Boundary Diffraction Wave Theory Research Articles

Uniform diffracted fields of the extended theory of BDW from the circular aperture on a perfectly magnetic conductive surface

Purpose This paper aims to examine the uniform diffracted fields from a perfectly magnetic conductive (PMC) surface with the extended theory of boundary diffraction wave (BDW) approach. Design/methodology/approach Miyamoto and Wolf’s symbolic expression of the vector potential was used in the extended theory of BDW integral. This vector potential is applied to the problem, and the nonuniform field expression found was made uniform. Here, the expression is made uniform, using the detour parameter with the help of the asymptotic correlation of the Fresnel function. The BDW theory for the PMC surface extended the diffracted fields, and the uniform diffracted fields were calculated. Findings The field expressions obtained were interpreted with the graphs numerically for different aperture radii and observation distances. It has been shown that the BDW is continuous behind the diffracting aperture. There does not exist any discontinuity at the geometrically light-to-shadow transition boundary, as is required by the theory. Originality/value The results were graphically compared with diffracted fields for other surfaces. As far as we know, the uniform diffracted fields from the circular aperture on a PMC surface were calculated for the first time with the extended theory of the BDW approach.

Sharp-edge diffraction under Bessel beam illumination: a catastrophe optics perspective.

Boundary diffraction wave theory and catastrophe optics have already proved to be a formidable combination in computational optics. In the present paper, a general paraxial theory aimed at dealing paraxial diffraction of Bessel beams by arbitrarily shaped sharp-edge apertures is developed. A key ingredient of our analysis is the δ-like nature of the angular spectrum of nondiffracting beams. This allows the diffracted wavefield to be effectively represented through two-dimensional integrals defined onto rectangular domains, whose numerical evaluation is easily achievable via standard Monte Carlo techniques. As a byproduct of the present analysis, a simple explanation of a recently observed property of some "heart-like" apertures to flatten the axial intensity of apodized Bessel beams is also provided.

Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the recently proposed paraxial boundary diffraction wave theory framework [J. Opt. Soc. Am. A 36, 1048 (2019)10.1364/JOSAA.36.001048)]. Surprisingly enough, exact closed-form expressions of the diffracted wavefield can be obtained by using only elementary calculus and Euclidean geometry. An interesting connection between paraxial optics and probability theory is also outlined.

Boundary diffraction wave theory approach to corner diffraction

The scattering process of plane waves by a discontinuous edge contour is studied with the three dimensional boundary diffraction wave theory. The edge and corner diffracted fields are obtained from the stationary phase and edge point evaluations of the line integral. A new corner diffraction coefficient is derived. The behaviors of the uniform edge and corner diffracted waves are investigated numerically.

Sharp-edge diffraction under Gaussian illumination: a paraxial revisitation of Miyamoto-Wolf’s theory

A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing with sharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysis is carried out in such a way the Young-Maggi-Rubinowicz boundary diffraction wave theory can be extended to deal with Gaussian beams in an apparently straightforward way. The key for achieving such an extension is the introduction of suitable "complex angles" within the integral representations of the geometrical and boundary diffracted wave components of the total diffracted wavefield. Surprisingly enough, such a simple (although not rigorously justified) mathematical generalization seems to work well within the Gaussian realm. The resulting integrals provide meaningful quantities that, once suitably combined, give rise to predictions that are in perfect agreement with results already obtained in the past. An interesting and still open theoretical question about how to evaluate "Gaussian geometrical shadows" for arbitrarily shaped apertures is also discussed.

Three dimensional theory of the boundary diffraction wave

The line integral of the boundary diffraction wave theory, which yields the diffracted fields by an edge discontinuity, is obtained from the surface integral of the modified theory of physical optics. The line integral is evaluated by using the edge point method. The generalization of the integral is performed for curved edges. In this case the kernel is a function of two variable angles.

The Uniform Scattered Fields from a Parabolic Surface with the Boundary Diffraction Wave Theory

The uniform scattered fields of the cylindrical wave from a parabolic surface are obtained with the theory of the boundary diffraction wave (TBDW). The non-uniform diffracted field is calculated with the regenerated vector potential and rearranged by considering the Fresnel function to obtain the uniform solution. The uniform scattered fields are calculated as the sum of the diffracted and the geometrical optic fields. The numerical analyses of the diffracted and scattered fields in both uniform and non-uniform solutions are in harmony with the literature. Full Text: PDF ReferencesBaker, B. B., Copson, E. T., The mathematical theory of the Huygens' principles, 2nd Edition, Oxford Press, (1950). DirectLink Lit, J. W. Y. "Boundary Diffraction Waves due to a General Point Source and Their Applications to Aperture Systems" J. Modern Opt., 19, 1007 (1972). CrossRef Otis, G., "Application of the Boundary Diffraction Wave Theory to Gaussian Beams", J. Opt. Soc. Am., 64, 1545 (1974). CrossRef Ganci, S., "Boundary Diffraction Wave Theory for Rectilinear Apertures", Eur. J. Phys., 18, 229 (1997). CrossRef Longhurst, R. S., Geometrical and Physical Optics, 2nd Edition, Longmans [London], (1968). DirectLink Maggi, G. A., "Sulla Propagazione Libra e Perturbata delle Onde Luminose in un Mezzo Izotropo", Ann. di Mat. IIa, 16, 21 (1888).Rubinowicz, A., "Die Beugungswelle in der Kirchoffschen Theorie der Beugungsercheinungen", Ann. Physik, 4, 257 (1917). CrossRef Miyamoto, K. and Wolf, E., "Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave Part I", J. Opt. Soc. Am., 52, 615 (1962). CrossRef Miyamoto, K., Wolf, E., "Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave Part II", J. Opt. Soc. Am., 52, 626 (1962). CrossRef Born, M. and Wolf, E. Principles of Optics Seventh edition, Cambridge Univ. Press, (1999). CrossRef Alt?ngöz, C., Yalç?n, U. "Calculation of the Diffracted Waves from the Edge of an Opaque Cut Cylinder by the Boundary Diffraction Wave Theory", Journal of the Faculty of Eng. and Arch. of Gazi University, 28, 85, (2013). CrossRef Yalç?n, U. "Yutucu Yar?m Düzlemin Kenar?ndan K?r?nan Üniform Alanlar?n S?n?r K?r?n?m Dalgas? Teorisi ile Hesab?", Çankaya Üniversitesi 2.Müh. ve Tek. Sempozyumu, (2009). (In national language) CrossRef Lee, S. W. and G. A. Deschamps, \A uniform asymptotic theory CrossRef Lee, S. W., "Comparison of uniform asymptotic theory and Ufimtsev's theory of electromagnetic edge diffraction," IEEE Trans. Antennas & Propagat., Vol. 25, 162-170, 1977. CrossRef Yalç?n, U., "Uniform Scattered Fields of the Extended Theory of Boundary Diffraction Wave for PEC Surfaces", PIER M, 7, 29, (2009) DirectLink Yalç?n, U., "Analysis of Diffracted Fields with the Extended Theory of the Boundary Diffraction Wave for Impedance Surfaces", Appl. Opt., 50, 296 (2011). CrossRef Sarn?k, M., Yalç?n, U., "Uniform scattered fields from a perfectly conducting parabolic reflector with modified theory of physical optics", Optik-International J. for Light and Electron Opt., 135, 320 (2017). CrossRef Sarn?k, M., Yalç?n, U., "Modified theory of physical optics and solution for scattering fields from a perfectly conducting parabolic reflector", 16th Int. Conference on Math. Met. in Electromagnetic T. (MMET), July 5-7, Ukraine, 349 (2016). CrossRef Umul, Y. Z., Yalç?n, U. "Asymptotic Evaluation of The Edge Diffraction In Cylindric Paraboloidal Surface Antennas", Mathematical & Computational App., 8, 143 (2003). CrossRef Yalç?n, U., "Scattering from a cylindrical reflector: modified theory of physical optics solution", J. Opt. Soc. Am. A, 24, 502 (2007). CrossRef

Heart diffraction.

A theoretical study of the plane-wave diffraction by a heart-like sharp-edge aperture corresponding to the involute of a circle is proposed here. Through the recently developed paraxial boundary diffraction wave theory, expressed via the language of catastrophe optics, the presence of pseudo-nondiffracting regions within the three-dimensional spatial intensity distribution of the diffracted wavefield is intuitively explained and quantitatively characterized. The results of some old, beautiful, but nearly forgotten, diffraction experiments have also been reconsidered from such a peculiar and rather unorthodox perspective.

Step-by-step Evolution of Young’s Double-slit Interference Fringes Using Boundary Diffraction Wave Theory

Present work reports formation of Young’s double-slit interference fringes using the Young's own theory of diffraction called the theory of boundary diffraction wave. Theory demands that double-slit interference fringes are generated due to superposition of boundary diffraction waves originating from the edges of the slits due to their physical interaction with the incident light. The theoretical development is further verified with the experimental observations.

Impedance surface diffraction analysis for a strip with the boundary diffraction wave theory

The content of the present paper is mainly about the application of the boundary diffraction wave theory to an impedance strip. This method reduces the diffraction surface integrals to line integrals. Hence, line integral directly gives the diffraction integral. Evaluation of diffraction integral gives only the diffracted fields. The vector potential which is used for the construction of the line integral is reduced to the modified theory of physical optics (MTPO) integral. With the assistance of this method diffracted fields are directly obtained and investigated numerically.

Boundary diffraction wave theory of junctions between two surfaces with different face impedances

The line integral of the boundary diffraction wave theory is derived for the diffraction process of waves by a junction between two surfaces with different face impedances. The exact solution of Maliuzhinets is used with this aim. The resultant integral is applied to the diffraction of waves by a circular junction between two impedance surfaces. The results are examined numerically.

Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory

We study the diffraction of Gaussian pulses and beams within the framework of boundary diffraction wave theory. For the first time the boundary diffraction wave theory is applied to pulsed Gaussian beams, and it is shown that the diffracted field of a pulsed Gaussian beam on a circularly symmetric aperture can be evaluated by a single 1D integration along the diffracting aperture at every point of interest. We compare theoretical simulations to experimental measurements of ultrashort pulses diffracted off a circular aperture, an opaque disc, an annular aperture, and a system of four concentric annular apertures. Using the recently developed SEA TADPOLE measurement technique, we obtain micron spatial and femtosecond temporal resolutions in the spatio-temporal measurements of the diffracted fields.

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.

Boundary diffraction wave theory of resistive surfaces with edge discontinuities

The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numerically.

Analysis of diffracted fields with the extended theory of the boundary diffraction wave for impedance surfaces

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.

Uniform boundary diffraction wave theory of Rubinowicz

Rubinowicz introduced a uniform asymptotic evaluation of the boundary diffraction wave at the transition region [Ann. Phys. (Leipzig) 378, 339 (1924)]. The uniform theory of Rubinowicz is generalized for the improved integrals of the boundary diffraction wave. The technique is applied to the scattering problem of plane waves by an impedance half-plane, and the diffracted waves are examined numerically.

Boundary diffraction waves at multiple Fresnel-Kirchhoff diffraction

The theory of boundary diffraction wave is generalized to the case of multiple Fresnel-Kirchhoff diffraction on several sequentially situated holes (screens). The generalized boundary wave is the sum of boundary diffraction waves with different multiplicities described by integrals whose maximal multiplicity is equal to the number of obstacles. It is shown that the proposed generalized boundary wave method provides a multiple time gain in calculations, as compared to the aperture integration method. Results of numerical calculations agree with experimental dependences.

Analytical and experimental remarks on the Sommerfeld's half plane solution

An experiment is performed in order to test some features of the Sommerfeld's half plane solution that is claimed to be a rigorous solution to a diffraction problem. Some remarks related to the boundary diffraction wave theory are accomplished.

Uniform version of the modified theory of physical optics based boundary diffraction wave theory

The potential function of the modified theory of physical optics based boundary diffraction wave theory is made uniform by using the principles of the uniform theory of diffraction. The line integration of this new function along the edge contour gives the uniform diffracted fields which are finite for the transition regions of the diffraction geometry. The method is applied to the diffraction problem by the edge of a curved surface.

Uniform theory of the boundary diffraction wave

A uniform version of the potential function of the Maggi–Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.