Microresonators on a photonic chip could enhance nonlinear optics effects, thus are promising for realizing scalable high-efficiency frequency conversion devices. However, fulfilling phase matching conditions among multiple wavelengths remains a significant challenge. Here, we present a feasible scheme for degenerate sum-frequency conversion that only requires the two-mode phase matching condition. When the drive and the signal are both near resonance to the same telecom mode, an efficient on-chip photon-number conversion efficiency upto 42% was achieved, showing a broad tuning bandwidth over 250GHz. Furthermore, cascaded Pockels and Kerr nonlinear optical effects are observed, enabling the parametric amplification of the optical signal to a distinct wavelength in a single device. The scheme demonstrated in this work provides an alternative approach to realizing high-efficiency frequency conversion and is promising for future studies on communications, atom clocks, sensing, and imaging.
Low loss microresonators have revolutionised nonlinear and quantum optics over the past decade. In particular, microresonators with the second order, chi(2), nonlinearity have the advantages of broad spectral tunability and low power frequency conversion. Recent observations have highlighted that the parametric frequency conversion in chi(2) microresonators is accompanied by stepwise changes in the signal and idler frequencies. Therefore, a better understanding of the mechanisms and development of the theory underpinning this behaviour is timely. Here, we report that the stepwise frequency con…
We study optical parametric oscillations in Kerr-nonlinear microresonators, revealing an intricate solution space -- parameterized by the pump-to-signal conversion efficiency -- that arises from an interplay of nonlinear processes. Using a three-mode approximation, we derive an efficiency-maximizing relation between pump power and frequency mismatch. To move beyond a three-mode approximation, a necessity for geometries such as integrated microring resonators, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We obse…
We experimentally demonstrate enhanced wavelength conversion in a Q=7500 deeply etched AlGaAs-nanowaveguide microresonator via degenerate continuous-wave four-wave mixing with a pump power of 24 mW. The maximum conversion efficiency is -43 dB and accounts for 12 dB enhancement compared to that of a straight nanowaveguide. The experimental results and theoretical predictions agree very well and show optimized conversion efficiency of -15 dB. This work represents a step toward realizing a fully integrated optical devices for generating new optical frequencies.
Microresonator-based platforms with $χ^{(2)}$ nonlinearities have the potential to perform frequency conversion at high efficiencies and ultralow powers with small footprints. The standard doctrine for achieving high conversion efficiency in cavity-based devices requires "perfect matching", that is, zero phase mismatch while all relevant frequencies are precisely at a cavity resonance, which is difficult to achieve in integrated platforms due to fabrication errors and limited tunabilities. In this Letter, we show that the violation of perfect matching does not necessitate a reduction in conver…
Optical frequency combs are key to optical precision measurements. While most frequency combs operate in the near-infrared regime, many applications require combs at mid-infrared, visible or even ultra-violet wavelengths. Frequency combs can be transferred to other wavelengths via nonlinear optical processes, however, this becomes exceedingly challenging for high-repetition rate frequency combs. Here, it is demonstrated that a synchronously driven high-Q microresonator with a second-order optical nonlinearity can efficiently convert high-repetition rate near-infrared frequency combs to visible…
Microresonator-based Kerr frequency comb (microcomb) generation can potentially revolutionize a variety of applications ranging from telecommunications to optical frequency synthesis. However, phase-locked microcombs have generally had low conversion efficiency limited to a few percent. Here we report experimental results that achieve ~30% conversion efficiency (~200 mW on-chip comb power excluding the pump) in the fiber telecommunication band with broadband mode-locked dark-pulse combs. We present a general analysis on the efficiency which is applicable to any phase-locked microcomb state. Th…
We demonstrate efficient second harmonic generation in a quasi-phase-matched, high quality factor ($Q_0 \approx 5.3\times 10^5$) racetrack microresonator. The observed normalized conversion efficiency is about $3.8\%~mW^{-1}$.
Adiabatic frequency conversion has some key advantages over nonlinear frequency conversion. No threshold and no phase-matching conditions need to be fulfilled. Moreover, it exhibits a conversion efficiency of $100\,\%$ down to the single-photon level. Adiabatic frequency conversion schemes in microresonators demonstrated so far suffer either from low quality factors of the employed resonators resulting in short photon lifetimes or small frequency shifts. Here, we present an adiabatic frequency conversion (AFC) scheme by employing the Pockels effect. We use a non-centrosymmetric ultrahigh-$Q$ m…
The transportation of photons and phonons typically obeys the principle of reciprocity. Breaking reciprocity of these bosonic excitations will enable the corresponding non-reciprocal devices, such as isolators and circulators. Here, we use two optical modes and two mechanical modes in a microresonator to form a four-mode plaquette via radiation pressure force. The phase-controlled non-reciprocal routing between any two modes with completely different frequencies is demonstrated, including the routing of phonon to phonon (MHz to MHz), photon to phonon (THz to MHz), and especially photon to phot…
A hollow bottle-like microresonator (BLMR) with ultra-high quality factor is fabricated from a microcapillary with nearly parabolic profile. At 1.55 $μm$ pumping, degenerate four-wave mixing can be observed for a BLMR of diameter 102 $μ$m. The parabolic profile of the BLMR guarantees a nearly zero waveguide dispersion, which is theoretically discussed in detail. From the simulation, at 1.55 $μ$m wavelength in such a BLMR, the fundamental bottle mode is in the anomalous dispersion regime, whilst the ordinary whispering gallery mode (WGM) confined at the center of the BLMR is in the normal dispe…
Frequency conversion in microresonators has revolutionised modern-day nonlinear and quantum optics. Here, we present a theory of the multimode second harmonic generation in microresonators under conditions when the parametric conversion back to the pump spectrum dominates through the large domain in the resonator parameter space. We demonstrate that the spectral tunability of the sideband generation in this regime is governed by a discrete sequence of the so-called Eckhaus instabilities. We report the transition to modelocking and generation of solitons, which have a double-pulse structure in …
We present an explicit sech-squared-soliton solution associated with the optical Pockels effect, achieved through the generation of the frequency combs via parametric down-conversion in optical microresonators with quadratic nonlinearity. This soliton contrasts the parametric sech-soliton describing the half-harmonic field in the limit of the large index mismatch, and associated with the cascaded-Kerr effect. We predict differences in the spectral profiles and powers of the Pockels and cascaded-Kerr solitons, and report that the pump power threshold of the former agree with the recent experime…
Multiple soliton regimes enabled by parametric down-conversion in $χ^{(2)}+χ^{(3)}$ microresonators
University of Bath（巴斯大学）；Centre for Photonics, University of Bath（巴斯大学光子学中心）；VTT Technical Research Centre of Finland（芬兰技术研究中心）；National Physical Laboratory（英国国家物理实验室）
Microresonator frequency combs based on the $χ^{(3)}$ nonlinearity are nowadays well understood and making their way into different applications. Recently, microresonator frequency combs based on the $χ^{(2)}$ nonlinearity are receiving increasing attention, as they promise certain benefits, but still require further study. Here, we demonstrate the generation of a $χ^{(2)}$ frequency comb, initiated via optical parametric oscillation (OPO) in a lithium niobate mm-sized microresonator. By pumping at 532 nm with 30 $μ$W of power, we observe 1-THz-wide comb spectra around 1064 nm with degenerate …
Recent experiments have demonstrated the generation of widely-spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb states. In particular, we show that the phase-matching required for the initial sideband generation is such that (at least) one of the sidebands experiences anomalous dispersion, enabling that sideband to drive frequency comb formation via degenerate and non-degenerate four-wave mixing. We validate our proposal through a combination of experimen…
We report on fabrication of high Q lithium niobate (LN) whispering-gallery-mode (WGM) microresonators suspended on silica pedestals by femtosecond laser microfabrication. The micrometer-scale (diameter ~82 μm) LN resonator possesses a Q factor of 2.5x10^5 around 1550 nm wavelength range. Moreover, second harmonic generation with a continuous-wave tunable single-longitudinal-mode pump laser in the on-chip LN microresonator is demonstrated in the on-chip LN microresonator. A fiber taper is employed to couple the pump laser into the microresonator, showing a normalized conversion efficiency of 1.…
Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advance…
High quality factor optical microcavities have been employed in a variety of material systems to enhance nonlinear optical interactions. While single-crystalline aluminum nitride microresonators have recently emerged as a low loss platform for integrated nonlinear optics such as four wave mixing and Raman lasing, few studies have investigated this material for second-harmonic generation. In this Letter, we demonstrate an optimized fabrication of dually-resonant phase-matched ring resonators from epitaxial aluminum nitride thin films. An unprecendented second-harmonic generation efficiency of 1…
Low-Threshold Degenerate Optical Parametric Oscillations in Bichromatically-Pumped Normal-Dispersion Photonic-Crystal Microresonator
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Faculty of Physics, Lomonosov Moscow State University（莫斯科国立大学物理系）
Mid-infrared (mid-IR) frequency combs have broad applications in molecular spectroscopy and chemical/biological sensing. Recently developed microresonator-based combs in this wavelength regime could enable portable and robust devices using a single-frequency pump field. Here, we report the first demonstration of a modelocked microresonator-based frequency comb in the mid-IR spanning 2.4 μm to 4.3 μm. We observe high pump-to-comb conversion efficiency, in which 40% of the pump power is converted to the output comb power. Utilizing an integrated PIN structure allows for tuning the silicon micror…
We propose a device architecture capable of direct quantum electro-optical conversion of microwave to optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that electro-optical (vacuum) coupling rates $g_0$ as large as$\sim 2π\, \mathcal{O}(10-100)$ kHz are achievable with currently available technology, due to the small mode volume of the planar microwave resonator. Operating at millikelvin temperatures, such a converter would enable high-efficienc…
Single photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at sub-watt pump powers. Using a quantum-mechanical Hamiltonian formalism, we present a detailed theoretical analysis of the conversion dynamics in these systems, and show that they are capable of converting single- and multi-photon quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability dens…
Nonlinear optical processes in whispering gallery mode (WGM) microresonators have attracted much attention. Owing to the strong confinement of light in a small volume, a WGM microresonator can dramatically boost the strength of light field, thereby promoting the nonlinear interaction between the light and the resonator material. However, realization of efficient nonlinear parametric process in microresonators is a challenging issue. The major difficulty is to simultaneously ensure the phase matching condition and a coherent multiple resonance condition for all the waves participating in the no…
Optical parametric oscillation (OPO) is distinguished by its wavelength access, that is, the ability to flexibly generate coherent light at wavelengths that are dramatically different from the pump laser, and in principle bounded solely by energy conservation between the input pump field and the output signal/idler fields. As society adopts advanced tools in quantum information science, metrology, and sensing, microchip OPO may provide an important path for accessing relevant wavelengths. However, a practical source of coherent light should additionally have high conversion efficiency and high…
Nonlinear optics in whispering-gallery-mode (WGM) microresonators have attracted much attention. Owing to strong confinement of the light in a small volume, a WGM microresonator can dramatically boost the strength of light field, giving rise to enhancement of the nonlinear interactions of light with the resonator material. Here, we demonstrate highly efficient second harmonic generation (SHG) and third harmonic generation (THG) in an on-chip monocrystalline lithium niobate (LN) microresonator. Benefitting from a cyclic phase matching scheme for the transverse-electric WGMs, nonlinear wavelengt…
Using a general Hamiltonian treatment, we theoretically study the generation of degenerate quadrature squeezing in a dual-pumped integrated microring resonator coupled to a waveguide. Considering a dual-pump four-wave mixing configuration in an integrated $\text{Si}_3\text{N}_4$ platform, and following the coupled-mode theory approach, we investigate the effects of parasitic quantum nonlinear optical processes on the generation of squeezed light. Considering five resonance modes in this approach allows us to include the most important four-wave mixing processes involved in such a configuration…
Microresonator-based frequency combs are strong contenders as light sources for wavelength-division multiplexing (WDM). Recent demonstrations have shown the potential of microresonator combs for replacing tens of WDM lasers with a single laser-pumped device. These experiments relied on microresonators displaying anomalous dispersion. Devices operating in the normal dispersion offer the prospect of attaining high power conversion efficiency - an aspect that will be crucial in the future for enabling energy-efficient coherent communications with higher order modulation formats or lighting severa…
The realization of ultrahigh quality (Q) resonators regardless of the underpinning material platforms has been a ceaseless pursuit, because the high Q resonators provide an extreme environment of storage of light to enable observations of many unconventional nonlinear optical phenomenon with high efficiencies. Here, we demonstrate an ultra-high Q factor (7.1*10^6) microresonator on the 4H-silicon-carbide-on-insulator (4H-SiCOI) platform in which both \c{hi}^(2) and \c{hi}^(3) nonlinear processes of high efficiencies have been generated. Broadband frequency conversions, including second-, third…
High spectral purity frequency agile room temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single frequency and multi frequency oscillators in the terahertz regime. Through optical to terahertz down conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8 octaves is achieved from 330 GHz to 2.3 THz, with 20 GHz cavity mode limited frequency tuning step…
Carrier-envelope phase stabilization of optical pulses enables exquisitely precise measurements by way of direct optical-frequency synthesis, absolute optical-to-microwave phase conversion, and control of ultrafast waveforms. We report such phase stabilization for Kerr-microresonator frequency combs integrated on silicon chips, and verify their fractional-frequency inaccuracy at <3x10-16. Our work introduces an interlocked Kerr-comb configuration comprised of one silicon-nitride and one silica microresonator, which feature nearly harmonic repetition frequencies and can be generated with one la…
In nonlinear microresonators driven by continuous-wave (cw) lasers, Turing patterns have been studied in the formalism of Lugiato-Lefever equation with emphasis on its high coherence and exceptional robustness against perturbations. Destabilization of Turing pattern and transition to spatio-temporal chaos, however, limits the available energy carried in the Turing rolls and prevents further harvest of their high coherence and robustness to noise. Here we report a novel scheme to circumvent such destabilization, by incorporating the effect of local mode hybridizations, and attain globally stabl…
We report the generation of high-purity twin photon pairs through cavity-enhanced non-degenerate four-wave mixing (FWM) in a high-Q silicon microdisk resonator. Twin photon pairs are created within the same cavity mode and are consequently expected to be identical in all degrees of freedom. The device is able to produce twin photons at telecommunication wavelengths with a pair generation rate as large as $(3.96\pm0.03)\times10^5 ~{\rm pairs/s}$, within a narrow bandwidth of 0.72 GHz. A coincidence-to-accidental ratio of $660\pm62$ was measured, the highest value reported to date for twin photo…
Optical frequency combs allow for precise measurement of optical frequencies and are used in a growing number of applications beyond spectroscopy and optical frequency metrology. A class of compact microresonator based frequency comb generators has emerged recently based on (hyper)-parametric frequency conversion, mediated by the Kerr-non-linearity, of a continuous wave laser beam. Despite the rapid progress and the emergence of a wide variety of micro-resonator Kerr-comb platforms, an understanding of the dynamics of the Kerr comb formation is still lacking. In particular the question in whic…
The mid-infrared spectral range (2 to 20 μm) is of particular importance for chemistry, biology and physics as many molecules exhibit strong ro-vibrational fingerprints. Frequency combs - broad spectral bandwidth coherent light sources consisting of equally spaced sharp lines - are creating new opportunities for advanced spectroscopy. Mid-infrared frequency comb sources have recently emerged but are still facing technological challenges, like achieving high power per comb line and tens of GHz line spacing as required for e.g. direct comb spectroscopy. Here we demonstrate a novel approach to cr…
Integrated nonlinear wavelength converters transfer optical energy from lasers or quantum emitters to other useful colors, but chromatic dispersion limits the range of achievable wavelength shifts. Moreover, because of geometric dispersion, fabrication tolerances reduce the accuracy with which devices produce specific target wavelengths. Here, we report nonlinear wavelength converters whose operation is not contingent on dispersion engineering; yet, the output wavelengths are controlled with high accuracy. In our scheme, coherent coupling between counter-propagating waves in a photonic crystal…
Optical logic has the potential to replace electronics with photonic circuits in applications for which optic-to-electronic conversion is impractical and for integrated all-optical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an all-optical, universal logic gate using counterpropagating light in which all signals have the same operating optical frequency. Such a device would make possible the routing of optical signals without the need for conversion into the electronic domain…
We present a theory of the frequency comb generation in the high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and 2nd harmonic frequencies supports a family of the bright soliton frequency combs providing the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, …
Bridging high-Q and Kerr-nonlinear photonics using modal phase matching
National Institute for Standards and Technology（国家标准与技术研究院）；Whiting School of Engineering, Johns Hopkins University（约翰斯·霍普金斯大学惠廷工程学院）；Beacon Photonics（灯塔光子学）；Joint Quantum Institute, NIST/University of Maryland（NIST/马里兰大学联合量子研究所）
A coherently driven Kerr optical cavity is able to convert a continuous-wave laser to a sequence of ultrashort soliton pulses, enabling the generation of broadband and mode-locked frequency combs. Kerr cavity solitons are balanced through an energy exchange with the driving pump field. Improving the energy conversion efficiency from the pump to the soliton is of great significance for practical applications, but remains an outstanding challenge due to a limited temporal overlap between the soliton and the pump. Here, we report the discovery of temporal Kerr solitons in mutually coupled cavitie…
THz oscillators generated via frequency-multiplication of microwaves are facing difficulty in achieving low phase noise. Photonics-based techniques, in which optical two tones are translated to a THz wave through opto-electronic conversion, are promising if the relative phase noise between the two tones is well suppressed. Here, a THz ($\approx$ 560 GHz) wave with a low phase noise is provided by a frequency-stabilized, dissipative Kerr microresonator soliton comb. The repetition frequency of the comb is stabilized to a long fiber in a two-wavelength delayed self-heterodyne interferometer, sig…
We investigate adiabatic frequency conversion using epsilon near zero (ENZ) materials and show that while the maximum frequency conversion for a given change of permittivity does not exhibit increase in the vicinity of ε=0 condition. However, that change can be achieved in a shorter length, and if the pump is also in the ENZ vicinity, at a lower pump intensity. This slow propagation effect makes the conversion efficiency in the ENZ material comparable to that in microresonators and other structured slow light schemes, but unlike the latter no nanofabrication is required for ENZ materials which…
We report on the experimental observation of a simultaneous threefold wavelength and spatial conversion process at telecommunication wavelengths taking place in a 6-LP-mode graded-index few-mode fiber. The physical mechanism is based on parallel and phase-matched frequency-degenerated intermodal four-wave mixing (FD-IFWM) phenomena occurring between the fundamental mode and higher-order spatial modes. More precisely, a single high-power frequency-degenerated pump wave is simultaneously injected in the four spatial modes LP01, LP11, LP02 and LP31 of a 1.8-km long graded-index few-mode fiber tog…
