Free-space Pulses Research Articles

Coupling to multi-mode waveguides with space-time shaped free-space pulses

Guided wave optics, including most prominently fiber optics and integrated photonics, very often considers only one or very few spatial modes of the waveguides. Despite being known and utilized for decades, multi-mode guided wave optics is currently rapidly increasing in sophistication in parallel with technological improvements and advancing simulation tools. The physics of multi-mode interactions are usually driven by some initial energy distribution in a number of spatial modes. In this work we introduce how, with free-space input beams having space-time couplings, the different modes can be excited with different complex frequency or time profiles. We cover fundamentals, the coupling with a few simple space-time aberrations, different waveguides, and a number of technical nuances. This concept of space-time initial conditions in multi-mode waveguides will provide yet another tool to study the rich nonlinear interactions in such systems.

Ultrashort pulse focusing through a planar interface between free space and a nonlinear medium

We present a method to calculate the spatiotemporal electric field distribution of ultrashort pulses focused by an aberration-free lens through a planar interface between free space and a nonlinear medium. The method combines the Fresnel diffraction integral, which is used to model the propagation of the focused pulse in free space, and the angular spectrum propagation method, used to propagate the focused pulse within the nonlinear medium by introducing the irradiance-dependent nonlinear refractive index in the angular spectrum propagator. We have modeled the propagation of ultrashort mildly focused pulses through a Ti:sapphire crystal, characterized only by its linear and nonlinear refractive indices, for pulses with different powers and durations, finding that the proposed method is able to reproduce the self-focusing phenomenon observed in nonlinear media. Our results show that the focal spot within the nonlinear medium is closer to the interface, and it is slightly wider for pulses with higher incident power. However, despite the dependence of the effective refractive index of the nonlinear medium on irradiance, which is the power per unit area, and assuming that the group velocity dispersion and the propagation time difference are suitably corrected, the focused pulse duration is essentially unaffected by the incident power and remains virtually constant during propagation in the nonlinear medium. Finally, the proposed method also reproduces the spatiotemporal coupling arising from the intrinsic correlation between spatial and temporal properties of the focused pulse.

Study on electromagnetic characteristics of plasma model-based on the symplectic multiresolution time-domain scheme

A novel numerical computation scheme, which is symplectic multiresolution time-domain (S-MRTD) scheme, for modeling plasma model is proposed. The loss plasma dispersive model is taken into account in S-MRTD scheme, and the detailed formulations of the proposed S-MRTD scheme are also provided. A one-dimensional perfectly matched layers (PML) are used to terminate the computational domain. The analyses of stability and numerical dispersion demonstrate that S-MRTD scheme is more efficient than traditional finite-different time-domain (FDTD) and MRTD methods. The energy conservation characteristics of S-MRTD scheme in electromagnetic simulation are proved by the propagation of pulse in free space for long-term simulation. In the end, the S-MRTD formulations are confirmed by computing the electric field intensity, reflection and the transmission coefficients for the pulse wave through an unmagnetized plasma slab. A favorable agreement between the numerical solutions is demonstrated, and the efficiency of the proposed scheme is verified. Meanwhile, numerical results show that plasma frequency, collision frequency and thickness are important factors affecting reflection and transmission coefficients.

Speed of structured light pulses in free space

A plane monochromatic wave propagates in vacuum at the velocity c. However, wave packets limited in space and time are used to transmit energy and information. Here it has been shown based on the wave approach that the on-axis part of the pulsed beams propagates in free space at a variable speed, exhibiting both subluminal and superluminal behaviours in the region close to the source, and their velocity approaches the value of c with distance. Although the pulse can travel over small distances faster than the speed of light in vacuum, the average on-axis velocity, which is estimated by the arrival time of the pulse at distances z ≫ ld (ld is the Rayleigh diffraction range) and z > cτ (τ is the pulse width) is less than c. The total pulsed beam propagates at a constant subluminal velocity over the whole distance. The mutual influence of the spatial distribution of radiation and the temporal shape of the pulse during nonparaxial propagation in vacuum is studied. It is found that the decrease in the width of the incident beam and the increase in the central wavelength of the pulse lead to a decrease in the propagation velocity of the wave packet.

Mass of the photon propagating in an optical medium and mass of its electromagnetic and mechanical components

A propagation of a photon or light pulse in an optical medium is accompanied by appearance of the mechanical momentum in a form of a mechanical motion of optical medium located between the leading and trailing edges of the pulse. As a result, a propagation of the pulse is accompanied by the mechanical momentum that is a part of total momentum of the pulse. Since a trajectory, momentum and speed of the pulse in an inhomogeneous optical medium are known, the pulse acceleration and the force applied to the pulse can be calculated. It turns out that directions of the acceleration and the force are different in a general case. Then the mass of the pulse based on the second Newton law cannot be presented by a single real number. It is shown that the total mass of the pulse can be expressed by a single complex number. Modulus of the mass increases by n2 times as compared with the mass of the same pulse in free space where n is the reflective index in the place where the pulse is propagating. Argument of the mass is equal to the double angle between the main normal to the pulse trajectory and the grad(n) in the same place. Electromagnetic component of the mass of the pulse is not changed and is equal to the pulse mass is free space. The mechanical component of the pulse mass is a difference between the total and electromagnetic masses.

Laser-Induced Linear-Field Particle Acceleration in Free Space

Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) has been studied for over 20 years, and its ability to eventually produce high-quality, high energy multi-particle bunches has remained a subject of great interest. Arguments can certainly be made that linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computational experiment. The formalism includes exact treatment of Maxwell’s equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the field amplitude. For example, 30 keV electrons (2.5% energy spread) are accelerated to 61 MeV (0.5% spread) and to 205 MeV (0.25% spread) using 250 mJ and 2.5 J lasers respectively. These findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields.

Intricate Plasma-Scattered Images and Spectra of Focused Femtosecond Laser Pulses.

We report on some interesting phenomena in the focusing and scattering of femtosecond laser pulses in free space that provide insights on intense laser plasma interactions. The scattered image in the far field is analyzed and the connection with the observed structure of the plasma at the focus is discussed. We explain the physical mechanisms behind the changes in the colorful and intricate image formed by scattering from the plasma for different compressions, as well as orientations of plano-convex lens. The laser power does not show significant effect on the images. The pulse repetition rate above 500 Hz can affect the image through slow dynamics The spectrum of each color in the image shows oscillatory peaks due to interference of delayed pulse that correlate with the plasma length. Spectral lines of atomic species are identified and new peaks are observed through the white light emitted by the plasma spot. We find that an Ar gas jet can brighten the white light of the plasma spot and produce high resolution spectral peaks. The intricate image is found to be extremely sensitive and this is useful for applications in sensing microscale objects.

Improved beam waist formula for ultrashort, tightly focused linearly, radially, and azimuthally polarized laser pulses in free space

We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly focused fundamental linearly polarized, radially polarized, and azimuthally polarized modes in free space. We compute the exact beam waist via numerical cubature to ascertain the accuracy with which our formula approximates the exact beam waist over a broad range of parameters of practical interest. Based on this, we describe a method of choosing parameters in the model given the beam waist and pulse duration of a laser pulse.

Propagation of a light pulse inside matter in a context of the Abraham–Minkowski dilemma

It is shown that a light pulse propagating in an optical medium exerts the optical pressure on the medium in the regions where leading and trailing edges are propagating. This effect is derived from analysis of unambiguous thought experiments which results contradict one other. It is shown that a magnitude of the pressure is equal to (n−1/n)W0, where n and W0 is the refractive index of the medium and the momentum flux density of the same pulse in free space, respectively. The Abraham form of the momentum of light is redundant if the optical pressure is taken into account. In this case the dilemma disappears because one of the rival alternatives disappears.

Entanglement in atomic systems interacting with single-photon pulses in free space

New technologies providing tightly focusing lenses and mirrors with large numerical apertures and electro-optic modulation of single photons are now available for the investigation of photon-atom interactions without a cavity. From the theoretical side, new models must be developed which take into account the intrinsic open system aspect of the problem as well as details about atomic relative positions and temporal (spectral) features of the pulses. In this paper, we investigate the generation of nonclassical correlations between two atoms in free space interacting with a quantized pulse containing just one single photon. For this purpose, we develop a general theoretical approach which allows us to find the equations of motion for single- and two-body atomic operators from which we obtained the system density operator. We show that one single photon is capable of promoting substantial entanglement between two initially ground-state atoms, and we analyze the dependence of these correlations on atomic relative positions (vacuum effects) and spectral features of the single-photon pulse.

Polarization properties of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses

The propagation behavior of the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses in free space is studied. Numerical calculation results are given to illustrate the dependence of spectral degree of polarization on the beam order, pulse frequency, temporal coherence length, pulse duration and spatial correlation length. It is shown that with increasing beam order M the position z of the on-axis spectral degree of polarization P=0 decreases, and the distribution of spectral degree of polarization is different for different values of M.

Efficient excitation of a two-level atom by a single photon in a propagating mode

State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized \textit{propagating} pulse in free space and study the probability $P_e(t)$ of finding the atom in the excited state at any time $t$. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\Lambda\in[0,8\pi/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then $P_e(t)$ can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single photon Fock state and coherent states and for various temporal shapes of the pulses.

Terahertz Digital Holography

Abstract: Terahertz (THz) technology is combined with digital holography for THz imaging. The characteristics of the propagation behaviour of the THz pulse in free space are investigated by using numerical simulations. The algorithm is based on the angular spectrum theory. The spatiotemporal coupling of the THz pulse during propagation results in a significant time‐dependent beam diameter and wave front. The two‐dimensional dynamic evolution of the THz pulse passing through an aperture is obtained. The diffraction is time‐dependent as the pulse travels through the object, which can be clearly observed in simulations. The simulation algorithm and result have been used to reconstruct the original object, with the spatiotemporal amplitude recorded by using a charge‐coupled device (CCD). The implementation of THz digital holography is presented and the corresponding experimental result given.

Implementation of a noninvasive data encryption technique based on a free-space spectral phase scrambling scheme

We investigate how to scale a free-space wavelength blocker to implement a spectral phase scrambling system to secure high data rate optical transmissions within a wavelength division multiplexing optical network. This technique belongs to the optical code-division multiple access family, and its implementation can be carried out using a free-space pulse shaping system based, for instance, on a wavelength blocker or spectral equalizer architectures. After a brief recall of the encryption principle, a model of the optical system is given, and we discuss the impact of phase distribution and the scrambling mask used to encrypt the data on penalty sources. We emphasize the importance of correctly choosing certain geometrical parameters, such as the beam waist in the spectral plane and the mask fill factor. The tolerance of this solution with respect to mask positioning errors is then investigated, and we finally discuss how such a solution could be implemented using existing devices, such as a wavelength blocker, for security applications without inducing additional system penalties.

Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources

A method of formation of the tightly confined, distortion-free, femtosecond pulses in two dimensions (2D) with the step-like decreasing of intensity after a finite length of propagation in free space is described. The pulses are formed by the Fresnel source of modes corresponding to a 2D hollow waveguide with perfectly reflecting walls (material waveguide). The source reproduces in free space a propagation-invariant pulse confined by the waveguide. Unlike the case of material waveguides, when the pulse goes out from the virtual waveguide formed by the Fresnel source its shape does not change, but the intensity immediately drops down to the near-zero level. It is also shown that there is a limit of the duration of pulse beyond which the step-like decay is not observed.

Breaking resolution limits in ultrafast electron diffraction and microscopy

Ultrafast electron microscopy and diffraction are powerful techniques for the study of the time-resolved structures of molecules, materials, and biological systems. Central to these approaches is the use of ultrafast coherent electron packets. The electron pulses typically have an energy of 30 keV for diffraction and 100-200 keV for microscopy, corresponding to speeds of 33-70% of the speed of light. Although the spatial resolution can reach the atomic scale, the temporal resolution is limited by the pulse width and by the difference in group velocities of electrons and the light used to initiate the dynamical change. In this contribution, we introduce the concept of tilted optical pulses into diffraction and imaging techniques and demonstrate the methodology experimentally. These advances allow us to reach limits of time resolution down to regimes of a few femtoseconds and, possibly, attoseconds. With tilted pulses, every part of the sample is excited at precisely the same time as when the electrons arrive at the specimen. Here, this approach is demonstrated for the most unfavorable case of ultrafast crystallography. We also present a method for measuring the duration of electron packets by autocorrelating electron pulses in free space and without streaking, and we discuss the potential of tilting the electron pulses themselves for applications in domains involving nuclear and electron motions.

Anharmonic pulses due to transition radiation

The possibility of using the transition radiation of an electron bunch to generate nonstationary anharmonic pulses in free space and in a dispersive medium is demonstrated. It is shown that the transition radiation of the bunch gives rise to an infinite train of nonstationary anharmonic pulses described by solutions to the Klein-Gordon equation. The polarization of the resulting field at its leading edge appears to be different from the field polarization at the interface. The leading edge becomes steeper with time. It is shown that the bunch density longitudinal distribution and the parameters of the dispersive medium can be determined from the values of the fields and their derivatives near the leading edge of the resulting signal.

Optical Deflection and Temporal Characterization of an Ultrafast Laser-Produced Electron Beam

The interaction of a laser-produced electron beam with an ultraintense laser pulse in free space is studied. We show that the optical pulse with a(0)=0.5 imparts momentum to the electron beam, causing it to deflect along the laser propagation direction. The observed 3-degree angular deflection is found to be independent of polarization and in good agreement with a theoretical model for the interaction of free electrons with a tightly focused Gaussian pulse, but only when longitudinal fields are taken into account. This technique is used to temporally characterize a subpicosecond laser-wakefield-driven electron bunch. Applications to electron-beam conditioning are also discussed.

Acceleration of electrons from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space

In this paper we describe a laser acceleration scheme where an electron is accelerated from rest to GeV energies by the longitudinal electric field of an ultrashort transverse magnetic ( TM01 ) optical pulse. The on-axis longitudinal electric field of the pulse is obtained from the free-space divergence equation beyond the so-called slowly-varying-envelope approximation. The instantaneous electron dynamics is studied; numerical simulations predict net energy gains in the GeV range for laser intensities reaching 10(22) W/ cm(2) .

Random and Non-Random Uncertainties in Precision GPR Measurements: Identifying and Compensating for Instrument Drift

The precision of ground penetrating radar (GPR) data is of increasing interest, as the technology finds ever increasing applications to near surface geophysical studies. Our group has undertaken a series of studies to identify the precision and accuracy with which GPR traveltimes, velocities and interval properties can be estimated under controlled conditions, recently reporting that random errors in two-way traveltime and velocity are on the order of ±0.7 ns and ±0.001 m/ns, respectively, at the 95% confidence level. The high degree of precision in that dataset makes it possible to observe non-random patterns in the independent estimates of the same parameter, suggesting possible systematic biases in the data. One source of systematic error that workers often encounter is the effect of back-scattering from above ground features. Another that we documented in our previous study is that the material properties of the subsurface may change from one survey to the next. A third possibility is non-random instrumentation error, one source of which, and the focus of the present report, is a variation in the time base. We address ways to identify its presence, to assess its influence on estimating GPR parameters, and how and when to compensate for its effects. Using a static transmitter (Tx) and receiver (Rx) offset to record a series of GPR traces over a nominal period of one hour, we find that time base drift can be significant for up to 25 min after turning on the instrument. Fortunately, the type of drift that we have found to be most apparent—time zero drift—can be readily identified and compensated for, if one employs the air phase at a number of Tx–Rx offsets. An invariant condition in a GPR survey is that the true velocity of the direct air phase should be the velocity of an electromagnetic pulse in free space. Thus, upon carefully determining the observed velocity of the air phase, and using the ratio between it and the true value of 0.29979 m/ns, one can correct the entire time base of a radargram. Guidelines for when to apply the air phase compensation technique are based on whether the observed velocity of the air phase falls outside the limits of an acceptable precision under the most ideal circumstances. We illustrate the compensation procedure using two CMPs collected on different days at the same survey position. Analyzing the uncompensated data unsurprisingly yields two different subsurface velocities, however the depth estimates of the same subsurface reflector differ by 0.5 m, which for this site is physically unlikely. The difference between the observed and the true air phase velocities for both data sets exceeded the minimum expected error according to our guidelines, thus after applying our time base correction, the difference between the depth estimates improves to 0.05~m.