Optical buffering via fiber delay lines is used for contention resolution in optical packet and optical burst switching nodes. This article addresses the problem of exactly finding the blocking probabilities in an asynchronous single-wavelength optical buffer. Packet lengths are assumed to be variable and modeled by phase-type distributions, whereas the packet arrival process is modeled by a Markovian arrival process that can capture autocorrelations in interarrival times. The exact solution is based on the theory of feedback fluid queues for which we propose numerically efficient and stable algorithms. We not only find the packet blocking probabilities but also the entire distribution of the unfinished work in this system from which all performance measures of interest can be derived.