Miniaturization of devices has been a primary objective in microelectronics and photonics for decades, aiming at denser integration, enhanced functionalities and drastic reduction of power consumption. Headway in nanophotonics is currently linked to the progress in concepts and technologies necessary for applications in information and communication, brain inspired computing, medicine and sensing and quantum information. Amongst all nanostructures, semiconductor photonic crystals (PhCs) occupy a prominent position as they enable the fabrication of quasi ultimate optical cavities. Low threshold laser diodes or Raman lasers , low power consuming optical memories , efficient single photon sources or single photon quantum gates are impressive examples of their capabilities. We report the demonstration of about 20 micron long PhC semiconductor optical parametric oscillator (OPO) at telecom wavelength exploiting nearly diffraction limited optical modes. The pump power threshold is measured below 0.2 mW. Parametric oscillation was reached through the drastic enhancement of Kerr optical Four Wave Mixing by thermally tuning the high Q modes of a nanocavity into a triply resonant configuration. Miniaturization of this paradigmatic source of coherent light paves the way for quantum optical circuits, dense integration of highly efficient nonlinear sources of squeezed light or entangled photons pairs.
A photonic realization of the Dirac oscillator (DO), i.e. of the relativistic extension of the quantum harmonic oscillator, is proposed for light propagation in fiber Bragg gratings. Transmission spectra clearly show the existence of electron and positron bound states of the DO, corresponding to resonance modes above and below the Bragg frequency, as well as the asymmetry of the energy spectrum for electron and positron branches.
We investigate optical parametric oscillations through four-wave mixing in resonant cavities and photonic crystals. The theoretical analysis underlines the relevant features of the phenomenon and the role of the density of states. Using fully vectorial 3D time-domain simulations, including both dispersion and nonlinear polarization, for the first time we address this process in a face centered cubic lattice and in a photonic crystal slab. The results lead the way to the development of novel parametric sources in isotropic media.
A new tuning mechanism is introduced in high-Q multimode photonic crystal resonators allowing to harness the resonant enhancement of the parametric resonance systematically. As a consequence, ultra-efficient stimulated and spontaneous Four Wave Mixing at continuous microWatt pumping levels are observed, and the scaling with Q is demonstrated. Experimental results are in perfect agreement with an analytical model without fitting parameters.
We report phase sensitive amplification in a 1.5mm long, $Ga_{0.5}In_{0.5}P$ dispersion engineered photonic crystal waveguide which has a flattened dispersion profile. A signal degenerate configuration with pulsed pumps whose total peak power is only 0.5W yields a phase sensitive extinction ratio of 10dB.
We demonstrate a free running 10GHz microresonator-based RF photonic hyper-parametric oscillator characterized with phase noise better than -60dBc/Hz at 10Hz, -90dBc/Hz at 100Hz, and -150dBc/Hz at 10MHz. The device consumes less than 25mW of optical power. A correlation between the frequency of the continuous wave laser pumping the nonlinear resonator and the generated RF frequency is confirmed. The performance of the device is compared with the performance of a standard optical fiber based coupled opto-electronic oscillator of OEwaves.
The ability to amplify optical signals is of pivotal importance across science and technology. The development of optical amplifiers has revolutionized optical communications, which are today pervasively used in virtually all sensing and communication applications of coherent laser sources. In the telecommunication bands, optical amplifiers typically utilize gain media based on III-V semiconductors or rare-earth-doped fibers. Another way to amplify optical signals is to utilize the Kerr nonlinearity of optical fibers or waveguides via parametric processes. Such parametric amplifiers of travell…
We consider the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers. The extended stability and the varying asymmetry of these modes allows for the introduction of a rich set of interesting modulation response features, such as sharp resonances and anti-resonance as well as efficient modulation at very high frequencies exceeding the free running relaxation frequencies by orders of magnitude.
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances, transmittance and known extraordinary scattering phenomena. We demonstrate a PT heterostructure with coherent perfect absorption-lasing, anisotropic transmission resonance, and parity symmetry of reflection coefficients at the frequencies of interest. In addition, with the parametric space and the analytical formula, the corresponding complex dielectric permitt…
We experimentally demonstrate an optomechanical cavity based on an air-slot photonic crystal cavity with optical quality factor Qo=4.2\times10^4 and a small modal volume of 0.05 cubic wavelengths. The optical mode is coupled with the in-plane mechanical modes with frequencies up to hundreds of MHz. The fundamental mechanical mode shows a frequency of 65 MHz and a mechanical quality factor of 376. The optical spring effect, optical damping and amplification are observed with a large experimental optomechanical coupling rate gom/2pi of 154 GHz/nm, corresponding to a vacuum optomechanical couplin…
Transfer of amplitude and phase noise from a continuous wave optical pump to the repetition rate of a Kerr frequency comb is studied theoretically, with focus on generation of spectrally pure radio frequency (RF) signals via demodulation of the frequency comb on a fast photodiode. It is shown that both the high order chromatic dispersion of the resonator spectrum and frequency-dependent quality factor of the resonator modes facilitate the optical-to-RF noise conversion that limits spectral purity of the RF signal.
We show experimentally that parametric interaction can induce a cooperative oscillation of non simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially extended system subjected to boundary conditions where nonlinear wave mixing of two nonresonant spatial modes can generate a resonant oscillation.
The light propagation through one-dimensional photonic crystal using Four-wave mixing (FWM) nonlinear process is modeled. The linear and nonlinear indexes of refraction are approximated with the first Fourier harmonic term. Based on this approximation, a complete set of coupled wave equations, including pump fields depletion, for description of FWM process and conversion efficiency from pump to signal and idler waves for periodic structures is presented. The derived coupled wave equations are evaluated numerically. Some of important system parameters effects on FWM performance are investigated…
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary…
Accurate phase-locked 3:1 division of an optical frequency was achieved, by using a continuous-wave (cw) doubly resonant optical parametric oscillator. A fractional frequency stability of 2*10^(-17) of the division process has been achieved for 100s integration time. The technique developed in this work can be generalized to the accurate phase and frequency control of any cw optical parametric oscillator.
In this paper, we report on a singly resonant optical parametric oscillator (OPO) pumped by an amplified spontaneous emission (ASE) source. The pump focusing conditions allow non-collinear phasematching, which resulted in a 230 nm (190 cm$^{-1}$) spectral bandwidth. Calculations indicate that such phasematching schemes may be used to further broaden OPO spectral bandwidths.
Canonical Four-Wave-Mixing occurs in a resonator with only the required number of modes, thereby inhibiting competing parametric processes. The properties of the recently introduced photonic crystal parametric oscillator, Marty et al. Nat. Photonics, 15, 53 (2021), are discussed extensively. We compare the bichromatic design with other geometries of photonic crystal resonators. Based on a statistical study over more than 100 resonators and 10 parametric oscillators, robustness against fabrication tolerances is assessed, performances are evaluated in terms of average values and their dispersion…
We demonstrate the first optical parametric oscillator (OPO) based on chalcogenide glass. The parametric gain medium is an As2Se3 chalcogenide microwire coated with a layer of polymer. The doubly-resonant OPO oscillates simultaneously at a Stokes and an anti Stokes wavelength shift of >50 nm from the pump wavelength that lies at λP = 1552 nm. The oscillator has a peak power threshold of 21.6 dBm and a conversion efficiency of >19 %. This OPO experiment provides an additional application of the chalcogenide microwire technology; and considering the transparency of As2Se3 glass extending far in …
An optical technique based on stability transfer among modes of a monolithic optical microresonator is proposed for long therm frequency stabilization of a radiofrequency (RF) oscillator. We show that locking two resonator modes, characterized with dissimilar sensitivity in responding to an applied forcing function, to a master RF oscillator allows enhancing the long term stability of a slave RF oscillator locked to two resonator modes having nearly identical sensitivity. For instance, the stability of a 10 MHz master oscillator characterized with Allan deviation of 10^-7 at 10^4s can be incre…
We combine a tunable continuous-wave optical parametric oscillator and a femtosecond Ti:Sapphire laser frequency comb to provide a phase-coherent bridge between the visible and mid-infrared spectral ranges. As a first demonstration of this new technique we perform a direct frequency comparison between an iodine stabilized Nd:YAG laser at 1064 nm and an infrared methane optical frequency standard at $3.39 μ$m.
We present a study of orbital angular momentum transfer from pump to down-converted beams in a type-II Optical Parametric Oscillator. Cavity and anisotropy effects are investigated and demostrated to play a central role in the transverse mode dynamics. While the idler beam can oscillate in a Laguerre-Gauss mode, the crystal birefringence induces an astigmatic effect in the signal beam that prevents the resonance of such mode.
We demonstrate a two-crystal mid-infrared dual-wavelength optical parametric oscillator, synchronously pumped by a high power femtosecond Yb:fiber laser. The singly-resonant ring cavity, containing two periodically poled lithium niobate crystals, is capable of generating two synchronized idler wavelengths, independently tunable over 30 THz in the 2.9 - 4.2 μm wavelength region, due to the cascaded quadratic nonlinear effect. The independent tunability of the two idlers makes the optical parametric oscillator a promising source for ultrafast pulse generation towards the THz wavelength region, b…
Steady-state and dynamics of the self-phase-locked (3ω==> 2ω, ω) subharmonic optical parametric oscillator are analyzed in the pump-and-signal resonant configuration, using an approximate analytical model and a full propagation model. The upper branch solutions are found always stable, regardless of the degree of pump enhancement. The domain of existence of stationary states is found to critically depend on the phase-mismatch of the competing second-harmonic process.
We present the controllability capabilities for the limit cycles of an extremely tunable photonic oscillator, consisting of two coupled semiconductor lasers. We show that this system supports stable limit cycles with frequencies ranging from a few to more than a hundred GHz that are characterized by a widely varying degree of asymmetry between the oscillations of the two lasers. These dynamical features are directly controllable via differential pumping as well as optical frequency detuning of the two lasers, suggesting a multi-functional oscillator for chip-scale radio-frequency photonics app…
We present a reliable, narrow linewidth (100 kHz) continuous-wave optical parametric oscillator (OPO) suitable for high-resolution spectroscopy applications. The OPO is based on a periodically-poled lithium-niobate crystal and features a specially designed intracavity etalon which permits its continuous tuning and stable operation at any desired wavelength in a wide operation range. We demonstrate Doppler-free spectroscopy on a rovibrational transition of methane at 3.39 um.
We present a tunable, hybrid waveguide-fiber optical parametric oscillator (OPO) synchronously pumped by an ultra-fast fiber laser exploiting four-wave mixing (FWM) generated in silicon nitride waveguides. Parametric oscillation results in a 35 dB enhancement of the idler spectral power density in comparison to spontaneous FWM, with the ability of wide wavelength tuning over 86 nm in the O-band. Measurements of the oscillation threshold and the efficiency of the feedback loop reveal how an integration of the OPO on a single silicon nitride chip can be accomplished at standard repetition rates …
We report a femtosecond optical parametric oscillator (OPO) based on the new semiconductor gain material orientation patterned gallium phosphide (OP-GaP), which enables the production of high-repetition-rate femtosecond pulses spanning 5-12 μm with average powers in the few to tens of milliwatts range. This is the first example of a broadband OPO operating across the molecular fingerprint region, and we demonstrate its potential by conducting broadband Fourier-transform spectroscopy using water vapor and a polystyrene reference standard.
By design access to laser wavelength, especially with integrated photonics, is critical to advance quantum sensors like optical clocks and quantum-information systems, and open opportunities in optical communication. Semiconductor-laser gain provides exemplary efficiency and integration but merely in developed wavelength bands. Alternatively, nonlinear optics requires control of phase matching, but the principle of nonlinear conversion of a pump laser to a designed wavelength is extensible. We report on laser-wavelength access by versatile customization of optical-parametric oscillation (OPO) …
We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode spacing uniformity of the comb at the Hz level. We also show that spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at ~2 μm.
We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness a…
A model of the steady-state operating, self-pumped singly resonant optical parametric oscillator (SPSRO) has been developed. The characteristics of quasi three-level laser gain medium pumped longitudinally have been taken into account. The characteristics of standing wave cavity, reabsorption losses, focusing Gaussian beams of the pump laser, fundamental laser and signal wave have been considered in the analyses. Furthermore, The power characteristics of threshold and efficiency have been analyzed, employing a Yb3+-doped periodically poled lithium niobate co-doped with MgO (Yb3+:MgO:PPLN) as t…
We report a general description of quasi-phase-matched parametric process in nonlinear photonic crystals (NLPC) by extending the conventional X-ray diffraction theory in solids. Under the virtual wave approximation, phase-matching resonance is equivalent to the diffraction of the scattered virtual wave. Hence a modified NLPC Ewald construction can be built up, which illustrates the nature of the accident for the diffraction of the virtual wave in NLPC and further reveals the complete set of diffractions of the virtual wave for both of the air-dielectric and dielectric-dielectric contacts. We s…
I present a theoretical treatment of parametric scattering in strong coupling semiconductor microcavities to model experiments in which parametric oscillator behaviour has been observed. The model consists of a non-linear excitonic oscillator coupled to a cavity mode which is driven by the external fields, and predicts the output power, below threshold gain and spectral blue shifts of the parametric oscillator. The predictions are found to be in excellent agreement with the experimental data.
We investigate the dynamical properties of a type-II optical parametric oscillator pumped by a structured light beam carrying orbital angular momentum. Different dynamical regimes are theoretically derived and experimentally demonstrated, depending on the anisotropy effects imposed by the nonlinear medium. In a weakly anisotropic regime, fine-tuning of the orbital angular momentum transfer is obtained by adjusting the crystal parameters. Under strong anisotropy, orbital angular momentum transfer is not possible and a sharp dynamical behavior is observed, with abrupt switching between different…
We report a singly resonant continuous-wave optical parametric oscillator (SRO), which is pumped by a semiconductor laser system and operates in the mid-infrared region (2.9 to 3.6 μm). Fast tuning of the mid-infrared output wavelength by more than 200 nm is demonstrated by scanning the pump laser wavelength through only 1.25 nm, without any need to adjust the SRO settings. The exceptionally large tuning range is obtained by choosing a pump wavelength (780 nm) that corresponds to a turning point of the group velocity mismatch between the phase-matched signal and idler waves of the SRO.
We built a 1-watt cw singly resonant optical parametric oscillator operating at an idler wavelength of 1.65~$μ$m for application to quantum interfaces. The non resonant idler is frequency stabilized by side-fringe locking on a relatively high-finesse Fabry-Perot cavity, and the influence of intensity noise is carefully analyzed. A relative linewidth down to the sub-kHz level (about 30 Hz over 2 s) is achieved. A very good long term stability is obtained for both frequency and intensity.
We report the soliton frequency comb generation in microring optical parametric oscillators operating in the down-conversion regime and with the simultaneous presence of the $χ^{(2)}$ and Kerr nonlinearities. The combs are studied considering a typical geometry of a bulk LiNbO$_3$ toroidal resonator with the normal group velocity dispersion spanning an interval between the pump and the down-converted signal. We have identified critical power signaling a transition between the relatively low pump power predominantly $χ^{(2)}$ combs and the high pump power ones shaped by the competition between …
We report the relative frequency stabilization of an intracavity frequency doubled singly resonant optical parametric oscillator on a Fabry-Perotétalon. The red/orange radiation produced by the frequency doubling of the intracavity resonant idler is stabilized using the Pound-Drever-Hall locking technique. The relative frequency noise of this orange light, when integrated from 1 Hz to 50 kHz, corresponds to a standard deviation of 700 Hz. The frequency noise of the pump laser is shown experimentally to be transferred to the non resonant signal beam.
The dynamics of photonic wavepacket in the effective oscillator potential is studied. The oscillator potential is constructed on a base of one dimensional photonic crystal with a period of unit cell adiabatically varied in space. The structure has a locally equidistant discrete spectrum. This leads to an echo effect, i.e. the periodical reconstruction of the packet shape. The effect can be observed in a nonlinear response of the system. Numerical estimations for porous-silicon based structures are presented for femtosecond Ti:Sapphire laser pump.
Optical parametric oscillators are widely-used pulsed and continuous-wave tunable sources for innumerable applications, as in quantum technologies, imaging and biophysics. A key drawback is material dispersion imposing the phase-matching condition that generally entails a complex setup design, thus hindering tunability and miniaturization. Here we show that the burden of phase-matching is surprisingly absent in parametric micro-resonators adopting monolayer transition-metal dichalcogenides as quadratic nonlinear materials. By the exact solution of nonlinear Maxwell equations and first-principl…
Spatio-temporal dynamics of singly resonant optical parametric oscillators with external seeding displays hexagonal, roll and honeycomb patterns, optical turbulence, rogue waves and cavity solitons. We derive appropriate mean-field equations with a sinc$^2$ nonlinearity and demonstrate that off-resonance seeding is necessary and responsible for the formation of complex spatial structures via self-organization. We compare this model with those derived close to the threshold of signal generation and find that back-conversion of signal and idler photons is responsible for multiple regions of spat…
Phase-stabilized 12-fs, 1-nJ pulses from a commercial Ti:sapphire oscillator are directly amplified in a chirped-pulse optical parametric amplifier and recompressed to yield near-transform-limited 17.3-fs pulses. The amplification process is demonstrated to be phase preserving and leads to 85-uJ, carrier-envelope-offset phase-locked pulses at 1 kHz for 0.9 mJ of pump, corresponding to a single-pass gain of 8.5 x 10^4.
The global structure of the Isochrons and the corresponding Phase Response Curves are, for the first time, investigated and numerically computed for the fundamental photonic oscillator consisted of an Optically Injected Laser. Their crucial role in the synchronization dynamics under a periodic modulation of the injection beam is shown, along with their capability for providing conditions for stable phase-locking and periodic outputs with discrete equidistant spectra in the form of frequency combs.
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent os…
This paper describes the development of a photonic local oscillator (LO) source based on a 3-stage Mach-Zehnder modulator (MZM) device. The MZM laser synthesizer demonstrates the feasibility of providing the photonic reference LO for the Atacama Large Millimeter Array telescope located in Chile. This MZM approach to generating an LO by radio RF modulation of a monochromatic optical source provides the merits of wide frequency coverage of 4-130 GHz, tuning speed of about 0.2 seconds, and residual integrated phase noise performance of 0.3 degrees RMS at 100 GHz.
We consider a Glauber-Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber-Fock oscillator.
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）
The feasibility and extraordinary properties of mirrorless parametric oscillations in strongly absorbing negative-index metamaterials are shown. They stem from the backwardness of electromagnetic waves inherent to this type of metamaterials.
We investigate parametric down-conversion in a hexagonally poled nonlinear photonic crystal, pumped by a dual pump with a transverse modulation that matches the periodicity of the nonlinear grating. A peculiar feature of this resonant configuration is that the two pumps simultaneously generate photon pairs over an entire branch of modes, via quasi-phasematching with both fundamental vectors of the reciprocal lattice of the nonlinearity. The parametric gain of these modes depends thus coherently on the sum of the two pump amplitudes and can be controlled by varying their relative intensities an…
In this letter we theoretically investigate the formation of localized temporal dissipative structures, and their corresponding frequency combs in doubly resonant dispersive optical parametric oscillators. We derive a nonlocal mean field model, and show that domain wall locking allows for the formation of stable coherent optical frequency combs.
We present an optical-electronic approach to generating microwave signals with high spectral purity. By circumventing shot noise and operating near fundamental thermal limits, we demonstrate 10 GHz signals with an absolute timing jitter for a single hybrid oscillator of 420 attoseconds (1Hz - 5 GHz).
We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices, and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, like such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry, and reduction in cost and system size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in t…
Highly coherent optical sources are a key element in several fields of physics, in particular in time frequency metrology. Over the past decennia, there has been particular efforts in developing such sources to the expense of sophisticated laser systems and relatively smart electronics. We propose here a new general principle of a self-adaptive oscillator where the intricate operation of a 100-m-long active optical resonator and a standard semiconductor laser offers a very high spectral purity and can be tailored to any wavelength. Single frequency operation of this self-adaptive photonic osci…
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network - a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the natu…
We use numerical modeling to study the features of parametric (quasi-Cherenkov) cooperative radiation arising when an electron bunch passes through a crystal (natural or artificial) under the conditions of dynamical diffraction of electromagnetic waves in the presence of shot noise. It is shown that in both Laue and Bragg diffraction cases, parametric radiation consists of two strong pulses: one emitted at small angles with respect to the particle velocity direction and the other emitted at large angles to it. Under Bragg diffraction conditions, the intensity of parametric radiation emitted at…
