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.
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.
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.
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.
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.
Abstract We demonstrate the nonreciprocal propagation of optical pulses in a linear dispersive medium with a time-varying refractive index. The change of refractive index with time breaks the time-translation symmetry of the spatially homogeneous medium compelling it to be inherently nonreciprocal. A time-reversal asymmetric field ratio of the counter-propagating optical pulses along with a frequency shift leading to spectral nonreciprocity in such dynamic media have been observed. The findings have emerged a new avenue to realize nonreciprocal light flow in dynamically tuned integration-feasible photonic systems.
Optical nonreciprocity is an essential property for a wide range of applications, such as building nonreciprocal optical devices that include isolators and circulators. The realization of optical nonreciprocity relies on breaking the symmetry associated with Lorentz reciprocity, which typically requires stringent conditions such as introducing a strong magnetic field or a high-finesse cavity with nonreciprocal coupling geometry. Here we discover that the collision effect of thermal atoms, which is undesirable for most studies, can induce broadband optical nonreciprocity. By exploiting the thermal atomic collision, we experimentally observe magnet-free and cavity-free optical nonreciprocity, which possesses a high isolation ratio, ultrabroad bandwidth, and low insertion loss simultaneously. The maximum isolation ratio is close to 40 dB, while the insertion loss is less than 1 dB. The bandwidth for an isolation ratio exceeding 20 dB is over 1.2 GHz, which is 2 orders of magnitude broader than typical resonance-enhanced optical isolators. Our work paves the way for the realization of high-performance optical nonreciprocal devices and provides opportunities for applications in integrated optics and quantum networks.
Topologically protected transport has recently emerged as an effective means to address a recurring problem hampering the field of slow light for the past two decades: its keen sensitivity to disorders and structural imperfections. With it, there has been renewed interest in efforts to overcome the delay-time-bandwidth limitation usually characterizing slow-light devices, on occasion thought to be a fundamental limit. What exactly is this limit, and what does it imply? Can it be overcome? If yes, how could topological slow light help, and in what systems? What applications might be expected by overcoming the limit? Our Perspective here attempts addressing these and other related questions while pointing to important new functionalities both for classical and quantum devices that overcoming the limit can enable.