In this chapter, after presenting a brief review of the various types of optical waveguides, we outline the key principles and parameters which describe and define the operation of optical waveguides and fibres The ways in which propagation through optical fibres affects the properties of the guided waves are discussed, including dispersion and non linear effects Power transfer between propagating waves is essential to the operation of a number of components and the fundamentals of coupling theory are reviewed In summary, the theory given provides the foundation for understanding the detailed operation of a wide variety of optical components and systems based on optical fibre technology

Optical waveguide theory

In this paper, we present two approximations for the fundamental mode of graded-index fibres. The first is a one-parameter analysis which involves computational effort comparable to that involved in the Gaussian approximation and yet gives much better results. The second is a two-parameter analysis which gives much better results than other existing approximations for all values ofV for most graded-index fibres.

The fundamental mode of graded-index fibres: simple and accurate variational methods

In a multimode optical fiber, the so-called multimode dispersion (mode-delay difference) is the principal cause that widens the transmitted pulse. The multimode dispersion can be controlled by the refractive-index profile. However, the optimum profile that minimizes the multimode dispersion has not yet been determined. This paper describes the computer-aided trial-and-error synthesis of the optimum refractive-index profile. It is shown that the group delay is reduced to about 10/sup -3/ times the value obtained with the uniform core fiber, to about 10 ps/km. This value is comparable to the material dispersion obtained with an ordinary fused-silica fiber and a typical semiconductor laser. It is also shown that the optimum profile is a smoothed W-shaped one.

Computer-Aided Synthesis of the Optimum Refractive-Index Profile for a Multimode Fiber

Transmission characteristics of multimode step-index W-type optical fibers are theoretically investigated by numerically solving the complex power flow equations. Spatial transients of power distribution and power level, as well as transmission length dependence of transmission bandwidth, are calculated for the mode-coupling condition from guided to lossy leaky modes, a characteristic of W-type fibers. The transmission characteristics of W-type fibers change from those of two singly clad reference fibers when the width of the intermediate layer is changed. The trade-off relation between the bandwidth and steady-state loss is also discussed.

Numerical solution of power flow in multimode W-type optical fibers.

A gradient index optical waveguide has an optimal index profile even though the relationship between concentration and refractive index is not linear. This is accomplished by varying the concentrations of the dopants as a function of the radial distance from the center of said core substantially as: C.sub.i (r)=C.sub.i.sup.0 +[(1-ξ.sub.i)(r/a).sup.α +ξ.sub.i (r/a) 2 α ]C i 1 where C i (r) denotes the concentration of the i th dopant as a function of radial distance r, C i 0 denotes the concentration at r=o of the i th dopant, C i 1 is the total change in concentration of dopants between r=o and r=a, α is the selected index profile, and ξ i are variable parameters relating the concentration of the i th dopant to radial distance r.

Optical waveguide having optimal index profile for multicomponent nonlinear glass

As the profile dispersion parameter P of graded-index fibres is wavelength-dependent. Marcatili's condition for achieving high bandwidth is usually satisfied only in a narrow wavelength range, if at all. This behaviour can be compensated by a wavelength-dependent refractive-index profile. This letter presents a profile function that compensates for a broad class of profile dispersions and may become a design criterion for fibres in the future, although its practical applicability is presently restricted by the limited variety of available glasses.

Compensation of profile dispersion in graded-index optical fibres

The bandwidth of graded-index fibres is limited not only by distortions of the refractive profile, but also by nonlinear profile dispersion caused by the dependence of the profile shape on wavelength. An efficient method is presented here, which helps to understand the interaction of both effects, shows a new way to minimise total dispersion by matching the two effects and simplifies the calculation of pulse broadening in imperfect real fibres.

Nonlinear profile dispersion aids optimisation of graded-index fibres

Dispersion in graded-index optical fibres can be calculated by ray-optical or wave-optical methods. This letter reports a seeming discrepancy between the results of both methods: in a fibre with a refractive profile that has been optimised by the WKB wave-optical method, helical rays may occur with a much larger transit-time spread than the modes computed with the WKB method. The question is what transit-time spread is relevant for the bandwidth of the fibre.

Dispersion in optical waveguides with graded refractive index

A gradient optical fiber with an optimized index of refraction profile characterized by the normalized difference in the index of refraction Δ is in a range of 0.005 to 0.011, with -(k o /Δ·dΔ/dk o ) being in a range of 0.09 to 0.11, an index of refraction profile function f(r/a) according to a formula of f(r/a)=(r/a).sup.α+ A((r/a).sup.α- (r/a) 2 α) and a profile dispersion function F N according to F N =f g wherein α is in the range of 2.013 to 2.015, A is in a range of 0.114 to 0.116, and g is in a range of 2.4 to 2.6.

Gradient optical fiber

The group delay of modes in graded-index fibres is often calculated by the method of Gloge and Marcatili. This method can, however, yield misleading results if the refractive profile of a fibre does not strictly follow a power law of the radius, e.g. if it is close to the optimum profile, but has statistical distortions. The letter presents a new method for the calculation of group delay which has a simplicity similar to that of the Gloge?Marcatili method and can be used in conjunction therewith as an easy way of finding reliable results for non-power-law refractive profiles.

S. Geckeler

Papers

Compensation of profile dispersion in graded-index optical fibres

Nonlinear profile dispersion aids optimisation of graded-index fibres

Dispersion in optical waveguides with graded refractive index

Gradient optical fiber

Group delay in graded-index fibres with non-power-law refractive profiles