A compact green Ti:Sapphire astro-comb with 43-GHz repetition frequency
Eunmi Chae, Eiji Kambe, Kentaro Motohara, Hideyuki Izumiura, Mamoru Doi, Kosuke Yoshioka
AA compact green Ti:Sapphire astro-comb with43-GHz repetition frequency E UNMI C HAE , E IJI K AMBE , K ENTARO M OTOHARA , H IDEYUKI I ZUMIURA , M AMORU D OI , AND K OSUKE Y OSHIOKA Photon Science Center, School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo, 113-8656,Japan Department of Physics, College of Science, Korea University, Seongbuk-gu, Seoul, 02841, Republic ofKorea Subaru Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku Pl., Hilo, HI, 96720USA Okayama Branch, Subaru Telescope, National Astronomical Observatory of Japan, Kamogata, Asakuchi,Okayama 719-0232, Japan Institute of Astronomy, School of Science, The University of Tokyo, Mitaka, Tokyo 181-0015, Japan Advanced Technology Center, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588,Japan * [email protected] Abstract:
A compact green astro-comb with 43-GHz repetition rate is developed based ona Ti:Sapphire optical frequency comb (OFC) and a mode-selecting cavity. The OFC’s largerepetition rate of 1.6 GHz eases the requirements for the mode-selecting cavity. Unnecessaryfrequency-modes of the OFC are suppressed down to 5 × − at 535 nm – 550 nm using a singlemode-selecting cavity with 70-MHz linewidth. The radial velocity precision 𝜎 ∼ . © 2021 Optical Society of America
1. Introduction
Since the first discovery in 1995, more than 900 exoplanets have been discovered to date by radialvelocity technique using high dispersion ( 𝜆 / Δ 𝜆 > , ) spectrographs, by which wobblemotions of stars caused by planets orbiting them are monitored. One of the fundamental aimsof exoplanet search is to detect earth-mass planets in the so called “Habitable Zone”, which isan orbital region where water can exist in liquid phase. Such searches for earth-mass planets inHabitable-Zone have been started around M dwarfs [1]. Owing to the low stellar mass and thesmall radial distance of the Habitable Zone of M dwarfs, the stellar radial-velocity variationscaused by such exoplanets reach as high as 1 m/s. The newly developed infrared spectrographsare used in these surveys as M dwarfs emit lights largely in infrared wavelength region.However, the most fascinating but challenging goal of exoplanet search is to detect Habitable-Zone earth-mass planets around solar-like stars, similar to our Sun (a G2V star). For this purpose,an optical high dispersion spectrograph with a precision of a few tens of centimeters per secondor less in radial velocity measurements has to be developed (e.g. 9 cm/s for the Earth around theSun). The efficiency of the radial velocity measurements is highest around 400 nm – 500 nm forsolar-type stars, considering their peak flux and abundant absorption features that can be used forradial velocity measurements [2].To achieve such an extremely high radial velocity precision, optical frequency combs (OFCs)for calibrating spectrometers at observatories, so called astro-combs, have been employed a r X i v : . [ a s t r o - ph . I M ] J a n idely since the demonstration [3, 4]. Many of astro-combs consist of two main components – afundamental OFC with the repetition frequencies of 100s MHz to several GHz and mode-selectingcavities [5]. Electro-optic frequency combs (EO combs) and micro-cavity OFCs with 10s of GHzrepetition frequencies have also shown surprising advances, widely covering infrared wavelengthranges [6, 7].Despite the recent advances in various types of astro-combs, construction of an astro-combat visible wavelengths remains a challenge mainly for two reasons. The first is that all thefundamental OFCs have spectra in the near- or mid-infrared range so that nonlinear processis inevitable to generate visible wavelengths. As a result, visible astro-combs developed sofar are made from Ti:Sapphire OFCs, amplified fiber OFCs, and EO combs with a nonlinearwavelength conversion such as self-phase modulation and/or second harmonic generation [7–11].The second reason is that it is very difficult to meet the two requirements for the dispersion of themode-selecting cavity at visible wavelengths: a sufficient suppression of the unwanted modes ofthe fundamental OFC and a coverage of wide wavelength range. The requirements become morechallenging when the fundamental OFC has a low repetition frequency ( 𝑓 rep ). Typically, multiplemode-selecting cavities are used in-series to overcome the difficulties when a fundamentalOFC with a 𝑓 rep of several hundreds of MHz is employed. As a result, the overall complexityof the system makes it difficult to maintain stable operation in the harsh environment at theobservatory [8, 9]. One can ease the requirements of the mode-selecting cavity by employing anOFC with high 𝑓 rep . Visible astro-combs based on Ti:Sapphire OFCs with 1-GHz 𝑓 rep have beendemonstrated, achieving either, not both, > 40 dB suppression of unnecessary modes [10] orwide wavelength coverage of about 300 nm [11] with fewer numbers of mode-selecting cavitiescompared to fiber-based astro-combs.In this manuscript, we report on a proof-of-principle demonstration of an astro-comb consistingof a Ti:Sapphire OFC with a high 𝑓 rep of 1.6 GHz and a single mode-selecting cavity, implementedat the High Dispersion Echelle Spectrograph (HIDES) for the Okayama 188-cm telescope ofthe National Astronomical Observatory of Japan (NAOJ) . By employing a Ti:Sapphire OFCwith the highest 𝑓 rep among astro-combs to this day, we were able to build a stable, compactastro-comb with 43 GHz 𝑓 rep using only a single mode-selecting cavity. The spectrum of theastro-comb was observed overnight at HIDES on the 188-cm telescope and utilized to calibratethe spectrometer. We will discuss the performance of our proto-type astro-comb with commercialoff-the-shelf cavity mirrors and possible improvements for the next generation.
2. Experimental setup
The overall astro-comb setup is depicted in Fig. 1, consisting of a fundamental Ti:Sapphire OFCand a single mode-selecting cavity. The details of each component are described in the followingsub-sections. The whole system is designed to be compact and transportable so that it can beeasily shipped and set up promptly at observatories. The overall setup can be fitted within 1 m by1 m by 2 m (height) space. Thanks to this compact and simple setup, the re-adjustment of theastro-comb can be completed within one day after shipping the whole setup to the observatory.
A home-made femtosecond mode-locked Ti:Sapphire oscillator is employed as the fundamentalOFC in this experiment. The round-trip length of the bow-tie laser cavity is about 20 cm, resultingin a high 𝑓 rep of 1.6 GHz. The output pulse has a spectrum that ranges from 700 nm to 900 nmwith an output power of about 500 mW at a 6 W pump power at 532 nm (Sprout-G, Lighthouse The 188-cm telescope was operated by the former Okayama Astrophysical Observatory of the National AstronomicalObservatory of Japan until the end of FY2017. Since FY2018 it has been operated under the council of the TokyoTech Exoplanet Observation Research Center, Asakuchi City and the National Astronomical Observatory of Japan. It isreferred to as "the Okayama 188-cm telescope of NAOJ" or "the 188-cm telescope", hereafter. ig. 1. Overall experimental setup of the astro-comb. The whole setup is designed tobe compact so that it can be fitted within 1 m by 1 m by 2 m (height) space. FP cavity:Fabry-Perot cavity, AOM: acousto-optic modulator, PCF: photonic crystal fiber, BS:beam splitter, PD: photo detector.
Photonics). The output of the fundamental OFC is frequency-broadened using a photonic crystalfiber (PCF) to cover from 500 nm to 1,100 nm (Fig. 2).
Fig. 2. Optical spectrum of the fundamental Ti:Sapphire OFC with the 𝑓 rep of 1.6 GHzafter spectrum broadening by a PCF. The carrier-envelop offset frequency ( 𝑓 CEO ) is detected using the self-reference technique.The 𝑓 CEO is stabilized to 327 MHz by applying a feedback signal to an acousto-optic modulator(AOM) that adjusts the pump power. The remaining degree of freedom of the frequency isstabilized by locking the heterodyne beat between one tooth of the OFC and a continuous-wave(CW) laser at 780 nm stabilized to an atomic transition ( Rb 5 S / (F=2) → P / (F=3)at 384 . 𝑓 rep of 1.6174 GHz covering from visible to near IR.The wavelengths between 530 nm -– 560 nm is used to form the astro-comb in this experiment. We employed off-the-shelf commercial mirrors (Layertec) to construct the mode-selecting cavityfor the astro-comb. The distance between the two cavity mirrors is set to about 3.5 mm to achievea free spectral range (FSR) of 43.670 GHz, which is 27 times of the 𝑓 rep of the fundamental OFC.The reflectivity of the cavity mirrors is 99.5%, corresponding to a linewidth of 70 MHz. Thisreflectivity is high enough to suppress the unwanted adjacent modes (sidemode suppression)because of the large 𝑓 rep of the fundamental OFC. The total group delay dispersion of the cavityfrom 530 nm to 560 nm is between 0 and −
80 fs mainly from the cavity mirrors (Fig. 3 (top)).Because of this dispersion, the FSR changes as a function of the wavelength so that it deviatesfrom 𝑛 × 𝑓 rep at some wavelength regions. This deviation results in discrepancy between theresonant frequencies of the cavity and the frequencies of the OFC (Fig. 3 (middle)), causingdecrease of the transmission of the OFC as shown in Fig. 3 (bottom). The wavelength dependenceof the sidemode suppression ratio is also plotted in Fig. 3 (bottom). One can confirm that thelarge 𝑓 rep of the fundamental OFC guarantees adequate main-mode transmissions and sidemodesuppressions over several 10s of nm wavelength region even with commercial off-the-shelf cavitymirrors.In the experiment, the light of the fundamental OFC with wavelengths shorter than 700 nm issent to the mode-selecting cavity (Fig. 1). A lens is utilized to match the spatial mode of theOFC with that of the cavity. The transmitted light from the cavity is split by a 50:50 beam splitter.One arm of the beam splitter is used for the stabilization of the cavity length by maximizing thetransmitted OFC power using a piezoelectric transducer attached to one of the cavity mirrors.The error signal for the stabilization is obtained by dithering the cavity length at 100 kHz. Theremaining arm of the beam splitter is coupled to a 30-m multimode fiber (FT600EMT, Thorlabs)which sends the light to HIDES. HIDES is an optical, cross-dispersed high dispersion echelle spectrograph of non-white pupiltype for the Okayama 188-cm telescope of NAOJ, located in its coude room [15]. It was originallyfed through the coude optical train of the telescope, and has been so with a fiber-link system thatconnects the Cassegrain focus of the telescope and the entrance of HIDES [16]. The spectrographcan cover about 400 nm wavelength region (e.g. 360 nm – 760 nm) simultaneously and itsmaximum wavelength resolution ( 𝜆 / Δ 𝜆 ) is about 110,000 (2 pixel sampling). We employ thehigh efficiency fiber-link (HE mode) to feed stellar lights into HIDES in the experiment. As aresult, the reciprocal resolution ( 𝜆 / Δ 𝜆 ) of the spectra shown in this paper is about 52,000. Forthe experiment, we slightly modified the calibration lamp box so that the astro-comb light andthe conventional wavelength calibration source, Th-Ar lamp, can be switched remotely.
3. Results and Discussion
After several test runs at The University of Tokyo, the entire setup was shipped to the Okayama188-cm telescope of NAOJ. Within one day after the arrival, the re-adjustment of the systemwas completed and the astro-comb was ready for the measurement owing to the simple overallexperimental setup.The spectra of the astro-comb were recorded every 50 seconds over 84 minutes at HIDES. Theexposure time of each spectrum was one second and it took 49 seconds to read out the data fromCCD. We attempted to take spectra of a bright star and the astro-comb alternately to demonstratethe performance of the astro-comb, but the weather did not permit us to observe the star. Hence, ig. 3. (top) Group delay dispersion of the cavity mirrors [14] and the air in between.The values vary from 0 to −
80 fs . (middle) Frequency difference between thefundamental OFC and the resonances of the mode-selecting cavity. The difference islarger than the linewidth of the cavity (70 MHz) outside of 535 nm - 550 nm becauseof the group delay dispersion of the cavity. (bottom) Mainmode transmission andsidemode suppression ratio of the mode-selecting cavity. Sidemode suppression ratiobelow 10 − 𝑓 rep of the fundamental OFC. we discuss the spectra of the astro-comb alone in this manuscript. Despite the harsh environmentof the observatory with severe vibrations caused by the dome’s rotation, the all stabilizations ofthe astro-comb were stable during the measurements. The 𝑓 CEO and the 𝑓 rep of the fundamentalOFC were monitored during the measurement for the determination of the absolute wavelengthsof the astro-comb. All the data were reduced by the Image Reduction and Analysis Facility (IRAF) in a standardmanner and wavelengths of the spectra were calibrated, thus the CCD detector pixel positionsare mapped to wavelength values, using Th-Ar spectrum obtained just before the sequence ofthe astro-comb exposures. Fig. 4 shows one of the astro-comb spectra obtained by HIDES. Thespectrum spans mainly from 530 nm to 560 nm wavelength range where the fundamental OFChas a high output power. When zoomed in, each mode of the astro-comb is clearly resolvedwith HIDES (Fig. 5). The observed wavelength separation agrees to the 43.670-GHz frequencyinterval of the astro-comb which is 27 times of the 𝑓 rep of the fundamental OFC. The spectrum IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association ofUniversities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. hows power modulation depending on wavelengths, possibly due to the self-phase modulationof the PCF and the interference of the multimode fiber.
Fig. 4. Overall spectrum of the astro-comb. The spectrum mainly covers from 530 nmto 560 nm where the fundamental OFC has a high output power.Fig. 5. Spectra of the astro-comb measured at HIDES. The wavelengths are in standardair. Black lines are the observed spectra by HIDES. Blue lines indicate calculatedwavelengths from the parameters of the astro-comb.
Wavelengths of the all modes of the astro-comb are precisely determined using the parameters ofthe fundamental OFC and the mode-selecting cavity. To map the CCD pixel positions to thewavelength using the astro-comb lines, detailed modeling of the observing spectra is necessary.Here we applied the technique typically used for precise radial velocity measurement usingan iodine cell [17, 18] in which a stellar spectrum superposed on iodine molecule absorptionlines (wavelength reference) is modelled to calculate radial velocity of the star. We devided theastro-comb spectrum into segments of about 3.6 angstrom width and modelled each segmentassuming a Gaussian instrumental profile which broadens the astro-comb lines. Then, the radialvelocity of spectra relative to the first spectrum of the sequence is calculated by averaging theshifts over 51 segments the detailed modelling of which are successfully converged for all thespectra. Since the RMS of radial velocity over 51 segments is about 10 m/s, the radial velocitymeasurement precision of the astro-comb spectrum is about 1.4 m/s in this experiment. Weexpect to have the radial velocity precision below 0.5 m/s with 10-fold increase of the availablespectral range of the astro-comb.he difference between the wavelengths calibrated by the Th-Ar lamp and by the astro-combis typically about 1/10 pixel, corresponding to 2 . × − nm in wavelength and 150 m/s in radialvelocity. This discrepancy is due to the limitation of wavelength calibration with Th-Ar lamp byIRAF which does not take into account the detailed shape of the instrumental profile. Fig. 6 shows the astro-comb spectrum drift on the CCD pixel during the 84-minuite measurementdeduced from 3 orders of lines, corresponding to 536 nm - 554 nm. This wavelength region isselected because of the excellent sidemode suppression ratio within this range. We also observeda distortion of the line shape profiles outside of this wavelength region in the spectrum measuredby HIDES. We suspect the distortion is from the fiber-modal noise and the imperfect sidemodesuppression due to the dispersion of the cavity mirrors (Fig. 3). The overall drift indicates a slowdistortion of the spectrograph mainly due to ambient temperature change. We calculated theRMS of the spectra of the astro-comb after removing the linear drift to estimate the short-term(exposure to exposure) scatter. The obtained RMS is about 8 m/s, which is smaller than thetypical tens of m/s scatter of stellar spectra obtained by HIDES with HE mode. This scatter islikely due to the fiber modal noise of the multiple mode fiber we used to guide the astro-comblight to the entrance slit of HIDES. The suppression of this scatter is one of important points toreach a higher precision of the radial velocity measurements.
Fig. 6. Drift of the spectrum at HIDES over 84 minutes. The overall drift indicatesthe slow change of the spectrometer. The RMS of the residual radial velocity afterremoving the linear drift is 8 m/s.
Employing an astro-comb with a wide spectral range is important to improve the precision of thecalibration of the spectrometer. Currently, the spectral range of the astro-comb is limited to about20 nm because of the uncompensated dispersion of the cavity mirrors. This dispersion causes theFSR of the cavity to depend on the wavelengths, leading to the discrepancy of the frequenciesbetween the resonant modes of the cavity and the modes of the fundamental OFC as shown in Fig.3. When the discrepancy exceeds the linewidth of the cavity, the transmission of main modes offundamental OFC decreases significantly and the sidemode suppression becomes inefficient (Fig.3). The observed spectral range of the astro-comb shown in Fig. 4 agrees with the range wherethe discrepancy is below the linewidth of the cavity. To cover a wide wavelength range of 500nm - 700 nm, more careful consideration is required to satisfy the necessary conditions of themode-selecting cavity.There are two requirements for the mode-selecting cavity. First, the linewidth of the cavity,determined by the reflectivity of the consisting mirrors, should be narrow enough to cut down theunnecessary adjacent modes. In order to detect the radial velocity change on the order of 10 cm/s,it is required to suppress the adjacent modes below a 10 − level compared to the main mode [10].Second, the total group delay dispersion of the cavity mirrors and the air in between should be asmall as possible, ideally equal to zero, to match the FSR of the cavity and the multiple of the 𝑓 rep of the fundamental OFC over the targeted wavelength range. In reality, the total dispersionshould be tailored so that the main-mode teeth of the OFC locate within the full width at halfmaximum (FWHM) of the cavity resonance to achieve the sidemode suppression of 10 − . As aresult, the dispersion requirement becomes stricter when the linewidth of the cavity is narrower.When a fiber-based OFC whose 𝑓 rep s are on the order of 100 MHz, the cavity mirrors withFSR of 40 GHz should have 99.985% of reflectivity, corresponding to a linewidth of 2 MHz,to achieve the needed 10 − sidemode suppression at visible wavelengths. The total groupdelay dispersion of the cavity should be tailored within the order of ± .
01 fs over the desiredwavelength range in order to match the FSR of the cavity and the 𝑓 rep of the astro-comb withinthis narrow linewidth. Since engineering the total dispersion at this level is extremely challenging,cascading multiple cavities with lower reflectivity are often employed, which makes the overallsetup more complicated [8, 9].Our Ti:Sapphire OFC with the 𝑓 rep of 1.6 GHz eases this requirement. The reflectivity of99.8%, which corresponds to a linewidth of 28 MHz, is enough to suppress the unwantedfrequency modes of the fundamental OFC down to 10 − using a single 40-GHz FSR cavity. Therequired total dispersion of the cavity mirrors is ± . over 500 – 700 nm.To reduce the systematic error of the radial velocity, it is desired for each mode of theastro-comb to maintain a stable power. Fig. 7 shows the current temporal power fluctuationsof the astro-comb modes during the 84-min measurement. The power of individual modesmeasured at HIDES changed gradually even though the stabilization of the cavity remainedstable. This signal power fluctuation can be caused by spatial modal noises of the multimodefiber because of the coherence of the astro-comb. Employing a mode-scrambler will remove thepower fluctuations and enhance the stability of the astro-comb [19]. Also, flattening the spectrumof the astro-comb using a special light modulator would increase the calibration precision for thespectrometer and the sensitivity of the radial velocity measurements. Fig. 7. Temporal power fluctuations of individual modes of the astro-comb during themeasurement. Data taken at every 8.4 minutes during the 84 minutes measurement areused for plotting.
4. Conclusion
As a conclusion, we built and characterized a simple, green 43.670-GHz astro-comb, composedof a Ti:Sapphire OFC and a single mode-selecting cavity. The whole system is designed to becompact, fitted within 1 m × × × − sidemodesuppression is achieved at 535 nm – 550 nm. The dispersion of the current cavity mirrors limitsthe wavelength range of the astro-comb to 20 nm, which can be further broadened by employingcustom-made dispersion-free cavity mirrors. Calibration of HIDES using the astro-comb resultsin a radial velocity precision of 𝜎 ∼ Funding
This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHIGrant Numbers JP20K05357, JP17H06205, The University of Tokyo Excellent YoungResearcher Program, and MEXT Quantum Leap Flagship Program (JPMXS0118067246). E.C.acknowledges support by National Research Foundation of Korea Grant Number2020R1A4A101801511 and 2020R1F1A107416211. H.I. was supported by JSPS KAKENHIGrant Number 16H02169. E.K. was partially supported by JSPS KAKENHI Grant Number16H01106.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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