Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration

One of the methods of obtaining a highly efficient second-harmonic generation (SHG) for laser pulses with random amplitudes and durations is mathematically modeled. The essence of the method proposed consists of the use of quadratic nonlinearity of the medium under conditions of a large mismatch between the wave numbers of the fundamental wave and the second harmonic. In the literature, the SHG under these conditions is referred to as the cascade SHG. Under certain conditions, this process is equivalent to the action similar to that of the cubic nonlinearity. This allows one to implement the both compression and decompression of laser pulses due to the cascade generation at a fairly low intensity of the pulses such that the Kerr nonlinearity does not manifest itself. The cascade generation is shown to enable one to implement tenfold or higher suppression of fluctuations of the input peak intensity of the laser radiation in the regime of free generation, which potentially makes it possible to implement the SHG under optimum conditions for all pulses in the sequence.     

Three-dimensional characterization of the effective second-order nonlinearity in periodically poled crystals

A novel technique for characterization of the second-order nonlinearity in nonlinear crystals is presented. It utilizes group-velocity walk-off between femtosecond pulses in type II SHG to achieve three-dimensional resolution of the nonlinearity. The longitudinal and transversal spatial resolution can be set independently. The technique is especially useful for characterizing quasi-phase-matched nonlinear crystals, and it is demonstrated in potassium titanyl phosphate.     

Soliton-like propagation modes of picosecond acoustic pulses in a paramagnetic crystal

The nonlinear propagation of picosecond acoustic pulses at an arbitrary angle to an external magnetic field is studied in an elastically isotropic paramagnetic crystal at low temperatures. Various soliton-like propagation modes arising due to spin-phonon interaction and acoustic anharmonicity are revealed, and the stability of these modes with respect to transverse perturbations is analyzed. In the case of defocusing cubic nonlinearity, the crystal can support the propagation of compression pulses, which undergo defocusing, and rarefaction pulses can propagate in the self-channeling mode. In the case of focusing cubic nonlinearity, only compression pulses can propagate if the conditions of stability with respect to self-focusing are satisfied.     

A singular perturbation theory for the FitzHugh-Nagumo nerve conduction equation

A singular perturbation theory is applied to the FitzHugh-Nagumo nerve conduction equation with cubic nonlinearity to obtain jacobian elliptic-function travelling-wave profiles. Starting with zeroth-order elliptic-function solutions, we obtain explicit first-order correction to the propagating waves and pulses.     

Nonlinear focusing of picosecond baseband pulses in paraelectric crystals

The nonlinear baseband electromagnetic pulses of a wide spectrum that lies in terahertz (THz) range are investigated theoretically in the paraelectric crystals like SrTiO₃ at the temperatures ~ 77 K. The frequency dispersion is important in THz range there. The dominating nonlinearity of the crystal is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability of long input envelope pulses, whereas in the transverse direction the modulation instability is absent. When the nonlinear wave is uniform in the transverse direction, the existence of soliton-like baseband pulses without a carrier frequency has been demonstrated. There exists a possibility to generate the regular sequences of short baseband pulses due to the nonlinearity in the paraelectric crystals. The nonlinear focusing of input long baseband pulses by the exciting antenna results in the formation of extremely short baseband pulses localized both in the longitudinal and transverse directions.     

Reflection of light from an induced moving lattice

The reflection, refraction, and penetration of a signal optical pulse upon interaction with a pumping-induced moving lattice in media with cubic nonlinearity has been investigated. Numerical simulation is performed for different lattices and signal pulses.     

Optical properties and CO_2 laser SHG with HgGa_2S_4

Optical properties and nonlinearity on phase-matching (PM) of two (yellow and orange) phase crystals were investigated in details. Damage threshold was determined in comparison with middle infrared (IR) crystal at identical experimental conditions. Second harmonic generation (SHG) of 30 ns TEA CO2 laser pulses was realized with 5% efficiency in energy and 6.9% in peak power.     

On the description of quadratic and cubic optical effects of propagation of femtosecond pulses within the framework of the model of the saturable potential

It is shown that, for describing the simultaneous manifestation of nonlinear effects of different orders (quadratic, cubic, etc.) in propagation of high-intensity femtosecond pulses, it is sufficient to use the saturable potential of the restoring force. With the use of computer simulation, it is demonstrated that the spectrum of the response of a medium calculated on the basis of the Duffing equation with quadratic and cubic nonlinearity is in qualitative agreement with the spectrum calculated on the basis of the equation with a saturable restoring force. The dependence of the frequency corresponding to the maximum spectral radiance on the duration of the interacting pulse is discussed. It is noted that, for ultrashort pulses, even in the case of their propagation in a linear medium, the response can occur at the natural frequency rather than at the frequency of the propagating pulse.     

Velocity of the maximum of the envelope of a frequency-modulated Gaussian pulse in an amplifying nonlinear medium

The variation in the velocity of propagation of a narrowband frequency-modulated pulse in a nonlinear medium with dispersion of gain or absorption is studied. It is shown that the self-phase modulation caused by a cubic nonlinearity of the Kerr type can “accelerate” optical pulses of a Gaussian shape up to superluminal velocities even in the case where an initial frequency modulation (chirp) is absent.     

Dynamics of ultimately short pulses in partially absorbing media

Propagation of broad-band ultimately short light pulses in a partially absorbing medium is analyzed in the framework of the three-level model. Nonlinear wave equations are obtained describing propagation of light pulses in media with quadratic (all three transitions are allowed) or cubic (one of the transitions is forbidden) nonlinearity in the range of optical transparency or with the sine-Gordon-type nonlinearity in the region of absorption. Using the averaged variational principle, the approximate solutions of equations in the form of unipolar soliton-like signals are found and conditions of their transverse stability are determined. A stable propagation of a broad-band pulse is shown to be possible under conditions when monochromatic signals exhibit self-focusing.     

Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media

Frequency-resolved optical gating is used to characterize the propagation of intense femtosecond pulses in a nonlinear, dispersive medium. The combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. The role of the phase of the input pulse is studied. The results are compared with the predictions of a three-dimensional nonlinear Schr?dinger equation.     

用SHG-FROG方法测量超短光脉冲的振幅和相位

介绍了二次谐波振荡频率分辨光学快门(SHGFROG)测量超短脉冲的实验系统和二维相位恢复算法,这种方法可以实现对超短脉冲振幅和相位的完全测量.利用矩阵方法数值模拟了几种常见超短脉冲的SHGFROG迹线,并用主元素广义投影算法(PCGPA)从这些无噪音的SHGFROG迹线中恢复了脉冲的振幅和相位,误差接近收敛的标准.研究结果表明,这种测量方法结构简单,算法可靠,是测量超短脉冲的理想方法之一.     

Experimental study of the origin of the second-order nonlinearities induced in thermally poled fused silica

Second-harmonic generation (SHG) experiments at the surfaces and in the volumes of thermally poled commercial fused-silica samples have been performed. The experimental results show, for the first time to our knowledge and in agreement with our model, that second-order nonlinearity is induced on both cathodic and anodic interfaces. No contribution from the bulk of the sample could be detected. Moreover, our data also reveal that reorientable moieties are at the origin of the induced nonlinearity. The second-order susceptibility, evaluated by a surface SHG experiment, is chi((2))(333)~1 pm/V . The estimated susceptibility associated with the dc Kerr effect is negligible.     

Solitary pulses in linearly coupled Ginzburg-Landau equations

This article presents a brief review of dynamical models based on systems of linearly coupled complex Ginzburg-Landau (CGL) equations. In the simplest case, the system features linear gain, cubic nonlinearity (possibly combined with cubic loss), and group-velocity dispersion (GVD) in one equation, while the other equation is linear, featuring only intrinsic linear loss. The system models a dual-core fiber laser, with a parallel-coupled active core and an additional stabilizing passive (lossy) one. The model gives rise to exact analytical solutions for stationary solitary pulses (SPs). The article presents basic results concerning stability of the SPs; interactions between pulses are also considered, as are dark solitons (holes). In the case of the anomalous GVD, an unstable stationary SP may transform itself, via the Hopf bifurcation, into a stable localized breather. Various generalizations of the basic system are briefly reviewed too, including a model with quadratic (second-harmonic-generating) nonlinearity and a recently introduced model of a different but related type, based on linearly coupled CGL equations with cubic-quintic nonlinearity. The latter system features spontaneous symmetry breaking of stationary SPs, and also the formation of stable breathers.     

Numerical analysis of the stability of optical bullets (2 + 1) in a planar waveguide with cubic–quintic nonlinearity

In this paper, we have presented a numerical analysis of the stability of optical bullets (2 + 1), or spatiotemporal solitons (2 + 1), in a planar waveguide with cubic–quintic nonlinearity. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L _D) and diffraction (diffraction length, L _d) with temporal and spatial auto-focusing behavior, respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic–quintic nonlinearity with the optical fields coupled by cross-phase modulation and considering several values for the non linear parameter α We have shown the existence of stable light bullets in planar waveguide with cubic–quintic nonlinearity through the study of spatiotemporal collisions of the light bullets.     

Soliton formation in the propagation of phase-modulated femtosecond pulses through an optical fiber with a cubic nonlinearity

A way of soliton self-formation upon propagation of femtosecond light pulses through an optical fiber with a cubic nonlinearity is described with allowance for the dispersion of the nonlinear response of the medium. For soliton formation to occur, a low-frequency phase modulation of the initial pulse is necessary. Several solitons formed in this way differ in both maximal intensities and group velocities. The duration of an individual soliton may be several (up to ten) times smaller than the initial duration of the input pulse.     

Group velocity control of femtosecond pulse in folded dielectric axes structures by electro-optic effect

Theoretical investigation on the group velocity control of ultra-fast pulses by transverse electro-optic effect as well as its cascading and cubic nonlinearity is presented. Numerical simulation shows that the group velocity can be tuned via conveniently modulating the external electric field strength or the intensity of input pulse. The response of group velocity modulation is in proportion to these two factors, and the advancement or delay can reach the magnitude of 1–2 fractional pulses, which could be a potential scheme for controlling the velocity of pulse in future high speed and large-capacity communication networks.     

On the electromagnetic field energy in an isotropic transparent nonlinear medium

Expressions for the energy density of an electromagnetic field in an isotropic transparent medium with cubic or higher order nonlinearity are derived. For comparatively long pulses, the local energy density is shown to depend not only on the squared modulus of the electromagnetic field envelope but also on the ellipticity of polarization of the radiation at the same point. (c) 2004 MAIK "Nauka/Interperiodica".     

Second harmonic generation due to quadrupole interaction in a photonic crystal slab: angle dependence and symmetry of the unit cell

We investigate second harmonic generation (SHG) from a photonic crystal slab consisting of centrosymmetric materials. The SHG signal is observed in the transmission direction when the incident laser excites the quasiwaveguide mode. As the SHG frequency approaches the exciton level, the SHG intensity increases resonantly. When the incident angle is exactly 0, the SHG signal vanishes even if the transmission dip is excited. This fact is readily explained by a quadrupole theory based on the Lorentz oscillator model, where the source of the nonlinearity is the Lorentz force. When the unit cell in the photonic crystal lacks inversion symmetry, the SHG signal is expected even for the normal incidence. It is experimentally demonstrated for a square array of triangular semiconductor slabs.     

Femtosecond cubic optical nonlinearity of thin nickel films

Transient pump-probe measurements of circular anisotropy in nickel films induced by 38-fs optical pulses show an instantaneous response that is related to the optical orientation of the spins of free electrons. Measurements in a sample of variable thickness, performed in both transmission and reflection, revealed that the surface significantly influences the degenerate cubic optical nonlinearity of the nickel films to a depth of approximately 4-5 nm into the bulk.