  The demands of proliferating big data and massive deep learning models,
against a backdrop of a mounting climate emergency and the abating of Moore's
law, push technologists to develop high-speed, high-throughput, low energy and
miniaturisable computer hardware. Using light as a fundamental resource,
free-space optical computing and on-chip photonic computing devices provide,
respectively, powers of natural parallelism and miniaturisability. Recent work
harnessing diffractive effects inside planar (or slab) waveguides has seemingly
combined the best elements of each competing technology. Yet, as this paper
argues, certain challenges will emerge as the clock-speeds of on-chip
diffractive systems are pushed to compete with legacy technologies. Using a
"time-aware" analytical approach to wave propagation, a prediction is made of
the presence of a time-based error term that has not yet been accounted for in
on-chip diffractive architectures. System operating frequency bounds in the
gigahertz range are quantified, above which time-based errors discernibly
affect the accuracy of system performance, and below which the errors can
safely be ignored, using design parameters from previously published work. The
analysis and related bounds presented hold value in any context where high
throughput on-chip diffractive operations may be exploited, including
beam-shaping, spectroscopy, sensing and communications.
