Electromagnetic Diffraction Theory Research Articles

An Asymptotic Expansion of the Solution to the Problem of the Electromagnetic Theory of Diffraction on Objects with Conical Points

A three-dimensional problem is considered for electromagnetic diffraction on a bound ideally conducting body containing a conical point. An asymptotic representation of the electromagnetic field is calculated in the vicinity of the conical point with the solution presented as the sum of singular and smooth parts.

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Research on modeling and simulation in overshadowing influence of coastal building on vessel traffic service radar

The reflection characteristics of radar waves in coastal high-rise buildings form a certain shielding area, which makes it difficult for vessel traffic service to control the ship dynamic situation in sheltered waters. To study the overshadowing influence of coastal buildings on the vessel traffic service radar, an expression model of shielding area is established based on the structure characteristics of buildings and the relative height of radar. Then, the coordinate system is established, and the range and height of the shelter area are calculated, according to the geometric relation. Based on the theory of radar electromagnetic wave diffraction, the target height is calculated. Finally, taking the prince’s Bay Cruise Terminal Building on the radar Shekou radar as an example, the shielding area and height are calculated and visualized by the numerical calculation model and verified by real vessel test and observation. The building with a height of 60 m has covered 973,090 m2 of sheltered area for Shekou radar. The results can be used not only to analyze the influence of buildings on existing vessel traffic service radar stations but also to provide an important reference for site selection of vessel traffic service radar stations.

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

Electromagnetic diffraction theory of refractive axicon lenses.

We study the field that is produced by a paraxial refractive axicon lens. The results from geometrical optics, scalar wave optics, and electromagnetic diffraction theory are compared. In particular, the axial intensity, the on-axis effective wavelength, the transverse intensity, and the far-zone field are examined. A rigorous electromagnetic diffraction analysis shows that the state of polarization of the incident beam strongly affects the transverse intensity distribution, but not the intensity distribution in the far zone.

ДИФРАКЦИЯ Е-ПОЛЯРИЗОВАННОЙ ВОЛНЫ НА БЕСКОНЕЧНОЙ ПЕРИОДИЧЕСКОЙ ЛЕНТОЧНОЙ РЕШЕТКЕ В ОТСУТСТВИЕ ОДНОЙ ЛЕНТЫ

PACS number: 41.20.Jb Purpose: The E-polarized wave diffraction by an infinite periodic strip grating without a single strip is considered. Design/methodology/approach: The total field is found as a sum of field of infinite periodical grating and field induced by the removal of a single strip. The problem is reduced to the singular integral equations with additional conditions. Findings: The directional patterns and field distribution in the domain above the grating are represented. Conclusions: The effective algorithm for study of the field which appeared as a result of absence of a single strip is suggested. Key words: infinite periodic grating, integral equation, diffraction Manuscript submitted 30.05.2016 Radio phys. radio astron. 2016, 21(3): 189-197 REFERENCES 1. SHESTOPALOV, V. P., 1971. The method of the Riemann-Hilbert problem in the theory of electromagnetic wave diffraction and propagation . Kharkiv: Kharkiv State University Press (in Russian). 2. SHESTOPALOV, V. P., LYTVYNENKO, L. M., MASALOV, S. A. and SOLOGUB, V. G., 1973. Wave diffraction by gratings . Kharkiv: Kharkiv State University Press,(in Russian). 3. SOLOGUB, V. G., 1975. On some method for studying the problem of diffraction by a finite number of strips in the same plane. Dokl. AN USSR . Ser. A . no. 6, pp. 549–552 (in Russian). 4. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2012. Wave diffraction by periodic multilayer structures . Cambridge: Cambridge Scientific Publishers. 5. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY,S. A., 2013. Wave diffraction by semi-infinite venetian blind type grating. IEEE Trans. Antennas Propag . vol. 61, no. 12, pp. 6120–6127. DOI: https://doi.org/10.1109/TAP.2013.2281510 6. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY,S. A., 2015. Diffraction of H-polarized electromagnetic waves by a multi-element planar semi-infinitegrating. Telecommunications and Radio Engineering . vol. 74, no. 9, pp. 753–767. DOI: https://doi.org/10.1615/TelecomRadEng.v74.i9.10 7. NEPA, P., MANARA, G. and ARMOGIDA, A., 2005. EM scattering from the edge of a semi-infinite planar strip grating using approximate boundary conditions. IEEE Trans.Antennas Propag . vol. 53, no. 1, pp. 82–90. DOI: https://doi.org/10.1109/TAP.2004.840523 8. GANDEL, YU. V., 1986. The method of discrete singularities in problems of electrodynamics. Voprosy Kibernetiki . no. 124, pp. 166–183 (in Russian) 9. GANDEL, YU. V., 2010. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J. Math. Sci. vol. 171, no. 1, pp. 74–88. DOI: https://doi.org/10.1007/s10958-010-0127-3 10. ZAGINAYLOV, G. I., GANDEL, Y. V., KAMYSHAN, O. P.,KAMYSHAN, V. V., HIRATA, A., THUMVONGSKUL, T. and SHIOZAWA, T., 2002. Full-wave analysis of the field distribution of natural modes in the rectangular waveguide grating based on singular integral equation method. IEEE Trans. Plasma Sci . vol. 30, no. 3. pp. 1151–1159. DOI: https://doi.org/10.1109/TPS.2002.801613 11. ZAMYATIN, YE. V. and PROSVIRNIN, S. L., 1986. Diffraction of electromagnetic waves by an array with small random fluctuations of the dimensions. Sov. J. Commun. Technol. Electron . vol. 31, no. 3, pp. 43–50. 12. ABRAMOWITZ, M. and STEGUN, I. A., eds., 1964. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables . Numder 55 in National Bureau of Standards Applied Mathematics Series. U. S. Government Printing Office, Washington, D. C. 13. FELSEN, L. B. and MARCUVITS, N., 1973. Radiation and Scattering of Waves . Englewood Cliffs, N.J.: Prentice-Hall.

Generation of 1D interference patterns of Bloch surface waves

Interference patterns of Bloch surface waves with a period that is significantly less than the wavelength of incident radiation are formed using dielectric diffraction gratings located on the surface of photonic crystal. The simulation based on electromagnetic diffraction theory is used to demonstrate the possibility of high-quality interference patterns due to resonant enhancement of higher evanescent diffraction orders related to the excitation of the Bloch surface waves. The contrast of the interference patterns is close to unity, and the period is less than the period of the diffraction structure by an order of magnitude.

Scattering in elements of plasmon optics suppressed by two-layer dielectric structures

Based on the results of simulations in the framework of a rigorous electromagnetic theory of diffraction, it is shown that a structure comprising two isotropic dielectric layers on a metal surface can be used to suppress parasitic scattering in elements of plasmon optics. The proposed dielectric structure makes possible a tenfold decrease (to 1–3%) in the level of scattering losses. This approach can also be applied in creating various elements of plasmon optics, in particular, lenses and Bragg reflection gratings.

Generalized surface current method in the macroscopic theory of diffraction radiation

The surface current method known in the theory of electromagnetic waves diffraction has been generalized to be applied to the problems of diffraction radiation generated by a charged particle moving nearby an ideally-conducting screen in vacuum. An expression for induced surface current density leading to the exact results in the theory of transition radiation has been derived, and by using this expression several exact solutions of diffraction radiation problems are found. Limits of applicability for the earlier known models based on the surface current conception are indicated. Properties of radiation from a semi-plane and from a slit in cylinder are investigated at the various distances to observer.

The Over-determined Boundary Value Problem Method in the Electromagnetic Waves Propagation and Diffraction Theory

The over-determined boundary value problems in the partial domains are proposed to be used as the auxiliary problems to investigate the wave processes in the complex structures. The necessary and su-cient conditions of solvability of the over-determined problem are the dependencies between the boundary functions. These dependencies can be obtained in terms of the Fourier transforms or Fourier coe-cients of the boundary functions. The difiraction problems for the electromagnetic waves on the conducting screens in the space and in the waveguides with metallic walls are considered as the examples. The method of partial domains is widely used in the electromagnetic wave propagation and difirac- tion theory to solve the conjugation problems and boundary value problems with mixed boundary conditions. In the case when the integral or summatorial representations of the fleld to be found are obtained in some parts of the waveguide structure it is possible to get the integral or summatorial equations equivalent to the initial problem. It is convenient to consider the over-determined boundary value problems in the partial domains as the auxiliary problems. By this we are to consider more boundary conditions on some pieces of the domains boundaries than it is necessary to choose the unique solution. The review of articles devoted to over-determined boundary value problem method for the partial difierential equations is given in the paper (1). The necessary and su-cient conditions of solvability of the over-determined problems have the form of the supplementary connections between the auxiliary boundary functions. These con- nections together with the initial boundary conditions and the conjunction conditions form the complete set of equations to determine the electromagnetic fleld. In many cases the conditions at the inflnity for the unbounded domains (the radiation conditions) can be formulated also as the auxiliary conditions for the boundary functions in the over-determined problem.

Design of axially super-resolving phase filters using the method of generalized projections

The design of pupil phase filters that super-resolve the axial intensity distribution with controlled side-lobe peak intensity under high numerical aperture conditions can be accomplished by incorporating the theory of electromagnetic diffraction in the method of generalized projections (MGP). The MGP results are however strongly dependent on the starting conditions and the applied constraints. In this report we study this dependence by investigating different starting pupil functions and introducing modifications to the applied constraints. Methods are described and implemented to generate a systematic set of starting conditions that enable a more thorough search of the solutions space. This approach generated results for which 95% have a super-resolved central-lobe, yet only a subset of those solutions offer a satisfactory compromise between super-resolution of the central-lobe and increased intensity of the axial side-lobes. These solutions are presented and discussed in the context of specific applications.

The rigorous theory of nonparaxial vectorial Gaussian beams diffracted at a slit

The rigorous electro-magnetic diffraction theory of nonparaxial vectorial beam is proposed and illustrated by the diffraction of nonparaxial vectorial Gaussian beam diffracted at a slit. A numerical comparison with the analytical expressions based on the vectorial Rayleigh-Sommerfeld diffractiion integrals is given to show the consistency between them. A futher extension of the theory is briefly discussed.

Comment on ‘Analytical results for a Bessel function times Legendre polynomials class integrals’

A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory.

Field enhancement in single subwavelength apertures

A peak of the detected fluorescence rate per molecule has recently been observed in experiments of fluorescence correlation spectroscopy carried out on subwavelength apertures in metallic screens, a phenomenon that appears at a diameter-to-wavelength ratio below the fundamental mode cutoff. Although the origin of the resonant transmission through a subwavelength aperture has been well explained in terms of excitation of plasmon surface modes on the aperture ridge, the origin of the maximum that occurs at a radius-to-wavelength ratio smaller than 1/4 was not clear. Using a rigorous electromagnetic theory of light diffraction in cylindrical geometry, we show that it is linked to the appearance of the fundamental mode propagating inside the aperture. We obtain good agreement between the theoretical and the experimental results.

Wideband four-level transmission gratings with flattened spectral efficiency

Four-level transmission-type surface relief grating profiles with nearly flat efficiency over a spectral octave are designed by rigorous electromagnetic diffraction theory. Parametric optimization of the relief depths and transition points of the profile steps of these leads to efficiencies in the range 50-60% over the entire octave if the ratio of the grating period and the mean spectral wavelength is greater than ~ 3.

Wave-front spacing in the focal region of high-numerical-aperture systems

The wave-front spacing in the focal region of an aplanatic focusing system is investigated by use of the vector theory of electromagnetic diffraction for monochromatic, linearly polarized incident light. It is shown that, in systems of high numerical aperture, the wave-front spacing near the focus is significantly larger than the wavelength of the incident light and that the wave-front spacing changes significantly within a few wavelengths of the focus and can be less than a wavelength.

Babinet Principle Applied to the Design of Metasurfaces and Metamaterials

The electromagnetic theory of diffraction and the Babinet principle are applied to the design of artificial metasurfaces and metamaterials. A new particle, the complementary split rings resonator, is proposed for the design of metasurfaces with high frequency selectivity and planar metamaterials with a negative dielectric permittivity. Applications in the fields of frequency selective surfaces and polarizers, as well as in microwave antennas and filter design, can be envisaged. The tunability of all these devices by an applied dc voltage is also achievable if these particles are etched on the appropriate substrate.

Designing diffractive optical elements for special functions using a rigorous method

The rapid miniaturization in technologies for signal, image processing and optical communication increases the need for diffractive optical elements (DOEs), whose scales move closer to that of the illumination wavelength. The optical behaviour of DOEs is dependent on the polarization of the incident light, and so it is necessary to use a rigorous electromagnetic theory of diffraction to accurately design and analyse its performance. An iterative optimization algorithm for designing two dimensional, finite aperture, aperiodic diffractive optical elements based on a rigorous electromagnetic computation model—the finite-difference time-domain method—has been introduced. The algorithm can present rigorous design results with reasonable computational cost. Two kinds of DOEs designed by our algorithm, one for realizing the beam deflection used for integration optical systems, etc, and the other for realizing 1-to-2 beam split and 1-to-3 beam split, used for optical interconnections, etc, are presented. The simulated results have shown that our method has advantages of good optimization potential, high convergence and is an attractive approach for the rigorous design of DOEs.

Dipole-wave theory of electromagnetic diffraction

A theory of diffraction is presented which systematically employs the wave approach used in the Kirchhoff method and, unlike the Kirchhoff integral, does not have severe applicability limitations. The diffraction problem is solved by using the Hertz vector instead of the field vector used in the Kirchhoff integral. The basic diffraction problems for linearly, radially, and azimuthally polarized radiation are solved analytically. The key qualitative feature of the solutions is the presence of 'poles' — zero field points within the diffraction pattern of light and dark fringes. The poles lie along the direction of the electric field vector. The solutions obtained satisfy the Maxwell equations and the reciprocity principle.

Solution of a second order difference equation using the bilinear relations of Riemann

A recently proposed technique to solve a class of second order functional difference equations arising in electromagnetic diffraction theory is further investigated by applying it to a case of intermediate complexity. The proposed approach is conceptually simple and relies on first obtaining well-defined branched solutions to a pair of associated first order difference equations. The construction of these branched expressions leads to an equation system whose solution requires relationships akin to Riemann’s bilinear relations for differentials of the first and third kinds; their derivation necessitates the application of Cauchy’s theorem on Riemann surfaces of, in this particular instance, genera one and three. Branch-free solutions of the second order difference equation are then obtained by taking appropriate linear combinations of the branched solutions of the first order equations. Analysis and computation demonstrate that the resulting expressions have the desired analytical properties and recover known solutions in the appropriate limit.