Frequency-domain versus time-domain analysis of slow-light mesophotonic waveguides: Theoretical insights for practically realizable devices

Slow-light mesophotonic waveguides have gained increasing interest in the recent years owing to their potential for time-delay control of optical signals, crucial for all-optical circuitry, as well as EM energy storage and field enhancement which is important for driving a stronger light-matter interaction. Yet, the design of such systems has hitherto been predominantly directed by modal-type of analyses in frequency domain. We discuss here why frequency domain analysis fails for real systems, leading to mistaken predictions for the effective propagation speed of the EM signal. In particular, by utilizing a time-domain analysis we demonstrate a slow-light paradigm waveguide system which contradicts the widespread notion that the group-index is generally a good measure of the light's speed effective slow-down factor within the waveguide. In particular, our counterexample shows that it is entirely possible when two modes are compared that it would be the one with the lower group index to yield effectively the larger light slow-down factor. We analyze the salient characteristics of the modes with the higher light slow-down-factor merit to understand how to enable slow light in practical platforms. Our results suggest that in order for a large group index to practically effect a large slowdown factor it should be accompanied by a large modal index bandwidth. This can occur when both the group velocity and the group-velocity dispersion are simultaneously near-zero.