In a perfect optical fiber, mode coupling would not occur because each mode have a different propagation constant (of effective index). However, because of imperfections in fibers, such as micro- and macro-bends, ellipticity, etc., propagation constants of each mode locally change, and it can happen that two modes have the same propagation constant at a given point. Each time it occurs, power is exchanged between the to modes, and mode coupling occurs.

One specialist about this subject is Joseph Kahn. He roughly define weak mode coupling as the coupling between modes having similar propagation constants, and strong mode coupling as the coupling between modes having unequal propagation constants.

Article Mode Coupling Effects in Multi-Mode Fibers

Charles described this very accuratey. Another way of thinking of weak vs strong vcoupling is as follows: Once there is some imperfection (change in diameter / ref. index / core shape), the "perfect" fiber modes, supported by the "perfect" fiber do not hold. The term local normal modes is better fitting this situation as each swecion new modes exist. But, they are excited by the "perfect" fiber modes just one step before. Now, because of the "imperfect modes" do not 100% corelate with the "imperfect" local modes, energy from the former transfers to the latter.

"Slow", or "adiabatic" propagation can be thought of when energy transfer is negligible per typical beat length between pair of local normal modes.

"Fast" , or "non-adiabatic" propagation is when within a typical beat length , significat energy transfers from certain mode to another.

Analytical term was suggested by Snyder & Love and by Birks in the 80s.

I appreciate sincerely their support I understand now with clarity. In plastic optical fiber this effect trade off the bandwidth. However, in terms of lenght the weak or strong coupling what means?

This means that energy would transfer between modes very shortly after launch or not. Generally Inter-Modal Dispersion is the bottle neck for multimode fiber pulse propagation, i.e. the pulse width broadening is mainly caused by the smearing effect between the fastest and slowest mode. Coupling to modes different from those excited by the source can either In reduce or increase the effect. But for 1st approximation I would rely on the sum of all dispersion teems - material, waveguide, inter-modal all together... Plastic fibers are usually implemented for short paths, so there may be good working rangr even for severe coupling.

I am also interested in this question. In Joseph Kahn's theory, the strong mode coupling and weak mode coupling are defined by the correlation length! But only one of correlation length parameter is not enough to define the strong mode coupling! The following is my understanding:

if there is a mode coupling event in the link and all of the modes were involved in this events, and the strength of each mode coupling coefficients are large enough, the overall transmission matrix of the FMF may show strong mode coupling even with short interaction length .On the other hand, if partial of modes involved in these random coupling events in the link, the modes that have not involved in these random coupling events will not couple with the other modes even after long haul transmission. 

How to define strong mode coupling in few mode fiber? - ResearchGate. Available from: https://www.researchgate.net/post/How_to_define_strong_mode_coupling_in_few_mode_fiber [accessed Dec 29, 2016].

Hello, Can anyone here know the limit for the numerical value of the distance of core separation of a dual core fiber for the weakly coupled regime? I do agree with the fact that the strong/weak coupled mode regime depend on the the core separation distance in case of dual core. Thanks in advance.

Following. Looking for a step by step derivation of the strong and weak coupling effects on fiber cables.