  We theoretically propose a new optical field state which is named
Laguerre-polynomial-weighted chaotic field. We show that such state can be
implemented, i.e., when a number state enters into a diffusion channel, the
output state is just this kind of states. We solve the master equation
describing the diffusion process by using the summation method within ordered
product of operators and the entangled state representaion. The solution
manifestly shows how a pure state evolves into a mixed state. The physical
difference between the diffusion and the amplitude damping is pointed out.
