In this paper, the sum capacity of the Poisson Z-interference channel that models optical communication systems with multiple transceivers is investigated. First, the capacity region of the Poisson Z-interference channel is shown to remain the same if we approximate the Poisson Z-interference channel with a discrete time memoryless binary input binary output Z-interference channel. Second, building on this result, the sum capacity of the Poisson Z-interference channel when the cross link coefficient is either sufficiently small or sufficiently large is characterized. When the cross link coefficient is sufficiently small, the sum capacity is achieved by treating interfering signal (if any) as noise. However, unlike the Gaussian Z-interference channel, the user not experiencing the interference does not necessarily transmit at its largest possible rate to achieve the sum capacity. When the cross link coefficient is sufficiently large, the sum capacity is achieved by letting the user experiencing the interference decode both messages.