Spatially induced spatiotemporally nonspreading Airy-Bessel wave packets

By studying the effect of spatially induced group velocity dispersion (SIGVD) during the propagation of ultrashort pulsed Bessel beams in free space, we numerically prove that third-order SIGVD can temporally cause Gaussian distribution of pulsed Bessel beams to gradually evolve as unsymmetrical trailing oscillatory structures. The pulse shape is confirmed to be temporal Airy distributions on the basis of the cross-correlation function. Therefore, it is demonstrated that the scheme of generating spatiotemporally nonspreading Airy-Bessel wave packets in free space is possible by using a precompensating second-order SIGVD. The results of numerical simulation show that the quasi-Airy pulses induced by third-order SIGVD are temporally nonspreading during propagation in dispersive media. The reasons for nonspreading of such Airy distribution pulses are phenomenologically analyzed by a time-frequency Wigner distribution function of the pulse.     

Generalized Bessel pulse beams

A generalization of type 3 ultrashort pulses (also known as pulse beams or isodiffracting pulses) is introduced. The Bessel beam form of this generalized beam consists of pulses that propagate in free space, without spreading, with a velocity that can be less than that of light. A model spectral distribution that is zero outside a finite range is investigated.     

Propagation properties of ultrashort pulsed bessel beams in dispersive media

A detailed study of ultrashort pulsed Bessel beams in linear dispersive media is performed. The spatial and temporal parts of pulsed Jn beams are separable in dispersive media, provided that the parameter a is independent of frequency omega. The spatial part keeps the Jn shape unchanged during propagation. The temporal evolution behavior of pulsed Jn beams depends on the material's dispersion and diffraction. The pulses can be broadening and become negatively chirped while propagating in anomalous dispersive media. In normal dispersive media, the pulses can be broadening and positively or negatively chirped; even dispersion-free propagation can be achieved if the beam and material parameters are suitably chosen. The condition under which higher-order dispersive effects can be neglected is also discussed.     

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.     

An intuitive model for on-axis pulse evolution of ultrashort pulsed Gaussian beams diffracted from a circular aperture

The diffraction of ultrashort pulsed Gaussian beams from a circular aperture is studied by means of Fresnel diffraction integral and Fourier transform method. A uniform analytical expression is derived for temporal pulse form of ultrashort pulsed Gaussian beams in two cases, i.e. with constant beam waist and with constant diffraction length. It is shown that the on-axis pulse can be formulated as a superposition of an unapertured pulse and an aperture-induced pulse. The superposition of these two pulses leads to an enhanced pulse intensity for small truncation parameters at certain distances in the near field. Our results may find applications in high-intensity laser waveform control.     

Tight focusing induces pulse delay and pulse compression of double-ring-shaped radially polarized ultrashort light pulses

The focusing of double-ring-shaped radially polarized ultrashort light pulses by a high-numerical aperture objective is investigated using vectorial Debye theory. After focusing, the double-ring-shaped radially polarized ultrashort light pulses slow down near the focus, and this pulse delay induces pulse compression in the propagation direction. That is, without changing the pulse duration, the spatial pulse length of the ultrashort light pulse is decreased near the focus. The velocity of the longitudinal component of the light pulse near the focus is lower than that of the radial component. The simulation results demonstrate that control of the ratio of the pupil radius to the beam radius affects not only the longitudinal component of the light pulse, but also the velocity and spatial pulse length of the light pulse because of the destructive interference between the longitudinal components of the inner and outer rings of the light pulse.     

High-current-density subnanosecond electron beams formed in a gas-filled diode at low pressures

The formation of electron beams in a gas diode filled with various gases at low and medium pressures under the action of nanosecond voltage pulses has been studied. It is shown that subnanosecond pulses of the beam current in helium, hydrogen, neon, nitrogen, argon, methane, sulfur hexafluoride, krypton, and xenon can be obtained both at atmospheric pressure and at a pressure of several units or dozens of Torr. In particular, a beam current density above 2 kA/cm² behind the foil at a pulse duration (FWHM) of 250 ps has been obtained in helium-filled diode. On the passage from the regime of ultrashort avalanche electron beam formation to the vacuum diode regime, the beam current pulse amplitude decreases, while both the beam pulse duration (FWHM) and the pulse front width increase.     

Physical significance of the group velocity in dispersive,ultrashort gaussian pulse dynamics

The properties of ultrashort gaussian pulse propagation in a dispersive, attenuative medium are reviewed with emphasis on the pulse velocity. Of particular interest is the group velocity whose physical interpretation loses meaning in causally dispersive materials as the temporal pulse width decreases into the ultrashort pulse regime. A generalized definition of the group velocity that applies to ultrashort pulses in causally dispersive materials is provided by the centroid velocity of the pulse Poynting vector whose properties are described here. In particular, it is shown that this physical velocity measure approaches the group velocity for any value of the initial pulse carrier frequency and at any fixed value of the propagation distance in the limit as the initial pulse width increases indefinitely. This then provides a convenient measure for determining when the group velocity approximation is valid.     

Scalar modified Bessel-Gauss beams and waves

For modified Bessel-Gauss beams, the modulating function for the Gaussian, instead of a Bessel function of real argument, is a Bessel function of imaginary argument. The modified Bessel-Gauss beams and their full wave generalizations are treated with particular attention to the spreading properties on propagation for the azimuthal mode numbers m=0 and m=1. The spreading on propagation of the peak and the null in the radiation pattern obtained in the propagation direction for m=0 and m=1, respectively, is substantially less for the modified Bessel-Gauss waves than that for the corresponding Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to assess the quality of the paraxial beam approximation for the wave. The powers in the Bessel-Gauss wave and the modified Bessel-Gauss wave are finite in contrast to that in the Bessel wave. With respect to both the spreading properties and the quality of the paraxial beam approximation, the modified Bessel-Gauss beam is an improvement over the Bessel-Gauss beam.     

New generalized Bessel-Gaussian beams

Analytical expressions are derived for a new set of optical beams, in which the radial dependence is described by a sum of Bessel distributions of different orders, modified by a flat-topped Gaussian function expressed in the form 1 - [1 - exp(-xi2)]M, where xi is a dimensionless parameter and M(> or = 1) is a scalar quantity. The flat-topped Gaussian function can be readily expanded into a series of the lowest-order Gaussian modes with different parameters; this situation makes it possible to express the optical beam as a series of conventional Bessel-Gaussian beams of different orders. The propagation features of this new set of optical beams are investigated to reveal how a windowed Bessel beam passes progressively from a smooth Gaussian window toward the hard-edge limit.     

Terahertz pulse propagation in the near field and the far field

We present a detailed investigation of the propagation properties of beams of ultrashort terahertz (THz) pulses emitted from large-aperture (LA) antennas. The large area of the emitter is demonstrated to have substantial influence on the temporal pulse profile in both the near field and the far field. We perform a numerical analysis based on scalar and vectorial broadband diffraction theory and are able to distinguish between near-field and far-field contributions to the total THz signal. We find that the THz beam from a LA antenna propagates like a Gaussian beam and that the temporal profile of the THz pulse, measured in the near field, contains information about the temporal and spatial field distribution on the emitter surface, which is intrinsically connected to the carrier dynamics of the antenna substrate. As a result of pulse reshaping, focusing of the THz beam leads to a reduced relative pulse momentum, with implications in THz field-ionization experiments.     

Phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams

The phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams are studied. Numerical calculation results are given to illustrate the dependence of phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams on the truncation parameter, topological charge, spatial parameter and propagation distance. It is shown that there always exists an optical vortex at the center of focused higher-order Bessel–Gauss pulsed beams and the topological charge is conserved during the propagation. The spectral switch appears in the neighborhood of the zero- or minimum-intensity position. With increasing topological charge or spatial parameter, the size of the vortex core increases and the spectral transition height decreases.     

Splitting of femtosecond laser pulses by using a Dammann grating and compensation gratings

When a Dammann grating is used to split a beam of femtosecond laser pulses into multiple equal-intensity beams, chromatic dispersion will occur in beams of each order of diffraction and with different scale of angular dispersion because the incident ultrashort pulse contains a broad range of spectral bandwidths. We propose a novel method in which the angular dispersion can be compensated by positioning an m-time-density grating to collimate the mth-order beam that has been split, producing an array of beams that are free of angular dispersion. The increased width of the compensated output pulses and the spectral walk-off effect are discussed. We have verified this approach theoretically and validated it through experiments. It should be highly interesting in practical applications of splitting femtosecond laser pulses for pulse-width measurement, pump-probe measurement, and micromachining at multiple points.     

Propagation of Bessel beams from a dielectric to a conducting medium

Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of ground penetrating radar systems has been considered. Therefore, an analysis of the propagation of Bessel beams in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e., the propagation of a Bessel beam generated by refracted inhomogeneous waves. The remarkable and unexpected result is that the incident Bessel beam does not change its shape even when propagating in the conducting medium.     

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.     

Modeling of CW annular arrays using limited diffraction Bessel beams

Presents a method for characterizing the linear field of any flat, continuous-wave annular array in terms of a set of known limited-diffraction Bessel beams. The technique uses Fourier-Bessel series to model the surface pressure of the transducer surface, with each term in the series giving rise to a Bessel beam with known propagation parameters. The analysis is applied numerically to two different transducers discussed previously in the literature. In both cases, a deeper understanding of the field emitted than was previously available is gained. Brief outlines for extending the technique to pulsed wave and non-annular arrays are also given     

Spatial and temporal properties of ultrashort pulses propagating in free space

Abstract

By means of the Rayleigh diffraction integral and analytic signal complex representation, the propagation equation of ultrashort pulses in free space is derived, which permits us to study spatial and temporal properties of ultrashort pulses during propagation in free space. It is shown that the pulse deformation and broadening, spectrum redshifting, narrowing and distortion can take place with increasing diffraction angle, and the pulse form changes with propagation distance in the near field, but is preserved in the far field. A comparison with previous work is also made.     

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.     

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO(3) crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.