Second-harmonic generation taking into account dispersion of nonlinear susceptibility

Second-harmonic generation in the field of an ultrashort pulse and the propagation of extremely short pulses in a medium with quadratic nonlinearity are analyzed. Second-harmonic generation is analyzed taking into account the effect of second-and third-order group velocity dispersion and dispersion of nonlinear susceptibility up to the second order. Corrections, whose order of smallness is determined by the parameter (ω_L t _p)^?1, where t _p is the pulse duration and ω_L is the carrier frequency of the pump wave, are obtained. For a large phase mismatch, two new solutions are found that describe the stationary evolution of solitary pump and second-harmonic waves in the regions of both anomalous and normal group velocity dispersions.     

Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

Normal modes of a probe field in the pulsed regime of electromagnetically induced transparency in a Λ-scheme of degenerate quantum transitions

The effect of separation of linearly polarized short probe pulses of electromagnetically induced transparency in the field of linearly polarized coupling radiation is modeled numerically. It is shown that the input-probe pulses polarized parallel or perpendicular to the input-probe field propagate in the medium without changing the state of their polarization. If the input-probe radiation is weak compared to the coupling radiation, then the probe field inside the medium is the sum of two independently propagating linearly polarized normal modes, which are excited by the projections of the input-probe pulse onto the direction of polarization of the coupling radiation and onto the perpendicular direction, respectively. The normal modes have the same phase velocities, but different velocities of their real envelopes. This circumstance leads to the rotation of the plane of polarization of the total probe field at short distances and to its separation into two pulses with mutually perpendicular directions of polarization at long distances. At a high intensity of the probe radiation, the input-probe pulse decays into pulses the planes of polarization of which are not mutually perpendicular. Under these conditions, it is impossible to represent the probe radiation as a sum of normal modes. The modeling is performed in the scheme of degenerate quantum transitions between states of levels ³ P ₀, ³ P ₁ ⁰, and ³ P ₂ of isotope ²⁰⁸Pb taking into account the Doppler broadening of spectral lines.     

On the third harmonic generation in a medium with negative pump wave refraction

The propagation of the pump and its third harmonic pulses in a cubically nonlinear medium is considered theoretically, provided that the linear properties of the medium are characterized by a negative refractive index at the pump frequency and a positive refractive index at the harmonic frequency. For low-intensity interacting waves, the pump and third harmonic pulses propagate in opposite directions, but sufficiently intense pulses can produce a simulton—a solitary two-frequency wave that propagates in a certain direction as a single whole. The system of equations is investigated numerically for a model that, apart from the harmonic generation, includes the second-order group velocity dispersion and the nonlinear self- and cross-phase modulations of the interacting waves. The separation of the pump and harmonic pulses due to the difference in the directions of their group velocities and peculiarities of the Manley-Rowe relation for parametric processes in metamedia are discussed.     

On reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

Long wave-short wave resonance in nonlinear negative refractive index media

We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.     

Inelastic interaction of ultrashort pulses of polarized light with an ensemble of isolated quantum dots

A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.     

Femtosecond laser control of intramolecular vibrations in a liquid

Optical control of coherent intramolecular oscillations in chloroform CHCl₃ and dimethyl sulfoxide (CH₃)₂SO is attained experimentally under normal conditions by means of femtosecond polarization spectroscopy. Nonresonant excitation of the medium is accomplished by a sequence of two linearly polarized laser pulses. The state of the medium is probed by the third pulse via the optical Kerr effect. We show that control over the vibrational dynamics of molecules on a sub-picosecond scale can be achieved by varying the delay between the excitation pulses and their relative intensity.     

Second harmonic generation in a polarized Dirac vacuum

The Dirac vacuum, polarized by a strong electric field E₀, is discussed as nonlinear medium for laser radiation (LR). It is shown that such a medium leads to (a) a LR refractive index appearing, (b) LR polarization plane rotation, (c) LR second harmonic generation. It is proposed to use these effects for E₀ field diagnostics.     

Spatiotemporal self-similar waves for the (3 + 1)-dimensional inhomogeneous cubic-quintic nonlinear medium

Spatiotemporal self-similar waves of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation, describing propagation of optical pulses in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain, are derived. A one-to-one correspondence between such self-similar waves and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss dynamical behaviors of self-similar waves in dispersion decreasing fiber.     

Propagation of elliptically polarized laser pulses in isotropic gyrotropic medium with relaxation cubic nonlinearity and anomalous frequency dispersion

The self-action of elliptically polarized Gaussian laser pulses in an isotropic gyrotropic medium with an anomalous frequency dispersion and cubic Kerr nonlinearity with a finite relaxation time on the order of the pulse duration is numerically studied. It is shown that, at the output of the medium, the pulse polarization nonmonotonically varies with time. The main peak of the pulse is additionally delayed compared to the time of passing the linear medium; the value of this delay significantly depends on the polarization of the incident pulse and achieves a maximum for incident pulses whose degree of ellipticity is equal to the ratio of the material constants characterizing the local and nonlocal nonlinear optical response of the medium. It seems promising to search for possible differences in relaxation times depending on the intensity of additions to the refractive indices of the right and left circularly polarized waves by investigating the time dependence of polarization characteristics at the output of the medium.     

Optical control of the anisotropy of the orientation of molecules in a liquid

The control of the anisotropy of the orientation of molecules in pure 1,2-dichlorobenzene, C₆H₄Cl₂ at room temperature is demonstrated experimentally. To accomplish the optical control, the medium is exposed to non-resonant excitation with two successive linearly polarized laser pulses with a duration of 60 fs. The state of transient anisotropy is probed with the third pulse by detecting the ultrafast optical Kerr effect via optical heterodyne detection and synchronous demodulation. It is shown that variations in the two parameters, the delay time between two pump pulses, and the angle between the polarization directions of the pump pulses ensure the control of the anisotropy of the orientation of molecules in the subpicosecond region.     

Random generation of coherent solitary waves from incoherent waves

The random generation of coherent solitary waves from incoherent waves in a medium with an instantaneous nonlinearity has been observed. One excites a propagating incoherent spin wave packet in a magnetic film strip and observes the random appearance of solitary wave pulses. These pulses are as coherent as traditional solitary waves, but with random timing and a random peak amplitude.     

Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves

This paper establishes surprisingly precise a priori bounds on theL -norm of certain singular solutions of a system of two nonlinear Sturm-Liouville equations which model solitary water waves.These solutions can be interpreted as homoclinic orbits for a system of four first order ordinary differential equations. The uniqueness of these homoclinic orbits is established for certain choices of a parameterc, the phase speed of the waves. These observations do not result from perturbation of linear theory, but are global.     

Time reversing solitary waves

We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear (shallow water) conservation law is regularized leading to a viscous shock profile. This enables time-reversal experiments beyond the critical time for shock formation. Furthermore, we present numerical experiments for the time-reversed refocusing of solitary waves in a regime where theory is not yet available. Solitary wave refocusing simulations are performed with a new Boussinesq model, both in transmission and in reflection.     

Self-precession and frequency shifts for three interacting waves for a nonlinear model equation in a dispersive medium

The wave-wave interaction of three interacting waves for a nonlinear model equation in a dispersive medium is studied. It is found that the nonlinear effect causes precession of the polarization ellipse as the wave propagates under the resonance condition ₁ = ₂ + ₃ and k₁ k₂ + k₃. The frequency shifts and the precessional frequencies are obtained under the above resonance conditions. A technique has been developed for the evaluation of self-precession and frequency shifts for circularly polarized waves.The author expresses his gratitude to Dr. B. Chakraborty, Department of Mathematics, Jadavpur University, Calcultta for his guidance in the preparation of this paper and also to the referee for his suggestion in the improvement of this paper.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system

Abstract

In this paper, we introduce and study rigorously a Hamiltonian structure and soliton solutions for a weakly dissipative and weakly nonlinear medium that governs two Korteweg–de vries (KdV) wave modes. The bounded solution and traveling wave solution such as cnoidal wave and solitary wave are obtained. Subsequently, the equation is numerically solved by Fourier spectral method for its two-soliton solution. These solutions may be useful to explain the nonlinear dynamics of waves for an equation supporting multi-mode weakly dispersive and nonlinear wave medium. In addition, we give an explicit explanation of the mathematics behind the soliton phenomenon for a better understanding of the equation.     

Observation of solitary elastic surface pulses

The formation of solitary elastic surface pulses from laser-generated pulselike initial conditions is reported. The nonlinearity of the medium is compensated by both normal dispersion and anomalous dispersion, which were realized by coating isotropic fused silica by a metal and titanium nitride film, respectively. As an anisotropic material, silicon covered with an oxide layer was studied. The experimental results agree with numerical simulations carried out with a nonlocal evolution equation, which describes nonlinear propagation of surface acoustic waves in a dispersive medium.