Analysis of the axial stability for an assembly of optical modes with stochastic fluctuations type Markov chain

We describe the engineering of optical modes whose axial structure follows fluctuations of Markov-chain-type. These stochastic processes are associated with a sequence of time subintervals of duration ∆T. Each subinterval is linked to a Bessel mode of integer order selected according to a Markov-chain-type process. The resulting optical field is implemented using computational simulations for Markov-chain-type Ehrenfest. This process was chosen because it models the thermodynamic equilibrium and it is related with the evolution and stability of optical systems. The matrix representation for the stochastic process allows to incorporate entropy properties for the calculation of the purity of the optical field.