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A reformulation of the asymptotic solution of the coupledmode equations with a periodic variation of the refractive index along the propagation length is presented. A first-order correction using the asymptotic solution and Piccard’s method are also determined. It is found that the first-order solution compares very well with the numerical solution throughout a wide range of coupling parameters. The key differences between the method presented here and elsewhere reside in the derivation of the asymptotic solution as well as in the carefull derivation of the higher order corrections.

Using the weakly guiding and exact field solutions of an optical fiber, we wrote a FORTRAN program to determine the fractional power that reaches the end of an optical fiber with an absorptive cladding. We have assumed that each mode of the fiber is equally excited. This corresponds to incoherent source excitation. The results were compared to a previous approximation published by Payne and Hale in 1993. We have found that, at low V-numbers, V

Experiments were conducted to verify a theoretical model on the injection efficiency of sources in the cladding of an optical fiber. The theoretical results predicted an increase in the injection efficiency for higher differences in refractive indices between the core and cladding. The experimental apparatus used consisted of a glass rod 50 cm long, coated at one end with a thin film of a fluorescent substance. The fluorescent substance was excited with side illumination, perpendicular to the rod axis, using a 476-nm argon-ion laser. Part of the excited fluorescence was injected into the core and guided to a detector. The signal was measured for several different cladding refractive indices. The cladding consisted of sugar dissolved in water, and the refractive index was changed by varying the sugar concentration in the solution. The results indicate that the power injected into the rod, due to evanescent wave injection, increases with the difference in refractive index, which is in qualitative agreement with theory.

A numerical model has been developed to calculate the modal phase shift of circular step index profile weakly guiding fibers under axial strain. Whenever an optical fiber is under stress, the optical path length, the index of refraction, and the propagation constants of each mode change. In consequence, the phase of each mode is also modified. A relationship for the modal phase shift is presented. This relation is applied to both single mode and two-mode fibers in order to determine the sensitivity characteristics of strained fibers. It was found that the phase shift is strongly dependent on the core refractive index, n(co). It was also found that it is possible to design fibers which are insensitive to axial strain. Practical applications of strain insensitive fibers are discussed.

Axial strain on an optical fiber can be determined by monitoring the phase shift of a variety of optical fiber sensors. The exact analytical solutions for optical fields that propagate in a circular core optical fiber are used here to determine the phase shifts that occur for TE and TM modes due to axial strain. Whenever an optical fiber is stressed, the optical path length, the index of refraction, and the propagation constant of each fiber mode change. In consequence, the modal phase term βz of the fields is shifted by an amount ΔΦ. In certain cases, it is desirable to control the phase sensitivity to make fibers that are either more or less sensitive to strain. We show that it can be accomplished by choosing appropriate fiber parameters.

The behavior of the power efficiency of an optical fiber with bulk distribution of sources in its cladding is analyzed. Marcuse's (1988) results for weakly guiding cylindrical fibers with fluorescent sources uniformly distributed in the cladding are confirmed for the bulk distribution case. It is found that power efficiency increases with wavelength and with difference in refractive indices. A new independent variable for the bulk distribution is found, and it is shown that the power efficiency does not always increase with the V number.

Axial strain can be determined by monitoring the modal pattern variation of an optical fiber. The results of a numerical model developed to calculate the modal pattern variation at the end of a weakly guiding optical fiber under axial strain is presented. Whenever an optical fiber is under stress, the optical path length, the index of refraction, and the propagation constants of each fiber mode change. In consequence, the modal phase term β in z of the fields and the fiber output pattern are also modified. For multimode fibers, very complicated patterns result. The predicted patterns are presented and an expression for the phase variation with strain is derived

The analytical treatment of power efficiency (P(eff) is undertaken for the case of a positively guiding optical fiber with a thin-film source distributed in the core-cladding interface. The approach adopts the exact solution of the cylindrical optical fiber with an infinite cladding to account for differences between the indices of refraction of the core and the cladding. The excitation of low-loss leaky modes by the cladding is ignored, and only the injection by the evanescent field is considered. The formulas permit the analysis of the power-injection efficiency of fibers with arbitrary differences in indices of refraction. P(eff) does not always increase with V number, but rather varies slightly with wavelength and fiber-core radius and varies significantly with the difference in the indices of refraction. The theoretical results of the work are of interest for designing an atomic-O chemical sensor based on evanescent-wave coupling.

The exact field solution of a step-index profile fiber was used to determine the injection efficiency of a thin-film distribution of polarized sources located in the cladding of an optical fiber. Previous results for random source orientation were confirmed. The behavior of the power efficiency, P(eff), of a polarized distribution of sources was found to be similar to the behavior of a fiber with sources with random orientation. However, for sources polarized in either the x or y direction, P(eff) was found to be more efficient.

The exact field solution of a step-index profile fiber was used to determine the excitation efficiency of a distribution of sources in the core of an optical fiber. We have compared previous results of a thin-film cladding source distribution to its core source counterpart. The behavior of power efficiency Peff with the fiber parameters was examined and found to be similar to the behavior exhibited by cladding sources. It was also found that a core source fiber is two orders of magnitude more efficient than a fiber with a bulk distribution of cladding sources. This result agrees, qualitatively, with previous ones obtained experimentally.