Yet, as shown in Fig. The relative linewidth of dual-comb source is another important factor that may limit the spectral resolving capability in a dual-comb system. Here the relative linewidth of the dual-comb lines after spectral broadening is measured using a narrow-linewidth CW laser at The signal is digitized by the data acquisition board, and the result is Fourier transformed to obtain its spectrum.
Since this wavelength, determined by the operating wavelength of the CW laser, is beyond the overlapped spectral window in this demonstration, the signal from the nm pulse is broadened with higher pump power to get enough signal power in the filter band. As shown in Fig. Further improving the laser, amplifier and spectral broadening stage [ 42 ] could improve the linewidth and reduce this part of the measurement errors. To illustrate the spectral measurement resolution of our scheme, the transmission spectral characteristics of the high-Q on-chip microring resonator device is first tested.
Because of the large waveguide cross-section, multiple transverse electric TE and transverse magnetic TM modes are supported. Between nm and nm, the resonance modes have spectral dips with FWHM widths ranging from 5 pm to around 1 pm. There are also a few much shallower and wider dips caused by a similar microring yet non-optimally coupled to the same bus waveguide.
After the signal light goes through the sample, the temporal trace shows a longer and small tail see Fig. A portion of the RF power spectrum generated from Fourier transform of 0.
It shows clearly resolved beatnotes as well as a zoom-in subplot showing the noise at other frequencies. The direct observation of beatnotes between each pair of frequency-comb modes illustrates the good, inherent coherence between the dual-comb pulses.
It shows the potential of free-running dual-comb fiber lasers for high-resolution, comb-tooth-resolved dual-comb measurements, in contrast to traditional free-running, dual-laser schemes [ 12 ]. The optical spectra obtained by averaging over 5 or interferograms, respectively, in the Fourier domain after phase correction in software [ 23,41 ] are shown in Fig. Since our laser spectrum is not referenced to a known laser frequency yet, in order to convert the RF features in the Fig. Though the averaged spectrum of 5 interferograms is noisy and the spectral features are not easy to identify, after averaging over 0.
The sharp spectral dips occur at the spectral positions when light is coupled into the corresponding high-Q modes of the device. It is noted that the noise on the comb lines are larger than that between them. To further reduce the noise caused by phase noise, the adoption of a referencing system and a carrier phase correction scheme as in [ 11,22,23 ] could likely further improve the SNR.
The inset is a zoom-in near the bottom of the comb teeth. As the rather small on-board memory of our data acquisition board limits our continuous acquisition time to 0. This approach can accumulate a relatively long data sequence, without using the advanced DSP board or on-board signal processing. Therefore, the experimental time required would be significantly longer than the acquisition time to obtain that length of data. It demands that system, especially the dual-comb source, remains stable enough for the spectral averaging over a longer than normal period of time.
As illustrated in Fig. Both curves have almost the same shape including the sharpest feature shown in the inset. The spectral position of the dip in the inset also corresponds to that shown in Fig. Inset: zoom-in of the sharpest dip. By acquiring interferograms based on the above data acquisition scheme, the transmission of the microring resonator is measured as shown in Fig. The result is compared with that obtained by scanning a narrow-linewidth CW tunable laser Agilent B, 0.
The state of polarization of the laser is set to excite both the TE and TM modes simultaneously. The FWHM width is measured to be 1.
Compared to that measured by scanning a high-end tunable laser and, our result clearly resolves the sharpest dip about slightly wider than 1 pm wide, just a few times of the comb tooth spacing. This indicates that the spectral resolving capability of our low-cost setup has the potential to approach that of many stabilized dual-comb systems [ 12 ]. We note that the shape of the dip in the laser scanning result is distorted and deviates from the more symmetric intrinsic spectral lineshape due to the thermal loading effect after the injection of the CW light into the resonator, while our dual-comb result gives a symmetric yet slightly wider shape.
It is also noted that because of the difference in the coupling conditions to the devices and different excitation state of polarization that results in varied coupling into different modes, the depths of the spectral dips could be somewhat different between our measurement and the scanning one. To demonstrate the broadband sensing capability and also quantify the resolution and accuracy of our scheme, the absorption spectrum of a gas cell containing acetylene is measured between and nm, whose spectral features are well-defined and documented.
The short wavelength limit is limited by the filtering range of the programmable filter used. To measure the spectral transmission, the reference path is used in parallel to the gas cell to generate a reference pulse undisturbed by the gas.
In this self-referenced architecture, one period of the interferogram contains both a signal and a reference, and both spectra can be retrieved, so can the transmission. Our current spectral measurement range is set by the tuning range of the programmable filter. To avoid aliasing, the transmission spectrum is measured over a 2 nm window each time and then spectral stitching is applied to obtain the transmission spectrum. Both these strong lines and weak lines of the experimental result match the calculated HITRAN results based on the gas parameter, both in its amplitude and spectral shapes, as shown in Fig.
This also illustrates that the spectrally broadened spectra of pulses with different center wavelength can maintain their spectral coherence at a level suitable for spectroscopy measurements. Good agreement between the experimental spectrum with the HITRAN data confirms the potential of our technique for high-resolution spectral measurements. The capability of averaging over many interferograms without causing significant distortion of the observed spectrum under a relatively low SNR show the stability of the dual-comb laser against common-mode noise.
In contrast, for dual-laser schemes, the directly averaged spectra under a constant clock would be complete smeared due to the random walk between the two uncorrelated lasers and do not allow for averaging [ 11 ]. Our results demonstrate that, despite the relatively narrow initial spectral widths, the dual-comb laser we propose to use here is capable of being applied to a wider spectral range through relatively simple spectral broadening. It should be noted that, compared to the highly-stabilized dual-comb systems, non-negligible spectral measurement uncertainty in our scheme remains, as shown above.
This is resulted from the nature of the free-running laser that unavoidably brings more jitter and drift into the comb lines, a price to pay for a much simplified system.
Besides the relative linewidth of the dual-comb pulses, by using a free-running fiber laser source, there are some additional factors that may affect the achievable spectral resolution. As in this demonstration our laser cavity is not actively environmentally controlled, the repetition rates would slowly drift as affected by temperature and other factors. Laser packaging and simple cavity stabilization schemes that are common for many commercial lasers can be implemented to reduce such uncertainties.
Also, it is noted that unlike the comb systems where the position of each comb line could be traced and locked to a specific frequency, it is not possible to do that for our system.
Yet, the prospect of locking one of the dual-comb outputs to a known standard to be a possible remedy for this shortcoming. Since the stability of the difference in the carrier-envolope offset CEO of the dual-comb pulses is critical to obtain high-quality spectroscopy results, our current results suggest that it could be relatively stable for our spectral measurement range by using a single-cavity dual-comb laser.
However, the CEO characteristics of the not-self-referenced dual-comb output deserve further investigation. Furthermore, as we use a long fiber-optic interferometric setup, the fiber after the laser is subject to thermal and acoustic fluctuations and induce significant jitter on the dual comb interference pattern. Our current results are obtained by applying the phase correction algorithm. Leveraging more stable setup would likely further improve the overall performance of the system.
For measuring a broadband spectral response, it would be necessary for the fiber laser output to be nonlinearly broadened to cover a larger spectral range that comb spectroscopy claims to be superior to previous schemes. Our current results indicates that, even after nonlinear spectral broadening, the spectral coherence and comb line correlations between the dual-comb signal generated by the dual-wavelength laser could be maintained.
We demonstrate the feasibility of constructing the so-far highly envied yet complex dual-comb spectroscopy system with three simple pieces built with widely available, low-cost commercial parts and modules: one free-running fiber laser, simple standard data acquisition electronics, and commonly used post-processing algorithms.
The correlation between two pulse trains oscillating in the same laser cavity enables natural locking of their comb characteristics. Our results and analyses unequivocally show the capability of such single-fiber-laser-based dual-comb spectroscopy system to reach a spectral resolution good enough for many real-world applications.
Our proposed single-fiber-laser-based dual-comb scheme could result in significant simplification in the implementation complexity and costs of dual-comb spectrometers, and provide an alternative approach to change the paradigm of low-complexity dual-comb-based instrumentations.
Such simple and portable systems built with standard off-the-shelf fiber-optic components would be more accessible and affordable to many more applications. We thank Prof.
Andrew M. Weiner and Minghao Qi from Purdue University for providing us the integrated device sample, and Prof. Udem, R. Holzwarth, and T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Adler, P. Foltynowicz, K. Cossel, T. Briles, I. Hartl, and J. Express 18 21 , — Yost, T. Allison, A. Ruehl, M. Fermann, I. Gerginov, C. Tanner, S. Diddams, A. Bartels, and L. Keilmann, C. Gohle, and R. Schliesser, M. Brehm, F. Keilmann, and D. Express 13 22 , — Bernhardt, A. Ozawa, P. Jacquet, M.
Jacquey, Y. Kobayashi, T. Holzwarth, G. Guelachvili, T. Hansch, and N. Photonics 4 1 , 55—57 Coddington, W. Swann, and N. A 82 4 , Ideguchi, A. Poisson, G. Guelachvili, N. Coddington, N. Newbury, and W. Connes, H. Delouis, P.
Connes, G. Guelachvili, J. Maillard, and G. Griffiths and J. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Sethna, A. Schmidt and J. Zaanen for discussions and communications. These studies were supported by the U. The inset shows one of the Bragg peaks. This image has been measured in the same FOV as a. The red circle indicates the location of the Bragg peak shown in the insets of Figure a ,c ,d ,f. The inset shows one of the resulting isotropic Bragg peaks confined in a single pixel same as in a.
The data shown in this image have been processed using the distortion correction algorithm. Fourteen Zn impurity resonances are distinguishable in this image. These data have been processed using the distortion correction algorithm.
A total time of ms has elapsed between the measurement of a and b. All subsequent image pairs represent the equivalent data at a different location. All data in this Figure were obtained from five maps with identical acquisition parameters, and have been processed using the distortion correction algorithm. Figure 4. The Bi blue atoms are directly above the Cu green atoms; in between the two atoms, there is an oxygen atom not pictured here.
Sometimes, a Zn impurity atom red is found at one of the Cu sites. The ellipse about the average displacement arrow corresponds to one standard deviation of the average displacement. The fast and slow scan directions are respectively indicated by the thicker and thinner arrows on the bottom right corner of this Figure. References Lawler M J et al. Schmidt A R et al. Electronic structure of the cuprate superconducting and pseudogap phases from spectroscopic imaging STM New Journal of Physics 13,.
Kohsaka Y et al. Gomes K K et al. Boyer M C et al. Niestemski F C et al. Yin Y et al. As Phys. Massee F et al.
Allan M P et al. Natl Acad. Slezak J A et al. Mesaros A et al. Chen C T et al. Pan S et al. Balatsky A V et al. Fujita1,2,3, S. Mukhopadhyay1,2, J. Orenstein4, H. Eisaki5, S. Uchida3, M. Power supply. Product safety. Hygienic approvals and certificates. Drinking water approvals: NSF. Configure to download the CAD drawings of this product. Spare parts Accessories. Search spare parts by number in drawing.
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