Optical EngineeringSimple and complete formulation to compute propagation constants of photonic crystal fibers and predict their total chromatic dispersion
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Within the scalar framework, a simple and complete formulation for the normalized propagation constants of the infinite cladding region of a photonic crystal fiber (PCF) with triangular lattice of air-holes is presented, which is dependent only on the ratio of air-hole diameters and their separation. The accuracy of the proposed formulation is depicted by comparing our results with those obtained by Russell. Then the refractive indices of the fundamental space-filling mode (nFSM) in the cladding region of the PCF from Russell's equation and the proposed relations are evaluated and the two indices are observed to match quite excellently for different values of relative air-hole size and wavelength. An equivalence between the two approaches of Russell and Saitoh is also sought. Finally, in order to check the validity of the formulation in problems of practical interest, the proposed relations are applied to evaluate the total chromatic dispersion in a PCF, treating it as a conventional step index fiber having its core and cladding indices as those of silica and nFSM, respectively. On comparison with the available results of Saitoh, the results match nicely.