Thin film synchronous pumping optical parametric oscillator

Abstract

An apparatus comprising a photonic integrated circuit, the photonic integrated circuit comprising one or more OPO, each OPO comprising: an input configured to receive a pump wave comprising a pulse or a frequency comb having a pump repetition rate; one or more non-linear portions as part of the resonator or coupled to a resonator having a free spectral range wherein at least one of the free spectral range or one of the harmonics thereof matches the pump repetition rate or the harmonics thereof; and one or more outputs configured to extract a wave generated by the OPO in response to the pump wave and / or a portion of the pump wave.

Description

[0001] Cross-reference to related applications

[0002] This application claims the following rights pursuant to Section 119(e) of 35 USC:

[0003] U.S. Provisional Application No. 63 / 466,188, entitled “THIN FILM SYNCHRONOUSLY PUMPEDOPTICAL PARAMETRIC OSCILLATORS” (CIT-9012-P), filed May 12, 2023, by Alireza Marandi, sLuis. M. Ledezma, Arkadev Roy, Ryoto Sekine, and Robert M. Gray; and

[0004] U.S. Provisional Application No. 63 / 532,648 entitled “ON-CHIP ULTRA SHORT PULSE SYNTHESIZER” (CIT-9055-P), filed on August 14, 2023, by Ryoto Sekine, Robert M. Gray, and Alireza Marandi;

[0005] Both applications are incorporated into this paper by reference.

[0006] Federally funded research and development

[0007] This invention was made with government support, under Air Force licenses FA9550-20-1-0040 and FA9550-23-1-0755, U.S. Army licenses W911NF-18-1-0285 and W911NF-23-1-0048, DARPA license D23AP00158, and National Science Foundation licenses ECCS1846273 and CCF1918549. The government holds certain rights to this invention. Background Technology

[0008] More and more efforts are being focused on nanophotonic platforms. 3-5 Broadband frequency combs are implemented in this system, with applications including dual-comb spectroscopy. 6 , optical communication 7 Optical frequency synthesis 8, 9 and laser ranging 10 However, the spectral coverage of integrated frequency comb sources still lags far behind its desktop counterparts, which use high-pulse-energy lasers and discrete components, and which have recently exceeded six octaves in spectral range. 11,12 Such frequency combs and short-pulse laser sources are useful for applications such as ultrashort pulse synthesis. 13Attosecond Science 14 and biochemical sensing and imaging 15-17 The application of this technology is valuable. What is needed is an improved method for generating coherent pulse sources and frequency combs. This disclosure fulfills this need. Summary of the Invention

[0009] This disclosure describes an on-chip optical parametric oscillator (OPO) pumped by a frequency comb at a repetition rate synchronized with the round-trip time of the OPO cavity. The on-chip OPO is fabricated on a microchip based on a thin-film nonlinear optical material. The on-chip OPO can generate a frequency comb that can be tuned over a wide and / or hard-to-access wavelength range, including but not limited to the visible, near-infrared, and mid-infrared wavelength ranges. The on-chip OPO can also generate an output frequency comb that covers a much wider spectral range than the pump frequency comb. The output frequency comb can cover one or more octaves of the electromagnetic spectrum. The on-chip OPO can also be pumped by a frequency comb having a repetition rate of harmonics of the OPO cavity round-trip time. In this scheme, the on-chip OPO can support multiple pulses simultaneously present within the on-chip OPO cavity. The on-chip OPO may include actuators in an on-chip resonator for adjusting the repetition rate of the output frequency comb and the carrier envelope offset.

[0010] This invention also discloses a multioctave frequency comb generation using an optical parametric oscillator (OPO) in nanophotonic lithium niobate, with only a femtojoule pump energy for synchronous pumping. Energy-efficient and robust coherent spectral broadening occurs well above the OPO's oscillation threshold and is detuned to its linear synchronization with the pump. We demonstrate that the OPO can undergo a time-self-cleaning mechanism by transitioning from an incoherent operating state (typical for operations well above the threshold) to an ultrawide coherent state (corresponding to a nonlinear phase compensation for OPO cavity detuning). This time-self-cleaning mechanism and the subsequent multioctave coherent spectroscopy have not been explored in previous OPO designs and are characterized by relaxed requirements on cavity quality factor and relatively narrow spectral coverage. Compared to other techniques, we achieve an order-of-magnitude reduction in energy requirements, confirm the comb's coherence, and present a path towards more efficient and broader spectral broadening. Our results pave the way for numerous applications in ultrashort pulse and ultrawideband on-chip nonlinear photonic systems.

[0011] This disclosure also discloses a pulse-time multiplexed nanophotonic optical parametric oscillator and its use with OPO-supported cavity secondary solitons. Attached Figure Description

[0012] Now refer to the accompanying drawings, where the same reference numerals always denote corresponding parts:

[0013] Figure 1. Principle and design of multi-octave band nanophotonic OPOs. a, Synchronously pumped OPO on thin-film lithium niobate highlighting key features. b, Microscopic image of several devices when one device in the center is pumped to 1 μm. The chip emits green light due to second harmonic generation (SHG). The top inset is a scanning electron microscope image of the helical region, and the bottom is an image of the entire chip containing 16 OPOs. c. An illustration demonstrating how short pump pulses can be used to engineer near-zero dispersion OPAs. A 60 fs pulse is shown at the top. 2 The simulated gain curves for the waveguides of 26 fs / mm half-harmonic GVD and 26 fs / mm GVM are shown, with the simulated gain curves for the near-zero dispersion waveguide shown at the bottom. The orange solid line marks the center wavelength of the pump, and the orange shaded area marks the 3-dB bandwidth (BW) of the 100-fs source. d depicts the different operating states of the OPO as a function of the pump pulse energy, and the round-trip time output of the OPO in each state.

[0014] Figure 2 OPO characterization. a) Oscillation peaks near the threshold of the OPO when the pump repetition rate is modulated at 600 Hz by a piezoelectric transducer (PZT) in the pump laser cavity. b) Signal spectra at a pump energy of 35 fJ for three different round-trip detunings. c) Efficiency η for different oscillation peaks and their slopes. SL The corresponding OPO signal growth is a function of pump energy. d represents the output spectrum, OPO oscillation peak, and beatnote measurements of the OPO cavity pumped at 54 FJ, 109 fJ, and 121 fJ. OPO oscillation peaks (ii), (v), and (viii) were obtained with the same detector amplification settings. RF beatnotes (iii), (vi), and (ix) were obtained between the free space and on-chip OPO sharing the same pump, with their repetition rate tuned over time.

[0015] Figure 3 Simulation results for different operating states of the nanophotonic OPO are shown. a) The transition from (i) near-threshold coherent operation to (ii) incoherent operation and (iii) back to coherent operation as the pump energy increases. Round-trip time evolution (i-iii) and output spectra (iv-vi) are shown for three different pump intensities using experimental parameters and with a cavity detuning of -10.5 fs. b) Trioctave coherent OPO. The same experimental parameters are used, except that the last millimeter of the PPLN is replaced by a chirped polarization period. The pump pulse energy is 250 fJ.

[0016] Figure 4(a) Performance comparison of integrated spectral broadening and (b) frequency comb synchronously pumped OPOs. a) Wavelength coverage and pump pulse energy of the integrated frequency comb spectral broadening scheme. Arrows indicate pump wavelengths. b) Comb repetition rate and pump threshold energy of the synchronously pumped OPO. The marker shapes indicate the different cavity and nonlinear (NL) element compositions of each OPO, categorized as free space, fiber, integrated and bulk, fiber, and nanophotonics. In both figures, the top legend indicates the material of the nonlinear element. Abbreviations: TFLN: Thin-film lithium niobate, OP: Orientation patterned, MF: Microstructured fiber, HNLF: Highly nonlinear fiber.

[0017] Figure 5 Key OPO design parameters as a function of waveguide geometry. a) Parameters for the spatiotemporal constraints used to tune pulses propagating through our nanophotonic waveguide. An example basic TE mode of 1 μm is shown in the waveguide core. b) Dispersion profile, c) Phase-matched polarization period, d) Optimal synchronous pump cavity length as a function of variations in waveguide top width and etch depth. Actual measured dimensions of our fabricated device are indicated by crosshairs.

[0018] Figure 6 Additional OPO parameters based on the waveguide geometry shown in Figure S1: a) Effective refractive index of the waveguide; b) Second harmonic microscopy image of the periodically polarized pre-waveguide pattern; c) Simulated propagation loss as a function of bending radius for different signal wavelengths. The blue dashed line at 77 μm represents the minimum bending radius used in designing the OPO cavity.

[0019] Figure 7 .OPO Coupler Design. a) Definition of the input / output coupler, and b) An example of output coupler adiabatic design. Here, width and gap refer to the width and gap at the top of the waveguide. c) Fundamental waveguide modes at 1 μm and 2 μm. d) Simulated coupler response using fabricated waveguide geometry. e) Comparison of theoretical coupler behavior with measured spectra of devices with and without couplers of other similar aspects at a 380 fJ pump.

[0020] Figure 8 Experimental setup. Abbreviations: PS: Phase-sensitive, MLL: Mode-locked laser, LP: Long-pass, BS: Beam splitter.

[0021] Figure 9 The measurements were extended to approximately 20 times the threshold. a. Pump pulse energies from the OPO cavity output spectrum up to 380 fJ. b. For the same energy, the top panel shows the OPO oscillation peaks when the PZT scanned the pump repetition rate. The bottom panel shows the RF difference frequency between free space and the on-chip OPO sharing the same pump, tuned over time at a repetition rate of 63.58 mHz.

[0022] Figure 10 The absorption characteristics of atmospheric molecules are compared with the OPO spectrum measured under a pump of 380 fJ. The spectra are taken from the HITRAN database [1].

[0023] Figure 11 Comparison of simulated mode crossovers with measured linear waveguide spectra. a. Simulated modes at the periodically polarized regions of the chip. The mode crossovers experienced by the fundamental TE mode are labeled M1 and M2. Close-ups of these are shown in b and c, respectively. d. Measured power spectral density of the periodically polarized nanophotonic waveguide without an OPO cavity as a function of pump pulse energy. The positions of M1 (680 nm) and M2 (1135 nm) are indicated by arrows.

[0024] Figure 12 OPO difference frequency measurement. a. Experimental setup. b. Two possible methods for OPO combs. CEO The state is illustrated depending on whether the detuned peak l is even or odd. c, (i) RF difference frequency and (ii) spectral overlap, showing interference fringes (blue), because the relative output delay between OPOs shares f in their time-self-cleaning state. CEO It was scanned under certain circumstances.

[0025] Figure 13 The OPO difference frequency is locked in the time-based self-cleaning state. The pump here is 121 fJ, and the pump repetition rate is locked to the value in the text. Figure 2 The OPO peak structure seen in the OPO oscillation peak in d(viii). The top panel shows f at a representative time. rep / 2 difference frequency, and the bottom panel shows the duration of the difference frequency over time. The jitter signal caused by free space and on-chip OPO cavity locking causes the main f... rep Two sets of side stripes with a frequency difference of / 2.

[0026] Figure 14 SHG difference frequency measurement. a. Experimental setup. b. Spectral overlap between chip SHG output and PCF. Sample difference frequencies measured at c, 380 fJ, d, 109 fJ, and e, 54 fJ, where different colors correspond to different pump frequencies. CEO Abbreviations: SP: Short pass, PCF: Photonic crystal fiber (Menlo Systems), HWP: Half-wave plate.

[0027] Figure 15 a) The extended state of operation of the nanophotonic OPO, and b) Based on the detuning peak (l) and cavity round-trip detuning (ΔT). RT OPO resonance marked with )

[0028] Figure 16 OPO characterization: l=2, φ CEO =0.

[0029] Figure 17 OPO characterization: l=0, φ CEO =0.

[0030] Figure 18 OPO characterization: l=-2, φ CEO =0.

[0031] Figure 19 OPO characterization: l=3, φ CEO =0.

[0032] Figure 20 OPO characterization: l=1, φ CEO =0.

[0033] Figure 21 .OPO characterization: l=-1, φ CEO =0.

[0034] Figure 22 .OPO characterization: l=-3, φ CEO =0.

[0035] Figure 23 l=-3, φ CEO The state =0 (iii) is further characterized by coherence. a. g (1) Coherence is expressed as a function of wavelength, PSD, and round-trip spectrum, with points having a simulated coherence greater than 0.6 represented by light green dots and the rest by pink. For the round-trip phase plot, points with a phase difference less than π / 6 compared to the previous round trip are plotted in green, and the rest are marked in pink. b, Simulated comb lines at the output. The 2-μm, 1-μm, 69-nm, and 500-nm combs correspond to the half-harmonic, pump, pumped sum-frequency generation, and pumped half-harmonic and second harmonic, respectively.

[0036] Figure 24 OPO characterization: peak value 2, φ CEO =π.

[0037] Figure 25 OPO characterization: peak value 0, φ CEO =π.

[0038] Figure 26 OPO characterization: peak value -2, φ CEO =π.

[0039] Figure 27 l=-3, φ CEOThe intensity and phase evolution within the crystal at half-harmonic (top) and pump (bottom) states (iii) = 0. For a(ii) and b(ii), the phase surrounds the region with an intensity greater than about 0.2 W, and makes the phase at the location with lower intensity more transparent.

[0040] Figure 28 The time output of the octave comb under different detuning conditions. In each case, the pink line showing the 3dB bandwidth of the center characteristic is approximately 4.2 fs. Here, φ CEO =0.

[0041] Figure 29 l=3, φ CEO Characterization of the triplet comb at =0. The coherence and normalized output spectrum of the simulated OPO are obtained, with additional duty cycle variations in the polarization period, to produce a triplet coherent frequency comb pumped at 248 fJ.

[0042] Figure 30. Secondary solitons in a nanophotonic cavity. (a) Concept of these solitons and pulse compression generated in a synchronously pumped OPO. (b) Dispersion parameters of a nanophotonic periodically polarized lithium niobate (PPLN) OPO as a function of waveguide top width and etch depth. A PPLN length of 5 mm and a resonator length of 11 mm were used.

[0043] Figure 31 : An ultrawide tunable frequency comb from a nanophotonic parametric oscillator. a) Schematic diagram of a dual-resonance optical parametric oscillator fabricated on an X-cut thin-film lithium niobate consisting of periodically polarized regions for effective parametric nonlinear interactions. Waveguides (size: 2.5 μm width, 250 nm etch depth) support guided modes in the mid-infrared corresponding to the idle wave. b) Quasi-phase-matched parametric gain tuning from visible to mid-infrared. The phase-matching curves result in tunable mid-infrared idle emission achieved by optical parametric oscillator devices with slightly different polarization periods (Λ) integrated on the same chip. The same chip is capable of generating a tunable visible frequency comb due to the sum-frequency generation (SFG) process between the pump and the signal and idle waves. Other accompanying upconversion processes include the second harmonic (SH) of the signal and the idle. Some second harmonic phase-matching curves are omitted for clarity. c) Emissions from the chip overlap with strong molecular absorption lines in the mid-infrared, covering a spectral window important for molecular spectra. The spectral coverage in visible light includes atomic transition wavelengths corresponding to commonly used trapped ions / neutral atoms / color centers.

[0044] Figure 32: Near-IR to mid-IR frequency combs from nanophotonic OPOs on a single chip. a) Schematic diagram of the experimental setup for pumping and measuring the optical parametric oscillator chip used for synchronous pumping. b) Experimental measurements of the spectral and temporal characteristics (intensity autocorrelation traces) of electro-optic pulse pumping, showing a pulse width of approximately 1 ps. c) Broadband infrared spectral coverage of the OPO chip showing its signal and idle spectra as its operation transitions from degenerate tuning to far non-degenerate. Individual colors represent outputs from different OPO devices on the same chip with different polarization periods. Magnified version shows the comb structure.

[0045] Figure 33 Characteristics of the frequency comb generated from a synchronously pumped on-chip OPO. a) Resonant peak structure obtained by scanning the pump center wavelength, typical of dual-resonant OPO operation. A magnified view of a single peak is shown in the inset. b) Existence range of a synchronously pumped OPO with a fixed pump power as the pump repetition rate varies. c) Fine tuning of the OPO frequency comb output achieved by tuning the pump center wavelength. d) Spectral broadening of the OPO operating under degeneracy corresponding to a sub-picosecond transform-limited duration of approximately 400 fs. e) Verification of the coherence of the OPO output evident from the presence of interference fringes (see inset) in the electric field cross-correlation trace. f) The close agreement between the spectrum measured by a spectrometer and the spectrum obtained by cross-correlation of the Fourier transform field confirms the coherence of the OPO output.

[0046] Figure 34 Visible frequency comb generation from an integrated optical parametric oscillator chip. a) The complete emission spectrum of the OPO (spectroscopy obtained from different spectrometers / spectrometers is stitched together). In addition to the emission of signal and idle waves, the OPO also produces output in the visible spectrum due to auxiliary nonlinear processes (i.e., second harmonic generation (SHG) and sum-frequency generation (SFG)). b) Optical microscopic images capturing visible light emission from various regions of the periodically polarized portion of the OPO device; c) Tunable visible frequency comb generation from the integrated OPO chip, where different colors indicate spectra obtained from OPOs with different polarization periods.

[0047] Figure 35 SEM images of the thermally adiabatic coupler region. a) Waveguide (size: 2.5 μm width, 250 nm etch depth) supports guided modes in the mid-infrared corresponding to the idle wave, showing its electric field distribution (basic TE mode). b) SEM image of the fabricated device showing the coupler region.

[0048] Figure 36 : Visible frequency comb generation. a), b), c) Tunable visible frequency combs (sum frequency generation between signal and pump) are obtained through pump frequency tuning experiments.

[0049] Figure 37 : Second harmonic generation of the signal frequency comb. a) Phase matching curves corresponding to different polarization periods of the second harmonic generation of the signal frequency comb. b) Coarse tuning of the second harmonic of the signal frequency comb obtained from the OPO chip. c) Fine tuning of the second harmonic of the signal frequency comb obtained from a single OPO via pump wavelength tuning.

[0050] Figure 38 Coupler response and OPO conversion efficiency. a) Signal conversion efficiency as a function of on-chip pump power. Experimental data fit well.

[0051] Figure 39 : Measurement data of average power for each comb line. Mid-infrared frequency comb (idle frequency comb) spectra obtained using a spectrometer used to calculate the power of each comb line. Spectrometer settings: resolution bandwidth 1 nm, sampling interval 0.05 nm, and frequency comb repetition rate approximately 19 GHz.

[0052] Figure 40 Electro-optical comb generation setup. a) Schematic diagram of the electro-optical comb generation setup for synchronous pumping of OPO. Arbitrary waveform generator (AWG), semiconductor optical amplifier (SOA), intensity modulator (IM), phase modulator (PM), ytterbium-doped fiber amplifier (YDFA), and optical spectrum analyzer (OSA). b, c, d) Simulated waveforms in the time and frequency domains at different stages of the pump preparation setup.

[0053] Figure 41 : Quasi-synchronous pumping OPO setup. a) Schematic diagram of the setup for generating an electro-optical comb that generates synchronous pumping for the OPO in quasi-mode operation. Arbitrary waveform generator (AWG), semiconductor optical amplifier (SOA), intensity modulator (IM), phase modulator (PM), ytterbium-doped fiber amplifier (YDFA), optical spectrum analyzer (OSA). b) Measured time-domain trace.

[0054] Figure 42 Schematic diagram of the setup used to estimate cavity FSR. Arbitrary waveform generator (AWG), semiconductor optical amplifier (SOA), intensity modulator (IM), ytterbium-doped fiber amplifier (YDFA).

[0055] Figure 43Spectral broadening and associated pulse compression in the degenerate state of OPO operation. a) Experimentally obtained spectrum plotted on the frequency axis after spectral shift, showing the effect of spectral broadening in the signal compared to the pump. b) Spectrum obtained from numerical simulation, showing the spectral broadening effect (assuming a sech-shaped pump pulse). c) Pump pulse and signal pulse in the time domain obtained from numerical simulation. d) The numerically obtained signal pulse represents approximately 2 times pulse compression when fitted with a sech-shaped pulse. e) Normalized round-trip evolution of the signal pulse initiated from the vacuum field until it reaches steady state.

[0056] Figure 44 [Coherence Verification Setup. a) Schematic diagram of the setup used to verify the coherence of the OPO output. b) RF difference frequency measurement corresponding to the repetition rate of the applied OPO during synchronous pumping.]

[0057] Figure 45: Fully integrated, envisioned universal frequency comb source. a) An example of a near-IR picosecond pump source based on lithium niobate nanophotonics, consisting of cascaded intensity and phase modulators followed by a dechirped helical waveguide. b) An example of a lithium niobate OPO chip consisting of an array of OPOs dedicated to covering different spectral regions, which can be programmably pumped by means of an MZI routing circuit in front of it.

[0058] Figure 46 Quasi-phase-matched temperature tuning. Quasi-phase-matched temperature tuning obtained from simulation a) the signal and idle wave, and b) their corresponding upconversion with the pump resulting in a visible frequency comb. The pump wavelength remains fixed at 1060 nm.

[0059] Figure 47 Experimental setup for measuring a 40-pulse time-multiplexed optical parametric oscillator. (a) An on-chip helical OPO cavity with a free spectral range of 250 MHz was pumped using an EO comb with a repetition rate of 10 GHz, resulting in the simultaneous oscillation of 40 independent signal pulses. The pump is characterized by its spectrum (b) and intensity autocorrelation (c). (d) Optical microscopic image of the fabricated on-chip helical cavity.

[0060] Figure 48 Experimental results show the interferometric behavior of the OPO output in degenerate (a) and non-degenerate (b) cases. Subplot (i) shows the spectra of both. (ii) Samples of the interferometric time trace data measured at the interferometer input compared to a reference. (iii) Histograms of the peaks measured in each time chamber, showing the expected discretization when the OPO is degenerate. (iv) Comparison of the theoretical probability mass function with the output level for the degenerate case.

[0061] Figure 49. Schematic diagram of pump sub-circuit and additional components.

[0062] Figure 50 Methods for manufacturing equipment.

[0063] Figure 51 Methods for operating the equipment. Detailed Implementation

[0064] In the following description of preferred embodiments, reference is made to the accompanying drawings, which form a part therein, and specific embodiments in which the invention can be practiced are illustrated by way of illustration. It should be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the invention.

[0065] Technical Description

[0066] Short-pulse frequency comb integrated sources typically generate picojoules or femtojoules of pulse energy. 2, 4, 18-20 Furthermore, their spectral coverage is almost no octave. 21, 22 This necessitates further spectral broadening stages for many applications, which to date have been strictly limited to those with discrete amplifiers and components. 1, 8, 23 This can be achieved through desktop systems. The femtojoule-level multi-octave coherent spectral broadening mechanism has so far exceeded the capabilities of current photonics technology; therefore, the path towards a fully integrated multi-octave frequency comb remains elusive.

[0067] Typically, this is achieved by passing femtosecond or picosecond pulses with energies from 0.1 nJ to 10 nJ through a secondary (χ²) array with various designs. (2) ) or Cole (χ (3) Significant spectral broadening can be achieved using nonlinear waveguides, crystals, or optical fibers. 1, 24-28 Among these schemes, waveguides with second-order nonlinearity are becoming increasingly effective, particularly due to recent advances in quasi-phase matching and dispersion engineering. 24, 26, 29 They also exhibit superior performance compared to their cubic counterparts. However, to reach octaves and beyond the coherent spectrum, they still require tens of picojoules of energy. 29 This far exceeds the capabilities of current integrated frequency comb sources.

[0068] Spectral broadening and enhanced resonance are expected to improve energy requirements. However, to date, such experiments remain below the octave. 23, 30, 31 This is primarily due to the overly constrained dispersion requirements of cubic coherent spectral broadening schemes, especially when combined with high Q requirements. Indeed, even linear components in nanophotonics with multioctave spectral responses remain challenging to design and implement. 32In contrast, second-order nonlinearity not only enables lower energy requirements in single-pass configurations, but also provides a wider range of nonlinear processes for broadening ultrawide coherent spectra resulting from nonlinear interactions in the far-end portions of the spectrum. 11, 12 However, proper resonator design is necessary to enable the sequence of second-order nonlinear processes to produce an operating scheme with coherent spectral broadening toward multioctave operation.

[0069] The path toward such octave-range nonlinear resonators is based on a synchronously (sync-)-pumped degenerate OPO, which has so far been successfully used in bulk optics for efficient phase-locked down-conversion via half-harmonic generation of a broadband frequency comb. 15, 33-35 Recent research by one or more of the inventors indicates the potential of synchronously pumped OPOs for extreme pulse shortening and spectral broadening while maintaining the coherence of the pump. 36 However, the lack of dispersion engineering, low parametric gain bandwidth, and high picojoule threshold in bulk nonlinear crystals have limited their applicability to compact and ultra-wideband frequency comb applications. Dispersion-engineered optical parametric amplifiers (OPAs) 37 Narrowband synchronous pumping OPO in lithium niobate nanophotonics 38 The latest developments have paved the way for overcoming these limitations and opening up new frontiers in ultrawideband, ultralow-energy nonlinear optics that were previously unattainable.

[0070] First embodiment: Multioctave frequency comb

[0071] 1. Equipment Structure

[0072] Figure 1a This illustrates the design of an on-chip synchronous pump OPO, in which the fabricated device, such as Figure 1b As shown. The input / output coupler is designed to allow resonance only around the pump's half-harmonic (see Supplementary Information section), and the cavity is designed to have minimal dispersion for these wavelengths. To phase and frequency lock the OPO, the OPO is pumped almost synchronously in a degenerate state, requiring a cavity round-trip time of 4 ns for a pump comb with a repetition rate of 250 MHz. Utilizing the effective refractive index of our nanophotonic lithium niobate waveguide (wgs), this corresponds to a cavity length of 53 cm.

[0073] To achieve ultra-high, ultra-wide, phase-sensitive gain capable of generating coherent broadband combs at fJ pump pulse energies, the OPO comprises a 10.8 mm OPA with appropriate dispersion engineering and quasi-phase matching (QPM). Specifically, our goal is to minimize group velocity dispersion (GVD) of the pump and signal, as well as group velocity mismatch (GVM) between the pump and signal. 37 . Figure 1dThis demonstrates the large gain bandwidth achievable when a 100-fs pump is coupled to a waveguide with a near-zero dispersion design, in contrast to the large dispersion waveguides favored by wide-tuned OPOs. 38, 39 The design of the polarization period, cavity length, and coupler for synchronous pumping operation can be found in the supplementary section.

[0074] Figure 1d Different operating states of the nanophotonic OPO are shown. At low pump pulse energies, the OPO exceeds a threshold when the gain overcomes the cavity losses. This is typically the state in which the OPO is operated to produce a phase-locked-to-pump coherent output. 34 At higher pump pulse energies, it is known that degenerate OPOs transition to an unstable operating state, where phase-locked operations decrease. 40, 41 However, here we find that well above the threshold, the OPO can undergo a phase-locked state transition due to cavity compensation of the nonlinear phase. This is highlighted in the accompanying time-domain plot as a time-self-cleaning mechanism, where, after a finite number of round trips, the output pulse intensity is seen to stabilize into an ultrashort characteristic over multiple octaves. The emergence of this coherence and ultrashort pulse formation is reminiscent of condensation and thermalization occurring in other nonlinear multimode systems. 42,43 .

[0075] 2. Experimental Results

[0076] exist Figure 2 a- Figure 2 In section c, we demonstrate the near-threshold performance of the nanophotonic OPO. With a scan pump repetition rate of 600 Hz, we observe the oscillating peaks of the OPO, such as... Figure 2 As shown in figure a. These peaks are characteristics of the double resonant operation. 34 We actively locked the pump repetition rate to the center of each of these peaks, and Figure 2 Figure b shows the pump repetition cycle and cavity round-trip time ΔT. RT The near-threshold signal spectrum of three such peaks at different detuning points. Figure 2 In c, we show the measured input-output pulse energy growth for these identical peaks. We extrapolate the threshold and slope efficiency η. SL Furthermore, the peak with the lowest threshold is defined as the zero-cavity detuning state. For this peak, we estimate the OPO threshold to be approximately 18 fJ.

[0077] exist Figure 2In section d, we present three characteristic output spectra of the OPO. At a pump of 54 fJ, we observe the typical OPO behavior. Spectral broadening occurs at the pump, half-harmonic, and second harmonic, with a significant sum-frequency generation (SFG) between the pump and half-harmonic. At a pump of 109 fJ, we observe a continuous spectrum from 600 nm to 2710 nm, and at 121 fJ, we observe a continuous spectrum from 443 nm to 2676 nm. The valley at 2.8 μm is associated with OH absorption peaks in LN and / or the buffer layer. 39, 44 Furthermore, the kinks near 680 nm and 1135 nm are due to mode crossover (see Supplementary Section). It is also noteworthy that the spectrum at 121 fJ exhibits some unique features on the long-wavelength side of the spectrum that are absent in the case of 109 fJ pumping.

[0078] To characterize the coherence of the OPO at these pump pulse energies, we used a 2.1 μm-centered filter to interfere with the chip output with the output of a free-space OPO pumped by the same laser. When operating in a coherent state, a degenerate OPO above a threshold can have two possible CEO frequencies, differing by half the pump repetition rate f. rep / 2, which depends on the oscillation peak 34 When an on-chip OPO has a different CEO than a free-space OPO, f should be observed when their outputs are superimposed spatially and temporally. rep The difference frequency at / 2. For Figure 2 The coherence measurement in d is the repetition rate of the pump scan over time. At a pump speed of 54 fJ, Figure 2 d(ii) shows the signature of the on-chip OPO at certain detuning points, which is caused by Figure 2 f between OPO in d(iii) rep / 2 Difference Frequency Reflection. The lack of these characteristics in both the OPO power and difference frequency at the pump at 109 fJ indicates that the on-chip OPO has transitioned from a coherent to an incoherent state. However, at 121 fJ, the OPO peak structure and RF difference frequency reappear, signifying the re-emergence of a coherent operating scheme.

[0079] The coherence of the second harmonic components of these spectra was confirmed by using a pumped spectral broadening output from a photonic crystal fiber. We interfered with this broadened pump using the second harmonic component of an on-chip OPO and observed the resulting carrier envelope offset frequency f. CEO The difference frequency and Figure 2The pump repetition rate of all pump pulse energies in d at 250 MHz, regardless of detuning (see Supplementary Section). Specifically, at a pump of 121 fJ, because both the half-harmonic comb and the second harmonic comb are coherent with respect to the pump, and all frequency components of our spectrum are generated through parametric processes of these three combs. 29 Therefore, we conclude that Figure 2 The continuous 2.6 octave spectrum in d is coherent. We lock the pump repetition rate to keep the OPO oscillating in this state, and in Supplementary Part IIE, we show the difference frequency signal held over time.

[0080] The dynamics of this OPO are far above a threshold, and we explore how numerical simulations can establish coherence over such a wide spectrum. To capture the multioctave nonlinear interactions occurring in the OPO, we model the electric field in the nanophotonic cavity as a single envelope in the frequency domain, which evolves using a split-step Fourier method for propagation in the PPLN region and cavity feedback using a linear filter (see Supplementary Section). Figure 3 In section a, we show how this captures different operational states when using parameters matched to those used in our experiments. At 16 fJ, the OPO exceeds the threshold and stabilizes after approximately 20 round trips. At this point, all frequency-transition components (OPO, SHG, pumped SFG, and OPO) are coherent relative to the pump, and they remain constant between round trips. As the pump pulse energy increases, fewer round trips are required to form the OPO, and at a pump of 137 fJ (approximately 9 times above the threshold), we observe that the OPO output is incoherent.

[0081] However, at a pump of approximately 204 fJ (about 13 times above the threshold), the half-harmonic is considered to acquire a π phase shift through nonlinear interaction with the pump during each single pass through the PPLN region. This can be compensated for by detuning the cavity with an odd number of OPO peaks, or by adding a constant phase offset π between the pump and the cavity, which corresponds to the phase offset φ of the pump's carrier envelope. CEO (See Supplementary Section IIIB). The former case is in Figure 3 As shown in a(iii), two octave-band coherent continuous combs are illustrated, which stabilize after approximately twenty round trips and have a time characteristic as short as 4 fs (see Supplementary Section IIIC). The output spectrum is also very similar. Figure 2 Experimental results of 121 fJ for detuning of d.

[0082] Simulations were used to further investigate how to extend the coherent operation of the OPO to even broader spectra. By replacing the last millimeter of the PPLN region with a chirped polarization period for efficient second harmonic and sum-frequency generation, we achieved... Figure 3b shows a coherent triplet continuous frequency comb with a pump energy of approximately 250 fJ.

[0083] exist Figure 4 In this figure, we compare our results with other integrated spectral broadening schemes and synchronously pumped OPOs. This figure highlights how our nanophotonic OPO design and its operating scheme achieve an order-of-magnitude improvement in energy efficiency for coherent spectral broadening. Our study represents the lowest-threshold synchronously pumped OPO achieved through its near-zero dispersion design. This ultra-low-threshold operation enables access to previously unexplored operating schemes for OPOs far above the threshold, where ultra-broad coherent spectral broadening is achieved due to the balance between cavity detuning and nonlinear phase shift.

[0084] In summary, we have experimentally demonstrated a near-synchronous pumped nanophotonic OPO operating under near-zero GVM, zero GVD, fs-pumping, high-gain, low-finess schemes, resulting in an ultrawideband coherent output with only about 121 fJ energy. The 2.6 octave frequency comb provides unprecedented opportunities for on-chip applications, including wavelength division multiplexing. 7 Dual-comb spectrum 45 and frequency synthesis 5 We demonstrate the OPO transition from incoherent to coherent operation schemes and show the path towards a wider frequency comb source in the femtojoule scheme.

[0085] 3. Manufacturing and characterization methods

[0086] Equipment manufacturing Our device is fabricated on a 700 nm thick X-cut MgO-doped lithium niobate film on a SiO2 / Si (NANOLN) substrate. According to... 37 The procedure involves stripping and applying voltage to periodically flip ferroelectric domains, patterning Cr / Au polarized electrodes with 16 fixed polarization cycles ranging from 4.955 to 5.18 μm. During polarization, the electrodes are removed, and the waveguide is etched using Ar polishing and a hydrogenated silicon silsesquioxane (HSQ) etch mask. Finally, the waveguide facets are mechanically polished to allow for butt coupling. Each OPO measures 0.5 mm x 13 mm.

[0087] Optical MeasurementMeasurements were performed using a Menlo Orange HP10Yb mode-locked laser (MLL) centered at 1045 nm. Pulses of 100 fs length were output at 250 MHz (tuning range ±1 MHz). Light was coupled to and from the chip using a Newport 50102-02 reflector, selected for its minimal chromatic aberration. All results described in this embodiment were performed on a device regulated at 26°C with a 5.075 μm polarization period by a thermoelectric cooler (TEC). The lowest OPO threshold was obtained from a pump repetition rate of 250.1775 MHz, which we defined as the zero-detuned state. The device exhibited a total throughput loss of 43.4 dB and, according to… 37 Using the method described above, we measured the input and output coupling losses to be 35.7 dB and 7.7 dB, respectively. For Figure 3 The results in d were obtained by collecting spectra using two different OSAs, specifically Yokogawa AQ6374 (350–1750 nm) and AQ6376 (1500–3400 nm). The OSAs were operated with high sensitivity 3 except for the case of a 121 fJ pump (where high 2 was used). Figure 2 The RF spectra in d were collected using an InGaAs high-speed photodiode (DSC2-40S) on an electronic spectrometer (Rhode & Schwarz FSW). SHG difference frequency analysis was performed using a high-speed silicon avalanche photodiode (Menlo Systems APD210).

[0088] Numerical simulation We use commercial software (Lumerical Inc.) to solve the waveguide modes shown in Supplementary Sections I and II, which allows us to perform dispersion engineering and quasi-phase matching on our device. For nonlinear optical simulations, we solve the analytical nonlinear envelope equations as described in Supplementary Section III. Unless otherwise specifically mentioned, simulations are performed without a constant phase offset between the pump and cavity. This parameter is effectively used as the carrier envelope offset phase φ of the pump. CEO Since the simulations were performed with a 1.7 ps time window, it should be noted that most of the short-wavelength side of the spectrum is outside our simulation time window. For example, the simulated GVM between our simulated reference frame at the 2090 nm half-harmonic signal wavelength and the pumped second harmonic at 522 nm is 721 fs / mm. As a result, the upconversion portion of the spectrum in the simulation tends to be smaller than the portion measured experimentally. In these simulations, we only incorporated χ²... (2) The effects of nonlinearity are not considered, and χ is not taken into account. (3)The impact of this. In particular, considering the low pulse energy and low fineness of our cavity, we consider this a good approximation, but this may be an additional reason for the small discrepancies between experiments and simulations.

[0089] References for the first embodiment

[0090] The following references are incorporated herein by reference.

[0091] [1] DR Carlson, DD Hickstein, W. Zhang, AJ Metcalf, F. Quinlan, SA Diddams, and SB Papp, Science 361, 1358 (2018).

[0092] [2] SA Diddams, K. Vahala, and T. Udem, Science 369, eaay3676 (2020).

[0093] [3] TJ Kippenberg, AL Gaeta, M. Lipson, and ML Gorodetsky, Science 361, eaan8083 (2018).

[0094] [4] L. Chang, S. Liu, and JE Bowers, Nature Photonics 16, 95 (2022).

[0095] [5] AL Gaeta, M. Lipson, and TJ Kippenberg, Nature Photonics13, 158 (2019).

[0096] [6] M. -G. Suh, Q. -F. Yang, KY Yang, X. Yi, and KJ Vahala, Science 354, 600 (2016).

[0097] [7] P. Marin-Palomo, JN Kemal, M. Karpov, A. Kordts, J. Pfeifle,MHP Pfeiffer, P. Trocha, S. Wolf, V. Brasch, MH Anderson, R.Rosenberger, K. Vijayan, W. Freude, TJ Kippenberg, and C. Koos, Nature546, 274 (2017).

[0098] [8] Spencer DT, Drake T, Briles TC, Stone J, Sinclair LC,C. Fredrick , Q. Li , D. Westly , BR Ilic , A Bluestone , N Volet , T. Komljenovic , L Chang , SH Lee , DY Oh , M. -G. Suh, KY Yang, MHPPfeiffer, TJ Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, NRNewbury, K. Srinivasan, JE Bowers, SA Diddams, and SB Papp, Nature557, 81 (2018).

[0099] [9] MA Tran, C Zhang, TJ Morin, L Chang, S Barik, Z Yuan,W. Lee, G. Kim, A. Malik, Z. Zhang, J. Guo, H. Wang, B. Shen, L. Wu, K. Vahala, JE Bowers, H. Park, and T. Komljenovic, Nature 610, 54 (2022).

[0100]

[10] J. Riemensberger, A. Lukashchuk, M. Karpov, W. Weng, E. Lucas,J. Liu, and TJ Kippenberg, Nature 581, 164 (2020).

[0101]

[11] DMB Lesko, H. Timmers, S. Xing, A. Kowligy, AJ Lind, andS. A. Diddams, Nature Photonics 15, 281 (2021).

[0102]

[12] U. Elu, L. Maidment, L. Vamos, F. Tani, D. Novoa, MH Frosz,V. Badikov, D. Badikov, V. Petrov, P. St. J. Russell, and J. Biegert, NaturePhotonics 15, 277 (2021).

[0103]

[13] A. Wirth, MT Hassan, I. Grguraš, J. Gagnon, A. Moulet, TTLuu, S. Pabst, R. Santra, ZA Alahmed, AM Azzeer, VS Yakovlev, V.Pervak, F. Krausz, and E. Goulielmakis, Science 334, 195 (2015).

[0104]

[14] PB Corkum and F. Krausz, Nature Physics 3, 381 (2007).

[0105]

[15] AV Muraviev, VO Smolski, ZE Loparo, and KLVodopyanov, Nature Photonics 12, 209 (2018).

[0106]

[16] N. Picqué and TW Hänsch, Nature Photonics 13, 146 (2019).

[0107]

[17] C.-I. Chang, Hyperspectral Imaging (Springer US, 2003).

[0108]

[18] M. Yu, D. Barton III, R. Cheng, C. Reimer, P. Kharel, L. He, L. Shao, D. Zhu, Y. Hu, HR Grant, L. Johansson, Y. Okawachi, AL Gaeta, M. Zhang, and

[0109] M. Lončar, Nature 612, 252 (2022).

[0110]

[19] Guo Q, Sekine R, Williams JA, Gutierrez BK, Gray RM,L. Ledezma, L. Costa, A. Roy, S. Zhou, M. Liu, and A. Marandi, Mode-lockedlaser in nanophotonic lithium niobate (2023), arXiv:2306.05314.

[0111]

[20] B. Stern, X. Ji, Y. Okawachi, AL Gaeta, and M. Lipson, Nature562, 401 (2018).

[0112]

[21] MHP Pfeiffer, C. Herkommer, J. Liu, H. Guo, M. Karpov, E. Lucas, M. Zervas, and TJ Kippenberg, Optica 4,684 (2017).

[0113]

[22] Li Q, Briles TC, Westly DA, Drake TE, Stone JR, Ilic BR, Diddams SA, Papp SB, and Srinivasan K, Optica 4, 193 (2017).

[0114]

[23] E. Obrzud, M. Rainer, A. Harutyunyan, MH Anderson, J. Liu, M. Geiselmann, B. Chazelas, S. Kundermann, S. Lecomte, M. Cecconi, A. Ghedina,E. Molinari, F. Pepe, F. Wildi, F. Bouchy, TJ Kippenberg, and T. Herr,Nature Photonics 13, 31 (2019).

[0115]

[24] T.-H. Wu, L. Ledezma, C. Fredrick, P. Sekhar, R. Sekine, Q. Guo,RM Briggs, A. Marandi, and SA Diddams, Visible to ultraviolet frequencycomb generation in lithium niobate nanophotonic waveguides (2023), arXiv:2305.08006.

[0116]

[25] Yoon Oh D, Yang KY, Fredrick C, Ycas G, Diddams SA, andK. J. Vahala, Nature Communications 8, 13922(2017).

[0117]

[26] M. Ludwig, F. Ayhan, TM Schmidt, T. Wildi, T. Voumard, R.Blum, Z. Ye, F. Lei, F. Wildi, F. Pepe, MA Gaafar, E. Obrzud, D. Grassani,F. Moreau, B. Chazelas, R. Sottile, V. Torres-Company, V. Brasch, LGVillanueva, F. Bouchy, and T. Herr.

[0118]

[27] J. M. Dudley, G. Genty, and S. Coen, Rev. Sci. Mod. Phys. 78,1135(2006)

[0119]

[28] S. Vasilyev, I. Moskalev, V. Smolsky, J. Peppers, M. Mirov, A. Muraviev, K. Vodopyanov, S. Mirov, and V. Gapontsev, Opt. Express 27, 16405(2019).

[0120]

[29] M. Jankowski, C. Langrock, B. Desiatov, A. Marandi, C. Wang, M. Zhang, CR Phillips, M. Lončar, and MM Fejer, Optics 7, 40(2020).

[0121]

[30] MH Anderson, R Bouchand, J Liu, W Weng, E Obrzud, T Herr, and TJ Kippenberg, Optica 8, 771(2021).

[0122]

[31] MH Anderson, W. Weng, G. Lihachev, A. Tikan, J. Liu, and TJ Kippenberg, Nature Communications 13, 4764 (2022).

[0123]

[32] S. Molesky, Z. Lin, AY Piggott, W. Jin, J. Vucković, and AW Rodriguez, Nature Photonics 12, 659 (2018).

[0124]

[33] McMahon PL, Marandi A, Haribara Y, Hamerly R, Langrock C,S. Science 354, 614 (2016) Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, RL Byer, MM Fejer, H. Mabuchi, and Y. Yamamoto.

[0125]

[34] A. Marandi, NC Leindecker, V. Pervak, RL Byer, and KLVodopyanov, Opt. Express 20, 7255 (2012).

[0126]

[35] A. Marandi, KA Ingold, M. Jankowski, and RL Byer, Optica3, 324(2016).

[0127]

[36] A. Roy, R. Nehra, S. Jahani, L. Ledezma, C. Langrock, M. Fejer,and A. Marandi, Nature Photonics 16, 162 (2022).

[0128]

[37] L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A. Marandi, Optics 9, 303 (2022).

[0129]

[38] A. Roy, L. Ledezma, L. Costa, R. Gray, R. Sekine, Q. Guo, M.Liu, RM Briggs, and A. Marandi, Visible-to-mid-ir tunable frequency combin nanophotonics (2022), arXiv:2212.08723.

[0130]

[39] L. Ledezma, A. Roy, L. Costa, R. Sekine, R. Gray, Q. Guo, R. Nehra, R. Briggs, and A. Marandi, Science Advances 9, eadf9711 (2023).

[0131]

[40] R. Hamerly, A. Marandi, M. Jankowski, M. Fejer, Y. Yamamoto,and H. Mabuchi, Phys. Rev. Fr. A 94, 063809 (2016).

[0132]

[41] S. Mosca, M. Parisi, I. Ricciardi, F. Leo, T. Hansson, M. Erkintalo, P. Maddaloni, P. De Natale, S. Wabnitz, and M. De Rosa, Phys. Rev.Lett. Rev. 121, 093903 (2018).

[0133]

[42] LG Wright, FO Wu, DN Christodoulides, and FW Wise, Nature Physics 18, 1018 (2022).

[0134]

[43] Krupa K, Tonello A, Shalaby BM, Fabert M, Barthélémy A,G. Millot, S. Wabnitz, and V. Couderc, Nature Photonics 11, 237 (2017).

[0135]

[44] M. Leidinger, S. Fieberg, N. Waasem, F. Kühnemann, K. Buse, andI. Breunig, Opt. Express 23, 21690 (2015).

[0136]

[45] N. Picqué and T. W. Hänsch, Nature Photonics 13, 146 (2019).

[0137]

[46] Y. Okawachi, M. Yu, B. Desiatov, B. Y. Kim, T. Hansson, M. Lončar, and A. L. Gaeta, Optica 7, 702 (2020).

[0138]

[47] M. Yu, B. Desiatov, Y. Okawachi, A. L. Gaeta, and M. Lončar,Opt. Lett. 44, 1222 (2019).

[0139]

[48] D. R. Carlson, D. D. Hickstein, A. Lind, J. B. Olson, R. W. Fox,R. C. Brown, A. D. Ludlow, Q. Li, D. Westly, H. Leopardi, T. M. Fortier, K.Srinivasan, S. A. Diddams, and S. B. Papp, Phys. Rev. Appl. 8, 014027 (2017).

[0140]

[49] B. Spaun, P. B. Changala, D. Patterson, B. J. Bjork, O. H.Heckl, J. M. Doyle, and J. Ye, Nature 533, 517 (2016).

[0141]

[50] Bjork BJ, Bui TQ, Heckl OH, Changal PB, Spaun B,P. Heu, D. Follman, C. Deutsch, GD Cole, M. Aspelmeyer, M. Okumura, and J.Ye, Science 354, 444(2016).

[0142]

[51] W. Weng, A. Kaszubowska-Anandarajah, J. He, PDLakshmijayasimha, E. Lucas, J. Liu, PM Anandarajah, and TJ Kippenberg,Nature Communications 12, 1425 (2021).

[0143]

[52] Y. Xu, Y. Lin, A. Nielsen, I. Hendry, S. Coen, M. Erkintalo, H. Ma, and SG Murdoch, Optics 7, 940 (2020).

[0144]

[53] E. Obrzud, S. Lecomte, and T. Herr, Nature Photonics 11, 600(2017) .

[0145]

[54] T. Inagaki, K. Inaba, R. Hamerly, K. Inoue, Y. Yamamoto, and H.Takesue, Nature Photonics 10, 415 (2016).

[0146]

[55] PS Devgan, J. Lasri, R. Tang, VS Grigoryan, WL Kath,and P. Kumar, Opt. Lett. Rev. 30, 1743 (2005).

[0147]

[56] A. Roy, R. Nehra, C. Langrock, M. Fejer, and A. Marandi, NaturePhysics 19, 427 (2023).

[0148]

[57] K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer,Opt. Lett. 40, 4368 (2015).

[0149]

[58] C. Langrock and M. M. Fejer, Opt. Lett. 32, 2263 (2007).

[0150]

[59] J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler,Opt. Lett. 27, 1675 (2002).

[0151]

[60] Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, Opt.Lett. 30, 1234 (2005).

[0152]

[61] J. E. Sharping, M. A. Foster, A. L. Gaeta, J. Lasri, O. Lyngnes,and K. Vogel, Opt. Express 15, 1474 (2007).

[0153]

[62] M. Gao, N. M. Lüpken, K.-J. Boller, and C. Fallnich, in OpticaAdvanced Photonics Congress 2022 (Optica Publishing Group, 2022) p. JTh4A.3.

[0154]

[63] A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto,Nature Photonics 8, 937 (2014).

[0155]

[64] OH Heckl, BJ Bjork, G. Winkler, PB Changala, B. Spaun, G. Porat, TQ Bui, KF Lee, J. Jiang, ME Fermann, PG Schunemann, and J. Ye, Opt. Lett. 41, 5405(2016).

[0156]

[65] D. Reid, G. Kennedy, A. Miller, W. Sibbett, and M. Ebrahimzadeh, IEEE Journal of Selected Topics in Quantum Electronics 4, 238 (1998).

[0157]

[66] R. Sekine, R. Gray, L. Ledezma, Q. Guo, and A. Marandi, inConference on Lasers and Electro-Optics (Optica Publishing Group, 2022) p.SM5K.2.

[0158]

[67] J. Li, C. Bao, Q.-X. Ji, H. Wang, L. Wu, S. Leifer, C. Beichman, and K. Vahala, Optica 9, 231 (2022).

[0159]

[68] KC Burr, CL Tang, MA Arbore, and MM Fejer, Opt. Lett. 22, 1458 (1997).

[0160]

[69] Further information about one or more embodiments of the invention can be found in Ryoto Sekine, Robert M. Gray, Luis Ledezma, Selina Zhou, Qiushi Guo, Alireza Marandi, Ultra-Low-Threshold Nanophotonic Parametric Oscillator https: / / arxiv.org / abs / 2309.04545.

[0161] Supplementary information for chip design and simulation for the first embodiment

[0162] The spatiotemporal profile of pulses propagating through our nanophotonic waveguides can be sculpted using several key fabrication parameters. Figure 5 The parameters marked in 'a' are the lithium niobate (LN) thickness, etch depth, top width, and sidewall angle. All these parameters directly affect the waveguide's effective refractive index, which in turn determines the near-zero dispersion geometry, quasi-phase-matched polarization period, and the cavity length required for synchronously pumping the OPO. Figure 5 b- Figure 5 As shown in d. We fabricated our device with a constant polarization period of 5.075 μm and a cavity length of 52.92 cm, and we measured the waveguide etch depth and top width to be 352 nm and 1753 nm, respectively. These dimensions are in Figure 5 b- Figure 5 The value in d is marked with a cross and shows that we have successfully designed our device to approach the optimal parameters for phase-matched operation with near-zero GVM and GVD. The resulting simulated effective refractive index n eff And the polarization cycle of manufacturing, such as Figure 6 As shown, the simulated bending loss is a function of the bending radius and wavelength. Figure 6 The blue dashed line at 77 μm in c indicates the minimum bending radius used to manufacture the helix, showing the small bending loss at all points in the helix for wavelengths shorter than 3.3 μm.

[0163] Input / output coupler design

[0164] like Figure 7 The input and output couplers of the OPO defined in a are symmetrical and identical, and adopt... Figure 7 The adiabatic shape depicted in b is given by parameters w1, w2, gap, and L of 1753 nm, 1900 nm, 980 nm, and 750 μm, respectively. Adiabatic couplers were chosen because of their broadband response and comparable fabrication insensitivity compared to other coupler geometries. For a waveguide design with a top width w2, the simulated fundamental TE modes at 1 μm and 2 μm are distributed as follows: Figure 7 As shown in c. The pulses passing through this adiabatic coupler follow the coupling mode equation.

[0165]

[0166] Where a1 and a2 are the amplitudes of the modes in each waveguide, κ is the coupling coefficient between waveguides, and Δβ = |β 1-β2| is the phase mismatch between the two waveguides. Solving equation (1) for our geometry, we obtain Figure 7 The power coupling curve in d shows that only signal wavelengths above 2 μm experience significant coupling. Figure 7 In e, we compare the spectral output of our OPO (a device with a coupler and cavity) with the spectral output of an adjacent straight waveguide that has no coupler but shares the same polarization and waveguide parameters. We find that the simulated valleys and peaks in the adiabatic coupler are reflected in the measured spectrum from the nanophotonic OPO, but not in the periodically polarized straight waveguide, matching our theoretically predicted coupler response.

[0167] set up

[0168] Our experimental setup is as follows: Figure 8 As shown, the detector in the PID loop allows the repetition rate of the pump comb to be locked to different oscillation peaks of the OPO while the spectrum is collected on an OSA spectrometer. The figure highlights the synergistic function of the pump and OPO in achieving multi-octave frequency comb generation.

[0169] Experimental data for the extension of the third octave spectrum

[0170] use Figure 8 In the experimental setup shown, we investigated the output spectrum of the OPO at different pump pulse energies, a subset of which is... Figure 2 As shown in d. Figure 9 a shows that the pump pulse energy extends to even higher levels. At a pump of 380 fJ, we observe a three-octave span spectrum from 362 nm to 3261 nm. However, after the process in Supplementary Part E1, Figure 9 The difference-frequency analysis of the free-space OPO shown in b indicates that the OPO here is incoherent.

[0171] Molecular absorption characteristics

[0172] for Figure 9 In the measured spectra above 2.5 μm, we observed spectral absorption lines that appear to originate from environmental molecules. Figure 10The experimental OPO spectrum was compared with the spectral lines of O2, CO2, and CH4. The overlap between the spectral features of water and OPO was particularly close, likely because H2O is the strongest absorber in this spectral region at atmospheric concentrations. We calculated that 9% of the 3 μm mode within the helical region is evanescent, suggesting that on-chip sensing is possible for a 53 cm helix. However, here we expect absorption to occur primarily between the chip output and the detector, as the system was not purged in this experiment. Furthermore, because no gas chamber was prepared, these absorption features originate from environmental molecules present in the laboratory.

[0173] As mentioned above, the notch at 2.83 μm is due to the OH absorption peak in the LN and / or SiO2 substrate buffer layer. Studies on the absorption of SiO2 used as a buffer layer for Si waveguides [2-4] show that the bottom cladding of SiO2 becomes very narrow, around 2.8 μm and above 3.5 μm. For current thin-film lithium niobate devices with a SiO2 buffer layer and a Si substrate, the upper absorption appears to be set at around 3.25 μm [5]. However, wavelengths between 2.8 and 3.8 μm have been measured on TFIN waveguides on sapphire substrates [6], indicating a path toward fabricating multioctave frequency combs with even longer wavelength components.

[0174] Pattern Cross

[0175] exist Figure 9 In the middle, significant spectral kinks are observed at 680 nm and 1135 nm across all pump pulse energies. These correspond to... Figure 11 The two mode crosses are shown in a. M1 is the mode cross between the basic TE mode and the second-order TM mode. Figure 11 b), while M2 is a mode crossover between the basic TE mode and the TM mode ( Figure 11 c). In fact, measurements were taken from a straight waveguide with the same waveguide geometry and polarization period as the OPO, and... Figure 11 In the spectrum plotted in section d, these mode crossovers, as well as the OH absorption discussed in section IIB, are even evident. Since this straight waveguide has no cavity, its half-harmonic spectrum is due to optical parametric generation (OPG).

[0176] Differential frequency downconversion

[0177] use Figure 12 The experimental setup in section a is used to study the coherence of the downconversion portion of the comb around the half-harmonic. The outputs of on-chip and free-space OPOs pumped by the same laser are interfered with. Depending on the detuning peak l of each OPO, we expect to see different characteristics in their radio frequency (RF) spectra and interference patterns. Here, the dimensionless detuning parameter l = 2fs ΔT RT , where ΔT RT It is a mismatch between the cavity round-trip time and the pump repetition cycle, f s This refers to the signal frequency. While OPOs with an even number of l have comb lines aligned with the pump's comb lines, OPOs with an odd number of l have a shift f. rep / 2 comb lines [7, 8]. This is in Figure 12 Example b. Therefore, when one OPO has an even number l and the other has an odd number l, the temporally and spatially overlapping OPO outputs are shown in f. rep f at / 2 CEO Difference frequency, such as Figure 12 The RF spectrum measurements in c(i) are shown. Furthermore, the two combs have different f... CEO At certain frequencies, when scanning the delay between two coherent OPO outputs, we do not expect to see interference fringes. For example... Figure 12 As shown by the orange trace in c(ii), no stripes were observed.

[0178] However, since OPOs are coherent and share the same even or odd detuning parameters and therefore the same f... CEO In this case, we did not expect and did not observe that in f rep The difference frequency at / 2. Furthermore, due to the comb sharing f... CEO We expected to see interference fringes when scanning their relative delays. This is indeed what we measured, as... Figure 12 The blue curve in c(ii) shows that at pumps of 109 fJ and 380 fJ, the downconversion portion of the nanophotonic OPO output is incoherent, and we did not observe... Figure 12 c(ii) of f rep No blue interference fringes were observed at the / 2 difference frequency.

[0179] Finally, the pump repetition rate can be locked to a characteristic in the OPO output signal. Figure 12 This demonstrates that we can reliably lock onto and stabilize the 2.6 octave comb state of the on-chip OPO output to the time-self-cleaning solution.

[0180] Upconversion difference frequency

[0181] The coherence of the upconversion portion of the pump was studied using a method similar to that used in [9, 10]. Specifically, the spectral broadening portion of the pump interferes with the second harmonic portion of the OPO on the chip, such as... Figure 13 exemplified in a. exist Figure 13 b shows Figure 2 The spectra of the three pump pulse energies mentioned in d overlap, where in Figure 13 c- Figure 13 The corresponding difference frequency is presented in e. In each case, we achieve this by tuning the pump f. CEO The shift is recorded to confirm that the difference frequency corresponds to f. CEO We conclude that the upconversion portion of the pump remains coherent, independent of the pump pulse energy or cavity detuning, as expected [9,10].

[0182] simulation

[0183] A. Method

[0184] We model the ultrawide spectral dynamics of nanophotonic OPOs by using a single envelope to represent the total electric field in the nanophotonic waveguide in the frequency domain [11,12].

[0185]

[0186] Where ω and Ω = ω - ω0 are the optical and envelope angular frequencies, ω0 is the analog center frequency, β0 is the waveguide propagation constant at ω0, and v ref Here, is the simulated reference frame velocity, x and y are the transverse waveguide coordinates, e(x, y, ω) is the mode transverse field distribution, and A(z, ω) is the complex amplitude of the field evolving during propagation. In our OPO simulation, ω0 is chosen as the center of the half-harmonic signal at 2090 nm, and v ref It is the group velocity of a half-harmonic. It is a rapidly changing envelope that contains the phase factor acquired during linear propagation. Additionally, A(z, ω) is the analytical signal, meaning it contains only positive frequencies (A(z, ω < 0) = 0).

[0187] Our simulation models each round trip in the OPO as two parts. The first considers nonlinear propagation in the polarization region of the waveguide, while the second consists of a linear filter that models the round trip evolution in the helical resonator

[13] . The output of this round trip evolution is fed back as a seed for subsequent nonlinear propagation. The first round trip is seeded with white noise at all frequencies except the pump, which is assumed to be an 80-fs pulse with a sech pulse profile centered at 1045 nm.

[0188] We find the unidirectional equation of motion describing the nonlinear propagation of A(z, Ω) by neglecting the backpropagation term (which is typically phase-mismatched) and assuming constant nonlinear coefficients and mode overlap integrals, both of which are weak functions of frequencies far removed from any material resonance. There is no limit to the maximum spectral bandwidth of the simulation. The resulting propagation equation is,

[0189]

[0190] Where d(z) = ±1 is the sign of the second-order nonlinear coefficient modulated in quasi-phase matching, α is the propagation loss coefficient, a(z, t) is the time-domain representation of A(z, Ω), and φ(z,t) = ω0t - (β0 - ω0 / v) ref )z, This is the Fourier transform of the Ω variable. The effective nonlinear coefficient X0 is defined as:

[0191]

[0192] in It is a second-order nonlinear magnetic susceptibility tensor, and j, k, l represent Cartesian components.

[0193] The nonlinear propagation in each round trip involves solving the evolution equation (3) using a split-step Fourier technique over a polarized waveguide length L = 10.8 mm. The nonlinear step is performed in the interaction picture (RK4IP) using the fourth-order Runge-Kutta method

[14] .

[0194] Propagation in a spiral resonator is modeled by applying a linear feedback function to the output of the polarization region. Specifically, the signal fed back to the input of the polarization region on the (n+1)th round trip. The field outside the polarization region during the nth round trip is obtained through the following expression. Related:

[0195]

[0196] Here, R(ω) is the frequency-dependent coupling factor of the designed adiabatic coupler. It is a complex dispersion operator describing propagation in a round-trip waveguide, possessing the parameters defined above for a polarized waveguide, L. RT =518.4 mm is the length of the reciprocating cavity, ΔT RT It is the detuning parameter that describes any timing mismatch between the pump repetition period and the cavity round-trip time, and φ0 is a constant phase offset that effectively represents the pump carrier envelope offset phase φ. CEO In addition to the feedback signal, a new pump pulse is injected, centered at t=0 on the fast time axis.

[0197] The simulation was performed on a 4096-size Fourier grid with a bandwidth of 2.4 kHz. The corresponding time window was 1.7 ps. To avoid wrapping within the time window during nonlinear propagation, a Tukey filter with zero-filled edges was applied in the time domain after each nonlinear step. Additionally, before applying the linear filter, the filter was applied to all frequency components that would have traveled out of the time window during the 518-mm propagation in the helical resonator. This has the undesirable effect of effectively reducing the simulation power in frequency modes far from the reference frequency (and thus experiencing significant discrepancies relative to the simulation reference velocity), but it ensures the effectiveness of the simulated nonlinear interactions.

[0198] In this case, we consider the nonlinear phase to be the phase accumulated in the PPLN section of the resonator due to nonlinear processes (excluding linear phase accumulation). We specifically focus on a narrow spectral range around the pump and its half-harmonics for spectral analysis, and in time analysis, we focus on the peak intensities around the pump and half-harmonics.

[0199] B. OPO kinetics under different conditions

[0200] As discussed in the main text, the ultrawideband OPO enters different operational states above the threshold. Figure 14 Figure a shows an extended version of the state shown in the text. Whether our near-zero dispersion OPO can achieve the coherent multioctave state represented as (iii) in the figure depends largely on the pump energy, cavity detuning (such as... Figure 14 (as shown in b) and the effective pump carrier envelope offset phase φ CEO We found that the kinetics of our OPO depend to a large extent on whether it has an even or odd detuning peak l, and its relative φ. CEO Is it 0 or π? We will examine each of these cases in more detail below.

[0201] 1. l∈even, φ CEO =0

[0202] When l∈even and φ CEO When =0, we find that when OPO almost reaches coherent octave comb, it never quite manages to achieve it completely. Figures 15 to 17In the case of l={2, 0, -2}, this is emphasized by the label (near iii). In all these cases, we see that in state (i) close to the threshold, the round-trip phase of the coherent OPO remains fixed once the OPO exceeds the threshold. After transitioning through the incoherent state in state (ii), the OPO phase is considered to be flipping π round-trip in the pumping scheme (iii). These periodic oscillations suggest that, perhaps in this state, the OPO consists of two coherent non-degenerate combs whose beat frequencies produce the observed phase fluctuations and the round-trip power fluctuations observed in the time and frequency domain plots of the OPO evolution. At even higher pumping energies, the OPO enters the fully saturated incoherent scheme of (iv).

[0203] 2. l∈odd, φ CEO =0

[0204] When l∈even and φ CEO At π = 0, the round-trip π phase reversal under a pumping condition of approximately 200 fJ indicates that a multioctave coherent comb can be maintained if the cavity phase can be detuned by π. One way to obtain this detuning is to select the OPO peak, where l ∈ odd, while maintaining φ. CEO =0, and Figures 20-21 In the diagram, we present the dynamics for the case of l = {3, 1, -1, -3}. As expected, near the threshold, i.e., in state (i), these OPOs exhibit round-trip π-phase flipping. However, in state (iii), we find that the OPOs exhibit time self-cleaning and are able to stabilize, thus exhibiting a fixed round-trip phase.

[0205] The coherence of the two octave band spectra in state (iii) can be further verified by calculating the coherence of the output pulse pairs and by directly examining the overlap of the combs generated by the half-harmonic, pump, second harmonic, and sum-frequency. Figure 22 As seen in the top panel of the device, we can see that, through measurements of coherence between pulse pairs obtained from the last 15 round trips of our simulation, the device displays a coherent spectrum exceeding two octaves. This can be further verified by examining the actual comb lines of the two-octave comb. Figure 22 Figure b shows the full comb spectrum and close-ups of the comb lines corresponding to different harmonic combs, which are shifted by f. rep The most recent multiple of f rep Center them at zero. Good overlap between the comb lines further indicates that the comb lines share f. CEO And therefore it is coherent. Note that, except for the pump comb at 1 μm which has f = 0. CEO Apart from the case where the second harmonic comb at 500 nm is not expected to share f with other harmonics. CEO This is usually assumed in our simulations.

[0206] 3.l is an even number, φ CEO = π

[0207] Along with selecting odd-numbered detuned peaks, in the case where l∈even, the round-trip phase of π can be directly added, corresponding to the effective pump carrier-envelope-offset phase φ. CEO =π. For l={2, 0, -2}, the result is in Figures 23-25 As shown in the diagram. Similar to having φ CEO In the case where π ∈ odd, OPO exhibits a round-trip phase flip at low power in state (i) and enters the oscillating state in state (ii) until it finally drops to a steady state at 200 fJ of pump. One limitation here is that since the phase is added to the signal rather than the pump in the analog, the coherence between the pump and higher harmonics is also preserved, although for signals with non-zero φ... CEO The pump is not experimentally real, as discussed in Supplementary Section IIIC.

[0208] C. Time-based self-cleaning

[0209] 1. Mechanism

[0210] exist Figure 2 In section d, we experimentally demonstrate that as the input pump pulse energy increases, our OPO transitions from a coherent, normal operating state to an incoherent operating state, but then recovers its coherence at higher pump pulse energies with appropriate cavity detuning. Figure 27 In the diagram, we show the intensity and phase propagation of the pump and the half-harmonic in the periodically polarized region of the cavity under a pump of approximately 200 fJ (i.e., in the TSC scheme). The evolution of the half-harmonic phase in a(ii) clearly shows the phase flip from -π to 0 at the location where the half-harmonic has a considerable intensity.

[0211] In Supplementary Part IIB, we show that this π-phase reversal in the half-harmonics of each single-pass of the PPLN can be compensated for by detuning the cavity with an odd number of OPO peaks (Part IIB2), or by adding a constant π-phase offset between the pump and the cavity, which corresponds to the pump's carrier envelope offset phase φ. CEO (Partial IIB3). Figure 22 This is an example of the former. Near the threshold (16 fJ), the OPO output experiences a π-phase flip in each round trip, but it is able to stabilize to a constant-phase output at a pumped rate of 204 fJ. Choosing an even-numbered detuning peak but φ CEO An example of the latter method for π is Figure 24Furthermore, we observed that in the 200 fJ pumped TSC scheme, the output phase stabilizes after approximately 40 cavity round trips. These examples demonstrate that single-pass phase accumulation in the PPLN can be compensated by appropriately detuning the cavity, or φ CEO This is the key to the operation of the TSC scheme. Therefore, the pump pulse energy at the point where TSC occurs depends on the OPO dispersion and nonlinear gain, which causes a π phase flip between the half-harmonic and the pump.

[0212] 2. Short pulse formation

[0213] As mentioned in the main text, the time self-cleaning mechanism of coherent multi-octave OPOs can lead to ultrafast characteristics at the OPO output. Figure 28 In the example, we explicitly show that for l = {2, 0, -2} and φ CEO The simulated time output for this state with =0 is shown. A narrow characteristic of up to 4.2 fs can be observed, indicating that the coherent multioctave comb mechanism could be used for extreme pulse compression and single-cycle / multi-cycle pulse synthesis in the future.

[0214] D. Extended to a triple band comb

[0215] By employing a chirped polarization period, the goal is to transfer energy to the second harmonic and sum-frequency generation terms; we can even induce a coherent spectrum with a third octave band. Specifically, we assume that the polarization period in the last 1 mm of the 10.8-mm polarization region smoothly varies between the periods required for quasi-phase-matched OPA between the pump at 1 μm and the signal at 2 μm, to phase-match the interaction between the pump at 1 μm and its second harmonic at 500 nm. Figure 3 The extended characterization of the results discussed in b is in Figure 29 As shown in the figure. Notably, this higher harmonic generation process acts as an effective loss of the 2 μm signal, resulting in a higher threshold for the OPO and a larger pump power requirement to reach the time-self-cleaning state. However, at a pump of 248 fJ, a multioctave comb is observed, where the additional higher harmonic process enables the formation of a coherent triplet spectrum by filling the spectral gap between the second harmonic at 500 nm and the sum-frequency component at 697 nm (Figures S25a-S25b).

[0216] References for supplementary information

[0217] The following references are incorporated herein by reference.

[0218] [1] I. Gordon, L. Rothman, J. Hill, R. Kochanov, Y. Tan, P. Bernath,M. Birk, V. Boudon, A. Campargue, C. Chance, B. Drouin, J. -M. Floud, R.Gamache, J. Hodges, D. Jacquemart, V. Perevalov, A. Perrin, K. Shine, M. -A.Smith, J. Tennyson, G. Toon, H. Tran, V. Tyuterev, A. Barbe, A. Császár, V.Devi, T. Furtenbacher, J. J. Harrison, J. M. Harrison. Hartmann, A. Jolly, T. Joh nson,T. Karman, I. Kleiner, A. Kyuberis, J. Loos, O. Lyulin, S. Massie, S.Mikhailenko, N. MoazzenAhmadi, H. Müller, O. Naumenko, A. Nikitin, O. Polyansky, M. Rey, M. Rotger, S. Sharpe, K. Sung, E. Starikova, G. Va. Tasrakh, J.Va. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. Zak, Journal ofQuantitative Spectroscopy and Radiative Tra nsfer 203, 3 (2017), hITRAN2016Special Issue.

[0219] [2] RA Soref, SJ Emelett, and WR Buchwald, Journal of OpticsA: Pure and Applied Optics 8, 840 (2006).

[0220] [3] SA Miller, M. Yu, X. Ji, AG Griffith, J. Cardenas, ALGaeta, and M. Lipson, Optica 4, 707 (2017).

[0221] [4] H. Lin, Z. Luo, T. Gu, LC Kimerling, K. Wada, A. Agarwal, andJ. Hu, Nanophotonics 7, 393(2018).

[0222] [5] A. Roy, L. Ledezma, L. Costa, R. Gray, R. Sekine, Q. Guo, M. Liu,RM Briggs, and A. Marandi, “Visible-to-mid-ir tunable frequency comb innanophotonics,” (2022), arXiv:2212. 08723.

[0223] [6] J. Mishra, M. Jankowski, AY Hwang, HS Stokowski, TPMcKenna, C. Langrock, E. Ng, D. Heydari, H. Mabuchi, AH Safavi-Naeini, andM. M. Fejer, Opt. Express 30 , 32752 (2022).

[0224] [7] A. Marandi, NC Leindecker, V. Pervak, RL Byer, and KLVodopyanov, Opt. Express 20, 7255(2012).

[0225] [8] M. Jankowski, Pulse formation and frequency conversion of indispersion-engineered nonlinear waveguides and resonators, Ph.D. D. thesis,Stanford University (2020).

[0226] [9] A. Marandi, K. A. Ingold, M. Jankowski, and R. L. Byer, Optica 3,324 (2016).

[0227]

[10] M. Jankowski, C. Langrock, B. Desiatov, A. Marandi, C. Wang, M.Zhang, C. R. Phillips, M. Lončar, and M. M. Fejer, Optica 7,40(2020).

[0228]

[11] C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, I. Hartl,and M. E. Fermann, Optics Express 19,18754 (2011).

[0229]

[12] L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A.Marandi, Optica 9, 303 (2022).

[0230]

[13] M. Jankowski, A. Marandi, C. Phillips, R. Hamerly, K. A. Ingold,R. L. Byer, and M. Fejer, Physical review letters 120, 053904(2018).

[0231]

[14] J. Hult, Journal of Lightwave Technology 25, 3770 (2007).

[0232] Second embodiment: Cavity secondary solito

[0233] Walk-off-induced temporal soliton formation in a degenerate optical parametric oscillator (OPO) based on pure quadratic nonlinearity can serve as a tool for simultaneously compressing and downconverting picosecond near-IR pulses. It has recently been shown that such secondary cavity solitons can be supported in both normal and anomalous group velocity dispersion states using benchtop experiments and exist in low-precision optical cavities that can lead to high conversion efficiency [1]. Experiments have also demonstrated giant pulse compression at picojoule pump energies exceeding 40 times. These results provide a method for generating high-efficiency dissipative secondary solitons that breaks down some of the barriers to the generation of Kerr solitons, which require high-Q cavities, have limited conversion efficiency, require anomalous dispersion for bright soliton formation, and have limited wavelength tunability. In this invention, we form such secondary cavity solitons in LN nanophotonics.

[0234] Synchronously pumped degenerate optical parametric oscillators (DOPOs) on thin-film lithium niobate (TFLN) offer unprecedented opportunities for extreme pulse compression with pump pulse energies of approximately 100 fJ, all on an integrated platform. The desired pulse compression can be achieved through dispersion engineering of the nanophotonic waveguide of the OPO, and even 1-ps pump pulses can be compressed to approximately 10 fs. How can a synchronously pumped OPO compress pulses with a frequency of 2ω and a pulse width of T... p The pump pulse is compressed to a frequency ω with a width of τ. sech The mechanism of the signal pulse is described in detail in [1] [and shown in Figure 30]. The group velocity mismatch (GVM) between the pump pulse and the signal pulse causes the signal pulse to pass through the pump. The portion of the signal pulse that overlaps most with the pump experiences the maximum gain. When the GVM between the pump and the signal is negligible, not only do all portions of the signal experience similar pump power, but the signal centroid is more likely to reach gain saturation, both of which result in significantly less pulse compression compared to the previous case. In fact, the optimal dispersion for pulse compression is when the signal centroid extracts the most energy from the pump by passing precisely through it, i.e., |GVM|=T. p / L PPLN L PPLN It is the length of the periodically polarized region. In this case, the output pulse width is determined by the group delay dispersion (GDD) of the cavity, such that...

[0235]

[0236] Where G0 is the gain at the threshold. When second-order dispersion can be eliminated, the output pulse width is limited by third-order dispersion (TOD). Therefore, in this scheme, the available pulse compression is determined by the amount of achievable dispersion tunability.

[0237] Experimental and fundamental studies have been conducted in discrete component cavities with finite dispersion engineering outside of optical fibers and nonlinear gain media. In contrast, TFLN allows for a large amount of dispersion engineering[2], making it an ideal platform for OPO-based second solitons and pulse compression. Figure 30b Simulation results show that, by appropriately selecting waveguide parameters, both large GVM and small GDD states can be accessed, which is ideal for pulse compression. For example, a green cross indicates that a 500-fs pump will be compressed to a geometry of 50 fs. A red star indicates the position where a 1-ps pump pulse will be compressed to the TOD limit of approximately 10 fs.

[0238] Besides dispersion engineering, TFLN-based synchronous pumped OPOs are also desirable due to their very low operating pump power. Low threshold energies of around 100 fJ have been measured [3], which are significantly lower than the pump power required by other integrated pulse compression techniques [1]. In addition, TFLNs allow for monolithic integration with other nanophotonic circuit elements, such as heaters, mode-locked lasers, and other parametric processes. In summary, DOPOs on TFLNs are an excellent platform for studying secondary solitons, with the aim of achieving pulse compression on-chip from approximately 1 ps pump pulses to approximately 10 fs signal pulses, such as... Figure 30b The waveguide design for the dispersion engineering is shown.

[0239] References for the second embodiment

[0240] The following references are incorporated herein by reference.

[0241] [1] A. Roy, R. Nehra, S. Jahani, L. Ledezma, C. Langrock, M. Fejer, and A. Marandi, Nature Photonics 16, 162 (2022).

[0242] [2] L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A. Marandi, Optica 9, 303 (2022).

[0243] [3] A. Roy, L. Ledezma, L. Costa, R. Gray, R. Sekine, Q. Guo, M. Liu, RM Briggs, and A. Marandi, Visible-to-mid-ir tunable frequency comb innanophotonics (2022), arXiv:2212. 08723.

[0244] The third embodiment of a visible-to-infrared comb pumped by a frequency comb

[0245] We demonstrate the generation of an ultrawide tunable frequency comb from an on-chip OPO in lithium niobate nanophotonics. Leveraging the ability to control phase matching through a combination of periodic polarization and dispersion engineering, we show an on-chip tuning range exceeding octave bands. We pump the OPO with picosecond pulses from an electro-optic frequency comb source in near-IR, which has been shown to be compatible with lithium niobate nanophotonics [18, 58, 59]. The demonstrated frequency comb covers typical communication bands and extends into the mid-infrared spectral region beyond 3 μm, with an instantaneous bandwidth supporting sub-picosecond pulse durations. Additionally, the same chip generates a tunable frequency comb in the visible region produced by upconversion processing. The realization of tunable visible frequency combs is challenging due to the lack of suitable broadband gain media and the typically large normal dispersion at these wavelengths in most integrated photonics platforms [14, 30].

[0246] Example device structure

[0247] To achieve a broadband and widely tunable frequency comb, we designed a dual-resonant OPO based on a nanowaveguide etched onto an X-cut 700 nm thick MgO-doped lithium niobate substrate [15, 24, 40], as shown below. Figure 31 As shown in (a). Unlike the three-resonator design [3, 16, 29], this design provides access to wide tunability of aligned phase matching (QPM) and avoids stringent requirements such as ensuring resonance of the pump [9]. By using two spectrally selective adiabatic couplers (in Figure 31(highlighted in (a)) control of the precise spectral response of the OPO resonator enables dual-resonance operation, with the two spectrally selective adiabatic couplers allowing only long wavelengths (signal and idle waves) to resonate in the OPO while allowing short wavelengths (pump and upconversion light) to exit the cavity (see Supplementary Section 3.6.2). This is important not only for achieving a wide tuning range for both signal and idle, but also for enabling non-resonant broadband and wide-tunable upconversion to visible light, in stark contrast to previous parametric sources in this range [14,30]. Another important aspect of on-chip OPO design is the dispersion engineering of the OPO’s main interactive waveguide, which, combined with periodic polarization, results in a wide spectral coverage of QPM tuning. Designing the dispersion of the rest of the resonator is another important degree of design freedom, which can be further used to implement secondary solitons and pulse compression mechanisms

[41] .

[0248] For the data presented in this paper, the second-order parametric nonlinear interaction occurs in a 5 mm long polarized waveguide region, with a fixed polarization period (Λ) for each OPO on the chip. The periodic polarization phase-matching parametric nonlinear interaction between the pump wave, signal wave, and idle wave can be tuned from degenerate to far non-degenerate. The chip consists of multiple OPOs with a polarization period of type 0 phase matching spanning the octave range for down-conversion of the non-resonant pump (approximately 1 μm wavelength in this case) and the resonant signal and idle wavelength (i.e., the OPO output). The QPM tuning profile is shown in... Figure 31 As shown in (b). In addition to these OPO outputs, the polarized waveguide provides additional parametric upconversion processes, particularly the second harmonic of the signal / idle, and sum-frequency generation from the pump and signal / idle. The entire tuning range of the chip overlaps with many molecular and atomic transitions, such as... Figure 31 As shown in (c). The strong spatiotemporal confinement of the interacting waves in the waveguide guarantees a substantial upconversion efficiency, which can be further enhanced by adding appropriate polarization periods and tailoring to specific applications (see Supplementary Section 3.6.1).

[0249] like Figure 31 As shown in (b), to continuously cover the visible to mid-infrared range, we tune the QPM by coarsely switching the polarization period and finely adjusting the pump wavelength at approximately 25 nm. This tuning range of the pump is compatible with existing semiconductor lasers

[50] . Furthermore, the coarse switching of the polarization period can be achieved without mechanical movement, for example, by electro-optic routing (see Supplementary Section 3.6.8). In addition, temperature tuning of the polarization region can provide another substantial tuning mechanism (see Supplementary Section 3.6.9 of the Supplementary Information). The emission coverage from the OPO chip corresponds to important wavelengths of atomic transitions in the visible light and molecular absorption lines in the mid-infrared ( Figure 31 (c)).

[0250] The OPO is synchronously pumped by pulses of approximately 1 ps length operating at a repetition rate of approximately 19 GHz [27, 36, 40]. The repetition rate is tuned to near the free spectral range of the OPO cavity or its harmonics (see Supplementary Section 3.6.5). The octave-wide tunability of the parametric oscillations from the OPO chip is achieved by tuning the pump center wavelength only between 1040 nm and 1065 nm. The pump is generated by an electro-optic frequency comb

[39] (see Supplementary Section 3.6.3). A schematic of the experimental setup is shown in Figure 32 The spectral and temporal characteristics of near-infrared pumping are shown in (a). Figure 32 As shown in (b).

[0251] Example Results

[0252] Figure 32 (c) shows a broad spectral coverage of the OPO output extending up to 3.3 μm in the mid-infrared region obtained from a single chip. The comb lines can be resolved by an OSA spectrometer and can be seen in the inset, where the peak separation corresponds to the pump repetition rate. For the near-degenerate OPO, the on-chip threshold corresponds to an average power of approximately 1 mW (approximately 50 mW of peak power and approximately 100 femtojoules of pulse energy). For the near-degenerate OPO, the signal conversion efficiency is close to approximately 5%, while for the far-non-degenerate OPO, the mid-infrared (3.3 μm) idle conversion efficiency exceeds 1% (see Supplementary Section 3.6.2). This corresponds to an estimated peak power of approximately 25 mW and a power of approximately 5 μW per comb line in the mid-infrared region.

[0253] The double resonant operation of the OPO is also achieved through, for example... Figure 33 The appearance of the resonant peak structure with varying pump center wavelength shown in (a) confirms this. Figure 33 (b) shows the tolerance of synchronous pump repetition rate mismatch relative to the optimal OPO operating point. Figure 33 (c) depicts the fine tunability of the OPO output spectrum provided by tuning the pump wavelength. The combination of fine and coarse tunability potentially enables continuous spectral coverage across the accessible spectral region. OPO output under degeneracy ( Figure 33 (d) corresponds to the time duration of the subpicosecond conversion limit (approximately 400 fs), indicating that the pulse compression factor relative to the pump exceeds 2 (see Supplementary Section 3.6.6).

[0254] We further evaluate the coherence of the output frequency comb by performing linear field cross-correlation on the output signal light, such as... Figure 33 As shown in (e), each OPO pulse interferes with another pulse delayed 10 round trips. The presence of interference fringes (see...) Figure 33(The illustration in (e)) combined with the Fourier transform of the cross-correlation trace and the consistency of the signal spectrum obtained using OSA serves as evidence of the coherence of the output frequency comb across the entire spectrum (see [reference]). Figure 33 (f)).

[0255] The occurrence of other second-order nonlinear processes, such as second-harmonic generation (SHG) and sum-frequency generation (SFG), leads to the formation of frequency combs in the visible spectral region. Figure 34 (a) shows the complete emission spectrum of the OPO, consisting of the second harmonics of the pump wave and signal wave, the sum-frequency component between the pump wave and signal / idle wave, and the typical signal / idle wave. Scattered visible light emitted from the chip was captured by an optical microscope image (see [link]). Figure 34 (b) illustrates the emission of the pump second harmonic (green) and the sum-frequency component (red). In the polarization region, green dominates on the input side, gradually being suppressed by the sum-frequency red component. The SFG between the pump wave and the signal wave results in the generation of a tunable visible frequency comb between 600 nm and 700 nm, as shown in [the diagram]. Figure 34 As shown in (c). Tuning the OPO further away from degeneracy causes the idle emission to further enter the mid-IR and the SFG component located on the bluer side of the visible spectrum.

[0256] Pumps for near-IR electro-optic combs can be incorporated into lithium niobate chips [6, 59]. With appropriate dispersion engineering, our OPO design can further achieve large instantaneous bandwidths with significant pulse compression

[41] , enabling the generation of femtosecond mid-infrared frequency combs in nanophotonics. Then, periodically polarized lithium niobate waveguides can be used on these femtosecond pulses to perform efficient supercontinuum generation requiring only a few picojoules of pulse energy for subsequent f-2f self-reference / comb stabilization

[20] .

[0257] In one or more embodiments, the OPO can be integrated with an electro-optic modulator for active locking of the OPO frequency comb. The on-chip OPO threshold can be further reduced by individually optimizing the mode overlap between the pump field and the signal / idle field of each OPO device to satisfy a dedicated spectral band, thereby improving waveguide loss and enhancing the effective nonlinear coefficient. We estimate that an on-chip threshold of less than 500 μW (for 10 GHz repetition rate operation) for near-degenerate operation is feasible. The low power requirement, combined with the need for a relatively narrow pump tunable range, allows for pumping the OPO chip with dock-coupled near-infrared diode lasers and a fully integrated solution for mid-infrared frequency comb generation based on lithium niobate nanophotonics [13,18, 25, 58] (see Supplementary Section 3.6.8).

[0258] Optimized coupler designs enable OPO operation with low threshold and high mid-infrared comb conversion efficiency. Advanced coupler designs, similar to those based on inverse design

[35] , can simultaneously meet the requirements of low pump coupling, high signal coupling, and optimal coupling of the idle wave, resulting in conversion efficiencies exceeding 30%. Implementing OPO devices in lithium niobate on sapphire would provide a wider transparency window, allowing frequency comb generation to penetrate deeper into the mid-infrared

[34] . Due to strong parametric nonlinear interactions, it is possible to use helical waveguides

[26] in the feedback arm of the OPO resonator to achieve frequency combs with low repetition rates (around 1 GHz), which would be useful for on-chip dual-comb spectroscopy applications. The mid-infrared emission overlaps with important molecular rotation vibration absorption lines and paves the way for novel integrated spectroscopy solutions.

[0259] Regarding the method and supplementary information of the third embodiment

[0260] The device was fabricated on a 700 nm thick X-cut MgO-doped lithium niobate silicon dioxide die (NANOLN). Periodic polarization was achieved by first patterning the electrodes using electron beam lithography, then electron beam evaporation of Cr / Au, followed by metal lift-off. Ferroelectric domain inversion was performed by applying a high-voltage pulse, and the polarization quality was examined using second-harmonic generation microscopy. The waveguide was patterned by electron beam lithography and coated with Ar2... + Plasma dry etching. Waveguide facets are polished using fiber polishing films. The OPO chip consists of multiple devices with polarization periods ranging from 5.55 μm to 5.7 μm (in 10 nm increments), providing parametric gain across octaves.

[0261] Spectra were recorded using a combination of near-infrared optical spectroscopy (OSA) (Yokogawa AQ6374), mid-infrared OSA (Yokogawa AQ6375B, AQ6376E), and CCD spectrometer (Thorlabs CCS200). OPOs were synchronously driven at their fundamental repetition rate (approximately 9.5 GHz) or its harmonics (approximately 19 GHz). Due to the short electro-optic pump pulses, harmonic repetition rate operation yielded a wide instantaneous bandwidth. OPOs operating at longer wavelengths exhibited higher thresholds (due to increased effective area, increased coupler losses corresponding to the signal wave, and a larger mismatch between the relative walk-off parameters of the signal and idle waves); therefore, we operated them intermittently in a so-called “quasi-synchronous” manner as a way to reduce average power and avoid thermal damage (see Supplementary Section 3.6.4). This limitation is primarily attributed to the avoidable input insertion loss (approximately 12 dB) in our current setup. With the help of a better fiber-to-chip coupling design / mechanism (with insertion loss on the order of 1 dB already reported in the context of thin-film lithium niobate), the IR OPO can be operated in a configuration of steady-state synchronous pumping

[17] .

[0262] 3.6 Single envelope simulation and visible frequency comb

[0263] To capture the generation process of the second harmonic and sum-frequency generation signals (responsible for the generation of the visible frequency comb), we resort to single nonlinear envelope simulation [5]. Figure 35 (a) shows the numerically obtained results, which imply the presence of visible frequency comb components. In our simulations, we have assumed the existence of non-ideals in the polarization period. These second harmonic and sum-frequency generating components are generated due to parasitic phase matching, which is attributed to duty cycle errors and / or higher-order phase matching of the visible components.

[0264] To improve the efficiency of the visible frequency comb generation process, an additional phase-matching component can be added to the output waveguide of the OPO. This will improve the conversion efficiency of the phase-matching component and also allow it to be designed to be broadband using chirped polarization periods. Figure 36 (b) simulates a scenario where the efficiency of the SFG component between the pump and the signal is enhanced. Similarly, it can be designed for other components, namely the idle wave and the pump's SFG, or the second harmonic frequency comb. We note that these visible frequency combs are single-pass due to the long-pass nature of the spectral response of the adiabatic coupler. The visible components inherit the extensive tunability of their parent signal / idle wave frequency comb.

[0265] It is evident that the fine tunability of the frequency comb (sum frequency generation between the signal and the pump) can also be achieved using pump wavelength control, such as... Figure 36 As shown in (c), the upconversion caused by the generation of the second harmonic of the signal also leads to the generation of the near-infrared frequency comb. The phase-matching curve is shown in... Figure 37 As shown in (a). Figure 37 (b) and Figure 37 (c) shows the coarse and fine tuning of the second harmonic signal comb obtained through experiments.

[0266] 3.6.2 Signal / idle wave conversion efficiency

[0267] Figure 38 a plot of the signal power as a function of pump power. OPO conversion efficiency is a function of escape efficiency, number of above-threshold actions, etc. [2]

[0268] The escape efficiency is determined by the OPO cavity output coupling, which is given by the frequency response of our adiabatic coupler. A schematic diagram of the geometry of our coupler is shown in [the diagram]. Figure 38 The geometric parameters are shown in (b). Figure 40 As mentioned in the description. The simulation performance from the coupler is... Figure 38As shown in (c). The coupler response was also experimentally characterized by illumination with a supercontinuum source. The results overlapped in Figure 38 (d)

[0269] The off-chip mid-infrared power we measured was approximately 300 nW. The spectrum is in... Figure 39 The corresponding on-chip average power is approximately 3 μW. The estimated pulse width for idle is approximately 500 fs (conversion limit). This indicates a peak power of approximately 25 mW. The power per combline is approximately 5 μW. Note that we have multiplied the power level by a quasi-pulse duty cycle of 100. The threshold for the extreme mid-infrared OPO is estimated to be approximately 10 times the threshold for the near-degenerate OPO (with an average power of approximately 1 mW).

[0270] 3.6.3 Pump Preparation / Electro-optic Frequency Comb Generation

[0271] The OPO is pumped by an electro-optic frequency comb, the repetition rate of which is tuned to near-cavity FSR. The pump pulse width is approximately 1 ps long, and based on the available electronics in our current version, the repetition rate can be tuned from 5 GHz to 20 GHz (the upper limit is determined by the bandwidth of the RF amplifier). The electro-optic frequency comb generation scheme closely follows the methods shown in [33, 39]. The center frequency can be tuned from 1040 nm to 1065 nm (the upper limit is determined by the operating range of the waveform shaper, while the lower limit is selected to ensure safe operation of the YDFA).

[0272] A schematic diagram of the pump setup is shown in Figure 40 As shown in (a), the output of the CW laser is modulated by a series of modulators. The modulators are driven by an RF signal generator, followed by an RF amplifier. The intensity modulator (IM) bias is selected so that pulses can be etched from a continuous wave. In this stage (Stage 1), the time-domain output is similar to... Figure 40 The simulated waveform is shown in (b). Next, the cascading of three phase modulators (PMs) allows for the addition of spectral sidebands separated by repetition rates. The phase modulators are driven synchronously by adjusting the electronic delay line. In this stage (Stage 2), the spectrum will resemble... Figure 40 The spectrum shown in (c) is used to amplify the resulting signal with the aid of a semiconductor optical amplifier (SOA), which then sends it to a waveform shaper. The programmable waveform shaper allows for pulse compression by applying appropriate dispersion to dechirp the input time waveform. In this stage (stage 3), the time-domain waveform will look like... Figure 40 The waveform shown in (d) illustrates the compressed pulse and the pre-compressed chirped pulse. Finally, the electro-optic frequency comb was characterized in the frequency domain using an OSA spectrometer and in the time domain using an intensity autocorrelator.

[0273] 3.6.4 Quasi-synchronous pump

[0274] Due to a combination of factors, the threshold for non-degenerate OPOs is higher. The adiabatic coupler was not custom-designed for each OPO; instead, a uniform coupler was implemented in this first-generation chip design. As a result, the non-degenerate operation of the OPOs leads to higher round-trip losses for the signal (due to the gradually increasing external coupling for smaller wavelengths). Furthermore, the effective nonlinear coefficients, considering the effective area of ​​the modes, and the field overlap between pump modes, signal modes, and idle wave modes are also reduced.

[0275] Higher threshold requirements necessitate more pump power, which is currently on the higher side due to the fairly high input coupling / insertion loss (approximately 10 to 12 dB). Several proposals and demonstrations have been made to reduce this figure to a few dB [54, 56]. In scenarios with low insertion loss availability, the required external pump power can be significantly reduced by approximately 10 dB. In these cases, threshold requirements far from degenerate operation can be easily achieved, even with suboptimal designs.

[0276] However, in our current implementation, unfortunately, we do suffer from excessive insertion loss, resulting in a required off-chip average power exceeding 60 mW. At these power levels, with the presence of undesirable back-reflection power, we are prone to burning / damaging the connector and affecting the YDFA. To ensure safe operation, we resort to quasi-synchronous pumping, thereby reducing the average power by applying pulses to the pump. This is achieved by using an arbitrary waveform generator (AWG) to drive a semiconductor optical amplifier (SOA), which generates microsecond-level pulses with repetition rates varying from 1 to 20 kHz (duty cycles from 1000 to 50). (Illustrated in...) Figure 41 As shown in (a), it is the same as the pump preparation settings for an SOA with an added AWG drive. Figure 41 (b) shows the time-domain traces of the pump pulse and signal pulse captured using a slow detector. We note that the slow detector cannot distinguish individual picosecond-level pulses within each quasi-pulse. In fact, there are on the order of thousands of pulses within each quasi-pulse.

[0277] 3.6.5 Estimating the cavity-free spectral range

[0278] Estimating the free spectral range (FSR) of the cavity is central to determining the repetition rate of the synchronously pumped OPO. This is absolutely necessary because the synchronous pump (EO comb) cannot be continuously tuned to search for the correct FSR. Each setup of the EO comb requires a specific combination of electronic phase delay line parameters and waveform shaper dispersion parameters, and tuning is a daunting task. Our OPO design precludes the use of a tunable CW source of approximately 1 μm to scan through multiple cavity resonances. The situation is exacerbated in the absence of a high-power tunable CW source of approximately 2 μm in our disposal. In these cases, we use... Figure 42 The measurement setup shown is used to estimate the cavity FSR.

[0279] In this method, we must operate the OPO in CW mode. We apply variable modulation over CW using an intensity modulator (IM). An arbitrary waveform generator is used to change the modulation frequency. The OPO output will be maximized near the correct cavity FSR. Unlike the EO comb, this setup can be continuously tuned.

[0280] 3.6.6. Spectral broadening / pulse compression in degenerate OPOs

[0281] The measured pump pulse width (assuming a Gaussian pulse extracted from the intensity autocorrelation trace) is approximately 1 ps. For a degenerate OPO, the estimated transform-limiting pulse width is 380 fs. Figure 43 As shown in (a), the experimental spectra of the pump and signal are frequency-shifted and overlap each other. Numerical simulation results obtained from the double envelope equation simulation... Figure 43 As shown in (be), it is in close agreement with the measurement data. With proper dispersion engineering (group velocity dispersion and group velocity mismatch)

[41] , it is possible to generate an OPO frequency comb with a wide instantaneous bandwidth, thereby causing very few optical cyclic pulses.

[0282] 3.6.7 Coherence Verification Using Field Cross-Correlation Techniques

[0283] To evaluate the coherence of the spectrum, we performed linear field cross-correlation (FCCR) on the output signal light, where each OPO pulse interferes with another pulse delayed by 10 round trips. This can be considered a modified FTIR measurement, where cross-correlation is performed instead of autocorrelation. A schematic diagram of the setup used for this purpose is shown in [link to diagram]. Figure 44 As shown in (a), the delay line corresponds to a delay of 10 OPO pulses, and therefore the evaluation of coherence characteristics is limited by the duration of the applied delay. The nonlinearity of the scanning stage is corrected using a reference HeNe laser beam. This is important for matching the spectrum obtained by the spectrometer and calculated by performing a Fourier transform of the FCCR trace.

[0284] We also detected a sharp RF beat frequency corresponding to the applied repetition rate of the OPO in the synchronous pump ( Figure 44 (b) The signal is obtained by measuring the OPO output pulse using a fast photodetector. A wavelength demultiplexer is used to reject the pump.

[0285] 3.6.8 System-wide integration and universal frequency comb source

[0286] A complete integrated solution for frequency comb generation can be based on lithium niobate nanophotonics combined with a laser chip. With several design improvements, the threshold for frequency comb generation can be significantly reduced, which allows pumping with commercially available DFB laser chips. Alternatively, an integrated external cavity and semiconductor gain chip can also be deployed for this purpose

[28] . Other key building blocks are: a) near-IR picosecond pump pulse generation [18, 58], b) a Mach-Zehnder interferometer mesh for routing pump light to the desired OPO

[51] , c) an OPO array, and d) periodically polarized lithium niobate waveguides that support ultra-low power supercontinuum generation for f-2f-based frequency comb stabilization [20, 38]. Our current study focuses on part c, while the rest have been demonstrated in lithium niobate nanophotonics.

[0287] 3.6.9. Temperature Tuning of Phase Matching Curves

[0288] In this embodiment, fine-tuning of the quasi-phase matching (QPM) has been performed by tuning the pump wavelength. The same effect can be achieved by means of temperature tuning while keeping the pump wavelength fixed. Figure 45 shows the phase matching curve as a function of temperature, which is calculated by evaluating the effective refractive index of the waveguide by considering the temperature-dependent Sellmeier equation

[10] . Temperature tuning can be achieved globally by placing the chip on top of the TEC heater element, or locally by implementing the resistive heater element near the periodically polarized region. We note that the expected tuning curve (obtained from simulation) is more tunable than that observed experimentally. We expect this may be due to the presence of thermal resistance between the heater element and the nanophotonic chip, and / or the mismatch of the coefficients of thermal expansion between the insulating layer and the thin-film lithium niobate layer, but this may be a subject for further investigation.

[0289] References for the third embodiment

[0290] The following references are incorporated herein by reference.

[0291] [1] Florian Adler, Kevin C Cossel, Michael J. Thorpe, Ingmar Hartl,Martin E Fermann, and Jun Ye. Phase-stabilized, 1.5w frequency comb at 2.8-4.8μm. Optics Letters, 34(9):1330-1332, 2009.

[0292] [2] Mark A. Arbore and Martin M. Fejer. Singly resonant opticalparametric oscillation in periodically poled lithium niobate waveguides.Optics Letters, 22(3):151-153, 1997.

[0293] [3] Alexander W. Bruch, Xianwen Liu, Zheng Gong, Joshua B. Surya,Ming Li, Chang-Ling Zou, and Hong X. Tang. Pockels soliton microcomb. NaturePhotonics, 15(1):21-27, 2021.

[0294] [4] Ian Coddington, Nathan Newbury, and William Swann. Dual-combspectroscopy. Optica, 3(4):414-426, 2016.

[0295] [5] Matteo Conforti, Fabio Baronio, and Costantino De Angelis.Nonlinear envelope equation for broadband optical pulses in quadratic media.Physical Review A, 81(5):053841, 2010.

[0296] [6] Camiel Op de Beeck, Felix M. Major, Styx Cuyvers, Styx Poelman,Jason F Herrmann, Okan Atalar, Timothy P. McKenna, Bahawal Haq, Wentao Jiang,Jeremy D. Witmer, et al. Iii / v-on-lithium niobate amplifiers and lasers.Optica, 8(10):1288-1289,2021.

[0297] [7] Scott A. Diddams, Kerry Vahala, and Thomas Udem. Opticalfrequency combs: Coherently uniting the electromagnetic spectrum. Science ,369(6501): 3676,2020.

[0298] [8] Majid Ebrahim-Zadeh and Irina T. Sorokina. Mid-infrared coherent sources and applications. Springer Science & Business Media , 2007 .

[0299] [9] Robert C. Eckardt, CD Nabors, William J. Kozlovsky, and RobertL. Byer. Optical Parametric Oscillator Frequency Tuning and Control. Journal of the Optical Society of America B, 8(3):646-667, 1991.

[0300]

[10] Ofer Gayer, Z. Sacks, E. Galun, and Ady Arie. Temperature andwavelength dependent refractive index equations for mgo-doped congruent andstoichiometric linbo3. Applied Physics B, 91(2):343-348, 2008.

[0301]

[11] Austin G. Griffith, Ryan K. W. Lau, Jaime Cardenas, YoshitomoOkawachi, Aseema Mohanty, Romy Fain, Yoon Ho Daniel Lee, Mengjie Yu,Christopher T. Phare, Carl B. Poitras, et al. Silicon-chip mid-infraredfrequency comb generation. Nature Communications, 6(1):1-5, 2015.

[0302]

[12] Hairun Guo, Clemens Herkommer, Adrien Billat, Davide Grassani,Chuankun Zhang, Martin H. P. Pfeiffer, Wenle Weng, Camille-Sophie Bres, andTobias J. Kippenberg. Mid-infrared frequency comb via coherent dispersivewave generation in silicon nitride nanophotonic waveguides. Nature Photonics,12(6):330-335,2018.

[0303]

[13] Qiushi Guo, Ryoto Sekine, Luis Ledezma, Rajveer Nehra, Devin J.Dean, Arkadev Roy, Robert M. Gray, Saman Jahani, and Alireza Marandi.Femtojoule femtosecond all-optical switching in lithium niobatenanophotonics. Nature Photonics, 16(9):625-631, 2022.

[0304]

[14] Xiang Guo, Chang-Ling Zou, Hojoong Jung, Zheng Gong, AlexanderBruch, Liang Jiang, and Hong X. Tang. Efficient generation of a near-visiblefrequency comb via cherenkov-like radiation from a Kerr microcomb. PhysicalReview Applied, 10:014012, Jul 2018. doi: 10.1103 / PhysRevApplied. 10. 014012.URL https: / / link.aps.org / doi / 10.1103 / PhysRevApplied. 10.014012.

[0305]

[15] Ryan Hamerly, Alireza Marandi, Marc Jankowski, Martin M. Fejer,Yoshihisa Yamamoto, and Hideo Mabuchi. Reduced models and design principlesfor half-harmonic generation in synchronously pumped optical parametricoscillators. Physical Review A, 94(6):063809, 2016.

[0306]

[16] Yang He, Qi-Fan Yang, Jingwei Ling, Rui Luo, Hanxiao Liang,Mingxiao Li, Boqiang Shen, Heming Wang, Kerry Vahala, and Qiang Lin. Self-starting bi-chromatic linbo 3 soliton microcomb. Optica, 6(9):1138-1144,2019.

[0307]

[17] Changran Hu, An Pan, Tingan Li, Xuanhao Wang, Yuheng Liu, ShiqiTao, Cheng Zeng, and Jinsong Xia. High-efficient coupler for thin-filmlithium niobate waveguide devices. Optics Express, 29(4):5397-5406, 2021.

[0308]

[18] Yaowen Hu, Mengjie Yu, Brandon Buscaino, Neil Sinclair, Di Zhu,Rebecca Cheng, Amirhassan Shams-Ansari, Linbo Shao, Mian Zhang, Joseph M.Kahn, et al. High-efficiency and broadband on-chip electro-optic frequencycomb generators. Nature Photonics, 16(10):679-685, 2022.

[0309]

[19] Andreas Hugi, Gustavo Villares, Stéphane Blaser, H. C. Liu, andJérôme Faist. Mid-infrared frequency comb based on a quantum cascade laser.Nature, 492 (7428):229-233,2012.

[0310]

[20] Marc Jankowski, Carsten Langrock, Boris Desiatov, AlirezaMarandi, Cheng Wang, Mian Zhang, Christopher R. Phillips, Marko Lončar, andMartin M. Fejer. Ultrabroadband nonlinear optics in nanophotonic periodicallypoled lithium niobate waveguides. Optica, 7(1):40-46, 2020.

[0311]

[21] Xingchen Ji, Xinwen Yao, Alexander Klenner, Yu Gan, Alexander L.Gaeta, Christine P. Hendon, and Michal Lipson. Chip-based frequency combsources for optical coherence tomography. Optics Express, 27(14):19896-19905,2019.

[0312]

[22] Tobias J. Kippenberg, Alexander L. Gaeta, Michal Lipson, andMichael L. Gorodetsky. Dissipative Kerr solitons in optical microresonators.Science, 361(6402):eaan8083, 2018.

[0313]

[23] Abijith S. Kowligy, David R. Carlson, Daniel D. Hickstein, HenryTimmers, Alexander J. Lind, Peter G. Schunemann, Scott B. Papp, and Scott A.Diddams. Mid-infrared frequency combs at 10ghz. Optics Letters, 45(13):3677-3680, 2020.

[0314]

[24] Luis Ledezma, Arkadev Roy, Luis Costa, Ryoto Sekine, RobertGray, Qiushi Guo, Ryan M Briggs, and Alireza Marandi. Widely-tunable opticalparametric oscillator in lithium niobate nanophotonics. arXiv preprint arXiv:2203.11482, 2022.

[0315]

[25] Luis Ledezma, Ryoto Sekine, Qiushi Guo, Rajveer Nehra, SamanJahani, and Alireza Marandi. Intense optical parametric amplification indispersionengineered nanophotonic lithium niobate waveguides. Optica, 9(3):303-308, 2022.

[0316]

[26] Hansuek Lee, Tong Chen, Jiang Li, Oskar Painter, and Kerry J.Vahala. Ultralow-loss optical delay line on a silicon chip. NatureCommunications, 3(1): 1-7,2012.

[0317]

[27] Jiang Li, Chengying Bao, Qing-Xin Ji, Heming Wang, Lue Wu,Stephanie Leifer, Charles Beichman, and Kerry Vahala. Efficiency of pulsepumped soliton microcombs. Optica, 9(2):231-239, 2022.

[0318]

[28] Mingxiao Li, Lin Chang, Lue Wu, Jeremy Staffa, Jingwei Ling,Usman A. Javid, Shixin Xue, Yang He, Raymond Lopez-Rios, Morin, et al.Integrated pockels laser. Nature Communications, 13(1):1-10, 2022.

[0319]

[29] Juanjuan Lu, Ayed Al Sayem, Zheng Gong, Joshua B. Surya, Chang-Ling Zou, and Hong X. Tang. Ultralow-threshold thin-film lithium niobateoptical parametric oscillator. Optica, 8(4):539-544, 2021.

[0320]

[30] Xiyuan Lu, Gregory Moille, Ashutosh Rao, Daron A. Westly, andKartik Srinivasan. On-chip optical parametric oscillation into the visible:Generating red, orange, yellow, and green from a near-infrared pump. Optica,7(10): 1417-1425,2020.

[0321]

[31] Luke Maidment, Peter G. Schunemann, and Derryck T. Reid.Molecular fingerprint-region spectroscopy from 5 to 12μm using anorientation-patterned gallium phosphide optical parametric oscillator. OpticsLetters, 41(18):42614264, 2016.

[0322]

[32] Pablo Marin-Palomo, Juned N. Kemal, Maxim Karpov, Arne Kordts,Joerg Pfeifle, Martin H. P. Pfeiffer, Philipp Trocha, Stefan Wolf, VictorBrasch, Miles H. Anderson, et al. Microresonator-based solitons for massivelyparallel coherent optical communications. Nature, 546(7657):274-279, 2017.

[0323]

[33] Andrew J. Metcalf, Connor D. Fredrick, Ryan C. Terrien, Scott B.Papp, and Scott A. Diddams. 30ghz electro-optic frequency comb spanning 300thz in the near infrared and visible. Optics Letters, 44(11):2673-2676, 2019.

[0324]

[34] Jatadhari Mishra, Timothy P. McKenna, Edwin Ng, Hubert S.Stokowski, Marc Jankowski, Carsten Langrock, David Heydari, Hideo Mabuchi,Martin M. Fejer, and Amir H. Safavi-Naeini. Mid-infrared nonlinear optics inthin-film lithium niobate on sapphire. Optica, 8(6):921-924, 2021.

[0325]

[35] Sean Molesky, Zin Lin, Alexander Y. Piggott, Weiliang Jin,Jelena Vucković, and Alejandro W. Rodriguez. Inverse design in nanophotonics.Nature Photonics, 12(11):659-670, 2018.

[0326]

[36] Ewelina Obrzud, Steve Lecomte, and Tobias Herr. Temporalsolitons in microresonators driven by optical pulses. Nature Photonics, 11(9):600-607, 2017.

[0327]

[37] Ewelina Obrzud, Monica Rainer, Avet Harutyunyan, Miles H.Anderson, Junqiu Liu, Michael Geiselmann, Bruno Chazelas, Stefan Kundermann,Steve Lecomte, Massimo Cecconi, et al. A microphotonic astrocomb. NaturePhotonics, 13(1):31-35, 2019.

[0328]

[38] Yoshitomo Okawachi, Mengjie Yu, Boris Desiatov, Bok Young Kim,Tobias Hansson, Marko Lončar, and Alexander L. Gaeta. Chip-based self-referencing using integrated lithium niobate waveguides. Optica, 7(6):702-707, 2020.

[0329]

[39] Alexandre Parriaux, Kamal Hammani, and Guy Millot. Electro-opticfrequency combs. Advances in Optics and Photonics, 12(1):223-287, 2020.

[0330]

[40] Arkadev Roy, Saman Jahani, Carsten Langrock, Martin Fejer, andAlireza Marandi. Spectral phase transitions in optical parametricoscillators. Nature Communications, 12(1):1-9, 2021.

[0331]

[41] Arkadev Roy, Rajveer Nehra, Saman Jahani, Luis Ledezma, CarstenLangrock, Martin Fejer, and Alireza Marandi. Temporal walk-off induceddissipative quadratic solitons. Nature Photonics, 16(2):162-168, 2022.

[0332]

[42] Anatoliy A. Savchenkov, Vladimir S. Ilchenko, Fabio Di Teodoro,Paul M. Belden, William T. Lotshaw, Andrey B. Matsko, and Lute Maleki.Generation of Kerr combs centered at 4.5μm in crystalline microresonatorspumped with quantum-cascade lasers. Optics Letters, 40(15):3468-3471, 2015.

[0333]

[43] Albert Schliesser, Nathalie Picqué, and Theodor W. Hänsch. Mid-infrared frequency combs. Nature Photonics, 6(7):440-449, 2012.

[0334]

[44] Brian Stern, Xingchen Ji, Yoshitomo Okawachi, Alexander L.Gaeta, and Michal Lipson. Battery-operated integrated frequency combgenerator. Nature, 562(7727):401-405, 2018.

[0335]

[45] Liron Stern, Jordan R. Stone, Songbai Kang, Daniel C. Cole,MyoungGyun Suh, Connor Fredrick, Zachary Newman, Kerry Vahala, John Kitching,Scott A. Diddams, et al. Direct Kerr frequency comb atomic spectroscopy andstabilization. Science Advances, 6(9):eaax6230, 2020.

[0336]

[46] Myoung-Gyun Suh and Kerry J. Vahala. Soliton microcomb rangemeasurement. Science, 359(6378):884-887, 2018.

[0337]

[47] Myoung-Gyun Suh, Xu Yi, Yu-Hung Lai, Stephanie Leifer, Ivan S.Grudinin, Gautam Vasisht, Emily C. Martin, Michael P. Fitzgerald, GregDoppmann, Ji Wang, et al. Searching for exoplanets using a microresonatorastrocomb. Nature Photonics, 13(1):25-30, 2019.

[0338]

[48] Yuxing Tang, Logan G. Wright, Kriti Charan, Tianyu Wang, ChrisXu, and Frank W. Wise. Generation of intense 100 fs solitons tunable from 2to 4.3 μm in fluoride fiber. Optica, 3(9):948-951, 2016.

[0339]

[49] Philipp Trocha, Maxim Karpov, Denis Ganin, Martin H. P.Pfeiffer, Arne Kordts, Stefan Wolf, Jonas Krockenberger, Pablo Marin-Palomo,Claudius Weimann, Sebastian Randel, et al. Ultrafast optical ranging usingmicroresonator soliton frequency combs. Science, 359(6378):887-891, 2018.

[0340]

[50] Paul A. Verrinder, Lei Wang, Joseph Fridlander, Fengqiao Sang,Victoria Rosborough, Michael Nickerson, Guangning Yang, Mark Stephen, LarryColdren, and Jonathan Klamkin. Gallium arsenide photonic integrated circuit

[0341] platform for tunable laser applications. IEEE Journal of SelectedTopics in Quantum Electronics, 28(1):1-9, 2021.

[0342]

[51] Cheng Wang, Mian Zhang, Xi Chen, Maxime Bertrand, AmirhassanShamsAnsari, Sethumadhavan Chandrasekhar, Peter Winzer, and Marko Lončar.Integrated lithium niobate electro-optic modulators operating atcmoscompatible voltages. Nature, 562(7725):101-104, 2018.

[0343]

[52] Christine Y. Wang, Lyuba Kuznetsova, Vasileios-Marios Gkortsas,Laurent Diehl, Franz X. Kaertner, Mikhail A. Belkin, Alexey Belyanin,Xiaofeng Li, Donhee Ham, Harald Schneider, et al. Mode-locked pulses frommid-infrared quantum cascade lasers. Optics Express, 17(15):12929-12943,2009.

[0344]

[53] Xingyuan Xu, Mengxi Tan, Bill Corcoran, Jiayang Wu, AndreasBoes, Thach G. Nguyen, Sai T. Chu, Brent E. Little, Damien G. Hicks, RobertoMorandotti, et al. 11 tops photonic convolutional accelerator for opticalneural networks. Nature, 589(7840):44-51, 2021.

[0345]

[54] Ni Yao, Junxia Zhou, Renhong Gao, Jintian Lin, Min Wang, YaCheng, Wei Fang, and Limin Tong. Efficient light coupling between an ultra-low loss lithium niobate waveguide and an adiabatically tapered single modeoptical fiber. Optics Express, 28(8):12416-12423, 2020.

[0346]

[55] Yu Yao, Anthony J. Hoffman, and Claire F. Gmachl. Mid-infraredquantum cascade lasers. Nature Photonics, 6(7):432-439, 2012.

[0347]

[56] Pan Ying, Heyun Tan, Junwei Zhang, Mingbo He, Mengyue Xu,Xiaoyue Liu, Renyou Ge, Yuntao Zhu, Chuan Liu, and Xinlun Cai. Low-loss edge-coupling thin-film lithium niobate modulator with an efficient phase shifter.Optics Letters, 46(6):1478-1481, 2021.

[0348]

[57] Mengjie Yu, Yoshitomo Okawachi, Austin G. Griffith, MichalLipson, and Alexander L Gaeta. Mode-locked mid-infrared frequency combs in asilicon microresonator. Optica, 3(8):854-860, 2016.

[0349]

[58] Mengjie Yu, Christian Reimer, David Barton, Prashanta Kharel,Rebecca Cheng, Lingyan He, Linbo Shao, Di Zhu, Yaowen Hu, Grant, et al.Femtosecond pulse generation via an integrated electro-optic time lens. arXivpreprint arXiv:2112.09204, 2021.

[0350]

[59] Mian Zhang, Brandon Buscaino, Cheng Wang, Amirhassan Shams-Ansari, Christian Reimer, Rongrong Zhu, Joseph M Kahn, and Marko Lončar.Broadband electro-optic frequency comb generation in a lithium niobatemicroring resonator. Nature, 568(7752):373-377, 2019.

[0351] Further information regarding one or more embodiments of the present invention can be found in Arkadev Roy et al., Visible-to-mid-IR tunable frequency comb in nanophotonics (Nature Communications volume 14, Article number: 6549 (2023)) and supporting information. https: / / www.nature.com / articles / s41467-023-42289-0

[0352] Fourth embodiment: 40-pulse time-multiplexed nanophotonic optical parametric oscillator

[0353] Time-multiplexed systems have become ubiquitous in many subfields of optics because they offer the ability to create large-scale graphics by storing information across different time chambers. Consequently, they have found applications in fields such as computing, quantum information, and the study of topological phenomena [1–3]. Time-multiplexed networks of optical parametric oscillators (OPOs), particularly degenerate OPOs, have attracted particular attention due to their ability to approximate the Ising Hamiltonian [4, 5]. Recent advances in thin-film lithium niobate, including demonstrations of extremely high parametric gains [6] and subsequent demonstrations of optical parametric oscillations [7], have brought the possibility of realizing such time-multiplexed systems on a chip scale. Here, we demonstrate an on-chip, 40-pulse, time-division multiplexed OPO. By using interferometry, we verified the independence of each of the 40 simultaneously oscillating pulses. This study represents a key milestone in the path to creating large-scale graphics in integrated photonic platforms.

[0354] Figure 47 The experimental setup is schematically depicted in the diagram. We used an electro-optic (EO) comb with a repetition rate of 10 GHz. Figure 1a (Left) to pump a 250 MHz on-chip optical parametric oscillator, causing 40 pulses to resonate in the cavity. After EO comb generation, our pump preparation includes an enhancement optical amplifier (BOA), a waveform shaper, and a ytterbium-doped fiber amplifier (YDFA) for amplification and dispersion compensation. The pump is characterized by its spectrum ( Figure 47 c) and intensity autocorrelation ( Figure 47 (d) demonstrates a 3 nm bandwidth and 1.6 ps autocorrelation width around a center wavelength of 1045 nm. Periodic polarization on the waveguide ( Figure 47 (a, center) provides phase matching between the pump and the signal near 2090 nm. The tapered coupler ensures coupling of the signal to the resonator while allowing the pump to pass through. Figure 47Figure b shows an optical microscope image highlighting the 53 cm helical resonator.

[0355] We use an unbalanced (1-pulse-delay) Mach-Zehnder interferometer (MZI) consisting of a 45:55 free-space thin-film beam splitter and a 50:50 fiber splitter to characterize the relative phase of the output pulse. Figure 47 (a, right side). One of the free-space arms has a delay stage that can be locked to a signal from a backpropagating CW laser at 1064 nm, coupled through an MZI output port and measured on a photodetector (PD2), using a piezoelectric transducer (PZT). Using this 100 ps delay, we perturb consecutive pulses in a 10 GHz pulse sequence. A 1 MHz photodetector (PD3) at another MZI output measures the average of these perturbations over many pulses. If the phases of the 40 pulses are random and independent of each other, we expect to see a different average interference value for each instance of the OPO. To measure this, we modulate the BOA in the pump preparation setup to etch 4 μs pulses at a repetition rate of 10 kHz on top of the 10 GHz comb. This is used to rapidly turn the OPO on and off. We also use a 92:8 surface film at the chip output to continuously monitor the MZI input on PD1 for both reference measurements and pump stabilization.

[0356] Figure 48 a shows the experimental results in the degenerate case, where the oscillation occurs at the half-harmonic of the pump, as confirmed in the measured optical spectrum (i). Here, the OPO is expected to oscillate only in two phase states, 0 or π. In the case of 40 pulses, the average of the resulting disturbances should have only 21 possible permissible levels. The probability of each level is determined by... Given, where N is the number of phase flips occurring in the string of 40 pulses. In subplot (ii), a sample string of an OPO instance is shown. The reference trace collected from the 8:92 splitter allows for post-correction of the measurement data to account for intensity noise in the OPO output. As expected, the time trace from the interference shown in the figure below exhibits significantly larger fluctuations than the reference. In (iii), a histogram of the interference output over a 2-second measurement time is shown. Here, the expected discrete state is clearly observed, indicating that the 40 pulses actually behave as independent, time-division multiplexed degenerate OPOs with random binary phases. Furthermore, we can use the histogram from (iii) to compute the probabilistic mass function and compare it with the theoretical probability. The results (iv) show good agreement between the experiment and the theory.

[0357] We also measured the case of non-degenerate oscillations, such as Figure 48As shown in b. Here, the optical spectrum indicates different signal and idler wave modes (i). As in the degenerate case, the samples of time trace data (ii) show that the fluctuations of the interference are greater than those of the reference measurement. However, unlike the degenerate case, the phase of the non-degenerate OPO is not limited to discrete energy levels, but can take any energy level. Therefore, we expect to see a continuous Gaussian distribution in the histogram, as observed in (iii).

[0358] In summary, we have demonstrated a 40-pulse, time-multiplexed, nanophotonic optical parametric oscillator operating under both degenerate and non-degenerate mechanisms. By measuring the average interference between successive pulses of numerous instances of the OPO, we have shown the independence of all 40 pulses. This result paves the way for the realization of on-chip optical time-multiplexed systems such as the Ising machine.

[0359] References for the Fourth Embodiment

[0360] The following references are incorporated herein by reference.

[0361] 1. C. Leefmans et al., Nat. Phys. 18, 442-449 (2022).

[0362] 2.S. Yokoyama et al., Nat. Photonics 7, 982-986 (2013).

[0363] 3. R. Nehra et al., Science 377, 1333-1337 (2022).

[0364] 4. A. Marandi et al., Nat. Photonics 8, 937-942 (2014).

[0365] 5. N. Mohseni et al., Nat. Rev. Phys. 4, 363-379 (2022).

[0366] 6. L. Ledezma et al., Optica 9, 303-308 (2022).

[0367] 7. L. Ledezma et al., arXiv preprint, arXiv:2203.11482 (2022).

[0368] Example pump circuit

[0369] Figure 49aThe photonic integrated circuit is shown to include a pump sub-circuit coupled to the OPO. Figure 49b An example is shown in which the pump sub-circuit includes a mode-locked laser, which includes a modulator (e.g., an electro-optic modulator) that includes an electrode metallization or heater coupled to the waveguide. Figure 48 c shows an example in which the pump circuit includes a Kerr resonator. Figure 48 Figure d shows an example in which the pump sub-circuit includes an electro-optic (EOM) modulator / phase modulator (e.g., including electrodes coupled to the waveguide portion). Figure 48 e illustrates an example in which the pump subcircuit includes an amplitude modulator (e.g., including electrodes coupled to a waveguide portion). In one or more embodiments, the Kerr resonator (e.g., including a loop) includes Kerr nonlinearity, i.e., it is not linear.

[0370] Figure 49f An example of a device in which the OPO can be integrated inside a laser cavity is illustrated, and Figure 49g Examples are shown where the OPO includes a laser gain element or where the pump pulse or frequency comb is generated inside the resonator.

[0371] Figure 49f -g illustrates the device described in Clause 1, wherein the circuitry includes additional components at the output of the OPO, including a nonlinear component 4910 for wavelength conversion, a nonlinear component 4910 for spectral broadening, linear components (such as filters and couplers), and actuators (such as electro-optic modulators).

[0372] Process steps

[0373] Figure 50 This is a flowchart illustrating a method of manufacturing a device according to one or more embodiments.

[0374] Box 5000 represents the formation of a photonic integrated circuit including an OPO (Optical Distribution Object) using photolithographic patterning of a substrate. The OPO includes one or more waveguides comprising a nonlinear material that responds to a pump wave output wave (signal and / or idle wave) using a parametric nonlinear process. Each waveguide has a width and height of less than 5 micrometers. The nonlinear material is phase-matched and dispersion-engineered to control an appropriate group velocity mismatch (GVM) between the pump pulse and the signal pulse to provide temporal overlap between the pump pulse and the signal / idle wave pulse. In one or more examples, the waveguide has a length appropriately tailored for dispersion engineering. Examples of nonlinear materials having (e.g., second-order) nonlinearity (and capable of forming a substrate chip) include, but are not limited to, lithium niobate, lithium tantalate, potassium titanate phosphate (KTP), aluminum nitride, gallium arsenide, indium phosphide, aluminum gallium arsenide, GaP, or InGaP. The invention is not limited to second-order nonlinearity; other nonlinear materials may be used, including but not limited to third-order nonlinear materials such as SiN and Si. In one or more examples, the substrate comprises lithium niobate on silicon dioxide, and the waveguide is patterned in the lithium niobate (monolithic integration of the waveguide). Other components, such as pump lasers, injection-locked inputs, or auxiliary resonators, may be patterned in the same substrate or on a different material substrate bonded to a substrate containing an OPO.

[0375] Actuators (e.g., electro-optic modulators, electric heaters, thermo-optic heaters, or piezoelectric transducers, for example, to modulate the phase or amplitude or refractive index of a wave using an electric field or temperature) can be fabricated by depositing metallides coupled to a waveguide formed in a lithium niobate / substrate.

[0376] The inputs to each of the OPOs and the outputs from each of the OPOs can each comprise an input coupler and an output coupler, which can be integrated into the device. The input coupler and output coupler can include thermally adiabatic couplers, directional couplers, Y-junctions, multimode interferometers, or reverse-designed couplers, which can be formed, for example, by etching a suitable combination of waveguides into a substrate (including a nonlinear material such as lithium niobate).

[0377] In one or more examples, the photonic integrated circuit includes a sub-circuit for pumping or coupled to a sub-circuit for pumping, for example, wherein the sub-circuit is configured to output a pump wave comprising pulses or a frequency comb having a pump repetition rate. The sub-circuit may be formed in a substrate comprising a nonlinear material or formed in a different substrate chip. In one or more examples, the Kerr frequency comb is fabricated by forming a ring waveguide with a gap coupled to a linear portion of the waveguide, as shown in Figure 49.

[0378] In another example, the subcircuit includes one or more actuators operable to adjust at least one of the repetition rate, carrier envelope offset, intensity, or wavelength of the pump wave. In one or more examples, the actuator is formed by depositing a metallization (e.g., a nonlinear material such as lithium niobate) coupled to a waveguide formed in a substrate. In one or more examples, the subcircuit includes at least one of a mode-locked laser, an electro-optic frequency comb source, a Kerr frequency comb source, an amplitude modulator, or a phase modulator. In one or more examples, the electro-optic comb source may include a modulator that can be implemented by depositing metal on lithium niobate (or a nonlinear material) or on a dielectric thin layer deposited on lithium niobate (or a nonlinear material). In one or more embodiments, the amplitude modulator or phase modulator may include metal deposited on top of an additional dielectric layer on the LN.

[0379] In other examples, the photonic integrated circuit includes additional components at the output of the OPO, including nonlinear components for wavelength conversion, nonlinear components for spectral broadening, linear components (such as filters and couplers), and actuators (such as electro-optic modulators). Examples of nonlinear components include, but are not limited to, her OPOS or other nonlinear waveguides or amplifiers; and nonlinear materials of the substrate (e.g., lithium niobate) used for mixing, harmonic generation (e.g., SHG), or parametric amplification processes.

[0380] In one or more embodiments, the OPO includes multiple parts and quasi-phase matching in the on-chip synchronous pumped OPO. Phase matching can also be achieved using other techniques such as modal phase matching.

[0381] In one or more examples, dispersion engineering involves fabricating specific cross-sectional geometries to provide appropriate group velocity dispersion (e.g., Figure 5 or Figure 30b ).

[0382] Box 5002 represents the final result, device, system, or apparatus. The device can be implemented in many ways, including but not limited to the following (see also Figure 1-). Figure 48 )

[0383] 1. A device, system, or apparatus 100, 3100, comprising:

[0384] Photonic integrated circuits 102 and 3102 include one or more optical parametric oscillators (OPOs) 104, each OPO including:

[0385] Inputs 106 and 3106 are configured to receive a pump wave 3108 comprising pulses or a frequency comb with a pump repetition rate (arrow 108 indicates the direction of the pump wave).

[0386] One or more nonlinear portions 110, 3110, as part of resonators 3112, 112 (including waveguides 113, 3113) or coupled to a resonator having a free spectral range, wherein at least one of the free spectral range or its harmonics (e.g., harmonics of the spectral range) matches (e.g., equal to or within 10%) the pump repetition rate or its harmonics.

[0387] One or more outputs 114, 3114 are configured to extract a portion of the wave generated by the OPO in response to the pump wave (arrow 118 indicates the direction of the extracted wave) and / or extract the pump wave (e.g., for other purposes).

[0388] 2. The apparatus according to Clause 1, wherein each of the nonlinear portions is phase-matched for one or more nonlinear optical processes, including degenerate optical parametric amplification, non-degenerate optical parametric amplification, upconversion of a wave in an OPO, downconversion of a wave in an OPO, and spectral broadening of a wave in an OPO. In one or more examples, the nonlinear waveguide may have different portions, each of which is phase-matched for a different nonlinear process, or the nonlinear portions in different OPOs may be phase-matched for different nonlinear processes.

[0389] 3. The device according to Clause 2, wherein phase matching is achieved by quasi-phase matching, for example by periodic or aperiodic polarization.

[0390] 4. The device according to Clause 1 or 2, wherein the nonlinear portion and / or other components of the resonator (e.g., the waveguide forming the resonator) are dispersion-engineered to adjust the spectrum of one or more waves generated in the OPO. In one or more examples, adjusting the spectrum refers to how the GVD and GVM can change the parametric gain, as an example, such as Figure 1c As shown.

[0391] 5. The apparatus according to any one of aspects 1 to 4, wherein the dispersion-engineered OPO supports the formation of temporal solitons. Temporal solitons are a specific type of nonlinear operation. Figure 30a , Figure 30b An example of a design that supports solitons is shown in the figure.

[0392] 6. The device according to any one of clauses 1-5, wherein the photonic integrated circuit further comprises one or more actuators 4906 for modulating and / or adjusting one or more of the following:

[0393] Phase matching condition for the nonlinear part,

[0394] Including the center frequency of the wave portion of the output wave,

[0395] The carrier envelope offset frequency of the output wave,

[0396] The free spectral range of the resonator

[0397] Spectral response of resonators

[0398] 7. The apparatus according to Clause 6, wherein the actuators may each independently include an electro-optic modulator, an electric heater, a thermo-optic heater, or a piezoelectric transducer.

[0399] 8. The device according to any one of Clauses 1-7, comprising a plurality of OPOs, wherein each OPO includes a nonlinear portion with different phase matching for different nonlinear processes. In one or more embodiments, the different OPOs have different phase matchings. In another embodiment, each of the OPOs has portions with different phase matchings or a series of different phase matchings.

[0400] 9. The device according to any one of clauses 1-8, wherein the photonic integrated circuit further comprises:

[0401] The switching circuit (e.g., a Mach-Zehnder interferometer (MZI) or multiple MZIs or an MZI network) is configured to selectively route the pump wave to different OPOs in the OPO, such that the output of the OPO independently or in combination includes outputs ranging from ultraviolet to mid-infrared wavelengths.

[0402] 10. The device according to any one of Clauses 1-9, wherein the photonic integrated circuit includes an integrated input coupler 3106 and the output includes an integrated output coupler 3114, for example, but not limited to, wherein the input coupler and / or the output coupler are coupled to the waveguide of the OPO through a gap.

[0403] 11. The device according to any one of Clauses 1-10, wherein the input coupler and the output coupler each independently comprise an adiabatic coupler 3106, a directional coupler, a Y-junction, a multimode interferometer, or a reverse-designed coupler.

[0404] 12. The device according to any one of clauses 1-11, wherein the resonator comprises a helical resonator or a resonator having a length of at least 10 cm.

[0405] 13. The device according to any one of clauses 1-12, wherein the output bandwidth is at least twice as wide as the input bandwidth of the pump input in Hertz.

[0406] 14. Figure 49aAn example of a device according to Clause 1 is illustrated, wherein the photonic integrated circuit includes a sub-circuit 4900 for pumping, for example, wherein the sub-circuit is configured to output a pump wave comprising pulses or a frequency comb having a pump repetition rate.

[0407] 15. Figures 49b-49e An example of a device according to Clause 14 is illustrated, wherein the sub-circuit includes at least one of a mode-locked laser 4902, an electro-optic frequency comb source, a Kerr frequency comb source 4904, an amplitude modulator 4906, or a phase modulator 4908.

[0408] 16. Figures 49b-49e The device according to Clause 14, wherein the sub-circuit includes one or more actuators 4906 operable to adjust at least one of the pump wave repetition rate, carrier envelope offset, intensity, or wavelength.

[0409] 17. The device according to any one of clauses 1 to 16, wherein the pump pulse has a length in the range of 1 picosecond to 100 picoseconds, and the OPO generates pulses shorter than 1 picosecond.

[0410] 18. Figure 49f Examples of devices according to any one of the terms 1 to 17 are shown, wherein the OPO is inside an integrated laser cavity or the OPO contains laser gain elements.

[0411] 19. The device according to any one of clauses 1-18, wherein the pump pulse or frequency comb is generated inside the resonator.

[0412] 20. The apparatus according to any one of clauses 1-19, wherein the pump frequency comb does not constitute a pulse in the time domain or includes a continuous wave frequency modulated wave.

[0413] twenty one. Figure 49f -g exemplifies the device described in any one of clauses 1-20, wherein the circuitry includes additional components at the output of the OPO, including:

[0414] Nonlinear component 4910 for wavelength conversion

[0415] 4910 nonlinear component for spectral broadening

[0416] Linear components such as filters and couplers,

[0417] Actuators such as electro-optic modulators.

[0418] 22. A computing system, metering system or communication system comprising the device described in any one of clauses 1-21.

[0419] 23. The equipment according to any one of clauses 1-22, wherein each of the OPOs:

[0420] The system includes a resonator comprising a waveguide coupled to a nonlinear portion, and the waveguide and the nonlinear portion are dispersion-engineered with selected geometries (e.g., cross-sectional geometries defining dispersion) such that the pump wave and the wave generated in the OPO, comprising a spectrum centered on the pump's half-harmonic, experience near-zero group velocity mismatch (e.g., less than 20% of the group velocity mismatch of the bulk material at the same wavelength) and have near-zero group velocity dispersion (e.g., less than 20% of the group velocity dispersion of the bulk material at the same wavelength), such that the pulses of the pump wave and the wave comprising the half-harmonic completely (or at least 90%) overlap (the time envelope of the half-harmonic is completely within or at least 90% overlaps with the time envelope of the pump wave), and the nonlinear portion is phase-matched for degenerate operation of the OPO, wherein the nonlinear process converts the pump wave into a wave comprising the half-harmonic; and

[0421] The input and output each include a coupler designed as a frequency-selective coupler to allow resonance only around the half-harmonic.

[0422] 24. The device according to Clause 23, wherein each coupler includes an input waveguide separated from a portion of the OPO waveguide by a gap, each of the portions of the input waveguide and the OPO waveguide having a width that gradually varies along its length, such that the input couples a pump wave into the cavity and the output coupler couples a half-harmonic or a signal including an output frequency comb out of the cavity.

[0423] 25. The apparatus according to Clause 23, wherein the pump has an energy higher than that that causes the OPO to transition from an incoherent operating state to an ultrawide coherent state, the incoherent operating state typically used for operation far (more than 5 times) above its oscillation threshold, thereby allowing the generation of an output frequency comb comprising a multioctave coherent spectrum.

[0424] 26. The equipment according to any one of clauses 1-22, wherein each of the OPOs:

[0425] The device includes a resonator comprising a waveguide coupled to a nonlinear portion, and the waveguide and the nonlinear portion are dispersion-engineered using selected geometry such that the pump wave and the generated wave, including a signal or idle wave, experience near-zero group velocity mismatch (e.g., less than 20% of the group velocity mismatch of a bulk material at the same wavelength) and have near-zero group velocity dispersion (e.g., less than 20% of the group velocity dispersion of a bulk material at the same wavelength), such that the pulses of the pump wave and the signal or idle wave completely or at least 90% overlap (the time envelope of the signal wave is completely within the time envelope of the pump wave or overlaps with the time envelope of the pump wave by at least 90%).

[0426] The nonlinear component is phase-matched and used for degenerate, non-degenerate, frequency up-conversion, or frequency down-conversion operations of the OPO, wherein the nonlinear process converts the pump wave into a signal and / or idle wave; and

[0427] The input and output each include an adiabatic coupler designed as a frequency-selective coupler to allow only the resonance of the wave that generates the output frequency comb, which has a wavelength range between the ultraviolet and mid-infrared and is extracted by the output.

[0428] 27. The device according to Clause 26, wherein each of the adiabatic couplers includes an input waveguide separated from a portion of the OPO waveguide by a gap, each of the input waveguide and the portion of the OPO waveguide having a width and phase mismatch that gradually varies along its length, such that the input couples a pump wave into the cavity, and the output coupler couples only a half-harmonic or output frequency comb signal out of the cavity.

[0429] 28. The device according to any one of clauses 1-27, wherein the resonator includes a waveguide defined by reflectors 3106, 3114 (e.g., couplers) or mirrors (e.g., couplers) to form a cavity.

[0430] 31. The device according to any one of Clauses 1-28, wherein the wave includes an electromagnetic wave or field having a wavelength in the ultraviolet to mid-infrared wavelength range.

[0431] 32. The device according to any one of clauses 1-31, wherein each of the optical parametric oscillators (OPO) is an optical resonator having parametric nonlinearity.

[0432] 33. The device according to any one of clauses 1-32, wherein at least one of the free spectral range or its harmonics is matched with the pump repetition rate or its harmonics, meaning NxFSR=MxFSR (where N and M are non-zero positive integers), and any harmonic of the FSR can be matched with any harmonic of the RR, wherein the simplest case is M=N=1. FSR is the free spectral range, and RR is the pump repetition rate.

[0433] 34. The apparatus according to any one of clauses 1-33, wherein dispersion engineering includes manufacturing a specific cross-sectional geometry to provide appropriate group velocity dispersion (e.g., Figure 5 or Figure 30b ).

[0434] 35. The apparatus according to any one of clauses 1-34, wherein the electro-optical comb source includes a modulator, which can be implemented by depositing metal on lithium niobate or on a dielectric thin layer deposited on lithium niobate.

[0435] 36. The device according to any one of clauses 1-35, wherein the resonator comprises a ring resonator.

[0436] Operation method

[0437] Figure 51 An example of a method for operating a device is illustrated, comprising the following steps.

[0438] Box 5100 represents pumping one or more OPOs with a pump wave comprising a pulse or a frequency comb having a pump repetition rate, wherein each OPO comprises one or more nonlinear portions 110, 3110 as part of or coupled to a resonator having a free spectral range 3112, 112 (including waveguides 113, 3113), wherein at least one of the free spectral ranges or one of its harmonics (harmonics of the spectral range) matches (e.g., equal to or within 10%) the pump repetition rate or at least one of its harmonics.

[0439] Box 5102 indicates the extraction of a portion of the wave generated by the OPO in response to the pump wave and / or the harmonics of the pump wave (arrow 118 indicates the direction of the extracted wave).

[0440] This method can be implemented using any of the devices specified in Clauses 1-36.

[0441] in conclusion

[0442] The foregoing description is a preferred embodiment of the present invention. One or more embodiments of the invention have been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the foregoing teachings. It is intended that the scope of the invention be limited not by this detailed description, but by the appended claims.

Claims

1. An apparatus comprising: a photonic integrated circuit comprising one or more OPOs, each OPO comprising: an input configured to receive a pump wave comprising pulses or a frequency comb having a pump repetition rate, one or more nonlinear sections being part of a resonator or coupled to a resonator having a free spectral range, wherein at least one of the free spectral range or one of its harmonics matches the pump repetition rate or a harmonic thereof, and one or more outputs configured to extract a part of the pump wave and / or waves generated by the OPO in response to the pump wave.

2. The apparatus of claim 1, wherein, each of the nonlinear sections is phase-matched for one or more nonlinear optical processes, the nonlinear optical processes including degenerate optical parametric amplification, non-degenerate optical parametric amplification, upconversion of the waves in the OPO, downconversion of the waves in the OPO, spectral broadening of the waves in the OPO.

3. The apparatus of claim 2, wherein, phase-matching is achieved by quasi-phase-matching.

4. The apparatus of claim 1, wherein, the nonlinear sections of the resonator and / or other parts thereof are dispersion-engineered to adjust the frequency spectrum of one or more of the waves generated in the OPO.

5. The apparatus of claim 4, wherein, the dispersion-engineered OPO supports the formation of temporal solitons.

6. The apparatus of claim 1, wherein, the photonic integrated circuit further comprises one or more actuators for modulating and / or adjusting one or more of: a phase-matching condition of the nonlinear sections, a center frequency of a part of the waves comprising the output waves, a carrier envelope offset frequency of the output waves, a free spectral range of the resonator, a spectral response of the resonator.

7. The apparatus of claim 6, wherein, the actuators comprise at least one of an electro-optic modulator, an electrical heater, a thermo-optic heater, or a piezoelectric transducer.

8. The apparatus of claim 1, comprising a plurality of OPOs, wherein, each of the OPOs comprises the nonlinear sections with different phase-matching for different nonlinear processes.

9. The apparatus of claim 8, wherein, the photonic integrated circuit further comprises: a switching circuit configured to selectively route the pump wave to different ones of the OPOs, such that the outputs of the OPOs independently or in combination comprise output in a range from ultraviolet to mid-infrared wavelengths.

10. The apparatus of claim 1, wherein, the photonic integrated circuit comprises an integrated input coupler and the outputs comprise an integrated output coupler, or the input coupler and the output coupler each independently comprise an adiabatic coupler, a directional coupler, a Y-junction, a multimode interferometer, or a counter- designed coupler.

11. The apparatus of claim 1, wherein, the resonator comprises a spiral resonator or a resonator having a length of at least 10 centimeters.

12. The apparatus of claim 1, wherein, an output bandwidth is at least 2 times wider than an input bandwidth of the pump input in Hertz.

13. The apparatus of claim 1, wherein, the photonic integrated circuit comprises a sub-circuit for the pump, wherein the sub-circuit is configured to output the pump wave comprising the pulses or the frequency comb having the pump repetition rate.

14. The apparatus of claim 13, wherein, the sub-circuit comprises at least one of a mode-locked laser, an electro-optic frequency comb source, a Kerr frequency comb source, an amplitude modulator, or a phase modulator.

15. The apparatus of claim 13, wherein, the sub-circuit comprises one or more actuators operable to adjust at least one of a repetition rate, a carrier envelope offset, an intensity, or a wavelength of the pump wave.

16. The apparatus of claim 1, wherein, The pump pulse has a length in the range of 1-100 picoseconds and the OPO generates pulses shorter than 1 picosecond.

17. The apparatus of claim 1, wherein, The OPO is inside an integrated laser cavity or the OPO comprises a laser gain element.

18. The apparatus of claim 1, wherein, The pump pulse or frequency comb is generated inside the resonator.

19. The apparatus of claim 1, wherein, The pump frequency comb does not constitute a distinct pulse in time domain or comprises a continuous wave frequency modulated wave.

20. The apparatus of claim 1, wherein, The circuit comprises additional components at the output of the OPO, including: a nonlinear component for wavelength conversion, a nonlinear component for spectral broadening, linear components such as filters and couplers, an actuator such as an electro-optical modulator.

21. A computing system, metrology system or communication system comprising the apparatus of claim 1.

Images