On the scalar approximation in fiber optics

It is widely accepted that the scalar approximation is valid when the gradient of the permittivity distribution del epsilon / epsilon is small. Such a condition is demanding since it precludes a rapidly varying permittivity distribution, which is usually the case in a practical optical fiber due to some kind of fluctuation in a fabrication process. Here, the scalar approximation is derived from the electric field integral equation. From the result it is seen that the applicability of the scalar approximation does not depend on the roughness in the permittivity distribution as long as the permittivity in the core is close to that in the cladding.