Nonlinear Optical Cavities Research Articles

Optomechanical entanglement manipulation and switching in a squeezed-cavity-assisted optomechanical system

Quantum entanglement is pivotal in modern quantum technologies, spanning applications from quantum networks to quantum metrology. Controllable quantum entanglement in cavity optomechanical systems has been an enduring pursuit. We propose a unique method for flexible manipulation and switching of optomechanical entanglement in a squeezed-cavity-assisted optomechanical system consisting of a χ(2)-nonlinear optical cavity and an optomechanical cavity. Squeezing the nonlinear optical cavity through parametric pumping allows effective control of light-light and light-vibration interactions within the system. This capability of the squeezed system plays a key role in manipulating quantum entanglement. We find that quantum entanglement between the unsqueezed cavity mode and the mechanical mode can be effectively regulated by adjusting the pump laser parameters. Furthermore, by turning the phase of the pump, we can achieve highly flexible quantum switching between entanglement and separability. Additionally, we demonstrate increased entanglement between the squeezed cavity mode and the mechanical mode when completely suppressing the pump-induced optical input noise. Our findings pave the way not only towards the manipulation and protection of fragile quantum entanglement but also to achieve photon-phonon quantum control by exploiting quantum squeezing.

Light squeezing enhancement by coupling nonlinear optical cavities

In this paper, we explore the squeezing effect generated by two coupled optical cavities. Each cavity contains a second-order nonlinear material and coherently pumped by a laser. Our results show that light intensity is strongly improved due to the presence of the nonlinearities and mainly depends on the detunings between external laser frequencies and cavity modes. More interestingly, the proposed scheme could enhance light squeezing for moderate coupling between cavities : the squeezing generated by one cavity is enhanced by the other one. For resonant interaction, highest squeezing effect is obtained near resonance. When fields are non resonant, squeezing increases near resonance of the considered cavity, but decreases for large detunings relative to the second cavity. Further, when the dissipation rate of the second cavity is smaller than the first, the squeezing could be improved, attaining nearly the perfect squeezing. While the temperature elevation has a negative impact overall on the nonclassical light, squeezing shows an appreciable resistance against thermal baths for appropriate parameter sets.

Delayed feedback control on wave dynamics in a nonlinear optical cavity with third-order chromatic dispersion

By taking into account third-order dispersion effects in the presence of feedback, we investigate the stability and nonlinear dynamic movements of waves created in microcavities and fiber cavities from numerical simulations of the extended Lugiato–Lefever equation. The current analysis emphasizes that third-order scattering, feedback strength, and feedback local and global components allow for the numerical observation of dissipative bound states of solitons and chaos with extended and antisymmetric interaction domains. In this regard, we demonstrate how the symmetry of the localized structural interactions is broken by the radiation that results from third-order dispersion.

Dynamics of frequency detuning in a hybrid Er-doped mode-locked fiber laser

Frequency detuning of mode-locked fiber lasers displays many remarkable nonlinear dynamical behaviors. Here we report for the first time the evolution of pulses from mode-locking through period pulsation to Q -switched mode-locking for three fundamental cases. Our experiments are performed in a hybrid actively and passively amplitude-modulated all-fiber polarization-maintaining mode-locked fiber laser, where the amplitude modulation frequency artificially deviates from the fundamental frequency of the cavity. We design and numerically simulate the laser with coupled Ginzburg–Landau equations. The experimentally observed dynamics of the mode detuning process is discussed with the assistance of the fitted model and numerical simulations, showing the generalizability of the optical mode detuning variation process. Our work provides fundamental insights for understanding perturbations in nonlinear optical resonant cavities and expands the ideas for studying chaotic path theory in hybrid mode-locked fiber lasers.

Kerr effect on optical induced transparency and group delays in a photothermal cavity

The thermal-induced nonlinear effect in a micro-cavity with small mode volume is extremely important for studying the optical cavity’s physical properties. In this work, we discuss the Kerr effect acting on the photothermally induced transparency (PTIT) and group delays in a photothermal cavity. We analyze the optical bistability with the thermal and Kerr nonlinear effects in the photothermal system, which directly impacts the dynamical stability and the threshold for bistability, eventually leading to an increase in the number of photons in the steady state. Meanwhile, the Kerr nonlinear effect greatly modifies the Fano-like PTIT in the system with photothermal effect, and the window is effectively compensated to symmetrical PTIT by Kerr-induced cavity frequency redshift. A group delay and advance are observed in the phase of the transmitted probe field, which enables light to be stored in the milliseconds range. The results demonstrate the possibility of enhancing or steering the performance of PTIT and group delay in nonlinear optical cavities, and it will find some applications in optical sensing and communications.

Low threshold Kerr solitons.

Pumping a nonlinear optical cavity with continuous wave coherent light can result in generation of a stable train of short optical pulses. Pumping the cavity with a non-degenerate resonant coherent dichromatic pump usually does not produce a stable mode-locked regime due to competition of the oscillations at the pump frequencies. We show that generation of stable optical pulses is feasible in a dichromatically pumped cavity characterized with group velocity dispersion optimized in a way that the group velocity value becomes identical for the generated pulses and the beat note of the pump harmonics. The power threshold of the process drops nearly four times in this case and the produced pulses become sub-harmonically locked to the dichromatic pump harmonics. The process is useful for generation of broadband optical frequency combs and optical time crystals.

Role of Eckhaus instability and pattern cracking in ultraslow dynamics of Kerr combs

The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wave-number periodic solutions become unstable against small-wave-number perturbations. Here we show that this instability can take place in Kerr combs corresponding to subcritical Turing patterns upon changes in the laser detuning. The development of the Eckhaus instability leads to the cracking of patterns and a long-lived transient where the peaks of the pattern rearrange in space due to spatial interactions. In the spectral domain, this results in a metastable Kerr comb dynamics with timescales that can be larger than 1 min. This time is, at least, seven orders of magnitude larger than the intracavity photon lifetime and is in sharp contrast with all the transient behaviors reported so far in cavity nonlinear optics that are typically only a few photon lifetimes long (i.e., in the picosecond to the microsecond range). This phenomenology, studied theoretically in the Lugiato-Lefever model and the observed dynamics is compatible with experimental observations in Kerr combs generated in ultra-high-$Q$ whispering-gallery mode resonators.

Photonic Spiking Neural Networks and Graphene-on-Silicon Spiking Neurons

Spiking neural networks are known to be superior over artificial neural networks for their computational power efficiency and noise robustness. The benefits of spiking coupled with the high-bandwidth and low-latency of photonics can enable highly-efficient, noise-robust, high-speed neural processors. The landscape of photonic spiking neurons consists of an overwhelming majority of excitable lasers and a few demonstrations on nonlinear optical cavities. The silicon platform is best poised to host a scalable photonic technology given its CMOS-compatibility and low optical loss. Here, we present a survey of existing photonic spiking neurons, and propose a novel spiking neuron based on a hybrid graphene-on-silicon microring cavity. A comparison among a representative sample of photonic spiking devices is also presented. Finally, we discuss methods employed in training spiking neural networks, their challenges as well as the application domain that can be enabled by photonic spiking neural hardware.

Achievements and perspectives of optical fiber Fabry\u2013Perot cavities

Fabry–Perot interferometers have stimulated numerous scientific and technical applications ranging from high-resolution spectroscopy over metrology, optical filters, to interfaces of light and matter at the quantum limit and more. End facet machining of optical fibers has enabled the miniaturization of optical Fabry–Perot cavities. Integration with fiber wave guide technology allows for small yet open devices with favorable scaling properties including mechanical stability and compact mode geometry. These fiber Fabry–Perot cavities (FFPCs) are stimulating extended applications in many fields including cavity quantum electrodynamics, optomechanics, sensing, nonlinear optics and more. Here we summarize the state of the art of devices based on FFPCs, provide an overview of applications and conclude with expected further research activities.

Thermo-optically induced transparency on a photonic chip

Controlling the optical response of a medium through suitably tuned coherent electromagnetic fields is highly relevant in a number of potential applications, from all-optical modulators to optical storage devices. In particular, electromagnetically induced transparency (EIT) is an established phenomenon in which destructive quantum interference creates a transparency window over a narrow spectral range around an absorption line, which, in turn, allows to slow and ultimately stop light due to the anomalous refractive index dispersion. Here we report on the observation of a new form of both induced transparency and amplification of a weak probe beam in a strongly driven silicon photonic crystal resonator at room temperature. The effect is based on the oscillating temperature field induced in a nonlinear optical cavity, and it reproduces many of the key features of EIT while being independent of either atomic or mechanical resonances. Such thermo-optically induced transparency will allow a versatile implementation of EIT-analogs in an integrated photonic platform, at almost arbitrary wavelength of interest, room temperature and in a practical, low cost, and scalable system.

Defect-engineered ring laser harmonic frequency combs

A monochromatic wave that circulates in a nonlinear and dispersive optical cavity can become unstable and form a structured waveform. This phenomenon, known as modulation instability, was encountered in fiber lasers, optically pumped Kerr microresonators and, most recently, in monolithic ring quantum cascade lasers (QCLs). In ring QCLs, the instability led to generation of fundamental frequency combs—optical fields that repeat themselves once per cavity round trip. Here we show that the same instability may also result in self-starting harmonic frequency combs—waveforms that repeat themselves multiple times per round trip, akin to perfect soliton crystals in ring Kerr microresonators. We can tailor the intermode spacing of harmonic frequency combs by placing two minute defects with a well-defined separation between them along the ring waveguide. On-demand excitation of frequency comb states with few powerful modes spaced by hundreds of gigahertz may find their use in future sub-terahertz generators.

Discrete light bullets in coupled optical resonators.

We consider arrays of coupled nonlinear optical cavities subject to coherent optical injection. These devices are described by the discrete generalized Lugiato-Lefever equation. We predict that stable three-dimensional localized structures, often called discrete light bullets, and clusters of them may form in the output of the coupled optical resonators. We consider both anomalous and normal dispersion and show that it results in the generation of, respectively, bright and dark discrete light bullets.

Dynamic analysis of the propagation of parallel light in a two-dimensional nonlinear optical cavity

We consider the Bose–Einstein condensation of parallel light in a two-dimensional nonlinear optical cavity, and study the propagation and conversion of the parallel light both in classical and quantum treatments. First, by combining the classical propagation equation of electric field and the Schrödinger equation of photons we derive a coupled wave equation which can be used to describe the conversion law of the parallel light in the condensate phase. It is found that in the condensate phase there exists a phase transition. Over the phase transition point, the fundamental wave can all be converted into the second harmonic. The interaction between the parallel light and the nonlinear medium is also investigated in the quantum framework. It is found that in the microcavity the traditional process of second harmonic generation can be explained as the coupling of two massive photons with each other to form a photon molecule. The conversion relation between photons and photon molecules is investigated. The results reveal the existence of a quantum phase transition in the ground state of the two-mode system, and it is consistent with the description using the classical-field method. Further investigation also shows that for the common condensate state the harmonic conversion rate is closely related to the order parameter or the initial imbalance of the system. The dependency relation between the harmonic conversion rate and the effective photon–photon interaction is also discussed.

Measurement backaction control of quantum dissipation in a nonlinear cavity-based Duffing oscillator

Quantum backaction from weak measurement affects the behavior of quantum systems. We consider a nonlinear driven Duffing oscillator system implementation in a nonlinear optical cavity, and we show that the choice of phase setting $\ensuremath{\phi}$ for a laser used in measurement can change the dissipation for the spread variables of the quantum state. This can considerably increase the energy absorbed via the energy channel of the spread variables and enhance quantum effects. This suggests novel applications to quantum control, as we demonstrate, including an example in which the energy in the spread variables allows for a dynamical tunneling between energetically separated dynamical stead-states.

Classical-field description of Bose–Einstein condensation of parallel light in a nonlinear optical cavity* *Project supported by the Graduate Science and Technology Innovation Project of Shanxi Normal University (Grant No. 01053011) and the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program (Grant No. 1G2017IHEPKFYJO1).

We study the Bose–Einstein condensation of parallel light in a two-dimensional nonlinear optical cavity, where the massive photons are converted into photon molecules (p-molecules). We extend the classical-field method to provide a description of the two-component system, and we also derive a coupled density equation which can be used to describe the conversion relation between photons and p-molecules. Furthermore, we obtain the chemical potential of the system, and we also find that the system can transform from the mixed photon and p-molecule condensate phase into a pure p-molecule condensate phase. Additionally, we investigate the collective excitation of the system. We also discuss the problem how the spontaneous decay of an atom is influenced by both the phase transition and collective excitation of the coupling system.

Stable tuning of photorefractive microcavities using an auxiliary laser.

Cavity nonlinear optics enables intriguing physical phenomena to occur at micro- or nano-scales with modest input powers. While this enhances capabilities in applications such as comb generation, frequency conversion, and quantum optics, undesired nonlinear effects including photorefraction and thermal bistability are exacerbated. In this Letter, we propose and demonstrate a highly effective method of achieving cavity stabilization using an auxiliary laser for controlling photorefraction in a z-cut periodically poled lithium niobate (LN) microcavity system. Our numerical study accurately models the photorefractive effect under high input powers, guiding future analyses and development of LN microcavity systems.

Justification of the Lugiato-Lefever Model from a Damped Driven ϕ4 Equation

The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schrödinger equation. It is a mathematical model describing complex phenomena in dissipative and nonlinear optical cavities. Within the last two decades, the equation has gained much attention as it has become the basic model describing microresonator (Kerr) frequency combs. Recent works derive the Lugiato-Lefever equation from a class of damped driven ϕ 4 equations closed to resonance. In this paper, we provide a justification of the envelope approximation. From the analysis point of view, the result is novel and non-trivial as the drive yields a perturbation term that is not square integrable. The main approach proposed in this work is to decompose the solutions into a combination of the background and the integrable component. This paper is the first part of a two-manuscript series.

Control of dissipative rogue waves in nonlinear cavity optics: Optical injection and time-delayed feedback.

We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose: the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation. We show that rogue waves are controllable by means of time-delayed feedback and optical injection. We show that without delayed feedback, transverse structures are stationary or oscillating. However, when the strength of the delayed feedback is increased, all the systems generate giant two-dimensional pulses that appear with low probability and suddenly appear and disappear. We characterize their formation by computing the probability distribution, which shows a long tail. Besides, we have computed the significant wave height, which measures the mean wave height of the highest third of the waves. We show that for all systems, the distribution tails expand beyond two times the significant wave height. Furthermore, we also show that optical injection may suppress the rogue wave formation in a semiconductor laser with a saturable absorber.

Selection of whispering-gallery modes and Fano resonance of prolate microbottle resonators

<sec>Optical microresonators supporting whispering-gallery modes have been intensively studied in past decades due to their practical applications ranging from fundamental science to engineering physics. Among such microresonators, microsphere resonators have been demonstrated to possess ultra-high quality (<i>Q</i>) factor, however, their shapes usually become non-standard spherical body, leading to irregular resonant spectra. Microring resonators have unique potential in integraibility on chip, but the fabrication imperfection limits their <i>Q</i>-factor only to 10<sup>6</sup>. In addition, the free spectral range (FSR) just depends on their radius. Due to the advantages of high <i>Q</i>-factor, standard shape, slender mode field distribution, the microbottle resonators are demonstrated to possess excellent performance in cavity quantum dynamics, nonlinear optics, high-sensitivity sensing, and micro-laser. </sec><sec>In this paper, we carry out a systematic study on the spectral characteristics of prolate microbottle resonator theoretically and experimentally. First, theoretically, the field distribution theory of the microbottle resonator is studied in detail based on Helmholtz equation. Experimentally, prolate microbottle resonators are fabriated via arc discharge technology. Second, the radial modes and axial modes of the microbottles are efficiently excited with the help of a coupled tapered fiber waveguide. By adjusting the coupling gap between the microbottle and the waveguide, The controlling of three cupling states i.e. undercoupling, critical coupling and overcoupling are realized. In our experiment, the whispering-gallery modes excited are identifiable and recognizable. The resonant mode with an ultra-high <i>Q</i>-factor of up to 1.78 × 10<sup>8</sup> is achieved. The characteristic of ultra-high <i>Q</i>-factor makes the microbottle hold great potential in biochemical sensing, nonlinear optics, and micro-laser. The tuning stability is enhanced by keeping the waveguide in touch with the microbottle. We investigate the selective excitation of whispering-gallery modes by adjusting different coupling points. As a result, clean spectra with robust coupling are observed. The stable device is suitable for improving the sensing performance. Finally, Fano resonance effect is obtained by choosing the diameter of the tapered fiber waveguide. The results presented in this paper will be of great significance for enhancing the sensing, nonlinear optics and cavity quantum dynamics.</sec>

Pattern formation in 2-μm Tm Mamyshev oscillators associated with the dissipative Faraday instability

We investigate numerically the pattern formation in 2-μm thulium-doped Mamyshev fiber oscillators, associated with the dissipative Faraday instability. The dispersion-managed fiber ring oscillator is designed with commercial fibers, allowing the dynamics for a wide range of average dispersion regimes to be studied, from normal to near-zero cavity dispersion where the Benjamin–Feir instability remains inhibited. For the first time in the 2-μm spectral window, the formation of highly coherent periodic patterns is demonstrated numerically with rates up to ∼100 GHz. In addition, irregular patterns are also investigated, revealing the generation of rogue waves via nonlinear collision processes. Our investigations have potential applications for the generation of multigigahertz frequency combs. They also shed new light on the dissipative Faraday instability mechanisms in the area of nonlinear optical cavity dynamics.