Phase Symmetry Breaking of Counterpropagating Light in Microresonators for Switches and Logic Gates

Alekhya Ghosh, Arghadeep Pal, Shuangyou Zhang, Lewis Hill, Toby Bi, Pascal Del'Haye

The rapidly growing field of integrated photonics is enabling a large number of novel devices for optical data processing, neuromorphic computing and circuits for quantum photonics. While many photonic devices are based on linear optics, nonlinear responses at low threshold power are of high interest for optical switching and computing. In the case of counterpropagating light, nonlinear interactions can be utilized for chip-based isolators and logic gates. In our work we find a symmetry breaking of the phases of counterpropagating light waves in high-Q ring resonators. This abrupt change in the phases can be used for optical switches and logic gates. In addition to our experimental results, we provide theoretical models that describe the phase symmetry breaking of counterpropagating light in ring resonators.

Linear and Nonlinear Coupling of Twin-Resonators with Kerr Nonlinearity

Arghadeep Pal, Alekhya Ghosh, Shuangyou Zhang, Lewis Hill, Haochen Yan, Hao Zhang, Toby Bi, Abdullah Alabbadi, Pascal Del'Haye

Nonlinear effects in microresonators are efficient building blocks for all-optical computing and telecom systems. With the latest advances in microfabrication, coupled microresonators are used in a rapidly growing number of applications. In this work, we investigate the coupling between twin-resonators in the presence of Kerr-nonlinearity. We use an experimental setup with controllable coupling between two high-Q resonators and discuss the effects caused by the simultaneous presence of linear and non-linear coupling between the optical fields. Linear-coupling-induced mode splitting is observed at low input powers, with the controllable coupling leading to a tunable mode splitting. At high input powers, the hybridized resonances show spontaneous symmetry breaking (SSB) effects, in which the optical power is unevenly distributed between the resonators. Our experimental results are supported by a detailed theoretical model of nonlinear twin-resonators. With the recent interest in coupled resonator systems for neuromorphic computing, quantum systems, and optical frequency comb generation, our work provides important insights into the behavior of these systems at high circulating powers.<br>

Frequency Comb Enhancement via the Self-Crystallization of Vectorial Cavity Solitons

Graeme Neil Campbell, Lewis Hill, Pascal Del'Haye, Gian-Luca Oppo

Long range interactions between dark vectorial temporal cavity solitons are induced though the spontaneous symmetry breaking of orthogonally polarized fields in ring resonators. Turing patterns of alternating polarizations form between adjacent solitons, pushing them apart so that a random distribution of solitons along the cavity length reaches equal equilibrium distances. Enhancement of the frequency comb is achieved through the spontaneous formation of regularly spaced soliton crystals, 'self-crystallization', with greater power and spacing of the spectral lines for increasing soliton numbers.<br>

Symmetry broken vectorial Kerr frequency combs from Fabry-Pérot resonators

Lewis Hill, Eva-Maria Hirmer, Graeme Campbell, Toby Bi, Alekhya Ghosh, Pascal Del'Haye, Gian-Luca Oppo

Spontaneous symmetry breaking of a pair of vector temporal cavity solitons has been established as a paradigm to modulate optical frequency combs, and finds many applications in metrology, frequency standards, communications, and photonic devices. While this phenomenon has successfully been observed in Kerr ring resonators, the counterpart exploiting linear Fabry-Pérot cavities is still unexplored. Here, we consider field polarization properties and describe a vector comb generation through the spontaneous symmetry breaking of temporal cavity solitons within coherently driven, passive, Fabry-Pérot cavities with Kerr nonlinearity. Global coupling effects due to the interactions of counter-propagating light restrict the maximum number of soliton pairs within the cavity - even down to a single soliton pair - and force long range polarization conformity in trains of vector solitons.

Real-time imaging of standing-wave patterns in microresonators

Haochen Yan, Alekhya Ghosh, Arghadeep Pal, Hao Zhang, Toby Bi, George N. Ghalanos, Shuangyou Zhang, Lewis Hill, Yaojing Zhang, et al.

Real-time characterization of microresonator dynamics is important for many applications. In particular, it is critical for near-field sensing and understanding light–matter interactions. Here, we report camera-facilitated imaging and analysis of standing wave patterns in optical ring resonators. The standing wave pattern is generated through bidirectional pumping of a microresonator, and the scattered light from the microresonator is collected by a short-wave infrared (SWIR) camera. The recorded scattering patterns are wavelength dependent, and the scattered intensity exhibits a linear relation with the circulating power within the microresonator. By modulating the relative phase between the two pump waves, we can control the generated standing waves’ movements and characterize the resonator with the SWIR camera. The visualized standing wave enables subwavelength distance measurements of scattering targets with nanometer-level accuracy. This work opens broad avenues for applications in on-chip near-field (bio)sensing, real-time characterization of photonic integrated circuits, and backscattering control in telecom systems.<br>

Controlled light distribution with coupled microresonator chains via Kerr symmetry breaking

Alekhya Ghosh, Arghadeep Pal, Lewis Hill, Graeme N Campbell, Toby Bi, Yaojing Zhang, Abdullah Alabbadi, Shuangyou Zhang, Gian-Luca Oppo, et al.

Within optical microresonators, the Kerr interaction of photons can lead to symmetry breaking of optical modes. In a ring resonator, this leads to the interesting effect that light preferably circulates in one direction or in one polarization state. Applications of this effect range from chip-integrated optical diodes to nonlinear polarization controllers and optical gyroscopes. In this work, we study Kerr-nonlinearity-induced symmetry breaking of light states in coupled resonator optical waveguides (CROWs). We discover a new type of controllable symmetry breaking that leads to emerging patterns of dark and bright resonators within the chains. Beyond stationary symmetry broken states, we observe periodic oscillations, switching and chaotic fluctuations of circulating powers in the resonators. Our findings are of interest for controlled multiplexing of light in photonic integrated circuits, neuromorphic computing, topological photonics and soliton frequency combs in coupled resonators.

Low-Temperature Sputtered Ultralow-Loss Silicon Nitride for Hybrid Photonic Integration

Shuangyou Zhang, Toby Bi, Irina Harder, Olga Ohletz, Florentina Gannott, Alexander Gumann, Eduard Butzen, Yaojing Zhang, Pascal Del'Haye

Silicon-nitride-on-insulator (Si3N4) photonic circuits have seen tremendous advances in many applications, such as on-chip frequency combs, Lidar, telecommunications, and spectroscopy. So far, the best film quality has been achieved with low pressure chemical vapor deposition (LPCVD) and high-temperature annealing (1200°C). However, high processing temperatures pose challenges to the cointegration of Si3N4 with pre-processed silicon electronic and photonic devices, lithium niobate on insulator (LNOI), and Ge-on-Si photodiodes. This limits LPCVD as a front-end-of-line process. Here, ultralow-loss Si3N4 photonics based on room-temperature reactive sputtering is demonstrated. Propagation losses as low as 5.4 dB m−1 after 400°C annealing and 3.5 dB m−1 after 800°C annealing are achieved, enabling ring resonators with highest optical quality factors of > 10 million and an average quality factor of 7.5 million. To the best of the knowledge, these are the lowest propagation losses achieved with low temperature Si3N4. This ultralow loss enables the generation of microresonator soliton frequency combs with threshold powers of 1.1 mW. The introduced sputtering process offers full complementary metal oxide semiconductor (CMOS) compatibility with front-end silicon electronics and photonics. This could enable hybrid 3D integration of low loss waveguides with integrated lasers and lithium niobate on insulator.

Microresonator soliton frequency combs via cascaded Brillouin scattering

Hao Zhang, Shuangyou Zhang, Toby Bi, George N. Ghalanos, Yaojing Zhang, Haochen Yan, Arghadeep Pal, Jijun He, Shilong Pan, et al.

We demonstrate Kerr soliton frequency comb generation that is seeded by a cascaded Brillouin scattering process. In this process, a pump laser is used to generate multiple orders of Brillouin sidebands in a microresonator, which in turn generate the soliton. In such a process, even orders of Brillouin scattering sidebands are co-propagating with respect to the pump laser while odd orders of Brillouin scattering are backwards propagating. In this work we present the generation of forward propagating Kerr solitons via a forward propagating second order Brillouin scattering process in a fused silica rod resonator. Importantly, we show that the Brillouin scattering process can bridge the gap between different microresonator mode families, such that the repetition rate of the Kerr soliton is independent from the Brillouin gain frequency shift (about 10 GHz in fused silica). In our work we demonstrate this by generating soliton pulse trains with a repetition rate of 107 GHz. Our work opens up a new way for using cascaded Brillouin lasing as a seed for microresonator frequency comb generation. This can be of particular interest for the realization of soliton frequency combs with low noise properties from Brillouin lasing while still having arbitrary repetition rates that are determined by the resonator size. Applications range from optical communication to LIDAR systems and photonic signal generation.

Geometry optimization for dark soliton combs in thin multimode silicon nitride microresonators

Yaojing Zhang, Shuangyou Zhang, Toby Bi, Pascal Del'Haye

Silicon nitride (Si3N4) has been well established as an ultralow-loss material for integrated photonics, particularly for the generation of dissipative Kerr soliton frequency combs, enabling various applications for optical metrology, biological imaging, and coherent telecommunications. Typically, bright soliton generation in Si3N4 devices requires thick (>600 nm) films to fulfill the condition of anomalous dispersion at telecom wavelengths. However, thick films of ultralow-loss Si3N4 (>400 nm) often suffer from high internal stress, leading to cracks. As an alternative approach, thin Si3N4 films (<400 nm) provide the advantage of one-step deposition and are widely applied for commercial use. Here, we provide insights into engineering an integrated Si3N4 structure that achieves optimal effective nonlinearity and maintains a compact footprint. A comparative analysis of Si3N4 resonators with varying waveguide thicknesses is conducted and reveals that a 400-nm thin Si3N4 film emerges as a promising solution that strikes a balance among the aforementioned criteria. Based on a commercially available 400-nm Si3N4 film, we experimentally demonstrate the generation of low-noise coherent dark pulses with a repetition rate of 25 GHz in a multimode Si3N4 resonator. The compact spiral-shaped resonator has a footprint of 0.28 mm2 with a high-quality factor of 4 × 106. Our demonstrated dark combs with mode spacings of tens of GHz have applications in microwave photonics, optical spectroscopy, and telecommunication systems.

Four-field symmetry breakings in twin-resonator photonic isomers

Alekhya Ghosh, Lewis Hill, Gian-Luca Oppo , Pascal Del'Haye

Symmetry and symmetry breaking of light states play an important role in photonic integrated circuits and have recently attracted lots of research interest that is relevant to the manipulation of light polarization, telecommunications, all optical computing, and more. We consider four-field symmetry breaking within two different configurations of photonic dimer systems, both comprised of two identical Kerr ring resonators. In each configuration we observe multiple degrees and levels of spontaneous symmetry breaking between circulating photon numbers and further, a wide range of oscillatory dynamics, such as chaos and multiple variations of periodic switching. These dynamics are of interest for optical data processing, optical memories, telecommunication systems, and integrated photonic sensors.

Dark solitons in Fabry-Pérot resonators with Kerr media and normal dispersion

Graeme, N. Campbell, Lewis Hill, Pascal Del'Haye, Gian-Luca Oppo

The ranges of existence and stability of dark cavity-soliton stationary states in a Fabry-Pérot resonator with a Kerr nonlinear medium and normal dispersion are determined. The Fabry-Pérot configuration introduces nonlocal coupling that shifts the cavity detuning by the round trip average power of the intracavity field. When compared with ring resonators described by the Lugiato-Lefever equation, nonlocal coupling leads to strongly detuned dark cavity solitons that exist over a wide range of detunings. This shift is a consequence of the counterpropagation of intracavity fields inherent to Fabry-Pérot resonators. In contrast with ring resonators, the existence and stability of dark soliton solutions are dependent on the size and number of solitons in the cavity. We investigate the effect of nonlocal coupling of Fabry-Pérot resonators on multiple dark solitons, and we demonstrate long-range interactions and synchronization of temporal oscillations.

Multi-stage spontaneous symmetry breaking of light in Kerr ring resonators

Lewis Hill, Gian-Luca Oppo, Pascal Del'Haye

Symmetry breaking of light states is of interest for the understanding of nonlinear optics, photonic circuits, telecom applications and optical pulse generation. Here we demonstrate multi-stage symmetry breaking of the resonances of ring resonators with Kerr nonlinearity. This multi-stage symmetry breaking naturally occurs in a resonator with bidirectionally propagating light with orthogonal polarization components. The derived model used to theoretically describe the system shows that the four circulating field components can display full symmetry, full asymmetry, and multiple versions of partial symmetry, and are later shown to result in complex oscillatory dynamics - such as four-field self-switching, and unusual pulsing with extended delays between subsequent peaks. To highlight a few examples, our work has application in the development of photonic devices like isolators and circulators, logic gates, and random numbers generators, and could also be used for optical-sensors, e.g. by further enhancing the Sagnac effect.

Theory of phase-adaptive parametric cooling

Alekhya Ghosh, Pardeep Kumar, Christian Sommer, Fidel G. Jimenez, Vivishek Sudhir, Claudiu Genes

We propose an adaptive phase technique for the parametric cooling of mechanical oscillators. Our scheme calls for a sequence of periodic adjustments of the phase of a parametric modulation of the mechanical oscillator that is conditioned on measurements of its two quadratures. The technique indicates an exponential loss of thermal energy at initial high occupancies, similar in performance to other optomechanical techniques such as cold-damping or cavity self-cooling. As the quantum ground state is approached, the phase adaptive scheme leads to residual occupancies at the level of a few phonons owing to the competition between parametric amplification of quantum fluctuations and the feedback action.

Quintic Dispersion Soliton Frequency Combs in a Microresonator

Shuangyou Zhang, Toby Bi, Pascal Del'Haye

Chip-scale optical frequency combs have attracted significant research interest and can be used in applications ranging from precision spectroscopy to telecom channel generators and lidar systems. In the time domain, microresonator based frequency combs correspond to self-stabilized soliton pulses. In two distinct regimes, microresonators are shown to emit either bright solitons in the anomalous dispersion regime or dark solitons (a short time of darkness in a bright background signal) in the normal dispersion regime. Here, the dynamics of continuous-wave-laser-driven soliton generation is investigated in the zero-group-velocity-dispersion regime as well as the generation of solitons that are spectrally crossing different dispersion regimes. In the measurements, zero-dispersion solitons with multipeak structures (soliton molecules) are observed with distinct and predictable spectral envelopes that are a result of fifth-order dispersion of the resonators. Numerical simulations and the analysis of bifurcation structures agree well with the observed soliton states. This is the first observation of soliton generation that is governed by fifth-order dispersion, which can have applications in ultrafast optics, telecom systems, and optical spectroscopy.

Electromagnetically induced transparency-like effect in a lithium niobate resonator via electronic control

Liu Yang, Yongyong Zhuang, Yifan Zhang, Yaojing Zhang, Shuangyou Zhang, Zhuo Xu, Pascal Del'Haye, Xiaoyong Wei

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.

On-the-fly precision spectroscopy with a dual-modulated tunable diode laser and Hz-level referencing to a cavity

Shuangyou Zhang, Toby Bi, Pascal Del'Haye

Advances in high-resolution laser spectroscopy have enabled many scientific breakthroughs in physics, chemistry, biology and astronomy. Optical frequency combs have pushed measurement limits with ultrahigh-frequency accuracy and fast-measurement speed while tunable diode laser spectroscopy is used in scenarios that require high power and continuous spectral coverage. Despite these advantages of tunable diode laser spectroscopy, it is challenging to precisely determine the instantaneous frequency of the laser because of fluctuations in the scan speed. Here we demonstrate a simple spectroscopy scheme with a frequency modulated diode laser that references the diode laser on-the-fly to a fiber cavity with sub-15 Hz frequency precision over an 11-THz range at a measurement speed of 1 THz/s. This is an improvement of more than two orders of magnitude compared to existing diode laser spectroscopy methods. Our scheme provides precise frequency calibration markers while simultaneously tracking the instantaneous scan speed of the laser. We demonstrate several applications, including dispersion measurement of an ultra-high-Q microresonator and spectroscopy of an HF gas cell, which can be used for absolute frequency referencing of the tunable diode laser. The simplicity, robustness and low costs of this spectroscopy scheme could prove extremely valuable for out-of-the-lab applications like LIDAR, gas spectroscopy and environmental monitoring.

Machine learning assisted inverse design of microresonators

Arghadeep Pal, Alekhya Ghosh, Shuangyou Zhang, Toby Bi, Pascal Del'Haye

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 yields the best results. The average error on the simulated data is well below 15%.

Proposal for a hybrid clock system consisting of passive and active optical clocks and a fully stabilized microcomb

Deshui Yu, Frank Vollmer, Pascal Del'Haye, Shougang Zhang

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 σy(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 σy(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 σy(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.

Counterpropagating light in ring resonators: Switching fronts, plateaus, and oscillations

Graeme N. Campbell, Shuangyou Zhang, Leonardo Del Bino, Pascal Del'Haye, Gian-Luca Oppo

We characterize the formation of robust stationary states formed by light plateaus separated by two local switching fronts in only one of two counterpropagating fields in ring resonators with normal dispersion. Such states are due to global cross coupling and allow for frequency combs to switch from one field to the other by simply tuning the input laser frequency. Exact expressions for the distance between fronts and for plateau powers are provided in excellent agreement with simulations. These demonstrate an unusual high degree of control over pulse and plateau duration in one of the fields upon changes of one of the input laser frequencies. We identify a wide parameter region in which light plateaus are self-starting and are the only stable solution. For certain values of the detunings we find multistable states of plateaus with switching fronts, slowly oscillating homogeneous states and nonoscillating homogeneous states of the counterpropagating fields. Robustness and multistability of these unusual single-field front solutions are provided in parameter ranges that are experimentally achievable in a wide variety of ring resonators.

Kerr frequency combs: a million ways to fit light pulses into tiny rings

Aurélien Coillet, Shuangyou Zhang, Pascal Del'Haye

Frequency combs can be generated in millimeter-sized optical resonators thanks to their ability to store extremely high light intensities and the nonlinearity of their materials. New frequencies are generated through a cascaded parametric amplification process which can result in various optical waveforms, from ultrastable pulse patterns to optical chaos. These Kerr frequency combs have been studied extensively, with a wealth of fascinating nonlinear dynamics reported, and myriads of applications being developed, ranging from precision spectroscopy and Lidars to telecom channel generators.

Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling

Jonathan M. Silver, Pascal Del'Haye

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.

A Kerr Polarization Controller

Niall Moroney, Leonardo Del Bino, Shuangyou Zhang, Michael T. M. Woodley, Lewis Hill, Thibault Wildi, Valentin J. Wittwer, Thomas Südmeyer, Gian-Luca Oppo, et al.

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operated close to the symmetry-breaking point.

Dark-Bright Soliton Bound States in a Microresonator

Shuangyou Zhang, Toby Bi, George N. Ghalanos, Niall P. Moroney, Leonardo Del Bino, Pascal Del'Haye

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling

Jonathan M. Silver, Pascal Del'Haye

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.

A Kerr Polarization Controller

Niall Moroney, Leonardo Del Bino, Shuangyou Zhang, Michael T. M. Woodley, Lewis Hill, Thibault Wildi, Valentin J. Wittwer, Thomas Südmeyer, Gian-Luca Oppo, et al.

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operated close to the symmetry-breaking point.

Dark-Bright Soliton Bound States in a Microresonator

Shuangyou Zhang, Toby Bi, George N. Ghalanos, Niall P. Moroney, Leonardo Del Bino, Pascal Del'Haye

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Critical dynamics of an asymmetrically bidirectionally pumped optical microresonator

Jonathan M. Silver, Kenneth T. V. Grattan, Pascal Del'Haye

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.

Nonlinear enhanced microresonator gyroscope

Jonathan M. Silver, Leonardo Del Bino, Michael T. M. Woodley, George N. Ghalanos, Andreas O. Svela, Niall Moroney, Shuangyou Zhang, Kenneth T. V. Grattan, Pascal Del'Haye

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. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Self-Switching Kerr Oscillations of Counterpropagating Light in Microresonators

Michael T. M. Woodley, Lewis Hill, Leonardo Del Bino, Gian-Luca Oppo, Pascal Del'Haye

We report the experimental and numerical observation of oscillatory antiphase switching between counterpropagating light beams in Kerr ring microresonators, where dominance between the intensities of the two beams is periodically or chaotically exchanged. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and crossphase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging, which restores the broken symmetry on average. Self-switching of counterpropagating light is robust for realizing controllable, all-optical generation of waveforms, signal encoding, and chaotic cryptography.

suggested by editors

Optical memories and switching dynamics of counterpropagating light states in microresonators

Leonardo Del Bino, Niall Moroney, Pascal Del'Haye

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. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License

Coherent suppression of backscattering in optical microresonators

Andreas Ø. Svela, Jonathan M. Silver, Leonardo Del Bino, Shuangyou Zhang, Michael T. M. Woodley, Michael R. Vanner, Pascal Del'Haye

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 the backscattering is essential. We demonstrate that introducing an additional scatterer in the near-field of a high-quality-factor microresonator can coherently suppress the amount of backscattering in a microresonator by more than 30 dB. The method relies on controlling the scatterer's position in order for the intrinsic and scatterer-induced backpropagating fields to 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 that both suffer from injection locking. Moreover, these findings are of interest for integrated photonic circuits in which backreflections could negatively impact the stability of laser sources or other components.

Spectral extension and synchronization of microcombs in a single microresonator

Shuangyou Zhang, Jonathan M. Silver, Toby Bi, Pascal Del'Haye

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.

Logic Gates Based on Interaction of Counterpropagating Light in Microresonators

Niall Moroney, Leonardo Del Bino, Michael T. M. Woodley, George N. Ghalanos, Jonathan M. Silver, Andreas O. Svela, Shuangyou Zhang, Pascal Del'Haye

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 Q-factor of 2 x 10(8). This method of optical logic gives a practical solution to the on-chip routing of light.

Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators

Lewis Hill, Gian-Luca Oppo, Michael T. M. Woodley, Pascal Del'Haye

Spontaneous symmetry breaking can occur in the powers of two optical modes coupled into a ring resonator, described by a pair of coupled Lorentzian equations, and featuring tunable self- and cross-phase modulation terms. Investigated is 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- and 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 generalized 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.

Critical Dynamics of an Asymmetrically Bidirectionally Pumped Optical Microresonator

Jonathan M. Silver, Kenneth T. V. Grattan, Pascal Del'Haye

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.

Terahertz wave generation using a soliton microcomb

Shuangyou Zhang, Jonathan Silver, Xiaobang Shang, Leonardo Del Bino, Nick Ridler, Pascal Del'Haye

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. 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 4.5x10(-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 9.6x10(-15) and 1.9x10(-17) are obtained at averaging times of 1 s and 2000 s respectively, indicating that the stability of the generated THz wave is 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. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License.

Thermo-optical pulsing in a microresonator filtered fiber-laser: a route towards all-optical control and synchronization

Maxwell Rowley, Benjamin Wetzel, Luigi Di Lauro, Juan S. Totero Gongora, Hualong Bao, Jonathan Silver, Leonardo Del Bino, Pascal Del'Haye, Marco Peccianti, et al.

We report on 'slow' pulsing dynamics in a silica resonator-based laser system: by nesting a high-Q rod-resonator inside an amplifying fiber cavity, we demonstrate that trains of microsecond pulses can be generated with repetition rates in the hundreds of kilohertz. We show that such pulses are produced with a period equivalent to several hundreds of laser cavity roundtrips via the interaction between the gain dynamics in the fiber cavity and the thermo-optical effects in the high-Q resonator. Experiments reveal that the pulsing properties can be controlled by adjusting the amplifying fiber cavity parameters. Our results, confirmed by numerical simulations, provide useful insights on the dynamical onset of complex self-organization phenomena in resonator-based laser systems where thermo-optical effects play an active role. In addition, we show how the thermal state of the resonator can be probed and even modified by an external, counter-propagating optical field, thus hinting towards novel approaches for all-optical control and sensing applications. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Sub-milliwatt-level microresonator solitons with extended access range using an auxiliary laser

Shuangyou Zhang, Jonathan M. Silver, Leonardo Del Bino, Francois Copie, Michael T. M. Woodley, George N. Ghalanos, Andreas O. Svela, Niall Moroney, Pascal Del'Haye

The recent demonstration of dissipative Kerr solitons in microresonators has opened a new pathway for the generation of ultrashort pulses and low-noise frequency combs with gigahertz to terahertz repetition rates, enabling applications in frequency metrology, astronomy, optical coherent communications, and laser-based ranging. A main challenge for soliton generation, in particular in ultra-high-Q resonators, is the sudden change in circulating intracavity power during the onset of soliton generation. This sudden power change requires precise control of the seed laser frequency and power or fast control of the resonator temperature. Here, we report a robust and simple way to increase the soliton access window by using an auxiliary laser that passively stabilizes intracavity power. In our experiments with fused silica resonators, we are able to extend the access range of microresonator solitons by two orders of magnitude, which enables soliton generation by slow and manual tuning of the pump laser into resonance and at unprecedented low power levels. Importantly, this scheme eliminates the sudden change in circulating power ("soliton step") during transition into the soliton regime. Both single-and multi-soliton mode-locked states are generated in a 1.3-mm-diameter fused silica microrod resonator with a free spectral range of similar to 50.6 GHz, at a 1554 nm pump wavelength at threshold powers <3 mW. Moreover, with a smaller 230-mu m-diameter microrod, we demonstrate soliton generation at 780 mu W threshold power. The passive enhancement of the soliton access range paves the way for robust and low-threshold microcomb systems and has the potential to be a practical tool for soliton microcomb generation.

Observation of Brillouin optomechanical strong coupling with an 11 GHz mechanical mode

G. Enzian, M. Szczykulska, J. Silver, L. Del Bino, S. Zhang, I. A. Walmsley, P. Del'Haye, M. R. Vanner

Achieving cavity-optomechanical strong coupling with high-frequency phonons provides a rich avenue for quantum technology development, including quantum state transfer, memory, and transduction, as well as enabling several fundamental studies of macroscopic phononic degrees of freedom. Reaching such coupling with GHz mechanical modes, however, has proved challenging, with a prominent hindrance being material- and surface-induced optical absorption in many materials. Here, we circumvent these challenges and report the observation of optomechanical strong coupling to a high-frequency (11 GHz) mechanical mode of a fused-silica whispering-gallery microresonator via the electrostrictive Brillouin interaction. Using an optical heterodyne detection scheme, the anti-Stokes light back-scattered from the resonator is measured, and normal-mode splitting and an avoided crossing are observed in the recorded spectra, providing unambiguous signatures of strong coupling. The optomechanical coupling rate reaches values as high as G/2 pi=39 MHz through the use of an auxiliary pump resonance, where the coupling dominates both optical (kappa/2 pi = 3 MHz) and mechanical (gamma(m)/2 pi = 21 MHz) amplitude decay rates. Our findings provide a promising new approach for optical quantum control using light and sound.

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Francois Copie, Michael T. M. Woodley, Leonardo Del Bino, Jonathan M. Silver, Shuangyou Zhang, Pascal Del'Haye

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 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.

Uniform Thin Films on Optical Fibers by Plasma-Enhanced Chemical Vapor Deposition: Fabrication, Mie Scattering Characterization, and Application to Microresonators

Zeba Naqvi, Mark Green, Krista Smith, Chaofan Wang, Pascal Del'Haye, Tsing-Hua Her

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 SiNx 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.

Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators

Michael T. M. Woodley, Jonathan M. Silver, Lewis Hill, Francois Copie, Leonardo Del Bino, Shuangyou Zhang, Gian-Luca Oppo, Pascal Del'Haye

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry-breaking mechanism in electrodynamics occurs between counterpropagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counterpropagating light in bidirectionally pumped microresonators finds application in the realization of optical nonreciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counterpropagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr interaction of counterpropagating light in a dielectric ring resonator. In particular, we study discontinuous behavior in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realize, for example, highly sensitive near-field or rotation sensors. We then generalize to a time-dependent model, which predicts different types of dynamical behavior, 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 polarization in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

μW-Level Microresonator Solitons with Extended Stability Range Using an Auxiliary Laser

Shuangyou Zhang, Jonathan M. Silver, Leonardo Del Bino, Francois Copie, Michael Woodley, George Ghalanos, Andreas Svela, Niall Moroney, Pascal Del'Haye

The recent demonstration of dissipative Kerr solitons in microresonators has opened a new pathway for the generation of ultrashort pulses and low-noise frequency combs with gigahertz to terahertz repetition rates, enabling applications in frequency metrology, astronomy, optical coherent communications, and laser-based ranging. A main challenge for soliton generation, in particular in ultra-high-Q resonators, is the sudden change of circulating intracavity power during the onset of soliton generation. This sudden power change requires precise control of the seed laser frequency and power or fast control of the resonator temperature. Here, we report a robust and simple way to increase the stability range of the soliton regime by using an auxiliary laser that passively stabilizes the intracavity power. In our experiments with fused silica resonators, we are able to extend the pump laser frequency stability range of microresonator solitons by two orders of magnitude, which enables soliton generation by slow and manual tuning of the pump laser into resonance and at unprecedented low power levels. Both single- and multi-soliton mode-locked states are generated in a 1.3-mm-diameter fused silica microrod resonator with a free spectral range of ~50.6 GHz, at a 1554 nm pump wavelength at threshold powers <3 mW. Moreover, with a smaller 230-{\mu}m-diameter microrod, we demonstrate soliton generation at 780 {\mu}W threshold power. The passive enhancement of the stability range of microresonator solitons paves the way for robust and low threshold microcomb systems with substantially relaxed stability requirements for the pump laser source. In addition, this method could be useful in a wider range of microresonator applications that require reduced sensitivity to external perturbations.

Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr effect

Leonardo Del Bino, Jonathan M. Silver, Michael T. M. Woodley, Sarah L. Stebbings, Xin Zhao, Pascal Del'Haye

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, resulting in light of a given frequency circulating 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 > 24 dB and develop a theoretical model for the power scaling of the attainable nonreciprocity. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Micro-combs: A novel generation of optical sources

Alessia Pasquazi, Marco Peccianti, Luca Razzari, David J. Moss, Stephane Coen, Miro Erkintalo, Yanne K. Chembo, Tobias Hansson, Stefan Wabnitz, et al.

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 [1-5]. 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 [61 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 [7-13] but also of optical sensors and compact light modulators [6,14].<br> In this framework, the demonstration of planar high-Q resonators, compatible with silicon technology [10-14], 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 [15-17]; 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.<br> Many information technology industries have recently focused on the development of integrated ring resonators to be employed for electrically-controlled light modulators [ 1417], greatly advancing the maturity of micro-resonator technology as a whole. Recently [11-13], 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. (C) 2017 The Author(s). Published by Elsevier B.V.

Soliton crystals in Kerr resonators

Daniel C. Cole, Erin S. Lamb, Pascal Del'Haye, Scott A. Diddams, Scott B. Papp

Self-organized solitons confined to an optical resonator would offer unique capabilities for experiments in communication, computation and sensing with light. Here, we report the observation of soliton crystals in monolithic Kerr microresonators-spontaneously and collectively ordered ensembles of co-propagating solitons whose interactions discretize their allowed temporal separations. We unambiguously identify and characterize soliton crystals through analysis of their 'fingerprint' optical spectra, which arise from spectral interference between the solitons. We identify a rich space of soliton crystals exhibiting crystallographic defects and we perform time-domain measurements to directly confirm our inference of their crystal structure. Soliton crystallization is explained by long-range soliton interactions mediated by resonator mode degeneracies, and we probe the qualitative difference between soliton crystals and the disorganized soliton liquid that would form in the absence of these interactions. Our work explores the physics of monolithic Kerr resonators in a regime of dense soliton occupation and offers a way to increase the efficiency of Kerr combs. Furthermore, the extreme degeneracy of the configuration space of soliton crystals suggests an implementation for an on-chip optical buffer.

Self-synchronization phenomena in the Lugiato-Lefever equation

Hossein Taheri, Pascal Del'Haye, Ali A. Eftekhar, Kurt Wiesenfeld, Ali Adibi

The damped driven nonlinear Schrodinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyperparametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation, we are led to a reduced nonlinear oscillator model that 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 class of self-synchronization processes in which coupling between nonlinear oscillators is governed by energy and momentum conservation.

Electronic synthesis of light

Katja Beha, Daniel C. Cole, Pascal Del'Haye, Aurelien Coillet, Scott A. Diddams, Scott B. Papp

We report on bidirectional frequency conversion between the microwave and optical domains using electro-optics. Advances in communications, time keeping, and quantum sensing have all come to depend upon the coherent interoperation of light wave and microwave signals. To connect these domains, which are separated by a factor of 10,000 in frequency, requires specialized technology that has until now only been achieved by ultrafast mode-locked lasers. In contrast, electro-optic modulation (EOM) combs arise deterministically by imposing microwave-rate oscillations on a continuous-wave laser. Here we demonstrate electro-optic generation of a 160 THz bandwidth super-continuum and realize f-2f self-referencing. Coherence of the supercontinuum is achieved through optical filtering of electronic noise on the seed EOM comb. The mode frequencies of the supercontinuum are derived from the electronic oscillator and they achieve < 5 x 10(-14) fractional accuracy and stability, which opens a novel regime for tunable combs with wide mode spacing apart from the requirements of mode locking.

Kerr superoscillator model for microresonator frequency combs

Jonathan M. Silver, Changlei Guo, Leonardo Del Bino, Pascal Del'Haye

Microresonator-based optical frequency combs ("microcombs") have attracted lots of attention in the past few years thanks to their promising applications in telecommunications, spectroscopy, and optical clocks. The process of comb generation in microresonators can be modeled in the frequency domain using coupled mode equations and has recently been successfully described in the time domain using a nonlinear Schrodinger equation known as the Lugiato-Lefever equation. Time-domain approaches have brought many interesting insights for the understanding of microcombs. In this paper we present an intuitive frequency-domain model of microcombs that describes the overall structure of the spectra in terms of a few collective excitations of groups of neighboring comb lines, which we term "superoscillators." This approach ties in nicely with the recently developed time-domain model based on soliton crystals and links the microcomb generation process with frequency response theory.

Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator

Leonardo Del Bino, Jonathan M. Silver, Sarah L. Stebbings, Pascal Del'Haye

Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) states of light to circulate in the resonator. Equivalently, this effect can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.

Roadmap on ultrafast optics

Derryck T. Reid, Christoph M. Heyl, Robert R. Thomson, Rick Trebino, Guenter Steinmeyer, Helen H. Fielding, Ronald Holzwarth, Zhigang Zhang, Pascal Del'Haye, et al.

The year 2015 marked the 25th anniversary of modern ultrafast optics, since the demonstration of the first Kerr lens modelocked Ti:sapphire laser in 1990 (Spence et al 1990 Conf. on Lasers and Electro-Optics, CLEO, pp 619-20) heralded an explosion of scientific and engineering innovation. The impact of this disruptive technology extended well beyond the previous discipline boundaries of lasers, reaching into biology labs, manufacturing facilities, and even consumer healthcare and electronics. In recognition of such a milestone, this roadmap on Ultrafast Optics draws together articles from some of the key opinion leaders in the field to provide a freeze-frame of the state-of-the-art, while also attempting to forecast the technical and scientific paradigms which will define the field over the next 25 years. While no roadmap can be fully comprehensive, the thirteen articles here reflect the most exciting technical opportunities presented at the current time in Ultrafast Optics. Several articles examine the future landscape for ultrafast light sources, from practical solid-state/fiber lasers and Raman microresonators to exotic attosecond extreme ultraviolet and possibly even zeptosecond x-ray pulses. Others address the control and measurement challenges, requiring radical approaches to harness nonlinear effects such as filamentation and parametric generation, coupled with the question of how to most accurately characterise the field of ultrafast pulses simultaneously in space and time. Applications of ultrafast sources in materials processing, spectroscopy and time-resolved chemistry are also discussed, highlighting the improvements in performance possible by using lasers of higher peak power and repetition rate, or by exploiting the phase stability of emerging new frequency comb sources.

Phase-coherent microwave-to-optical link with a self-referenced microcomb

Pascal Del'Haye, Aurelien Coillet, Tara Fortier, Katja Beha, Daniel C. Cole, Ki Youl Yang, Hansuek Lee, Kerry J. Vahala, Scott B. Papp, et al.

Precise measurements of the frequencies of light waves have become common with mode-locked laser frequency combs(1). 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(2). Such advances will significantly impact fields ranging from spectroscopy and trace gas sensing(3) to astronomy(4), communications(5) and atomic time-keeping(6,7). Yet, in spite of the remarkable progress shown over recent years(8-10), microresonator frequency combs ('microcombs') have been without the key function of direct f-2f self-referencing(1), 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.

Broadband dispersion-engineered microresonator on a chip

Ki Youl Yang, Katja Beha, Daniel C. Cole, Xu Yi, Pascal Del'Haye, Hansuek Lee, Jiang Li, Dong Yoon Oh, Scott A. Diddams, et al.

The control of dispersion in fibre optical waveguides is of critical importance to optical fibre communications systems(1,2) and more recently for continuum generation from the ultraviolet to the mid-infrared(3-5). The wavelength at which the group velocity dispersion crosses zero can be set by varying the fibre core diameter or index step(2,6-8). Moreover, sophisticated methods to manipulate higher-order dispersion so as to shape and even flatten the dispersion over wide bandwidths are possible using multi-cladding fibres(9-11). Here we introduce design and fabrication techniques that allow analogous dispersion control in chip-integrated optical microresonators, and thereby demonstrate higher-order, wide-bandwidth dispersion control over an octave of spectrum. Importantly, the fabrication method we employ for dispersion control simultaneously permits optical Q factors above 100 million, which is critical for the efficient operation of nonlinear optical oscillators. Dispersion control in high-Q systems has become of great importance in recent years with increased interest in chip-integrable optical frequency combs(12-32).

Self-synchronization of Kerr-nonlinear Optical Parametric Oscillators

Hossein Taheri, Pascal Del'Haye, Ali A. Eftekhar, Kurt Wiesenfeld, Ali Adibi

We introduce a new, reduced nonlinear oscillator model governing the spontaneous creation of sharp pulses in a damped, driven, cubic nonlinear Schroedinger equation. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pulse formation. We identify attracting solutions corresponding to stable cavity solitons and Turing patterns. Viewed in the optical context, our results explain the recently reported π and π/2 steps in the phase spectrum of microresonator-based optical frequency combs.

Self-referencing a continuous-wave laser with electro-optic modulation

Katja Beha, Daniel C. Cole, Pascal Del'Haye, Aurélien Coillet, Scott A. Diddams, Scott B. Papp

We phase-coherently measure the frequency of continuous-wave (CW) laser light by use of optical-phase modulation and f-2f nonlinear interferometry. Periodic electro-optic modulation (EOM) transforms the CW laser into a continuous train of picosecond optical pulses. Subsequent nonlinear-fiber broadening of this EOM frequency comb produces a supercontinuum with 160 THz of bandwidth. A critical intermediate step is optical filtering of the EOM comb to reduce electronic-noise-induced decoherence of the supercontinuum. Applying f-2f self-referencing with the supercontinuum yields the carrier-envelope offset frequency of the EOM comb, which is precisely the difference of the CW laser frequency and an exact integer multiple of the EOM pulse repetition rate. Here we demonstrate absolute optical frequency metrology and synthesis applications of the self-referenced CW laser with <5E-14 fractional accuracy and stability.

Phase steps and resonator detuning measurements in microresonator frequency combs (vol 6, 5668, 2015)

Pascal Del'Haye, Aurelien Coillet, William Loh, Katja Beha, Scott B. Papp, Scott A. Diddams

Phase steps and resonator detuning measurements in microresonator frequency combs

Pascal Del'Haye, Aurelien Coillet, William Loh, Katja Beha, Scott B. Papp, Scott A. Diddams

Experiments and theoretical modelling yielded significant progress toward understanding of Kerr-effect induced optical frequency comb generation in microresonators. However, the simultaneous Kerr-mediated interaction of hundreds or thousands of optical comb frequencies with the same number of resonator modes leads to complicated nonlinear dynamics that are far from fully understood. An important prerequisite for modelling the comb formation process is the knowledge of phase and amplitude of the comb modes as well as the detuning from their respective microresonator modes. Here, we present comprehensive measurements that fully characterize optical microcomb states. We introduce a way of measuring resonator dispersion and detuning of comb modes in a hot resonator while generating an optical frequency comb. The presented phase measurements show unpredicted comb states with discrete pi and pi/2 steps in the comb phases that are not observed in conventional optical frequency combs.

Microresonator frequency comb optical clock

Scott B. Papp, Katja Beha, Pascal Del'Haye, Franklyn Quinlan, Hansuek Lee, Kerry J. Vahala, Scott A. Diddams

Optical frequency combs serve as the clockwork of optical clocks, which are now the best time-keeping systems in existence. The use of precise optical time and frequency technology in various applications beyond the research lab remains a significant challenge, but one that integrated microresonator technology is poised to address. Here, we report a silicon-chip-based microresonator comb optical clock that converts an optical frequency reference to a microwave signal. A comb spectrum with a 25 THz span is generated with a 2 mm diameter silica disk and broadening in nonlinear fiber. This spectrum is stabilized to rubidium frequency references separated by 3.5 THz by controlling two teeth 108 modes apart. The optical clock's output is the electronically countable 33 GHz microcomb line spacing, which features stability better than the rubidium transitions by the expected factor of 108. Our work demonstrates the comprehensive set of tools needed for interfacing microcombs to state-of-the-art optical clocks.

Phase and coherence of optical microresonator frequency combs

William Loh, Pascal Del'Haye, Scott B. Papp, Scott A. Diddams

We use a combination of theoretical analysis, numerical simulation, and experimental measurement to investigate the near-threshold phase and coherence properties of parametric optical frequency combs generated in low-loss dielectric microresonators. Our analysis reveals that near threshold the phases of the comb lines do not stabilize to a constant value across the spectrum, although well-defined phase relationships relative to the pump laser do exist. Our results are supported by numerical simulations of two different microresonator combs operated under varying conditions of input drive, dispersion, and detuning. These results are also experimentally confirmed through phase measurements of the individual comb lines. We also investigate the processes leading to the breakdown of the equidistant frequency spacing of the modes in a microresonator comb.

Self-Injection Locking and Phase-Locked States in Microresonator-Based Optical Frequency Combs

Pascal Del'Haye, Katja Beha, Scott B. Papp, Scott A. Diddams

Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results that show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are phase stable but have nondeterministic phase relationships between individual comb modes.

Parametric seeding of a microresonator optical frequency comb

Scott B. Papp, Pascal Del'Haye, Scott A. Diddams

We have investigated parametric seeding of a microresonator frequency comb (microcomb) by way of a pump laser with two electrooptic-modulation sidebands. We show that the pump-sideband spacing is precisely replicated throughout the microcomb's optical spectrum, and we demonstrate a record absolute line-spacing stability for microcombs of 1.6 x 10(-13) at 1 s. The spectrum of a microcomb is complex, and often non-equidistant subcombs are observed. Our results demonstrate that parametric seeding can not only control the subcombs, but can lead to the generation of a strictly equidistant microcomb spectrum. (C) 2013 Optical Society of America

Mechanical Control of a Microrod-Resonator Optical Frequency Comb

Scott B. Papp, Pascal Del'Haye, Scott A. Diddams

We report on the stabilization of a microresonator-based optical frequency comb (microcomb) by way of mechanical actuation. These experiments use novel CO2-laser-machined microrod resonators, which are introduced here and feature optical Q >= 5 x 10(8), less than 1 minute processing time, and tunable geometry. Residual fluctuations of our 32.6 GHz microcomb line spacing reach a stability level of 5 x 10(-15) for 1 s averaging, thereby highlighting the potential of microcombs to support modern optical-frequency standards. Furthermore, measurements of the line spacing with respect to an independent frequency reference reveal stabilization of different spectral slices of the comb with a <0.5-mHz variation among 140 comb lines spanning 4.5 THz. Together, these results demonstrate an important step in the development of microcombs, namely, that they can be fabricated and precisely controlled with simple and accessible techniques.

Laser-machined ultra-high-Q microrod resonators for nonlinear optics

Pascal Del'Haye, Scott A. Diddams, Scott B. Papp

Optical whispering-gallery microresonators are useful tools in microphotonics and non-linear optics at very low threshold powers. Here, we present details about the fabrication of ultra-high-Q whispering-gallery-mode resonators made by CO2-laser lathe machining of fused-quartz rods. The resonators can be fabricated in less than 1 min and the obtained optical quality factors exceed Q = 1 x 10(9). Demonstrated resonator diameters are in the range between 170 mu m and 8mm (free spectral ranges between 390 GHz and 8 GHz). Using these microresonators, a variety of optical nonlinearities are observed, including Raman scattering, Brillouin scattering, and four-wave mixing.

Mid-infrared optical frequency combs at 2.5 µm based on crystalline microresonators

Christine Y. Wang, Tobias Herr, Pascal Del'Haye, Albert Schliesser, Johannes Hofer, Ronald Holzwarth, T. W. Hänsch, Nathalie Picqué, Tobias J. Kippenberg

The mid-infrared spectral range (λ~2–20 μm) is of particular importance as many molecules exhibit strong vibrational fingerprints in this region. Optical frequency combs—broadband optical sources consisting of equally spaced and mutually coherent sharp lines—are creating new opportunities for advanced spectroscopy. Here we demonstrate a novel approach to create mid-infrared optical frequency combs via four-wave mixing in a continuous-wave pumped ultra-high Q crystalline microresonator made of magnesium fluoride. Careful choice of the resonator material and design made it possible to generate a broadband, low-phase noise Kerr comb at λ=2.5 μm spanning 200 nm (≈10 THz) with a line spacing of 100 GHz. With its distinguishing features of compactness, efficient conversion, large mode spacing and high power per comb line, this novel frequency comb source holds promise for new approaches to molecular spectroscopy and is suitable to be extended further into the mid-infrared.

Hybrid Electro-Optically Modulated Microcombs

Pascal Del'Haye, Scott B. Papp, Scott A. Diddams

Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microresonators ("microcombs") has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: Combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spanning spectra but mode spacings beyond electronic detection limits. However, it has not yet been possible to achieve these two key requirements simultaneously, as will be critical for most microcomb applications. Here we present a route to overcome this problem by interleaving an electro-optic comb with the spectrum from a parametric microcomb. This allows, for the first time, direct control and stabilization of a microcomb spectrum with large mode spacing (>140 GHz) with no need for an additional mode-locked laser frequency comb. The attained residual 1-sec instability of the microcomb comb spacing is 10(-15), with a microwave reference limited absolute instability of 10(-12) at a 140 GHz mode spacing. DOI: 10.1103/PhysRevLett.109.263901

Octave Spanning Tunable Frequency Comb from a Microresonator

Pascal Del'Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, Ronald Holzwarth, Tobias J. Kippenberg

We report the generation of an octave-spanning optical frequency comb in a continuous wave laser pumped microresonator. The generated comb spectrum covers the wavelength range from 990 to 2170 nm without relying on additional external broadening. Continuous tunability of the generated frequency comb over more than an entire free spectral range is demonstrated. Moreover, the linewidth of individual optical comb components and its relation to the pump laser phase noise is studied. The ability to derive octave-spanning spectra from microresonator comb generators represents a key step towards f-2f self-referencing of microresonator-based optical frequency combs.

Octave Spanning Tunable Frequency Comb from a Microresonator

Pascal Del'Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, Ronald Holzwarth, Tobias J. Kippenberg

Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion

Pascal Del'Haye, Olivier Arcizet, Michael L. Gorodetsky, Ronald Holzwarth, Tobias J. Kippenberg

Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion

Pascal Del'Haye, Olivier Arcizet, Michael L. Gorodetsky, Ronald Holzwarth, Tobias J. Kippenberg

Although invented for precision measurements of single atomic transitions, frequency combs have also become a versatile tool for broadband spectroscopy in recent years. Here, we present a novel and simple approach for broadband spectroscopy, combining the accuracy of an optical fibre-laser-based frequency comb with the ease of use of a tunable external cavity diode laser. The scheme enables broadband and fast spectroscopy of more than 4 THz bandwidth at scanning speeds up to 1 THz s(-1) at sub-MHz resolution. We use this method for spectroscopy of microresonator modes and precise measurements of their dispersion, which is relevant in the context of broadband optical frequency comb generation, having recently been demonstrated in these devices. Moreover, we find excellent agreement between measured microresonator dispersion with predicted values from finite element simulations, and we show that microresonator dispersion can be tailored by adjusting their geometrical properties.

Full Stabilization of a Microresonator-Based Optical Frequency Comb

Pascal Del'Haye, Olivier Arcizet, Albert Schliesser, Ronald Holzwarth, Tobias J. Kippenberg

We demonstrate control and stabilization of an optical frequency comb generated by four-wave mixing in a monolithic microresonator with a mode spacing in the microwave regime (86 GHz). The comb parameters (mode spacing and offset frequency) are controlled via the power and the frequency of the pump laser, which constitutes one of the comb modes. Furthermore, generation of a microwave beat note at the comb's mode spacing frequency is demonstrated, enabling direct stabilization to a microwave frequency standard.

Full Stabilization of a Microresonator-Based Optical Frequency Comb

Pascal Del'Haye, Olivier Arcizet, Albert Schliesser, Ronald Holzwarth, Tobias J. Kippenberg

Optical frequency comb generation from a monolithic microresonator

Pascal Del'Haye, A. Schließer, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg

Optical frequency combs(1-3) provide equidistant frequency markers in the infrared, visible and ultraviolet(4,5), and can be used to link an unknown optical frequency to a radio or microwave frequency reference(6,7). Since their inception, frequency combs have triggered substantial advances in optical frequency metrology and precision measurements(6,7) and in applications such as broadband laser- based gas sensing(8) and molecular fingerprinting(9). Early work generated frequency combs by intra- cavity phase modulation(10,11); subsequently, frequency combs have been generated using the comb- like mode structure of mode- locked lasers, whose repetition rate and carrier envelope phase can be stabilized(12). Here we report a substantially different approach to comb generation, in which equally spaced frequency markers are produced by the interaction between a continuous- wave pump laser of a known frequency with the modes of a monolithic ultra- high- Q microresonator(13) via the Kerr nonlinearity(14,15). The intrinsically broadband nature of parametric gain makes it possible to generate discrete comb modes over a 500- nm- wide span (similar to 70 THz) around 1,550 nm without relying on any external spectral broadening. Optical- heterodyne- based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3 x 10(-18). In contrast to femtosecond mode- locked lasers(16), this work represents a step towards a monolithic optical frequency comb generator, allowing considerable reduction in size, complexity and power consumption. Moreover, the approach can operate at previously unattainable repetition rates(17), exceeding 100 GHz, which are useful in applications where access to individual comb modes is required, such as optical waveform synthesis(18), high capacity telecommunications or astrophysical spectrometer calibration(19).

Optical frequency comb generation from a monolithic microresonator

P. Del'Haye, A. Schließer, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg

Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres

R. Ma, Albert Schließer, Pascal Del'Haye, A. Dabirian, Georg Anetsberger, Tobias J. Kippenberg

Quantitative measurements of the vibrational eigenmodes in ultrahigh-Q silica microspheres are reported. The modes are excited via radiation-pressure-induced dynamical backaction of light confined in the optical whispering-gallery modes of the microspheres (i.e., via the parametric oscillation instability). Two families of modes are studied and their frequency dependence on sphere size investigated. The measured frequencies are in good agreement both with Lamb's theory and numerical finite-element simulation and are found to be proportional to the sphere's inverse diameter. In addition, the quality factors of the vibrational modes are studied. (C) 2007 Optical Society of America.

Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres

R. Ma, Albert Schließer, Pascal Del'Haye, A. Dabirian, Georg Anetsberger, Tobias J. Kippenberg

Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction

Albert Schliesser, Pascal Del'Haye, Nima Nooshi, K. J. Vahala, Tobias Kippenberg

Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction

Albert Schliesser, Pascal Del'Haye, Nima Nooshi, K. J. Vahala, Tobias Kippenberg

Cooling of a 58 MHz micromechanical resonator from room temperature to 11 K is demonstrated using cavity enhanced radiation pressure. Detuned pumping of an optical resonance allows enhancement of the blueshifted motional sideband (caused by the oscillator's Brownian motion) with respect to the redshifted sideband leading to cooling of the mechanical oscillator mode. The reported cooling mechanism is a manifestation of the effect of radiation pressure induced dynamical backaction. These results constitute an important step towards achieving ground state cooling of a mechanical oscillator.