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By analyzing theoretical scheme of quantum controlling through photon addition, we propose a new optical field whose density operator as \(\rho  = \lambda (1 - \lambda )^l :L_l \left( {\tfrac{{ - \lambda ^2 a^\dag  a}}{{1 - \lambda }}} \right)e^{ - \lambda a^\dag  a}\): (here:: denotes normal ordering symbol), which is named Laguerre-polynomialweighted chaotic state. We show that such state is the solution to the master equation \(\frac{d}{{dt}}\rho  =  - \kappa \left( {a^\dag  a\rho  + \rho aa^\dag   - a\rho a^\dag   - a^\dag  \rho a} \right)\), describing a diffusion channel, with the initial number state |l〉〈l|, and λ = 1/(1 + κt). This new state is characteristic of possessing photon number l + κt at time t, so the photon number by adjusting the diffusion parameter κ can be controlled. This master equation is solved using the summation method within ordered product of operators and the entangled state representation. The physical difference between the diffusion and the amplitude damping is noted.

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