Modal cutoffs in single- and few-mode fiber couplers

Optical coupling, or crosstalk, between two parallel, identical single- or few-mode fibers is describable as a superposition of the modes of the composite waveguide. Like the modes of a single-fiber waveguide, the modes of the two-fiber waveguide are cut off. Exact and simple accurate asymptotic formulae are derived giving the cutoff value as a function of separation. For single-mode couplers, perturbation theory gives the fundamental and second modes
\Psi+
and
\Psi-
as the sum and difference of the fundamental modes
\Psi_{1}
and
\Psi_{2}
of each fiber. In reality
\Psi+
is the fundamental mode of the composite waveguide, whereas
\Psi-
is the second mode and has a finite cutoff. This limits the smallest
V
-value for which low-loss coupling is possible. The limitation is least severe for step-profile fibers.