A Heat‐Equation Approach to Mixed Ray and Modal Representations of Green's Functions for ∇ 2  +  κ  2 | Zendy

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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.

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