  Following the pioneering work of Prof. Hermann A. Haus, a general quantum
theory for bi-directional nonlinear optical pulse propagation problems is
developed and applied to study the quantum properties of fiber Bragg grating
solitons. Fiber Bragg grating solitons are found to be automatically amplitude
squeezed after passing through the grating and the squeezing ratio saturates
after a certain grating length. The optimal squeezing ratio occurs when the
pulse energy is slightly above the fundamental soliton energy. One can also
compress the soliton pulsewidth and enhance the squeezing simultaneously by
using an apodized grating, as long as the solitons evolve adiabatically.
