Volume-consumption comparisons of free-space and guided-wave optical interconnections

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) x N(1/2) points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is O1(N(3/2)), where O denotes the order, it is only O2(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 O3(N3). 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 O4(N), with O4 < O2, and O5(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.