Pulsed Beam Propagation Research Articles

Temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian beams in dispersive media

The temporal and spectral properties of ultrashort pulsed Laguerre–Gaussian (LG) beams propagating in dispersive media are studied both theoretically and numerically. It is shown that the on-axis pulse broadens with increasing propagation distance and the on-axis spectrum is blueshifted. For the off-axis spectrum the blueshifts decrease and then the spectrum becomes redshifted as the radial distance increases. The propagation of ultrashort pulsed LG beams in free space and of ultrashort pulsed Gaussian beams can be regarded as special cases of our results, and some interesting properties are discussed.

SPECTRUM INDUCED CHANGE IN THE DIFFRACTION OF VECTORIAL NONPARAXIAL PULSED BEAM

A vectorial nonparaxial correction to an arbitrary scalar paraxial solution of ultrashort pulsed beam is obtained by application of the Fourier transform and angular spectrum presentation methods. In general, the vectorial and nonparaxial property of pulsed beam depends on the pulse shape and its spectrum distribution. As the pulse duration decreases, changes of vectorial and nonparaxial correction depend on the pulse spectrum. Results of three typical pulse shapes are studied for comparison to show the spectrum-induced changes in vectorial nonparaxial propagation of ultrashort pulsed beam.

Stable propagation of pulsed beams in Kerr focusing media with modulated dispersion

We propose the modulation of dispersion to prevent collapse of planar pulsed beams that propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatiotemporal soliton stabilized by dispersion management. We have studied the existence and properties of these solitary waves both analytically and numerically. We show that the adequate choice of the modulation parameters optimizes the stabilization of the pulse.

Numerical modeling of (D+1)-dimensional solitons in a sign-alternating nonlinear medium with an adaptive fast Hankel split-step method

We present a novel technique to numerically solve transverse and pulsed optical beam or light bullet propagation in a layered alternating self-focusing and self-defocusing medium based on the scalar nonlinear Schrodinger equation in two and three dimensions with cylindrical and spherical symmetry, respectively. Using fast algorithms for Hankel transform along with adaptive longitudinal stepping and transverse grid management in a symmetrized split-step technique, it is possible to accurately study many nonlinear effects, including the possibility of spatiotemporal collapse, or the collapse-arresting mechanism due to a sign-alternating nonlinearity coefficient. Also, by using the variational approximation technique, we can prove that stable (D+1)-dimensional soliton beams and optical bullets exist in these media.

A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames

A new time domain (TD) representation for radiation from apertures, wherein the field is expanded in a discrete lattice of shifted, tilted, and retarded pulsed beam (PB) propagators is proposed. The PB representation provides a uniformly accurate systematic framework for ray-based tracking of ultrawide-band transient fields in complex configurations, e.g., slowly or abruptly varying inhomogeneous media. The excitation coefficients of the PBs are extracted from the aperture source distribution via a new discretized local slant stack transform. The formulation is structured upon a new class of frames, termed windowed Radon transform frames. The sets of expansion and analysis functions are shown to be dual frames, thus, facilitating representation of arbitrary bandlimited source fields. Explicit expressions for the processing windows (the analysis frame set) and for the PB propagators (the expansion set) are provided for the class of isodiffracting PBs. Accuracy of the PB expansion technique is demonstrated for a focusing aperture case, that tends to fail the conventional ray shooting schemes.

Theory of spatially and spectrally partially coherent pulses

A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space-frequency domain and in the space-time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space-frequency domain is considered and their coherent-mode representation is presented.

Local spectrum analysis of field propagation in an anisotropic medium Part II Time-dependent fields

In Part I of this two-part investigation [J. Opt. Soc. Am. A 22, 1200 (2005)], we presented a theory for phase-space propagation of time-harmonic electromagnetic fields in an anisotropic medium characterized by a generic wave-number profile. In this Part II, these investigations are extended to transient fields, setting a general analytical framework for local analysis and modeling of radiation from time-dependent extended-source distributions. In this formulation the field is expressed as a superposition of pulsed-beam propagators that emanate from all space-time points in the source domain and in all directions. Using time-dependent quadratic-Lorentzian windows, we represent the field by a phase-space spectral distribution in which the propagating elements are pulsed beams, which are formulated by a transient plane-wave spectrum over the extended-source plane. By applying saddle-point asymptotics, we extract the beam phenomenology in the anisotropic environment resulting from short-pulsed processing. Finally, the general results are applied to the special case of uniaxial crystal and compared with a reference solution.

Parametric generation of light X waves by Bessel beam pump

Spatial and temporal localization of light energy is of great importance for various applications. The diffraction-free and dispersion-free propagation of pulsed beams (usually called as X waves) can be achieved both in linear [1–3] and nonlinear media. In a quadratic medium X waves are formed spontaneously through a trigger mechanism of conical emission via mismatched second harmonic generation [4–9]. An appearance of conical emission is a result of noncollinear interactions which are strictly controlled by phase matching conditions of different components of spatial-temporal spectrum of the waves. It was demonstrated that angular dispersion of the waves excited in optical parametric generator (OPG) by quasimonochromatic plane pump wave corresponds to angular dispersion of X waves [10, 11]. In this paper we reveal an existence of different X wave modes in OPG pumped by quasimonochromatic Bessel beam. An X wave can be represented as a superposition of Bessel beams, the frequencies ω, wave vectors k, and half-cone angles ψ of which are related in dispersive medium by an equation

Propagating pulsed Bessel beams in periodic media

An analytical study of vectorial pulsed Bessel beam propagation in one-dimensional photonic bandgaps, based on a Wannier-function approach, is presented, and the conditions for dispersion-free and diffraction-free propagation are derived. The analysis is applied, as a particular case, to Bessel beam propagation in periodic layered structures.

Propagation of pulsed beam beyond the paraxial approximation in free space

We study the propagation of ultrashort pulsed beam (down to the limit of single-cycle pulse) beyond the paraxial approximation in free space. By application of the perturbation method, the nonparaxial corrections to an arbitrary paraxial solution are given in a series form. The rigorous nonparaxial results are obtained for comparison by numerical simulation. It shows that the second-order correction can guarantee a good precision in describing the nonparaxial propagation of a single-cycle pulsed beam, whose beam waist width is of the order of the central wavelength. The nonparaxial propagation of isodiffracting pulsed Gaussian beam is given in detail. It shows the temporal distribution inevitably influences the spatial distribution of the correction due to the inherent spatiotemporal coupling in the pulsed beam.

Propagation of ultrashort pulsed beams in dispersive media

Starting from the Rayleigh diffraction integral, the propagation equation of ultrashort pulsed beams in dispersive media is derived without making the paraxial approximation and slowly varying envelope approximation (SVEA). The spatiotemporal properties of ultrashort pulsed beams in dispersive media, such as spectrum redshifting, narrowing and pulse distortion are illustrated with pulsed Gaussian beams. It is stressed that the ``antibeam'' behaviour of ultrashort pulsed beams can be avoided, if a suitable truncation function is chosen.

Physical wavelets and their sources: real physics in complex spacetime

For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the Fourier sources as compared to the rather convoluted spacetime expressions obtained from the original wavelets. This suggests that the associated pulsed-beam propagators may play a fundamental role in emission and absorption processes including focus or "directivity." It also opens the way to constructing FFT-based algorithms for pulsed-beam analyses of acoustic and electromagnetic waves.

Vectorial nature of nonparaxial ultrashort pulsed beam propagation in free space

We present a rigorous approach to the propagation of a fully vectorial nonparaxial ultrashort pulsed beam in free space. By using the Fourier transform and the vectorial angular-spectrum formalism, we derive an exact fully vectorial integral solution of Maxwell's equations for an ultrashort pulsed beam whose pulse duration is as short as a single optical oscillation period. From this general expression we develop a Taylor expansion of electric field, and obtain all-order corrections to the paraxial pulsed beam solution, which is assumed to be known. Furthermore, the influence of vectorial nature on nonparaxial pulsed beam propagation is analysed and the vectorial nonparaxial correction is given in this paper.

The production and elimination of the spatial singularity for ultrashort chirp ed pulse-beam propagation in free space

We study the propagation of ultrashort chirped pulsed beams in free space. We find that the slowly-varying envelope approximation and complex amplitude envelope are not suitable for ultrashort chirped pulsed beams anymore, because they lead to the spatial singularity that is inconsistent with the physical significanc e of the beam propagation. And the chirp influences the spatial singularity mor e seriously than the width of the pulsed beam does. The spatial singularity can be eliminated by using the complex analytical signal theory. In this paper, we g ive the simulations of spatial singularity about ultrashort chirped pulsed Gauss ian beams with a series of parameters, and the conditions that lead to the spati al singularity etc. We think that the broad spectrum of the ultrashort pulsed be am is the original reason for the spatial singularity.

Spatial nonparaxial correction of the ultrashort pulsed beam propagation in free space.

In this paper, a family of integral solutions representing ultrashort pulsed beam propagation in free space is studied by using the comoving frame coordinates and the Fourier transformation for time variable in terms of well-known paraxial approximation. The pulsed Gaussian-like beam solution is obtained as a special case of the integral solution, where the pulsed Gaussian beam solution is included. Further, starting from the nonparaxial pulsed beam propagation equation in the temporal-frequency domain and making use of the spatial Fourier transform, the nonparaxial pulsed beam solution is derived based on the paraxial pulsed beam solution, where the nonparaxiality is evaluated by a series of expansions.

Vector analysis of the propagation of ultrashort pulsed beams in free space

By using a Fourier transform technique and applying the paraxial approximation in the frequency domain, we derive an integral solution for the transverse and longitudinal components of the light field of an ultrashort pulsed beam propagating in free space. In particular, on the basis of the theory of complex analytical signals, the solutions for the components of a pulsed Gaussian-like beam, in rectangular coordinates, are derived and compared with those derived from slowly varying envelope approximation (SVEA). The corresponding numerical investigations are carried out and show that for sub-cycle pulses, the SVEA will cause spatial singularity for both transverse and longitudinal components of the light field.

Ultrashort pulsed bessel beams and spatially induced group-velocity dispersion.

We find a new family of solutions of the nonparaxial wave equation that represents ultrashort pulsed light beam propagation in free space. The spatial and temporal parts of these pulsed beams are separable; the spatial transverse part is described by a Bessel function and remains unchanged during propagation, but the temporal profile can be arbitrary. Therefore the pulsed beam exhibits diffraction-free behavior with no transverse spreading, but the temporal part changes as if in a dispensive medium; the change is dominated by what we call spatially induced group-velocity dispersion. The analytical and numerical investigations show that the even- and odd-order spatially induced dispersions partially compensate for each other so as to give rise to pulse spreading, weakening, asymmetry, and center shift.

Diffraction-free and dispersion-free pulsed beam propagation in dispersive media

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.

Propagation of intense pulsed proton beam through z‐discharged plasma channel in the presence of return channels

AbstractExperimental studies are presented on the propagation of an intense, pulsed proton beam (890 kV, 50 ns) through a z‐discharged plasma channel (50 cm long, 1.1 to 10 Torr, air) in the presence of return channels (30 cm long). From the measurements by an image converter camera and a small‐sized magnetic probe, we have found the compression (deformation) of the main channel due to the presence of the return channels. Enhancement of the beam power density has also been observed. Good efficiency of the propagation (approximately 33%) has been observed through the main channel. © 2001 Scripta Technica, Electr Eng Jpn, 136(4): 1–6, 2001

Hybrid Ray-Fdtd Moving Coordinate Frame Approach for Long Range Tracking of Collimated Wavepackets

Modeling of long range propagation of collimated wavepackets poses some major difficulties with the conventional FDTD scheme. The difficulties arise from the vast computer resources needed to discretize the entire region of interest and the accumulation of numerical dispersion error. As a means for circumventing these difficulties, the moving frame FDTD approach is in this work. In this approach, the computational grid size is limited to the order of the pulse length, and it and moves along with the pulse. The issues discussed in conjunction with this method are those of numerical dispersion, which is shown to be reduced substantially compared with the stationary formulation, numerical stability, and absorbing boundary conditions at the leading, trailing and side boundaries, Numerical results of pulsed beam propagation in both homogeneous and plane stratified media are shown, and the capability of the method is demonstrated with propagation distances exceeding the order of 10 4 pulse lengths.