The course introduces the concepts related to optical propagation in dielectric planar waveguides and optical fibres.
After a short introduction using optical rays to define the concepts, we will switch to the electromagnetic
point of view in order to be able to describe the optical modes and their propagation in planar waveguides and in optical fibers. As telecommunications are in perspective, we restrict to the weak guidance approximation that provides analytical results. Attenuation will be briefly described and dispersion will be detailed as these are major parameters in the propagation of information on long distances and at high rates.

We will also consider the coupling of one mode to an other in the same waveguide, as well as the coupling of modes propagating in neighbouring waveguides. This will allow the basis for important componants such as multiplexers, bragg filters ou interferometers.

Planar waveguides
The one dimensional step index waveguide : transverse modes, guiding condition, longitudinal propagation constant, TE and TM modes, their amplitude disptribution and confinement, cut-off frequency; graphic solutions.
The one dimensional quadratic index waveguide
Weakly guiding Optical fibers :
Scalar approximation of the propagation equation, the LP modes, their cut-off frequency, effective refractive index, normalised propagation constant and confinement.
The gaussian approximation of the fundamental mode and its application to the estimation of connexion loses.
Mode coupling :
The origines of mode coupling in the propagation equation : coupling constant and phase matching condition. The coupling between the modes of neighbouring waveguide, its application to 3 dB couplers, multiplexers and interferometers. Surface or volume gratings coupling two modes of the same waveguides; co-directionnal and contra-directionnal coupling application to Bragg gratings components.

Requirements : Physics : Maxwell equations in dielectrics Continuity of the fields at interfaces propagation equation Maths : Vector calculus Second order linear differential equations System of 2 coupled first order linear differential equations

Evaluation mechanism : 2 hours written exam

Last Modification : Tuesday 11 September 2012