Third harmonic generation of laser radiation in Fe- and Zn-doped polyvinylpyrrolidone

The results of third-order nonlinear susceptibilities studies of Fe- and Zn-doped polyvinylpyrrolidone (PVP) aqueous solution in processes of third harmonic generation of Nd:YAG laser radiation are presented. Nonlinear susceptibilities of PVP:Fe and PVP:Zn were calculated to be 5×10^-13 esu and 3×10^-13 esu respectively. Third harmonic conversion efficiencies in these metallocomplexes were measured to be 8×10^-7 and 5×10^-7 respectively. The Z-scan method was applied to determine Kerr effect influence on frequency conversion process. The value of nonlinear refractive index of PVP:Fe at the wavelength of λ = 1064 nm was measured to be n ₂ = - 6.7×10^-13 esu. Received 30 November 2001 / Received in final form 27 March 2002 Published online 28 June 2002     

Ellipticity dependence of atomic and molecular high harmonic generation

High harmonic generation is compared in the dependence on the ellipticity of the fundamental laser radiation for an atomic and a molecular system. In particular argon and nitrogen are compared employing molecular beams and intense ( 3×10¹⁴ W/cm²) and ultrashort (80 fs) 800 nm laser pulses. It turns out that for all the harmonics under investigation (H5, H13 and H21) the harmonic yield decreases slower with the ellipticity for the molecule than for the atom. This indicates differences in atomic and molecular high harmonic generation. Received 24 April 2002 Published online 24 September 2002     

Asymptotic behaviour and general properties of harmonic generation susceptibilities

We use the Kubo response function formalism to derive the asymptotic behaviour of the harmonic generation susceptibilities to all orders n. The results show a stringent correspondence with the ones previously obtained from the classical anharmonic oscillator model. They are characterized by a dependence and a coefficient proportional to the trace of the (n+1)th derivative of the potential energy on the equilibrium density matrix. Using the above results we derive new Kramers-Kr?nig relations and sum rules for all orders of harmonics susceptibilities. Received 17 April 2000     

Electromagnetically induced transparency in asymmetric double quantum wells

We show how to compute nonlinear optical absorption spectra of an Asymmetric Double Quantum Well (ADQW) in the region of intersubband electronic transitions. The method uses the microscopic calculation of the dephasing due to electron-electron and electron-phonon scattering rates and the macroscopic real density matrix approach to compute the electromagnetic fields and susceptibilities. The polarization dephasing and the corrections to the Rabi frequencies due to the electron-electron interaction are also taken into account. For a proper choice of the QW widths and of the driving fields we obtain electromagnetically induced transparency. This transparency has a very narrow linewidth when a single driving field is applied resonant to the transition between the second and the third subband. In the case of two resonant driving fields or of a driving field resonant between the first and third subband we obtain a large transparency enhancement over the entire absorption spectrum. Results are given for GaAs/GaAlAs QWs and experiments are proposed. Received 21 June 2001 and Received in final form 21 January 2002     

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kr?nig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators. Received 25 January 1999 and Received in final form 26 April 1999     

High order harmonic generation optimization with an apertured laser beam

We report a systematic study of high order harmonic generation with an infrared laser apertured by an iris, as a function of the aperture size. Measurements were made of harmonic generation efficiency for different gas species, laser energies and focal geometries. Harmonic efficiencies as a function of aperture show a characteristic peaked shape, which is independent of gas species and harmonic order. A one dimensional, time dependent simulation of harmonic generation in a gas cell, taking into account experimentally measured transverse coherence of the laser, closely reproduces the observed behaviours. We show that the aperture diameter which maximizes harmonic yield is the result of a compromise between considerations of focal geometry and ionization (which favour small apertures); and harmonic dipole amplitude and phase (which favour large apertures). Received 31 May 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: kazamias@ensta.fr RID="b" ID="b"UMR 7639 du CNRS     

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.     

Wavelength dependence of nonlinear absorption in a bis-phthalocyanine studied using the Z-scan technique

The wavelength dependence of the nonlinear absorption of a bis-phthalocyanine, Nd(Pc)₂, dissolved in dimethyl formamide was studied in the rising part of the Q-band using the open aperture Z-scan technique, to determine the wavelength region over which the nonlinear absorption changes from reverse saturable absorption to saturable absorption. It was found that the sample could be used as a reverse saturable absorber, and hence as an optical limiter, up to a wavelength of about 604 nm. The imaginary part of the third order susceptibility was also calculated for these wavelengths. Resonant enhancement of the imaginary part of the third order susceptibility was clearly observed. Received: 26 April 2002 / Revised version: 30 June 2002 / Published online: 20 December 2002 RID="*" ID="*"Corresponding author. Fax: +91-484/576-714, E-mail: kpu@cusat.ac.in RID="**" ID="**"Present address: Optical Sciences Center, University of Arizona, Tucson, USA     

Second- and third-harmonic generations for a nondilute suspension of coated particles with radial dielectric anisotropy

We derive expressions for the effective nonlinear susceptibility tensors for both the second harmonic generation (SHG) and induced third harmonic generation (THG) of nonlinear composite materials, in which nondilute coated particles with radial dielectric anisotropy are randomly embedded in the linear host. Two types of coated particles are considered. The first is that the core possesses a second order nonlinear susceptibility and the shell is linear and radially anisotropic, while the second is that the core is linear with radial anisotropy and the shell has a second order nonlinear susceptibility. We observe greatly enhanced SHG and THG susceptibilities at several surface plasmon resonant frequencies. For the second model, due to the coating material being metallic, there exists two fundamental resonant frequencies ω_c1 and ω_c2, whose difference ω_c2-ω_c1 is strongly dependent on the interfacial parameter and the radial dielectric anisotropy. Furthermore, in both systems, the adjustment of the dielectric anisotropy results in larger enhancement of both SHG and induced THG susceptibilities at surface plasmon resonant frequencies than the corresponding isotropic systems. Therefore, both the core-shell structure and the dielectric anisotropy play important roles in determining the nonlinear enhancement and the surface resonant frequencies.     

Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator

Delayed differential equation of motion with multiple lags is derived for an anharmonic stub resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity. Received 14 March 2002 / Received in final form 25 November 2002 Published online 14 March 2003     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

Ab initio calculations of the second dynamic hyperpolarizability of LiH by means of Floquet theory approach

Floquet theory is used to describe the response of a molecule to applied radiation electric field. The method of ab initio calculation of frequency dependent (hyper)polarizabilities based on combination of perturbation theory with the finite field method has been developed. Electron correlation is taken into account by means of the CIPSI algorithm. The total wave function expansion involves spectral, pseudo-spectral states and polynomial terms. The developed approach is applied to the calculation of the second hyperpolarizability of the lithium hydride molecule subjected to the superposition of harmonic and static electric fields. The method can be used to calculate the higher order nonlinear properties of molecules. Received 23 November 2000 and Received in final form 25 March 2001     

Evaluation of QCD sum rules for light vector mesons at finite density and temperature

QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons ρ, ω and φ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the ρ- and ω-mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the ρ-meson and can lead to a change of the sign of the ω-meson mass shift as a function of the density. In contrast, the in-medium mass of the φ-meson is directly related to the chiral strange quark condensate which seems correspondingly accessible. Received: 15 May 2002 / Accepted: 31 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: Kaempfer@fz.rossendorf.de Communicated by A. Sch?fer     

Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation

An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u₀ with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x-u_{0 s} (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented. Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002     

Silver-island films probed by hyper-Rayleigh scattering and atomic force microscopy

Incoherent second-harmonic generation, or hyper-Rayleigh scattering (HRS), and atomic force microscopy (AFM) are proposed as a combined probe of nonlinear optical and structural properties of silver-island films. HRS and linear (Rayleigh) scattering indicatrices are measured. The correlation function, deduced from the HRS indicatrices and characterising spatial fluctuations of the total polarisation at second-harmonic frequency, has a length scale significantly larger than that of the correlation functions that are obtained from the AFM data and characterise spatial fluctuations of quadratic optical susceptibilities of the dipole and quadrupole types. This difference is interpreted as indicating that the HRS indicatrix shape is determined by the long-range fluctuations of the local-field factors. Received: 16 October 2001 / Revised version: 16 April 2002 / Published online: 6 June 2002     

Generation of zonal flows by interchange modes in a plasma

The generation of zonal flows by flute-like interchange modes in a nonuniform magnetoplasma is considered. The guiding center particle drifts are then used to derive a system of coupled mode equations. The latter are Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the excitation of zonal flows by the ponderomotive force of the interchange modes. The growth rate of the parametrically driven zonal flows is obtained. Received 26 July 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: ps@tp4.ruhr-uni-bochum.de     

Lattice effects in the quasiparticle dynamics and kinetics

In this work we present a full selfconsistent set of nonlinear equations which unifies the nonlinear elasticity theory equations, the Boltzmannn transport theory and the Maxwell equations for quasiparticles with arbitrary dispersion laws in nonstationarily deformed crystals with arbitrary (but linear) constitutive relations. Transformations to replace the Galilean ones are obtained, the quasiparticle mechanics in a Hamiltonian form is deduced, and a Boltzmann-type transport equation (valid in the whole Brillouin zone) is derived. The theory may be applied to metals, semiconductors, quantum crystals, low-dimensional structures etc. Received 20 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: dipushk@issp.bas.bg     

On the slow dynamics of density fluctuations near the colloidal glass transition

Slow dynamics of density fluctuations near the colloidal glass transition is discussed from a new viewpoint by numerically solving a nonlinear stochastic diffusion equation for the density fluctuations recently proposed by one of the present authors (MT). The effects of spatial heterogeneities on the dynamics of density fluctuations are then investigated in an equilibrium system. The spatial heterogeneities are generated by the nonlinear density fluctuations, while in a nonequilibrium system they are described by a nonlinear deterministic equation for the average number density. The dynamics of equilibrium density fluctuations is thus shown to be quite different from that of nonequilibrium ones, leading to a logarithmic decay followed by less distinct α- and β-relaxation processes. Received 9 March 2002 and Received in final form 19 September 2002     

Laser nonlinear-optical probing of silicon/SiO2 interfaces: Surface stress formation and relaxation

A nonlinear optical technique based on optical second harmonic generation in reflection is shown to provide information on the surface layer structure of semiconductor crystals, thin films and layered systems. The second harmonic intensity is sensitive to inhomogeneous stress in centrosymmetric materials via spatial selection rules and the appearance of an electric dipole contribution to the second order nonlinear optical susceptibility. The technique is used to monitor mechanical stress relaxation in the SiO₂/Si interface during several annealing procedures.     

Modeling of enhancement of nonlinearity in oxide and chalcogenide glasses by introduction of nanometals

In this Letter we extended T-matrix to calculate the nonlinear susceptibilities of a composite nonlinear host and guest medium, and then applied this model to calculate the nonlinear susceptibilities of oxide and chalcogenide glasses by introduction of nanometals. The results of the model is in good agreement with experimental ones.