Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

1 × 4 space switching and simultaneous all-optical wavelength conversion at 2.488Gbit/s using a single monolithically integrated multiwavelength laser

A novel InGaAs/InGaAsP/InP integrated multiwavelength grating cavity laser is presented, which has been used to demonstrate space switching and simultaneous all-optical wavelength conversion at bit rates of 2.488 Gbit/s. This has been achieved using a single monolithically integrated device without the need for post-filtering to separate the converted signal from the input.

All-optical switching in a vertical coupler space switch employing photocarrier-induced nonlinearity

A novel compact integrated nonlinear optical switch is demonstrated. Using a high-power picosecond pulse of 5-ps pulsewidth and 250-MHz repetition rate, all-optical switching with a contrast ratio of 23 dB has been achieved using an in-fiber input power < 14 dBm (100 pJ/pulse). The switch speed depends on the carrier sweep-out time, which can be reduced to the 10 ps range by either applying a reverse bias or by introduction of carrier recombination centers in the active layer.