Optimum power allocation in parallel Poisson optical channel

In this paper we investigate the Shannon capacity of single and parallel Poisson channels in different scenarios. At first, by examining the capacity equation of the single Poisson channel, the minimum average power that maximizes the capacity is found. Then, applying the method of Lagrange multipliers on the capacity expression of the parallel Poisson channel, we obtain the optimum power allocation maximizing the parallel Poisson channel capacity.