12,904 research outputs found
An analytical model for turbulence scattered rays in the shadow zone for outdoor sound propagation calculation
In outdoor sound propagation, an inherent problem of the ray tracing method is its inability to determine the sound pressure level in the shadow zone, where geometrical rays do not penetrate. This is a serious problem in a turbulent atmosphere where significant sound energy will be scattered into the shadow. Empirical corrections that are determined from measurements or numerical simulations are limited to situations within the bounds of the empirical corrections. This paper describes a different approach where the ray tracing model is modified analytically into a scattered ray model. Rays are first diffracted from the shadow boundary, which is determined by the geometrical ray paths. The diffracted rays are then scattered by turbulence in their way to the receiver. The amount of scatter is determined from turbulence statistics that are determined from a Gaussian turbulence model. Most of the statistics are determined analytically except one element, which is determined empirically from numerical simulations. This turbulence scattered ray model is shown to have good accuracy against calculations based on the parabolic equation, and against previously published measurement data. It was found that the agreement is good both with and without turbulence, at distance up to 2 km from the shadow boundary.
© 2009 Acoustical Society of Americ
Time dependent behavior of a localized electron at a heterojunction boundary of graphene
We develop a finite-difference time-domain (FDTD) method for simulating the dynamics of graphene electrons, denoted GraFDTD. We then use GraFDTD to study the temporal behavior of a single localized electron wave packet, showing that it exhibits optical-like dynamics including the Goos–Hänchen effect [ F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947)] at a heterojunction, but the behavior is quantitatively different than for electromagnetic waves. This suggests issues that must be addressed in designing graphene-based electronic devices analogous to optical devices. GraFDTD should be useful for studying such complex time-dependent behavior of a quasiparticle in graphene
Single freeform surface design for prescribed input wavefront and target irradiance
In beam shaping applications, the minimization of the number of necessary
optical elements for the beam shaping process can benefit the compactness of
the optical system and reduce its cost. The single freeform surface design for
input wavefronts, which are neither planar nor spherical, is therefore of
interest. In this work, the design of single freeform surfaces for a given
zero-\'etendue source and complex target irradiances is investigated. Hence,
not only collimated input beams or point sources are assumed. Instead, a
predefined input ray direction vector field and irradiance distribution on a
source plane, which has to be redistributed by a single freeform surface to
give the predefined target irradiance, is considered. To solve this design
problem, a partial differential equation (PDE) or PDE system, respectively, for
the unknown surface and its corresponding ray mapping is derived from energy
conservation and the ray-tracing equations. In contrast to former PDE
formulations of the single freeform design problem, the derived PDE of
Monge-Amp\`ere type is formulated for general zero-\'etendue sources in
cartesian coordinates. The PDE system is discretized with finite differences
and the resulting nonlinear equation system solved by a root-finding algorithm.
The basis of the efficient solution of the PDE system builds the introduction
of an initial iterate constuction approach for a given input direction vector
field, which uses optimal mass transport with a quadratic cost function. After
a detailed description of the numerical algorithm, the efficiency of the design
method is demonstrated by applying it to several design examples. This includes
the redistribution of a collimated input beam beyond the paraxial
approximation, the shaping of point source radiation and the shaping of an
astigmatic input wavefront into a complex target irradiance distribution.Comment: 11 pages, 10 figures version 2: Equation (7) was corrected;
additional minor changes/improvement
Double freeform illumination design for prescribed wavefronts and irradiances
A mathematical model in terms of partial differential equations (PDE) for the
calculation of double freeform surfaces for irradiance and phase control with
predefined input and output wavefronts is presented. It extends the results of
B\"osel and Gross [J. Opt. Soc. Am. A 34, 1490 (2017)] for the illumination
design of single freeform surfaces for zero-\'etendue light sources to double
freeform lenses and mirrors. The PDE model thereby overcomes the restriction to
paraxiality or the requirement of at least one planar wavefront of the current
design models in the literature. In contrast with the single freeform
illumination design, the PDE system does not reduce to a Monge-Amp\`ere type
equation for the unknown freeform surfaces, if nonplanar input and output
wavefronts are assumed. Additionally, a numerical solving strategy for the PDE
model is presented. To show its efficiency, the algorithm is applied to the
design of a double freeform mirror system and double freeform lens system.Comment: Copyright 2018 Optical Society of America. One print or electronic
copy may be made for personal use only. Systematic reproduction and
distribution, duplication of any material in this paper for a fee or for
commercial purposes, or modifications of the content of this paper are
prohibite
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