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.

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**:

**Linear index profile:**

**Parabolic index profile:**

**Exponential index profile:**

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

**Gaussian index profile:**

where n_{max} is the maximum index value x_{0} is the peak position, and h is the

normalized value of FWHM

**Alpha-peak index profile:**

where n_{max }is the maximum index value, and Δ is the normalized index difference.

The difference is defined as

**Alpha-dip index profile:**

where n_{max} is the maximum index value, and Δ is the normalized index difference.