Linear and Nonlinear Coupling of TwinResonators with Kerr Nonlinearity
Arghadeep Pal, Alekhya Ghosh, Shuangyou Zhang, Lewis Hill, Haochen Yan, Hao Zhang, Toby Bi, Abdullah Alabbadi, Pascal Del'Haye
https://arxiv.org/abs/2404.05646
(2024)
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Nonlinear effects in microresonators are efficient building blocks for<br>alloptical computing and telecom systems. With the latest advances in<br>microfabrication, coupled microresonators are used in a rapidly growing number<br>of applications. In this work, we investigate the coupling between<br>twinresonators in the presence of Kerrnonlinearity. We use an experimental<br>setup with controllable coupling between two highQ resonators and discuss the<br>effects caused by the simultaneous presence of linear and nonlinear coupling<br>between the optical fields. Linearcouplinginduced mode splitting is observed<br>at low input powers, with the controllable coupling leading to a tunable mode<br>splitting. At high input powers, the hybridized resonances show spontaneous<br>symmetry breaking (SSB) effects, in which the optical power is unevenly<br>distributed between the resonators. Our experimental results are supported by a<br>detailed theoretical model of nonlinear twinresonators. With the recent<br>interest in coupled resonator systems for neuromorphic computing, quantum<br>systems, and optical frequency comb generation, our work provides important<br>insights into the behavior of these systems at high circulating powers.<br>
Frequency Comb Enhancement via the SelfCrystallization of Vectorial Cavity Solitons
Graeme Neil Campbell, Lewis Hill, Pascal Del'Haye, GianLuca Oppo
https://arxiv.org/abs/2403.16547
(2024)
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Long range interactions between dark vectorial temporal cavity solitons are<br>induced though the spontaneous symmetry breaking of orthogonally polarized<br>fields in ring resonators. Turing patterns of alternating polarizations form<br>between adjacent solitons, pushing them apart so that a random distribution of<br>solitons along the cavity length reaches equal equilibrium distances.<br>Enhancement of the frequency comb is achieved through the spontaneous formation<br>of regularly spaced soliton crystals, 'selfcrystallization', with greater<br>power and spacing of the spectral lines for increasing soliton numbers.<br>
Symmetry broken vectorial Kerr frequency combs from FabryPérot resonators
Lewis Hill, EvaMaria Hirmer, Graeme Campbell, Toby Bi, Alekhya Ghosh, Pascal Del'Haye, GianLuca Oppo
Communications Physics
7
82
(2024)

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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 FabryPérot 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, FabryPérot cavities with Kerr nonlinearity. Global coupling effects due to the interactions of counterpropagating 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.
Realtime imaging of standingwave patterns in microresonators
Haochen Yan, Alekhya Ghosh, Arghadeep Pal, Hao Zhang, Toby Bi, George N. Ghalanos, Shuangyou Zhang, Lewis Hill, Yaojing Zhang, et al.
Realtime characterization of microresonator dynamics is important for many applications. In<br>particular it is critical for nearfield sensing and understanding lightmatter interactions. Here,<br>we report camerafacilitated imaging and analysis of standing wave patterns in optical ring<br>resonators. The standing wave pattern is generated through bidirectional pumping of a<br>microresonator and the scattered light from the microresonator is collected by a shortwave<br>infrared (SWIR) camera. The recorded scattering patterns are wavelength dependent, and the<br>scattered intensity exhibits a linear relation with the circulating power within the microresonator.<br>By modulating the relative phase between the two pump waves, we can control the generated<br>standing waves’ movements and characterize the resonator with the SWIR camera. The<br>visualized standing wave enables subwavelength distance measurements of scattering targets<br>with nanometerlevel accuracy. This work opens new avenues for applications in onchip nearfield<br>(bio)sensing, real time characterization of photonic integrated circuits and backscattering<br>control in telecom systems.
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, GianLuca Oppo, et al.
https://arxiv.org/abs/2402.10673
(2024)
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Within optical microresonators, the Kerr interaction of photons can lead to<br>symmetry breaking of optical modes. In a ring resonator, this leads to the<br>interesting effect that light preferably circulates in one direction or in one<br>polarization state. Applications of this effect range from chipintegrated<br>optical diodes to nonlinear polarization controllers and optical gyroscopes. In<br>this work, we study Kerrnonlinearityinduced symmetry breaking of light states<br>in coupled resonator optical waveguides (CROWs). We discover a new type of<br>controllable symmetry breaking that leads to emerging patterns of dark and<br>bright resonators within the chains. Beyond stationary symmetry broken states,<br>we observe periodic oscillations, switching and chaotic fluctuations of<br>circulating powers in the resonators. Our findings are of interest for<br>controlled multiplexing of light in photonic integrated circuits, neuromorphic<br>computing, topological photonics and soliton frequency combs in coupled<br>resonators.<br>
2023
LowTemperature Sputtered UltralowLoss 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
Siliconnitrideoninsulator (Si3N4) photonic circuits have seen tremendous advances in many applications, such as onchip frequency combs, Lidar, telecommunications, and spectroscopy. So far, the best film quality has been achieved with low pressure chemical vapor deposition (LPCVD) and hightemperature annealing (1200°C). However, high processing temperatures pose challenges to the cointegration of Si3N4 with preprocessed silicon electronic and photonic devices, lithium niobate on insulator (LNOI), and GeonSi photodiodes. This limits LPCVD as a frontendofline process. Here, ultralowloss Si3N4 photonics based on roomtemperature 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 frontend 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.
https://doi.org/10.48550/arXiv.2312.15506
(2023)
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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 copropagating 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
Optics Express
31(25)
4142041427
(2023)

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Silicon nitride (Si3N4) has been well established as an ultralowloss 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 ultralowloss 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 onestep 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 400nm thin Si3N4 film emerges as a promising solution that strikes a balance among the aforementioned criteria. Based on a commercially available 400nm Si3N4 film, we experimentally demonstrate the generation of lownoise coherent dark pulses with a repetition rate of 25 GHz in a multimode Si3N4 resonator. The compact spiralshaped resonator has a footprint of 0.28 mm2 with a highquality 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.
Fourfield symmetry breakings in twinresonator photonic isomers
Alekhya Ghosh, Lewis Hill, GianLuca Oppo , Pascal Del'Haye
Physical Review Research
5(4)
L042012
(2023)

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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 fourfield 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 FabryPérot resonators with Kerr media and normal dispersion
Graeme, N. Campbell, Lewis Hill, Pascal Del'Haye, GianLuca Oppo
Physical Review A
108(3)
033505
(2023)

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The ranges of existence and stability of dark cavitysoliton stationary states in a FabryPérot resonator with a Kerr nonlinear medium and normal dispersion are determined. The FabryPérot 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 LugiatoLefever 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 FabryPérot 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 FabryPérot resonators on multiple dark solitons, and we demonstrate longrange interactions and synchronization of temporal oscillations.
Symmetry Broken Vectorial Kerr Frequency Combs from FabryPérot Resonators
Lewis Hill, EvaMaria Hirmer, Graeme Campell, Toby Bi, Alekhya Ghosh, Pascal Del'Haye, GianLuca Oppo
https://doi.org/10.48550/arXiv.2308.05039
(2023)
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Optical frequency combs find many applications in metrology, frequency standards, communications and photonic devices. We consider field polarization properties and describe a vector comb generation through the spontaneous symmetry breaking of temporal cavity solitons within coherently driven, passive, FabryPérot cavities with Kerr nonlinearity. Global coupling effects due to the interactions of counterpropagating 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.
Multistage spontaneous symmetry breaking of
light in Kerr ring resonators
Lewis Hill, GianLuca Oppo, Pascal Del'Haye
Communications Physics (6)
208
(2023)

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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 multistage symmetry breaking of the resonances of ring resonators with Kerr nonlinearity. This multistage 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 fourfield selfswitching, 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 opticalsensors, e.g. by further enhancing the Sagnac effect.
Theory of phaseadaptive parametric cooling
Alekhya Ghosh, Pardeep Kumar, Christian Sommer, Fidel G. Jimenez, Vivishek Sudhir, Claudiu Genes
Physical Review A
107
053521
(2023)

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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 colddamping or cavity selfcooling. 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
Chipscale 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 selfstabilized 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 continuouswavelaserdriven soliton generation is investigated in the zerogroupvelocitydispersion regime as well as the generation of solitons that are spectrally crossing different dispersion regimes. In the measurements, zerodispersion solitons with multipeak structures (soliton molecules) are observed with distinct and predictable spectral envelopes that are a result of fifthorder 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 fifthorder dispersion, which can have applications in ultrafast optics, telecom systems, and optical spectroscopy.
Electromagnetically induced transparencylike
effect in a lithium niobate resonator via
electronic control
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 electrooptic 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 EITlike resonance lineshapes. By varying the electric field applied to the LN WGMR, the full dynamic of the EITlike 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 EITlike effect, which could have potential applications in light storage, quantum information processing, and enhanced sensing techniques.
Onthefly precision spectroscopy with a dualmodulated tunable diode laser
and Hzlevel referencing to a cavity
Advances in highresolution laser spectroscopy have enabled many scientific breakthroughs in physics, chemistry, biology and astronomy. Optical frequency combs have pushed measurement limits with ultrahighfrequency accuracy and fastmeasurement 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 onthefly to a fiber cavity with sub15 Hz frequency precision over an 11THz 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 ultrahighQ 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 outofthelab applications like LIDAR, gas spectroscopy and environmental monitoring.
Machine learning assisted inverse design of
microresonators
Optics Express
31(5)
80208028
(2023)

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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
Optics Express
31(4)
62286240
(2023)

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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 microresonatorbased nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chipscale 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 shortterm 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 shotnoiselimited 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 onchip optical frequency comparison, synthesis, and synchronization.
2022
Counterpropagating light in ring resonators: Switching fronts, plateaus, and oscillations
Graeme N. Campbell, Shuangyou Zhang, Leonardo Del Bino, Pascal Del'Haye, GianLuca 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 selfstarting 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 singlefield front solutions are provided in parameter ranges that are experimentally achievable in a wide variety of ring resonators.
We propose an adaptive phase technique for the parametric cooling of<br>mechanical resonances. This involves the detection of the mechanical<br>quadratures, followed by a sequence of periodic controllable adjustments of the<br>phase of a parametric modulation. The technique allows the preparation of the<br>quantum ground state with an exponential loss of thermal energy, similarly to<br>the case of colddamping or cavity selfcooling. Analytical derivations are<br>presented for the cooling rate and final occupancies both in the classical and<br>quantum regimes.<br>
Kerr frequency combs: a million ways to fit light pulses into tiny rings
Frequency combs can be generated in millimetersized 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
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 crossphase modulation, fourwave mixing, thirdharmonic 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 crossphase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetrybreaking dynamics of two counterpropagating modes of a loop resonator and prove that crossphase modulation is exactly twice as strong as selfphase 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, GianLuca Oppo, et al.
Nature Communications (13)
398
(2021)

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Kerreffectinduced 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 modelocked lasers. Here, we demonstrate that the Kerr effect in a highfinesse FabryPérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearlypolarized input field is converted into a left or rightcircularlypolarized field, controlled via the optical power. The observations are explained by Kerrnonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The alloptical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effectbased polarization controllers is generic to highQ Kerrnonlinear 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 symmetrybreaking point.
DarkBright Soliton Bound States in a Microresonator
Shuangyou Zhang, Toby Bi, George N. Ghalanos, Niall P. Moroney, Leonardo Del Bino, Pascal Del'Haye
Physical Review Letters
128(3)
033901
(2021)

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Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chipscale 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 darkbright 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 Kerrinduced crossphase 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.
2021
Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling
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 crossphase modulation, fourwave mixing, thirdharmonic 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 crossphase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetrybreaking dynamics of two counterpropagating modes of a loop resonator and prove that crossphase modulation is exactly twice as strong as selfphase 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, GianLuca Oppo, et al.
Nature Communications (13)
398
(2021)

Journal

PDF
Kerreffectinduced 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 modelocked lasers. Here, we demonstrate that the Kerr effect in a highfinesse FabryPérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearlypolarized input field is converted into a left or rightcircularlypolarized field, controlled via the optical power. The observations are explained by Kerrnonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The alloptical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effectbased polarization controllers is generic to highQ Kerrnonlinear 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 symmetrybreaking point.
DarkBright Soliton Bound States in a Microresonator
Shuangyou Zhang, Toby Bi, George N. Ghalanos, Niall P. Moroney, Leonardo Del Bino, Pascal Del'Haye
Physical Review Letters
128(3)
033901
(2021)

Journal

PDF
Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chipscale 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 darkbright 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 Kerrinduced crossphase 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 thirdorder, 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 crossphase 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 crossphase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of criticalpointenhanced optical gyroscopes and nearfield 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 ringlaser gyroscopes (RLGs) or fiberoptic gyroscopes (FOGs). With the recent rapid progress in the field of ultrahighquality optical whisperinggallery mode and ring microresonators, attention has been focused on the development of microresonatorbased Sagnac gyroscopes as a more compact alternative to RLGs and FOGs. One avenue that has been explored is the use of exceptional points in nonHermitian systems to enhance the responsivity to rotation. We use a similar phenomenon, namely, the critical point of a spontaneous symmetrybreaking transition between counterpropagating light, to demonstrate a microresonator gyroscope with a responsivity enhanced by a factor of around 10(4). We present a proofofprinciple 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 chipbased 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
SelfSwitching Kerr Oscillations of Counterpropagating Light in Microresonators
Michael T. M. Woodley, Lewis Hill, Leonardo Del Bino, GianLuca Oppo, Pascal Del'Haye
Physical Review Letters
126(4)
043901
(2021)

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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. Selfswitching 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 symmetrybroken states combined with attractor merging, which restores the broken symmetry on average. Selfswitching of counterpropagating light is robust for realizing controllable, alloptical 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
Optics Express
29(2)
21932203
(2021)

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The Kerr nonlinearity can be a key enabler for many digital photonic circuits as it allows access to bistable states needed for alloptical 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, opticallytunable 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 crossphase 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 proofofprinciple 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 alloptical 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
2020
Spectral extension and synchronization of microcombs in a single microresonator
Shuangyou Zhang, Jonathan M. Silver, Toby Bi, Pascal Del'Haye
Nature Communications
11(1)
6384
(2020)

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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 repetitionratesynchronized 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 crossphasemodulationmediated repetitionrate 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 crossphase 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
Journal of Lightwave Technology
38(6)
14141419
(2020)

Journal
Optical logic has the potential to replace electronics with photonic circuits in applications for which optictoelectronic conversion is impractical and for integrated alloptical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an alloptical, 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 counterpropagating 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 Qfactor of 2 x 10(8). This method of optical logic gives a practical solution to the onchip routing of light.
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 qualityfactor whisperinggallerymode microresonators, this intrinsic backscattering is primarily caused by either surface or bulk material imperfections. For several types of microresonatorbased 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 nearfield of a highqualityfactor 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 scattererinduced backpropagating fields to destructively interfere. This technique is useful in microresonator applications where backscattering is currently limiting the performance of devices, such as ringlaser 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.
Optical memories and switching dynamics of counterpropagating light states in microresonators
The Kerr nonlinearity can be a key enabler for many digital photonic circuits as it allows access to bistable states needed for alloptical 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, opticallytunable 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 crossphase 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 proofofprinciple 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 alloptical memories, switches, routers and logic gates that can operate at a single laser frequency with no additional electrical power.
Effects of self and crossphase modulation on the spontaneous symmetry breaking of light in ring resonators
Lewis Hill, GianLuca 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 crossphase modulation terms. Investigated is a wide variety of nonlinear materials by changing the ratio of the self and crossphase 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 crossphase 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 alloptical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.
2019
Critical Dynamics of an Asymmetrically Bidirectionally Pumped Optical Microresonator
Jonathan M. Silver, Kenneth T. V. Grattan, Pascal Del'Haye
An optical ring resonator with thirdorder, 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 crossphase 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 symmetricallypumped resonator and then for the general case of asymmetric pumping conditions and self and crossphase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of criticalpointenhanced optical gyroscopes and nearfield 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, spaceborne radiometers for Earth remote sensing, astrophysics, and imaging. In particular optically generated THz waves are of high interest for lownoise signal generation. Here, we propose and demonstrate stabilized terahertz wave generation using a microresonatorbased frequency comb (microcomb). A unitravellingcarrier photodiode (UTCPD) converts lownoise optical soliton pulses from the microcomb to a terahertz wave at the soliton's repetition rate (331 GHz). With a freerunning 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 inhouse hydrogen maser, inloop 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 proofofprinciple demonstration of terahertz imaging of peanuts. Combining the monolithically integrated UTCPD with an onchip microcomb, the demonstrated technique could provide a route towards highly stable continuous terahertz wave generation in chipscale packages for outofthelab applications. In particular, such systems would be useful as compact tools for highcapacity 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.
Thermooptical pulsing in a microresonator filtered fiberlaser: a route towards alloptical 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.
Optics Express
27(14)
1924219253
(2019)

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We report on 'slow' pulsing dynamics in a silica resonatorbased laser system: by nesting a highQ rodresonator 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 thermooptical effects in the highQ 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 selforganization phenomena in resonatorbased laser systems where thermooptical 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, counterpropagating optical field, thus hinting towards novel approaches for alloptical 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.
Submilliwattlevel 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 lownoise frequency combs with gigahertz to terahertz repetition rates, enabling applications in frequency metrology, astronomy, optical coherent communications, and laserbased ranging. A main challenge for soliton generation, in particular in ultrahighQ 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 singleand multisoliton modelocked states are generated in a 1.3mmdiameter 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 230mu mdiameter 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 lowthreshold 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 cavityoptomechanical strong coupling with highfrequency 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 surfaceinduced optical absorption in many materials. Here, we circumvent these challenges and report the observation of optomechanical strong coupling to a highfrequency (11 GHz) mechanical mode of a fusedsilica whisperinggallery microresonator via the electrostrictive Brillouin interaction. Using an optical heterodyne detection scheme, the antiStokes light backscattered from the resonator is measured, and normalmode 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 TimeReversal 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 alloptical logic gates, synchronously pumped optical frequency comb generation, and resonatorbased sensor technologies.
2018
Uniform Thin Films on Optical Fibers by PlasmaEnhanced Chemical Vapor Deposition: Fabrication, Mie Scattering Characterization, and Application to Microresonators
Zeba Naqvi, Mark Green, Krista Smith, Chaofan Wang, Pascal Del'Haye, TsingHua Her
Journal of Lightwave Technology
36(23)
55805586
(2018)

Journal
We demonstrate deposition of azimuthally uniform single or multiplelayer thin films of silicon nitride and silica on fibers using plasmaenhanced 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 noninvasive 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 1μmthick 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 symmetrybreaking 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, GianLuca Oppo, Pascal Del'Haye
Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetrybreaking 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 PTsymmetric 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 nearfield or rotation sensors. We then generalize to a timedependent model, which predicts different types of dynamical behavior, including oscillatory regimes that could enable Kerrnonlinearitydriven alloptical oscillators. The physics of our model can be applied to other systems featuring Kerrtype interaction between two distinct modes, such as for light of opposite circular polarization in nonlinear resonators, which are commonly described by coupled LugiatoLefever equations.
μWLevel 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 lownoise frequency combs with gigahertz to terahertz repetition rates, enabling applications in frequency metrology, astronomy, optical coherent communications, and laserbased ranging. A main challenge for soliton generation, in particular in ultrahighQ 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 multisoliton modelocked states are generated in a 1.3mmdiameter 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}mdiameter 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 ultrahighQ 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
Microcombs: 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 ultrafast, highprecision optical clocks is reflected in the large number of highimpact papers on the topic published in the last few years. This interest has been catalysed by the impact that highprecision optical frequency combs (OFCs) have had on metrology and spectroscopy in the last decade [15]. OFCs are often referred to as optical rulers: their spectra consist of a precise sequence of discrete and equallyspaced 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 selfreferenced 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 microcavities [61 are contributing to the development of OFC sources. These efforts may open up the way to realise ultrafast and stable optical clocks and pulsed sources with extremely high repetitionrates, in the form of compact and integrated devices. Indeed, the fabrication of highquality factor (highQ) microresonators, capable of dramatically amplifying the optical field, can be considered a photonics breakthrough that has boosted not only the scientific investigation of OFC sources [713] but also of optical sensors and compact light modulators [6,14].<br> In this framework, the demonstration of planar highQ resonators, compatible with silicon technology [1014], has opened up a unique opportunity for these devices to provide entirely new capabilities for photonicintegrated 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 copperbased interconnections, significantly increasing the chip power dissipation to beyond practical levels [1517]; hence, conventional approaches to chip design must undergo radical changes. Onchip optical networks, or optical interconnects, can offer high speed and low energy per transferredbit, and microresonators 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 electricallycontrolled light modulators [ 1417], greatly advancing the maturity of microresonator technology as a whole. Recently [1113], the demonstration of OFC sources in microresonators fabricated in electronic (i.e. in complementary metal oxide semiconductor (CMOS)) compatible platforms has given microcavities 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 microcavities which can radically change the nature of information transport and processing. Even in telecommunications, perhaps a more conventional environment for optical technologies, novel timedivision multiplexed optical systems will require extremely stable optical clocks at ultrahigh pulse repetitionrates 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 highcapacity optical coherent communication systems. This review will summarise the recent exciting achievements in the field of microcombs, namely optical frequency combs based on highQ 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.
2017
Soliton crystals in Kerr resonators
Daniel C. Cole, Erin S. Lamb, Pascal Del'Haye, Scott A. Diddams, Scott B. Papp
Selforganized 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 microresonatorsspontaneously and collectively ordered ensembles of copropagating 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 timedomain measurements to directly confirm our inference of their crystal structure. Soliton crystallization is explained by longrange 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 onchip optical buffer.
Selfsynchronization phenomena in the LugiatoLefever 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 anomalousdispersion dissipative cavities, where NLSE is usually referred to as the LugiatoLefever 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 selfsynchronization 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 electrooptics. 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 modelocked lasers. In contrast, electrooptic modulation (EOM) combs arise deterministically by imposing microwaverate oscillations on a continuouswave laser. Here we demonstrate electrooptic generation of a 160 THz bandwidth supercontinuum and realize f2f selfreferencing. 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
Microresonatorbased 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 LugiatoLefever equation. Timedomain approaches have brought many interesting insights for the understanding of microcombs. In this paper we present an intuitive frequencydomain 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 timedomain model based on soliton crystals and links the microcomb generation process with frequency response theory.
Symmetry Breaking of CounterPropagating 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 counterpropagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counterpropagating (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 Kerrnonlinearitymediated interaction between the counterpropagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, alloptical switching, nonlinearenhanced rotation sensing, optical flipflops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
2016
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 ElectroOptics, CLEO, pp 61920) 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 freezeframe of the stateoftheart, 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 solidstate/fiber lasers and Raman microresonators to exotic attosecond extreme ultraviolet and possibly even zeptosecond xray 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 timeresolved 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.
Phasecoherent microwavetooptical link with a selfreferenced 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 modelocked 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 outofthelab 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 timekeeping(6,7). Yet, in spite of the remarkable progress shown over recent years(810), microresonator frequency combs ('microcombs') have been without the key function of direct f2f selfreferencing(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 octavespanning spectrum and subsequently fully phasestabilized to an atomic clock. We show phasecoherent control of the comb and demonstrate its lownoise operation.
Broadband dispersionengineered 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 midinfrared(35). The wavelength at which the group velocity dispersion crosses zero can be set by varying the fibre core diameter or index step(2,68). Moreover, sophisticated methods to manipulate higherorder dispersion so as to shape and even flatten the dispersion over wide bandwidths are possible using multicladding fibres(911). Here we introduce design and fabrication techniques that allow analogous dispersion control in chipintegrated optical microresonators, and thereby demonstrate higherorder, widebandwidth 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 highQ systems has become of great importance in recent years with increased interest in chipintegrable optical frequency combs(1232).
Selfsynchronization of Kerrnonlinear 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 microresonatorbased optical frequency combs.
2015
Selfreferencing a continuouswave laser with electrooptic modulation
Katja Beha, Daniel C. Cole, Pascal Del'Haye, Aurélien Coillet, Scott A. Diddams, Scott B. Papp
We phasecoherently measure the frequency of continuouswave (CW) laser light by use of opticalphase modulation and f2f nonlinear interferometry. Periodic electrooptic modulation (EOM) transforms the CW laser into a continuous train of picosecond optical pulses. Subsequent nonlinearfiber 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 electronicnoiseinduced decoherence of the supercontinuum. Applying f2f selfreferencing with the supercontinuum yields the carrierenvelope 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 selfreferenced CW laser with <5E14 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
Experiments and theoretical modelling yielded significant progress toward understanding of Kerreffect induced optical frequency comb generation in microresonators. However, the simultaneous Kerrmediated 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.
2014
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 timekeeping 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 siliconchipbased 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 stateoftheart 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 nearthreshold phase and coherence properties of parametric optical frequency combs generated in lowloss 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 welldefined 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.
SelfInjection Locking and PhaseLocked States in MicroresonatorBased Optical Frequency Combs
Pascal Del'Haye, Katja Beha, Scott B. Papp, Scott A. Diddams
Microresonatorbased 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 frequencydomain experiments that illuminate the transition of microcombs into phaselocked 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.
2013
Parametric seeding of a microresonator optical frequency comb
We have investigated parametric seeding of a microresonator frequency comb (microcomb) by way of a pump laser with two electroopticmodulation sidebands. We show that the pumpsideband spacing is precisely replicated throughout the microcomb's optical spectrum, and we demonstrate a record absolute linespacing stability for microcombs of 1.6 x 10(13) at 1 s. The spectrum of a microcomb is complex, and often nonequidistant 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 MicrorodResonator Optical Frequency Comb
We report on the stabilization of a microresonatorbased optical frequency comb (microcomb) by way of mechanical actuation. These experiments use novel CO2lasermachined 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 opticalfrequency 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 <0.5mHz 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.
Lasermachined ultrahighQ microrod resonators for nonlinear optics
Optical whisperinggallery microresonators are useful tools in microphotonics and nonlinear optics at very low threshold powers. Here, we present details about the fabrication of ultrahighQ whisperinggallerymode resonators made by CO2laser lathe machining of fusedquartz 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 fourwave mixing.
Midinfrared 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 midinfrared 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 midinfrared optical frequency combs via fourwave mixing in a continuouswave pumped ultrahigh Q crystalline microresonator made of magnesium fluoride. Careful choice of the resonator material and design made it possible to generate a broadband, lowphase 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 midinfrared.
Optical frequency combs based on modelocked 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 whisperinggallery mode microresonators ("microcombs") has been developed recently, which represents a promising route towards chiplevel integration and outofthelab 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 octavespanning 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 electrooptic 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 modelocked laser frequency comb. The attained residual 1sec 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
2011
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 octavespanning 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 octavespanning spectra from microresonator comb generators represents a key step towards f2f selfreferencing of microresonatorbased 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
Physical Review Letters
107(6)
063901
(2011)

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2009
Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion
Pascal Del'Haye, Olivier Arcizet, Michael L. Gorodetsky, Ronald Holzwarth, Tobias J. Kippenberg
Nature Photonics
3(9)
529533
(2009)

Journal

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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 fibrelaserbased 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 subMHz 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.
2008
Full Stabilization of a MicroresonatorBased 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 fourwave 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 MicroresonatorBased Optical Frequency Comb
Pascal Del'Haye, Olivier Arcizet, Albert Schliesser, Ronald Holzwarth, Tobias J. Kippenberg
Physical Review Letters
101(5)
053903
(2008)

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2007
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(13) 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
Quantitative measurements of the vibrational eigenmodes in ultrahighQ silica microspheres are reported. The modes are excited via radiationpressureinduced dynamical backaction of light confined in the optical whisperinggallery 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 finiteelement 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.
Radiationpressuredriven vibrational modes in ultrahighQ silica microspheres
R. Ma, Albert Schließer, Pascal Del'Haye, A. Dabirian, Georg Anetsberger, Tobias J. 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.
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