The time-bandwidth limit is a mathematical tenet that affects all reciprocal resonators, stating that the product of the spectral bandwidth that can couple into a resonant system and its characteristic energy decay time is always equal to 1. Here, we develop an analytical and numerical model to show that introducing nonreciprocal coupling to a generalized resonator changes the power balance between the reflected and intracavity fields, which consequently overcomes the time-bandwidth limit of the resonant system. By performing a full evaluation of the time-bandwidth product (TBP) of the modeled resonator, we show that it represents a measure of the increased delay imparted to a light wave, with respect to what the bandwidth of the reciprocal resonant structure would allow to the same amount of in-coupled power. No longer restricted to the value 1, we show that the TBP can instead be used as a figure of merit of the improvement in intracavity power enhancement due to the nonreciprocal coupling.
The time-bandwidth limit is a mathematical tenet that affects all reciprocal resonators, stating that the product of the spectral bandwidth that can couple into a resonant system and its characteristic energy decay time is always equal to 1. Here, we develop an analytical and numerical model to show that introducing nonreciprocal coupling to a generalized resonator changes the power balance between the reflected and intracavity fields, which consequently overcomes the time-bandwidth limit of the resonant system. By performing a full evaluation of the time-bandwidth product (TBP) of the modeled resonator, we show that it represents a measure of the increased delay imparted to a light wave, with respect to what the bandwidth of the reciprocal resonant structure would allow to the same amount of in-coupled power. No longer restricted to the value 1, we show that the TBP can instead be used as a figure of merit of the improvement in intracavity power enhancement due to the nonreciprocal coupling.
This thesis aims at investigating the performance of figure-9 (figure-of-nine) optical fiber resonators as a practical solution for light storage, light generation and manipulation. The first part of the thesis focuses on a theoretical and experimental study describing the performance of the figure-9 laser as a function of different coupling strengths and output coupling conditions. The study provides new insights on Sagnac interferometer-based fiber lasers, which can be useful also for other types of cavities that include this structure, such as the figure-8 (figure-of-eight) or the theta cavity laser. The work on the figure-9 laser is then followed by a generalized theoretical model, validated by numerical results, to demonstrate that resonant systems with a decoupled input and output energy rates can exhibit an arbitrarily high time-bandwidth performance, thus providing a longer delay/storage time. The developed model shows that the time-bandwidth product (TBP) of such a resonant system is only limited by the cavity finesse. This description fits with the time-bandwidth limit (TBL), which states that the cavity bandwidth Δωcav is the inverse of the photon lifetime τ (i.e. Δωcav⋅τ=1), only when the resonator is reciprocal. The results also show that a longer storage time is accompanied by a significant improvement of the intra-cavity power enhancement, with respect to that provided by a reciprocal resonator, which is strongly desirable in all the applications that demand high efficiency in nonlinear processes. By comparing the total power enhancement in the reciprocal and nonreciprocal case, we prove that the TBP can be used as a figure of merit that characterizes the gain of total power enhancement, attained over one free spectral range (FSR) through nonreciprocal coupling, with respect to the reciprocal case considering the same amount of in-coupled power. The model is then used as a reference for an experimental implementation of such a system, at telecommunication wavelengths (around 1.55μm), using a time-variant figure-9 cavity. The results report a TBP that exceeds by a factor of 30 the TBL and is limited only by experimental constraints of the setup used. Lastly, the Sagnac interferometer in the context of generation of light is explored as to achieve electro-optic comb generation with a flat-topped spectral shape.
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's bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, 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. In this work, using a simple macroscopic, fiber-optic resonator where the nonreciprocity is induced by breaking its time-invariance, we report, in full agreement with accompanying numerical simulations, a time-bandwidth product (TBP) exceeding the 'fundamental' limit of ordinary resonant systems by a factor of 30. We show that, although in practice experimental constraints limit our scheme, the TBP can be arbitrarily large, simply dictated by the finesse of the cavity. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband and possessing long storage times, thereby offering a potential for new functionalities in wave-matter interactions.
The time-bandwidth limit inherently relates the lifetime of a resonance and its spectral bandwidth, with direct implications on the maximum storage time of a pulse versus its frequency content. It has been recently argued that nonreciprocal cavities may overcome this constraint, by breaking the strict equality of their incoupling and outcoupling coefficients. Here, we generally study the implications of nonreciprocity on resonant cavities and derive general relations, stemming from microscopic reversibility, that govern their dynamics. We show that nonreciprocal cavities do not provide specific advantages in terms of the time-bandwidth limit, but they may have other attractive properties for nanophotonic systems.
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.
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.