Electromagnetic Diffraction Theory Research Articles

Electromagnetic study of the surface-plasmon-resonance contribution to surface-enhanced Raman scattering

We present a new study of the surface-plasmon contribution to surface-enhanced Raman scattering from molecules adsorbed onto metallic gratings. To this end, we use a rigorous electromagnetic theory of diffraction, i.e., a theory in which the groove depth is not considered as a perturbative parameter. The rigorous feature of this formalism leads to the introduction of an important and until now unknown result: There is an optimal groove depth of the grating for which the surface-plasmon contribution to surface-enhanced Raman scattering is the strongest. The enhancement of the electromagnetic field is calculated for different metals and wavelengths. An enhancement factor as high as 3.8\ifmmode\times\else\texttimes\fi{}${10}^{4}$ is found when a pyridine film is deposited onto a silver grating suitably optimized.

Optical lithography: The implications of the electromagnetic field theory

Optical projection lithography and the contact printing of a half plane are treated, based on the electromagnetic diffraction theory. Integral representations are given for the time-average electric-energy density distribution of the projected edges which are illuminated by a linearly polarized monochromatic wave or by a quasi-monochromatic incoherent beam. The image space is either homogeneous or a perfectly conducting screen is inserted normal to the optical axis. Contact printing is treated in terms of rigorous electromagnetic-field theory, by which the electromagnetic-field distribution is derived in a stratified substrate, each layer of which may have an arbitrary refraction index. Numerical results for boil contact printing and projection are given for edges which are illuminated by coherent beams with the polarization either normal or along the edge. In addition, the distribution due to the projection of an incoherent edge is given. The distributions obtained through contact printing are presented in the resist layer, Which is applied directly on the aluminum substrate or on an amorphous silicon antireflection coating as the intermediate stratum. The ultimate positive and negative resist patterns are systematically compared.

The theory of electromagnetic wave diffraction on two cylinders

The theory of electromagnetic wave diffraction on two cylinders

Comparison of uniform asymptotic theory and Ufimtsev's theory of electromagnetic edge diffraction

High-frequency asymptotic solutions of electromagnetic edge diffraction by two different theories are studied. One is the uniform asymptotic theory which is a refinement of Keller's geometrical theory of diffraction. The other is Ufimtsev's theory of the edge wave, representing an improvedment over the classical physical optics theory. These two theories are summarized, their features compared, and their relations discussed. When the observation point is away from shadow boundaries and caustics, both uniform asymptotic theory and Ufimtsev's theory, up to (and including) order k^{-1/2} , agree with Keller's theory. Near or on shadow boundaries, uniform asymptotic theory gives an explicit field solution, while Ufimtsev's result contains a physical optics integral. The evaluation of that integral is not a trivial task. In a two-dimensional test problem, it is shown that both theories do give, up to order k^{-1/2} , an identical field solution everywhere including the edge, shadow boundaries, and transition regions.

A uniform asymptotic theory of electromagnetic diffraction by a curved wedge

Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order of k^{-1/2} included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.

Focussed surface acoustic waves on an anisotropic crystal, studied by optical probing

Efficient focussing of surface acoustic waves has been achieved using a properly shaped gold film deposit on the −22.3° rotated Y-cut surface of quartz. The acoustic wave field was studied with laser probing techniques. A more than threefold increase in intensity and a tenfold decrease in beam width was observed at the focal point. The focussing action was obtained with the elastic wave equivalent of the Fresnel phase-reversal zone plate of optics. The multiple foci of this device allowed a simultaneous generation of acoustic waves in nearly all directions on the surface. Consequently, the surface wave velocity anisotropy could be determined completely. The experimental results are in very good agreement with the calculated velocity anisotropy. Electromagnetic diffraction theory is adopted to the two dimensional anisotropic system to analyse the performance of the focussing device.

On the theory of electromagnetic wave diffraction in active media: PMM vol. 33. n≗4, 1969, pp. 638–647

On the theory of electromagnetic wave diffraction in active media: PMM vol. 33. n≗4, 1969, pp. 638–647

Diffraction Theory of Sinusoidal Gratings and Application to In Situ Surface Self-Diffusion Measurements

Computer calculations of the diffracted intensities from a sinusoidal surface grating have been carried out using analytical methods developed independently by Brekhovskikh, Senior, Stroke, and Petit from the electromagnetic theory of diffraction. These calculations provide a theoretical foundation for the newly developed laser-diffraction technique for continuously monitoring surface self-diffusion of solids under ultrahigh vacuum conditions. The calculated patterns were characterized by an absolute maximum in intensity, which occurs at increasingly higher orders as the amplitude of the profile increases; the order of the maximum is designated nmax. Calculations were carried out at normal incidence for both Ē and H̄ parallel to the groove direction, but no sensible polarization effect was found in the range of amplitude and periods investigated. The effect of angle of incidence θi was also determined, and it was shown theoretically that, as θi increases, nmax on the +n-side of the pattern shifts toward the zero order, but on the −n-side nmax passes through a maximum before slowly decreasing. This effect also has been verified by experiment. In addition to these analyses, the phase modulation treatment used in communication theory has been examined and it is shown that this approach is the limiting case of the rigorous electromagnetic theory when the period of the grating becomes very large compared to the amplitude. Excellent agreement has been obtained between theoretical and experimental intensity distributions. This agreement provides a fundamental basis for the linear relationship between the amplitude A of the profile and the diffraction order of maximum intensity, nmax. which has been previously established experimentally and is used to follow the decay in A during a diffusion experiment. While nmax (A) is linear in the range of amplitudes and periods most frequently used in surface-diffusion measurements, the theory predicts nonlinearities in nmax (A) when the amplitude-to-period ratio is greater than about 0.08; these deviations are important in very low temperature diffusion studies. As an example of the application of the diffraction theory of sinusoidal gratings, the experimental determination of the surface self-diffusivity of a (110) nickel surface is presented. The laser-diffraction method has been used in conjunction with a low-energy electron-diffraction system, permitting the surface structure and cleanliness to be determined at any time during a diffusion experiment. An activation energy of 19.0 kcal/mole and a D0=0.01 cm2/sec have been measured for a (110) Ni C2 structure in the temperature range 800° to 1080°C.

Asymptotic Theory of Electromagnetic and Acoustic Diffraction by Smooth Convex Surfaces of Variable Curvature

A general method is presented for obtaining successive terms in short wavelength asymptotic expansions of the diffracted field produced by plane acoustic and electromagnetic waves incident on an arbitrary smooth convex surface. By introducing the geodesic coordinate system on arbitrary surfaces of non-constant curvature, both scalar and vector integral equations governing the surface fields are solved directly. The expressions for leading and second-order terms in the asymptotic expansion of the diffracted fields are obtained explicitly and the differences between acoustic and electromagnetic creeping waves are shown.

Partial Polarization in Three Theories of Electromagnetic Diffraction at an Aperture

This paper continues the study initiated by B. Karczewski and E. Wolf concerning the comparison of three theories of electromagnetic diffraction at an aperture. The general case of a partially polarized incident field is investigated, and the degree of polarization of the diffracted field, as predicted by three theories, is expressed as a function of the degree of polarization of the incident field. The results obtained by Karczewski and Wolf are shown to hold in the limiting cases.

Comparison of Three Theories of Electromagnetic Diffraction at an Aperture* Part I: Coherence Matrices

Three theories of electromagnetic diffraction at an aperture in a screen, associated with the names of Kottler, Luneburg, Severin, and Vasseur, are reviewed and on the basis of these theories the coherence matrices relating to the far field are derived. These matrices will be used in Part II of this investigation to analyze systematically the structure of the far field as predicted by these theories.

Comparison of Three Theories of Electromagnetic Diffraction at an Aperture* Part II: The Far Field

Using the coherence matrices derived in Part I of this investigation, a systematic study is made of the structure of the far field, on the basis of several different theories. First the case of a completely polarized incident field is considered and the distribution of the energy density and the state of polarization are examined. Then the case of diffraction of an unpolarized field is studied, particular attention being paid to the degree of polarization of the diffracted field. Analytical as well as some numerical results are presented. The predictions of the three theories are compared with each other and with those of the classical scalar theory of Huygens, Fresnel, and Kirchhoff.

On an integral equation in electromagnetic diffraction theory

This paper contains investigations on the integral equations ±a(x) + ∝ s n(x) × [▽ x 1 ¦x − y¦ × a(y)] dS y = 0 which are of interest in the study of the behavior of totally reflected stationary electromagnetic wave fields as the frequency tends to zero. It is shown that both integral equations have exactly p linearly independent solutions where p is the topological genus of S.

Principles of Optics. Electromagnetic theory of propagation, interference, and diffraction of light. Max Born and Emil Wolf. Pergamon, London; Macmillan, New York, ed. 2, 1964. xxviii + 808 pp. Illus. $17.50

Principles of Optics. Electromagnetic theory of propagation, interference, and diffraction of light. Max Born and Emil Wolf. Pergamon, London; Macmillan, New York, ed. 2, 1964. xxviii + 808 pp. Illus. $17.50

THE FRESNEL FIELD IN KOTTLER'S DIFFRACTION THEORY

The Kottler theory of electromagnetic diffraction has been shown to be in good agreement near the boundary of geometrical shadow with the Kirchhoff scalar approach.

Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory

Communications on Pure and Applied MathematicsVolume 16, Issue 1 p. 45-56 Article Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory Richard C. Morgan, Richard C. Morgan Currently instructor of mathematics at St. John's University.Search for more papers by this authorSamuel N. Karp, Samuel N. KarpSearch for more papers by this author Richard C. Morgan, Richard C. Morgan Currently instructor of mathematics at St. John's University.Search for more papers by this authorSamuel N. Karp, Samuel N. KarpSearch for more papers by this author First published: February 1963 https://doi.org/10.1002/cpa.3160160107Citations: 4 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume16, Issue1February 1963Pages 45-56 RelatedInformation

Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light

Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light

Comments on the treatment of diffraction of plane waves: Addendum to ‘The edge conditions and field representation theorems in the theory of electromagnetic diffraction’

Comments on the treatment of diffraction of plane waves: Addendum to ‘The edge conditions and field representation theorems in the theory of electromagnetic diffraction’

The edge conditions and field representation theorems in the theory of electromagnetic diffraction

In 1897 Rayleigh(14) pointed out that it is possible to obtain a family of solutions to certain problems in diffraction theory, notably those involving plane obstacles, by the simple operation of differentiation of some one solution. This, of course, alters the nature of the solution, especially so in the neighbourhood of a sharp edge. For, at an edge the parent solution may be finite and yet its derivative can become infinite. Further, such a differentiated solution may produce an infinite total energy in the neighbourhood of the edge. It is, therefore, natural to ask what conditions are required to make the solutions of these problems physically and mathematically acceptable and thus define the boundary-value problem uniquely.

On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen

On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen