Rigorous theory for modes of optical fibres with cladding limited by a plane

Vector modal solution of evanescent coupler

“…This gap may be explained by considering the modal parameters of the planar waveguide. The relationship between the propagation constants in the rectangular coordinate system is (9) In this equation, the left-hand side is nearly constant for a mode of the planar waveguide because the propagation constant in the -direction, must provide for approximately one-half wavelength across the slab (for lower-order modes). The right-hand side of the equation includes , the propagation constant in the -direction, which must be complex for a bounded mode.…”

“…The following relations between the cladding field expansion coefficients in the Cartesian and cylindrical representations have been derived by Marcuse [8] and Vassallo [9]. We provide them here for completeness Here, and may be regarded as reflection coefficients relating the exponentially increasing and decreasing components of the cladding fields.…”

Analysis of the Bound Modes in Optical D-Fibers

“…It is possible to solve (7) and (8) by appropriate relations of Bessel functions integrals [2]- [3]. The equation coefficients of (7) and (8) are express by:…”

“…The procedure for connecting the corresponding field expressions in both coordinate systems is the same as used by [2], [3]. The field components, which are expressed in both systems, are matched in the plane interface.…”

Calculation of the wavelength filter properties of the fiber-slab waveguide structure using vector mode expansion

“…In Marcuse's model the cladding has been modified by introducing a plane boundary to an infinite half-space rather than another waveguide. The interaction of the cladding fields with the fields in the half-space are described by means of reflection coefficients [10]. Those coefficients match the cladding fields in cylindrical form with the fields of the half-space in Cartesian coordinates.…”