Principal modes in multimode waveguides.

We generalize the concept of principal states of polarization and prove the existence of principal modes in multimode waveguides. Principal modes do not suffer from modal dispersion to first order of frequency variation and form orthogonal bases at both the input and the output ends of the waveguide. We show that principal modes are generally different from eigenmodes, even in uniform waveguides, unlike the special case of a single-mode fiber with uniform birefringence. The difference is most pronounced when different eigenmodes possess similar group velocities and when their field patterns vary as a function of frequency. This work may provide a new basis for analysis and control of dispersion in multimode fiber systems.