Bends in optical dielectric guides

TLDR: In this article, light transmission through a curved dielectric rod of rectangular cross section embedded in different dielectrics is analyzed in closed-form, though approximate form, in three ranges: (i) small cross section guides such as a thin glass ribbon surrounded by air; making its width 1 percent of the wavelength, most of the power travels outside of the glass; the attenuation coefficient of the guide is two orders of magnitude smaller than that of glass; and the radius of curvature that doubles the straight guide loss is around 10,000Λ.

Abstract: Light transmission through a curved dielectric rod of rectangular cross section embedded in different dielectrics is analyzed in closed, though approximate form. We distinguish three ranges: (i) Small cross section guides such as a thin glass ribbon surrounded by air—Making its width 1 percent of the wavelength, most of the power travels outside of the glass; the attenuation coefficient of the guide is two orders of magnitude smaller than that of glass, and the radius of curvature that doubles the straight guide loss is around 10,000Λ. (ii) Medium cross section guide for integration optics—It is only a few microns on the side and capable of guiding a single mode either in low loss bends with short radii of curvature or in a high Q closed loop useful for filters. Q's of the order of 108 are theoretically achievable in loops with radii ranging from 0.04 to 1 mm, if the percentage refractive index difference between guide and surrounding dielectric lies between 0.1 and 0.01. (iii) Large cross section guides—They are multimode and are used in fiber optics. Conversion to higher order modes are found more significant than radiation loss resulting from curvature.