OPTICS OF INSTANTANEOUS WAVES

This review is devoted to the transient optical phenomena, displayed both in the spatiotemporal dynamics of ultrashort single - cycle wave pulses in free space and dispersive dielectrics as well as to interaction of light with non-stationary media. The interplay of diffractive and dispersive phenomena, including the coupled processes of amplitude and phase reshaping, spectral variations, polarity reversal for different types of light pulses, is examined in frequency and time domains. Reflection - refraction effects on the interfaces of media with time-dependent dielectric susceptibility are considered by means of exact analytical solutions of Maxwell equations for these media. The non - stationarity - induced dispersion is shown to provide a dynamical regime of reflectivity of non-stationary media, depending upon both instantaneous dielectric susceptibility and its temporal derivative; the relevant generalization of Fresnel formulae is presente

Fourier transform techniques for fast physical optics modeling

Motivated by the ever-growing demand for high-quality optical systems, the field tracing approach becomes increasingly significant in physical-optics modeling. Instead of employing a universal Maxwell solver for the whole system, we follow the concept of field tracing, to decompose the system into regions and apply various regional Maxwell solvers. The field solvers may work in the spatial (x) or the spatial frequency (k) domain. To enable the connection of different solvers and functions, the transforming between the x and k domains is a crucial step. Since the Fourier transform gives the connection between these two domains, it becomes paramount to optimize the Fourier-transforming step. The Fast Fourier Transform (FFT) constitutes a huge improvement on the original Discrete Fourier Transform (DFT), since its (the former’s) numerical effort is approximately linear on the sample number of the function to be transformed. However, this orders-of-magnitude improvement in the number of operations required can fall short in optics, where the tendency is to work with field components that present strong wavefront phases. In this work, we propose two innovative Fourier transform techniques. The Semi-analytical Fourier Transform (SFT) is a rigorous approach without any approximation, in which we avoid the sampling of quadratic phases, handling them analytically instead. The homeomorphic Fourier transform (HFT) is an approximate approach, but highly efficient and accurate for fields with intense wavefront phases. Furthermore, we investigate these Fourier transform techniques (FFT, SFT, and HFT) applied to the problem of light propagation, to verify their influence on the system modeling. Consequently, the unified free space propagation operator is concluded. All proposed techniques in this thesis are implemented and diverse numerical examples are presented to illustrate their vast potential

Forward scatter radar for air surveillance: Characterizing the target-receiver transition from far-field to near-field regions

A generalized electromagnetic model is presented in order to predict the response of forward scatter radar (FSR) systems for air-target surveillance applications in both far-field and near-field conditions. The relevant scattering problem is tackled by developing the Helmholtz-Kirchhoff formula and Babinet's principle to express the scattered and the total fields in typical FSR configurations. To fix the distinctive features of this class of problems, our approach is applied here to metallic targets with canonical rectangular shapes illuminated by a plane wave, but the model can straightforwardly be used to account for more general scenarios. By exploiting suitable approximations, a simple analytical formulation is derived allowing us to efficiently describe the characteristics of the FSR response for a target transitioning with respect to the receiver from far-field to near-field regions. The effects of different target electrical sizes and detection distances on the received signal, as well as the impact of the trajectory of the moving object, are evaluated and discussed. All of the results are shown in terms of quantities normalized to the wavelength and can be generalized to different configurations once the carrier frequency of the FSR system is set. The range of validity of the proposed closed-form approach has been checked by means of numerical analyses, involving comparisons also with a customized implementation of a full-wave commercial CAD tool. The outcomes of this study can pave the way for significant extensions on the applicability of the FSR technique

Boundary diffraction wave integrals for diffraction modeling of external occulters

An occulter is a large diffracting screen which may be flown in conjunction with a telescope to image extrasolar planets. The edge is shaped to minimize the diffracted light in a region beyond the occulter, and a telescope may be placed in this dark shadow to view an extrasolar system with the starlight removed. Errors in position, orientation, and shape of the occulter will diffract additional light into this region, and a challenge of modeling an occulter system is to accurately and quickly model these effects. We present a fast method for the calculation of electric fields following an occulter, based on the concept of the boundary diffraction wave: the 2D structure of the occulter is reduced to a 1D edge integral which directly incorporates the occulter shape, and which can be easily adjusted to include changes in occulter position and shape, as well as the effects of sources---such as exoplanets---which arrive off-axis to the occulter. The structure of a typical implementation of the algorithm is included.Comment: 13 pages, 5 figure

Aircraft noise propagation

Sound diffraction experiments conducted at NASA Langley Research Center to study the acoustical implications of the engine over wing configuration (noise-shielding by wing) and to provide a data base for assessing various theoretical approaches to the problem of aircraft noise reduction are described. Topics explored include the theory of sound diffraction around screens and wedges; the scattering of spherical waves by rectangular patches; plane wave diffraction by a wedge with finite impedence; and the effects of ambient flow and distribution sources