2,912 research outputs found
Paraxial Theory of Direct Electro-Optic Sampling of the Quantum Vacuum
Direct detection of vacuum fluctuations and analysis of sub-cycle quantum
properties of the electric field are explored by a paraxial quantum theory of
ultrafast electro-optic sampling. The feasibility of such experiments is
demonstrated by realistic calculations adopting a thin ZnTe electro-optic
crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing
of a short near-infrared probe pulse with multi-terahertz vacuum field modes
leads to an increase of the signal variance with respect to the shot noise
level. The vacuum contribution increases significantly for appropriate length
of the nonlinear crystal, short probe pulse durations, tight focusing, and
sufficiently large number of photons per probe pulse. If the vacuum input is
squeezed, the signal variance depends on the probe delay. Temporal positions
with noise level below the pure vacuum may be traced with a sub-cycle accuracy.Comment: 10 pages, 6 figure
Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects
Geometric phases are a universal concept that underpins numerous phenomena
involving multi-component wave fields. These polarization-dependent phases are
inherent in interference effects, spin-orbit interaction phenomena, and
topological properties of vector wave fields. Geometric phases have been
thoroughly studied in two-component fields, such as two-level quantum systems
or paraxial optical waves. However, their description for fields with three or
more components, such as generic nonparaxial optical fields routinely used in
modern nano-optics, constitutes a nontrivial problem. Here we describe
geometric, dynamical, and total phases calculated along a closed spatial
contour in a multi-component complex field, with particular emphasis on 2D
(paraxial) and 3D (nonparaxial) optical fields. We present several equivalent
approaches: (i) an algebraic formalism, universal for any multi-component
field; (ii) a dynamical approach using the Coriolis coupling between the spin
angular momentum and reference-frame rotations; and (iii) a geometric
representation, which unifies the Pancharatnam-Berry phase for the 2D
polarization on the Poincar\'e sphere and the Majorana-sphere representation
for the 3D polarized fields. Most importantly, we reveal close connections
between geometric phases, angular-momentum properties of the field, and
topological properties of polarization singularities in 2D and 3D fields, such
as C-points and polarization M\"obius strips.Comment: 21 pages, 11 figures, to appear in Rep. Prog. Phy
Theory and applications of free-electron vortex states
Both classical and quantum waves can form vortices: with helical phase fronts
and azimuthal current densities. These features determine the intrinsic orbital
angular momentum carried by localized vortex states. In the past 25 years,
optical vortex beams have become an inherent part of modern optics, with many
remarkable achievements and applications. In the past decade, it has been
realized and demonstrated that such vortex beams or wavepackets can also appear
in free electron waves, in particular, in electron microscopy. Interest in
free-electron vortex states quickly spread over different areas of physics:
from basic aspects of quantum mechanics, via applications for fine probing of
matter (including individual atoms), to high-energy particle collision and
radiation processes. Here we provide a comprehensive review of theoretical and
experimental studies in this emerging field of research. We describe the main
properties of electron vortex states, experimental achievements and possible
applications within transmission electron microscopy, as well as the possible
role of vortex electrons in relativistic and high-energy processes. We aim to
provide a balanced description including a pedagogical introduction, solid
theoretical basis, and a wide range of practical details. Special attention is
paid to translate theoretical insights into suggestions for future experiments,
in electron microscopy and beyond, in any situation where free electrons occur.Comment: 87 pages, 34 figure
Propagation of a laser beam in a plasma
This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent
All-optical three-dimensional electron pulse compression
We propose an all-optical, three-dimensional electron pulse compression
scheme in which Hermite-Gaussian optical modes are used to fashion a
three-dimensional optical trap in the electron pulse's rest frame. We show that
the correct choices of optical incidence angles are necessary for optimal
compression. We obtain analytical expressions for the net impulse imparted by
Hermite-Gaussian free-space modes of arbitrary order. Although we focus on
electrons, our theory applies to any charged particle and any particle with
non-zero polarizability in the Rayleigh regime. We verify our theory
numerically using exact solutions to Maxwell's equations for first-order
Hermite-Gaussian beams, demonstrating single-electron pulse compression factors
of in both longitudinal and transverse dimensions with experimentally
realizable optical pulses. The proposed scheme is useful in ultrafast electron
imaging for both single- and multi-electron pulse compression, and as a means
of circumventing temporal distortions in magnetic lenses when focusing
ultrashort electron pulses.Comment: 21 pages, 7 figure
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