1. Introduction

In recent years, the generation of coherent supercontinuum from ultrafast mode-locked lasers has been attracting considerable attention due to its large variety of applications. In many cases, the generated supercontinuum is used for the self-refencing and stabilization of optical frequency combs (OFCs), where octave-spanning spectra are required to detect the carrier-envelope offset frequency (f_CEO) via f-2f interferometry [1–3]. Once stabilized, the resulting low-noise OFCs constitute a crucial tool in spectroscopy, for which a broad spectral bandwidth extending into the mid-infrared is desirable [4–6].

For most applications, increasing the generated spectral bandwidth while decreasing the input power requirement at the same time is of high interest. In this context, the recent progress of nanophotonic technologies has played a major role [7,8]. These platforms have led to the development of highly efficient nonlinear devices reducing the power required for supercontinuum generation (SCG) from hundreds of picojoules inside traditional photonic crystal fibers [9], to few picojoules using nanophotonic waveguides [10,11], and recently hundreds of femtojoule in resonant devices [12]. Besides radically reducing power requirements, the emergence of this new class of nanophotonic devices adds further prospects in the development of fully integrated spectroscopic measurement devices.

Initially, nearly all demonstrations of SCG in integrated devices were relying on third-order nonlinearities, driven inside materials such as silicon nitride [13,14], silicon [15–17], and more recent ones such as germanium-based platforms [18–20]. While χ⁽³⁾-based SCG enables broad bandwidth spanning across several spectral regions, these devices typically operate with hundreds of picojoules and often require a separate second-harmonic generation (SHG) stage when used for f-2f self-referencing. In practice, this SHG stage is challenging to achieve at the typically low generated power levels and represents an added source of experimental complexity.

An alternative approach consists in driving SCG in platforms that exhibit both a χ⁽²⁾ and χ⁽³⁾ nonlinear response. In these devices, the combination of efficient harmonic generation and spectral broadening leads to the formation of supercontinua composed of multiple overlapping combs. This regime offers the possibility to detect the f_CEO beatnotes directly at the waveguide output, which simplifies f-2f detection by eliminating the discrete SHG stage. Previously reported in weakly confining waveguides [21–23], this technique was recently achieved in integrated devices [24–26]. There, the thin-film lithium niobate (TFLN) platform emerged as one of the leading solutions [10,26–28]. However, nearly all works based on TFLN utilize a silica bottom-cladding, which results in high absorption loss beyond 2500 nm and hinders further spectral extension into the mid-infrared region. In contrast, sapphire substrate features high transparency up to 4.5 µm, and thus stands out as a promising alternative to silica for realizing compact and efficient MIR sources [29–31].

In this work, we demonstrate for the first time ultraviolet-to-mid-infrared SCG using TFLN-on-sapphire waveguides, and subsequently show the suitability of this platform for on-chip f_CEO detection. We periodically pole TFLN waveguides to achieve quasi-phase-matched SHG at a fundamental wavelength of 2100 nm, and use geometric dispersion engineering to eliminate leading-order dispersive effects for efficient and broadband nonlinear conversion. We note here that this approach is inspired from previous demonstrations that have used quasi-static nonlinear interactions to achieve efficient SCG [10,11,27]. We further discuss the dispersion engineering design of the waveguides in the next section. As a result, driving the TFLN waveguides with only few picojoules of on-chip pump-pulse energy, we observe saturated SHG that manifests by the onset of spectral broadening for both harmonics. The spectrum of the two combs further broaden as we increase the driving power and merge around 22 pJ of on-chip pulse energy. Using the overlap between these two combs, we detect f_CEO beatnotes directly at the output of the waveguide, showing the spectral broadening mechanism maintains a high degree of coherence across large spectral bandwidths. Furthermore, the high nonlinearities featured by the nanophotonic waveguides enable the generation of multiple higher-order harmonics occurring simultaneously with SHG. Remarkably, with only 10 pJ of input pulse energy, we detect harmonics up to the fifth order. These harmonics exhibit strong spectral broadening with increased pump-pulse energies and finally merge at the -45-dB level for in-coupled pulse energies between 20-25 pJ. To the best of our knowledge, this is the first time that such a high number of harmonics is reported in integrated devices. When pumped at a maximum pulse energy of 45 pJ, these devices achieve a broad supercontinuum extending from 360 nm to 2660 nm. These results have multiple prospective impacts. Besides demonstrating the suitability of the TFLN-on-sapphire platform for self-referencing MIR sources such as Tm-based laser oscillators, this work will open new opportunities to further investigate the underlying physics of broadband high harmonic generation inside nonlinear nanophotonic devices.

2. Design of the waveguides

We first discuss the design criteria of the TFLN waveguides. Recently, a novel approach for efficient and broadband SCG based on saturated second-order nonlinear interactions was presented [27,32]. This work showed that driving phase-matched SHG in nanophotonic waveguides in a regime where leading-order dispersive effects are negligible enables SCG at an unprecedented low pulse energy. Furthermore, they demonstrate that SCG by saturated quasi-static SHG is advantageous for f-2f detection, since the f_CEO beatnotes generated by the overlapping spectra remain in phase across very large spectral ranges. This technique requires the first- and second-order dispersion effects to be negligible. In this perspective, we dispersion engineer the TFLN waveguides through their cross-sectional geometry to minimize both the group velocity mismatch (GVM) and group velocity dispersion (GVD) for a fundamental pulse centered around 2050 nm and its second harmonic. The devices consist of 5-mm long TFLN ridge waveguides with a top width of 1520 nm, a film thickness of 931 nm and an etch depth of 608 nm (Fig. 1(a)). The nominal poling period for quasi-phase-matching (QPM) is 6.30 µm. Figure 1(b) shows the GVM and GVDs as a function of the wavelengths for the waveguide geometry considered here. We observe a zero-crossing of the GVM around 2000 nm and 2250 nm, with the magnitude remaining below 15 fs/mm over more than 360 nm of fundamental bandwidth, between 1910-2275 nm. At the nominal fundamental wavelength of 2050 nm, this waveguide geometry leads to a low simulated GVM of 6 fs/mm, a fundamental GVD of 20 fs²/mm, and second harmonic GVD of <5 fs²/mm. We note here the presence of discontinuities in the dispersion curves around a fundamental and corresponding second harmonic wavelength of 2500 nm and 1250 nm, respectively. This effect is due to an avoided crossing between second harmonic modes at 1250 nm. The periodic poling and subsequent fabrication procedures are similar to the one described in [29]. We fabricate a total of 27 pairs of waveguides with a 10-nm poling period step between each adjacent pair. This way, we cover a total poling period range of 6.30 ± 0.135 µm to compensate for potential fabrication errors. We use temperature for fine tuning of the phase-matching. Each poling region accommodates two adjacent waveguides with similar dimensions, separated by an 8-µm gap that is wide enough to avoid cross talk. While the fabrication yield of the waveguide is close to 100%, we observe significant differences in the quality of the facets, which affects the maximum achievable coupling efficiency. The waveguide used throughout the article achieves 1.5% of coupling efficiency.

 

Fig. 1. (a) Schematic of the waveguide design. (b) Simulated GVM (black, left y-axis) and GVD of the fundamental (blue, right axis) and second harmonic (red, right axis) as a function of the fundamental (bottom axis) and second harmonic (top axis) wavelengths. The presence of an avoided crossing between second harmonic modes at 1250 nm causes discontinuities in the GVM (black) and second harmonic GVD (red).

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3. Experimental setup

The experimental setup is shown in Fig. 2. The fundamental driving pulses are delivered by a synchronously pumped degenerate optical parametric oscillator (OPO), similar to that described in [33]. The spectrum of the driving pulses displays a full-width at half-maximum spectral bandwidth of 130 nm centered around 2090 nm. Assuming transform limited pulses, we estimate the pulse duration from the spectrum to be around 40 fs. We note here that while these waveguides were originally designed to be pumped by a 2050-nm Tm:KYW mode-locked laser, we ultimately used a 2090-nm OPO. This wavelength offset is well covered by the range of available poling periods, and only has minor effects on the SCG dynamics by having a slightly larger GVM than originally designed. The OPO delivers a p-polarized beam with a fixed output power of 300 mW at 100 MHz repetition rate. Reflective filters are used to control the power at the input of the waveguides. The input beam is coupled into the waveguides using a reflective inverse-Cassegrain objective (Thorlabs LMM-40X-P01). While the obscuration of the reflective objective greatly limits the transmission of a Gaussian beam, it offers the advantage of avoiding achromatic and temporal dispersion. The objective transmission (∼15%) and the mismatch between the input beam at the focus and the waveguide mode (∼10% overlap) result in an overall coupling efficiency of ∼1.5%, which limits the maximum on-chip input pulse energy to 45 pJ. A similar objective is used to collect the beam at the waveguides output. In this case, the collection efficiency is only limited by the Cassegrain transmission, and was previously estimated to be around 35% in the 2.0-µm region [30]. For the rest of the paper, the input and output pulse energies are reported directly inside the waveguide. The waveguide chip is mounted on an aluminum holder that is temperature stabilized. The aluminum holder is placed on an XY-axis translation stage controlled by piezo actuators. The longitudinal position of the focus at the input facet of the chip is adjusted by moving the reflective objective along the optical axis of the input beam. During the waveguide alignment procedure, the output modes of the fundamental and second harmonic were imaged on a camera to confirm the excitation of the TE₀₀ mode. To characterize the generated spectrum, we use two different optical spectrum analyzers sensitive between 350-1750 nm (Yokogawa AQ6374) and 1500-3400 nm (Yokogawa AQ6376E), respectively. We verify that the fibers used to couple the light into the spectrum analyzers are transparent over the entire spectral ranges.

 

Fig. 2. Experimental setup.; ND filters, variable neutral density filter; Obj., reflective objective; PP-TFLN., Periodically-poled thin-film lithium niobate waveguide; Flip, flip mirror; LPF, long-pass filter; APD, avalanche photodetector; OSA, fiber-coupled optical spectrum analyzers.

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In the last section, we discuss the carrier-envelope-offset frequency detection. To detect the f_CEO beatnotes, the output of the waveguide is directly focused using the reflective objective onto an avalanche photoreceiver (APD310), which features a sensitivity range between 850-1650 nm. A long pass filter with a cut-off wavelength of 1350 nm is used to limit the detected wavelength range to the overlap region between the first two harmonics, which suppresses saturation due to shorter wavelengths that do not contribute to the f_CEO beatnote.

4. Supercontinuum generation

Figure 3 shows the power spectral density as a function of the input pulse energy. Below 1 pJ, the waveguides are driven in the unsaturated regime, and we observe the formation of a broadband second harmonic centered around 1045 nm. In this unsaturated regime, we measure a distance between the zeros of the second harmonic spectrum of 27 THz, which gives a GVM of nearly 7.5 fs/mm, assuming negligible higher-order dispersion coefficients [34]. Above 3 pJ, we observe the formation of fringes and side lobes centered around the peak of the pump and signal spectra (Fig. 3, spectrum 5 pJ). These features become asymmetric and more finely patterned as we increase the pulse energy. For pump pulse energies in excess of ∼12 pJ, the fundamental spectrum experiences strong broadening towards shorter wavelengths, accompanied with the formation of larger side-lobes (Fig. 3, spectrum 15 pJ). This behavior is characteristic of spectral broadening driven by saturated SHG in presence of negligible group velocity mismatch and group velocity dispersion [32], which is consistent with the waveguides design. The fundamental and second harmonic spectra continue broadening as we increase the pump power, and overlap above the spectrometer noise floor at -55 dB for pulse energies in excess of 22 pJ. At higher input pulse energies, the second harmonic spectrum is notably flat over a large bandwidth and displays a distinctive oscillatory pattern, which is again consistent with spectral broadening based on saturated quasi-static SHG. We note here that while the spectral broadening of the first two harmonics exhibits reasonable agreement with what we expect from our heuristic model [32], we observe an overall factor of two between experiment and theory for the on-chip pulse energy required to achieve SCG. We attribute this discrepancy to a combination between finite poling depth and a deviation of the mean duty cycle from 50%. In these latter cases the effective nonlinear coupling is reduced due to a weaker overlap between the interacting modes, which increases the pulse energy needed to achieve supercontinuum generation by a constant factor.

 

Fig. 3. Generated power spectral density as a function of the on-chip pulse energy. A selection of power spectral densities is plotted in one dimension on top of the graphic to highlight the main features described in the text. The color scale is in dB.

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In addition to the fundamental and second harmonic, we observe the onset of the third, fourth and fifth harmonics with pulse energies as low as 2, 7, and 12 pJ, respectively. These three higher-order harmonics experience a strong spectral broadening and merge with the fundamental and first harmonics between 20-25 pJ of input pulse energy. For pulse energies in excess of 25 pJ, the supercontinuum composed of the five first harmonics continue broadening at a reduced rate. When the pump-pulse energy reaches a maximum of 45 pJ, the generated supercontinuum spans nearly three octaves above the spectrometer noise floor, extending from 360 nm to 2660 nm within a -55-dB dynamic range. It is worth noting that the third and higher harmonics do not feature the oscillatory pattern observed on the first two harmonic spectra, which is expected since the frequency mixings responsible for the presence of higher order harmonics do not achieve quasi-static interactions. A detailed investigation of the physics underlying the nonlinear dynamics is beyond the scope of this paper; it requires consideration of all the possible nonlinear paths, as well as a large set of parameters such as higher-order QPM grating coefficients, the phase-matching of higher-order waveguide modes, or linear coupling between waveguide modes [35]. A theoretical analysis of broadband nonlinear interactions such as SCG and harmonic generation in TFLN waveguides has recently been discussed in [36], using the experimental configuration described here as a case study.

We close this section by commenting on the limit of the generated supercontinuum. While we expect the fundamental harmonic spectrum to broaden symmetrically around the carrier frequency, we observe much greater broadening on its blue tail. As a consequence, the extension of the supercontinuum is restricted on the long-wavelength side below 2700 nm. The effective refractive indices of the fundamental TE and TM modes indicate the presence of a crossing between those two modes. Preliminary investigations show that this crossing may result in a coupling from TE to TM mode that would ultimately restrict the spectral broadening below 2700 nm. We note here that this TE-TM mode crossing is different from the avoided crossing between second harmonic modes previously mentioned (Fig. 1(b)). Another possible reason is the presence of strong variations of the nonlinearity dispersion at large wavelengths. Further investigations will be carried out to confirm these assumptions. Finally, the short-wavelength tail of the supercontinuum nearly reaches the lower bound of the TFLN transparency window.

5. Carrier-envelope offset frequency detection

We use the generated supercontinuum to measure the f_CEO of the driving source. As described in section 3, the fundamental and second harmonic spectra overlap for input pulse energy in excess of 22 pJ. Provided coherent harmonic generation and spectral broadening, the overlapping combs give rise to f-2f beatnotes. Thus, when the overlap between the two combs becomes sufficient, the generated beatnotes can be detected directly at the output of the waveguide. In this experiment, we detect the beatnotes between the fundamental and second harmonic by focusing the waveguide output onto an InGaAs avalanche photodetector (experimental setup Fig. 2). Since we only want to measure the spectral contents contained within the fundamental and second harmonic, we suppress the rest of the supercontinuum using a long-pass filter with a cutoff wavelength of 1350 nm. The InGaAs sensor of the avalanche photodetector filters out wavelengths above 1800 nm. It is worth noting that conventional approaches often require much narrower spectral filtering of few tens of nanometers to obtain sufficiently large f_CEO beatnotes with respect to the f_rep peak [21].

Figure 4 shows the radio-frequency spectrum corresponding to the f-2f beatnotes obtained driving the waveguides with 45 pJ. We observe the presence of four peaks. The highest peak (peak 3) located at 100 MHz corresponds to the repetition frequency of the driving source. The three remaining peaks are f-2f beatnotes. From left to right, these three peaks feature a frequency of 22 MHz, 78 MHz and 122 MHz, which correspond to f_CEO, f_rep-f_CEO and f_rep+ f_CEO, respectively. Remarkably, the intensity of the f-2f beatnotes is only 25 dB below the repetition frequency, which indicates they remain coherent and in-phase across a large overlapping region. This result aligns well with the properties of supercontinuum generation driven by saturated quasi-static SHG [32]. In the current configuration, the f_CEO beatnotes features a signal-to-noise ratio (SNR) of 13 dB in a 10-kHz resolution bandwidth, limited by the noise floor of the avalanche detector. While 13 dB of SNR remains too low for subsequent f_CEO stabilization, the fact they are only 25 dB below the f_rep peak, which also presents a relatively low SNR, indicates further improvement of the detection setup should allow a substantial increase of the beatnotes SNR.

 

Fig. 4. Radio-frequency spectrum measured with 10-kHz resolution bandwidth and acquired using 45 pJ of input pulse energy. From left to right, the frequency of the peaks corresponds to f_CEO, f_rep-f_CEO, f_rep and f_rep+ f_CEO, where f_rep and f_CEO are the repetition rate and carrier-envelope offset frequencies, respectively.

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6. Conclusion

In this paper, we have demonstrated SCG inside TFLN-on-sapphire nanophotonic waveguides. When driven with picojoules of pulse energies, these devices achieve broadband and efficient SHG. At higher input power, a cascade of mixing processes occurs in the waveguide, giving rise to the generation of higher harmonics which merge together and form a broad supercontinuum spanning from ultraviolet to MIR frequency range. This is the first time TFLN-on-sapphire waveguides are used for SCG, and the performances are comparable to state-of-the-art results achieved in conventional TFLN-on-silica devices. Therefore, this work establishes this MIR-compatible platform as a promising solution for efficient and broadband nonlinear interactions with picojoule-level pulse energies. Furthermore, using the broad and coherent overlap between the fundamental and second harmonic combs, we could detect f_CEO beatnotes of the driving source directly at the waveguide output. Thus, we believe this work will open new solutions for self-referencing high repetition rate MIR ultrafast lasers such as Tm-based oscillators, which is of topical interest for applications in research and industry.