A simple and accurate theoretical investigation is presented, based on a novel, effective, and straightforward ABCD matrix technique, in relation to estimation of optimum coupling efficiency between the laser diode and the photonic crystal fiber (PCF) with a hyperbolic microlens (HML) on its tip. By tailoring different parameters, such as the air-filling factor and lattice constant of the PCF, the criteria for achieving maximum coupling are predicted and reported for two different light wavelengths of practical interest. It is observed that such fiber parameters play a crucial role in predicting the optimum focal length of HML for a particular wavelength. The formulation should find application in the design of HML, for achieving a long working distance between the laser source facet and the fiber tip.
We report a simple and complete approach to estimate macrobending losses in index-guiding photonic crystal fibers with given optogeometrical parameters. The approach is based on a previously developed simpler formulation of their effective cladding indices valid in the entire single mode region of such fibers. To check the validity of our approach, we compare our results with those obtained by an earlier scalar effective index method which is not so easily accessible. We observe our results to match fairly well with the available results. Our approach should find wide attention by system designers for its ease of use.
We present a simpler, more complete and versatile formulation for the effective cladding index of a solid-core photonic crystal fiber (PCF) with a triangular lattice of air holes in the cladding region. This index depends on two fundamental geometrical parameters: the air hole diameters and their separation in the endlessly single mode region of the PCF corresponding to a prescribed upper limit of relative air hole size as well as the wavelength of the light used. Our earlier available formulation for the normalized propagation constants of the infinite cladding region of the same PCF and hence its effective cladding index takes care only of the dependence on the relative air hole size and wavelength at a particular hole pitch. Now, the hole pitch dependence is also taken into account to make the formulation complete in all senses. The proposed new formulation is shown to be accurate on the basis of a comparison of our results with those obtained by available techniques. Further, to check its validity in different problems of practical interest, we apply our new formulation to evaluate various propagation characteristics of the PCF. On comparison with the previously available results, our results are seen to agree excellently with them. The formulation should find wide use for simple verification by system designers and users.
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.
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