Negative Refractive Index Cladding Graded Index Core Optical Waveguide Dispersion

Recently, Negative Index of Refraction Material, or, Left Handed Material, as a new type metamaterial, has generated great interest. Its unusual electro- magnetic properties demonstrate that it has potential but important applied values in optical and electromagnetic wave field.In this paper, the propagation theory of step-index optical fibers is reviewed firstly. And then a graded-index fiber formed by a core with usual homogeneous dielectric and a cladding with negative refractive index are studied. Under the assumption of weakly-grading, the boundary value problems of the fiber are solved strictly by the method of vector-field. The eigenvalue equations and cutoff frequency formulae for all propagation modes are obtained. The influence of the permittivity ratio ξ and the permeability ratio η, between the core and the cladding, on the dispersion curves and the cut-off frequencies of the guided modes is investigated. The cutoff frequency curves and the dispersion curves are obtained. According to the former result, it is found that the dispersion of this kind of fiber is depressed.The creativities of this paper are listed as followed: Firstly, the Negetive Index of Refraction Material, as a newtype metamaterial is used with conventional material to form a newtype optical fiber, which has a core with usual homogeneous dielectric and a cladding with negative refractive index. The wave equation is solved strictly by the method of vector-field under the assumption of weakly-grading, and a simple and high accurate eigenvalue equation and cutoff frequency formulae of all propagation modes are obtained. Secondly, the permittivity ratio ξ and the permeability ratio η, between the core and the cladding, are defined, and the influence of them on the dispersion curves and the cut-off frequencies of the guided modes are investigated. Thirdly, the cutoff frequency curves are painted, and it is shown that HE_m1 modes have no cutoff frequency. Fourthly, thedispersion properties of optical fibers with negative index material are contrasted with that made by conventional materials.