Index Profile of Fibers or Slab Waveguides

Compatibility:

The radial distribution of the fiber refractive index is called the index profile. In the
case of a slab waveguide, the transverse refractive index is called the index profile.
The index profile determines guiding properties of the fiber or slab waveguide. In
general, the core region has a higher index than the cladding region. However, the
index profile can have regions where the index is lower than the cladding value.
Modern fiber or slab waveguide designs are based on index profiles that assure
proper operation within a range of wavelengths.

For example, a dispersion flattened fiber design involves a few concentric index
regions.

Optical Grating - Fiber Profile

In OptiGrating 4.2, regions define a fiber or slab waveguide profile. Each region has
its dimension (width) and refractive index profile. The default refractive index profile
options are listed below, where x is the region’s local coordinate, w is the width of the
region.

Constant index profile:

Optical Grating - equation1

Linear index profile:

Optical Grating - equation2

Parabolic index profile:

Optical Grating - equation3

Exponential index profile:

Optical Grating - equation4

where n (0), n (w) is the refractive index at x=0 and x=w, respectively.

Gaussian index profile:

Optical Grating - equation5

where nmax is the maximum index value x0 is the peak position, and h is the
normalized value of FWHM

Alpha-peak index profile:

Optical Grating - equation6

where nmax is the maximum index value, and Δ is the normalized index difference.
The difference is defined as

Optical Grating - equation7

Alpha-dip index profile:

Optical Grating - equation8

where nmax is the maximum index value, and Δ is the normalized index difference.