On a Gaussian beam in an amplifying medium

The model of a Gaussian beam in an amplifying medium is analyzed within the framework of the paraxial (quasi-optical) approximation. Upon violation of the obtained restrictions, the model leads to a physically inconsistent conclusion about an infinitely high radiation power after a passage of an ordinary Gaussian beam through a layer of the amplifying medium. The importance of a limitation on the transverse dimensions of the amplifying medium or of the introduction of intracavity angular selection is demonstrated. The fundamental mode in the form of a Gaussian beam appears in the model with a quadratic dependence of the gain on the transverse coordinates.     

Transformation of a Gaussian pulse reflecting from a nonlinear medium

The transformation of the envelope of a Gaussian pulse incident on and reflecting from a nonlinear dispersive medium is studied. It is shown that the pulse envelope transforms considerably upon reflection near the optical resonance frequency and the nonlinearity of the medium may appreciably distort the reflected pulse. Away from the resonance frequency, conditions may arise when the shift of the reflected pulse does not lead to the loss of the Gaussian form. In this case, the influence of nonlinearity is insignificant.     

On the propagation of a light pulse in a layer of an amplifying medium

The inferences of a paper by N.S. Bukhman on the appearance of waves with opposite directions of the phase and group velocities in a layer of an amplifying medium (Opt. Spectrosc. 123 (5), 783 (2017)) are analyzed. It is shown that these inferences need additional substantiation.     

Behavior of the soliton pulse envelope in a nonlinear medium in the subpicosecond range

The impact of additional higher dispersion and nonlinear terms in the model equation on the properties of short pulses is studied. The analysis is based on two mutually complementary asymptotic approaches. We found explicit expressions describing distortions in the amplitude and phase of the signal envelope. The conditions under which the additional terms compensate for each other are examined. Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of the Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1117–1124, September, 1998.     

Reflection of a Gaussian laser pulse by an active medium

The reflected laser pulse is both temporally and spatially displaced due to spatial and chromatic dispersions when a Gaussian laser pulse is incident onto an active medium. In the case of no chromatic dispersion, the temporal shift is linearly related to the spatial Goos-Hänchen shift. Furthermore, for an incident TE-mode laser pulse, the transmitted laser pulse shifts spatially and temporally by exactly a half of that of the reflected laser pulse. We further point out that, compared to the Goos-Hänchen shift at the critical angle which was conventionally considered the maximum, the Goos-Hänchen shift for the grazing incidence is bigger by one order of magnitude. This can greatly ease the direct experimental study of the Goos-Hänchen shift.     

光脉冲在激光放大介质中的非线性传播

在考虑了激光放大介质中基质的克尔非线性效应和群速度色散以及活性粒子的增益分布后,导出了光脉冲在激光放大介质中传播的基本方程。并在光脉冲中心频率与介质增益峰值频率时重合时,对皮秒超高斯光脉冲在钕玻璃激光放大介质中传播的脉冲形状进行了分析讨论。     

光脉冲在激光放大介质中的非线性传播

 在考虑了激光放大介质中基质的克尔非线性效应和群速度色散以及活性粒子的增益分布后，导出了光脉冲在激光放大介质中传播的基本方程。并在光脉冲中心频率与介质增益峰值频率时重合时，对皮秒超高斯光脉冲在钕玻璃激光放大介质中传播的脉冲形状进行了分析讨论。     

Linear dynamics of a Gaussian frequency-modulated pulse in a single-mode fiber with a complex refractive index

By using a frequency-modulated Gaussian pulse as an example, it is shown within the framework of the linear model taking into account the second-order dispersion effects that the presence of the imaginary part of the dispersion parameter of the group velocity substantially affects the pulse dynamics in a single-mode optical fiber with gain. Absorption insignificantly influences the dispersion characteristics of the fiber and its transformation properties. The possibility of the realization of “supercompression,” under which the pulse duration τ_p → 0, as well as of compression of a pulse without initial frequency modulation, is revealed. It is shown that in these fibers, the propagation of the pulse peak with a faster-than-light velocity and the wavefront reversal effect are possible.     

Gaussian pulse transformation upon reflection from a resonant medium

The transformation and longitudinal shift of “the center of gravity” of a Gaussian pulse reflected from the plane surface of a semi-infinite resonant medium are analyzed numerically. The regions of carrier frequencies in which the maximum and minimum deformations of the reflected pulse are observed are determined.     

Propagation of a soliton-like pulse in a weakly nonlinear medium

Numerical methods are used to study the decay dynamics of a soliton-like signal in a medium with a cubic nonlinearity (using the nonlinear Shrödinger equation). We consider the influence of the initial pulse area, shape, and random modulations in its amplitude and phase on the decay process, as well as the effects of absorption and pumping in the medium.V. D. Kuznetsov Physico-Technical Institute, Tomsk State University, Siberia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 36–40, April, 1995.     

Transmission of a light pulse by a nonlinear medium

Resonance interaction is considered for a pulse of monochromatic radiation in a medium of phthalocyanin type, on the basis of a two-level model. The change in pulse width and height are deduced, as is the degree of bleaching.     

Study of nonlinear propagation of chirped optical pulses in laser amplifying medium

In chirped pulse amplification, the amplification of an optical pulse in laser amplifying medium is a very important link. After considering dispersion, Kerr nonlinear effect, gain distribution and loss of the medium, the physical model that the optical pulse propagates in the medium has been established, which is suitable for the general situation where the optical pulse propagates in the amplifying medium. Using a split-step Fourier method, the propagation state of a chirped optical pulse in the amplifying medium has been numerically simulated, and the influences of the gain dispersion of the medium and the frequency detuning of the pulse on the optical pulse have been discussed emphatically. The results show that, with the amplification and propagation of the ultrashort chirped pulse in the amplifying medium, gain saturation and Kerr nonlinear effect of the medium will cause distortion of the optical pulse. For the optical pulse with a wideband spectrum, gain dispersion will cause the gain narrowing effect, so it is equivalent to a loss mechanism. The frequency detuning of the optical pulse will cause distortion of the pulse, which can be used to weaken the impact of gain saturation, thus reshaping the optical pulse.     

Wavefront study in a Gaussian beam passed through a nonlinear optical medium

We present a numerical model to study the wavefront of a Gaussian laser beam propagated through a nonlinear Kerr media. The model is based on the Gaussian decomposition method. The interaction between a laser beam and a self-focusing or self-defocusing media is discussed from the viewpoint of wavefront distortion. The method is useful for simulation of the wavefront of the beam next to the sample. We also compare our results with those obtained from z-scan method. There is a quite good agreement between data from z-scan method and our results.     

Defocusing as a means of light removal from an amplifying medium

Defocusing as a means of light removal from an amplifying medium is studied. The wave propagation in a simple layer and in an Epstein layer is considered. It is shown that defocusing leads to additional nonsaturatable, nonresonante losses. When defocusing is optimum, it is profitable to operate in the saturation regime with no limitations on the length of the active medium. Defocusing naturally leads to a single-mode regime and to a high directivity of the output radiation. Experiment showed that defocusing is present in the superluminescence of a dye excited by a narrow knife-shaped pumping beam. The properties of defocusing layers and fibers are, in some respects, familiar to those of unstable resonators.     

Effect of perturbations on the soliton evolution in an amplifying medium

The laser-medium model that can be reduced to the Maxwell-Bloch equations for a two-level medium with a pumping is considered. The evolution of a soliton in such a medium is studied in the context of a model close to the integrable one with small perturbations and an arbitrary pumping taken into account. Conditions for the quasi-periodic and chaotic dependence of the soliton parameters on the spatial coordinate are found.     

Velocity of the pulse envelope in tunnel-coupled optical waveguides with strongly differing parameters

The dynamics of a wave packet propagating in active tunnel-coupled optical waveguides with different gains in the channels is studied. It is shown that, in structures of such a type, radiation breaks up into autonomous partial pulses with different values of the velocities of the maxima of their envelopes. The conditions of realization of superluminal or negative values of these velocities in such a structure are studied.     

Propagation of an ultimately short electromagnetic pulse in a nonlinear medium described by the fifth-order Duffing model

We discuss propagation of an ultimately short (single-cycle) pulse of an electromagnetic field in a medium whose dispersion and nonlinear properties can be described by the cubic-quintic Duffing model, i.e., by an oscillator with third-and fifth-order anharmonicity. A system of equations governing the evolution of a unidirectional electromagnetic wave is analyzed without using the approximation of slowly varying envelopes. Three types of solutions of this system describing stationary propagation of a pulse in such a medium are found. When the signs of the anharmonicity constants are different, then the amplitude of a steady-state pulse is limited, but its energy may grow on account of an increase in its duration. The characteristics of such a pulse, referred to as an electromagnetic domain, are discussed.     

Effective equation of nonlinear pulse evolution in a randomly anisotropic medium

Propagation of a light pulse through a weakly inhomogeneous optical fiber is analyzed. The non-linear envelope equation describing the evolution of polarized pulses is determined by statistical properties of inhomogeneities in the optical fiber. The isotropic Manakov system of equations is shown to be applicable in the presence of high-frequency small-scale defects in the fiber. In the presence of only large-scale inhomogeneities, the signal dynamics are described by an anisotropic system of equations.     

Instability analysis of Gaussian beam propagation in a nonlinear refractive index medium

In this paper, we use a thin filament two dimensional Gaussian beam to model the self-trapping filament. The instability of the propagation of a Gaussian beam through a nonlinear refractive index media is investigated, theoretically and numerically. Specifically, the small scale instability of the beam is examined. The numerical results show that the propagation of the two dimensional Gaussian beam presents one or more nonlinear focal points.