By Pyotr Ya. Ufimtsev
This booklet is the 1st entire and complete description of the fashionable actual concept of Diffraction (PTD) in response to the concept that of ordinary part waves (EEWs). the idea is tested with the instance of the diffraction of acoustic and electromagnetic waves at completely reflecting gadgets. The derived analytic expressions sincerely clarify the actual constitution of the scattered box and describe intimately the entire mirrored and diffracted rays and beams, in addition to the fields within the area of caustics and foci. Shadow radiation, a brand new primary component to the sector, is brought and confirmed to comprise 1/2 the complete scattered power.
__________Книга представляет собой первое полное и всестороннее описание современной физической теории дифракции, основанной на понятии элементарных краевых волн. Теория показана на примере дифракции акустических и электромагнитных волн на идеально отражающих предметах. Полученные аналитические выражения чётко объясняют физическую структуру рассеянного поля и подробно описывают все отражённые и дифрагированные лучи и пучки, а также поля в окрестности каустиков и фокусов. Вводится теневое излучение - новая фундаментальная составляющая поля и показывается, что она содержит половину всей рассеянной энергии.
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Extra info for Fundamentals of the Physical Theory of Diffraction
15) applied to the circular region S of a small radius ε and with the center at ρ = 0 (Fig. 3). For small values kρ 1, the function u(kρ) and its normal derivative du/dn = du/dρ (at the boundary of the region S) are described by the asymptotic approximations u(ρ) ≈ c1 i2 ln(kρ), π du(ρ) i2 ≈ c1 , dρ πρ with kρ 1. 36) By substitution of these quantities into the Green theorem and taking the limit with ε → 0, we ﬁnd c1 = I0 /i4 and u(ρ) = 1 (1) I0 H0 (kρ). 3 A circular region (0 ≤ ρ ≤ ε, 0 ≤ φ ≤ 2π ) with the radiating source at the center.
Here, Ez and Hz are the components (of vectors E and H) that are parallel to the edge of the wedge. 1 CLASSICAL SOLUTIONS Diffraction at a wedge with a straight edge and inﬁnite planar faces is an appropriate canonical problem to derive asymptotic expressions for the edge waves scattered from arbitrary curved edges. In the particular case of the wedge, which is a semi-inﬁnite half-plane, the exact solution of this canonical problem was found by Sommerfeld (1896), who constructed so-called branched wave functions.
7). The Bessel functions Jvl (kr) can be used in the region r ≤ r0 , because they are ﬁnite at the edge r = 0, and the Hankel functions are appropriate in the region r ≥ r0 , because they satisfy Sommerfeld’s radiation condition at inﬁnity: lim √ r du − iku = 0, dr with r → ∞. 15). These expressions satisfy the boundary conditions, as well as the reciprocity principles; that is, they do not change after interchanging r and r0 , ϕ and ϕ0 . 2. This contour consists of two arcs r = r0 − ε, r = r0 + ε and two radial sides ϕ = ϕ0 − ψ, ϕ = ϕ0 + ψ.