Line integral representation of physical optics scattering from a perfectly conducting plate illuminated by a Gaussian beam modeled as a complex point source (original) (raw)
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Geometrical representation of Gaussian beams propagating through complex paraxial optical systems
Applied Optics, 1993
Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters fQ and fQ, the propagation path is described by a ray line similar to the ray line in the y diagram method, whereas the path in the plane of beam receiver parameters e and A is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ray matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems.
Complex source point theory of paraxial and nonparaxial cosine-Gauss and Bessel–Gauss beams
Optics Letters, 2013
It shown how cosine-Gauss and Bessel-Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel-Gauss beams is also indicated.
Vectors and Fourier transforms in optics
Optik, 1999
Multidimensional Fourier transforms of vector functions are considered. Various relationships are presented, including those for differentiation, convolutions and correlations, and power and energy. This formalism has applications, amongst others, in diffraction, imaging, tomography, scattering and antennas.
Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems
Journal of the Optical Society of America A, 1995
A novel 3 3 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements. Unlike in a previous generalized ray matrix formalism, optical elements that possess gain or loss such as Gaussian apertures, complex lenslike media, and amplifiers are included; and a new beam transformation is found. In addition, a novel exponential variable-reflectivity mirror, which displaces a Gaussian beam without changing its spot size, and a complex prismlike medium are introduced.
Radio Science, 1995
A high-frequency analysis of the reflection and diffraction of well-focused electromagnetic Gaussian beams (GBs) by a perfectly conducting parabolic surface with an edge is presented for the two dimensional case. The fields are evaluated analytically via the physical optics (PO) approximation, and only the reflected field is expressed as a GB. The GB procedure developed here is expected to be highly efficient in applications involving large reflector antennas, since it avoids the conventional timeconsuming numerical evaluation of the PO integrals. Some numerical results are provided to indicate the accuracy of the analytical expressions obtained. The threedimensional case will be reported separately.
Numerical implementation of complex geometrical optics
Radiophysics and Quantum Electronics, 2000
We propose a numerical scheme for calculation of the wave field, based on the geometrical-optics method generalized for complex values, The main advantage of the complex-value method is a possibility to take into account diffraction effects using only the ordinary differential equations of the geometrical optics. This allows one to significantly reduce the amount of computations and, hence, computation time. The efficiency of this algorithm is illustrated by two numerical examples that allow comparison with the kntown analytical solutions: the plane-wave field behind the caustic in the linearly inhomogeneous layer and the field of a Gaussian beam in a homogeneous medium.
Journal of the Optical Society of America A
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the incident constituent plane wave fields to obtain the reflected and transmitted constituent plane wave fields. We derive these matrices and describe the complete formalism by implementing these matrices. This formalism, though physically equivalent to Fresnel formalism, has greater mathematical elegance and computational efficiency as compared to the latter. We utilize exact 3D expressions of the constituent plane wavevectors and electric fields of the incident, reflected and transmitted waves, which enable us to seamlessly analyse plane waves, paraxial and non-paraxial beams, highly diverging and tightly focused beam-fields as well as waves of miscellaneous wavefront-shapes and properties using the single formalism. The exact electric field expressions automatically include the geometric phase information; while we retain the wavefront curvature information by using appropriate multiplicative factors. We demonstrate our formalism by obtaining the reflected and transmitted fields in a simulated Gaussian beam model; in particular, by exploring the existence and nature of phase vortex in the longitudinal electric field component of the reflected beam-thus showing spin-to-orbital angular momentum conversion. Finally, we briefly discuss how our generalized formalism is capable of analysing the reflection-transmission problem of a very large class of complex optical waves-by referring to some novel works from the current literature as exemplary cases.
IEEE Transactions on Antennas and Propagation, 2016
In a previous publication, the problem of 2D beam diffraction by a wedge has been solved via the complex source (CS) approach. However, the straightforward CS formulation may be applied only when the incident beam is diverging as it hits the edge, but not when it is converging as it hits the wedge. In the present paper, we generalize the CS setup so that it can address both problems. The surprising result is that the CS approach can be applied for the converging beam case, but only if the CS coordinates are defined in specific fashion. We then formulate the angular harmonics and the spectral integral representations for both cases, and also derive for both cases, uniform asymptotic expressions for beam diffraction by a wedge. The validity of the results is verified by calculating the diffracted field via each one of these formulations, and comparing them with yet another approach wherein the field of the incident diverging or converging beam is synthesized using a plane wave integral, and the diffracted field is then calculated via multipole expansion. The overall goal of this research is the derivation of techniques for the analysis of 3D beam diffraction by a cone.