Fresnel’s and Snell’s laws for the multimode optical waveguide of circular cross section

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Abstract
Exact attenuation and power-transmission coefficients are derived to describe the radiation loss of all weakly refracting and tunnelling rays, for incidence from the core at arbitrary angles to the curved interface of the nonabsorbing optical waveguide of circular cross section. The power-transmission coefficients are expressible as simple functions of the classical Fresnel coefficients for a planar interface. An extension to Snell’s classical laws is introduced for tunnelling rays. For such rays, curvature of the interface rotates the plane of the normal and emergent transmitted ray relative to the plane of incidence.

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