Mode coupling condition

Question

A multimode fiber is employed to couple light into a single mode fiber. Both of the fibers have the similar total diameter. Explain the coupling in brief. Use equations, MATLAB, and so on if necessary.

Answer 1

The number of modes that can be supported by a fiber of core radius ‘r’ and operating wavelength λ is determined by the V-number,

….(1)

The refractive index of the core is nco and that of the cladding is ncl.

For single mode (SM) fibers, only the lowest order mode is supported, V ≤ 2.405. Multimode (MM) fibers support higher order modes.

For the given case, the core radius of the SM fiber and MM fiber are the same i.e. “r”. So from equation (1), the V-numbers for the SM and MM fibers is given by:

….(2)

….(3)

n₁ and n₂ are the cladding refractive indices of the MM and SM fiber respectively.

Dividing (2) by (3), we get:

….(4)

This is the mode coupling condition for the given configuration.

Only those modes supported by the SM fiber will be coupled from the MM fiber.