Premium
A Heat‐Equation Approach to Mixed Ray and Modal Representations of Green's Functions for ∇ 2 + κ 2
Author(s) -
Kurss Herbert
Publication year - 1970
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs005i007p01085
Subject(s) - laplace transform , modal , green's function for the three variable laplace equation , function (biology) , mathematical analysis , green s , integral equation , physics , mixing (physics) , scope (computer science) , green's function , mathematics , inverse laplace transform , mathematical physics , computer science , quantum mechanics , chemistry , evolutionary biology , polymer chemistry , biology , programming language
A Green's function G for ∇ 2 + κ 2 is interpreted essentially as a Laplace transform of a Green's function H for ∇ 2 ‐ ∂/∂ t . The Laplace integral is evaluated by selecting a mixing parameter T and representing H by rays in (0, T ) and modes in ( T , ∞). This procedure enables one to systematize, simplify, and extend the scope of the technique originated by Ewald (1916). As an illustration, G for a parallel‐plate wave guide is detailed.