of the light intensity (fifth-order nonlinearity) leads to desirable functional features of the switching mirror. The analysis provides insight into the complex nonlinear effects and serves as a tool for designing a nonlinear intra-cavity mirror for a novel pulsed laser.

Determinations of third- and fifth-order nonlinearities by the use of the top-hat-beam Z scan: theory and experiment

We made a theoretical investigation on the top-hat-beam Z scan when the nonlinear media possess third- and fifth-order nonlinearities simultaneously. A high-accuracy method was proposed to allow the determination of the nonlinear refraction coefficients related to the third- and fifth-order effects. We also reconfirmed the common procedure for dividing the contributions of the third- and fifth-order effects to the nonlinearity in the top-hat-beam Z-scan measurements; the results indicated that the common procedure can be still employed for the determination of the third-order nonlinearity, whereas it is inapplicable for the fifth-order nonlinearity. We investigated experimentally, as a test, the nonlinear refraction of a Disperse Yellow 7 thin film by using the top-hat-beam Z-scan technique, with 35-ps-duration pulses at a 1064-nm wavelength.

A fifth-order multiple-scale solution for Hopf bifurcations

The subject of this paper is the multiple-time-scale analysis of Hopf bifurcations up to fifth-order nonlinearities. It is shown how an asymptotic fifth-order expansion captures the change in the nature of the limit cycle from stable to unstable and viceversa. The formulation is validated by applying it to a simple mechanical system for which there exists an analytical limit-cycle solution. Applications include the pre- and post-flutter behavior of a typical section with nonlinear spring having a stable limit cycle (supercritical Hopf bifurcation) that turns into an unstable one, because of fifth-order nonlinearities.

Nonlinear optical properties of CdS and ZnS nanoparticles doped into zirconium oxide films

The nonlinear refraction and nonlinear absorption of ZrO2 thin films doped with CdS and ZnS nanoparticles and various metals were investigated using the Z-scan technique. The structural properties of these films (TEM, EDX) were compared with their optical and nonlinear optical characteristics. The values of nonlinear refractive index of these films were measured to be of the order of at a laser intensity of 9 ? 109?W?cm?2. Sign variations of ? of ZrO2:CdS(Cr) and ZrO2:ZnS(Mn) films due to fifth-order nonlinearities were observed and analysed using the intensity-dependent Z-scan studies of nonlinear optical parameters.

Theory of pump–probe propagation in third-and higher-order, nonlinear optical media

A theory to treat the propagation of an intense pump pulse and a weak probe pulse in nonlinear media is presented. We give a general formalism applicable to the pump–probe propagation in a variety of nonlinear optical media. Based on this formalism, we obtain first an analytic, closed-form solution of pump–probe propagation in a third-order nonlinear medium, including linear absorption, nonlinear refraction, and two-photon absorption. The effects of velocity mismatch are also considered in our results. The general formalism leads further to analytic results for pump–probe propagation in a medium with both third- and fifth-order nonlinearity.

Fifth-order optical nonlinearity of pseudoisocyanine solution at 529 nm

Evidence of the interference between third- and fifth-order nonlinear optical processes is shown in the studies of pseudoisocyanine (PIC) dye aqueous solution using 529 nm radiation (t = 475 fs) and the Z -scan technique. The third-order nonlinear refractive index of the PIC solution was measured to be −8 × 10 −14 cm 2 W −1 .W e have shown th at PIC solution changes from being self-defocusing to self-focusing at high laser intensity that was attributed to the influence of fifth-order nonlinearity. The fifth-order nonlinear refractive index was measured to be 4 × 10 −24 cm 4 W −2 .T he bleaching properties of PIC solution were analysed, and the imaginary part of third-order nonlinear susceptibility was measured to be Im χ (3) =− 2 × 10 −12 esu.