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Ray theory of electromagnetic surface‐wave modes in integrated optical systems
Author(s) -
Blok H.
Publication year - 1979
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/rs014i002p00333
Subject(s) - physics , electromagnetic radiation , electromagnetic field , eigenvalues and eigenvectors , surface wave , wave propagation , surface (topology) , optics , transverse plane , waveguide , ordinary differential equation , field (mathematics) , mathematical analysis , classical mechanics , computational physics , differential equation , geometry , mathematics , quantum mechanics , structural engineering , engineering , pure mathematics
A systematic ray theory of electromagnetic surface‐wave modes in integrated optical systems is presented. It is shown that in a slowly varying, horizontally layered optical waveguide the vertical components of the electromagnetic field satisfy two separate second‐order differential equations that correspond to TE and TM modes, respectively. In the horizontal direction, we develop a ray theory; in the vertical direction the application of the transverse resonance conditions leads to an eigenvalue problem. In the vertical direction the resulting solutions then behave as ordinary surface‐wave modes, while in the horizontal direction they possess all properties of two‐dimensional electromagnetic rays. The properties of the surface‐wave ray modes are discussed, in particular their propagation coefficients, for which a stationary expression (in the variational sense) is derived. Applications are briefly indicated.