Maria Calvo

Initial field and energy flux in absorbing optical waveguides. II. Implications

We present here numerical estimates of the density and flux of energy based on physical parameters associated with the absorption properties of certain types of absorbing optical waveguides. These results are based on a theoretical formalism established previously for the initial field incident upon the entrance pupil of an absorbing optical waveguide. Based on these results, the mechanisms of confined energy transmission and possible cross talk between neighboring waveguides are discussed. Some comments on the behavior of Bessel functions with complex arguments are also included in the discussion.

Initial field and energy flux in absorbing optical waveguides. I. Theoretical formalism.

An exact formulation of the electromagnetic field striking an optical waveguide is presented and compared with the decomposition relationship used in the literature. The expression for the critical angle is derived as a natural consequence of this formulation. Equations for the total fraction of power confined within a waveguide are derived and analyzed for the special case of absorbing waveguides. An explicit expression is derived for the fraction of energy confined within a waveguide supporting two sets of modes.

Three-dimensional analysis of bending losses in dielectric optical waveguides with arbitrary refractive-index profile

A three-dimensional analysis of bending losses in dielectric optical waveguides is presented. It constitutes a nontrivial generalization of previous two- and three-dimensional studies by other authors. Our analysis is based on homogeneous integral equations for the total radiation field and suitable asymptotic approximations for Green’s functions. A key role is played by a new three-dimensional approximation for a relevant Bessel function with large order and argument (the former being larger than the latter). A nontrivial check of the consistency of all those approximations is given. General formulas are presented for the radiated field and the energy flow and for a bending-loss coefficient in three dimensions. Numerical results are also given, in order to assess the difference between the results of other authors and ours. Such a difference is rather small for monomode behavior near cutoff, increases as the behavior of the waveguide changes from monomode to multimode, and decreases as the parameter V increases for a given core radius and propagation mode.

An analysis of the modal field in absorbing optical waveguides and some useful approximations

The authors present a mathematically exact formation of the initial field striking the aperture of an absorbing optical waveguide, via an integral equation description. An analysis of the residual scattering by the waveguide is presented. Because of the presence of the non-negligible absorption coefficient, the solution for the fraction of the confined power is obtained by performing non-trivial integrations of Bessel and Hankel functions with complex arguments. In order to carry out a numerical analysis a specific computational method is applied by using an approximated polynomial expansion whose validity is also discussed.

Diffraction Of Light By A Cascade Linear Optical System In The Fresnel Regime

We outline ,a systematic procedure for formulating the general transfer function of a compound optical system working in the Fresnel regime.