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ABSTRACT: Mie theory is one of the main tools describing scattering of propagating electromagnetic waves by spherical particles. Evanescent optical fields are also scattered by particles and exert radiation forces which can be used for optical near-field manipulations. We show that the Mie theory can be naturally adopted for the scattering of evanescent waves via rotation of its standard solutions by a complex angle. This offers a simple and powerful tool for calculations of the scattered fields and radiation forces. Comparison with other, more cumbersome, approaches shows perfect agreement, thereby validating our theory. As examples of its application, we calculate angular distributions of the scattered far-field irradiance and radiation forces acting on dielectric and conducting particles immersed in an evanescent field.
Optics Express 03/2013; 21(6):7082-95. · 3.59 Impact Factor
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ABSTRACT: Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, when passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behavior is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.
Physical Review Letters 03/2013; 110(9):093601. · 7.37 Impact Factor
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ABSTRACT: We consider relativistic deformations of interfering paraxial waves moving in
the transverse direction. Owing to superluminal transverse phase velocities,
noticeable deformations of the interference patterns arise when the waves move
with respect to each other with non-relativistic velocities. Similar
distortions also appear on a mutual tilt of the interfering waves, which causes
a phase delay analogous to the relativistic time delay. We illustrate these
observations by the interference between a vortex wave beam and a plane wave,
which exhibits a pronounced deformation of the radial fringes into a fork-like
pattern (relativistic Hall effect). Furthermore, we describe an additional
relativistic motion of the interference fringes (a counter-rotation in the
vortex case), which become noticeable at the same non-relativistic velocities.
02/2013;
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ABSTRACT: We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatiotemporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) nondiffracting spatiotemporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatiotemporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic) and have potential applications in particle collisions, optics of moving media, quantum communications, and astrophysics.
Phys. Rev. A. 09/2012; 86(3).
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ABSTRACT: The dual symmetry between electric and magnetic fields is an important
intrinsic property of Maxwell equations in free space. This symmetry underlies
the conservation of optical helicity, and, as we show here, is closely related
to the separation of spin and orbital degrees of freedom of light (the helicity
flux coincides with the spin angular momentum). However, in the standard
field-theory formulation of electromagnetism, the field Lagrangian is not dual
symmetric. This leads to problematic dual-asymmetric forms of the canonical
energy-momentum, spin, and orbital angular momentum tensors. Moreover, we show
that the components of these tensors conflict with the helicity and energy
conservation laws. To resolve this discrepancy between the symmetries of the
Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian
formulation of classical electromagnetism. This dual electromagnetism preserves
the form of Maxwell equations, yields meaningful canonical energy-momentum and
angular momentum tensors, and ensures a self-consistent separation of the spin
and orbital degrees of freedom. This provides rigorous derivation of results
suggested in other recent approaches. We make the Noether analysis of the dual
symmetry and all the Poincar\'e symmetries, examine both local and integral
conserved quantities, and show that only the dual electromagnetism naturally
produces a complete self-consistent set of conservation laws. We also discuss
the observability of physical quantities distinguishing the standard and dual
theories, as well as relations to quantum weak measurements and various optical
experiments.
08/2012;
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ABSTRACT: We present a space-time generalization of the known spatial (monochromatic)
wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the
propagation direction. Generic spatio-temporal vortex beams are polychromatic
and can carry intrinsic OAM at an arbitrary angle to the mean momentum.
Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a
monochromatic Bessel beam, we construct a family of either (i) time-diffracting
or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions
of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are
able to describe either photon or electron vortex states (both relativistic and
nonrelativistic), and can find applications in particle collisions, optics of
moving media, quantum communications, and astrophysics.
05/2012;
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ABSTRACT: We examine the propagation of the recently-discovered electron vortex beams
in a longitudinal magnetic field. We consider both the Aharonov-Bohm
configuration with a single flux line and the Landau case of a uniform magnetic
field. While stationary Aharonov-Bohm modes represent Bessel beams with flux-
and vortex-dependent probability distributions, stationary Landau states
manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore,
the Landau-state beams possess field- and vortex-dependent phases: (i) the
Zeeman phase from coupling the quantized angular momentum to the magnetic field
and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams.
Remarkably, together these phases determine the structure of Landau energy
levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial
evolution of images formed by various superpositions of modes. We demonstrate
that, depending on the chosen superposition, the image can rotate in a magnetic
field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero
frequency. At the same time, its centroid always follows the classical
cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the
non-rotating superpositions reproduce stable multi-vortex configurations that
appear in rotating superfluids. Our results open up an avenue for the direct
electron-microscopy observation of fundamental properties of free quantum
electron states in magnetic fields.
04/2012;
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ABSTRACT: We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin-Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices and mechanical flywheels and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales, from elementary spinning particles, through classical light, to rotating black holes.
Physical Review Letters 03/2012; 108(12):120403. · 7.37 Impact Factor
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ABSTRACT: We consider a p-polarized surface electromagnetic wave (a classical surface
polariton) at the interface between the vacuum and a metal or left-handed
medium. We show that the evanescent electromagnetic waves forming the surface
polariton inevitably possess a backward spin energy flow, which, together with
a superluminal orbital energy flow, form the total Poynting vector. This spin
energy flow generates a well-defined (but not quantized) spin angular momentum
of surface polaritons which is orthogonal to the propagation direction. The
spin of evanescent waves arises from the imaginary longitudinal component of
the electric field which makes the polarization effectively elliptical in the
propagation plane. We also examine the connection between the spin and
chirality of evanescent modes.
01/2012;
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ABSTRACT: We present a general theory of spin-to-orbital angular momentum (AM) conversion of light in focusing, scattering, and imaging optical systems. Our theory employs universal geometric transformations of non-paraxial optical fields in such systems and allows for direct calculation and comparison of the AM conversion efficiency in different physical settings. Observations of the AM conversions using local intensity distributions and far-field polarimetric measurements are discussed.
Optics Express 12/2011; 19(27):26132-49. · 3.59 Impact Factor
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ABSTRACT: Motivated by the recent discovery of electron vortex beams carrying orbital angular momentum (AM), we construct exact Bessel-beam solutions of the Dirac equation. They describe relativistic and nonparaxial corrections to the scalar electron beams. We describe the spin and orbital AM of the electron with Berry-phase corrections and predict the intrinsic spin-orbit coupling in free space. This can be observed as a spin-dependent probability distribution of the focused electron vortex beams. Moreover, the magnetic moment is calculated, which shows different g factors for spin and orbital AM and also contains the Berry-phase correction.
Physical Review Letters 10/2011; 107(17):174802. · 7.37 Impact Factor
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ABSTRACT: We examine the recently introduced measure of chirality of a monochromatic
optical field [Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010)]
using the momentum (plane-wave) representation and helicity basis. Our analysis
clarifies the physical meaning of the measure of chirality and unveils its
close relation to the polarization helicity, spin angular momentum, energy
density, and Poynting energy flow. We derive the operators of the optical
chirality and of the corresponding chiral momentum, which acquire remarkably
simple forms in the helicity representation.
12/2010;
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ABSTRACT: We show, both theoretically and experimentally, that high-numerical-aperture (NA) optical microscopy is accompanied by strong spin-orbit interaction of light, which translates fine information about the specimen to the polarization degrees of freedom of light. An 80 nm gold nanoparticle scattering the light in the focus of a high-NA objective generates angular momentum conversion, which is seen as a nonuniform polarization distribution at the exit pupil. We demonstrate remarkable sensitivity of the effect to the position of the nanoparticle: Its subwavelength displacement produces the giant spin-Hall effect, i.e., macroseparation of spins in the outgoing light. This brings forth a far-field optical nanoprobing technique based on the spin-orbit interaction of light.
Physical Review Letters 06/2010; 104(25):253601. · 7.37 Impact Factor
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Konstantin Y. Bliokh
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ABSTRACT: We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometro-dynamical interrelations illuminate a dual physical nature of the phenomena. Comment: 25 pages, 4 figures, review to appear in special issue of J. Opt. A: Pure Appl. Opt
03/2009;
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ABSTRACT: We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a noninertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam-Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nanostructure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.
Physical Review Letters 08/2008; 101(3):030404. · 7.37 Impact Factor
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ABSTRACT: We consider a p-polarized surface electromagnetic wave (a classical surface polariton) at the interface between the vacuum and a metal or left-handed medium. We show that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which, together with a superluminal orbital energy flow, form the total Poynting vector. This spin energy flow generates a well-defined (but not quantized) spin angular momentum of surface polaritons which is orthogonal to the propagation direction. The spin of evanescent waves arises from the imaginary longitudinal component of the electric field which makes the polarization effectively elliptical in the propagation plane. We also examine the connection between the spin and chirality of evanescent modes.
Phys. Rev. A. 85(6).
