Fiber is a typical cylindrical dielectric waveguide; the essence of analyzing the fiber optical field distribution is to solve the Maxwell equations. The solutions to Maxwell equations in fiber are TE, TM, HE, EH modes, which are named natural patterns or intrinsic patterns. Under the condition of weak bounding waveguide, natural patterns will degenerate forming a linear polarized mode, namely LP mode. The field equations for the optical fiber are:

The equations describe field distribution of the electromagnetic wave in a cylindrical dielectric waveguide, where k^{2}n = w^{2}^e, and propagation factor e^{—ez} are omitted in all formulas. Refractive index difference between core and cladding of the ordinary optical fiber is much smaller than one (0.0042 e.g. for G.652 fiber), which belongs to weak bounding conditions, i.e. ni ^ n_{2} = n, k^{2}n « в^{2} for the HE mode, (w^/P)(B/A) = 1; and for the EH mode, (w^/P)(B/A) = — 1. To take the above conditions into the equation, we can assume that the electric field amplitude A = 1 to simplify the formula, this normalization does not affect the specific form of light intensity distribution. Thus we can get a solution to field distribution equation under the weak bounding conditions: