Dispersionless Single-Mode Lightguides With a Index Profile

Recently, single-mode lightguides have been developed that achieve transmission losses as low as 0.5 dB/km and 0.2 dB/km at wavelengths of 1.3 /nm and 1.55 jum, respectively.1 When the total lightguide dispersion is reduced to zero at the operating wavelength, a transmission system can be realized with wide repeater spacings and extremely large band widths.2"4 In fact, band widths in excess of 1 GHz/100 km are expected. Clearly, such a lightguide system would be ideal for undersea cable and other long-distance transmission applications. The design of single-mode lightguides with zero total dispersion requires an accurate description of this parameter in terms of profile shape, materials properties, and core radius. This necessitates a solution of Maxwell's equations for the fundamental HEu lightguide mode as well as the TEoi and TM0 modes. For radially inhomogeneous media, it is usually not possible to obtain these solutions as analytical expressions of a closed form. To a 583 very large extent the design of single-mode lightguides has in the past focused on rectangular-shaped index profiles. This is because Maxwell's equations are very much easier to solve in this case. When nonrectangular profiles have been considered, numerous approximations have often been employed. To avoid these difficulties, we have developed a numerical technique to obtain exact solutions to the vector form of Maxwell's equations.5 These equations are written as four coupled simultaneous first-order differential equations.