  We present experimental and numerical studies on principal modes in a
multimode fiber with mode coupling. By applying external stress to the fiber
and gradually adjusting the stress, we have realized a transition from weak to
strong mode coupling, which corresponds to the transition from single
scattering to multiple scattering in mode space. Our experiments show that
principal modes have distinct spatial and spectral characteristic in the weak
and strong mode coupling regimes. We also investigate the bandwidth of the
principal modes, in particular, the dependence of the bandwidth on the delay
time, and the effects of the mode-dependent loss. By analyzing the path-length
distributions, we discover two distinct mechanisms that are responsible for the
bandwidth of principal modes in weak and strong mode coupling regimes. Taking
into account the mode-dependent loss in the fiber, our numerical results are in
good agreement with our experimental observations. Our study paves the way for
exploring potential applications of principal modes in communication, imaging
and spectroscopy.
