When a tunneling leaky ray propagates along the core of a nonabsorbing, multilayered, dielectric waveguide of slab or cylindrical geometry, the tunneling coefficient describing the power loss at a reflection or turning point is a simple product of fundamental quantities: (i) a WKB integration over the continuous part of the refractive index profile in the evanescent region between the reflection or turning point and the position at which the ray reappears; and (ii) a factor |<i>T</i><sub><i>F</i></sub>| at each jump in the refractive index profile between adjacent layers in the evanescent region, where <i>T</i><sub><i>F</i></sub> is the analytic continuation of the Fresnel power transmission coefficient as defined between two half-spaces of constant refractive indices corresponding to the values on either side of the jump. The ray power attenuation coefficient is equal to the tunneling coefficient divided by the distance along the waveguide axis between successive reflections or turning points at which power is lost.
© 1978 Optical Society of America
John D. Love and Clive Winkler, "Attenuation and tunneling coefficients for leaky rays in multilayered optical waveguides," J. Opt. Soc. Am. 67, 1627-1633 (1977)