Temperature and dopant concentration in single mode 5 micron diameter optical fiber-cooling through the die : Implications for laguerre orders in optical refractive synchronization

The object of this paper is to evaluate both the temperature distribution and the dopant concentration for a 5 micron diameter single mode SiO 2 fiber optic that is doped with GeO 2 . Fundamentally, what drives the need to know this information springs from a theoretical model which suggests that the index of refraction, leading from the center to the edge, follows a parabolic curve. It is the contention of this paper that the index of refraction in an optical fiber follows more of a Lorentizean curve rather than a truncated parabolic, [1],[2],[3],[4] i.e., n 2 (x) = n f 2 (1-x 2 / 2 ) xo , or a-1/2 cosh profile, i.e., n 2 = n s 2 +2n s Δn/2 cosh 2x/h, or an exponential profile, although the exponential more closely follows what is described in this paper, i.e., n 2 (x) = n s 2 +2 n s Δn e(-2|x|/h). In this analysis one will find that the temperature gradient from the center to the edge of the radius is more than substantially steep. Additionally, one finds from the diffusivity of GeO 2 in the liquid SiO 2 , that it takes only 0.07 seconds for the temperature to drop to the point where the GeO 2 freezes. Because of the diffusion of the GeO 2 in the SiO 2 one finds a depletion at the center of 28.44% and a continuing diminution as one proceeds outward to a radius of 1.25(10 -6 ) meters where the accretion of GeO 2 begins and continues to increase until, at the wall, the outer radius has an accretion of 27.24%.