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The design of fabrics for terabit packet switches and routers needs to consider the limitations imposed by electronic technologies. In particular, attention has to be paid to information density and to power consumption and dissipation, as well as to power supply and footprint requirements. Optical technologies can overcome some of these limitations. We analyze the use of optical fabrics to interconnect line cards in terabit packet switches and routers. For this purpose, single-plane and multiplane optical interconnection architectures are proposed that exploit wavelength agility at line cards to implement the required switching functionality. The physical-layer scalability and feasibility of these architectures are studied by using realistic models, mostly based on the characteristics of commercially available optoelectronic devices. As a result, the considered architectures can be characterized in terms of power budget and signal-to-noise ratio, enabling the computation of the maximum achievable port count and aggregate switching capacity. Our results show that aggregate capacities of the order of a few terabits per second are possible in very simple optical switching fabrics and that the multiplane architectures permit a complexity trade-off between the wavelength and space domains, making the overall design more feasible.