39 research outputs found
How to SYN in seven easy steps
The calculation of expected spectral line strengths and profiles is a
powerful tool for the analysis of the solar atmosphere, and other stellar
atmospheres. We present here a recipe in seven easy steps for the development
of such spectral synthesis software.Comment: 4 pages, 1 figure, 1 tabl
Rigorous analysis of grazing-angle scattering of electromagnetic waves in periodic gratings
Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in
slanted non-uniform periodic gratings, when the diffracted order satisfying the
Bragg condition propagates at a grazing angle with respect to the boundaries of
a slab-like grating. Rigorous analysis of GAS of bulk TE electromagnetic waves
is undertaken in holographic gratings by means of the enhanced T-matrix
algorithm. A comparison of the rigorous and the previously developed
approximate theories of GAS is carried out. A complex pattern of numerous
previously unknown resonances is discovered and analysed in detail for gratings
with large amplitude, for which the approximate theory fails. These resonances
are associated not only with the geometry of GAS, but are also typical for wide
transmitting gratings. Their dependence on grating amplitude, angles of
incidence and scattering, and grating width is investigated numerically.
Physical interpretation of the predicted resonances is linked to the existence
and the resonant generation of special new eigenmodes of slanted gratings. Main
properties of these modes and their field structure are discussed.Comment: 21 pages, 13 figure
Optical application and measurement of torque on microparticles of isotropic nonabsorbing material
We show how it is possible to controllably rotate or align microscopic
particles of isotropic nonabsorbing material in a TEM00 Gaussian beam trap,
with simultaneous measurement of the applied torque using purely optical means.
This is a simple and general method of rotation, requiring only that the
particle is elongated along one direction. Thus, this method can be used to
rotate or align a wide range of naturally occurring particles. The ability to
measure the applied torque enables the use of this method as a quantitative
tool--the rotational equivalent of optical tweezers based force measurement. As
well as being of particular value for the rotation of biological specimens,
this method is also suitable for the development of optically-driven
micromachines.Comment: 8 pages, 6 figure
Calculation of the T-matrix: general considerations and application of the point-matching method
The T-matrix method is widely used for the calculation of scattering by
particles of sizes on the order of the illuminating wavelength. Although the
extended boundary condition method (EBCM) is the most commonly used technique
for calculating the T-matrix, a variety of methods can be used.
We consider some general principles of calculating T-matrices, and apply the
point-matching method to calculate the T-matrix for particles devoid of
symmetry. This method avoids the time-consuming surface integrals required by
the EBCM.Comment: 10 pages. 2 figures, 1 tabl
Numerical Modelling of Optical Trapping
Optical trapping is a widely used technique, with many important applications
in biology and metrology. Complete modelling of trapping requires calculation
of optical forces, primarily a scattering problem, and non-optical forces. The
T-matrix method is used to calculate forces acting on spheroidal and
cylindrical particles.Comment: 4 pages, 4 figure
Multipole expansion of strongly focussed laser beams
Multipole expansion of an incident radiation field - that is, representation
of the fields as sums of vector spherical wavefunctions - is essential for
theoretical light scattering methods such as the T-matrix method and
generalised Lorenz-Mie theory (GLMT). In general, it is theoretically
straightforward to find a vector spherical wavefunction representation of an
arbitrary radiation field. For example, a simple formula results in the useful
case of an incident plane wave. Laser beams present some difficulties. These
problems are not a result of any deficiency in the basic process of spherical
wavefunction expansion, but are due to the fact that laser beams, in their
standard representations, are not radiation fields, but only approximations of
radiation fields. This results from the standard laser beam representations
being solutions to the paraxial scalar wave equation. We present an efficient
method for determining the multipole representation of an arbitrary focussed
beam.Comment: 13 pages, 7 figure
Rigorous analysis of extremely asymmetrical scattering of electromagnetic waves in slanted periodic gratings
Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in
thick, slanted, periodic gratings. It is realised when the scattered wave
propagates parallel to the front boundary of the grating. Its most important
feature is the strong resonant increase in the scattered wave amplitude
compared to the amplitude of the incident wave: the smaller the grating
amplitude, the larger the amplitude of the scattered wave. In this paper,
rigorous numerical analysis of EAS is carried out by means of the enhanced
T-matrix algorithm. This includes investigation of harmonic generation inside
and outside the grating, unusually strong edge effects, fast oscillations of
the incident wave amplitude in the grating, etc. Comparison with the previously
developed approximate theory is carried out. In particular, it is demonstrated
that the applicability conditions for the two-wave approximation in the case of
EAS are noticeably more restrictive than those for the conventional Bragg
scattering. At the same time, it is shown that the approximate theory is
usually highly accurate in terms of description of EAS in the most interesting
cases of scattering with strong resonant increase of the scattered wave
amplitude. Physical explanation of the predicted effects is presented.Comment: 14 pages, 7 figures; v2: corrections to metadata and bibliographical
info in preprin
Calculation and optical measurement of laser trapping forces on non-spherical particles
Optical trapping, where microscopic particles are trapped and manipulated by
light is a powerful and widespread technique, with the single-beam gradient
trap (also known as optical tweezers) in use for a large number of biological
and other applications.
The forces and torques acting on a trapped particle result from the transfer
of momentum and angular momentum from the trapping beam to the particle.
Despite the apparent simplicity of a laser trap, with a single particle in a
single beam, exact calculation of the optical forces and torques acting on
particles is difficult. Calculations can be performed using approximate
methods, but are only applicable within their ranges of validity, such as for
particles much larger than, or much smaller than, the trapping wavelength, and
for spherical isotropic particles.
This leaves unfortunate gaps, since wavelength-scale particles are of great
practical interest because they are readily and strongly trapped and are used
to probe interesting microscopic and macroscopic phenomena, and non-spherical
or anisotropic particles, biological, crystalline, or other, due to their
frequent occurance in nature, and the possibility of rotating such objects or
controlling or sensing their orientation.
The systematic application of electromagnetic scattering theory can provide a
general theory of laser trapping, and render results missing from existing
theory. We present here calculations of force and torque on a trapped particle
obtained from this theory and discuss the possible applications, including the
optical measurement of the force and torque.Comment: 10 pages, 5 figure
Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method
We use the effective-mass approximation and the density-functional theory
with the local-density approximation for modeling two-dimensional
nano-structures connected phase-coherently to two infinite leads. Using the
non-equilibrium Green's function method the electron density and the current
are calculated under a bias voltage. The problem of solving for the Green's
functions numerically is formulated using the finite-element method (FEM). The
Green's functions have non-reflecting open boundary conditions to take care of
the infinite size of the system. We show how these boundary conditions are
formulated in the FEM. The scheme is tested by calculating transmission
probabilities for simple model potentials. The potential of the scheme is
demonstrated by determining non-linear current-voltage behaviors of resonant
tunneling structures.Comment: 13 pages,15 figure