Knife-edge effect
Encyclopedia
In electromagnetic wave propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....

, the knife-edge effect or edge diffraction is a redirection by diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 of a portion of the incident radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

 that strikes a well-defined obstacle such as a mountain range or the edge of a building.

The knife-edge effect is explained by Huygens-Fresnel principle
Huygens-Fresnel principle
The Huygens–Fresnel principle is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction.-History:...

, which states that a well-defined obstruction to an electromagnetic wave acts as a secondary source, and creates a new wavefront
Wavefront
In physics, a wavefront is the locus of points having the same phase. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described...

. This new wavefront propagates into the geometric shadow area of the obstacle.

The knife-edge effect is an outgrowth of the half-plane problem, originally solved by Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...

 using a plane wave spectrum formulation. A generalization of the halfplane problem is the wedge problem, solvable as a boundary value problem in cylindrical coordinates. The solution in cylindrical coordinates was then extended to the optical regime by Joseph B. Keller, who introduced the notion of diffraction coefficients through his geometrical theory of diffraction (GTD). Pathak and Kouyoumjian extended the (singular) Keller coefficients via the uniform theory of diffraction
Uniform theory of diffraction
In numerical analysis, the uniform geometrical theory of diffraction is a high-frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point. UTD is an extension of Joseph Keller's...

(UTD).
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