A new optical field state as an output of diffusion channel when the input being number state

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.