In the reconstruction process of photo acoustic experiments, it was observed that adding a passive element to the
experimental setup, improves the quality of the reconstruction of the object. This contribution analyzes this effect
in some detail. We consider a cylindrical configuration. We start from an artificial and theoretically constructed
optical absorption distribution that radiates sound waves when interrogated by the optical pulse. We analyze in
the experimental setup the addition of the passive element to this example. The reported investigation is a part
of a larger study on the existence, uniqueness and stability of photo acoustic inverse source reconstructions.
The properties of the natural modes in a dispersive stratified
N-layer medium are investigated. Especially the focus is on
the (over)completeness properties of these modes. Also the distribution of the natural frequencies are considered. Both the
degree of (over)completeness and the natural frequency distribution turn out to be totally different from what is known for
the non-dispersive case.
The scattering of electromagnetic waves by a slab whose refractive index is changing along its boundary planes is exactly calculated in a closed analytical form. The key feature of the calculation is the introduction of a new set of modes. As an specific example the reflected and transmitted field generated by the interaction of an incoming plane wave by a N-layered medium whose layers are perpendicular to the boundary planes of a slab are given.
A scattering theory for finite photonic crystals in terms of the natural modes of the scatterer is developed. This theory generalizes the classical Hilbert-Schmidt type of bilinear expansions of the propagator to a bilinear expansion into natural modes. It is shown that the Sturm-Liouville type of expansions for dispersive media differs considerably from those for non-dispersive media, they are e.g. overcomplete.
We derive the Sommerfeld precursor and present the first calculations for the Brillouin precursor that result from the transmission of a pulse through a photonic crystal. The photonic crystal is modelled by a one-dimensional N-layer medium and the pulse is a generic electromagnetic plane wave packet which is incident perpendicular onto the crystal. Each layer of the crystal consists of two slabs that may differ in their relative thickness and in their refractive indices. The resulting precursors are then compared to those that would arise after propagation through a reference homogeneous medium of the same length and the same optical length in order to isolate the effect of the slab contrast onto the shapes of the precursors. The Sommerfeld precursor is not influenced by this slab contrast; its wavefront invariantly propagates at the speed of light in vacuum and its amplitude and period only depend on the spatial average of the two squared plasma frequencies of the slabs which coincides with the plasma frequency squared of the reference medium. The Brillouin precursor does experience the slab contrast; its arrival time increases with increasing slab contrast.
KEYWORDS: Diffusion, Scattering, Rayleigh scattering, Mie scattering, Signal attenuation, Photons, Absorption, Light scattering, Monte Carlo methods, Radio propagation
Diffusion theory is an approximation ofthe equation of radiative transport, that is used to describe light propagation in turbid media. This approximation is very popular because ofits simplicity, possibilities to describe time-resolved light propagation, and for its appeal to physical intuition. However, it has also its restrictions. It is the aim ofthis contribution to discuss this method, and to evaluate what can be undertaken to avoid the deviations caused by its restrictions, based on results obtained with the equation of radiative transport.
We report on the results of a new and exact scattering theory, which describes reflection and transmission of light at the surface of an arbitrarily shaped photonic crystal by "equivalent suface current distributions," (strata). The method is applied for the calculation of the transmission coefficients of an incoming plane wave by a number of slabs with different widths made of a photonic crystal material. These transmission coefficients show a double exponential behavior as a function of the width. A generic model is presented leading to a qualitative interpretation of this result. (Summary only available)
We present a new method to calculate the scattering of light at the surface of a photonic crystal. The problem is solved in terms of virtual surface-current distributions and the calculation takes full advantage of the existing infinite-space plane-wave expansion method for obtaining the photonic band structure. Working with surface currents makes the calculations less-time consuming by means of reduction of the dimensionality in the problem. The method is tested and illustrated for semi-infinite two-dimensional photonic crystals of small and large dielectric contrast.
We consider an anisotropically scattering layered cylinder or sphere illuminated by a point source. The scattered field generated by these bodies is calculated in terms of the appropriate mode decomposition of the radiance. This leads to mode-expansions for the radiance which are very similar to the mode expansions derived for the diffraction- scattering problems of classical mathematical physics.
We will present tow methods leading to the solution for the problem of anisotropical light scattering by arbitrarily shaped bodies. Each method converts the equation of radiative transfer and the boundary conditions valid at the boundary of the scattering medium into a set of Fredholm integral equations of the second kind, i.e. an inhomogeneous set of linear equations for the unknown boundary values of the intensity. The two different equations will be derived for the sphere and cylinder resp., and shown to be valid for arbitrarily shaped bodies. Numerical results will be presented. The integral equation approach leads to the construction of a class of non-radiating source distributions and invisible bodies.
We present a method to determine the back reflected radiance from an isotropically scattering halfspace with matched boundary. The bonus of this method lies in the fact that it is capable, in principle, to handle the case of narrow beams, something which, to our knowledge, no other analytic method can do. Essentially, the method derives from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grown exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree well with what is found in literature.
The specific intensity arising from an anisotropically scattering illuminated cylinder is calculated using the equation of radiative transfer. The solution is obtained in closed analytical form. A new simple liner integral equation is derived for the values of the specific intensity at the boundary of the cylinder. The novel method used for the solution of this problem leads immediately in a straightforward and systematical way to the appropriate basic equations for the problem at hand. This method applies equally well to similar scattering problems with other geometries.
The specific intensity arising from an anisotropically scattering illuminated slab or half space is calculated using the equation of radiative transfer. The solution is obtained in closed analytical form. The novel method used for the solution of this problem leads immediately in a straightforward- and systematical way to the known appropriate basic equations valid for the problem at hand, derived otherwise by ad-hoc methods. A new simple linear equation for the specific intensities at the boundary surfaces is also derived. This method applies equally well to similar scattering problems with other geometries.
The diffusion approximation, which is often used to describe the propagation of light in biological tissues, is only good at a sufficient distance from sources and boundaries. Light- tissue interaction is however most intense in the region close to the source. It would therefore be interesting to study this region more closely. Although scattering in biological tissues is predominantly forward peaked, explicit solutions to the transport equation have only been obtained in the case of isotropic scattering. Particularly, for the case of an isotropic point source in an unbounded, isotropically scattering medium the solution is well known. We show that this problem can also be solved analytically if the scattering is no longer isotropic, while everything else remains the same.
Analytic theory of anisotropic random flight requires the expansion of phase-functions in spherical harmonics. The number of terms should be limited while a g value should be obtained that is as high as possible. We describe how such a phase function can be constructed for a given number N of spherical components of the phasefunction, while obtaining a maximum value of the asymmetry parameter g.
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