A.2      Optical Fiber Waveguide

A.2.1       Comparison with a slab waveguide

In circular core fibers, the general behavior of the electromagnetic field and of the modes is qualitatively similar to that of the slab waveguide. However, the presence of a dielectric discontinuity on a surface involving both the x and y variables has two consequences

-         The modes label will contain two indices instead of one, the first index being related to the radial propagation constant and the second index to the azimutal periodicity of the field

-         It is no longer possible to assume that there is no variation of fields along the y-axis, and we will thus find that some eigenmodes (especially the fundamental one) are not purely transversely polarized but rather have a small longitudinal component for both the electric and magnetic fields. These modes are called HE and EH modes

A.2.2      Maxwell's equations

We consider a circular core fiber (Fig. A-2).

Fig. A-2 Circular core fiber geometry

We define the relative refractive index difference D as

In practice, D is smaller than 1 %, allowing the use of the scalar wave approximation (errors below 0.1 % are found for the mode characteristics) where in cylindrical coordinates the Maxwell's equations reduce to

The normalized frequency V can be expressed in terms of D