Mutual influence of the spectral components of perturbations on the modulation instability frequency interval in a cubic nonlinear medium

The influence of the shape of a Gaussian pulse propagating in a cubic nonlinear medium on the development of its modulation instability is analyzed, taking into account the time dispersion of the nonlinear response as well. Analytical dependences of the frequency interval of the perturbation development on the dispersion of the nonlinear response, the pulse duration, and the number of simultaneously acting perturbations, which affect each other due to the inhomogeneous pulse shape, are obtained. It is shown that, with increasing dispersion of nonlinear response, the frequency interval of the instability development initially narrows and then expands. Qualitative agreement between the analytical dependences and the results of computer simulation is demonstrated. The frequency interval of the modulation instability development in a medium without the nonlinear response dispersion that was previously determined by different authors under the assumption of “long” pulses is found to coincide with that obtained in this study for the Gaussian pulse under the assumption of the simultaneous action of a large number of perturbations.     

Passive mode-locking upon limitation of the spectral width of a laser emission

An analysis is presented of passive locking of modes in lasers with an additional intracavity element that limits the spectral width of a laser emission due to frequency dispersion of an order higher than quadratic. It is found that spectral limitation of this type may give rise to a multiple-pulse regime of passive mode-locking. The laser mode of operation established after a transient process, in this case, appears to be multistable, with the number of pulses per axial period being dependent on the initial conditions of the lasing. It is shown that the dependence of the number of pulses on the pump power is of hysteretic character. The theoretical analysis and numerical simulation are carried out using an equation close to the Ginzburg-Landau equation. Specifically, the nonlinear losses and nonlinear refractive index are supposed to be inertia-less and proportional to the light intensity; the frequency dispersion of the gain and the refractive index are approximated by a quadratic dependence; and the frequency-dependent losses related to the additional spectral limitation of the laser emission are determined by fourth-order frequency dispersion. The possibility of using the characteristic features of mode-locking predicted for control of regimes of formation and propagation of ultrashort light pulses is discussed.     

On the modulation instability of femtosecond light pulses propagating in an optical fiber

The well-known problem of the modulation instability of femtosecond light pulses propagating in a cubic nonlinear medium is considered on the basis of computer simulation with allowance made for the time dispersion of the nonlinear response. The dependence of the maximum perturbation frequency at which the instability takes place on the parameter characterizing the time dispersion of the nonlinearity is studied. The numerical experiments carried out verified the previous conclusion of the authors, based on an original approach to the analysis of propagation of a femtosecond pulse, that the frequency interval of the modulation instability can increase with increasing influence of the dispersion of the nonlinear response. This conclusion is at variance with the conclusion drawn by other researchers on the basis of linear analysis.     

Nonlinear control of the propagation of optical pulses in doped optical fibers

Results of study of nonlinear processes occurring during the propagation of light pulses in optical fibers doped with atoms of rare-earth elements under conditions of atomic coherence and interference are presented. For a three-level Λ scheme of interaction, the linear (χ⁽¹⁾) and nonlinear (χ⁽³⁾) susceptibilities of such a medium are calculated. It is shown that the coefficients of Kerr nonlinearity and nonlinear absorption can reach extremely large values and can be negative. The competition between linear and nonlinear processes in the Λ scheme allows one to obtain compensation regimes when the coefficients of dispersion or absorption of the optical fiber material vanish. The efficient control of the optical properties of such a system over wide limits proves to be possible owing to variations in the parameters of light pulses at the input of the medium. The necessary conditions for realizing regimes with “slow” light, as well as for self-compression of a probing pulse on ultimately small spatial scales in a doped optical fiber, were obtained.     

Transformation of electromagnetic radiation by rapidly moving inhomogeneities of a transparent medium

A theory of reflection and transmission of electromagnetic radiation by inhomogeneities of the parameters of a static transparent medium moving at the velocity of light is developed. Expressions are obtained for the Doppler frequency shift of radiation; it turns out that, under the condition of pronounced frequency dispersion, the frequency of incident radiation corresponds to two frequencies of reflected radiation (complementary waves). It is found that, as the velocity of an inhomogeneity tends to the phase velocity of radiation in the medium, the reflection and transmission coefficients of radiation by the inhomogeneity indefinitely increase. It is shown that the electromagnetic radiation frequency may increase severalfold, with a transformation coefficient of about unity, due to the Doppler shift by the inhomogeneities of a nonlinear medium that are induced by pulses (solitons) of intense counterpropagating radiation.     

Phase and group synchronization in second-harmonic generation of ultrashort light pulses in one-dimensional photonic crystals

It is shown, on the basis of an analysis of the dispersion relation for an infinite one-dimensional periodic multilayer structure and direct numerical integration of Maxwell’s equations by the finite-difference method, that structures with photonic band gaps (PBGs) make it possible to provide simultaneously conditions for phase and group synchronizations for second-harmonic generation with participation of extremely short light pulses. The phase and group detunings, which arise as a result of the dispersion of the nonlinear medium, are compensated by the dispersion of the PBG structure. The use of this regime of nonlinearly optical interactions opens up the possibility of attaining high frequency conversion efficiencies irrespective of the synchronization length in the interior volume of a nonlinear material.     

On the analytical description of self-frequency shift of a pulse propagating in the region of zero group-velocity dispersion

An analytical expression describing the frequency shift of nonsoliton pulses in a nonlinear Raman-active medium is obtained by the method of moments. The regime of propagation in which the central frequency of the signal falls into the region of zero group-velocity dispersion is analyzed.     

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.     

Pulse dynamics upon three-wave parametric interaction in the presence of cubic and quadratic nonlinearities

The features of the three-wave parametric interaction in a medium with quadratic and cubic nonlinearities upon low-frequency pumping and nonzero detuning from the phase matching were studied. It has been shown that the common wave packet formed by the signal and idle waves is decayed into partial pulses, whose dynamics is determined by effective dispersion parameters. The presence of two types of nonlinearities extends the possibilities of controlling the dynamics of the forming partial pulses due to the variation of the pump wave power. The velocity of recession of partial pulses can reach large values and even exceed the speed of light in the vacuum.     

Modeling the terahertz radiation generation process,obtained by filtration of spectral supercontinuum,formed during propagation of femtosecond laser pulse in GaAs crystal

We present the results of theoretical studies of the process of generation of terahertz radiation arising via interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium. Numerical time-integration, by the finite-difference method, of the system of nonlinear Maxwell equations has been performed. We consider the interaction of mutually-orthogonal linearly polarized pulses, both having the central wavelength of 1.98 μm, durations of 30 fs, and the energies of 30 nJ, propagating along the normal to the 〈110〉 plane in a 1 mm-thickness GaAs crystal. In the nonlinear part of the medium polarization the without-inertia nonlinear second-order susceptibility is taken into account. The process of formation of a terahertz pulse arising via spectral filtration of supercontinuum formed in the spectra of pump pulses at the output of nonlinear crystal is studied. The dependences of both the current frequency of the pump pulses on time for different lengths of nonlinear crystal and of pump pulse durations on the crystal length are obtained. Also the dependences of the current frequency of the terahertz pulse on time at different crystal lengths, as well as of the efficiency of generation of terahertz radiation on the length of nonlinear crystal and on the energy of pump pulses are obtained.     

LC-SLM像素型结构对4f脉冲整形系统的影响

液晶空间光调制器的离散型相位调制和像素间隙是4f脉冲整形系统的主要失真原因,基于以上因素的分析,建立了完善的4f脉冲整形系统数学模型,数值模拟了不同相位调制变化率、不同像元尺寸、不同间隙尺寸以及不同色散关系下的离散型相位调制和像素间隙导致的失真情况。模拟结果表明:离散型相位调制会导致整形脉冲中出现副本脉冲,相位调制变化率越大或像元尺寸越大均会导致这种副本脉冲越强,输出目标脉冲失真越严重;像素间隙也会导致整形脉冲中出现副本脉冲,间隙尺寸越大会导致这种副本脉冲越强,输出目标脉冲失真越严重;两种副本脉冲均呈等间隔分布,其周期由每个像元对应的频谱宽度决定,非线性光谱色散会使副本脉冲啁啾化且强度变小。     

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.     

Theory of nonlinear Sagnac effect

A nonlinear wave interaction is considered as a technique to increase the rotation sensitivity of the ring laser. The gyroscopic scale factor K is calculated in an active laser gyro with a dispersive medium. K is in reverse proportion to the group index n* = n + vdn/dv of the medium. In a monolithically-integrated GaAs ring laser, the value K ∼5000 is obtainable (radius ∼1 cm) in a linear case. In the presence of a strong wave, the dynamic nonlinear anomalous dispersion can provide an increase of K by 10–100 times in the vicinity of critical points where n* passes zero. An expression of K is derived for the nonlinear Sagnac effect. The nonlinear dispersion is discussed in terms of “slow/fast” light.     

Evolution of optical pulses in the presence of third-order dispersion

We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.     

TEMPORAL OPTICAL SOLITONS VIA MULTISTEP χ(2) CASCADING

We consider a multistep χ⁽²⁾ cascading for light pulses with the dispersion of the system taken into account. Using the method of multiple scales we derive a set of coupled envelope equations governing the nonlinear evolution of the fundamental, second and third harmonic waves involved simultaneously in two nonlinear optical processes, i.e. second harmonic generation and sum frequency mixing. We show that three-wave temporal optical solitons are possible in three-and four-step cascading in the presence of a group-velocity mismatch between different pulses.     

Few‐cycle,broadband, mid‐infrared optical parametric oscillator pumped by a 20‐fs Ti:sapphire laser

A few‐cycle, broadband, singly‐resonant optical parametric oscillator (OPO) for the mid‐infrared based on MgO‐doped periodically‐poled LiNbO₃ (MgO:PPLN), synchronously pumped by a 20‐fs Ti:sapphire laser is reported. By using crystal interaction lengths as short as 250 µm, and careful dispersion management of input pump pulses and the OPO resonator, near‐transform‐limited, few‐cycle idler pulses tunable across the mid‐infrared have been generated, with as few as 3.7 optical cycles at 2682 nm. The OPO can be continuously tuned over 2179‐3732 nm (4589‐2680 cm^‐1) by cavity delay tuning, providing up to 33 mW of output power at 3723 nm. The idler spectra exhibit stable broadband profiles with bandwidths spanning over 422 nm (FWHM) recorded at 3732 nm. The effect of crystal length on spectral bandwidth and pulse duration is investigated at a fixed wavelength, confirming near‐transform‐limited idler pulses for all grating interaction lengths. By locking the repetition frequency of the pump laser to a radio‐frequency reference, and without active stabilization of the OPO cavity length, an idler power stability better than 1.6% rms over >2.75 hours is obtained when operating at maximum output power, in excellent spatial beam quality with TEM₀₀ mode profile. Photograph shows a multigrating MgO:PPLN crystal used as a nonlinear gain medium in the few‐cycle femtosecond mid‐IR OPO. The visible light is the result of non‐phase‐matched sum‐frequency mixing between the interacting beams.     

Holography of wave packets

We describe the principles of holographic storage and reconstruction of ultrashort light pulses using spectrally nonselective media. This can be achieved by the application of a 3-D recording medium and by the holography of waves produced by spatial spectral decomposition of light pulses. We also describe various transformations of optical temporal signals based on holographic spectral filtering and nonlinear interaction of spectral decomposition waves.     

Self-action dynamics of ultrashort electromagnetic pulses

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.     

Discrete dispersion of optical pulses on nonlinear-induced moving lattice

A theory of the interaction of an optical pulse with a concurrently moving lattice created in a nonlinear medium by a biharmonic pump wave is presented. Regimes for the partitioning of a solitary signal into subpulses, trapping a pulsed signal into a parametric soliton, and eliminating the lattice dispersion of pulses with a certain velocity are found.