In this communication we have considered propagation in a weakly anisotropic dielectric waveguide. It is shown that for a positive anisotropy the fractional power carried by the guide core increases over the isotropic case and that the anisotropy has an increasing effect as cutoff is approached. For negative anisotropy the effect is reversed. The increase in the fractional power varies linearly with the value of anisotropy with slope increasing as cutoff is approached. The degeneracy between the HE_n+1,m and EH_n+1,m modes present in the isotropic weakly guiding approximation is broken, and it is physically significant to distinguish between EH and HE modes. The anisotropy in retinal receptors (considered as dielectric waveguides) increases the stability of modal power with variation of the wavelength, although the effect is too small to explain the observation.

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