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 <i>N</i><sup>1/2</sup> × <i>N</i><sup>1/2</sup> points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is <i>O</i><sub>1</sub>(<i>N</i><sup>3/2</sup>), where <i>O</i> denotes the order, it is only <i>O</i><sub>2</sub>(<i>N</i>) 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 <i>O</i><sub>3</sub>(<i>N</i><sup>3</sup>). 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 <i>F</i>#<sub>opt</sub> for space-variant optical elements are, respectively, (5<i>N</i>)<sup>1/2</sup>/4 for a single microaperture-per-channel geometry and (5<i>N</i>)<sup>1/2</sup>/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 <i>O</i><sub>4</sub>(<i>N</i>), with <i>O</i><sub>4</sub> < <i>O</i><sub>2</sub>, and <i>O</i><sub>5</sub>(<i>N</i><sup>3/2</sup>), 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.
© 2000 Optical Society of America
(050.1960) Diffraction and gratings : Diffraction theory
(130.3120) Integrated optics : Integrated optics devices
(200.2610) Optics in computing : Free-space digital optics
(200.4650) Optics in computing : Optical interconnects
(200.4960) Optics in computing : Parallel processing
Yao Li and Jan Popelek, "Volume-Consumption Comparisons of Free-Space and Guided-Wave Optical Interconnections," Appl. Opt. 39, 1815-1825 (2000)