Gradient Fiber Dispersion And Power Characteristics Vector Analysis

In this paper, we reviewed the transmission theory of step-index and graded-index optical fiber first. And then, under the assumption of weakly-grading, the boundary value problems of the optical fiber which has a homogeneous or inhomogeneous cladding are solved strictly by the method of vector-field. The eigenvalue equations and cutoff frequency formulae for all propagation modes in an optical fiber with a core, whose index is parabolic and diameter is finite, are obtained. These results are simple and are of high accuracy. To the optical fibers with homogeneous cladding, we defined a parameter called "permittivity ratio", and analyzed the dependence of the cutoff frequency to it. The curves of cutoff frequencies varying with permittivity ratio are given. To the fibers with inhomogeneous cladding, we studied the dispersive characteristics using a parameter τ , which is the ratio of axial-permittivity to transverse-permittivity in the cladding. Finally, the paper studied the power-frequency characteristics of the parabolic index optical fiber with a uniaxial crystal cladding. The expression of hybrid ratio (which is proportional to the ratio of axial component of magnetic field to that of electric field) is obtained. According to the former results, the paper analyzed the influence of r to the power of the fundamental mode. It is shown that the influence is obvious for lower frequency area, but is negligible for higher frequency area. Using the material having large r to make the cladding is advantaged for the single-mode transmission in this kind of fiber.The creativities of this paper are listed as follows: First, to the optical fiber with a core which index is parabolic and diameter is finite, we solved the wave equation strictly by the method of vector-field under the assumption of weakly-grading. We got the simple and high accurate eigenvalue equations and cutoff frequency formulae of all propagation modes. Second, to the optical fiber with homogeneous cladding, we defined the "permittivity ratio", and we got the simple and high accurate connection of cutoff frequency to the ratio. Third, to the fiber with inhomogeneous cladding, weanalyzed the dispersive and power-frequency characteristics.In conclusion, the research method used and the results obtained in this paper will supplement the propagation theory of fiber optics, and might be helpful to the designation and applications of graded-index optical fibers.