Lower bound for the communication volume required for an optically interconnected array of points

The information-carrying capacity of optical fields is usually stated in terms of an area density as being related to communication through a surface. We render these well-understood results in a form such that they can be interpreted as a volume-density limit, applicable to an arbitrary array of points communicating with one another. An important example of such a situation is an optically interconnected computing system. We show that regardless of their actual spread or mutual overlap, optical communication links may be viewed as solid wires of minimum cross section λ2/2π for the purpose of calculating bounds on volumes and cross sections. Thus the results of area–volume complexity theory for solid wires are also applicable to optically communicating systems. The maximum number of binary pulses that may be in transit in an optical communication network occupying volume V is found to be ρ2πV/λ3, ρ denoting the modulation bandwidth normalized by the carrier frequency. Previously suggested optical-interconnection schemes are discussed in this context.

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