Technical Background
Index Profile of Fibers or Slab Waveguides
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,…
Waveguide Modes
In a waveguide, light propagates in the form of modes. OptiGrating 4.2 uses LP Fiber modes, Vector Fiber modes, and Slab Waveguide modes. LP Fiber Modes The designation of Linearly Polarized (LP) Fiber modes is based on the assumption of weak guidance. Weakly guiding fibers have a small difference between core and cladding refractive index. The LP…
Material and Waveguide Dispersion
Material refractive index varies with wavelength and therefore causes the group velocity to vary; it is classified as material dispersion. The wavelength dependence of refractive index can be expressed by Sellmeier’s equation. Waveguide dispersion is the result of wavelength-dependence of the propagation constant of the optical waveguide. It is important in single-mode waveguides. The larger…
Complex Index Profile
In OptiGrating 4.2, the index profile of the fiber or slab waveguide can be complex. The imaginary part of the modal effective index can be calculated by the perturbation method based on the coupled mode theory as: where N is the number of layers of the waveguide index profile, Ki is the imaginary part of…
Photosensitivity Profile of the Fiber and the Slab Waveguide
It is well known that a germanium-doped silica fiber exhibits photosensitivity, i.e., a permanent change in the refractive index of the core when it is exposed to light from an appropriate laser. High photosensitivity can be achieved by increasing concentration of germanium, codoping suitable elements which has enhanced photosensitivity, and high pressure hydrogen loading etc.…
Grating Device Modeling
Single Grating Formula A grating can be represented by the formula that combines a grating shape function, an average index modulation function, a period chirp function, and an apodization function: where n0 – waveguide refractive index Δn – index modulation amplitude θ -grating tilt angle ƒ[Λ(z)/cosθ, z] – shape function Δn0(z) – average index modulation function Λ(z) –…
Coupled Mode Equations
Assume the electric field is a linear combination of the ideal modes (with no grating perturbation), such that where ai(+) and ai(-) are the slowly varying amplitudes of ith mode traveling in the +z and –z directions. βi and is the propagation constant and modal field of the ith mode. The above electric field is used…
