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In this study, we theoretically proposed a method to achieve an electromagnetically induced transparency (EIT)-like effect in a whispering gallery mode resonator (WGMR) and experimentally validated the method in a lithium niobate (LN) device. Benefitting from the electro-optic and inverse piezoelectric effects of the LN material, two modes of the LN WGMR that are close in frequency can be tuned at different tuning rates, resulting in EIT-like resonance lineshapes. By varying the electric field applied to the LN WGMR, the full dynamic of the EIT-like phenomenon can be precisely controlled. The experimental results agreed well with the calculations based on the coupled mode theory. Moreover, we observed a hysteresis resulting from the photorefractive effect of LN. We believe our proposed method and demonstrated devices offer a way to control an EIT-like effect, which could have potential applications in light storage, quantum information processing, and enhanced sensing techniques.

Optical logic has the potential to replace electronics with photonic circuits in applications for which optic-to-electronic conversion is impractical and for integrated all-optical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an all-optical, universal logic gate using counterpropagating light in which all signals have the same operating optical frequency. Such a device would make possible the routing of optical signals without the need for conversion into the electronic domain, thus reducing latency. The operating principle of the device is based on the Kerr interaction between counter-propagating beams in a whispering gallery mode resonator which induces a splitting between the resonance frequencies for the two propagating directions. Our gate uses a fused silica microrod resonator with a \textit{Q}-factor of $\SI{2e8}{}$. This method of optical logic gives a practical solution to the on-chip routing of light.

Backward Brillouin scattering in whispering-gallery-mode micro-resonators offers an exciting avenue to pursue both classical and quantum optomechanics applications. Our team-the Quantum Measurement Lab-together with our collaborators, are currently utilizing this regime and the favourable properties it affords for non-Gaussian motional state preparation of the acoustic field. In particular, the high mechanical frequencies, and low optical absorption and heating provide a promising route to overcome current hindrances within optomechanics. Three of our recent experimental results in this area include: (i) Brillouin optomechanical strong coupling, (ii) single-phonon addition or subtraction to a thermal state of the acoustic field, and (iii) performing phase-space tomography of non-Gaussian states generated by single- and multi-phonon subtraction. This SPIE presentation will cover these three results, what they enable, and the broader direction of our lab including the prospects of this platform for quantum-memory applications.

The high demand for fabricating microresonators with desired optical properties has led to various techniques to optimize geometries, mode structures, nonlinearities and dispersion. Depending on applications, the dispersion in such resonators counters their optical nonlinearities and influences the intracavity optical dynamics. In this paper, we demonstrate the use of a machine learning (ML) algorithm as a tool to determine the geometry of microresonators from their dispersion profiles. The training dataset with ~460 samples is generated by finite element simulations and the model is experimentally verified using integrated silicon nitride microresonators. Two ML algorithms are compared along with suitable hyperparameter tuning, out of which Random Forest (RF) yields the best results. The average error on the simulated data is well below 15%., Comment: 9 pages, 4 figures

Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of σ y (τ) = 9.3 × 10−14τ−1/2 with the averaging time τ, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches σ y (τ) = 6.2 × 10−15τ−1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of σ y (τ) = 1.9 × 10−11τ−1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.

Optical gyroscopes based on the Sagnac effect have been the mainstay of inertial navigation in aerospace and shipping for decades. These gyroscopes are typically realized either as ring-laser gyroscopes (RLGs) or fiber-optic gyroscopes (FOGs). With the recent rapid progress in the field of ultrahigh-quality optical whispering-gallery mode and ring microresonators, attention has been focused on the development of microresonator-based Sagnac gyroscopes as a more compact alternative to RLGs and FOGs. One avenue that has been explored is the use of exceptional points in non-Hermitian systems to enhance the responsivity to rotation. We use a similar phenomenon, namely, the critical point of a spontaneous symmetry-breaking transition between counterpropagating light, to demonstrate a microresonator gyroscope with a responsivity enhanced by a factor of around 10 4 . We present a proof-of-principle rotation measurement as well as a characterization of the system’s dynamical response, which shows the universal critical behaviors of responsivity enhancement and critical slowing down, both of which are beneficial in an optical gyroscope. We believe that this concept could be used to realize simple and cheap chip-based gyroscopes with sensitivities approaching those of today’s RLGs and FOGs.

A consequence of the Kerr effect in ring microresonators is that light can not always circulate simultaneously in both directions. Instead, under the appropriate conditions of input power and detuning, light can couple into the resonator only in one direction while the other continues on the coupling waveguide [1] – [3] . The two resulting light states, clockwise (CW) and counterclockwise (CCW), can be interpreted as the digital states 1 and 0 as shown in Fig. 1 (c) . Microresonators have been theorized to be a suitable solution for on-chip logical processing and switching [4] . Here we present an all-optical bistable device based on the difference of the Kerr effect for co-propagating and counterpropagating light. The device does not require any electrical power, and relies only on a single laser input for its operation. The optical state is set by the dominant input power direction. The system exhibits hysteresis ( Fig. 1 (d) ) hence the optical state is maintained until an significant input in the opposite direction is received. The hysteresis provides resilience to fluctuations in the inputs up to half of the total input power.

When on-chip microresonators were first fabricated in 2005, it became apparent that these cavities exhibit op-tomechanical properties, evident by the parametric oscillation instability that was observed [1] , [2] . This behaviour, resulting from radiation pressure, was then exploited for experiments involving cavity cooling [3] , and coherent amplification in the form of a phonon laser [4] .

Optical modes in whispering-gallery-mode (WGM) resonators generally come in pairs of degenerate modes with opposite propagation directions: a clockwise and a counter-clockwise mode. However, sub-wavelength-size imperfections on the surface and in the bulk material of the resonators, usually cause some amount of Rayleigh scattering between the modes [1] . For sufficiently high levels of backscattering, the coupling between the modes can be observed as a resolvable splitting in the frequency domain [2] . Coupling of the modes is unfavourable for some WGM resonator applications, for example gyroscopes [3] , dual frequency combs [4] , and applications relying on symmetry breaking of counter-propagating light [5] , [6] .

We present experimental and numerical evidence of self-switching behaviours between counterpropagating optical modes in a Kerr microresonator [1] . Switching indicates the restoration on average of symmetry in a previously symmetry-broken state [2] , [3] . The time-evolution of the electric field amplitudes, E ± , of the two counter-propagating modes is accurately described by the following coupled system of ordinary differential equations: \begin{equation*}\frac{{d{E_ \pm }}}{{dt}} = {E_{in}} - \left[ {1 + i\left( {\theta - A{{\left| {{E_ \pm }} \right|}^2} - B{{\left| {{E_ \mp }} \right|}^2}} \right)} \right]{E_ \pm }\end{equation*}

Birefringence - the difference in refractive index for othogonally polarized light - can manifest in the linear coupling between orthogonal modes in a given polarization basis. Inside of a resonator, birefringence leads to different resonance frequencies depending on the light’s polarization. Generally, at high intracavity powers the Kerr nonlinearity induces an intensity-dependent refractive index. In the case of circular polarized light in a cavity, the light can experience two types of Kerr effects: self-phase modulation (SPM) of the light wave with itself and cross-phase modulation (XPM) with a circular polarized lightwave of opposite handedness. In general, the effects of SPM and XPM have different magnitudes, with XPM being twice as strong in silica [1] .

The Kerr nonlinearity can be a key enabler for many digital photonic circuits as it allows access to bistable states needed for all-optical memories and switches. A common technique is to use the Kerr shift to control the resonance frequency of a resonator and use it as a bistable, optically-tunable filter. However, this approach works only in a narrow power and frequency range or requires the use of an auxiliary laser. An alternative approach is to use the asymmetric bistability between counterpropagating light states resulting from the interplay between self- and cross-phase modulation, which allows light to enter a ring resonator in just one direction. Logical HIGH and LOW states can be represented and stored as the direction of circulation of light, and controlled by modulating the input power. Here we study the switching speed, operating laser frequency and power range, and contrast ratio of such a device. We reach a bitrate of 2 Mbps in our proof-of-principle device over an optical frequency range of 1 GHz and an operating power range covering more than one order of magnitude. We also calculate that integrated photonic circuits could exhibit bitrates of the order of Gbps, paving the way for the realization of robust and simple all-optical memories, switches, routers and logic gates that can operate at a single laser frequency with no additional electrical power., 10 pages, 10 figures

We achieve an all-optical, universal logic gate based on the Kerr-effect in whispering gallery mode resonators. Switching is achieved via direction-dependent and nonreciprocal Kerr interaction between counter-propagating light.

We demonstrate how the Kerr nonreciprocity in microresonators can be used for all-optical switching, routing, and memories. We explore different materials allowing potential bitrates of 10 Gbps and power thresholds as low as 1 µW.

We demonstrate the spectral extension of microcombs by bichromatic pumping of a single microresonator. One of the seed lasers generates a soliton that synchronizes with the repetition rate of the second frequency comb via cross-phase modulation.

We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can therefore be used as a foundation for describing any phenomenon resulting from any combination of linear coupling, scattering and Kerr nonlinearity, such as bending and surface roughness losses, geometric backscattering, self- and cross-phase modulation, four-wave mixing, third-harmonic generation and Kerr frequency comb generation. The theory is then applied to a translationally symmetric waveguide in order to calculate the evanescent coupling strength to the modes of a microresonator placed nearby, as well as the Kerr self- and cross-phase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetry-breaking dynamics of two counterpropagating modes of a loop resonator and prove that cross-phase modulation is exactly twice as strong as self-phase modulation only in the case that the two counterpropagating modes are otherwise identical., Comment: 11 pages, 0 figures

We report the experimental observation of oscillatory antiphase switching between counter-propagating light beams in Kerr ring microresonators, including the emergence of periodic behaviour from a chaotic regime. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging that restores the broken symmetry on average. Self-switching of counter-propagating light is robust for realising controllable, all-optical generation of waveforms, signal encoding and chaotic cryptography., 5 pages, 5 figures

As light propagates along a waveguide, a fraction of the field can be reflected by Rayleigh scatterers. In high-quality-factor whispering-gallery-mode microresonators, this intrinsic backscattering is primarily caused by either surface or bulk material imperfections. For several types of microresonator-based experiments and applications, minimal backscattering in the cavity is of critical importance, and thus, the ability to suppress backscattering is essential. We demonstrate that the introduction of an additional scatterer into the near field of a high-quality-factor microresonator can coherently suppress the amount of backscattering in the microresonator by more than 30 dB. The method relies on controlling the scatterer position such that the intrinsic and scatterer-induced backpropagating fields destructively interfere. This technique is useful in microresonator applications where backscattering is currently limiting the performance of devices, such as ring-laser gyroscopes and dual frequency combs, which both suffer from injection locking. Moreover, these findings are of interest for integrated photonic circuits in which back reflections could negatively impact the stability of laser sources or other components., Comment: 7 pages, 4 figures, 2 supplemental pages

We describe spontaneous symmetry breaking in the powers of two optical modes coupled into a ring resonator, using a pair of coupled Lorentzian equations, featuring tunable self- and cross-phase modulation terms. We investigate a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self-/cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalised description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators., 10 pages, 10 figures

The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-$Q$ microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counterintuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy scheme that allows us to measure power dependent resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at 10 mW of pump power. The required power to split the resonance by one cavity linewidth is only $286\text{ }\text{ }\ensuremath{\mu}\mathrm{W}$. In addition, we demonstrate threefold resonance splitting when taking into account four-wave mixing and two counterpropagating probe lasers. These Kerr splittings are of interest for applications that require two resonances at optically controlled offsets, e.g., for optomechanical coupling to phonon modes, optical memories, and precisely adjustable spectral filters.

Broadband optical frequency combs are extremely versatile tools for precision spectroscopy, ultrafast ranging, as channel generators for telecom networks, and for many other metrology applications. Here, we demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be extended by bichromatic pumping: one laser with a wavelength in the anomalous dispersion regime of the microresonator generates a bright soliton microcomb while another laser in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a repetition-rate-synchronized second frequency comb. Numerical simulations agree well with experimental results and reveal that a bright optical pulse from the second pump is passively formed in the normal dispersion regime and trapped by the primary soliton. In addition, we demonstrate that a dispersive wave can be generated and influenced by cross-phase-modulation-mediated repetition-rate synchronization of the two combs. The demonstrated technique provides an alternative way to generate broadband microcombs and enables the selective enhancement of optical power in specific parts of a comb spectrum., Broadband frequency combs are a key enabling technology for frequency metrology and spectroscopy. Here, the authors demonstrate that the spectrum of a soliton microcomb can be extended by bichromatic pumping resulting in two combs that synchronize their repetition rate via cross-phase modulation.

We show > 30 dB suppression of intrinsic backscattering in ultra-high-quality factor whispering gallery mode resonators by controlling the position of a sub-wavelength scatterer within the evanescent field of the resonator.

We observe two-fold and three-fold splitting of optical modes in ultra-high-Q microresonators induced by the Kerr effect. This can be used for applications that require multiple resonances with precisely controlled offset.

We use kerr-interaction between counter-propagating light waves in a whispering gallery mode resonator to demonstrate a universal, all-optical, logic gate. This provides a novel path for on-chip routing of light.

We demonstrate that the optical spectrum of microcomb can be coherently extended by bichromatic pumping: one generates a bright soliton microcomb while a second pump generates a second frequency comb via cross-phase modulation.

We demonstrate the generation of highly stable THz-waves using a microresonator-based optical frequency comb. The compact chip-based photonic THz source is characterized for ultra-low phase noise operation. Potential applications range from telecommunication systems to THz-spectroscopy.

We demonstrate deposition of azimuthally uniform single- or multiple-layer thin films of silicon nitride and silica on fibers using plasma-enhanced chemical vapor deposition by continuously rotating the fibers during growth. Our fibers exhibit distinctive and uniform iridescence that strongly depends on coating configuration. We also report a non-invasive technique to measure refractive index and film thickness of coated fibers simultaneously based on Mie scattering. We found the films grown on fibers have very different characteristics from those grown on flat substrates. We deposit a 1-μm-thick SiN x film on a spheroidal microrod resonator, which is shown numerically to push the guided fundamental mode into the silica core. We demonstrate a Q factor of 2.2 × 106, indicating reasonably good thin film quality that could be further increased with improved process control. Our technique can be applied to coat whispering gallery mode microresonators with engineered (e.g., step, graded, or stratified) refractive index profiles, which are expected to enable many new applications.

An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions. This is due to the effects of self- and cross-phase modulation on the resonance frequencies in the two directions. The critical point of this symmetry breaking exhibits universal behaviors including divergent responsivity to external perturbations, critical slowing down, and scaling invariance. Here we derive a model for the critical dynamics of this system, first for a symmetrically-pumped resonator and then for the general case of asymmetric pumping conditions and self- and cross-phase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of critical-point-enhanced optical gyroscopes and near-field sensors, but is also applicable to nonlinear critical points in a wide range of systems., Comment: 8 pages, 3 figures

The Terahertz or millimeter wave frequency band (300 GHz - 3 THz) is spectrally located between microwaves and infrared light and has attracted significant interest for applications in broadband wireless communications, space-borne radiometers for Earth remote sensing, astrophysics, and imaging. In particular optically generated THz waves are of high interest for low-noise signal generation. In particular optically generated THz waves are of high interest for low-noise signal generation. Here, we propose and demonstrate stabilized terahertz wave generation using a microresonator-based frequency comb (microcomb). A unitravelling-carrier photodiode (UTC-PD) converts low-noise optical soliton pulses from the microcomb to a terahertz wave at the soliton's repetition rate (331 GHz). With a free-running microcomb, the Allan deviation of the Terahertz signal is 4.5*10^-9 at 1 s measurement time with a phase noise of -72 dBc/Hz (-118 dBc/Hz) at 10 kHz (10 MHz) offset frequency. By locking the repetition rate to an in-house hydrogen maser, in-loop fractional frequency stabilities of 9.6*10^-15 and 1.9*10^-17 are obtained at averaging times of 1 s and 2000 s respectively, limited by the maser reference signal. Moreover, the terahertz signal is successfully used to perform a proof-of-principle demonstration of terahertz imaging of peanuts. Combining the monolithically integrated UTC-PD with an on-chip microcomb, the demonstrated technique could provide a route towards highly stable continuous terahertz wave generation in chip-scale packages for out-of-the-lab applications. In particular, such systems would be useful as compact tools for high-capacity wireless communication, spectroscopy, imaging, remote sensing, and astrophysical applications.

Precise measurements of the frequencies of light waves have become common with mode-locked laser frequency combs1. Despite their huge success, optical frequency combs currently remain bulky and expensive laboratory devices. Integrated photonic microresonators are promising candidates for comb generators in out-of-the-lab applications, with the potential for reductions in cost, power consumption and size. Such advances will significantly impact fields ranging from spectroscopy and trace gas sensing to astronomy, communications and atomic time-keeping. Yet, in spite of the remarkable progress shown over recent years, microresonator frequency combs (‘microcombs’) have been without the key function of direct f–2f self-referencing, which enables precise determination of the absolute frequency of each comb line. Here, we realize this missing element using a 16.4 GHz microcomb that is coherently broadened to an octave-spanning spectrum and subsequently fully phase-stabilized to an atomic clock. We show phase-coherent control of the comb and demonstrate its low-noise operation.

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations., Comment: 8 pages, 5 figures

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator (e.g. a fiber loop resonator or whispering gallery microresonator) that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

Nonreciprocal light propagation is important in many applications, ranging from optical telecommunications to integrated photonics. A simple way to achieve optical nonreciprocity is to use the nonlinear interaction between counterpropagating light in a Kerr medium. Within a ring resonator, this leads to spontaneous symmetry breaking, with the result that light of a given frequency can circulate in one direction, but not in both directions simultaneously. In this work, we demonstrate that this effect can be used to realize optical isolators and circulators based on a single ultra- high-Q microresonator. We obtain isolation of more than 24 dB and develop a theoretical model for the power scaling of the attainable nonreciprocity., 11 pages, 3 figures, to be published in Optica, supplementary information rely on the same list of references as the main article

The quest towards the integration of ultra-fast, high-precision optical clocks is reflected in the large number of high-impact papers on the topic published in the last few years. This interest has been catalysed by the impact that high-precision optical frequency combs (OFCs) have had on metrology and spectroscopy in the last decade [ [1] , [2] , [3] , [4] , [5] ]. OFCs are often referred to as optical rulers: their spectra consist of a precise sequence of discrete and equally-spaced spectral lines that represent precise marks in frequency. Their importance was recognised worldwide with the 2005 Nobel Prize being awarded to T.W. Hansch and J. Hall for their breakthrough in OFC science [ 5 ]. They demonstrated that a coherent OFC source with a large spectrum – covering at least one octave – can be stabilised with a self-referenced approach, where the frequency and the phase do not vary and are completely determined by the source physical parameters. These fully stabilised OFCs solved the challenge of directly measuring optical frequencies and are now exploited as the most accurate time references available, ready to replace the current standard for time. Very recent advancements in the fabrication technology of optical micro-cavities [ 6 ] are contributing to the development of OFC sources. These efforts may open up the way to realise ultra-fast and stable optical clocks and pulsed sources with extremely high repetition-rates, in the form of compact and integrated devices. Indeed, the fabrication of high-quality factor (high-Q) micro-resonators, capable of dramatically amplifying the optical field, can be considered a photonics breakthrough that has boosted not only the scientific investigation of OFC sources [ [8] , [13] , [11] , [12] , [10] , [7] , [9] ] but also of optical sensors and compact light modulators [ [14] , [6] ]. In this framework, the demonstration of planar high-Q resonators, compatible with silicon technology [ [14] , [13] , [11] , [12] , [10] ], has opened up a unique opportunity for these devices to provide entirely new capabilities for photonic-integrated technologies. Indeed, it is well acknowledged by the electronics industry that future generations of computer processing chips will inevitably require an extremely high density of copper-based interconnections, significantly increasing the chip power dissipation to beyond practical levels [ [15] , [16] , [17] ]; hence, conventional approaches to chip design must undergo radical changes. On-chip optical networks, or optical interconnects, can offer high speed and low energy per-transferred-bit, and micro-resonators are widely seen as a key component to interface the electronic world with photonics. Many information technology industries have recently focused on the development of integrated ring resonators to be employed for electrically-controlled light modulators [ [14] , [15] , [16] , [17] ], greatly advancing the maturity of micro-resonator technology as a whole. Recently [ [13] , [11] , [12] ], the demonstration of OFC sources in micro-resonators fabricated in electronic (i.e. in complementary metal oxide semiconductor (CMOS)) compatible platforms has given micro-cavities an additional appeal, with the possibility of exploiting them as light sources in microchips. This scenario is creating fierce competition in developing highly efficient OFC generators based on micro-cavities which can radically change the nature of information transport and processing. Even in telecommunications, perhaps a more conventional environment for optical technologies, novel time-division multiplexed optical systems will require extremely stable optical clocks at ultra-high pulse repetition-rates towards the THz scale. Furthermore, arbitrary pulse generators based on OFC [ [18] , [19] ] are seen as one of the most promising solutions for this next generation of high-capacity optical coherent communication systems. This review will summarise the recent exciting achievements in the field of micro-combs, namely optical frequency combs based on high-Q micro-resonators, with a perspective on both the potential of this technology, as well as the open questions and challenges that remain.

We demonstrate optical nonreciprocity based on Kerr interaction of counterpropagating light in whispering gallery microresonators. This effect is used to realize compact optical isolators and circulators with >20 dB isolation.

We study the occurrence of two symmetry breaking processes in ring resonators pumped by short pulses. Different scenarios are predicted depending on the input characteristics, including a complex dynamical interplay between the two mechanisms.

The damped driven nonlinear Schr\"odinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyper-parametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation (LLE), we are led to a new, reduced nonlinear oscillator model which uncovers the essence of the spontaneous creation of sharply peaked pulses in optical resonators. We identify attracting solutions for this model which correspond to stable cavity solitons and Turing patterns, and study their degree of stability. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pattern formation, and represents a novel class of self-synchronization processes in which coupling between nonlinear oscillators is governed by energy and momentum conservation., Comment: This manuscript is published in Physical Review A. Copyright 2017 by the American Physical Society. arXiv admin note: text overlap with arXiv:1602.08523

The Nonlinear interaction between counterpropagating light has attracted significant attention in the context of unidirectional lasing in ring resonators and in nonlinear loop mirrors. In this work we demonstrate that Kerr-nonlinearity-mediated interaction between counterpropagating light in a passive ultra-high-Q microresonator can produce spontaneous symmetry breaking. When sending light of the same frequency, polarisation, and power in counterpropagating directions into a microresonator we observe a resonance frequency splitting such that light will only couple into the resonator in one (randomly chosen) direction.