HMO in nonlinear optics

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Analysis on the effect of nonlinear polarization evolution in nonlinear amplifying loop mirror

By considering the cross phase modulation (XPM) between the two orthogonal poparization components, the nonlinear birefringence and nonlinear polarization evolution (NPE) in highly-nonlinear fiber (HNLF), as well as the unequal evolutions of the state of polarization (SOP) between the clockwise (CW) and counter-clockwise (CCW) waves in a nonlinear amplifying loop mirror (NALM) are analyzed. It is pointed out that the traditional cosine expression is no longer valid for the power transmission of NALM due to uncompleted interference under the high power condition. The analytical expression considering NPE effect is derived, and the experimental result is presented.     

Adaptive synchronization with nonlinear input

This paper considers the adaptive synchronization problem of the drive—response type chaotic systems. Using a transmitted scalar signal with an unknown time-delay, a response system is constructed. By appropriately selecting the observer gain and designing the controller, synchronization can be achieved in the presence of the drive system's disturbances and unknown parameters. A well-known chaotic system, Chua's circuit, is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.     

Theoretical investigation electroopticalof nonlinear properties ofchromophores

Organic electrooptical (EO) chromophores are now gaining more attention because the property of organic photorefrative (PR) materials could be controlled by doped EO chromophores. In this paper, nonlinear optical (NLO) properties of a new group of organic electrcoptical chromophores, synthesized recently in our laboratory, were elucidated theoretically with the quantum chemical density functional theory (DFT) and the intermediate neglect of differential overlap Hamilton and the configuration interaction (INDO/CI), as well as semiemperical Austin Modlel 1 (AM1) methods. The electronic transition intensity, dipole moment and the second- order polarizability were obtained. The results show this group of chromophores possess appropriate optical absorption property and good electrooptical property and optical activity. The second-order polarizabilities β are as large as the order of 10^-29 to 10^-28 ESU, indicating the promising applications in the future. The physical mechanism of NLO is discussed by means of molecular orbital and electronic charge distribution.     

Stochastic feedback,nonlinear families of Markov processes,and nonlinear Fokker–Planck equations

We discuss two fundamental aspects of Fokker–Planck equations that are nonlinear with respect to probability densities. First, we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions. Second, we demonstrate that nonlinear Fokker–Planck equations can be interpreted as linear Fokker–Planck equations describing nonlinear families of Markov diffusion processes. We exploit this finding in order to derive complete hierarchies of probability densities from nonlinear Fokker–Planck equations.     

Wavelength-dependent nonlinear absorption of gold nanocages

The dipole resonances of gold nanocages were investigated theoretically using finite difference time domain method.The results show that field enhancement is obtained at the walls of the gold nanocages.It is believed that the effect can cause a strong optical nonlinear property.To test the hypothesis,nonlinear absorption was investigated using a broadband 5 ns Z scan.It was found that at low intensities the sample shows saturable absorption(SA),while at higher intensities a switch from SA to reverse SA occurs.Moreover,the nonlinear absorption of the sample is sensitively wavelength-dependent,and,in the resonant region,saturation intensity is the largest.     

Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping,via nonlinear normal modes

In this paper an Euler–Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system?s characteristics on this critical amplitude has also been discussed.     

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.     

Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

A generalized Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equation is constructed by the Darboux matrix method. As applications, the Nth-order rogue wave solutions of the coupled cubic–quintic nonlinear Schrödinger equation have been obtained. In particular, the dynamics of the general first- and second-order rogue waves are discussed and illustrated through some figures.     

Chirped optical solitons and stability analysis of the nonlinear Schr?dinger equation with nonlinear chromatic dispersion

The present paper aims to investigate the chirped optical soliton solutions of the nonlinear Schr?dinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index. The exquisite balance between the chromatic dispersion and the nonlinearity associated with the refractive index of a fiber gives rise to optical solitons, which can travel down the fiber for intercontinental distances. The effective technique, namely, the new extended auxiliary equation method is implem...     

Computer simulation of acoustic nonlinear parameter tomography

I.IntroductionUltrasonicimaginghasbcenwide1yusedinthcfie1dofclinicaldiagnosis,becauseitcanvisualizethetissuetharacterizationandinternalstructureofbiologicalobjectsbyacousticwave.Usingconventionalultrasonicimagingtechnique,theimagesofacousticlinearparameterssuchassoundve1ocity,acousticimpedenccandattenuationcoefficientmaybeobtained.Thesehavebecometheeffectivemethodsofu1trasonicdiagnosis.How-ever,inordertoobscrvctheearlystageofcanccr,weintendtoobtainmoreaccurateandmorecompleteinformationaboutth…     

Intense DC beam nonlinear transport-analysis & simulation

The intense dc beam nonlinear transport was analyzed with the Lie algebraic method, and the particle trajectories of the second order approximation were obtained. Based on the theoretical analysis a computer code was designed. To get self-consistent solutions, iteration procedures were used in the code. As an example, we calculated a beam line (drift-electrostatic quadrupole doublet-drift). The results agree to the results calculated by using the PIC method.     

Periodic solutions of nonlinear Schro^edinger type equations

By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions.     

Feynman diagram theory for multifrequency nonlinear acoustics

The Feynman diagram theory with the state-space formalism isadopted to study the multifrequency nonlinear acoustics effects.By establishingthe relation between the strain magnitude corresponding to any final stateS(m_1,…,m_n;x)and the number of paths from the initial state of the interactingphonons to the final state,not only the complete perturbation solutions but alsothe corresponding analytical expressions of the acoustic harmonics andintermodulation products have been obtained.For a few special cases,results ofour theory is consistent with those obtained by conventional methods.While thegeneral solution for any number of frequencies can easily be obtained by our the-ory,this is impossible by using conventional methods.     

Kramers-Krönig relations in nonlinear optics

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency arguments. Nonlinear dispersion relations have been shown to be very useful as they usually only require integration over a limited frequency range (corresponding to frequencies at which the absorption changes), unlike the conventional linear Kramers-Krönig relation which requires integration over all absorbing frequencies. Furthermore, calculation of refractive index changes using dispersion relations is easier than a direct calculation of the susceptibility, as transition rates (which give absorption coefficients) are, in general, far easier to calculate than the expectation value of the optical polarization. Both resonant (generation of some excitation that is long lived compared with an optical period) and nonresonant instantaneous optical nonlinearities are discussed, and it is shown that the nonlinear dispersion relation has a common form and can be understood in terms of the linear Kramers-Krönig relation applied to a new system consisting of the material plus some perturbation. We present several examples of the form of this external perturbation, which can be viewed as the pump in a pump-probe experiment. We discuss the two-level saturated atom model and bandfilling in semiconductors among others for the resonant case. For the nonresonant case some recent work is included where the electronic nonlinear refractive coefficient,n ₂, is determined from the nonlinear absorption processes of two-photon absorption, Raman transitions and the a.c. Stark effect. We also review how the dispersion relations can be extended to give alternative forms for frequency summation which, for example, allows the real and imaginary parts of ⁽²⁾ to be related.     

Soliton guidance and nonlinear coupling for polarized vector spiraling elliptic Hermite–Gaussian beams in nonlocal nonlinear media

We investigate the incoherent beams with two orthogonal polarizations in nonlocal nonlinear media, one of which is a fundamental Gaussian beam and the other is spiraling elliptic Hermite–Gaussian beam carrying the orbital angular momentum(OAM).Using the variational approach, we obtain the critical power and the critical OAM required for the vector spiraling elliptic Hermite–Gaussian solitons.In the strong nonlocality region, two components of the vector beam contribute to the nonlinear refractive index in a linear manner by the sum of their respective power.The nonlinear refractive index exhibits a circularly symmetrical profile in despite of the elliptic shapes for spiraling Hermite–Gaussian beams.We find that in the strong nonlocality region, the critical power and the rotational velocity are the same regardless of the relative ratio of the constituent powers.The nonlinear refractive index loses its circular symmetry in weak nonlocality region, and the nonlinear coupling effect is observed.Due to the radiation of the OAM, the damping of the rotation is predicted, and can be suppressed by decreasing the proportion of the spiraling elliptic component of the vector beam.     

Nonlinear order-parameter relaxation in the nonlinearσ-model

An equation of motion for the order parameter of a relaxational nonlinear-model is derived by renormalization-group considerations ind=2+ dimensions. The result is then used to describe the nonlinear relaxation of the order parameter after switching off an initial symmetry-breaking field below the critical temperature.     

Theoretical investigation of nonlinear properties of electrooptical chromophores

Organic electrooptical (EO) chromophores are now gaining more attention because the property of organic photorefrative (PR) materials could be controlled by doped EO chromophores. In this paper, nonlinear optical (NLO) properties of a new group of organic electrooptical chromophores, synthesized recently in our laboratory, were elucidated theoretically with the quantum chemical density functional theory (DFT) and the intermediate neglect of differential overlap Hamilton and the configuration interaction (INDO/CI), as well as semiemperical Austin Model 1 (AM1) methods. The electronic transition intensity, dipole moment and the second- order polarizability were obtained. The results show this group of chrormophores possess appropriate optical absorption property and good electrooptical property and optical activity. The second-order polarizabilities βare as large as the order of 10-29 to 10-28 ESU, indicating the promising applications in the future. The physical mechanism of NLO is discussed by means of molecular orbital and electronic charge distribution.     

Generation of large fifth-order nonlinear phase shifts by use of lossless χ~((2)) cascaded nonlinear processes

Theinherentthird-ordernonlinearityofmaterialc(3)isnormallyweak.Toaccumulatealargenonlinearphaseshift,highlaserintensityandlongopticalpathinmaterialareneeded.Whilethevalueofnonlinearitycouldbemadelargerneartheregionofabsorptionresonance,astronglosswillbeaccompaniedthroughtheprocessoftwo-photonabsorption.Inordertorealizestrongthird-ordernonlinearitywithcontrollableenergyloss,thec(2)(w;2w,-w)︰c(2)(2w;w,w)cascadingprocesshasbeenproposed,whichisequivalenttothethird-ordernonlinearityc(3)(w;w,w,-w)w…