Journal ArticleDOI
Aperture and far-field distributions expressed by the Debye integral representation of focused fields
George C. Sherman,Weng Cho Chew +1 more
TLDR
In this paper, the anomalous asymptotic behavior of the Debye integral far from focus that occurs in the vicinities of the axis of the focusing system and the boundary of the geometrical-optics shadow was studied.Abstract:
We study the anomalous asymptotic behavior of the Debye integral far from focus that occurs in the vicinities of the axis of the focusing system and the boundary of the geometrical-optics shadow. The first terms in the asymptotic power series of the far field valid on the axis, on the shadow boundary, in the shadow, and in the geometrical illuminated region off axis are obtained to show how they change discontinuously as the field point passes from one region to another. We obtain the second-order term in the asymptotic power series valid in the last-named region to show how it grows without limit as the field point approaches the axis or the shadow boundary. We then derive an approximation valid far from focus that remains continuous as the field point approaches the axis and the shadow boundary. This approximation agrees with the asymptotic power-series results where they are valid. The continuous approximation is applied to determine the sizes of the regions where the field does not approximate the geometrical-optics field.read more
Citations
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Journal ArticleDOI
Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers
TL;DR: In this article, qualitative and quantitative arguments are presented that elucidate the modifications that the whole three-dimensional structure of the diffracted field undergoes as the Fresnel number is gradually decreased, and contours of equal intensity in the focal region are presented for systems of selected Fresnel numbers, which focus uniform waves.
Journal ArticleDOI
Stationary-phase analysis of generalized axicons
TL;DR: In this paper, simple asymptotic expressions based on diffraction and the method of stationary phase are derived for the axial line images produced by generalized axicons, and the role of the radial and azimuthal hologram variations in axicon image formation is elucidated.
Journal ArticleDOI
Stratton–Chu vectorial diffraction of electromagnetic fields by apertures with application to small-Fresnel-number systems
Wenyue Hsu,Richard Barakat +1 more
TL;DR: In this paper, the Stratton-Chu theory of electromagnetic scattering is used to develop a Kirchhoff formalism of the diffraction of EM waves by an aperture and the focal shift is then calculated with the vectorial aspects taken into account.
Journal ArticleDOI
Structure of focused fields in systems with large Fresnel numbers
TL;DR: In this paper, a new and simple formula valid within the framework of the Debye theory is derived for determining the structure of focused fields in diffraction-limited systems, and an estimate is obtained for the distance from focus at which the field behaves as a cutoff portion of a uniform spherical wave.
Journal ArticleDOI
Uniform asymptotic theory of diffraction by apertures
TL;DR: In this paper, simple and explicit formulas that represent uniform asymptotic approximations to double integrals are derived and applied to obtain a uniform theory of diffraction by apertures.
References
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Journal ArticleDOI
Generalization of the maggi-rubinowicz theory of the boundary diffraction wave part I
Kenro Miyamoto,Emil Wolf +1 more
TL;DR: In this article, a new vector potential W(Q,P) is associated with any monochromatic scalar wavefield U(P), which has the property that the normal component of its curl, taken with respect to the coordinates of any point Q on a closed surface S surrounding a field point P, is equal to the integrand of the Helmholtz-Kirchhoff integral.
Journal ArticleDOI
Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie
Journal ArticleDOI
Conditions for the validity of the Debye integral representation of focused fields
Emil Wolf,Yajun Li +1 more
TL;DR: In this article, a simple sufficiency condition is obtained, under which the Debye diffraction integral may be expected to give a good approximation to the solution of a boundary value problem that is generally taken to represent a field in the region of focus.
Journal ArticleDOI
Asymptotic approximations to angular-spectrum representations
TL;DR: In this article, the angular spectrum of plane waves is represented as a sum of two double integrals, one of which is a superposition of homogeneous plane waves and the other (ui) is an inhomogeneous plane wave superposition.
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Conditions for the validity of the Debye integral representation of focused fields
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