Pulse Propagation In Media Research Articles

Optimization of nonlinear enhancement through linear dispersion engineering

We consider nonlinear pulse propagation in media with a dispersion relation exhibiting J periodically spaced identical maxima in a co-moving frame. The nonlinear interactions lead to J pulses centered at each of these frequencies. These pulses propagate at the same group velocity and interfere, leading to a highly non-uniform signal in time. This results in the enhancement of effective nonlinear effects, as we recently demonstrated experimentally [Nat. Phys. 18, 59 (2022)NPAHAX1745-247310.1038/s41567-021-01400-2]. Here we present a detailed theoretical and numerical study of this nonlinear enhancement. We show that the amplitudes of the frequency components approximately follow a simple relation, which allows us to derive that the nonlinear enhancement factor increases as 0.687 J . Hence, enhancements of order 10 can be achieved with 15 frequency components.

Diffraction Limit in Theory of Light Bullets

An averaged variational procedure has been developed to study the propagation of light bullets in optical fibers using the propagation of light pulses in media with Kerr and quadratic nonlinearities as examples. Criteria for the correct choice of trial solutions are discussed. The condition under which the dispersion length is much greater than the length of diffraction spreading is called the diffraction limit. It is shown that, in this limit, the temporal and spatial dynamics of a bullet are independent of each other, while finding the dynamic parameters of a soliton is reduced to finding various solutions of the nonstationary linear Schrodinger equation for an imaginary quantum particle. The efficiency of the proposed approach is demonstrated by the example of finding solutions in the form of optical vortices in a waveguide for nonlinearities of both types.

Study of chiroptical fiber nonlinearities with new formulation of constitutive equations

A theoretical study of a light pulse propagating in a chiroptical fiber considering with Kerr effect is presented in this article. The novel effects of chirality are characterized through our proposed formalism, to highlight the nonlinear effect in a chiral medium, which is due to the magnetization vector under the influence of a strong electric field. These simulations are based on the split-step Fourier method for solving the nonlinear Schrödinger equation. The latter is one of the most used pseudo-spectral methods to study the propagation of pulses in media, nonlinear, and dispersive. The obtained results presented in this article illustrate nonlinear chirality parameter that becomes the key factor to estimate chiroptical fiber dispersion and nonlinearity.

Self-similar Shape Mode of Optical Pulse Propagation in Medium with non-stationary Absorption

We discuss laser pulse propagation with the self-similar shape in a medium with instantaneous nonlinear absorption. We consider two cases of the laser pulse propagation. First one corresponds to problem of laser-induced plasma generation in silica under action of TW laser pulse. The second one corresponds to femtosecond laser pulse propagation in medium with nanoparticles of noble metals. In both cases the mode of the self-similar shape of pulse is of interest. We discuss also a physical mechanism of non-linear acceleration or slowing-down for laser pulse propagation in a medium with nanoparticles. The last phenomena are important, in particular, for a problem of data processing of all optical method. We used analytical approach for considered problem as well as computer simulation.

Self-similar Shape Mode of Optical Pulse Propagation in de-focusing Medium with Two-Photon Absorption

We investigate the self-similar shape mode of laser pulse propagation in medium with two-photon and multi-photon absorption under action of either cubic nonlinearity or resonant nonlinearity. The annalitycal solution for laser pulse propagation under the detuning between carrier frequency of a wave packet and energy transition frequency for atom or molucule is developed. An existance of the self-similar shape mode for laser beam propagation in de-focusing medium is predicted if the nonlinear absoption takes place. This mode takes place along some distance of laser pulse propagation. We used as analytical approach for considered problem as well as computer simulation.

Phase-controlled pulse propagation in media with cross coupling of electric and magnetic probe field component

Light propagation is discussed in media with a cross coupling of the electric and magnetic component of an applied probe field. We derive the wave equations for a probe pulse propagating through such a medium and solve them analytically in Fourier space using the slowly varying envelope approximation. Our analysis reveals the influence of the different medium response coefficients on the propagation dynamics. We apply these results to a specific example system in which cross couplings are induced in an atomic medium by additional control fields. We show that the cross couplings render the propagation dynamics sensitive to the relative phase of the additional fields, and this phase dependence enables one to control the pulse during its propagation through the medium. Our results demonstrate that the magnetic field component of a probe beam can crucially influence the system dynamics already at experimentally accessible parameter ranges in dilute vapors.

Propagation of unipolar strain pulses in media with hysteretic nonlinearity

A theoretical study of the propagation of unipolar strain pulses in a solid medium with an arbitrary power-law hysteretic nonlinearity is carried out. Exact analytical expressions are derived for describing the propagation and evolution of initially sine-shaped and triangular pulses in such media. The solutions found are analyzed both numerically and graphically.

Beyond the spatio-temporal model in femtosecond optics

We use the method of amplitude envelopes to obtain a class of linear nonparaxial amplitude equations, governing the propagation of short optical pulses in media with dispersion, dispersionless media and vacuum. The equations are solved using the method of Fourier transforms and fundamental and exact analytical solutions are obtained. Nonparaxiality leads to nonsymmetrical diffraction enlargement of light pulses and to their transformation in light disks on several diffraction lengths.

Diffraction of femtosecond pulses; nonparaxial regime

We present a systematic study of linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media, and vacuum. The applied method of amplitude envelopes makes it possible to estimate the limits of the slowly varying amplitude approximation and to describe an amplitude integrodifferential equation governing propagation of optical pulses in the single-cycle regime in solids. The well-known slowly varying amplitude equation and the amplitude equation for the vacuum case are written in dimensionless form. Three parameters are obtained defining different linear regimes of optical pulse evolution. In contrast to previous studies we demonstrate that in the femtosecond region the nonparaxial terms are not small and can dominate over the transverse Laplacian. The normalized amplitude nonparaxial equations are solved using the method of Fourier transforms. Fundamental solutions with spectral kernels different from those according to Fresnel are found. Exact unidirectional analytical solution of the nonparaxial amplitude equations and the 3D wave equations with initial conditions compatible with Gaussian light bullets are obtained also. One unexpected new result is the relative stability of light bullets (pulses with spherical and spheroidal spatial form) when we compare their transverse enlargement with paraxial diffraction of light beams in air. It is important to emphasize here the case of light disks, i.e., pulses whose longitudinal size is small with respect to the transverse one, which in some partial cases are practically diffractionless over distances of a thousand kilometers. A new formula that calculates the diffraction length of optical pulses is suggested. Finally, propagation of single-cycle pulses in air and vacuum was investigated, and a coronal (semispherical) form of diffraction at short distances was observed.

Relaxation dynamics of a broadband nanosecond acoustic pulse in a bubbly medium

The first experimental observation of the propagation dynamics of a short broadband acoustic pulse in a resonance medium with gas bubbles is carried out. The probing pulse is generated using the optoacoustic effect. It is shown that the theory of short pulse propagation in media with generalized resonance relaxation adequately and accurately describes the dynamics of short pulse dispersion. A possibility to determine the relaxation and resonance parameters of media by the pulsed testing technique is demonstrated.

Nonlinear propagation of ultraslow pulses in media with electromagnetically induced transparency

The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrödinger-like wave equation that considers only instantaneous Kerr nonlinearity.

Solitons and decoherence in left-handed metamaterials

We present exact electromagnetic solitary pulses that can be experimentally obtained within nonlinear left-handed metamaterials. The effect of pulse decoherence on the modulation instability of partially incoherent electromagnetic waves is also investigated. The results may contribute to a better understanding of nonlinear electromagnetic pulse propagation in media with negative index of refraction.

Pulse propagation in media with deterministic and random dispersion variations

We obtain a widely valid description of pulse broadening in dispersion-managed fiber with a random component in the dispersion. For short distances, a quasi-linear approach in the form of a simple perturbation expansion suffices to capture the broadening for each realization of the random dispersion. For intermediate distances, over which the noise and nonlinearity interact, we demonstrate that the partial differential equation can be reduced to a relatively simple system of nonlinear stochastic ordinary differential equations . Finally, we demonstrate that, over long distances, the slow evolution of the pulse width can be obtained by applying an appropriate multiple-scales averaging procedure to yield a new, scaled noise process effecting pulse broadening.

Correction: Gain-assisted superluminal light propagation

Nature, 406, 277–279 (2000). It has been drawn to our attention that we inadvertently did not cite a previous paper by Segard and Macke1 on the topic of observed superluminal light pulse propagation in media with heavy absorption using a direct pulse shape detection technique. We did, however, cite an earlier paper by Chu and Wong2 on this topic using a different technique.

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.

A spring model for the simulation of the propagation of ultrasonic pulses through imperfect contact interfaces

A spring model for the simulation of the propagation of ultrasonic pulses in arbitrarily complex heterogeneous media is proposed in the framework of the local interaction simulation approach (LISA). The algorithm used allows us to include heuristically additional local interaction mechanisms. In particular, the problem of propagation of pulses across imperfect contact interfaces is considered. A contact quality tensor, which is expected to be connected, although not necessarily in a trivial way, to the bond quality, is introduced directly into the model in order to treat interface flaws, such as delaminations and/or slipping bonds. To demonstrate the applicability of the technique, which is particularly suitable for parallel processing, a few examples of numerical simulation of pulse propagation in media with various kinds of imperfections are presented.

Velocity of pulse propagation in media with amplitude nonlinearity

The propagation velocity of optical wave fronts can be accelerated by the influence of gain saturation. We report systematic measurements for the specific case of Brillouin gain in optical fibers. A simplified analytic rate equation approach permits a qualitative understanding of the observations in terms of a pure amplitude nonlinearity. We point out that there is a close analogy to a mode-locked laser with gain saturation. Pursuing this analogy, we can explain why the changes in propagation velocity are hardly measurable for synchronously pumped lasers, but easily amount to several percent for amplifiers or lasers based on stimulated Brillouin scattering.

Ray and diffraction effects of acoustic waves when atmospheric conditions produce nonlinear acoustic velocity profiles

The propagation of acoustic pulses in a medium with refractive index n=(a+be−αz)ν, where a, b, ν, α are constants, is discussed within both the ray and diffraction analysis. This work is of relevance to the propagation of acoustic pulses in media which have temperature gradients and/or wind gradients. It is shown that both treatments are amenable to exact solution. A new class of analytical solutions are presented that are of relevance to scientists working in the area of wave propagation in the atmosphere. In the ray treatment a generalization of the linear gradient is obtained that suggests greater bending as compared to the linear case, while in the diffraction limit, the solutions of the wave equation are shown to be particular examples of confluent hypergeometric and Papperitz functions. Qualitative discussions of the solutions are presented.

Pulse propagation in media with small velocity dispersion and relaxation time spectrum of the form 1/ρ. exact solution

Pulse propagation in a medium whose dispersion-dissipative properties correspond to the presence of relaxation mechanisms in the medium, whose relaxation times form a spectrum of the form g (ρ) ~ 1ρ, is considered. In the case of small velocity dispersion an exact solution is obtained for the pulse shape and it is shown that it is equivalent to the description of pulse propagation in a medium with “Ei-rmmemory”.

Pulse propagation in media with frequency‐dependent Q

Recent publications have indicated that a significant dependence of the quality factor Q on frequency may occur in the interior of the earth, and thus an analysis of pulse propagation in media with Q dependent on frequency is appropriate. It is shown that a simple scaling law describes the degradation of an initially sharp pulse as it propagates in a linear viscoelastic medium in which Q has a power‐law dependence on frequency. Of particular interest is the variation of the pulse rise time with path, as this parameter may be useful in estimating the Q structure of the earth.