Software modeling of the propagation of electromagnetic beams through different media
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Propagation and focusing of electromagnetic beams through layered anisotropic medium is of interest in the field of optical data storage, where thin layers are mounted on glass substrates, display technology, where polarised light passes through liquid crystals, and in biological and material sciences, where objects are portrayed through thin sheet glass. In the case of computing a focused or diffracted field of a three-dimensional optical problem, it would be required to evaluate two-dimensional integrals with amplitude and phase functions. Obtaining numerical results for these kinds of problems, is a difficult task because of the rapidly oscillating integrands and the singularities in the Fresnel transmission and the reflection coefficients. If a layered medium is an anisotropic crystal, the numerical analysis is complicated significantly, as it gives rise to birefringence and mode coupling. Research within this field is jointly being conducted by the Department of Engineering at the University College of Bergen [HIB] and the Department of Physics and Technology at the University of Bergen [UIB]. Their researchers have obtained both exact and asymptotic results for propagated and focused fields in uniaxial crystals, and they have been adopting various techniques to obtain numerical results. The double integrals, which can be used for obtaining the results, can be reduced to single integrals by means of applying parabolic approximations to the phase and amplitude functions, and even though the approximations tend to give numerical results, the procedure is time-consuming. As such obtaining numerical results from this sort of procedure might take a few minutes to several computing hours. To date, they have typically written software in Fortran, in order to achieve the numerical results, and this intermediary data is then used as input data for the MATLAB software, in order to present the final results. This process of having to code one program for producing results that are passed to another, just to able to produce the final results, is convoluted, the use of different programs in series for producing the final result creating unnecessary work for the user. As such, the researchers have requested a singular software solution that will handle both the numerical calculations and the graphical presentation of the propagated electromagnetic fields from the initial data, which describes the characteristics of the medium and the type of electromagnetic wave.