Thin-film synchronous pumping optical parametric oscillator

Abstract

The device includes a photonic integrated circuit, the photonic integrated circuit comprises one or more OPOs, each OPO comprising: an input, one or more nonlinear parts, and one or more outputs, the input being configured to receive a pump wave including a pulse or frequency comb at a pump repetition rate, the one or more nonlinear parts being resonators having a free spectral region, or coupled to resonators having a free spectral region, at least one of the free spectral region or one of its harmonics being matched to the pump repetition rate or its harmonics, and the one or more outputs being configured to output a portion of the wave generated by the OPO in response to the pump wave.

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims priority under 35 U.S.C. Section 119(e) (Title 35, United States Code, Section 119(e)) to U.S. Provisional Patent Application No. 63 / 466188, filed May 12, 2023, by Alireza Marandi, Luis. M. Ledezma, Arkadev Roy, Ryoto Sekine, and Robert M. Gray, titled "THIN FILM SYNCHRONOUSLY PUMPED OPTICAL PARAMETRIC OSSCLATORS" (CIT - 9012 - P) and U.S. Provisional Patent Application No. 63 / 532648, filed Aug. 14, 2023, by Ryoto Sekine, Robert M. Gray, and Alireza Marandi, titled "ON - CHIP ULTRA SHORT PULSE SYNTHESIZER" (CIT - 9055 - P), and incorporates herein by reference both of these patent applications.

[0002] Federally Sponsored Research and Development This invention was made with government support under award numbers FA9550 - 20 - 1 - 0040 and FA9550 - 23 - 1 - 0755 from the U.S. Air Force, award numbers W911NF - 18 - 1 - 0285 and W911NF - 23 - 1 - 0048 from the U.S. Army, award number D23AP00158 from DARPA (Defense Advanced Research Projects Agency), and award numbers ECCS1846273 and CCF1918549 from the National Science Foundation. The government has certain rights in this invention.

Background Art

[0003] Background of the Invention Increasing efforts have been made in dual - comb spectroscopy 6 (Non - Patent Document 6), optical communication 7(Non-patent document 7), optical frequency synthesis 8,9 (Non-patent documents 8, 9), and laser ranging 10 The focus is on realizing broadband frequency combs in nanophotonics platforms with applications including (Non-Patent Document 10). However, the spectral coverage of integrated frequency comb sources remains far inferior to that of tabletop types using high-pulse-energy lasers and discrete components, which recently surpass tabletop types with a 6-octave spectrum. 11,12 (Non-patent documents 11, 12). Such frequency combs and short-pulse laser sources are ultrashort pulse synthesis 13 (Non-patent document 13), atto-second science 14 (Non-patent document 14), and biochemical sensing and imaging (imaging) 15-17 It is of high value for applications such as those described in Non-Patent Documents 15-17. What is needed is an improved method for generating a coherent pulse source and frequency comb. The present invention satisfies this need. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] DR Carlson, DD Hickstein, W. Zhang, AJ Metcalf, F. Quinlan, SA Diddams, and SB Papp, Science 361, 1358 (2018) [Non-Patent Document 2] SA Diddams, K. Vahala, and T. Udem, Scirnce 369, eaay3676 (2020) [Non-Patent Document 3] TJ Kippenberg, AL Gaeta, M. Lipson, and ML Gorodetsky, Science 361, eaan8083 (2018) [Non-Patent Document 4] L. Chang, S. Liu, and JE Bowers, Nature Photonics 16, 95 (2022)

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[0005] This disclosure describes an on-chip optical parametric oscillator (OPO), which is pumped (excited) by a frequency comb having a repetition rate synchronized with the round-trip time of the OPO cavity. These on-chip OPOs are fabricated on a microchip based on a thin-film nonlinear optical material. These on-chip OPOs 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. These on-chip OPOs can also generate an output frequency comb that covers a much wider spectral range than the pump (excitation) frequency comb. This output frequency comb can cover more than one octave of the electromagnetic spectrum. These on-chip OPOs can also be pumped by a frequency comb having a repetition rate that is a harmonic of the round-trip time of the OPO cavity. In this regime, these on-chip OPOs can support multiple pulses simultaneously present inside the on-chip OPO cavity. These on-chip OPOs may include actuators within the on-chip resonator for adjusting the repetition rate and carrier-envelope offset of the output frequency comb.

[0006] This invention further discloses multi-octave frequency comb generation using an optical parametric oscillator (OPO) in nanophotonic lithium niobate having only femtojoule-level synchronously pumped pump energy. Such energy-efficient and robust coherent spectral broadband generation occurs far above the OPO's oscillation threshold, detuning from linear synchronization with the pump. The inventors demonstrate that a transient self-cleaning mechanism arises when the OPO transitions from an incoherent operating regime, common for operation far above the threshold, to an ultra-broadband coherent regime corresponding to a nonlinear phase that compensates for the detuning of the OPO cavity. Such a transient self-cleaning mechanism, and the subsequent multi-octave coherent spectrum, have not been explored in previous OPO designs and feature a relaxation of requirements regarding the cavity's Q factor and relatively narrow spectral coverage. The inventors have achieved an order of magnitude reduction in energy requirements compared to other technologies, confirmed comb coherence, and presented a path toward more efficient and broader spectral bandwidth. The inventors' results "pave the way" to ultrashort pulse, ultrabroadband on-chip nonlinear photonic (photon) systems for a wide range of applications.

[0007] This disclosure further discloses a pulsed time-division multiplexed nanophotonic optical parametric oscillator and a method for supporting cavity second-order solitons using an OPO.

[0008] The following refers to drawings, and throughout these drawings, similar reference numbers indicate corresponding parts. [Brief explanation of the drawing]

[0009] [Figure 1]This figure illustrates the principle and design of a multi-octave nanophotonic OPO. a. An example of a synchronously pumped OPO on a thin film of lithium niobate, highlighting its key features. b. Microscope images of multiple devices as the central one is pumped at 1 μm. The chip emits green light due to second harmonic generation (SHG). The top inset is a scanning electron microscope image of a spiral region, and the bottom is an image of the entire chip containing 16 OPOs. c. An example showing how short pump pulses can utilize an optically phased array (OPA) designed for near-zero dispersion. The simulated gain profiles are shown at the top for wavelengths with half-harmonic GVD (group velocity dispersion) of 60 fs² / mm and GVM (group velocity mismatch) of 26 fs / mm, and at the bottom for wavelengths with near-zero dispersion. The solid orange line indicates the center wavelength of pumping, and the orange shaded area indicates the 3dB bandwidth (BW) of the 100fs source. d. The expression of different operating regimes of the OPO as a function of pump pulse energy is shown, along with the OPO output for each round-trip time in each regime. [Figure 2]This figure shows the characteristics of the OPO. a. The oscillation peak of the OPO near the threshold as 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 (femtojoules) for three different reciprocal detunings. c. Figure showing the corresponding OPO signal growth as a function of pump energy for different oscillation peaks and their gradient coefficient ηSL. d. Output spectra, OPO oscillation peaks, and beat measurements from the OPO cavity for pumps of 54 fJ, 109 fJ, and 121 fJ. OPO oscillation peaks (ii), (v), and (viii) were acquired under the same detector amplification settings. RF (radio frequency) beats (iii), (vi), and (ix) were acquired between free space and the on-chip OPO sharing the same pump, with the repetition rate of this pump adjusted over a long period of time. [Figure 3] These are simulation results showing different operating regimes of a nanophotonic OPO. a. Transition from (i) coherent operation near the threshold to (ii) incoherent operation, and (iii) transition back to coherent operation as pump energy increases. The round-trip time progression (i)~(iii) and output spectra (iv)~(vi) are shown for three different pump intensities using experimental parameters at -10.5 fs cavity detuning. b. 3-octave coherent OPO. The same experimental parameters are used except that the last 1 mm of PPLN (periodically polled lithium niobate) is replaced with a chirp-polling (polarization reversal) period. The pump pulse energy was 250 fJ. [Figure 4]This figure shows a performance comparison between (a) integrated spectral broadbanding and (b) frequency comb-synchronous pumping OPOs. a. Wavelength coverage and pump pulse energy of the spectral broadbanding scheme (method) of the integrated frequency comb. The arrow indicates the pump wavelength. b. Comb repetition rate and pump threshold energy of the synchronous pumping OPO. The shape of the markers (labels) represents different cavities and nonlinear (NL) elements for each OPO, and the categories are free space, fiber, integrated and bulk, fiber, and nanophotonic, respectively. In both figures, the legend at the top represents the material of the nonlinear element. The abbreviations are TFLN (thin-film lithium niobate), OP (orientation patterned), MF (microstructured fiber), and HNLF (highly nonlinear fiber). [Figure 5] This figure shows the main OPO design parameters as a function of the waveguide geometry. a. Parameters for adjusting the spatiotemporal confinement of pulses propagating through the nanooptical waveguide of the present invention. An example of a basic TE (transverse electric) mode at 1 μm is shown within the waveguide core. b. Dispersion profile. c. Phase-matched polling period. d. This figure shows the optimal synchronous pumping cavity length as a function of the change in waveguide top width and etching depth. Measured dimensions of devices manufactured according to the present invention are indicated by an "x". [Figure 6] This figure shows additional OPO parameters based on the waveguide geometry shown in Figure S1. a. Effective refractive index of the waveguide. b. Second harmonic microscope image of the waveguide front pattern obtained by periodic polling. c. A figure showing the propagation loss obtained by simulation as a function of bending radius for different signal waveguides. The blue dotted line is at 77 μm, where the minimum bending radius is used when designing the OPO cavity. [Figure 7]This figure shows the design of an OPO coupler. a. Definition of input / output couplers. An example of adiabatic design for the output coupler. Here, width and gap refer to those at the top of the waveguide. c. Basic TE modes of the waveguide at 1 μm and 2 μm. d. Coupler response simulated using the geometric shape of the fabricated waveguide. e. A figure showing the theoretical behavior of the coupler compared with the spectra measured in a 380 fJ pump for otherwise identical coupled and uncoupled devices. [Figure 8] This diagram shows the experimental setup. The abbreviations are: PS (phase sensitive), MLL (mode-locked laser), LP (long pass), and BS (beam splitter). [Figure 9] This figure shows measurements extended up to ~20 × the threshold. Output from the OPO cavity with pump energy up to 380 fJ. b. For the same energy, the upper panel shows the OPO oscillation peak when the pump repetition rate is scanned by PZT. The lower panel shows the RF hum between the free space and the on-chip OPO sharing the same pump, with the pump repetition rate tuned to 63.58 mHz over a long period of time. [Figure 10] This figure shows the absorption characteristics of atmospheric molecules compared with the OPO spectrum measured in a 380 fJ pump. The spectral lines were obtained from the HITRAN (high-resolution transmission) database [1] (Non-Patent Literature 1). [Figure 11]This figure shows the simulated mode crossings compared with the measured spectrum of a linear waveguide. a. Simulated modes in the periodically polled region of the chip. Mode crossings caused by basic TE modes are marked M1 and M2. Close-ups of these are shown in b. and c., respectively. d. This figure shows the measured power spectral density of a periodically polled nanophotonic waveguide with an OPO cavity as a function of pump pulse energy. The positions of M1 (680 nm) and M2 (1135 nm) are indicated by arrows. [Figure 12] This figure shows measured beat values ​​for OPOs. a. Experimental setup, b. Two possible fCEO values ​​for an OPO comb are illustrated depending on the detuning peak, where l is odd or even. c. (i) RF beat, and (ii) spectral overlap, showing interference fringes (blue) when the relative output delay between OPOs is manipulated when the OPOs share one fCEO in a temporary self-cleaning regime. [Figure 13] This figure shows the OPO beat locked in a temporary self-cleaning regime. The pump here is 121 fJ, and the pump repetition rate is locked to the OPO peak structure seen in the OPO oscillation peak in Figure 2d(viii) of the text. The upper panel shows the frep / 2 beat at a typical time, and the lower panel shows the beat that persists over a longer period. Dither signals from free space and on-chip OPO cavity locks cause two sets of side fringes (stripes) to appear in the main frep / 2 beat. [Figure 14]This figure shows measured SHG (second harmonic generation) beats. a. Experimental setup. b. Spectral overlap between the chip SHG output and the PCF. c. Simple beats measured at 380 fJ, d. 109 fJ, and e. 54 fJ are shown in different colors corresponding to different pump fCEOs. Abbreviations are SP (short pass), PCF (photonic crystal fiber) (Menlo Systems), and HWF (half wave plate). [Figure 15] a. An extended regime of nanophotonic OPO operation, and b. OPO resonances labeled with respect to the detuning peak (l) and the reciprocal detuning (ΔTRT) of the cavity. [Figure 16] This figure shows the characteristics of OPO: l = 2, φCEO = 0. [Figure 17] This diagram shows the characteristics of OPO: l = 0, φCEO = 0. [Figure 18] This figure shows the characteristics of OPO: l = -2, φCEO = 0. [Figure 19] This figure shows the characteristics of OPO: l = 3, φCEO = 0. [Figure 20] This diagram shows the characteristics of OPO: l = 1, φCEO = 0. [Figure 21] This figure shows the characteristics of OPO: l = -1, φCEO = 0. [Figure 22] This figure shows the characteristics of OPO: l = -3, φCEO = 0. [Figure 23]This figure shows a further characterization of the coherence of regime (iii) for l=-3 and φCEO=0. ag(1) Coherence is shown as a function of wavelength, PSD (position sensing detector), and round-trip spectrum, with points having simulation coherence greater than 0.6 represented by light green dots, and the rest marked in pink. For the round-trip phase plot, points where the phase difference compared to the previous round trip is less than π / 6 are plotted in green, and the other points are marked in pink. b. Simulated comb wires at the output. The 2μm, 1μm, 697nm, and 500nm combs correspond to the half-harmonic, pump, sum frequency generation of the pump and half-harmonic, and the second harmonic of the pump, respectively. [Figure 24] This figure shows the characteristics of OPO, peak 2, and φCEO = π. [Figure 25] This figure shows the characteristics of OPO, with peak 0 and φCEO = π. [Figure 26] This figure shows the characteristics of OPO, with peak -2 and φCEO = π. [Figure 27] This figure shows the intensity and phase progression within the crystal for the half-harmonics (upper) and pumps (lower) of regime (iii) for l=-3 and φCEO=0. For a(ii) and b(ii), the phases in the region with intensity greater than ~0.2W are circled, and the phases at positions with lower intensity are made more transparent. [Figure 28] This figure shows the temporal output of a two-octave comb at different detunings. In all cases, the pink line, which represents the 3dB bandwidth of the central feature, is ~4.2fJ. Here, φCEO = 0. [Figure 29] This figure shows the characterization of a 3-octave comb at l=3 and φCEO=0. It shows the simulated coherence and normalized output spectrum of the OPO with additional duty cycle changes in the polling period to generate a 3-octave coherent frequency comb with a 248 fJ pump. [Figure 30]This figure shows nanophotonic cavity secondary solitons. (a) Concept of these solitons and resulting pulse compression in a synchronous pumping OPO. (b) Dispersion parameters of a nanophotonic periodic poling lithium niobate (PPLN) OPO are shown as a function of waveguide top width and etching depth. A PPLN length of 5 mm and a resonator length of 11 mm were used. [Figure 31] This figure shows an ultra-broadband 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 a region periodically polled for efficient parametric nonlinear interaction. The waveguide (dimensions: 2.5 μm width, 250 nm etching depth) supports the mid-infrared waveguide mode corresponding to the idler wave. b) Pseudo-phase-matched parametric gain tuning from visible to mid-infrared (mid-IR). Phase-matched curves resulting in tunable idler emission, made possible by optical parametric oscillator devices with slightly different polling periods (Λ) integrated on the same chip. Thanks to a sum frequency generation (SFG) process of the above signal and idler wave, the same chip can generate a tunable visible frequency comb. Other accompanying upconversion processes include the second harmonic (SH) and idler of the above signal. Some second-harmonic phase-matching curves have been omitted for clarity. c) Emission from the tip overlaps with strong molecular absorption lines in the mid-infrared region, covering a spectral window important for molecular spectroscopy. The visible spectral coverage includes atomic transition wavelengths corresponding to commonly used trap ions / neutral atoms / color centers. [Figure 32]This figure shows a near-infrared to mid-infrared frequency comb using a nanophotonic OPO on a single chip. a) Schematic diagram of the experimental setup used to pump and measure a synchronously pumping optical parametric oscillator chip. Images of the OPO chip are shown side by side. Experimental measurements of the spectral and temporal characteristics (intensity autocorrelation trace (recording curve)) of electro-optic pulse pumping, showing pulse widths of ~1 ps. c) Shows the broadband infrared spectral coverage range of the OPO chip, signal spectra and idler spectra when the operation is adjusted from degenerate to far non-degenerate. Different colors represent outputs from different OPO devices with different polling periods on the same chip. The zoomed-in version shows the linear structure of the comb. [Figure 33] This figure shows the characteristics of the frequency comb generated from a synchronous pumping on-chip OPO. a) Resonance peak structure obtained by sweeping the pump center wavelength, which is characteristic of dual-resonance OPO operation. A zoomed-in view of a single peak is shown in the insert. b) The range of existence of the synchronous pumping OPO for a fixed pump power when the pump repetition rate is changed. c) Fine-tuning of the OPO frequency comb output made possible by adjusting the pump center wavelength. d) Spectral broadbanding of the OPO operating in degeneracy corresponding to a sub-picosecond (less than picosecond) conversion limit duration of ~400 fs (femtoseconds). e) Verification of the coherence of the OPO output, evident from the presence of interference fringes (see insert) in the cross-correlation trace of the electric field. f) The close agreement between the spectrum obtained by optical spectrum analyzer measurement and the spectrum obtained by Fourier transforming the cross-correlation of the electric field supports the coherence of the OPO output. [Figure 34]This figure shows visible frequency comb generation from an integrated parametric oscillator chip. a) Complete emission spectrum of the OPO (summarized from spectra obtained from different spectral analyzers / spectrometers). Apart from the generation of signal and idler waves, the OPO also generates outputs in the visible spectrum through auxiliary nonlinear processes, namely second harmonic generation (SHG) and sum frequency generation (SFG). b) Optical microscope images capturing visible light emitted from various regions of the periodically polled portion of the OPO device. c) Adjustable visible frequency comb generation from an integrated OPO chip; different colors indicate spectra obtained from OPOs with distinct polling periods. [Figure 35] These are SEM (scanning electron microscope) images of the adiabatic coupler region. a) The waveguide (dimensions: width 2.5 μm, etching depth 250 nm) supports the mid-infrared waveguide mode corresponding to the idler wave and shows the electric field distribution of the idler wave (basic TE mode). b) The SEM image of the fabricated device shows the coupler region. [Figure 36] This diagram shows the generation of a visible frequency comb. a), b), c) An experimentally adjustable visible frequency comb (sum frequency generation between the signal and the pump) obtained by adjusting the pump frequency. [Figure 37] This figure shows the second harmonic generation of a signal frequency comb. a) Phase matching curves for different polling periods corresponding to 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 the signal OPO by pump wavelength adjustment. [Figure 38] This figure shows the coupler response and OPO conversion efficiency. a) Signal conversion efficiency as a function of on-chip pump power. The experimental data fit well. [Figure 39]This figure shows measurement data for the average power per comb line. The mid-infrared frequency comb (idler frequency comb) was obtained using the optical spectrum analyzer used to calculate the power per comb line. Optical spectrum analyzer settings: resolution bandwidth 1 nm, sampling interval 0.05 nm, and frequency comb repetition rate 19 GHz. [Figure 40] This figure shows the settings for electro-optic comb generation. a) Schematic diagram of the settings for electro-optic comb generation used for synchronous pumping of OPO. Arbitrary Waveform Generator (AWG), Semiconductor Optical Amplifier (SOA), Intensity Modulator (IM), Phase Modulator (PM), Ytterbium Doped Fiber Amplifier (YDFA), Optical Spectrum Analyzer (OSA). b, c, d) Simulation waveforms in the time domain and frequency domain at different stages of the pump preparation settings. [Figure 41] This figure shows the settings for a pseudo-synchronous pumping OPO. a) Schematic diagram of the settings for electro-optic comb generation used for synchronous pumping of the OPO in a pseudo-mode of 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. [Figure 42] This is a schematic diagram of the setup for estimating the cavity FSR (free spectral range: resonant frequency interval, free spectral range). It includes an arbitrary waveform generator (AWG), a semiconductor optical amplifier (SOA), an intensity modulator (IM), and a ytterbium-doped fiber amplifier (YDFA). [Figure 43]This figure shows spectral broadening and associated pulse compression in the degenerate regime of OPO operation. a) The experimentally obtained spectrum after spectral transformation is plotted on the frequency axis to show the effect of spectral broadening in the signal compared to the pump. b) The spectrum obtained from numerical simulation shows the spectral broadening effect (assuming a pump pulse shaped with the sech function). c) Pump and signal pulses in the time domain obtained from numerical simulation. d) When the numerically obtained signal pulse is fitted to a pulse shaped with the sech function, it represents approximately 1 / 2 pulse compression. e) Normalized round-trip progression from a signal pulse starting from a vacuum field until it reaches a steady state. [Figure 44] This diagram shows the settings for coherence verification. a) A schematic diagram of the settings used to verify the coherence of the OPO output. b) A measured value of the RF beat frequency corresponding to the applied repetition rate of the synchronous pumping OPO. [Figure 45] This figure shows a hypothetical complete integration of a universal frequency comb source. a) An example of a lithium niobate nanophotonics-based near-infrared picosecond pump source consisting of a cascade of intensity modulators and phase modulators followed by a dechirp spiral waveguide. b) An example of a lithium niobate OPO chip consisting of an array of OPOs specialized to cover different spectral regions, which can be programmably pumped with the help of a preceding MZI (Mach-Zehnder interferometer) routing circuit. [Figure 46] This figure shows the temperature adjustment for pseudo-phase matching. a) Signal wave and idler wave, and b) Temperature adjustment for pseudo-phase matching obtained from simulations of upconversion by a pump that provides a visible frequency comb corresponding to these. The pump wavelength is fixed at 1060 nm. [Figure 47]FIG. is a diagram showing an experimental setup for measuring a 40-pulse time-division multiplexed optical parametric oscillator. **(a)** Using an EO (electro-optic) comb with a repetition rate of 10 GHz to pump an on-chip spiral OPO cavity with a free spectral range of 250 MHz, resulting in the simultaneous oscillation of 40 independent signal pulses. The pump is characterized by its spectrum **(b)** and the autocorrelation of its intensity **(c)**. **(d)** Optical microscope image of the fabricated on-chip spiral cavity. [Figure 48] FIG. shows experimental results demonstrating the interference behavior of the OPO output for the degenerate **(a)** and non-degenerate **(b)** cases. Sub-figure **(i)** shows the spectra for both. **(ii)** A sample of the interference time-trace data measured at the interference input compared to a reference. **(iii)** Histogram of the peak values measured within each time bin, showing the discretization expected when the OPO is in the degenerate state. **(iv)** Comparison with the theoretical probability mass function of the output level for the degenerate case. [Figure 49] FIG. is a schematic diagram of the pump sub-circuit and additional components. [Figure 50] FIG. shows a method for fabricating the device. [Figure 51] FIG. shows a method for operating the device. **[Embodiments for Carrying Out the Invention]**

[0010] **Detailed Description of the Invention** In the following description of the preferred embodiments, reference is made to the accompanying drawings which form a part of this specification, and in these drawings, specific embodiments in which the invention can be implemented are shown for illustrative purposes. It should be understood that other embodiments can be utilized and structural changes can be made without departing from the scope of the invention.

[0011] Integrated sources of short-pulse frequency combs generally generate pulse energies of a few picojoules or a few femtoseconds 2,4,18-20 (Non-Patent Documents 2, 4, 18, 20), and their spectral coverage ranges barely reach 1 octave.21,22 (Non-patent documents 21, 22). This necessitates further spectral broadbanding stages for numerous applications, which have so far been achieved strictly using tabletop systems with separate amplifiers and components. 1,8,23 (Non-patent documents 1, 8, 23). Femtojoule-level, multi-octave, coherent spectral broadbanding mechanisms have so far exceeded the current limits of photonic technology, and therefore, the path toward fully integrated frequency combs has remained elusive.

[0012] Significant spectral broadening generally involves using femtosecond or picosecond pulses with energies of 0.1 to 10 nJ (nanojoules) in a waveguide, i.e., a secondary (χ) design. (2) ) or Kerr (tertiary) (χ (3) This is achieved by passing the material through a crystal or fiber having nonlinear properties. 1,24-28 (Non-patent documents 1, 24, 28). Of these schemes (methods), waveguides with second-order nonlinearity have become particularly advanced due to recent advances in pseudo-phase matching and distributed design. 24,26,29 (Non-patent documents 24, 26, 29) are becoming increasingly efficient and exhibit superior performance against third-order nonlinearity. However, reaching and exceeding one octave of spectrum requires tens of picojoules of additional energy. 29 (Non-patent document 29) This energy far exceeds the current capabilities of integrated frequency comb sources.

[0013] Resonance enhancement through spectral broadening is expected to improve energy requirements. However, such experiments have so far remained below one octave. 23,30,31 (Non-patent documents 23, 30, 31). This is mainly due to the variance requirements of third-order coherent spectral broadbanding schemes, which are excessively constrained, especially when combined with the requirement for a high Q-factor (quality factor). In fact, even linear components in nanophotonics with multi-octave spectral responses remain challenging to design and realize. 32In contrast, second-order nonlinearity not only leads to lower energy requirements in single-pass configurations, but also provides broader nonlinear processes for ultra-broadband coherent spectral broadening resulting from nonlinear interactions in distant parts of the spectrum. 11,12 (Non-patent documents 11, 12). However, appropriate resonance design is necessary to enable an operating regime in which a series of second-order nonlinear processes can produce coherent spectral broadbanding toward multi-octave operation.

[0014] This path toward multi-octave nonlinear resonators is based on synchronous pumping degenerate OPOs, which have been successfully used in bulk optics for efficient phase-locked down-conversion by half-harmonic generation of broadband frequency combs. 15,33-35 (Non-patent documents 15, 33-35). Recent studies by one or more of the inventors indicate the possibility of extreme pulse shortening and spectral broadening while maintaining the pump's coherence characteristics. 36 (Non-patent document 36). However, the lack of dispersion design in bulk nonlinear crystals, low parametric gain bandwidth, and multiple picojoule thresholds have limited their applicability for small, ultra-wideband frequency comb applications. Dispersion-designed optical parametric amplifiers (OPOs) 37 (Non-patent document 37), and recent developments of narrowband synchronous pumping OPOs in lithium niobate nanophotonics promise a path toward overcoming these limitations and accessing novel regimes of ultra-broadband, ultra-low-energy nonlinear optics that were previously inaccessible. [Examples]

[0015] First Embodiment: Multi-octave frequency comb 1. Device Structure Figure 1a shows the design of the on-chip synchronous OPO, and Figure 1b shows the fabricated device. The input / output coupler is designed to allow resonance only before and after the pump's half-harmonics (see Supplementary Information section), and the cavity is designed to be minimally dispersive for these wavelengths. To phase-lock and frequency-lock the OPO, the OPO is nearly synchronously pumped in degeneracy, requiring a round-trip time of 4 ns for a pump comb with a repetition rate of 250 MHz. According to the effective refractive index of the nanophotonic lithium niobate waveguide of the present invention, this round-trip time corresponds to a cavity of length 53 cm.

[0016] To achieve extremely high, ultra-wideband, and phase-sensitive gain with a pump pulse energy of fJ that enables coherent, wideband comb generation, the OPO includes a 10.8 mm OPA with appropriate dispersion design and quasi-phase matching (QPM). Specifically, the inventors aimed to minimize group velocity dispersion (GVD) between the pump and signal, as well as group velocity mismatch (GVM) between the pump and signal. 37 (Non-patent document 37). Figure 1c shows the high-gain bandwidth accessible when a 100fs pump is coupled to a waveguide with a near-zero dispersion design, which is different from the large dispersion preferred for a broadband tunable OPO. 38,39 (Non-patent documents 38, 39). Polling periods, cavity lengths, and coupler designs for synchronous operation can be found in the supplementary section.

[0017] Figure 1d shows different regimes of operation for this nanophotonic OPO. At low pump pulse energies, the OPO exceeds a threshold once the gain overcomes the losses inside the cavity. This is a regime in which the OPO conventionally operates to produce a pulse-locked coherent output to the pump. 34 (Non-patent document 34). It is known that at higher pump pulse energies, the degenerate OPO transitions to an unstable operating regime in which phase-locked operation weakens. 40,41(Non-patent documents 40, 41). However, the inventors have found that, far above the threshold, a transition to a phase-locked regime can occur in the OPO as a result of the nonlinear phase being compensated by the cavity. The attached time-domain plot highlights this as a transient self-cleaning mechanism, in which, after a finite number of round trips, the output pulse intensity stabilizes with an extremely short appearance in the multi-octave case. The appearance of such coherence and ultrashort pulse formation is reminiscent of condensation and thermalization that occur in other nonlinear multimode systems. 42,43 (Non-patent documents 42, 43).

[0018] 2. Experimental Results Figures 2a-2c show the near-threshold performance of the nanophotonic OPO. The inventors observed the oscillation peaks of the OPO shown in Figure 2a by scanning the pump's repetition rate at 600 Hz. These peaks exhibit characteristics of double-resonant operation. 34 (Non-Patent Document 34). The inventors actively lock the pump repetition rate to the center of each of these peaks, and the pump repetition period and the round-trip time ΔT of the cavity. RT Figure 2b shows the signal spectra of the three such peaks near the threshold in the distinct detuning between and . Figure 2c shows the measured input-output pulse energy growth of these same peaks. The inventors have identified the threshold and gradient coefficient η SL By extrapolating and interpolating, the peak with the lowest threshold was defined as the zero cavity detuning state. For this peak, the inventors estimated an OPO threshold of ~18 fJ.

[0019] Figure 2d shows three characteristic output spectra of the OPO. At a 54 fJ pump, the inventors observed the behavior of a conventional OPO. The pump, half-harmonic, and second-harmonic were all spectrally broadbanded, and a significant sum-frequency generation (SFG) was present between the pump and the half-harmonic. At a 109 fJ pump, the inventors observed a continuous spectrum from 600 nm to 2710 nm, and at 121 fJ, a continuous spectrum from 443 nm to 2676 nm. The dip at 2.8 μm is related to the OH (hydroxyl group) absorption peak in the LN (LiNbO3: lithium niobate) and / or buffer layer. 39,44 (Non-patent documents 39, 44), the kinks (defects) around 680 nm and 1135 nm are due to mode crossing (see Supplementary section). It is also noteworthy that the spectrum at 121 fJ has several characteristic features on the longer wavelength side of the spectrum that are not present in the case of pumping at 109 fJ.

[0020] To characterize the coherence of the OPO at these pump pulse energies, the inventors interfered the chip output with the output of a free-space OPO pumped by the same laser using a filter centered around 2.1 μm. When operated with a coherent regime, a degenerate OPO above a threshold can have two possible CEO (carrier envelope offset) frequencies, these CEO frequencies being half the pump repetition rate f depending on the oscillation peak. rep The only difference is / 2 34 (Non-patent document 34). When an on-chip OPO has a different CEO than a free-space OPO, if these outputs are overlapped spatially and temporally, f rep A beat should be observed at / 2. The measurements in Figure 2d are obtained by scanning the pump's repetition rate over a long period of time. In the 54fJ pump, the on-chip OPO exhibits characteristics at specific detunings, and these characteristics are shown in Figure 2d(iii) between the OPOs at f repFigure 2d(ii) shows that this is reflected by the / 2 beat. The absence of these signs in both the OPO power and beat at the 109 fJ pump indicates that the on-chip OPO transitioned from a coherent regime to an incoherent regime. At a power of 121 fJ, the OPO peak structure and RF beat reappear, indicating the return of the coherent operating regime.

[0021] The coherence of the second harmonic portion of these spectra was confirmed using the output of a pump whose spectrum was broadened by a photonic crystal fiber. For all of the pump pulse energies in Figure 2d, the inventor interfered this broadband pump with the second harmonic portion of the on-chip OPO, independently of detuning, to obtain the resulting carrier-envelope offset frequency f CEO This was observed along with a pump repetition rate of 250 MHz (see Supplementary Section). In particular, in the 121 fJ pump, both the half-harmonic comb and the second-harmonic comb are coherent with respect to the pump, and all frequency parts of the spectrum are generated by the parametric process of these three combs. 29 (Non-Patent Literature 29), the inventors concluded that the continuous 2.6-octave spectrum in Figure 2d is coherent. The inventors locked the pump's repetition rate to keep the OPO in this oscillating state, and the supplemental IIE section shows that the beat signal is maintained over a long period of time.

[0022] The dynamic characteristics of the OPO far above the threshold, and how coherence is established across this broadband spectrum, were investigated using numerical simulations. To capture the multi-octave nonlinear interactions occurring within the OPO, the inventors modeled the electric field within the nanophotonic cavity as a single envelope in the frequency domain, using the split-step Fourier method for propagation within the PPLN domain and a linear filter for cavity feedback. Figure 3a shows the capture of an operational regime that distinguishes this when using parameters consistent with experimental parameters. At 16 fJ, the OPO stabilizes after approximately 20 round trips above the threshold. At this point, all frequency-converted components (OPO, SHG, pump, and OPO's SFG) are coherent with respect to the pump, and these components remain invariant between round trips. As the pump pulse energy increases, fewer round trips are required for the OPO to take shape, and with a 137 fJ pump (~9 times above the threshold), the inventors confirmed that the output of the OPO is incoherent.

[0023] However, with a 204fJ pump (approximately 13 times above the threshold), it is observed that for each single pass through the PPLN region, a phase shift of π occurs in the half-harmonics due to the nonlinear interaction with the pump. This phase shift can be compensated by detuning the cavity by an odd number of OPO peaks, or by adding a constant phase offset of π between the pump and the cavity, and this constant phase offset corresponds to the pump's carrier-envelope offset phase φ. CEO This corresponds to (see Supplementary Section IIIB). The former case is shown in Figure 3a(iii), which shows a 2-octave coherent continuous comb that stabilizes after approximately 20 round trips with a temporal appearance of only 4 fJ (see Supplementary Section IIIC). The output spectrum also changes similarly to the detuned 121 fJ experimental results in Figure 2d.

[0024] Using simulations, we further investigated methods to extend the coherent operation of the OPO to a wider spectrum. By replacing the last 1 mm of the PPLN region with a chirp-polling period and generating efficient second harmonics and sum frequencies, the inventors have realized a coherent 3-octave continuous frequency comb with a pump energy of ~250 fJ, as shown in Figure 3b.

[0025] Figure 4 compares the results of the present invention with other integrated spectral broadbanding schemes and synchronous pumping OPOs. This figure highlights how the design and operating regime of the nanophotonic OPO of the present invention enables an improvement of several orders of magnitude in the energy efficiency of coherent spectral broadbanding. The inventor's achievement represents a lowest threshold synchronous pumping OPO, which is made possible by its near-zero design. Such ultra-low threshold operation allows access to operating regimes of OPOs far above the threshold, which have not been previously studied, in which ultra-broadband coherent spectral broadbanding is established as a result of balancing cavity detuning and nonlinear phase shift.

[0026] In summary, the inventors experimentally demonstrated a nearly synchronous pumping nanophotonic OPO that operates with near-zero GVM, zero GVM, fs (femtosecond) pumping, and high-gain low-finesse, producing an ultra-wideband coherent output with only ~121 fJ of energy. This 2.6-octave frequency comb is wavelength division multiplexed. 7 (Non-patent document 7), Dual-comb spectroscopy 4,5 (Non-patent documents 4 and 5), and frequency synthesis 5 This enables unprecedented opportunities for on-chip applications, including (Non-Patent Literature 5). The inventors demonstrate an OPO transition from an incoherent operating regime to a coherent operating regime, demonstrating a path toward a much broader bandwidth frequency comb source with a femtojoule regime.

[0027] 3. Manufacturing and Characterization Methods Device manufacturing. The device of the present invention was fabricated on a 700 nm thick X-cut (registered trademark) MgO-doped thin film of lithium niobate (NANOLN: nano lithium niobate) on an SiO2 / Si substrate. 37 Following the procedure in (Non-Patent Document 37), the Cr / Au polling electrode was patterned with 16 fixed polling periods in the range of 4.955 to 5.18 μm using the lift-off method, and a voltage was applied to periodically flip (invert) the ferroelectric domains. During polling, the electrode was removed, and the waveguide was etched using Ar milling and hydrogen silsesquioxane (HSQ) as an etching mask. Finally, the facets of the waveguide were mechanically polished to enable butt coupling. Each OPO has a footprint of 0.5 mm × 13 mm.

[0028] Optical measurements were performed using a Menlo Orange HP10 Yb mode-locked laser (MLL) with a central wavelength of 1045 nm. This MLL outputted 100 fs pulses at 250 MHz with an adjustment range of ±1 MHz. The light was coupled to the chip using a Newport 50102-02 reflective objective lens selected for its minimum chromatic aberration. All results described in this embodiment were performed on a device with a polling period of 5.075 μm at 26°C, adjusted by a thermoelectric cooler (TEC). The lowest OPO threshold was obtained at a pump repetition rate of 250.1775 MHz, which the inventors defined as the zero detuning state. This device has a total performance loss of 43.4 dB. 37Following the method described in Non-Patent Document 37, the inventors measured the input and output coupling losses to be 35.7 dB and 7.7 dB, respectively. For the results in Figure 3d, spectra were collected using two different optical spectrum analyzers (OSAs), specifically Yokogawa Electric's AQ6374 (350-1570 nm) and AQ6376 (1500-3400 nm). These OSAs were operated at HIGH3 sensitivity except for the 121 fJ pump, where HIGH2 was used. The RF spectrum in Figure 2d was collected using an electron spectrum analyzer (Rhode & Schwarz FSW) with an InGaAs high-speed photodiode (DSC2-40S). SHG beats were acquired using a high-speed silicon avalanche photodiode (Menlo Systems APD210).

[0029] Numerical simulation. The inventors used commercially available software (Lumerical) to solve the waveguide modes shown in Supplementary Sections I and II, which enabled the distributed design and pseudo-phase matching of the device of the present invention. For nonlinear optical simulations, analytical nonlinear evolution equations were solved as described in Supplementary Section III. These simulations were performed without a constant phase offset between the pump and the cavity, unless otherwise specified. This parameter is the carrier-envelope offset phase φ of the pump. CEO It functions effectively as such. Since the simulation was run with a time window of 1.7 ps (picoseconds), it should be said that the shorter wavelength side of the spectrum falls outside the inventor's simulation time window. For example, the simulated GVM between the inventor's 2090 nm half-harmonic signal wavelength simulation reference frame and the 522 nm pump's second harmonic is 721 fs / mm. As a result, the unconverted portion of the spectrum in the simulation tends to be smaller than that measured experimentally. In these simulations, the inventor uses χ (2) Including only the effects of nonlinearity, χ (3)The effect of was not considered. In particular, given the low pulse energy and low finesse nature of the cavity of the present invention, the inventors are confident that this is a good approximation, although it may be one reason for small differences between experiment and simulation.

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[69] Additional information regarding one or more embodiments of the present invention can be found in Multi-Octave Frequency Comb from an Ultra-Low-Threshold Nanophotonic Parametric Oscillator, by Ryoto Sekine, Robert M. Gray, Luis Ledezma, Selina Zhou, Qiushi Guo, and Alireza Marandi, https: / / arxiv.org / abs / 2309.04545 (Non-Patent Literature 69).

[0031] Supplemental information regarding chip design and simulation of the first embodiment The spatiotemporal profile of pulses propagating through the nanophotonic waveguide of the present invention can be imprinted by a few key manufacturing parameters. Labeled in Figure 5a, these parameters are the lithium niobate (LN) thickness, etching depth, top width, and sidewall angle. As shown in Figures 5b-d, all of these parameters directly affect the effective refractive index of the waveguide, which determines the near-zero dispersion geometry, the quasi-phase-matched polling period, and the cavity length required for synchronous pumping of the OPO of the present invention. The inventors manufactured the device of the present invention with a constant polling period of 5.075 μm and a cavity length of 52.92 cm, and measured the waveguide etching depth and top width at 352 nm and 1753 nm, respectively. These dimensions are indicated by an "x" in Figures 5b-d, indicating that the inventors successfully designed the device of the present invention to be close to the optimal parameters for near-zero GVM and GVD phase-matched operation. The resulting simulation yields the effective refractive index η eff The polling period used in the manufacturing process is shown in Figure 6, along with the simulated bending loss as a function of bending radius and wavelength. The blue dotted line at 77 μm in Figure 6c indicates the minimum bending radius used in manufacturing the spiral, and at all points in the spiral, small bending losses are observed for wavelengths smaller than 3.3 μm.

[0032] Design of input / output couplers The input and output couplers of the OPO are identical and symmetrical, as defined in Figure 7a, and have an adiabatic shape as shown in Figure 7b, with parameters w1, w2, gap, and L being 1753 nm, 1900 nm, 980 nm, and 750 μm, respectively. The adiabatic coupler was selected for its broadband response and reasonable manufacturability compared to the geometric shapes of other couplers. The simulated TE mode profiles at 1 μm and 2 μm for waveguide design with upper width w2 are shown in Figure 7c. Pulses propagating through this adiabatic coupler follow the following coupled mode equation:

number

[0033] Here, a1 and a2 are the amplitudes of the modes in each waveguide, and Δβ = |β1 - β2| is the pulse mismatch between the two waveguides. Solving equation (1) for the geometric shape of the present invention, the inventors obtained the power coupling curve in Figure 7d. The inventors observed that significant coupling occurs only at signal wavelengths greater than 2 μm. In Figure 7e, the spectral output of the OPO (device having a coupler and cavity) of the present invention is compared with the spectral output from an adjacent straight waveguide, which does not have a coupler but shares the same polling and waveguide parameters. The inventors found that the dips and peaks in the adiabatic coupler, as determined by simulation, are reflected in the spectrum measured from the nanophotonic OPO but are not present in the periodically polled straight waveguide, which is consistent with the coupler response theoretically predicted by the inventors.

[0034] Setup The inventor's experimental setup is shown in Figure 8. The detector within the PID (proportional-integral-derivative) loop allowed the pump comb's repetition rate to be locked to completely different oscillation peaks of the OPO, during which the spectrum was collected on an optical spectrum analyzer (OSA). The synergistic characteristics of the pump and OPO that enabled multi-octave frequency comb generation are highlighted in the figure.

[0035] Experimental data extended to a 3-octave spectrum

[0036] Using the experimental setup shown in Figure 8, the inventors investigated the output spectra of the OPO at different pump pulse energies, a subset of which is shown in Figure 2d. Figure 9a shows an extension to even higher pump pulse energies. At a 380 fJ pump, the inventors observed spectra spanning three octaves from 362 nm to 3261 nm. However, beat analysis by the free-space OPO shown in Figure 9b, following the procedure in Supplementary Section E1, indicates that the OPO here is incoherent.

[0037] Characteristics of molecular absorption For the spectral measurements above 2.5 μm in Figure 9a, features were observed that appear to originate from spectral absorption lines derived from environmental molecules. Figure 10 compares the experimentally obtained OPO spectrum with the spectral lines of H2O, CO2, and CH4. The overlap between the spectral characteristics of water and OPO is particularly close and similar because H2O is the strongest absorber in this spectral region at atmospheric concentrations. The inventors calculated that 9% of the 3 μm modes within the spiral region are evanescent, suggesting that on-chip sensing may be possible with a 53 cm spiral. However, the inventors anticipate that absorption mainly occurs between the chip output and the detector, as neither system was purged (cleaned) in this experiment. Furthermore, these absorption characteristics are attributed to environmental molecules present in the laboratory, as no gas cell was used.

[0038] As mentioned above, the notch at 2.83 μm is due to the OH absorption peak in the buffer layer of the LN and / or SiO2 substrate. Studies of the absorption of SiO2 used as a buffer layer for Si waveguides [2-4] (Non-Patent Literature 71-73) have shown that the cladding layer at the bottom of the SiO2 becomes unacceptably narrow at around 2.8 μm and beyond 3.5 μm. For current thin-film lithium niobate (TFLN) devices having an SiO2 buffer and a Si substrate, the upper absorption appears to fall around 3.25 μm [5] (Non-Patent Literature 74). However, wavelengths of 2.8 to 3.8 μm have been measured on TFLN waveguides on sapphire substrates [6] (Non-Patent Literature 75), suggesting a path toward the fabrication of multi-octave frequency combs with even longer wavelength components.

[0039] Mode Crossover Figure 9 shows spectral kinks at 680 nm and 1135 nm, which are clear across the entire pump pulse energy. These spectral kinks correspond to the two mode crossings shown in Figure 11a. M1 is the mode crossing between the fundamental TE mode and the second-order TM (transverse magnetic) mode (Figure 11b), while M2 is the mode crossing between the fundamental TE mode and the TM mode (Figure 11c). In fact, these mode crossings, as well as the OH absorption described in Section IIB, are even clearer in the spectrum measured from a straight waveguide with the same waveguide geometry and Poling period as OPO, and plotted in Figure 11d. Since this straight waveguide has no cavity, its half-harmonic spectrum is due to optical parametric generation (OPG).

[0040] Down-conversion of growling The coherence of the down-converted portion of the comb before and after the half-harmonic was investigated using the experimental setup shown in Figure 12a. The output of an on-chip OPO pumped by the same laser and the output of a free-space OPO were interfered with. Depending on the detuning peak l of the OPO, the inventors expected to see different indications in these radio frequency (RF) spectra and interference patterns. Here, the dimensionless detuning parameter l = 2f s ΔT RT And here Δ RT This is a mismatch between the round-trip time of the cavity and the repetition period of the pump, and f s is the signal frequency. OPOs with an even number l (L) have a comb line aligned (positioned) with the pump's comb line, whereas OPOs with an odd number l (L) have f rep It has a comb line that is shifted by 2 [7,8] (Non-patent documents 76, 77). This is shown in Figure 12b. As a result, when one OPO has an odd l (L) and the other has an odd l (L), the outputs of the OPOs that overlap in time and space are f, as shown in the RF spectral measurements in Figure 12c(i). rep f at / 2 CEO It exhibits a beating sound. Furthermore, in this case, the two combs have different frequencies f CEO The inventors did not expect to see interference fringes when scanning the delay between the two coherent OPO outputs. As shown by the orange trace in Figure 12c(ii), no interference fringes were observed.

[0041] However, if the OPOs are coherent and share the same even or odd detuning parameters, the inventor can say that f rep We did not expect to observe a beat of / 2. Furthermore, the comb has one f CEO Since they share a common frequency, it was anticipated that interference fringes would be observed when scanning the relative delays between these combs. This was actually measured by the inventors and is shown by the blue curve in Figure 12c(ii). In the 109fJ and 380fJ pumps, the down-converted portion of the nanophotonic OPO output is incoherent, and the inventors anticipated that f repNeither the / 2 beat nor the blue interference fringes in Figure 12c(ii) were observed.

[0042] Finally, the pump repetition rate can be locked to a feature in the OPO output signal. Figure 12 shows that the output of the on-chip OPO can indeed be locked and stabilized to a 2.6-octave comb state in a transient self-cleaning regime.

[0043] Upconversion roar The coherence of the upconverted portion of the pump was investigated using a method similar to that described in [9,10] (Non-Patent Documents 78, 79). Specifically, as shown in Figure 13a, the spectrally broadband portion of the pump was interfered with the second harmonic portion of the on-chip OPO. The spectral overlap for three of the pump pulse energies described in Figure 2d is shown in Figure 13b, and the corresponding beats are shown in Figures 13c to e. In each case, the inventors determined the f of the pump. CEO By recording the beat shift when adjusting, the beat is f CEO The inventors confirmed that this corresponds to the expected result. The upconverted portion of the pump remains coherent regardless of pump pulse energy or cavity detuning [9,10] (Non-Patent Documents 78, 79).

[0044] simulation A. Method The inventors model the dynamics of the ultra-broadband spectrum of a nanophotonic OPO by representing the total electric field in the nanophotonic waveguide using a single envelope in the frequency domain, as shown in the following equation [11,12] (Non-Patent Literature 80, 81).

number

[0045] Here, ω and Ω = ω - ω0 are the angular frequencies of light and the envelope, ω0 is the center frequency of the simulation, β0 is the propagation constant of the waveguide at ω0, and v ref ω is the reference frame rate of the simulation, x and y are the coordinates of the lateral waveguide, e(x,y,ω) is the lateral electric field distribution of the mode, and A(z,ω) is the complex amplitude of the electric field that unfolds during propagation. In the inventor's OPO simulation, ω0 was selected to be the center of the half-harmonic signal at 2090 nm, and v ref This is the group velocity of the half-harmonics. (outside 1) JPEG2026518928000004.jpg13127 is a rapidly changing envelope, and the phase factor e obtained during linear propagation is -iβ(ω)z This includes the following. In addition, A(z,ω) is an analytic signal, meaning it contains only positive frequencies (A(z,ω<0)=0).

[0046] The inventor's simulation models each round trip within the OPO into two parts. The first part consists of nonlinear propagation within the polling region of the waveguide, while the second part consists of a linear filter that models the progression of the round trip within the spiral resonator

[13] (Non-Patent Literature 82). The output of this round trip progression 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, and this white noise is acquired as an 80 fs pulse with a pulse profile of a sech function centered at 1045 nm.

[0047] The inventors, by ignoring the counterpropagation term (which is usually phase-mismatched) and assuming constant nonlinear coefficients and mode overlap integrals, derive a unidirectional equation of motion describing the nonlinear propagation of A(z,Ω), where both the nonlinear coefficients and mode overlap integrals are weak functions of frequencies far removed from the resonances of any material. No limit is placed on the maximum spectral bandwidth of the simulation. The resulting propagation equation is as follows:

number

[0048] Here, d(z)=±1 is the sign of the quadratic nonlinear coefficient corrected in pseudo-phase matching, α is the propagation loss coefficient, a(z,t) is the time-domain representation of A(a,Ω), and φ(z,t)=ω0t-(β-ω0 / v ref )z, (outside 2) JPEG2026518928000006.jpg2013 is the Fourier transform of the variable Ω. The effective nonlinear coefficient X0 is defined as follows:

number

[0049] Here, (Outside 3) JPEG2026518928000008.jpg1414 is a second-order nonlinear susceptibility tensor, where j, k, and l represent the Cartesian components.

[0050] The nonlinear propagation in each round trip involves solving the evolution equation (3) using the split-step Fourier technique over the entire length L = 10.8 mm of the polled waveguide. This nonlinear step uses the fourth-order Runge-Kutta method in the interaction picture (RK4IP)

[14] (Non-Patent Literature 83).

[0051] Propagation within a spiral waveguide is modeled by applying a linear feedback function to the polled region. In particular, for the (n+1) round trip, the signal is fed back to the input of the polled region. (outside 4) JPEG2026518928000009.jpg1331 is the nth round trip. (outside 5) In JPEG2026518928000010.jpg1631, the electric field emanating from the polled region is given by the following equation:

number

[0052] Here, R(ω) is the frequency-dependent coupling coefficient of the designed adiabatic coupler,

number

[0053] The simulation was performed on a 4096-size Fourier grid with a bandwidth of 2.4 PHz (petahertz). The corresponding time window was 1.7 ps. To avoid other (time) stretching within the time window during propagation, a Tukey filter with zero-padding edges was applied in the time domain after each nonlinear step. In addition, before applying the linear filter, all frequency components that would fall outside the time window during the 518 mm propagation in the spiral resonator were filtered out. This has the undesirable effect of effectively reducing the power of the simulation in frequency modes far from the reference frequency (and thus causing a significant walk-off from the reference velocity of the simulation), but it ensures the effectiveness of the nonlinear interaction in the simulation.

[0054] In this relationship, the inventor considers the nonlinear phase to be the phase accumulated within the PPLN portion of the resonator, resulting from a nonlinear process (excluding the accumulation of linear stages). For spectral analysis, the inventor clearly focuses on the narrow spectral range before and after the pump and its half harmonics, and for time analysis, the inventor clearly focuses on the peak intensity before and after the pump and its half harmonics.

[0055] B. Dynamics of OPO under different conditions

[0056] As explained in the main text, the ultra-broadband OPO enters a different operating regime far above the threshold. An extended version of the regime shown in the main text is shown in Figure 14a. Whether the near-zero dispersion OPO of the present invention can reach the coherent multi-octave state shown as (iii) in the drawings depends on the pump energy, cavity detuning (shown in Figure 14b), and the effective pump carrier-envelope offset phase φ CEO It largely depends on whether the OPO of the present invention has an even number of detuning peaks l(l) or an odd number of detuning peaks l(l), and the relative φ of the OPO. CEO The inventors have found that it largely depends on whether the value is 0 or π. The inventors will explore each of these cases in detail below.

[0057] 1. l (L) ∈ even numbers, φ CEO =0 l(L) ∈ even and φ CEOWhen = 0, the OPO is almost reaching a coherent multi-octave comb, but the OPO is never quite there. In the case of l = {2, 0, -2} in Figures 15-17, this is highlighted by the label (approximately iii). In all of these cases, the inventors find that in regime (i) near the threshold, once the OPO exceeds the threshold, the round-trip phase of the coherent OPO remains fixed. After transitioning through the incoherent state in regime (ii), the phase of the OPO is found to reverse by π round trip in pump regime (iii). These periodic oscillations suggest that, perhaps in this state, the OPO is composed of two coherent non-degenerate combs, and the beats of these combs generate the observed phase fluctuations, as well as the power fluctuations observed in the time-domain and frequency-domain plots of the OPO's evolution. At even higher pump energies, the OPO enters the fully saturated, incoherent regime of (iv).

[0058] 2.l(el)∈odd, φ CEO =0 l(L) ∈ even and φ CEO When =0, the phase inversion of π per round trip in the case of pumping at ~200fJ suggests that if the cavity phase can be detuned by π, a multi-octave coherent comb can be maintained. One way to obtain such detunement is to select the peak of OPO, where φ CEO While l = 0 is maintained, l ∈ odd, and Figures 20 and 21 show the dynamic characteristics when l = {3, 1, -1, -3}. As expected, near the threshold, i.e., in regime (i), these OPOs show a phase inversion of π with each round trip. However, in regime (iii), the inventors find that the OPOs exhibit transient self-cleaning and can stabilize, showing a fixed phase with each round trip.

[0059] The coherence of the two-octave spectrum in regime (iii) is g across multiple pairs of output pulses. (1)This can be further verified by calculating coherence and by directly examining the overlap of the half-harmonics, pump, second harmonic, and sum harmonics that generated the comb. As can be seen in the upper panel of Figure 22a, the inventors obtained the g between multiple pairs of pulses from the last 15 round trips of the inventors' simulation. (1) Coherence measurements confirmed that the device exhibits a coherent spectrum of more than two octaves. This can be further verified by focusing on the actual comb lines of the two-octave comb. The entire comb spectrum, as well as the comb lines corresponding to different harmonic combs, are shown at the nearest f rep Figure 22b shows the result of shifting by a multiple of and centering on zero. Good overlap between comb lines is when these combs are one f CEO This is a further manifestation of sharing and therefore being coherent. Note that the 500nm second harmonic comb has a 1μm pump comb with a frequency of 0 f CEO Except when it has other harmonics and one f CEO It was not expected to share, and the 1μm pump comb is 0 f CEO The inventor's simulations assume in most cases that this feature is present.

[0060] 3. l (L) ∈ even numbers, φ CEO =π When l(エル) ∈ even, which corresponds to the effective pump's carrier-envelope offset phase = π, odd-numbered detuning peaks can be extracted, and the round-trip phase of π can be directly added. The results of this are shown in Figures 23-25 ​​for l(エル) = {2, 0, -2}. CEO Similar to the case where =0, OPO exhibits phase inversions for each round trip in the low-power regime (i), and eventually enters the oscillating state of regime (ii) before settling into a steady state at the 200 fJ pump. One requirement here is that the simulation adds phase to the signal rather than the pump, so coherence between the pump and higher harmonics is also preserved, but non-zero φ, as explained in Supplementary Section IIIC. CEOFor pumps that have this feature, this is not experimentally true.

[0061] C. Temporary self-cleaning 1. Mechanism In Figure 2, the inventors demonstrate that as the input pump pulse energy increases, the OPO of the present invention transitions from a coherent conventional operating regime to an incoherent operating regime, but then regains its coherence state through appropriate cavity detuning at higher pump pulse energies. Figure 27 shows the propagation of pump and half-harmonic intensity and phase within the periodically polled region of the cavity (i.e., in the TSC (temporal self-cleaning) regime) with a pump of ~200 fJ. The progression of the half-harmonic phase in a(ii) clearly shows a phase inversion of -π→0 where the half-harmonic has a substantial intensity.

[0062] In the supplementary section IIB, the inventors detune the cavity by an odd number of OPO peaks (section IIB2), or by the carrier-envelope offset phase φ of the pump. CEO It has been shown that by adding a constant phase offset of π between the pump and the cavity (Section IIB3), the phase inversion of π in each single pass through the PPLN can be compensated for. Figure 22 shows an example of the former. Near the threshold (16 fJ), a phase inversion of π occurs in the OPO output with each round trip, but in the case of a 204 fJ pump, the OPO output can be stabilized to a constant phase output. Even detuning peaks, where π is φ CEO Figure 24 shows an example of the latter method for selecting the appropriate component. Here, the inventors have observed that in the TSC regime of a 200 fJ pump, the output phase can be stabilized after approximately 40 cavity reciprocations. These examples demonstrate that by appropriately detuning the cavity, or φ CEOThis demonstrates that compensating for the phase accumulation of a single pass in the PPLN is essential for operation with the TSC regime. Therefore, the pump pulse energy when TSC occurs depends on the dispersion of OPO and the nonlinear gain that induces a π phase inversion between the half-harmonics and the pump.

[0063] 2. Short pulse formation As described in the main text, the transient self-cleaning mechanism of a coherent multi-octave OPO can impart an ultrafast characteristic to the OPO output. Figure 28 shows the transient output of this regime from a simulation, with l = {-3,-1,1,3} φ CEO The case where =0 is clearly shown. A narrow feature of only 4.2fs can be observed, suggesting that the regime of a coherent multi-octave comb can be utilized for extreme pulse compression and single / few-cycle pulse synthesis.

[0064] Extension to D.3 Octave Comb By employing a chirp-polling period that targets energy transfer to the second harmonic and sum-frequency generation terms, the present invention can further induce a 3-octave coherent spectrum. In particular, the polling period in the last 1 mm of the 10.8 mm polled region is assumed to smoothly change over the period necessary to phase-match the interaction between the 1 μm pump and the 2 μm signal, and between the 1 μm pump and the 500 nm second harmonic of the pump. An extended characterization of the results described in Figure 3b is shown in Figure 29. It is noteworthy that this higher-order harmonic generation process acts as an effective loss for the 2 μm signal, resulting in a slightly higher threshold for the OPO and a greater pump power requirement to reach the transient self-cleaning regime. However, in the 248fj pump, a multi-octave comb was observed, accompanied by an additional higher-order harmonic process that allows for the formation of a coherent three-octave spectrum (Figures 25a-b) by filling the gap between the second harmonic at 500nm and the sum-frequency component at 697nm.

[0065] References for supplementary information The following references are included herein by reference. [1] I. Gordon, L. Rothman, C. Hill, R. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. Chance, B. Drouin, J.-M. Flaud , 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. Csaszar, V. Devi, T. Furtenbacher, J. Harrison, J.-M Hartmann, A. Jolly, T. Johnson, T. Karman, I. Kleiner, A. Kyuberis, J. Loos, O. Lyulin, S. Massie, S. Mikhailenko, N.S. MoazzenAhmadi, H. Muller, O. Naumenko, A. Nikitin, O. Polyansky, M. Rey, M. Rotger, S. Sharpe, K. Sung, E. Starikova, S. Tashkun, JV Auwera, G. Wagner, J. Wilzewski, P. Wcislo, S. Yu, and E. Zak Transfer 203.3 (3017), hlTRAN2016 Special Issue [2] RA Soref, SJ Emelett, and WR Buchwald, Journal of Optics A Pure and Applied Optics 8, 840 (2006)(Reference 71); [3] SA Miller, M. Yu, X. Ji, AG Griffith, J. Cardenas, AL Gaeta, and M. Lipson, Optica 4, 707 (2017)(Reference 72); [4] H. Lin, Z. Luo, T. Gu, LC Kimerling, K. Wada, A. Agarwal, and J. Hu, Nanophotonics 7, 393 (2018) [5] A. Roy, L. Ledezma, L. Costa, R. Gray, R. Sekine, Q. Guo, M. Liu, RM Briggs, and A. Marandi. (2022), arXiv.2212.08723(notebook 74) [6] J. Mishra, M. Jankowski, AY Hwang, HS Stolowski, TP McKenna, C. Langrock, E. Ng, D. Heydari, H. Mabuchi, AH Safavi-Naeini, and MM Fejer, Opt. Express 30, 32752 (2022) [7] A. Marandi, NC Leindecker, V. Pervak, RL Byer, and KL Vodopyanov, Opt. Express 20, 7255 (2012)(Reference No. 76) [8] M. Jankowski, Pulse formation and frequency conversion in dispersion-engineered nonlinear waveguides and resonators, Ph.D. D. thesis, Stanford University (2020) [9] A. Marandi, KA Ingold, M. Jankowski, and RL Byer, Optica 3, 324 (2016) (Non-licensed Document 78)

[10] M. Jankowski, C. Langrock, B. Desiatov, A. Marandi, C. Wang, M. Zhang, CR Phillips, M. Loncar, and MM Fejer, Optica 7, 40 (2020) (Non-licensed Document 79)

[11] C. Phillips, C. Langrock, JS Pele, MM Fejer, I. Hartl, and ME Fermann, Optics Express 19, 18754 (2011) (Non-licensed document 80)

[12] L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A. Marandi, Optica 9, 303 (2022) (Non-licensed Document 81)

[13] M. Jankowski, A. Marandi, C. Phillips, R. Hamerly, KA Ingold, RL Byer, and M. Fejer, Physical review letters 120, 053904 (2018) (Non-licensed document 82)

[14] J. Hult, Journal of Lightwave Technology 25, 3770 (2007) (Non-licensed Document 83)

Example

[0066] The second form: Kirito's secondary form Weak-off induced time soliton formation in degenerate optical parametric oscillators (OPOs) based on pure second-order nonlinearity can serve as a tool for simultaneously compressing and downconverting picosecond near-infrared pulses. Using tabletop experiments, it has been shown that such second-order cavity solitons can support normal and anomalous group velocity dispersion regimes and can result in high conversion efficiencies [1] (Non-Patent Literature 84). Huge pulse compressions of less than 1 / 40th of picojoule-level pump energies have also been demonstrated. These results promise a method for generating energy-efficient dissipation second-order solitons for Kerr soliton generation, breaking some barriers, a method that requires high Q-factor cavities, features limited conversion efficiencies, anomalous dispersion for bright soliton formation, and has limited wavelength tuning capabilities. In this invention, the inventors form second-order cavity solitons within LN nanophotonics.

[0067] A synchronous pumping degenerate optical parametric oscillator (DOPO) on thin-film lithium niobate (TFLN) offers an unprecedented opportunity for extreme pulse compression with pump pulse energies of ~100 fj. The desired amount of pulse compression can be achieved by dispersive design of the nanophotonic waveguide of the OPO, allowing for further compression of a 1 ps pump pulse to ~10 fs. The synchronous pumping OPO allows for pulse width T p , pulses with frequency 2ω and width T sech, the mechanism of the method that can be compressed into a single pulse of frequency ω is described in detail in [1] (Non-Patent Document 84) and illustrated in FIG. 30. The group velocity mismatch (GVM) between the pump and the single pulse causes the signal pulse to travel through the pump. The maximum gain occurs in the part of the signal pulse that overlaps most with the pump. When there is a non-negligible GVM between the pump and the signal, not only does the same pump power occur in all parts of the signal, but the centroid of the signal is much more likely to reach gain saturation, and both of these result in significantly smaller pulse compression compared to the previous case. In fact, the optimal dispersion for pulse compression is when the centroid of the signal extracts the maximum energy by traveling exactly through the pump, i.e., |GVM| = T p / L PPLN when it is, where L PPLN is the length of the periodically poled region. When the output pulse width is determined by the group delay dispersion (GDD) of the cavity, it is as follows:

Equation

[0068] Here, G0 is the gain at the threshold. When second-order dispersion can be excluded, the output pulse width comes to be limited by third-order dispersion (TOD). Therefore, in this scheme, the amount of available pulse compression is determined by the amount of dispersion adjustment that can be achieved.

[0069] Experiments and basic studies were performed in the cavities of discrete (independent) components with a dispersed design limited to the nonlinear gain medium through optical fibers. In contrast, TFLN allows for a much larger amount of dispersed design [2] (Non-Patent Literature 85), and is therefore an ideal platform for second-order solitons and second-order solitons based on pulse compression. The simulation results in Figure 30b show that by appropriately selecting waveguide parameters, large GVM and small GDD regimes can be accessed, and these regimes are ideal for pulse compression. For example, the green X marks represent the geometric shape in which a 500 fs pump is compressed to 50 fs.

[0070] Apart from the distributed design, the TFLN-based synchronous pumping OPO is also desirable due to its very low operating pump power. A low threshold energy of around ~100 fJ has been measured [3] (Non-Patent Literature 86), which is significantly lower than the pump power required for other integrated means of pulse compression [1] (Non-Patent Literature 84). On this OPO, the TFLN enables monolithic integration with other nanophotonic circuit elements such as heaters, mode-locked lasers, and other parametric processes. In summary, the DOPO on TFLN is an excellent platform for exploring second-order solitons with the goal of obtaining on-chip pulse compression of signal pulses ranging from ~1 ps to ~10 fs, as shown in the waveguide design with a distributed design in Figure 30b.

[0071] References for the second embodiment The following references are included herein by reference. [1] A. Roy, R. Nehra, S. Jahani, L. Ledezma, C. Langrock, M. Fejer, and A. Marandi, Nature Photonics 16, 162 (2022) (Non-patent Document 84) [2] L. Ledezma, R. Sekine, Q. Guo, R. Nehra, S. Jahani, and A. Marandi, Optica 9, 303 (2022)(Non-Patent Document 85) [3] A. Roy, L. Ledezma, L. Costa, R. Gray, R. Sekine, Q. Guo, M. Liu, R. M. Briggs, and A. Marandi, Visible-to-mid-ir tunable frequency comb in nanophotonics (2022), arXiv 2212 08723(Non-Patent Document 86)

Example

[0072] Third Embodiment of Visible~Infrared Comb Pumped by Frequency Comb The inventors demonstrate ultra-broadband tunable frequency comb generation from an on-chip OPO in lithium niobate nanophotonics. Utilizing the ability to control phase matching by periodic poling combined with dispersion engineering, the inventors show an on-chip tuning range exceeding 1 octave. The inventors pump the OPO with near-infrared picosecond pulses from an electro-optic frequency comb source, which has been demonstrated to be compatible with nanophotonic lithium niobate [18,58,59] (Non-Patent Documents 104, 144, 145). The demonstrated frequency comb covers typical communication bands, extends into the mid-infrared spectral region beyond 3 μm, and has an instantaneous bandwidth that supports the duration of such picosecond pulses. In addition, the same chirp generates a tunable frequency comb in the visible region resulting from an up-conversion process. Realizing a tunable visible frequency comb has continued to be challenging in most integrated photonic platforms due to the absence of a suitable broadband gain medium and typically large normal dispersion at these wavelengths [14,30] (Non-Patent Documents 100, 116).

[0073] Example of Device Structure To realize a broadband and widely adjustable frequency comb, the inventors designed a dual-resonance OPO based on nanowaveguides etched onto 700 nm thick MgO-doped lithium niobate with an X-cut® pattern, as shown in Figure 31(a) [15,24,40] (Non-Patent Literature 101, 110, 126). Unlike the triple-resonance design [3,16,29] (Non-Patent Literature 89, 102, 115), this design provides access to widely adjustable pseudo-phase matching (QPM) and avoids stringent requirements such as compensating for pump resonance [9] (Non-Patent Literature 95). The dual-resonance operation is achieved by controlling the precise spectral response of the OPO resonator using two spectrally selectable adiabatic couplers (highlighted in Figure 31(a)), which allow only long wavelengths (signal and idler) to resonate within the OPO while short wavelengths (pump and upconverted light) exit the cavity (see Supplementary Section 3.6.2). This is important not only for achieving a wide tuning range for the signal and idler, but also for enabling non-resonant, broadband, and widely tunable upconversion to the visible region, which is in stark contrast to previous parametric sources in this range [14,30] (Non-Patent Literature 100, 116). Another important aspect of the above on-chip OPO design is the dispersion design of the OPO's primary interaction wavelength, which, combined with periodic polling, results in a wide spectral coverage range for QPM tuning. Designing the remaining dispersion of the resonator is another important degree of design freedom that can be further utilized to realize second-order soliton and pulse compression mechanisms

[41] (Non-Patent Literature 127).

[0074] For the data presented in this specification, a second-order parametric nonlinear interaction occurs within a 5-mm long poled waveguide region, and this second-order parametric nonlinear interaction has a fixed poling period (Λ) for each OPO on the chip. The periodic poling step is adapted to the parametric nonlinear interaction among the pump wave, the signal wave, and the idler wave, and this parametric nonlinear interaction can be adjusted from degenerate to widely non-degenerate. The chip is composed of a plurality of OPOs, and these OPOs have a poling period for resonance signals and idler wavelengths over one octave of non-resonant pumps, i.e., for type 0 phase matching of down-conversion to the OPO output (in this case, a wavelength of around 1 micron). The OPM adjustment curve is shown in Fig. 31(b). In addition to the outputs of these OPOs, the poled waveguide also provides an additional parametric up-conversion process, particularly the second harmonic of the signal / idler, and sum frequency generation from the pump and the signal / idler. As shown in Fig. 31(c), the entire adjustment range of the chip overlaps with a number of molecular and atomic transitions. The strong spatio-temporal local confinement of the waves interacting within the waveguide ensures a large up-conversion efficiency, and the up-conversion efficiency can be further enhanced by adding an appropriate poling period and adapting to specific applications.

[0075] As shown in Fig. 31(b), in order to continuously cover the visible to mid-infrared, the inventors adjusted the QPM by roughly switching the poling period and finely adjusting the pump wavelength by more than ~25 nm. Such an adjustment range of the pump is compatible with existing semiconductor lasers

[50] (Non-Patent Document 136). Furthermore, the rough switching of the poling period can be realized without mechanical movement, for example, by electro-optical means. In addition, temperature adjustment of the poled region can provide other substantial adjustment mechanisms (see Section 3.6.9 of the Supplementary Information). The light emission from the OPO chip covered important wavelengths corresponding to atomic transitions in the visible region and molecular absorption lines in the mid-infrared region (Fig. 31(c)).

[0076] The OPO was synchronously pumped with 1 ps-long pulses operating at a repetition rate of approximately 19 GHz [27, 36, 40] (Non-Patent Literature 113, 122, 126). This repetition rate was tuned to be close to the free spectral region or its harmonics of the OPO cavity (see Supplementary Section 3.6.5). The octave width adjustment of the parametric oscillation from the OPO chip was achieved by adjusting the pump's center frequency to only 1040 nm to 1065 nm. The pump was generated from an electro-optic frequency comb

[39] (Non-Patent Literature 125). A schematic diagram of the experimental setup is shown in Figure 32(a). The spectral and temporal characteristics of the near-infrared pump are shown in Figure 32(b).

[0077] Example of results Figure 32(c) shows the broad spectral coverage of an OPO extending to 3.3 μm in the mid-infrared region obtained from a single chip. The comb lines can be resolved by an optical spectrum analyzer (OSA) and are visible in the inset, with peak separation corresponding to the pump repetition rate. For near-degenerate OPOs, the on-chip threshold is approximately 1 mW of average power (~50 mW of peak power and ~100 femtojoules of pulse energy). The signal conversion efficiency approaches ~5% for near-degenerate OPOs, while for far-degenerate non-degenerate OPOs, the idler conversion efficiency in the mid-infrared (3.3 μm) exceeds 1% (see Supplementary Section 3.6.2). This conversion efficiency corresponds to an estimated peak power of ~25 mW and ~5 μW of power per comb line in the mid-infrared region.

[0078] The OPO's dual-resonant operation is also confirmed by the appearance of a resonant peak structure with a change in the pump center frequency, as shown in Figure 33(a). Figure 33(b) shows the acceptable range of mismatch for the synchronous pumping repetition rate relative to the optimal OPO operating point. Figure 33(c) shows the fine-tuning capability of the OPO's output spectrum provided by tuning the pump wavelength. The combination of fine-tuning and coarse-tuning capability can enable a continuous spectral coverage range across the entire accessible spectral region. The OPO output in degeneracy (Figure 33(d)) corresponds to a sub-picosecond (less than picosecond) conversion limit duration (~400 fs), representing a pulse compression ratio that is less than half of the pump.

[0079] The inventors further evaluated the coherence of the output frequency comb by performing linear field cross-correlation of the output signal light, as shown in Figure 33(e), where each OPO pulse was interfered with another pulse delayed by 10 round trips. The presence of interference fringes (see inset in Figure 33(e)), combined with the invariance of the Fourier transform of the cross-correlation traces and the signal spectrum obtained using OSA, serves as evidence of the coherence of the output frequency comb across the entire spectrum.

[0080] The generation of other second-order nonlinear processes, such as second-harmonic generation (SHG) and sum-frequency generation (SFG), results in frequency comb formation in the visible spectrum. The complete emission spectrum of the OPO, consisting of the pump's second harmonic and signal wave, and the sum-frequency component of the pump and signal / idler wave, is shown in Figure 34(a) along with the normal signal / idler. The visible light scattered from the chip is captured by an optical microscope image (see Figure 34(b)) to show the emission of the pump's second harmonic (green) and sum-frequency component (red). In the polling region, green is dominant on the input side and is gradually overwhelmed by the red component of the sum-frequency. The SFG of the pump and signal wave results in a tunable visible frequency comb generation from 600 nm to 700 nm, as shown in Figure 34(c). Tuning the OPO further away from degeneracy results in idler emission entering the mid-infrared region, as well as the SFG component located on the bluer side of the visible spectrum.

[0081] The pump is a near-infrared electro-optic comb that can be contained within a lithium niobate chip. With appropriate dispersion design, the OPO design of the present invention can additionally achieve a large instantaneous bandwidth achieved by significant pulse compression

[41] (Non-Patent Literature 127), enabling femtosecond mid-infrared frequency combs in nanophotonics. Thus, efficient supercontinuum generation requiring only 2 picojoules of pulse energy can be performed on these femtosecond pulses using a periodically polled lithium niobate waveguide for stabilization of a subsequent f~2f self-reference / comb

[20] (Non-Patent Literature 106).

[0082] In one or more embodiments, the OPO can be integrated with an electro-optic modulator for actively locking the frequency comb of the OPO. The threshold of the OPO can be further reduced by improving waveguide losses and strengthening the effective nonlinear coefficient by separately optimizing the mode overlap between the pump and the signal / idler electromagnetic field for each OPO device according to its dedicated spectral band. The inventors estimate that an on-chip threshold for near-degenerate operation at an average power of less than 500 μW is achievable (for operation at a 10 GHz repetition rate). This low power requirement, combined with a relatively narrow pump tunable range, enables pumping the OPO chip with a butt-coupled near-infrared diode laser and a fully integrated solution for generating mid-infrared frequency combs based on lithium niobate nanophotonics [13,18,25,58] (Non-Patent Literature 99, 101, 111, 144) (see Supplementary Section 3.6.8).

[0083] Optimizing coupler design enables OPO operation at lower thresholds and higher mid-infrared comb conversion efficiencies. Advanced coupler designs, such as those based on inverse design

[35] (Non-Patent Literature 121), can simultaneously satisfy low coupling for pumps, high coupling for signals, and optimal coupling for idler waves, resulting in conversion efficiencies exceeding even 30%. Realizing OPO devices within lithium niobate on sapphire allows access to a wider transparent window, resulting in frequency comb generation that penetrates deeper into the mid-infrared region. Thanks to strong parametric nonlinear interactions, frequency combs with lower repetition rates (~1 GHz) can be realized using spiral waveguides

[26] (Non-Patent Literature 112) within the feedback arms of the OPO resonator, which is useful for on-chip dual-comb spectroscopy applications. Emissions in the mid-infrared region overlap with important molecular vibrational rotational absorption lines, paving the way for novel integrated spectrometer solutions.

[0084] Supplemental information regarding the method and the third embodiment The above device was fabricated on a 700 nm thick X-cut (registered trademark) MgO-doped lithium niobate die. First, electrodes were patterned using electron beam lithography, followed by periodic poling by electron beam heating and deposition of Cr / Au, and then subsequent metal lift-off. Ferroelectric domain inversion was induced by applying high-voltage pulses, and the poling quality was inspected using second-harmonic microscopy. Waveguides were patterned using electron beam lithography and Ar + The waveguide facets were polished using a fiber polishing film (thin film). The OPO chip consists of multiple devices with polling periods ranging from 5.55 μm to 5.7 μm (in 10 nm increments) that provide parametric gain over one octave.

[0085] Optical spectra were recorded using a near-infrared optical spectrum analyzer (OSA) (Yokogawa Electric AQ6374), a mid-infrared OSA (Yokogawa Electric AQ6375B, AQ6376E), and a CCD (charge-coupled device) spectrometer (Thorlabs CCS200). Multiple OPOs were driven synchronized at either the fundamental frequency repetition rate (~9.5 GHz) or its harmonics (~19 GHz). The optical spectrum results were obtained using the harmonic repetition rate because the shorter electro-optic pump pulses result in a wider instantaneous bandwidth. OPOs operating at longer wavelengths have higher thresholds (due to increased effective area, increased coupler loss corresponding to the signal wave, and greater mismatch in relative walk-off parameters between the signal wave and idler wave), and therefore the inventors have operated these OPOs intermittently in what the inventors call "pseudo-synchronous" operation as a way to reduce average power and avoid thermal damage (see Supplementary Section 3.6.4). This limitation is mainly due to the avoidable input insertion loss (~12 dB) in the inventors' current setup. With the help of better fiber-tip coupling designs / mechanisms (in the context of thin-film lithium niobate, insertion losses of the order of 1 dB have been reported), mid-infrared OPOs can be operated in a steady-state synchronous pumping configuration

[17] (Non-Patent Literature 103).

[0086] Single envelope simulation and visible frequency comb To capture the generation process of the second harmonic signal and sum frequency generated signal (involved in the generation of the visible frequency comb), the inventors use a simulation of a single nonlinear envelope as a last resort [5] (Non-Patent Literature 91). The numerically obtained results are shown in Figure 35(a), which suggest the presence of the visible frequency comb component. The inventors assumed the presence of non-idealism in the polling period in their simulation. These second harmonic and sum frequency generated components are generated by parasitic phase matching resulting from duty cycle errors and / or higher-order phase matching in the visible component.

[0087] To enhance the efficiency of the visible frequency comb generation process, an additional phase matching section can be added to the OPO's output waveguide. This increases the conversion efficiency of the phase-matched components and allows for designing a broadband configuration using chirp-polling periods. Figure 36(b) simulates such a scenario in which the efficiency of the SFG components between the pump and signal is increased. Similarly, these scenarios can be designed for other components, namely the SFG between the idler and pump, or the second harmonic frequency comb. The inventors note that these visible frequency combs are single-pass due to the long-path spectral response of the adiabatic coupler. The visible components inherit the broad tunability of their underlying signal / frequency comb.

[0088] The fine-tuning of the visible frequency comb (sum frequency generation of signal and pump) can also be achieved using pump wavelength control, as shown in Figure 36(c). Upconversion resulting from the generation of the second harmonic of the signal also leads to the generation of a near-infrared frequency comb. The phase matching curve is shown in Figure 37(a). The coarse and fine adjustments of the experimentally obtained second harmonic signal comb are shown in Figures 37(b) and 37(c), respectively.

[0089] 3.6.2 Signal / Idler Conversion Efficiency Figure 38(a) plots the signal power as a function of pump power. The conversion efficiency of the OPO is a function of the escape efficiency, the number of times the threshold operation is exceeded, etc. [2] (Non-Patent Literature 88).

[0090] The escape efficiency is determined by the OPO cavity output coupling, which is given by the frequency response of the adiabatic coupler of the present invention. A schematic diagram of the geometric shape of the coupler of the present invention is shown in Figure 38(b). The geometric parameters are indicated in the heading of Figure 40. The performance of the coupler obtained by simulation is shown in Figure 38(c). The coupler response is also characterized by illumination with a hypercontinuous light source. The results are superimposed in Figure 38(d).

[0091] The inventor measured the off-chip (outside the chip) mid-infrared power of ~300 nW. This spectrum is shown in Figure 39. The corresponding on-chip average power is ~3 μW. The estimated pulse width for the idler is ~500 fs (conversion limit). This value represents a peak power of ~25 mW. The power per comb line is ~5 μW. The inventor multiplied the power level by 100 pseudo-pulse duty cycles. The threshold for this extreme mid-infrared OPO is estimated to be approximately 10 times that of the near-infrared OPO (with an average power of ~1 mW).

[0092] 3.6.3 Pump preparation / Generation of electro-optical frequency comb The OPO is pumped by an electro-optic frequency comb, with its repetition rate tuned to near the cavity's FSR. The pump pulse width is approximately 1 ps in length, and based on available electronic components, the inventor's current version allows the repetition rate to 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 strictly follows the method demonstrated in [33,39] (Non-Patent Documents 119,125). The center frequency can be tuned from 1040 nm to 1065 nm (the upper limit is determined by the operating range of the waveshaper, while the lower limit is selected to ensure safe operation of the YDFA).

[0093] A schematic diagram of the pump preparation setting is shown in Fig. 40(a). The output of a CW (continuous wave) laser is modulated by a series of modulators. These modulators are driven by an RF signal generator followed by an RF amplifier. The bias of the intensity modulator (IM) is selected such that pulses are cut out from the continuous wave. At this stage (stage 1), the output in the time domain is similar to the waveform by simulation shown in Fig. 40(b). Next, a cascade connection of three phase modulators (PM) enables the addition of spectral sidebands, and the spectral sidebands are separated by the repetition rate. Multiple phase modulators can be driven synchronously by adjusting an electronic delay line. At this stage (stage 2), the spectrum is similar to that shown in Fig. 40(c). The resulting signal is amplified with the help of a semiconductor optical amplifier (SOA) and then sent to a wave shaper. A programmable wave shaper enables the compression of pulses by detuning the input time waveform by the application of appropriate dispersion. At the third stage (stage 3), the time domain waveform looks like that shown in Fig. 40(d), showing both the compressed pulses and the chirped pulses before compression. Finally, the electro-optic frequency comb is characterized in the frequency domain using an optical spectrum analyzer (OSA) and in the time domain using an intensity autocorrelator.

[0094] The threshold of the far-detuned non-degenerate OPO is higher due to the combination of multiple resonators. The adiabatic coupler is not designed for each OPO. Instead, in such first-generation chip designs, the coupler is realized uniformly. As a result, the far-detuned non-degenerate operation of the OPO results in a signal with a higher round-trip signal (due to the output coupling that gradually increases as the wavelength decreases). Furthermore, the effective nonlinear coefficient considering the effective area of the mode and the overlap of the fields among the modes of the pump, signal, and idler also deteriorates.

[0095] The higher the threshold requirement, the greater the pump power required, and this pump power is currently on the high side due to considerably high input coupling loss / insertion loss (approximately 10-12 dB). Several proposals and demonstrations exist for reducing this value to 2-3 dB [54, 56] (Non-Patent Literature 140, 142). In scenarios where low insertion loss is available, the required external pump power can be dramatically reduced to about 10 dB. Under these circumstances, the threshold requirement for non-degenerate operation can be easily utilized even in suboptimal designs.

[0096] However, in the inventor's current implementation, the inventor is unfortunately plagued by excessive insertion loss, which necessitates an out-of-chip average power exceeding 60 mW. At these power levels, the inventor is prone to burning / damaging the connector and adversely impacts the YFDA in the presence of unwanted back-reflected power. To ensure safe operation, the inventor employs pseudo-synchronous pumping as a last resort, thereby reducing the average power by pulsed pump operation. This can be achieved by driving a semiconductor optical amplifier (SOA) using an arbitrary waveform generator (AWG), resulting in microsecond-scale pulses with a repetition rate varying from 1 to 20 kHz (1000 to 50 duty cycles). A schematic diagram is shown in Figure 41(a), which is the same as the pump preparation setup with the addition of an AWG-driven SOA. The time-domain trace and signal pulse captured using a slow detector for the pump are shown in Figure 41(b). The inventors note that the slow detectors did not have the resolution to detect individual picosecond-scale pulses within each pseudo-pulse. In fact, there are thousands of pulses within each pseudo-pulse.

[0097] 3.6.5 Estimating the free spectral region of the cavity Estimating the free spectral range (FSR) of the cavity is central to determining the repetition rate of the synchronous pumping OPO. This is absolutely necessary because the synchronous pump (EO (electro-optical modulator) comb) cannot be continuously tuned to find the correct FSR. The core setting of the EO comb requires a specific combination of electron phase delay line parameters and waveshaper dispersion parameters, and tuning this is a difficult task. The OPO design of the present invention eliminates the use of a tuneable CW light source around 1 μm for scanning across multiple cavity resonances. In the processing of the present invention, this situation worsens without a high-power tuneable CW light source around 2 μm. Under these circumstances, the inventors estimate the cavity FSR using the measurement settings shown in Figure 42.

[0098] This method requires the OPO to be operated in CW mode. The inventor applies variable modulation over CW using an intensity modulator (IM). The modulation frequency is varied using an arbitrary waveform generator. The OPO output is maximized at a proper cavity FSR. Unlike the EOcom, this setting can be continuously adjusted.

[0099] 3.6.6 Spectral broadbanding / pulse compression in degenerate OPO The measured pump pulse width (assuming a Gaussian pulse extracted from the intensity autocorrelation trace) is ~1 ps. The estimated conversion limit pulse width for an OPO operating in degenerate mode is 380 fs. As shown in Figure 43(a), the experimental spectra of both the pump and the signal are converted to frequencies and superimposed (overlaid) onto each other. The numerical simulation results obtained from the simulation of the dual envelope equations are shown in Figures 43(b) to (e), and these results are in strict agreement with the measured data. With appropriate dispersion design (dispersion and mismatch of group velocities)

[41] (Non-patent Literature 127), it is possible to generate frequency combs of OPOs with wide instantaneous bandwidth, resulting in a small number of optical cycle pulses.

[0100] 3.6.7 Coherence Verification Using Field Cross-Correlation Techniques To evaluate the spectral coherence, the inventors performed a linear field cross-correlation (FCCR) of the output signal light, interfering each OPO pulse with another pulse delayed by 10 round trips. This can be considered an improved FTIR (Fourier transform infrared spectroscopy) measurement, where the inventors perform cross-correlation instead of autocorrelation. A schematic diagram of the setup used for this purpose is shown in Figure 44(a). The delay lines correspond to delays 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 optical spectrum acquired by the optical spectrum analyzer with the optical spectrum calculated by performing a Fourier transform of the FCCR trace.

[0101] The inventor also detects a sharp RF beat frequency corresponding to the repetition rate of the applied synchronous pumping OPO (Figure 44(b)). This signal is obtained by measuring the output pulse of the OPO using a high-speed photodetector. The pump is rejected using a wavelength demultiplexer.

[0102] 3.6.8 Full System Integration and General-Purpose Frequency Comb Generators A fully integrated solution for frequency comb generation can be based on lithium niobate nanophotonics in conjunction with a laser chip. Several design enhancements can significantly lower the threshold for frequency comb generation, which can enable pumping with commercially available distributed-feedback (DFB) laser chips. Alternatively, an integrated external cavity can be placed for this purpose together with a semiconductor gain chip

[28] (Non-Patent Literature 114). Other crucial building blocks (components) are: a) near-infrared picosecond pump pulse generation [18,58] (Non-Patent Literature 104, 144), b) Mach-Zehnder interferometer mesh

[51] (Non-Patent Literature 137) for routing the pump light to the desired OPO, c) an array of OPOs, and d) periodically polled lithium niobate waveguides [20,38] (Non-Patent Literature 106, 124) for f~2f-based frequency comb stabilization and to support ultra-low power supercontinuum generation. The inventor's current research focuses on element c), but the rest have already been demonstrated in lithium niobate nanophotonics.

[0103] 3.6.9 Temperature adjustment of the phase matching curve In this embodiment, fine-tuning of the quasi-phase matching (QPM) was performed by adjusting the pump wavelength. The same can be achieved with the help of temperature adjustment 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 taking into account the temperature-dependent Sellmeier (dispersion) equation

[10] (Non-Patent Literature 96). Temperature adjustment can be achieved either globally by placing the chip on the TEC heater element or locally by implementing the resistive heater element near the region that is periodically polled. The inventors note that the expected adjustment curve (obtained from simulation) is more tunable than that observed during experimentation. This may be due to the presence of thermal resistance between the heater element and the nanophotonic chip, and / or a mismatch in the coefficient of thermal expansion between the insulator layer and the thin-film lithium niobate layer, which the inventors predict may be subject to further investigation.

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[60] Further information regarding one or more embodiments of the present invention can be found in Arkadey Roy et al., Visible-to-mid-IR tunable frequency comb in nanophotonics, Nature Communications volume 14, Article number 6548 (2023) (Non-Patent Literature 146) and supplementary information: https: / / www.nature.com / articles / s41467-023-42289-0. [Examples]

[0105] Fourth embodiment, 40-pulse time-resolved nanophotonic optical parametric oscillator Time-division systems are becoming ubiquitous in many subfields of optics because they offer the ability to construct large graphs by storing information across distinct time bins. For this reason, time-division systems have found applications in areas such as computer computing, quantum information, and topology [1-3] (Non-Patent Literature 147-149). Time-division networks of optical parametric oscillators (OPOs), specifically degenerate OPOs, have remained of particular interest due to their ability to approximate the Ising Hamiltonian [4,5] (Non-Patent Literature 150, 151). Recent advances in thin-film lithium niobate, including demonstrations of extremely high parametric gain [6] (Non-Patent Literature 152) and subsequent demonstrations of optical parametric oscillation, offer the possibility of realizing such time-division systems at the chip scale. Here, the inventors demonstrate an on-chip, 40-pulse time-division OPO. Using interferometry techniques, the inventors verified the independence of each of the 40 simultaneously oscillating pulses. This research represents a definitive milestone on the path toward creating large-scale graphs in integrated photonic platforms.

[0106] The experimental setup is schematically shown in Figure 47. The inventors used an electro-optical (EO) comb (left side of Figure 1a) at a repetition rate of 10 GHz to pump a 250 MHz on-chip optical parametric oscillator, thereby generating 40 pulses that resonated within the cavity. Following the EO comb generation, the inventors' pump preparation included a booster optical amplifier (BOA), a waveshaper, and a ytterbium-doped fiber amplifier (YDFA) for amplification and dispersion compensation. The pump was characterized by its spectrum (Figure 47c)) and intensity autocorrelation (Figure 47d)), demonstrating a bandwidth of over 3 nm around a central wavelength of 1045 nm and an autocorrelation width of 1.6 ps. Periodic polling on the waveguide (center of Figure 47a) provided phase matching between the pump and the signal around 2090 nm. A tapered coupler ensured that the signal was coupled to the resonator while allowing the pump to pass through. Figure 47b) shows an optical microscope image highlighting the 53 cm spiral resonator.

[0107] The inventors characterized the relative phase of output pulses using an unbalanced (one-pulse delay) Mach-Zehnder interferometer (MZI) consisting of a 45:55 free-space pellicle beam splitter and a 50:50 fiber splitter (right side of Figure 47a). One of the free-space arms has a delay stage, which can be locked to a signal from a 1064 nm backpropagation CW laser using a piezoelectric transducer (PZT). This signal is coupled through one MZI output port and measured using a photodetector (PD2). Using this 100 ps delay, the inventors interfered pulses within a 10 GHz pulse train. A 1 MHz photodetector (PD3) at the other MZI output measured the average value of these interferences over a number of pulses. The inventors expected that different average interference values ​​would be observed for each OPO case, given that the phases of 40 pulses were random and independent of each other. To measure this, the inventor modulated the BOA in the pump preparation setting to extract 4μs pulses on a 10GHz comb at a repetition rate of 10kHz. This helped to rapidly switch the OPO on and off. Additionally, the inventor continuously monitored the MZI input on PD1 using a 92:8 pellicle at the chip output, both for measurement reference and for pump stabilization.

[0108] Figure 48a) shows the experimental results in the degenerate case, and as can be seen in the measured optical spectrum (i), oscillation occurs in the pump's half harmonics. Here, it was expected that the OPO would oscillate in only two phase states, namely 0 and π. With 40 pulses, the average value of the resulting interference should have only 21 possible acceptable levels. The probability of each level is (outside 6) The image is provided by JPEG2026518928000014.jpg3375, where N is the number of pulse inversions occurring in a sequence of 40 pulses. Subfigure (ii) shows a sample sequence of an example OPO. A reference trace collected from an 8:92 splitter allows for post-correction of the measurement data to eliminate intensity noise in the OPO output. Shown in the lower panel, the time trace (time-varying curve) from the interference shows, as expected, a much larger variation than the reference. A histogram of the interference output over a measurement time of 2 seconds is shown in (iii). Here, the expected discrete states are observed, indicating that the 40 pulses actually behave like a time-divided degenerate OPO with independent, random binary phases. In addition, the inventors can use the histogram from (iii) to calculate the probability mass function and compare it with the theoretical probability. The result (iv) shows a good agreement between experiment and theory.

[0109] The inventors also measured the case of non-degenerate oscillation, as shown in Figure 48b). Here, the optical spectrum shows the distinguishable signal modes and idler modes. As in the degenerate case, the time trace data (ii) shows larger interference variations than the reference measurement. However, unlike the degenerate case, the phase of the non-degenerate OPO is not constrained to discrete levels, but can take any level. Therefore, the inventors expect to see a continuous Gaussian (normal) distribution in the histogram, as observed in (iii).

[0110] In conclusion, the inventors demonstrated a 40-pulse time-resolved nanophotonic optical parametric oscillator that operates in both degenerate and non-degenerate regimes. By measuring the average interference between consecutive pulses for numerous examples of OPOs, the inventors demonstrated the independence of all 40 pulses. This result opens the way for on-chip optical time-resolved systems such as Ising machines.

[0111] References for the fourth embodiment The following references are included herein by reference. 1.C. Leefmans, et al., Phys. 18, 442-449 (2022) (Non-patent document 147) 2.S. Yokoyama, et al., Nat. Photonics 7, 982-986 (2013) (Non-patent document 148) 3.R. Nehra, et al., Science 377, 1333-1337 (2022) (Non-patent document 149) 4.A. Marandi, et al., Nat. Photonics 8, 937-942 (2014) (Non-patent document 150) 5.N. Mohseni, et al., Rev. Phys. 4, 363-379 (2022) (Non-patent document 151) 6.L. Ledezma, et al., Optica 9, 303-308 (2022) (Non-patent document 152) 7.L. Ledezma, et al., arXiv:2203.11482 (2022) (Non-patent document 153)

[0112] Example of a pumping subcircuit Figure 49a shows an example in which a photonic integrated circuit may include a pumping subcircuit coupled to the OPO. Figure 49b shows an example in which the pumping subcircuit comprises a mode-locked laser, which comprises a modulator (e.g., an electro-optic modulator), and the modulator comprises an electrode metallide or heater coupled to the waveguide. Figure 49c shows an example in which the pumping subcircuit comprises a Kerr resonator. Figure 49d shows an example in which the pumping subcircuit comprises an electro-optic modulator (EOM) / phase modulator (e.g., with electrodes coupled to the waveguide portion). Figure 49e shows an example in which the pumping subcircuit comprises an amplitude modulator (e.g., with electrodes coupled to the waveguide portion). In one or more embodiments, the Kerr resonator (e.g., with a loop) exhibits Kerr nonlinearity (i.e., is not linear).

[0113] Figure 49f shows an example of a device in which the OPO can be located inside an integrated laser cavity, and Figure 49g shows an example in which the OPO includes a laser gain element, or in which a pump pulse or frequency comb is generated inside a resonator.

[0114] Figures 49f to 49g illustrate the device of Section 1, where the circuit has additional components at the output of the OPO, including a nonlinear component 4910 for wavelength conversion, a nonlinear component 4910 for spectral broadbanding, linear components such as filters and couplers, and actuators such as electro-optic modulators.

[0115] Processing steps Figure 50 is a flowchart showing a method for fabricating a device according to one or more embodiments.

[0116] Block 5000 demonstrates the formation of a photonic integrated circuit using lithography to pattern a substrate, the integrated circuit comprising an OPO, the OPO comprising one or more waveguides, the waveguides comprising a nonlinear material that outputs waves (signal and / or idler) in response to a pump wave using a parametric nonlinear process. Each waveguide has a width and height of less than 5 micrometers. These nonlinear materials are phase-matched and distributed to control an appropriate group velocity mismatch (GVM) between the pump and the signal pulse, resulting in a temporal overlap between the pump and the signal / idler pulse. In one or more examples, the waveguides have lengths appropriately adjusted for the distributed design. Examples of nonlinear materials that are (e.g., second-order) nonlinear (and can form a substrate chip) include, but are not limited to, lithium niobate, lithium tantalate, potassium titanyl phosphate (KTP), aluminum nitride, gallium arsenide, indium phosphide, aluminum gallium arsenide, GaP, or InGaP. The present invention is not limited to second-order nonlinearity, and other nonlinear materials can 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 within the lithium niobate (monolithic integration of the waveguide). A pump laser, injection synchronous input, or auxiliary resonator can be patterned within the same substrate or within a substrate of different materials coupled to a substrate containing the OPO.

[0117] By depositing a metallized material coupled to a waveguide formed in a lithium niobate / substrate, actuators (e.g., electro-optic modulators, electric heaters, thermo-optic heaters, or piezoelectric transducers, which use an electric field or temperature to change the phase or amplitude of a wave, or the refractive index of a waveguide) can be manufactured.

[0118] Each input to and output from an OPO may be provided with an input coupler and an output coupler, respectively, and these couplers may be integrated within the device. The input and output couplers may include adiabatic couplers, directional couplers, Y-junctions, multimode interferometers, or inversely designed couplers, and these couplers may be formed, for example, by etching a suitable combination of waveguides into a substrate (including a nonlinear material such as lithium niobate).

[0119] In one or more examples, the photonic integrated circuit includes, or is coupled to, a subcircuit for pumping, which is configured to output a pump wave containing pulses or frequency combs at the pump repetition rate. This subcircuit can be formed in a substrate containing a nonlinear material or in different substrate chips. In one or more examples, as shown in Figure 49, a Kerr frequency comb is fabricated by forming a loop waveguide coupled to a straight portion of the waveguide by a gap.

[0120] In further examples, the subcircuit comprises one or more actuators, which are operable to adjust at least one of the pump wave repetition rate, carrier-envelope offset, intensity, or wavelength. In one or more examples, the actuators are formed by depositing a metallide coupled to a waveguide formed in a substrate (including, for example, a nonlinear material such as lithium niobate). In one or more examples, the subcircuit 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. In one or more examples, the electro-optic comb source may include a modulator, which can be realized by depositing a metal on lithium niobate (or a nonlinear material) or on a thin layer of dielectric deposited on lithium niobate (or a nonlinear material). In one or more embodiments, the amplitude modulator or phase modulator may comprise a metal deposited on an additional dielectric layer on the LN.

[0121] In yet another example, the photonic integrated circuit may have additional components at the output of the OPO, these additional components including nonlinear components for wavelength conversion, nonlinear components for spectral broadbanding, linear components such as filters and couplers, and actuators such as electro-optic modulators. Examples of nonlinear components include, but are not limited to, nonlinear waveguides or amplifiers in a nonlinear material of a substrate (e.g., lithium niobate) that perform the above or other OPOs, frequency mixing processes, harmonic generation (e.g., SHG) processes, or parametric amplification processes.

[0122] In one or more embodiments, the OPO comprises multiple parts within an on-chip synchronous pumping OPO and has pseudo-phase matching. Phase matching can also be achieved by other techniques such as mode phase matching.

[0123] In one or more examples, the distribution design involves creating a specific geometric shape to provide appropriate group velocity dispersion (as in Figure 5 or Figure 30b).

[0124] Block 5002 represents the final result, device, system, or apparatus. A device can be embodied in numerous ways, including, but not limited to, the following (see also Figures 1-48):

[0125] 1. A device, system, or apparatus 100, 3100 comprising photonic integrated circuits 102, 3102, wherein the photonic integrated circuit comprises one or more optical parametric oscillators (OPOs) 104, and each OPO is: Inputs 106, 3106, One or more nonlinear portions 110, 3110, It is equipped with one or more outputs 114, 3114, The input is configured to receive a pump wave 3108 (arrow 108 indicates the direction of the pump wave) containing a pulse or frequency comb at the pump repetition rate. One or more nonlinear portions are part of resonators 3112, 112 (equipped with waveguides 113, 3113) or coupled to resonators having a free spectral region, wherein at least one of the free spectral region or one of its harmonics (e.g., harmonics of this spectral region) is matched with at least one of the pump repetition rates or its harmonics (e.g., equal to or within 10% of the difference), One or more outputs 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 to extract the pump wave (for other applications).

[0126] 2. The device of Section 1, wherein each of the above nonlinear portions is phase-matched in one or more nonlinear optical processes, and the one or more nonlinear optical processes include degenerate optical parametric amplification, non-degenerate optical parametric amplification, upconversion of waves in OPO, downconversion of waves in OPO, and spectral broadbanding of waves in OPO. In one or more examples, the nonlinear waveguide may have different portions, each of which is phase-matched in a different nonlinear matching, or different nonlinear portions in OPO are phase-matched in different nonlinear processes.

[0127] 3. The device described in Section 2, wherein the above-mentioned phase matching is achieved by pseudo-phase matching, for example, by periodic or aperiodic polling.

[0128] 4. The device of Section 1 or 2, wherein the nonlinear portion and / or other portion of the resonator (e.g., the waveguide forming the resonator) is designed to tune the spectrum of one or more waves occurring within the OPO. In one or more examples, tuning the spectrum refers to a way in which the GVD and GVM can change their parametric gain, as shown in Figure 1c, as an example.

[0129] 5. A device from any of Sections 1-4 in which the distributed-designed OPO supports the formation of time solitons. A time soliton is a specific type of nonlinear operation. An example of a design to support solitons is illustrated in Figures 30a and 30b.

[0130] 6. The above photonic integrated circuit Phase matching state of the above nonlinear portion, The center frequency of the portion of the above wave that includes the output wave, The carrier-envelope offset frequency of the above output wave, The free spectral region of the above resonator, Spectral response of a resonator A device according to any of sections 1 to 5, further comprising one or more actuators 4906 for changing and / or adjusting one or more of the above.

[0131] 7. The actuators described in Section 6, each of which may independently comprise an electro-optic modulator, an electric heater, a thermo-optic heater, or a piezoelectric transducer.

[0132] 8. A device according to any of Sections 1 to 7, comprising multiple OPOs, each of which comprises a nonlinear portion having different phase alignments in different nonlinear processes, for example. In one or more embodiments, different OPOs have different phase alignments. In yet another embodiment, each of these OPOs has multiple portions or ranges of different phase alignments.

[0133] 9. The photonic integrated circuit comprises a switching circuit (e.g., a Mach-Zehnder interferometer (MZI) or a group of MZIs or a network of MZIs) configured to set paths for sending a pump wave to different of the OPOs, thereby causing the outputs of these OPOs, individually or in combination, to include outputs in the range from ultraviolet to mid-infrared wavelengths, as described in Sections 1 to 8.

[0134] 10. Any device from Sections 1 to 9, wherein the photonic integrated circuit comprises an integrated input coupler 3106 and the output comprises an integrated output coupler 3114, and for example, these input and / or output couplers are coupled to the waveguide of the OPO by a gap.

[0135] 11. The input coupler and the output coupler are, individually, any of the devices in Sections 1 to 10, including an insulated coupler 3106, a directional coupler, a Y-connector, a multimode interferometer, or an inverse coupler.

[0136] 12. The devices of Sections 1 to 11, wherein the resonator includes a spiral resonator or a resonator having a length of at least 10 centimeters.

[0137] 13. Any device from Sections 1 to 12, wherein the bandwidth of the above output is at least twice as wide as the input bandwidth of the pump input in Hertz.

[0138] 14. Figure 49a shows an example of the device of Section 1, in which the photonic integrated circuit includes a subcircuit 4900 for the pump, which is configured to output a pump wave including the pulse or frequency comb at the pump repetition rate.

[0139] 15. Figures 49b to e show an example of the device of Section 14, the subcircuit comprising at least one of the following: 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.

[0140] 16. Figures 49b-e, the device of Section 14, wherein the subcircuit comprises one or more actuators 4906, which are operable to adjust at least one of the repetition rate, carrier-envelope offset, intensity, or wavelength of the pump wave.

[0141] 17. Any device from sections 1 to 16, wherein the pulse has a length in the range of 1 to 100 picoseconds, and the OPO generates pulses shorter than 1 picosecond.

[0142] 18. Figure 49f shows an example of any of the devices in Sections 1 to 17, in which the OPO is located inside an integrated laser cavity, or the OPO includes a laser gain element.

[0143] 19. Any device from Sections 1 to 18, wherein the above-mentioned pump pulse or frequency comb is generated inside the above-mentioned resonator.

[0144] 20. Any device from Sections 1 to 19, wherein the frequency comb of the pump described above does not constitute pulses in the time domain, or includes a continuous wave frequency modulated wave.

[0145] 21. Figures 49f to 49g illustrate any of the devices in sections 1 to 20, wherein the circuit has additional components at the output of the OPO, and these additional components are: Nonlinear component 4910 for wavelength conversion, Nonlinear component 4910 for spectral broadbanding, Linear components such as filters and couplers, Actuators such as electro-optic modulators Includes.

[0146] 22. A computer system, measurement system, or communication system that includes any of the devices described in Sections 1 to 21.

[0147] 23. Each of the above OPOs comprises the above resonator, which comprises a waveguide coupled to the above nonlinear portion, and the waveguide and the above nonlinear portion are selected such that the pump wave and the waves generated within the OPO have a spectrum centered before and after the half harmonics of the pump, resulting in near-zero group velocity mismatch (e.g., mismatch of less than 20% of the group velocity of the bulk material at the same wavelength) and near-zero group velocity dispersion (e.g., less than 20% of the group velocity of the bulk material at the same wavelength) (e.g., the geometry of the cross section that defines the dispersion). The distribution is designed to have a specific shape, so that the pulses of the pump wave and the wave containing the half-harmonics completely (or at least 90%) overlap (the temporal envelope of the half-harmonics is entirely within the temporal envelope of the pump wave, or at least 90% of the temporal envelope of the half-harmonics overlaps with the temporal envelope of the pump wave), the nonlinear parts are phase-matched in the degenerate operation of the OPO, and the nonlinear process converts the pump wave into the wave containing the half-harmonics. A device according to any of sections 1 to 22, wherein each of the above inputs and outputs is equipped with a coupler designed as a frequency-selective coupler, thereby enabling resonance only before and after the above half-harmonics.

[0148] 24. The device of Section 23, wherein each of the couplers comprises an input waveguide separated by a gap from a portion of the waveguide of the OPO, and each of the input waveguide and the portion of the waveguide of the OPO has a width that gradually changes along its entire length, thereby the input coupling the pump wave into the cavity, and the output coupler coupling the signal including the half-harmonics or output frequency comb out of the cavity.

[0149] 25. The device of Section 23, wherein the pump has energy exceeding the value that causes the OPO to transition from an incoherent operating regime to an ultra-broadband coherent regime, and the value is representative of operation far above (more than 5 times) the oscillation threshold of the OPO.

[0150] 26. Each of the above OPOs comprises the above resonator, which comprises a waveguide coupled to the above nonlinear portion, and the waveguide and the above nonlinear portion are designed to have a geometric shape such that the pump wave and the waves generated in the above OPO include a signal wave or idler wave, and there is a near-zero group velocity mismatch (e.g., a mismatch of less than 20% of the group velocity of the bulk material at the same wavelength) and a near-zero group velocity dispersion (e.g., less than 20% of the group velocity of the bulk material at the same wavelength), so that the pulses of the pump wave and the signal wave or idler wave completely (or at least 90%) overlap (the temporal envelope of the signal wave is completely within the temporal envelope of the pump wave, or at least 90% of the temporal envelope of the signal wave overlaps with the temporal envelope of the pump wave), The above nonlinear parts are phase-matched in the degenerate, non-degenerate, frequency up-conversion, or frequency down-conversion operation of the above OPO, and the above nonlinear process converts the pump wave into the signal wave and / or idler wave. The devices of Sections 1 to 22, wherein each of the above inputs and outputs comprises an adiabatic coupler designed as a frequency-selective coupler, allowing only the resonance of waves having wavelengths in the ultraviolet to mid-infrared range that generate an output frequency comb extracted by the above output.

[0151] 27. Each of the above-mentioned insulated couplers comprises an input waveguide separated by a gap from a portion of the waveguide of the OPO, and each of the above-mentioned input waveguide and the portion of the waveguide of the OPO has a gradually changing width and phase mismatch along its entire length, thereby the input coupling the pump wave into the cavity, and the output coupler coupling the signal including the half-harmonics or output frequency comb to the outside of the cavity. The device in Section 26.

[0152] 28. Any device from Sections 1 to 27, wherein the resonator comprises a waveguide that forms a cavity with reflectors 3106, 3114 (e.g., couplers) or mirrors (e.g., couplers) as boundaries.

[0153] 31. Any device from Sections 1 to 28, wherein the above-mentioned wave includes an electromagnetic wave or electric field having a wavelength in the range from ultraviolet wavelengths to mid-infrared wavelengths.

[0154] 32. Any device from Sections 1 to 31, wherein each of the above-mentioned optical parametric oscillators (OPOs) is an optical resonator having parametric nonlinearity.

[0155] 33. Any device from Sections 1 to 32, wherein at least one of the free spectral region or one of the harmonics of said free spectral region matches the pump repetition rate or its harmonics, so that NxFSR = MxFSR (where N and M are non-zero positive integers), and any harmonic of FSR can match any harmonic of RR, the simplest case being M=N=1. FSR is the free spectral region, and RR (repetition rate) is the pump repetition rate.

[0156] 34. A device according to any of Sections 1-33, wherein the distributed design includes creating a specific cross-sectional geometric shape to provide appropriate group velocity dispersion (such as in Figure 5 or Figure 30b).

[0157] 35. Any device from Sections 1 to 34, wherein the electro-optic comb source includes a modulator, which can be realized by depositing a metal on lithium niobate or on a thin layer of dielectric deposited on lithium niobate.

[0158] 36. Any of the devices in Sections 1 to 35, wherein the resonator includes a ring resonator.

[0159] Figure 51 shows how to operate the device, and this method includes the following steps.

[0160] How to operate Block 5100 represents pumping one or more OPOs with a pump wave, each of which comprises one or more nonlinear portions 110, 3110 as part of resonators 3112, 112 (having waveguides 113, 3113), or coupled to resonators having a free-spectrum region, wherein at least one of the free-spectrum region or one of its harmonics (harmonics of the free-spectrum region) is matched with the pump repetition rate or at least one of its harmonics (e.g., equal to or within 10%).

[0161] Block 5102 represents the OPO extracting a portion of the wave generated in response to the pump wave and / or its harmonics (arrow 118 indicates the direction of the extracted wave).

[0162] This method can be implemented using any of the devices described in Sections 1 to 36.

[0163] knot This conclusion concludes the description of preferred embodiments of the present invention. The above description of one or more embodiments of the present invention has been presented for illustrative and explanatory purposes. It is not intended to be exhaustive or to limit the invention to any express form disclosed herein. Numerous modifications and variations are possible in light of the above teachings. The scope of the present invention is intended to be limited not by the detailed description, but rather by the claims appended herein.

Claims

1. A device comprising a photonic integrated circuit, wherein the photonic integrated circuit comprises one or more optical parametric oscillators (OPOs), and each of the OPOs is Input and One or more nonlinear parts, It comprises one or more outputs, The input is configured to receive a pump wave containing pulses or frequency combs at a pump repetition rate. The one or more nonlinear portions are part of a resonator having a free spectral region, or coupled to a resonator having a free spectral region, and at least one of the free spectral region or one of the harmonics of the free spectral region is matched with the pump repetition rate or the harmonics of the pump repetition rate. The one or more outputs are configured to extract a portion of the waves generated by the OPO in response to the pump wave. device.

2. The device according to claim 1, wherein each of the nonlinear portions is phase-matched in one or more nonlinear optical processes, the one or more nonlinear optical processes include degenerate optical parametric amplification, non-degenerate optical parametric amplification, upconversion of the wave in the OPO, downconversion of the wave in the OPO, and spectral broadbanding of the wave in the OPO.

3. The device according to claim 2, wherein the phase matching is achieved by pseudo-phase matching.

4. The device according to claim 1, wherein the nonlinear portion and / or other portions of the resonator are dispersedly designed to adjust the spectrum of one or more waves generated within the OPO.

5. The device according to claim 4, wherein the distributed-designed OPO supports the formation of a time soliton.

6. The aforementioned photonic integrated circuit Phase matching state of the aforementioned nonlinear portion, The center frequency of the portion of the wave that includes the output wave, The carrier-envelope offset of the output wave, The free spectral region of the resonator The device according to claim 1, further comprising one or more actuators for changing and / or adjusting one or more of the following.

7. The device according to claim 6, wherein the actuator comprises at least one of an electro-optic modulator, an electric heater, a thermo-optic heater, or a piezoelectric transducer.

8. The device according to claim 1, comprising a plurality of the OPOs, each of which comprises the nonlinear portion having different phase matching in different nonlinear processes.

9. The device according to claim 8, wherein the photonic integrated circuit further comprises a switching circuit configured to set paths for sending the pump wave to different OPOs, so that the outputs of the OPOs, individually or in combination, have outputs in the range from ultraviolet to mid-infrared wavelengths.

10. The device according to claim 1, wherein the photonic integrated circuit comprises an integrated input coupler, and the output comprises an integrated output coupler, each of which independently includes an adiabatic coupler, a directional coupler, a Y-shaped junction, a multimode interferometer, or an inversely designed coupler.

11. The device according to claim 1, wherein the resonator includes a spiral resonator or a resonator having a length of at least 10 centimeters.

12. The device according to claim 1, wherein the bandwidth of the output is at least twice as wide as the input bandwidth of the pump input in Hertz units.

13. The device according to claim 1, wherein the photonic integrated circuit includes a subcircuit for a pump, the subcircuit is configured to output the pump wave, which includes the pulse or the frequency comb, at the pump repetition rate.

14. The device according to claim 13, wherein the subcircuit 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 device according to claim 13, wherein the subcircuit comprises one or more actuators, the actuators being operable to adjust at least one of the repetition rate, carrier-envelope offset, intensity, or wavelength of the pump wave.

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

17. The device according to claim 1, wherein the OPO is located inside an integrated laser cavity, or the OPO includes a laser gain element.

18. The device according to claim 1, wherein the pulse of the pump wave or the frequency comb is generated inside the resonator.

19. The device according to claim 1, wherein the frequency comb of the pump wave does not constitute a distinct pulse in the time domain, or includes a frequency-modulated wave of a continuous wave.

20. The photonic integrated circuit comprises an additional component at the output of the OPO, and the additional component is Nonlinear components for wavelength conversion, Nonlinear components for spectral broadbanding, Linear components such as filters and couplers, Actuators such as electro-optic modulators The device according to claim 1, including the device described in claim 1.

21. A computer system, a measurement system, or a communication system comprising the device described in claim 1.

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