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It is well-known that linearly polarised (LP) modes in optical fiber are due to the superposition of true HE or EH modes and that each LP mode has several degenerate modes. Although LP modes are not the exact modes of step-index fiber, they are useful in understanding and analysing field structures and transmission characteristics. There is currently a lot of interest in making optical components such as optical switches, modal couplers, and frequency shifters, etc., using the special properties of few-mode fiber.' Unfortunately, most investigations are obstructed by the mode degeneracy and instability of the lobe orientations in circular-core fiber. Elliptical-core (e-core) fiber can overcome this problem because of its stable mode intensity distribution. As e-core fiber finds more and more applications in optical communication systems and optical fiber sensors,2,3 there is an increasing need for a better understanding of the modal fields and their propagation. Although many papers have contributed to the understanding of light propagation in circular fiber, only a few approximate approaches have been used to study the two lowest-order modes (LP01 mode and LP11 even mode) in e-core fiber.4,5 In this paper, we make a more rigorous analysis of LP modes and their propagation characteristics in e-core fiber.

The LP mode in e-core fiber has been analyzed theoretically. It is found that the solution of the modal fields of e-core fiber is a combination of Mathieu and modified Mathieu functions. The modal eigenvalue equations are derived. The mode nondegeneracy and cutoff frequency are discussed. In addition to deriving a general expression for propagation constant, we have also obtained the propagation characteristics curves of several lower-order modes for different core ellipticities.