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British and Irish Conference on Optics and Photonics (BICOP)

Overcoming the time-bandwidth limit

Sebastian A. Schulz, Davide Grassani, C. Ivan, Simon J. Fabbri, Jeremy Upham, Robert W. Boyd, Kosmas L. Tsakmakidis, Camille‐Sophie Brès

Published Dec 1, 2018• 0 citations
Publisher

Abstract

We are so accustomed to the time-bandwidth limit that we often take it to be a fundamental relation that cannot be overcome. Contrary to this belief we here propose that the storage/delay time of a system can in fact be decoupled from the operating bandwidth, by breaking Lorentz reciprocity. We discuss two different mechanisms for breaking Lorentz reciprocity and show that - in the correct system layout - both can result in systems that exceed the conventional time bandwidth limit by orders of magnitude.

DOI
10.1109/bicop.2018.8658316

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We are so accustomed to the time-bandwidth limit that we often take it to be a fundamental relation that cannot be overcome. Contrary to this belief we here propose that the storage/delay time of a system can in fact be decoupled from the operating bandwidth, by breaking Lorentz reciprocity. We discuss two different mechanisms for breaking Lorentz reciprocity and show that - in the correct system layout - both can result in systems that exceed the conventional time bandwidth limit by orders of magnitude.
Most present-day resonant systems, throughout physics and engineering, are characterized by a strict time-reversal symmetry between the rates of energy coupled in and out of the system, which leads to a trade-off between how long a wave can be stored in the system and the system bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, atomic, or of any other nature) wave for more time, will inevitably also reduce the bandwidth of the system. Until recently, this time-bandwidth limit has been considered fundamental, arising from basic Fourier reciprocity. A recent theory suggested that it might in fact be overcome by breaking Lorentz reciprocity in the resonant system, reinvigorated a debate about whether (or not) this was indeed the case. Here, we report an experimental realization of a cavity where, inducing nonreciprocity by breaking the time invariance, we do overcome the fundamental time-bandwidth limit of ordinary resonant systems by a factor of 30, in full agreement with accompanying numerical simulations. We show that, although in practice experimental constraints limit our scheme, the time bandwidth product can be arbitrarily large, simply dictated by the finesse of the cavity. Our experimental realization uses a simple macroscopic, time-variant, fiber-optic cavity, where we break Lorentz reciprocity by non-adiabatically opening the cavity, injecting a pulse of large bandwidth, and then closing the cavity, storing the pulse which can be released on-demand at a later time. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband (i.e., ultrafast) and possessing long storage times, thereby unleashing fundamentally new functionalities in wave physics and wave-matter interactions.
Typical, reciprocal resonant systems are always limited to a time-bandwidth product of 1, causing a fundamental trade-off between long storage times and large acceptance bandwidths. A recent theory suggests that this limit may be arbitrarily overcome by breaking Lorentz reciprocity. We report an experimental realization of this concept using a time-variant fiber-optic cavity, where we can completely open the cavity, injecting a pulse of large bandwidth, and then close the cavity, storing the pulse and releasing it on-demand at a later time. We attain a time-bandwidth product of 30 and show that, although in practice it is only limited by experimental constraints, there is virtually no upper theoretical limit. Our results open the path for designing resonant systems that are broadband and ultrafast, while simultaneously allowing long interaction times, thereby unleashing fundamentally new functionalities in wave physics and light-matter interactions.
Several different definitions of the coherence time Δτ can be found in the literature and it is generally assumed that, in cases of practical interest, the different definitions give values of the same order of magnitude. The same remark applies also to definitions of the effective bandwidth Δν. Moreover it is generally supposed that these two quantities are related by the order of magnitude formula Δτ similar 1/Δν. It is shown from a detailed examination of one particular case of practical interest that the bandwidths as defined by two of the previously proposed formulae are of quite different orders of magnitude, although the correspondingly defined coherence times differ only by a factor of order unity. Similarly it may happen that the two values of Δ r differ greatly, whereas the corresponding values of Δν are nearly equal. This discussion shows that the reciprocity relation Δτ similar 1/Δν must be treated with caution, especially in the case of multiple-peaked distributions, such as arise in optical masers.
All resonant systems throughout science and engineering, independent of their physical implementation have a bandwidth that is inversely related to the decay time. A similar relation exists in all slow-light systems, where the group index (and therefore the delay for a given footprint) is inversely related to the bandwidth. Therefore, resonant or slow-light systems can either store a broad signal for a short time, or a narrow signal for a long time, but cannot achieve large delay for broad bandwidth signals.Here we discuss our recent work on non-reciprocal optical systems that are not constrained by the delay-bandwidth limit. We show that large, broadband optical delay is not a pipe dream and is achievable with current optical technology. We discuss the underlying physics of delay and bandwidth in non-reciprocal optical systems and present an experimental implementation, based on a figure-9 cavity. We demonstrate a delay-bandwidth product 30 times above the seemingly fundamental time-bandwidth limit of traditional systems. Furthermore, we show that the optical pulse can be released after an arbitrary number of round trips, providing the control and tunability lacking from conventional spiral waveguide or fibre loop delay lines.