We demonstrated the selection of a single comb-line from an optical frequency comb (OFC) of a mode-locked femtosecond fiber laser with a 250 MHz pulse repetition rate, and applied for precision spectroscopy of Rb atoms at 1529 nm. The single comb-line was selected from the fiber-OFC with a 1.5 GHz mode-spacing using spectral-mode-filtering and femtosecond laser injection-locking. When the repetition rate of the mode-locked femtosecond fiber laser was scanned over the range of 382.6 Hz at 250 MHz, we observed the double-resonance optical pumping spectra of the 5S 1/2-5P 3/2-4D 3/2 transition of Rb atoms using the selected comb-line of an OFC scanned over the range of 300 MHz at 196 037 213.8 MHz.
©2011 Optical Society of America
A frequency-stabilized femtosecond laser has been employed in optical-frequency measurement, optical atomic clocks, length metrology, astronomical spectrography, and high-resolution precision spectroscopy [1–17]. Ever since high-resolution precision spectroscopy with a mode-locked pulse laser was reported in the 1970s [9–11], A. Marian et. al. first introduced the term ”direct frequency comb spectroscopy (DFCS)” . They reported direct comb excitation of Rb atoms and obtained extensive spectroscopy information . Also, an optical frequency comb was directly used for high-resolution spectroscopy of one-photon and two-photon transitions in Rb atoms . Mode-locked pulse lasers have been used for direct frequency comb spectroscopy (DFCS) in one-photon and two-photon transitions [9–17]. DFCS is useful for the study of multiple atomic transitions and the absolute frequency measurement of an atomic spectrum. Although DFCS has many advantages for high-resolution precision spectroscopy, it requires the elimination of undesired frequency components from the optical frequency comb (OFC). This is because the undesired frequency components of the OFC may cause light shift of a transition and result in a low signal-to-noise ratio (SNR).
However, each comb-line of a frequency-stabilized femtosecond laser is considered to be a continuous-wave (CW) optical source with accurate optical frequency and narrow spectral width. J. D. Jost et. al. first demonstrated experimentally a continuously tunable singlefrequency CW laser using an OFC . If the desired comb-lines are selected from the OFC, they will serve as the ideal light sources for high-resolution precision spectroscopy. The femtosecond laser injection-locking (FSLIL) technique based on a mode-locked laser with a high repetition rate enabled us to select and amplify the desired comb-line from the OFC that was composed of more than 105 comb-lines [19–24]. A mode-locked laser with a high-repetition rate is effective for comb-line selection using FSLIL, because the frequency difference between the adjacent comb-lines and the desired comb-line is large. So far, most of the spectroscopy studies based on FSLIL have employed a titanium-doped sapphire (Ti:sapphire) laser with a 1 GHz repetition rate. The selected and amplified comb-line from the mode-locked Ti:sapphire has been applied successfully for precision spectroscopy in the one-photon transitions of 40Ca, 85Rb, and 133Cs atoms [20–23]. However, the mode-locked fiber laser (MLFL) allows for a relatively long-term stable operation using a powerful amplifier with Erdoped fiber and well-established fiber devices. The OFC based on an MLFL offers advantages as the tool for DFCS, but there are disadvantages with regard to its application of the FSLIL technique because of the relatively low repetition rate in the range of a few tens of megahertz to 250 MHz. Because the repetition rate of a mode-locked laser is determined by the laser cavity length, it is practically difficult to realize an MLFL with a short cavity length. Recently, the MLFL with a high repetition rate on the order of a few gigahertz was achieved using a spectralmode- filtering (SMF) method with an external Fabry-Pérot cavity [25–30]. The MLFL with a high repetition rate enables the relatively easy and stable selection of the desired comb-lines from the OFC for precision spectroscopy.
In this paper, we demonstrate the selection and amplification of a single optical frequency component from MLFL using the FSLIL and SMF methods. The single comb-line was selected from an OFC with a 1.5 GHz mode-spacing based on an MLFL, which was applied to double-resonance optical pumping (DROP) spectroscopy of the 5S 1/2-5P 3/2-4D 3/2 transition in Rb atoms. When the repetition rate of the MLFL was scanned, we could not only observe the DROP spectrum in the 1.5 μm region, but we could also measure the absolute optical frequency of the selected comb-line of the MLFL. To the best of our knowledge, the first application for precision spectroscopy using of the selected single comb-line from an OFC based on an MLFL has been presented for the first time in this paper.
2. Experimental setup
Figure 1 is the experimental setup for precision spectroscopy in a rubidium vapor cell using the selected comb-line from an OFC based on an MLFL. Our experimental setup consists of three parts. The first part contains the OFC based on an MLFL with 1.5 GHz mode spacing. The laser used in our experiment was a mode-locked femtosecond fiber laser with a repetition rate of around 250 MHz. The mode-locked fiber laser pulse width was approximately 100 fs and the center wavelength was 1560 nm. The average power was approximately 200 mW. The repetition rate frequency (f rep) was stabilized to an H-maser and the carrier-envelope-offset frequency (f ceo) was be stabilized by employing an f-to-2f interferometer.
The output of the MLFL was passed through a Fabry-Pérot cavity with the free spectral range 1.5 GHz to extract the integer multiple of the 1.5 GHz modes corresponding to the sixth harmonic of 250 MHz from the OFC based on an MLFL. The cavity mirrors of the Fabry-Pérot cavity filter had approximately 99 % reflectivity and optimized low group delay dispersion (GDD) (< 3 fs2) in the 1480 nm to 1620 nm range. The finesse of the cavity was estimated to be approximately 300 and the total transmission efficiency was measured to be approximately 1 %. To stabilize the length of the Fabry-Pérot cavity filter, we detected the light transmitted from the Fabry-Pérot cavity filter by a photodiode and stabilized the length of the cavity to one of comb modes. With extra frequency modulation for the PZT of the Fabry-Pérot cavity, we are able to obtain a dispersion-like signal by setting the phase sensitive detector of the lock-in amplifier. The error signals obtained by the lock-in amplifier, after being treated by the PID controller, are feedback to the PZT of the Fabry-Pérot cavity for the compensation of the cavity length .
The second part consists of the selection and amplification of a comb-line using injection-locking. A weak OFC with 1.5 GHz mode-spacing was amplified using an Er-doped fiber amplifier (EDFA) with a maximum output of 23 dBm. To prevent the optical damage of the distributed feedback (DFB) laser used as the slave laser, an array waveguide grating (AWG) was used as a filter with 50 GHz bandwidth at a near-resonance wavelength of 1529.3 nm. The output of the AWG was injected into the DFB laser using a circulator. The DFB laser was single-mode operated at 1529.3 nm near the resonance on the 5P 3/2-4D 3/2 transition of Rb atom. The output power of the DFB laser is 10 mW, but the laser was used at around 1 mW for this experiment. The optically locked DFB laser is identified with the comb-line of an OFC based MLFL [20–23].
To use the injection-locked DFB laser for high-precision spectroscopy, a 100-m-long optical fiber delivers the selected comb-line to the DROP spectroscopy experimental setup located in a different part of the building. For the DROP experiment, the delivered DFB laser was used as the coupling laser (LC), and the grating-feedback external cavity diode laser (ECDL) operating in a single mode was used as the probe laser (LP). Figure 2 shows an energy-level diagram of the 5S 1/2-5P 3/2-4D 3/2 transitions of the two isotopes 85Rb (I=5/2) and 87Rb (I=3/2). To obtain the DROP spectrum in the 5P 3/2-4D 3/2 transition, the repetition rate of the MLFL was scanned over the range of 382.6 Hz at 250 MHz, and hence the frequency of LC was scanned over the range of 300 MHz at 196 037 214 MHz. This scanning range is sufficient to observe the DROP spectra of the 5P 3/2-4D 3/2 transition of Rb atoms. The frequency of LP is fixed on the cycling transition of the 5S 1/2-5P 3/2 transition of the Rb D2 line using saturated absorption spectroscopy (SAS) in a 5-cm-long Rb vapor cell. The optical powers of LC and LP entering the Rb cell were measured to be 90 μW and 15 μW, respectively. The LC and LP counterpropagated each other and were overlapped in the 10-cm-long Rb vapor cell at room temperature after passing though two apertures (AP) with a diameter of 1.5 mm. The polarizations of both lasers were linear and parallel. The experimental details of the DROP spectroscopy can be found in Refs [31,32].
3. Experimental results & discussion
For the easy and long-term stable selection of the desired single comb-line from the OFC, it is necessary to broaden the mode-spacing of the OFC based on an MLFL. We generated the OFC based on an MLFL with 1.5 GHz mode-spacing and investigated its characteristics. Figure 3 shows the beat spectra of the MLFL observed by a spectrum analyzer before and after the spectral-mode-filtering using the Fabry-Pérot cavity with a free spectral range 1.5 GHz. The MLFL with a repetition rate of 250 MHz is the frequency comb with a regular mode-spacing of 250 MHz, as shown in Fig. 3(a). The SNR of the MLFL was measured to exceed 30 dB. For spectral-mode-filtering, the modes of 250 MHz and 1.5 GHz should correspond to the mode-spacing of the self-MLFL and the Fabry-Pérot cavity, respectively. After spectral-mode-filtering with a mode-spacing of 1.5 GHz, we can simultaneously see the small modes of 250 MHz and the large modes of 1.5 GHz, as shown in Fig. 3(b). The ratio of the extracted 1.5 GHz modes to the suppressed neighbor 250 MHz modes is found to be more than 35 dB. This ratio is dependent on the finesse and the free spectral range of the Fabry-Pérot cavity and good agreement with the calculated result.
To prevent any optical damage to the DFB laser being used as a slave laser, the injected optical power into the DFB laser should be as low as possible. To eliminate the undesired modes of the OFC before injection to the DFB laser, the OFC with 1.5 GHz mode-spacing was passed through one of the ports of the AWG with a 50 GHz bandwidth at 1529.3 nm center wavelength. The total power after passing through one port of the AWG was measured to be 130 μW. The mode number transmitted to the AWG with a 50 GHz bandwidth was estimated to be approximately 33, and hence, the power per mode was estimated to be approximately 3.9 μW.
When the 33 comb-lines were injected into the DFB laser, the characteristics of the injection-locked DFB laser were investigated. Figure 4 shows the process of the optically injected locking of the DFB laser according to the frequency of the DFB laser near the frequency of the desired comb-line. The relative power spectra of the DFB laser corresponding to the relative frequency differences between the comb-line and the DFB laser of 0.42 GHz (a), 0.27 GHz (b), and 0.20 GHz (c) are shown in Fig. 4. As shown in Figs. 4(a) and 4(b), the relative difference between the frequency of the desired comb-line and that of the DFB laser is broader than the locking bandwidth. We can see the operation of the two independent modes of the comb-line and the self-DFB laser. When the frequency of the DFB laser is more closed to the comb-line, the DFB is transferred to the comb-line. When the frequency difference was 0.20 GHz, the DFB was optically locked into the single comb-line. The characteristics of the optically locked DFB laser are identified with the selected comb-line from the fiber OFC.
Figure 5 shows the relative power spectrum of the optically locked DFB laser when the optical frequency of the comb-line is scanned over the range of 1.00 GHz at 196 037 GHz. The power of the single comb-line injected into the DFB laser is approximately 3.9 μW. To scan the frequency of the comb-line in the range of 1.00 GHz at 196 037 GHz, the repetition rate of the MLFL was scanned over the range of 1.27 kHz at 250 MHz. In Fig. 5, the blue and the red curves represent the spectra of the optically locked DFB laser for the fixed and the scanned comb-line, respectively. The red curve denotes the peak-hold spectrum of the DFB laser during the frequency at which the comb-line was scanning. We can clearly distinguish the locking and unlocking of the DFB laser from this red curve. The locking bandwidth is estimated to be 340 MHz. In our experiment, when the injected power per mode increased from 1.9 �Wto 3.9 �W, the locking bandwidth of the DFB laser increased almost linearly with a slope 88±2 MHz/�W. Next, we prepared to perform precision spectroscopy in the range of the locking bandwidth of 340 MHz with the free-running DFB laser.
The selected and amplified comb-line was delivered to the Rb vapor via a 100-m-long single-mode optical fiber. The power of the delivered coupling laser (LC) from the selected and amplified comb-line was measured to be 0.8 mW, but a power of 90 μW was used for DROP spectroscopy in the 5S 1/2-5P 3/2-4D 3/2 transition of the 87Rb atom. The typical DROP spectrum in the ladder-type atomic system shown in Fig. 2 was obtained by measuring the transmission of LP fixed on the cycling transition of the 5S 1/2(F = 2)-5P 3/2(F′ = 3) transition, while the frequency of LC was scanned over the range of the hyperfine structure components of 4D 3/2 .
To scan the frequency of the delivered coupling laser (LC) from the comb-line, the frequency of the microwave synthesizer referenced to an H-maser should be scanned over, because the repetition rate (f rep) of the MLFL is stabilized by the microwave synthesizer. Figure 6 shows DROP spectrum as a function of f rep of MLFL, while the carrier-envelope offset frequency (f ceo) of the MLFL is stabilized at 20 MHz referenced to an H-maser. The absolute optical frequency (f opt) of the selected comb-line is calculated using the relation f opt = n × f rep ± f ceo, where the integral times (n) of the repetition rate (f rep) of the MLFL is 784 152.
Figure 6 shows the DROP spectrum in the 5P 3/2(F′ = 3)-4D 3/2(F″ = 2, 3) transition of87Rb when the repetition rate of the MLFL was scanned over the range of 320 Hz at 250 MHz, where the polarizations of both LP and LC were linear and parallel. The horizontal axis of the figure represents the frequency difference between f rep and the repetition rate 249 998 972 Hz. The absolute optical frequency (f opt) at the zero value of the horizontal axis is 196 037 214 MHz, corresponding to the 5P 3/2(F′ = 3)-4D 3/2(F″ = 3) transition, where the sign of f ceo is positive. Further, the f rep value of the 5P 3/2(F′ = 3)-4D 3/2(F″ = 2) transition is estimated to be approximately 249 998 874 Hz, and the resulting f opt value is calculated to be 196 037 137 MHz. These results are in good agreement with the findings of a previous study by the authors .
We can observe the absorption signal on the horizontal axis at 68 Hz. When n = 784 152 is considered, the frequency difference between the 4D 3/2(F″ = 3) state and the absorption signal is calculated to be 54 MHz. This absorption signal accounts for the velocity-selective effect and the difference between the Doppler shift of LC and LP due to the atom group with the non-zero velocity. To enable an interpretation of the absorption signal, we show the simple energy-level diagram of the 5S 1/2(F = 2)-5P 3/2(F = 2, 3)-4D 3/2(F″ = 1, 2, 3) transition, as shown in Fig. 7 . The typical DROP spectrum is a transmittance signal from the atom group with zero velocity to the propagation direction of the lasers [31,32]. However, the atom group with 208 m/s velocity has a Doppler shift of + 136 MHz to counter-propagating LC and −267 MHz to co-propagating LP, respectively. In the case of the atom group with 208 m/s velocity, the LP is resonant on the 5S 1/2(F = 2)-5P 3/2(F′ = 2) transition and the LC is capable of resonance on the 5P 3/2(F′ = 2)-4D 3/2(F″ = 2) transition when the frequency of LC is increased to 54 MHz. In the atomic ladder-type system without any cycling transition such as the 5S 1/2(F = 2)-5P 3/2(F′ = 2)-4D 3/2(F″ = 2) transition of 87Rb, the transmittance due to DROP and electromagnetically induced transparency (EIT) is suppressed and the absorption peak due to two-photon coherence appears . Therefore, the absorption peak is due to two-photon absorption in the 5P 3/2(F′ = 2)-4D 3/2(F″ = 2) transition.
We selected the comb-line from an MLFL with a 250 MHz pulse repetition rate, and we demonstrated precision spectroscopy in the 5P 3/2-4D 3/2 transition of Rb atoms after delivering the comb-line to the DROP spectroscopy experiment located in a different part of the building via a 100-m-long single mode optical fiber. The easy and stable selection of the desired single comb-line from the MLFL with a 250 MHz pulse repetition rate was possible using spectral-mode-filtering and femtosecond laser injection-locking methods. In the process of spectral-mode-filtering with the Fabry-Pérot cavity, an OFC from MLFL with 250 MHz pulse repetition rate was generated with 1.5 GHz mode-spacing and a 35 dB suppression ratio to neighboring 250 MHz modes. In the next process of femtosecond laser injection-locking, the DFB laser was optically locked to the single comb-line of the fiber-OFC when the approximately 33 comb-lines passing though the AWG were injected into the DFB laser. Under the condition of injection power per mode being 3.9 μW, the locking bandwidth was measured to be 340 MHz.
When the selected and amplified comb-line was used as the coupling laser (1529.3 nm), the DROP spectra of the 5S 1/2-5P 3/2-4D 3/2 transition of 87Rb atoms were observed as the repetition rate of the selected comb-line was scanned. The optical frequency of the comb-line from the repetition rate of the MLFL was used to determine the absolute optical frequencies of the 5P 3/2(F′ = 3)-4D 3/2(F″ = 2,3) transition of 87Rb, which were 196 037 137 MHz and 196 037 214 MHz, respectively. Additionally, the velocity-selective two-photon absorption signal was observed in the 5S 1/2(F = 2)-5P 3/2(F′ = 2)-4D 3/2(F″ = 2) transition of the Rb atom group with nonzero velocity. The absorption peak accounted for two-photon coherence in the atomic ladder-type system without any cycling transition. The optical frequency of this absorption signal was understood as the velocity-selective effect and the difference between the Doppler shift of LC and LP due to the atom group with the nonzero velocity. The optical frequencies of the absorption signals were in good agreement with the estimated results, taking into account the velocity-selective effect and the Doppler effect. We believe that our results will help to establish a useful technique in the fields of precision spectroscopy and optical frequency standards based on the MLFL in the 1.5 μm region.
This work was supported by the National Research Foundation of Korea (2009-0073051 and 2009-0070668).
References and links
1. Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999). [CrossRef]
2. J. Reichert, M. Niering, R. Holzwarth, M. Weitz, Th. Udem, and T. W. Hänsch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett. 84(15), 3232–3235 (2000). [CrossRef] [PubMed]
3. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]
6. J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010). [CrossRef]
7. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008). [CrossRef] [PubMed]
8. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008). [CrossRef] [PubMed]
9. R. Teets, J. Eckstein, and T. W. Hänsch, “Coherent Two-Photon Excitation by Multiple Light Pulses,” Phys. Rev. Lett. 38(14), 760–764 (1977). [CrossRef]
10. Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of 2-photon absorption of super-narrow pulses in a gas,” Appl. Phys. (Berl.) 12(1), 97–99 (1977). [CrossRef]
11. J. N. Eckstein, A. I. Ferguson, and T. W. Hänsch, “High-Resolution Two-Photon Spectroscopy with Picosecond Light Pulses,” Phys. Rev. Lett. 40(13), 847–850 (1978). [CrossRef]
13. D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998). [CrossRef]
14. A. Marian, M. C. Stowe, D. Felinto, and J. Ye, “Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics,” Phys. Rev. Lett. 95(2), 023001 (2005). [CrossRef] [PubMed]
15. M. C. Stowe, F. C. Cruz, A. Marian, and J. Ye, “High resolution atomic coherent control via spectral phase manipulation of an optical frequency comb,” Phys. Rev. Lett. 96(15), 153001 (2006). [CrossRef] [PubMed]
16. S. Reinhardt, E. Peters, T. W. Hänsch, and Th. Udem, “Two-photon direct frequency comb spectroscopy with chirped pulses,” Phys. Rev. A 81(3), 033427 (2010). [CrossRef]
17. J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81(4), 043840 (2010). [CrossRef]
18. J. Jost, J. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002). [PubMed]
20. T. M. Fortier, Y. L. Coq, J. E. Stalnaker, D. Ortega, S. A. Diddams, C. W. Oates, and L. Hollberg, “Kilohertz-resolution spectroscopy of cold atoms with an optical frequency comb,” Phys. Rev. Lett. 97(16), 163905 (2006). [CrossRef] [PubMed]
21. H. S. Moon, E. B. Kim, S. E. Park, and C. Y. Park, “Selection and amplification of modes of an optical frequency comb using a femtosecond laser injection-locking technique,” Appl. Phys. Lett. 89(18), 181110 (2006). [CrossRef]
22. S. E. Park, E. B. Kim, Y.-H. Park, D. S. Yee, T. Y. Kwon, C. Y. Park, H. S. Moon, and T. H. Yoon, “Sweep optical frequency synthesizer with a distributed-Bragg-reflector laser injection locked by a single component of an optical frequency comb,” Opt. Lett. 31(24), 3594–3596 (2006). [CrossRef] [PubMed]
23. H. S. Moon, S. E. Park, and E. B. Kim, “Coherent multi-frequency optical source generation using a femto-second laser and its application for coherent population trapping,” Opt. Express 15(6), 3265–3270 (2007). [CrossRef] [PubMed]
24. H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008). [CrossRef] [PubMed]
25. C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb Vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007). [CrossRef] [PubMed]
27. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009). [CrossRef]
28. M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380(2), 839–847 (2007). [CrossRef]
29. M. J. Thorpe, F. Adler, K. C. Cossel, M. H. G. de Miranda, and J. Ye, “Tomography of a supersonically cooled molecular jet using cavity-enhanced direct frequency comb spectroscopy,” Chem. Phys. Lett. 468(1-3), 1–8 (2009). [CrossRef]
30. H. Y. Ryu, S. H. Lee, E. B. Kim, H. S. Suh, and H. S. Moon, “A discretely tunable multifrequency source injection locked to a spectral-mode-filtered fiber laser comb,” Appl. Phys. Lett. 97(14), 141107 (2010). [CrossRef]
31. H. S. Moon, L. Lee, and J. B. Kim, “Double-resonance optical pumping of Rb atoms,” J. Opt. Soc. Am. B 24(9), 2157–2164 (2007). [CrossRef]
32. H. S. Moon, W.-K. Lee, and H. S. Suh, “Hyperfine-structure-constant determination and absolute-frequency measurement of the Rb 4D3/2 state,” Phys. Rev. A 79(6), 062503 (2009). [CrossRef]
33. H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S1/2–5P3/2–5D3/2 transition of 87Rb atoms,” J. Phys. At. Mol. Opt. Phys. 44(5), 055004 (2011). [CrossRef]