Effective Refractive Index | <<< | >>> | Feedback |
Definition: a number quantifying the phase delay per unit length in a waveguide, relative to the phase delay in vacuum
In homogeneous transparent media, the refractive index n can be used to quantify the increase in the wavenumber (phase change per unit length) caused by the medium: the wavenumber is n times higher than it would be in vacuum. The effective refractive index neff has the analogous meaning for light propagation in a waveguide; the propagation constant of the waveguide is the effective index times the vacuum wavenumber:
Note that the effective refractive index depends not only on the wavelength but also (for multimode waveguides) on the mode in which the light propagates. For this reason, it is also called modal index. Obviously, the effective index is not just a material property, but depends on the whole waveguide design. Its value can be obtained with numerical mode calculations, for example. It can vary substantially near a mode cut-off.
The effective index may be a complex quantity. In that case, the imaginary part describes gain or loss – see the article on propagation constant for more details.
A common but wrong belief is that the effective refractive index is a kind of weighted average of the refractive index of core and cladding of the waveguide, with the weight factors determined by the fractions of the optical power propagating in the core and cladding. This impression may result from the common observation that higher-order modes, e.g. of a fiber, have a lower effective index and also a lower mode overlap with the core. However, consider e.g. a step-index multimode waveguide with a high numerical aperture and large core diameter. Here, all modes overlap to nearly 100% with the core (i.e. the mode overlaps are very similar), whereas the effective indices differ substantially.
See also: propagation constant, refractive index, waveguides, Spotlight article 2007-10-07
