1. Introduction

Optical frequency combs with a wide mode spacing have a high power per mode, and each mode can be resolved with diffraction gratings or optical filters, which is essential for applications such as mode-resolved direct frequency comb spectroscopy [1,2] and line-by-line arbitrary optical waveform synthesis [3]. In particular, the wavelength calibration of astronomical spectrographs is expected to lead to breakthroughs in exoplanet exploration and cosmological research by improving the precision of radial velocity (RV) measurement [4,5]. RV measurement using the Doppler shift of the stellar spectrum is known as the “Doppler method” [6] and was used in the discovery of the first exoplanet around a Sun-like star [7]. In addition to the exoplanet exploration, highly precise RV measurement is expected to realize the direct verification of accelerating expansion of the universe [8,9] and the stability test of fundamental constant [10,11], and for these goals, wavelength standards with higher precision are needed to improve the RV measurement precision. For example, a few cm/s precision maintained over several years is needed to find Earth-like exoplanets with the Doppler method [12,13], and a few cm/s precision maintained over a few decades is needed to verify accelerating expansion of the universe [14]. Such precision is difficult to achieve with conventional wavelength standards such as Th-Ar lamps and iodine cells because of their ununiform line spacing and intensity. To cope with this situation, an optical frequency comb or “astro-comb,” has been proposed and developed as the wavelength standard for RV measurement [13,15–35].

Astro-combs require a mode spacing several times wider than a resolution of a high-dispersion spectrograph (>10 GHz) and broad spectral coverage that depends on the celestial body being observed. A frequency comb with a wide spacing needs a high average power to obtain the pulse energy required for spectral broadening due to nonlinear optical effects. In addition, the development of astro-combs is made more difficult because they must be robust and durable for long-term remote operation at observatories. The scheme frequently employed for astro-combs involves increasing the sub-GHz mode spacing of a mode-locked laser to more than 10 GHz using mode-filtering cavities [13,16–18]. The advantages of this scheme are that it is relatively easy to achieve self-referencing and obtain 100 fs-level optical pulses. There are two main methods for obtaining a wide comb spacing over a wide wavelength range using mode-filtering optical cavities; one is to broaden the spectrum before filtering [29], and the other is to broaden it after filtering [19,32]. The latter method is used in this study. The difficulty with the latter method is that unnecessary modes attenuated by the optical cavities are revived through the spectral broadening process [19,20]. On the other hand, there have been reports of astro-combs generated by modulating a CW laser with electro-optic modulators [21–24] and by the Kerr effect in a micro-cavity [25,26] as ways of directly realizing combs with a mode spacing exceeding 10 GHz but without mode-filtering cavities.

The spectral range of the astro-comb is also important. The wavelength most often used in the RV measurement of celestial bodies is the visible region where there are abundant atomic absorption lines. Ytterbium (Yb) doped-fiber-laser-based [27,28], and the titanium-sapphire-laser-based [29–31] combs have been reported as schemes for obtaining visible broadband astro-combs, because of their short wavelength and high output power. In particular, Yb-fiber-based astro-combs have produced actual results, and combs have been reported with a mode spacing of 18 GHz or 25 GHz and a wavelength coverage of 455 nm-691 nm [32]. This coverage reaches 48 % of the visible region, and RV measurement precision at the 1 cm/s level has been reported. Note that we define the visible wavelength region as 360 nm-830 nm in this paper.

In this paper, we describe an astro-comb scheme that combines a robust erbium (Er) comb, Fabry-Perot resonators (cavities) for mode-filtering, spectral broadening with highly nonlinear fiber (HNLF) and multi-order harmonic generation with a chirped periodically-poled lithium-niobate waveguide (cPPLN-WG), and a wavelength-stabilized laser. We have achieved unprecedented spectral coverage while ensuring a sufficient mode-spacing frequency and unnecessary-mode suppression ratio (UMSR). We also discuss the possibility of spectral extension to all visible wavelengths.

2. Overview of comb system

Figure 1(a) shows an overview of the broadband, visible, and wide-mode-spacing comb system. We employ an Er-doped-fiber-based mode-locked laser as the comb source. Its carrier-envelope offset frequency ($f_\text {CEO}$) and repetition frequency ($f_\text {rep}$) were phase-locked to reference frequencies from an atomic clock. Comb modes have been filtered with Fabry-Perot optical cavities since the early days of astro-comb research [16]. Methods have been proposed for filtering out the broadband optical frequency comb generated by a mode-locked laser [13,30], and to further broaden the filtered comb with a highly nonlinear fiber [33]. For its further development, methods for avoiding the degradation of side-mode suppression caused by nonlinear processes in broadband comb extraction by using phase conjugate cavity pairs [35] and by using multiple low-finesse cavities in series [18] have been reported. In this study, we used three Fabry-Perot cavities to increase the comb mode spacing to 30 GHz by tuning one of the 130 comb modes to the cavity transmission mode frequency and suppressing the power of other unnecessary comb modes. Using three Fabry-Perot cavities, the comb mode-spacing was increased to 30 GHz by matching one of every 130 modes of the comb to the cavity transmission mode frequency and suppressing the power of other unnecessary comb modes. Here, we used a wavelength-stabilized laser to stabilize the lengths of three Fabry-Perot cavities and successfully extract desired comb modes at 30 GHz intervals with good reproducibility. The comb was amplified with two polarization-maintaining Er-doped fiber amplifiers (EDFAs) inserted between the cavities, and then the comb spectrum was broadened in the infrared region with a polarization-maintaining HNLF [36]. We then input the broadband comb into a cPPLN-WG; the second to fourth-order harmonic generation processes converted the comb in the infrared region into a broadband comb in the visible region. This is an evolution of the previous high-order harmonic generation of frequency combs [37–40]. For details of each part, see Supplement 1.

 

Fig. 1. Experimental schematic of an Er-fiber-based visible-broad frequency comb with a 30 GHz mode-spacing. (a) Schematic of the comb system. (1) $f_\text {rep}$ and $f_\text {CEO}$ are stabilized to reference frequencies by controlling an intracavity piezoelectric-transducer and the pump power for the mode-locked laser, respectively. (2) The beat note between the wavelength-stabilized laser and the comb is fed forward to an acousto-optic modulator (AOM) to match the frequency-shifted wavelength-stabilized laser to the comb-mode frequency. We call this frequency-shifted light a reference laser. (3) The wavelength-stabilized laser is phase-modulated with an electro-optic modulator (EOM). (4) The lengths of three mode-filtering cavities are stabilized to the frequency-shifted wavelength-stabilized laser with a Pound-Drever-Hall scheme. BPF, electrical bandpass filter, EDFA, Er-doped-fiber amplifier, H, half-wave plate, Q, quarter-wave plate, P, polarizer, PM, polarization-maintaining, NDF, normal-dispersion fiber, SMF, single-mode fiber, HNLF, highly non-linear fiber, cPPLN-WG, chirped-periodically-poled lithium niobate waveguide. (b) Frequency relation between the comb modes, the transmission modes of the mode-filtering cavities, and the reference laser in the optical frequency domain.

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Figure 1(b) shows the frequency relationship between the comb modes, the transmission modes of the mode-filtering cavities, and the wavelength-stabilized laser. The $f_\text {rep}$ and $f_\text {CEO}$ of the comb source were stabilized at 230 MHz and 30 MHz, respectively. The wavelength-stabilized laser was frequency-stabilized to a $^{13}$C$_2$H$_2$ absorption line at a wavelength of 1542 nm ($\nu _1 + \nu _3$ $P(16)$) [41]; not referring to the comb. The output of the laser wave was divided into two parts; one of which was used for beat detection with the comb. The other was frequency-shifted with an acousto-optic modulator (AOM), phase-modulated with an electro-optic modulator (EOM) for Pound-Drever-Hall locking [42] and used for the length stabilization of mode-filtering cavities. Here $f_\text {CEO}$ and $f_\text {rep}$ were set so that the beat frequency ($f_\text {beat}$) between the wavelength-stabilized laser and the nearest comb mode was approximately 40 MHz. The laser frequency output from the AOM was feed-forward controlled [43] to match one of the comb mode frequencies by applying the $f_\text {beat}$ signal to the AOM. This frequency-controlled laser was used as a “reference laser” for the three mode-filtering cavities. The cavity lengths were controlled to allow the reference laser to transmit. We set the free spectral ranges (FSRs) of the three cavities at approximately 2.00 GHz ($130f_\text {rep}/15$), 1.77 GHz ($130f_\text {rep}/17$), and 2.14 GHz ($130f_\text {rep}/14$), respectively. The combination of these FSRs resulted in a high UMSR after the comb had passed through the three cavities connected in series. The resultant transmitted comb mode spacing was approximately 30 GHz ($130f_\text {rep}$), and the calculated UMSR was more than 60 dB at a finesse of 100 (see Fig. 3). During the cavity locking procedure, we scanned the optical cavity length and observed the transmitted reference laser power and the total transmitted comb power simultaneously; we locked the cavity mode with the maximum total transmitted comb power to the reference laser wavelength. Thus, the FSR of the optical cavity was closest to the rational multiple of $f_\text {rep}$; a high transmittance over a broad spectral region was obtained for the extracted comb modes.

3. Spectral range

We employed chirp-pulse amplification [44] to obtain optical pulses with sufficient peak power for spectral broadening using a 205 cm-long HNLF. As shown in Fig. 1(a), 70 % of the output from the mode-locked laser was first highly chirped using a 15 m-long normal-dispersion fiber (NDF), and then passed through three cavities and two EDFAs in the order shown in the figure. The temporal pulse width stretched with the NDF was gradually compressed with anomalous-dispersion fibers used in the mode-filtering and amplification parts. Then, the temporal width of the pulses was compressed so that it was chirp-free by using an anomalous-dispersion polarization-maintaining single-mode fiber (PM-SMF) after the third cavity. The temporal width of the pulse measured with frequency-resolved optical gating (FROG) was 180 fs. From the average power of 880 mW, the peak power was estimated to be 0.13 kW. The compressed 30 GHz-repetitive optical pulse train was incident into the HNLF to broaden the spectrum in the near-infrared region.

Figure 2(a) shows the spectra of the 30 GHz pulse trains at the HNLF input (solid black line) and output (solid red line). The spectrum at the output of the HNLF calculated with the split-step Fourier method is also shown in Fig. 2(a) (dashed blue line). The measured and calculated spectra were in good agreement. See Supplement 1 for details of the simulation. Figure 2(b) shows comb-resolved spectra at 1550 nm observed with a high-resolution optical spectrum analyzer (OSA) at the HNLF input (black line) and output (red line). The contrast was approximately 55 dB at the input and 40 dB at the output. Thus, we observed that the spectral contrast at the HNLF output was lower than that at the input. The spectra were also observed in the 1350 nm-1400 nm, 1525 nm-1625 nm, and 1650 nm-1700 nm ranges, where similar mode-resolved comb spectra were observed. The spectral contrast is discussed in detail in the next subsection.

 

Fig. 2. (a) Comb spectrum in the near-infrared region. The solid black line shows the spectrum of the comb at the HNLF input, shifted by −30 dB. The solid red and dashed blue lines, respectively, show the measured and simulated spectra of the comb at the HNLF output. (b) Spectrum of the comb at the cPPLN-WG output in the visible region. The dotted black line corresponds to the $10^7$ photons per comb mode, which is a sufficient number of photons for use as the wavelength reference by the high-dispersion spectrograph. (c) Comb-resolved spectrum at the HNLF output (1600 nm). (d) Comb-resolved spectrum at the input (black line) and output (red line) of the HNLF (1550 nm). The difference between the center wavelengths of each mode of the two spectra is due to drift in the instrument (OSA). (e) Comb-resolved spectrum at the HNLF output (1350 nm). (f) Comb-resolved spectrum at the output from a cPPLN-WG.

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The broadband comb in the near-infrared region broadened with the HNLF was incident in a 10 mm-long cPPLN-WG to generate the second to fourth-order harmonics; the infrared comb was converted into broadband combs in the visible range. The cPPLN-WG had a poling period that varied linearly from 19.4 µm (input) to 12.8 µm (output) and was designed to satisfy the quasi-phase-matching condition of the second harmonic generation from the wavelength range 1350 nm-1600 nm to 675 nm-800 nm. More detailed information about the cPPLN-WG is provided in Supplement 1. The average power incident into the cPPLN-WG was 700 mW; the power per mode of the incident comb exceeded 10 µW in the design wavelength range of the cPPLN-WG.

Figure 2(c) shows the spectrum of the broadband comb output from the cPPLN-WG observed with an OSA (solid green line) through a multi-mode fiber (core diameter: $\sim$50 µm). Figure 2(d) shows the spectrum at a wavelength of 800 nm with high resolution that we observed in the same way, and we obtained well-resolved comb modes. The CCD image sensor used in the high-dispersion spectrograph in which the comb system will be installed begins to saturate when the number of photons detected per pixel reaches $10^5$ [45]. Considering the pixel area, the imaging area of the comb, quantum efficiency of the sensor and optical coupling, the signal begins to saturate when the photon number of the comb mode reaches $10^8$. We assume that the spectrograph can use a comb mode as a wavelength reference if the mode has 1/10 of the saturation photon number at an exposure time of 1 s. In other words, we defined the available wavelength range in which we can obtained $10^{7}$ photons/(s$\cdot$mode). Then, the available harmonic component ranges are 664 nm-873 nm, 453 nm-543 nm, and 350 nm-408 nm, as shown in Fig. 2(c). The available wavelength coverage of the obtained comb reaches approximately 62 % of the visible wavelength region in the frequency domain when the visible region is defined as 360 nm-830 nm. This is the best coverage for a visible-range comb with a mode spacing in the 30 GHz class.

4. Spectral contrast

For precise RV measurement with high-dispersion spectrograph, the imaged comb-spectrum must have a high contrast. The spectral contrast is primarily determined by the quantity of amplified spontaneous-emission (ASE) and the UMSR; the effect of ASE is not negligible for spectral observation with a spectrograph due to its wide resolution bandwidth. In this study, we assume that the noise in the visible region that originated from the near-infrared ASE is sufficiently suppressed thanks to the placement of the final optical cavity after the final EDFA, in addition to the weak temporal overlap between the ultrashort optical pulses and the ASE. Therefore, we considered that the UMSR was the dominant factor determining the contrast. We measured the UMSR of the comb at the HNLF input, the HNLF output, and the cPPLN-WG output using a CW laser as a probe. For details of the measurement procedures, see Supplement 1.

Figure 3 shows the observed UMSR of the comb at the HNLF input (1542 nm, open blue circles), the HNLF output (1542 nm, filled red circles), and the cPPLN-WG output (514 nm, green diamonds). The light blue line shows the UMSR of the comb output from three mode-filtering cavities, which is calculated from the ratio of the cavity FSRs to the comb $f_\text {rep}$ and the finesse of the cavities ($\sim$100). This is almost equivalent to the observed USMR of the comb at the HNLF input. When the order of a certain transmitted mode is considered to be zero, the comb modes with orders of integer multiples of 130 are transmitted modes, and the others are unnecessary modes. In each wavelength range, the UMSR can be determined by measuring the suppression ratio from mode order 0 to 65 due to the symmetry of the transmittance of the Fabry-Perot cavity. The measured minimum UMSR of the comb at the HNLF input was $\sim$65 dB at a wavelength of 1542 nm, which agreed well with the calculated value. The minimum UMSR of the comb at the HNLF output at 1542 nm was degraded to $\sim$40 dB. The minimum UMSR at 1350 nm was $\sim$37 dB. It is known that the self-phase modulation induced in the HNLF reduces the UMSR [19,20]; a degradation of 20 dB-25 dB was observed here. This is consistent with the degradation in the suppression ratio observed in the spectrum of the comb at the HNLF input and output shown in Fig. 2(b). For the comb output from the cPPLN-WG, only the five signals with low UMSRs could be measured since the signal-to-noise ratios (SNRs) of the beat signals at 514 nm were low. The minimum UMSR was $\sim$40 dB. We did not observe any significant degradation of the UMSR in the harmonic. Therefore, we believe that a UMSR level ($\sim$37 dB) similar to that in the fundamental comb is obtained at other visible wavelengths.

 

Fig. 3. Unnecessary-mode suppression ratio of infrared and visible combs. Unnecessary-mode suppression ratio (UMSR) measured from the SNR of the beat signals between a probe laser and the modes of (A) comb input to the HNLF (1542 nm, open black circles), (B) comb output from the HNLF (1542 nm, filled red circles), (C) comb output from the HNLF (1350 nm, green triangles), and (D) comb output from the cPPLN-WG (514 nm, blue diamonds). A continuous-wave laser (1542 nm, 1350 nm, and 514 nm) was used as the probe by sweeping a range of $\sim$20 GHz. The black chain, dashed red, green chain, and solid blue lines show the measurement limits of the UMSRs for (A), (B), (C), and (D), respectively, which are limited by the SNR of each beat signal. (E) The gray line shows the transmittances of comb modes calculated from the designed finesses of the three optical cavities and the ratios of the FSRs of the cavities to the comb’s $f_\text {rep}$.

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The exhaustive UMSR measurements of the comb can precisely evaluate the spectral shape of the 30 GHz-spacing comb observed by the spectrograph in advance. When comb spectra are imaged using a spectrograph, the asymmetry of the unnecessary modes on the short and long wavelength sides of the transmitted modes causes shifts in the spectral positions of the optical comb modes, resulting in RV measurement errors. In particular, the asymmetry causes a significant error when the suppression ratio is low. Here, we calculated the spectral center-of-gravity shifts of the transmitted modes imaged on the spectrograph [19] by assuming that the shifts are caused by the power difference of 0.5 dB (about 10 %) of $\pm 9$th-order unnecessary-mode pairs (40 dB at 514 nm and 37 dB at 450 nm, respectively), which have the lowest suppression ratio of the unnecessary modes near the transmitted modes. As a result, the estimated frequency shifts were 24 kHz and 48 kHz, respectively. These correspond to RV shifts of 1.2 cm/s and 2.2 cm/s for the Doppler method in the 514 nm and 450 nm wavelength regions, respectively, which are sufficiently small for most astronomical applications.

5. Spectral stability and device durability

First, we investigated the long-term spectral stability of the broadband 30 GHz-spacing comb in the visible range. Figure 4(a) shows spectra obtained at 4 h intervals over 36 h, and there was no significant change in the comb spectrum. Even after more than a year of intermittent use, there was no noticeable change in the output spectrum. In this system, much of the optical system is composed of polarization-maintaining fibers, which suppress temporal fluctuations in the spectrum due to changes in the polarization state caused by environmental changes such as variations in temperature and atmospheric pressure.

 

Fig. 4. Long-term stability of comb spectrum. (a) Spectrum of a broadband comb in the visible range with a mode-spacing of 30 GHz recorded every 4 hours for 36 hours. The spectral shape is almost unchanged. (b) The spectrum recorded with 29-month interval.

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Next, we discuss the durability of the optical devices. Compared with frequency combs based on solid-state lasers such as titanium sapphire lasers, fiber-laser-based combs are robust, almost maintenance-free, and have excellent long-term functionality. In particular, Er-doped-fiber-laser-based optical combs have been widely studied [46–48]. It is also important to remember that the durability of the optical devices depends on the broadband comb generation scheme in the visible region. In this study, HNLF and the ridge-type cPPLN-WG, which are known for their high durability, are responsible for the spectral broadening and wavelength conversion of the comb, respectively. As a result, the generated visible comb power is less than 100 mW for all wavelengths (360 nm-830 nm); there is a low risk of green-induced infrared absorption and other phenomena that can cause damage to nonlinear optical crystals. Figure 4(b) shows the spectrum of the broadband 30 GHz-spacing comb in visible range measured 29 months after Fig. 4(a) was measured. During the 29 months (total operating time: over 6000 hours), we operated the EDFA #3 only at night and at slightly weaker pump power compared to the maximum power to extend the lifetime of the EDFA. The EDFA was operated at the power also in the measurement of Fig. 4(b) and this probably resulted in a slightly narrower spectral range at the HNLF output. On the other hand, there is no noticeable decrease of the spectral power density in visible, which indicates there is no decrease in wavelength conversion efficiency due to the degradation of the cPPLN-WG. The total power calculated by integrating the spectral power density in visible increased from 22.4 mW to 84.5 mW. This is because the spectral power density in the wavelength range satisfying the phase matching condition of the cPPLN-WG increased due to the narrower spectral range of the near-infrared comb at the cPPLN-WG input. These results shows that there is no degradation of the HNLF and cPPLN-WG for at least the 6000 hours of operation, and we can expect the system to operate for a longer period of time without their replacement.

6. Discussions

It is important to discuss the possibility of generating a 30 GHz-spacing comb over almost the entire visible wavelength region with minor modifications to the parameters used in the abovementioned scheme. Specifically, we assume the following changes. (1) Increase the output power of EDFA #3 to broaden the output spectrum from HNLF. (2) Extend the chirp range of the poling period of the cPPLN-WG to match the infrared spectrum of the comb output from the HNLF.

Here, we estimate how broad a spectrum can be achieved by the above improvements. Considering the available wavelength range of the third harmonics, which has the lowest power among the harmonics generated in this study (Fig. 2(b)), the power at the short wavelength end (453 nm) appears to be limited by the fundamental comb power (40 µW per comb mode at 1359 nm). Thus, we assumed this power per comb mode as a requirement for high harmonics generation. On the other hand, the long wavelength end (543 nm) in this work seems to be limited by the design of the cPPLN-WG, which can be improved through its design optimization. Figure 5 shows simulation results revealing the way in which the spectrum of the comb output from the HNLF changes when the average power of the optical pulses input to the HNLF can be increased without changing the HNLF or the spacing frequency (30 GHz) of the comb used in this study. The HNLF length was adjusted to the value where the calculated spectrum was broadest for each power. In the simulation, when the average power input to the HNLF was 3 W, the wavelength range at which the power per mode of the output comb exceeded 40 µW increased to 1279 nm-1761 nm. By designing the cPPLN-WG to satisfy the phase-matching condition in this wavelength range, the available spectral range of the second, third, and fourth harmonics were estimated to be 640 nm-881 nm, 426 nm-587 nm, and 320 nm-440 nm, respectively, which corresponds to 91 % of the frequency range in the visible wavelength region if the second-order supercontinuum processes with PPLN work as they do here.

 

Fig. 5. Measured and simulated spectra of comb output from HNLF. The current spectrum of the broadband comb in the near-infrared range and the simulated spectra that would be obtained were the output power from the final-stage EDFA to be enhanced. The HNLF length was optimized for each condition.

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Our comb improves the precision of RV measurement and will contribute to the exploration of Earth-like exoplanets, the direct verification of the accelerating expansion of the universe, the stability testing of fundamental constants, and thus to our understanding of the origin of the solar system and the universe. The spectrum of our comb reaches below a wavelength of 350 nm, which is shorter than previously reported, and a visible wavelength coverage of 62 % is achieved. Moreover, the simulation shows the possibility that 91 % coverage can be achieved by increasing the output power of EDFA #3. Therefore, our comb can cover the wavelength range of the absorption lines called the Lyman-alpha forest, which is important as a probe of the acceleration of cosmic expansion. We can obtain information about the history of cosmic expansion by precisely measuring the time variation of the redshift of the Lyman-alpha forest observed in the spectrum of light from distant quasars [9,14]. Our comb can directly calibrate the spectrograph over a wide wavelength range of the Lyman-alpha forest and is therefore expected to statistically improve the precision of RV measurements by increasing the number of absorption lines available for observation. The ability to measure the time evolution of the redshift over a wide redshift range (i.e., the age of the universe) would provide direct verification of the accelerating expansion of the universe. In addition, our comb will provide long-term stable operation and long durability and will contribute significantly not only to the verification of the cosmic accelerating expansion, which requires observations of the order of decades mentioned above, but also to Earth-like exoplanet exploration [12,13] and testing the stability fundamental constants [10,11].

7. Summary

In summary, we realized a broadband frequency comb in the visible range based on an Er-doped fiber laser for the wavelength calibration of a high-dispersion spectrograph for astronomical observations. The mode spacing, available spectral coverage, and spectral contrast of the realized comb exceeded 30 GHz, 62 % of the visible wavelength region, and nearly 40 dB, respectively. The results also showed excellent potential as a practical astro-comb for high-precision RV measurements, with a long-term stable spectrum, durable nonlinear optical devices, and easy frequency reproducibility using a wavelength-stabilized laser. Furthermore, simulations showed that if the comb power input into the HNLF were increased to 3 W, the spectrum of the output comb would cover 91 % of the visible wavelength region. This high-performance, easy-to-use, broadband, visible, and wide-mode-spacing comb will be a powerful tool that will encourage the widespread use of astro-combs and to take astronomical research in such fields as exoplanet exploration, the accelerated expansion of the universe, and the stability test of fundamental constants to the next stage. Such combs will open the door to applications where the heterodyne-beat method is inapplicable, as well as provide existing applications with both inspiration and benefit.