We compare volume-consumption characteristics of free-space and guided-wave optical interconnections. System volume consumption is used as a fundamental measure of various point-to-point space-invariant and space-variant interconnections of two-dimensional arrays of N 1/2 × N 1/2 points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is O 1(N 3/2), where O denotes the order, it is only O 2(N) for microaperture optics. For free-space and space-variant operations only microaperture optics is possible without fundamental power losses. The corresponding minimum volume consumption is O 3(N 3). We show that single microaperture-per-channel implementations of either space-invariant or space-variant operations are, in general, more volume efficient than are their two-cascade microaperture-per-channel counterparts. We also show that, for minimizing volume consumption, the optimum relative apertures F#opt for space-variant optical elements are, respectively, (5N)1/2/4 for a single microaperture-per-channel geometry and (5N)1/2/2 for a two-cascade microaperture-per-channel geometry. In guided-wave or fiber interconnect cases our study shows that the volume consumption for space-invariant and space-variant operations is O 4(N), with O 4 < O 2, and O 5(N 3/2), respectively. Thus an important conclusion of the study is that free-space optics is less volume efficient than is guided-wave optics in both space-invariant and space-variant interconnect applications.
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