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Abstract
We have achieved the simultaneous generation of a 2.6-octave-wide supercontinuum (SC) spectrum over 400–2500 nm and third-harmonic light solely by a dispersion-controlled silicon-nitride waveguide (SiNW). To increase the visible intensity of the SC light component, we fabricated low-loss 5-mm-long deuterated SiNWs with spot-size converters by low-temperature deposition. We succeeded in measuring the carrier-envelope-offset (CEO) signal with a 34-dB signal-to-noise ratio because this short deuterated SiNW provides a large temporal overlap between the f and 3f components. In addition, we have demonstrated this method of CEO locking at telecommunications wavelengths with f-3f self-referencing generated solely by the SiNW without the use of highly nonlinear fiber and an additional nonlinear crystal. Compared with the method of CEO locking with a highly nonlinear fiber and a standard f-2f self-referencing interferometer, this method is not only simple and compact but also stable.
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1. Introduction
Carrier-envelope offset (CEO)-locked optical frequency combs (OFCs) have revolutionized precise optical frequency measurements by making it possible to directly link microwave and optical frequencies [1–3]. Nowadays, they have become indispensable tools in a variety of applications, such as optical frequency metrology [4], optical clocks [5], astronomical observation [6], optical communications [7], low-noise microwave generation [8–11], and LiDAR [12,13]. Furthermore, CEO-locked OFCs integrated on a chip to provide compact and robust systems have great potential for use in various applications such as low-noise microwave generation with an electro-optic modulator [9,10]. For these applications, the use of a single waveguide for both spectral broadening and CEO detection is desired because it eliminates the need for a highly nonlinear fiber and an additional nonlinear crystal. Hartl et al. have demonstrated a fully integrated self-referenced Er-doped fiber frequency-comb system without a highly nonlinear fiber [14], in which they used a single periodically poled lithium niobate (PPLN) waveguide. In general, lithium niobate is suitable for generating a supercontinuum (SC) spectrum because it has a large nonlinear index [15]. However, the signal-to-noise ratio (SNR) of the detected CEO signal with a high-order self-referencing interferometer (SRI) was not sufficient compared with that obtained with a standard f-2f SRI. On the other hand, a simple method with CMOS-compatible materials would be advantageous for both spectral broadening and stabilization of the CEO signal with a chip size. So far, an SC spectrum with more than one-octave bandwidth for an SRI has been generated with Si [16,17] and SiN [18–22] waveguides. In addition, a SiN waveguide (SiNW) has been used to achieve a simple CEO-locked OFC, and a chip-scale f-2f SRI with a SiNW was demonstrated, but the SNR of the detected CEO signal was low [23]. This might be because SiN-based materials are centrosymmetric and their second-harmonic conversion efficiency is very low. Moreover, a very simple and attractive method for f-3f self-referencing directly from a SiNW has been reported [24]. However, CEO signals with a low SNR could not be stabilized. The device design, including the waveguide dimensions and dispersion, was not well optimized for an f-3f SRI, which might require a longer SiNW. This result might be due to the small temporal overlap between the f and 3f spectral components. Therefore, even though the SC spectrum could be generated to detect the CEO signal with an f-3f SRI, the SNR of the CEO signal was less than 30 dB.
Here, we report the demonstration of a simple CEO-locked OFC with f-3f self-referencing directly from a deuterated dispersion-controlled SiNW. We designed low-loss and dispersion-controlled SiNWs by changing their widths and increasing their thicknesses. Using a 1.3-µm-wide, 1.0-µm-thick and 5-mm-long deuterated SiNW, we generated an SC spectrum (400–2500 nm) spanning more than a 2.6-octave bandwidth at a -45-dB level with 422-pJ coupled pulse energy in the TE mode. With this dispersion-controlled waveguide, the intensity of the visible SC light component can be increased. The temporal overlap between the f and 3f components is increased due to the short length of the SiNW. The 2fceo signal with f-3f self-referencing directly from the SiNW was observed with an SNR of about 34 dB and finally stabilized by using a feedback circuit and standard RF signal.
2. Device design concept
We fabricated low-loss 5-mm-long SiNWs with spot-size converters (SSCs) to increase the SNR of the CEO signal with an f-3f SRI. The width and adiabatic taper length of the SSCs are 0.5 and 300 µm. Since the nonlinear interaction length is short enough compared to the device length, the dispersion variation due to the SSC region is negligible. Figure 1(a) shows a schematic view of the SiNW. SiN film was deposited by electron-cyclotron-resonance (ECR)-PECVD at 200 °C. The source gas was hydrogen-free deuterated silane (SiD4). This deposition technique, which we developed previously, avoids the the formation of N-H bonds, which induce strong optical absorption at the pump wavelength of around 1.55 µm. Since the atomic mass of deuterium (D) is larger than that of hydrogen, the absorption band due to newly formed N-D bonds shifts to further beyond 2 µm. A detailed material composition analysis was performed by our group in Ref. [25]. The measured wavelength dispersion curve of a deuterated 100-nm-thick SiN film from 300 to 2500 nm is shown in Fig. 1(b). At the wavelength of 630 nm, the refractive index n of 1.87 is found. We designed the dispersion of SiNWs by varying their width from 1.3 to 2.0 µm and setting the thickness to 1.0 µm. We fabricated 1.0-µm-thick SiNWs to increase their anomalous dispersion regime. The SiNW dispersions were designed so that the pump laser pulse is in the anomalous-dispersion regime [Fig. 1(c)]. Figure 1(d) shows a scanning electron microscopy image of the cross-sectional structure with a width of 1.3 µm. Both sides of the SiNWs are covered by SiO2 cladding, while the upper layer is planarized by chemical mechanical polishing. The calculated SC spectrum dependence on propagation lengths up to 20 mm is depicted in Fig. 1(e). A SiNW width of 1.3 µm and coupled pump pulse energy of 422 pJ with a duration of 74 fs were assumed. For our simulation, we used fiberdesk software [26], which consists of the modeling analysis of the nonlinear Schrödinger equation with the split-step Fourier method. For an efficient f-3f SRI, we found that a sufficient soliton fission effect can be obtained if the nonlinear interaction length exceeds 5 mm. Controlling the wavelength at which dispersive waves (DWs) are generated is also an important design guideline for achieving the CEO signal detection with a higher SNR in an f-3f SRI. For this purpose, we precisely controlled the dispersion by the waveguide width and experimentally searched for the optimal DW generation conditions in the wavelength range of 500 to 550 nm.
Fig. 1. (a) Top view of the incident side of the SiNW (one-step inverse taper waveguide).
(b) Reflactive index (n) of our a l00-nm-thick deuterated SiN film measured by spectroscopy ellipsometry. (c) Dependence of dispersion on SiNW width. (d) Cross-sectional image of a 1.3-µm-wide SiNW. (e) Dependence of the SC spectrum on the SiNW length with 1.3-µm-width using a 422-pJ coupled pulse energy in calculation.
3. Experimental setup
The experimental setup is shown in Fig. 2. We used a passively mode-locked Er-doped fiber laser amplifier system (Menlo Systems GmbH), which delivers 74-fs Lorentz pulses at a repetition rate frep of 250 MHz with a center wavelength of 1560 nm. A laser beam from the Er-doped fiber laser was collimated in free space by a collimating lens and then launched into the SiNWs with typical coupling efficiency of 32% by using an aspherical lens (NA = 0.55) in free space. We experimentally investigated the characteristics of the SC spectrum in SiNWs with a cross section of 1.3–2.0 (width) 1.0 µm (thickness). We found that in calculation, the region of anomalous dispersion of SiNWs can be expanded by increasing SiNW thickness and its wavelength adjusted by changing the SiNWs-width from 1.3 to 2.0 µm as shown in Fig. 1(c). The output spectrum after the SiNWs spans more than a 2.6-octave bandwidth at a -45-dB level when the Er-doped fiber laser with 422-pJ coupled pulse energy in the TE mode is launched into the 1.3-µm-wide and 5-mm-long SiNWs. The pink dashed square in Fig. 2 outlines the SC spectrum measurement setup, which comprises a multimode fiber and three optical spectrum analyzers (Hamamatsu C10083CA, Yokogawa AQ6370D, and Yokogawa AQ6375). With these optical spectral analyzers, the broadband optical spectrum can be measured in the wavelength range from 0.32 to 2.5 µm. The blue dashed square in Fig. 2 shows the CEO detection setup. A transmission grating selects the 533-nm wavelength component from the SC spectrum. The CEO frequency 2fceo from the interference between comb modes 3fn and f3n due to simultaneously generated third-harmonic light and the SC spectrum, respectively, is given by 3fn – f3n =3(nfrep + fceo) - (3nfrep + fceo) 2fceo. The 2fceo signal was measured with a Si avalanche photodiode. Finally, by using the feedback circuit, the 2fceo signal was locked to a 20-MHz sinusoidal wave emitted from the local oscillator synchronized to a GPS signal.
Fig. 2. Experimental setup. PMF : Polarization maintaining fiber. MMF : Multi-mode fiber. OSA : Optical Spectrum Analyzer. PD : Photodetector.
4. Flat spectral broadening with dispersion-controlled SiNWs
Figure 3 shows the dependence of the SC spectrum on the coupled laser pulse energy in the TE mode with a 1.3-µm-wide SiNW. This figure shows the raw data of the SC spectrum without normalization. The SC spectrum widens as the coupled laser pulse energy increases. The SC light is generated mainly by self-phase modulation. An SC spectrum spanning more than one-octave bandwidth is observed at the coupled laser pulse energy of 250 pJ. The DW is generated at the wavelength of about 500 nm from our simulation results. When the coupled laser pulse energy is increased to the maximum of 422 pJ, an SC spectrum is generated with more than 2.6-octave bandwidth, and the SC shape becomes flatter in the visible wavelength region. The high intensity of the visible SC light component shows the possibility of CEO detection with a higher SNR. In our experimental setup, the CEO signal with the highest SNR is observed at 533 nm. The SC intensity at 533 nm becomes only -18 dB lower compared with that at 1560 nm by pumping at coupled laser pulse energy of 422 pJ. Our designed SiNW contributes to generating the flat SC shape due to the optimum dispersion control and low propagation loss. The propagation loss of the SiNW is around 0.5 dB/cm in the telecommunications band of 1.3–1.6 µm. While the fundamental mode of TE polarization is a dominant factor in broadening the SC spectrum, multiple peaks around 500 nm are found for all width parameters in Fig. 4. These multiple peaks may be due to third-harmonic generation to higher-order modes. Another reason for the multiple peaks could be the generation of multiple DWs when TE01 and TE10 modes are excited during the propagation over the SSC region. The latter case is similar to that in Ref. [27], where it was proved that multiple phase-matching conditions should appear when the soliton index matches that of the DWs.
Fig. 4. Dependence of SC spectrum on SiNW width (1.3-, 1.5-, 1.7-, and 2.0-µm) with 422-pJ coupled laser pulse energy in TE mode. The black line shows the spectrum of the Er-doped fiber laser before the SiN waveguide.
Next, we investigated the characteristics of the SC spectrum for SiNWs with widths from 1.3 to 2.0 µm. Figure 4 shows the SiNW width dependence of the SC spectrum when the Er-doped fiber laser was launched into the waveguides at the coupled pulse energy of 422 pJ in the TE mode. The widest SC spectrum spanning with more than 2.6-octave width (400–2500 nm) at a -45-dB level is generated with the 1.3-µm-wide and 5-mm-long SiNW. It is considered that the 1.3-µm-wide SiNW provides strong light confinement owing to its smaller mode area and thus exhibits stronger self-phase modulation. Furthermore, since the anomalous dispersion regime expands to shorter wavelengths with the 1.3-µm-wide SiNW, higher visible intensity of the SC spectrum can be generated. We also observed the polarization dependence of the SC spectrum with a 1.3-µm-wide SiNW (see Fig. 5). The coupling efficiency into the SiNW in the TM mode is about 29%, which is smaller than in the TE mode. We found that the polarization dependence of SC generation is almost the same in both the TE and TM modes.
Fig. 5. Polarization dependence of SC spectrum with the 1.3-µm-wide SiNW at 185-pJ coupled laser pulse energy. The red and blue lines show the TE and TM mode, respectively.
5. CEO locking with f-3f self-referencing directly from a SiNW
SiN is suitable for detecting 2fceo with an f-3f SRI because of its high third-order nonlinearity χ(3). For detecting CEO signals with a higher SNR, we fabricated short-length and dispersion-controlled SiNWs (see Sections 1 and 2). In our experiment, we observed CEO signals at several wavelength components of SC light, indicating that third-harmonic lights were generated at several wavelengths. To investigate which wavelength we should use for obtaining the 2fceo with the largest SNR, we made the SC spectrum monochromatic using a transmission grating and a slit. Then, using an optical signal analyzer (Hamamatsu Photonics C10083CAH) and a Si avalanche photodiode, we measured the wavelength components of the SC light when we obtained the CEO signal with the highest SNR. We found that the largest 2fceo SNR could be obtained in the 533-nm region [see Fig. 6(a)]. Furthermore, to verify that the CEO signal measured in Fig. 6(a) is 2fceo signal from an f-3f SRI, we also performed the measurements with a collinear f-2f SRI. The frequency of fceo measured with the collinear f-2f SRI was half the frequency of the CEO signal measured in Fig. 6(a). Therefore, the CEO signal obtained directly from the SiNW is not fceo but 2fceo. The 2fceo signal was observed with about a 34-dB SNR at the RF spectrum analyzer set to 100-kHz resolution bandwidth. It was reported that large walk-off between the f and 3f spectral components with SiNWs leads to a CEO signal with insufficient SNR [24]. It is therefore important to generate the f and 3f spectra from the SiNW as short as possible. To solve this problem, we used the shortest SiNW as mentioned in Section 1. In our calculation, the walk-off between the f and 3f at 533 nm is estimated to be as small as less than 738 fs. Finally, by using the feedback circuit, the 2fceo signal was locked to a 20-MHz sinusoidal wave emitted from the local oscillator synchronized to a GPS signal. Figure 6(b) shows the stability of 2fceo signals, obtained with a frequency counter at the gate time of 1 s. The 2fceo signals were frequency-stabilized for more than 1 h. Figure 6(c) shows Allan deviations with our f-3f SRI, which is 3.0×10−15 (=1.2 Hz) at gate time of 1 s. The τ-1 dependence of Allan deviation is classified as white phase-modulated noise or flicker phase-modulated noise [28]. We compared the frequency stability of our f-3f self-referencing directly from the SiNW and with that of a highly nonlinear fiber and our collinear 2f-3f SRI [29]. The Allan deviation with the f-3f SRI is half that with the 2f-3f SRI because the CEO signal with f-3f SRI is 2fceo. This result shows that the CEO-locked frequency comb with f-3f self-referencing directly from the SiNW is not only simple and compact, but also can improve the stability of the CEO frequency. Figure 6(d) shows the experimental phase noise of 2fceo signal with f-3f self-reference generated solely by the SiNW. Compared with the phase noise of the CEO signal in the free-running case, that of the stabilized 2fceo signal is reduced at the offset frequency below 20 kHz.
6. Conclusion
By controlling the dispersion in SiNWs, we have experimentally demonstrated 2.6-octave-span SC generation with a 1.3-µm-wide, 1.0-µm-thick, and 5-mm-long dispersion-controlled SiNW. We have achieved a CEO-locked OFC with f-3f self-referencing solely by a SiNW without an external nonlinear crystal. Our simple method will be an important technique for achieving portable and robust CEO-locked OFCs. We hope this method will promote the use of OFCs outside the laboratory and expand their application fields.
Fig. 6. (a) Beat note 2fceo signal with f – 3f self-referencing due to simultaneous SC and third harmonic light. (b) Frequency of 2fceo stabilized to 20 MHz for 3,600 s. (c) Allan deviation of 2 fceo signal with f – 3f SRI and fceo signal with 2f – 3fceo SRI. (d) Experimental phase-noise spectrum with beat note 2fceo signal with f – 3f self-referencing.
Funding
Japan Society for the Promotion of Science (19H02156, 19K15054, 20H00357).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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