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Coupled modes with random propagation constants
Author(s) -
Rowe Harrison E.,
Mack Iris M.
Publication year - 1981
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/rs016i004p00485
Subject(s) - power dividers and directional couplers , physics , constant (computer programming) , monotonic function , propagation constant , function (biology) , coupling (piping) , power (physics) , division (mathematics) , optics , mathematical analysis , mathematics , quantum mechanics , materials science , arithmetic , evolutionary biology , computer science , metallurgy , biology , programming language
An exact theory for two coupled modes traveling in the same direction with white random propagation constants is developed. Applications include tolerance studies for integrated optical directional couplers. The expected fields and the expected powers of the two modes are determined versus distance along the coupler, with the ratio of propagation‐constant spectral density B 0 to coupling C as a parameter. For small values of B 0 / C the powers in the two modes behave in a damped oscillatory manner, with distance along the coupler. For large values of B 0 / C the behavior is monotonic. In all cases, equal power division occurs for sufficiently large distance along the coupler when heat loss is absent. For an optical switch the maximum B 0 / C is given as a function of the required switch performance by the present results. The dividing line between oscillatory and monotonic behavior of the powers in the two modes versus distance occurs for B 0 / C = 4. This choice of parameters yields a power divider of minimum length whose performance is insensitive to the dimensions.