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 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.
We discuss the parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are deduced. The results are compared with the results for gravita- tional wave interferometers LIGO and LIGO Voyager.
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.
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 …
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 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.
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 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 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 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.
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.
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.
We present an experimental technique allowing to stabilize the frequency of the non resonant wave in a singly resonant optical parametric oscillator (SRO) down to the kHz level, much below the pump frequency noise level. By comparing the frequency of the non resonant wave with a reference cavity, the pump frequency noise is imposed to the frequency of the resonant wave, and is thus subtracted from the frequency of the non resonant wave. This permits the non resonant wave obtained from such a SRO to be simultaneously powerful and frequency stable, which is usually impossible to obtain when the …
Within a synchronously pumped optical parametric oscillator (SPOPO), the inherent synchronism between the pump and the resonating signal is the magic to partly transfer the coherence property of the pump to the signal. In our demonstration, Vernier effect is observed within a femtosecond SPOPO by simply detuning the FSR of the cavity, generating signal pulses at tunable repetition rate from several GHz to 1 THz with a maximum 22.58 nm full width half maximum (FWHM) bandwidth supporting 160 fs pulses covering the C- and L-bands of the telecom wavelength region. This technique offers a simple me…
A compact and versatile femtosecond mid-IR source is presented, based on an optical parametric oscillator (OPO) synchronously pumped by a commercial 250-MHz Er:fiber laser. The mid-IR spectrum can be tuned in the range 2.25-2.6 μm (signal) and 4.1-4.9 μm (idler), with average power from 20 to 60 mW. At 2.5 μm a minimum pulse duration of 110 fs and a power of 40 mW have been obtained. Active stabilization of the OPO cavity length has been achieved in the whole tuning range.
An inversionless gain of anti-Stokes radiation above the oscillation threshold in an optically-dense far-from-degenerate double-Lambda Doppler-broadened medium accompanied by Stokes gain is predicted. The outcomes are illustrated with numerical simulations applied to sodium dimer vapor. Optical switching from absorption to gain via transparency controlled by a small variation of the medium and of the driving radiation parameters which are at a level less than one photon per molecule is shown. Related video/audio clips see in: A.K. Popov, S.A. Myslivets, and T.F. George, Optics Express Vol. 7, …
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.
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.
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 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…
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 discuss one possible method for suppression of the nonlinear effect of a parametric oscillatory instability in a Fabry-Perot cavity of the next generation of gravitational wave detectors by determination of optimal radii of curvature of interferometers' mirrors. Varying the radii of curvature of the mirrors we can change the frequencies of the optical modes of the Fabry-Perot resonators and distributions of optical fields in optical modes, which, in turn, can change the number of unstable modes, leading to parametric oscillatory instability. The determination of the optimal values of the ra…
Spatially localized and periodic field patterns in periodically modulated optical parametric amplifiers and oscillators are studied. In the degenerate case (equal signal and idler beams) we elaborate the systematic method of construction of the stationary localized modes in the amplifiers, study their properties and stability. We describe a method of constructing periodic solutions in optical parametric oscillators, by adjusting the form of the external driven field to the given form of either signal or pump beams.
We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the -3dB limit in the noise reduction, associated to parametric resonance, with a best experimental result of -7.4dB. In a moderately cooled system, our technique can be efficiently exploited to produce strong squeezing of …
The evolution versus pump power of the spectrum of a singly resonant optical parametric oscillator based on an MgO-doped periodically poled stoichiometric lithium tantalate crystal is observed. The onset of cascade Raman lasing due to stimulated Raman scattering in the nonlinear crystal is analyzed. Spurious frequency doubling and sum-frequency generation phenomena are observed and understood. A strong reduction of the intracavity Raman scattering is obtained by a careful adjustment of the cavity losses.
We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadr…
Similariton-like pulses are found to be formed in synchronously pumped singly resonant optical parametric oscillators (OPO) by numerical simulation. The nonlinear coupled-wave equations can be reduced to inhomogeneous nonlinear Schrödinger equation. The signal pulses with parabola-like temporal intensity profile and linear chirp are presented in OPO. The similariton-like pulses in OPO have many practical and potential applications.
We investigate the transverse mode effects on the frequency combs generated by a type-I optical parametric oscillator (OPO) below threshold. We take the diffraction effects fully into account, considering usual OPO architectures instead of the self-imaging design. Further, we show that an OPO pumped with structured light produces multiple frequency combs simultaneously, corresponding to different combinations of spatial modes in the downconverted fields. This result may apply to the production of hybrid multipartite entanglement in the spatiotemporal modes of a single OPO.
We develop reduced models that describe half-harmonic generation in a synchronously-pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simulton-like sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs. nondegenerate operation, and stability are derived and compared to numerical and experimental results.
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network - two coupled parametric oscillators, where the oscillators never reach a steady state, but show persistent, full-scale, coherent beats, whose frequency reflects the coupling properties and strength. We present a detailed theoretical and experimental study and show that this new dynamical regime appears over a wide range of parameters near the oscillation thresh…
We generated time-multiplexed degenerate optical parametric oscillator (DOPO) pulses using a nonlinear fiber Sagnac loop as a phase-sensitive amplifier (PSA) where the pump and amplified light in pump-signal-idler degenerate four-wave mixing can be spatially separated. By placing the PSA in a fiber cavity, we successfully generated more than 5,000 time-multiplexed DOPO pulses. We confirmed the bifurcation of pulse phases to 0 or $π$ relative to the pump phase, which makes them useful for representing Ising spins in an Ising model solver based on coherent optical oscillator networks. We also co…
Mode locking in lasers is a collective effect, where due to a weak coupling a large number of frequency modes lock their phases to oscillate in unison, forming an ultrashort pulse in time. We demonstrate an analogous collective effect in coupled parametric oscillators, which we term "pairwise mode-locking", where many pairs of modes with twin frequencies (symmetric around the center carrier) oscillate simultaneously with a locked phase-sum, while the phases of individual modes remain undefined. Thus, despite being broadband and multimode, the emission is not pulsed and lacks first-order cohere…
The stability of phase domains and spatial solitons in DOPO under the presence of an injected signal is investigated. The injected signal prevents the nondegenerate regime and, for a particular value of the phase, preserves the equivalence between the two homogeneous states, allowing the domain formation and, in particular, the stability of solitons. The main conclusion is that injection facilitates the experimental observation of solitons in degenerate OPOs.
We propose a flexible scheme based on three coupled optical microcavities which permits to achieve stable oscillations in the microwave range, the frequency of which depends only on the cavity coupling rates. We find the different dynamical regimes (soft and hard excitation) to affect the oscillation intensity but not their period. This configuration may permit to implement compact hyper-parametric sources on an integrated optical circuit, with interesting applications in communications, sensing and metrology.
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent Ising machine (CIM) that efficiently solves computationally hard optimization problems. In the companion paper, we studied experimentally the minimal realization of a CIM, i.e. two coupled parametric oscillators [L. Bello, M. Calvanese Strinati, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 123, 083901 (2019)]. We found that the presence of an energy-co…
We analytically and numerically study the direct soliton generation in a cw-pumped doubly resonant degenerate optical parametric oscillator via pump frequency scanning. By means of bifurcation and linear stability analysis of the homogeneous solutions, we discriminate distinctive soliton forming mechanisms and corresponding dynamics, depending on pump and signal group velocity dispersions (GVDs). To the best of our knowledge, this is the first study regarding the dynamics of pure quadratic solitons. In addition, we discuss how to extend soliton existing regime and easily access quadratic solit…
We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most-efficient mode does not correspond generically to the ground state of the Ising model. We infer that netwo…
