光頻梳和穩頻雷射的發展，對於物理精密量測、原子分子結構的研究、量測學、光通訊系統和光鐘的研究都扮演非常重要的角色。以往我們利用特定的原子分子躍遷譜線做為雷射穩頻的基準，得到頻率精準且穩定的雷射光源。而這些躍遷譜線的絕對頻率量測需要經由複雜的頻率鏈，將微波波段的頻率標準連結到光頻的範圍。直到光頻梳的實現使得從紫外光到紅外光波段的絕對頻率都可以快速的測得。

本論文利用實驗室的光頻梳系統，分別量測兩套穩頻雷射的絕對頻率。其一為利用調制傳遞光譜法的532 nm碘穩頻雷射系統，調制傳遞光譜法得到的光譜訊號有零背景的好處，且雷射頻率沒有調制。我們量測碘分子R(56) 32-0躍遷的a10超精細譜線，得到訊噪比~300的譜線訊號，利用此訊號回授穩定雷射頻率。我們連續15天(每天兩次)測量此穩頻雷射的絕對頻率，量測結果的平均值為563,260,233,510.3 kHz，約低於CIPM的建議值2.7 kHz，在建議值的不準度內。

其二為雙光子躍遷光譜法(two photon transition spectroscopy)的822 nm銫原子穩頻雷射(由中研院原分所鄭王曜老師提供)，雙光子躍遷光譜法可以消除都卜勒線寬，我們量測銫原子6S1/2到8S1/2中F3→F3與F4→F4雙光子躍遷譜線。當積分時間設為10 ms時，其光譜訊號訊噪比可達1800。我們量測F3→F3雙光子躍遷的絕對頻率為364,507,238,394 kHz，F4→F4雙光子躍遷的絕對頻率為364,503,080,326 kHz。測得之絕對頻率都較T. W. Hänsch團隊的量測結果低約20 kHz，但是這兩個躍遷譜線的頻率差(即6S1/2到8S1/2 的hyperfine splitting)與T. W. Hänsch團隊相差只有2 kHz。

Optical frequency comb (OFC) and stabilized lasers play important roles in the development of atom and molecule physics, metrology, communication systems and optical clock. In the past, to get frequency stable light source lasers are stabilized to certain atomic or molecular transitions. But the frequency needs to be calibrated by the complicated harmonic chain which links the frequency standard from GHz to THz region. With the realization of optical frequency comb, now we can easily measure the absolute frequency from UV to IR region.

In this thesis, we represent two kinds of stabilized laser systems. One is 532 nm iodine stabilized laser by the method of modulation transfer spectroscopy (MTS). MTS provides nearly zero background baseline and frequency unmodulated laser source. The other is 822 nm cesium stabilized by the means of two photon spectroscopy. It provides Doppler free line-width to get precise resonant frequency. We measure the absolute frequencies of both laser systems by our OFC system. We measure the hyperfine component a10 of iodine ro-vibrational transition R(56) 32-0. Its signal to noise ratio (S/N) is 300. Our measured absolute frequency is only 2 kHz below the value recommended by CIPM. The absolute frequencies of cesium 6S1/2 to 8 S1/2 hyperfine transitions are also measured. The S/N ratio of the observed two photon spectrum is 1800 (integration = 10 ms). Our results on absolute frequencies are ~ 20 kHz below Hänsch’s group. However, the hyperfine splitting between F3→F3 and F4→F4 two photon transitions agrees with Hänsch’s group very well.

[1] H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle and G. Zinner, “First Phase-Coherent Frequency Measurement of Visible Radiation,” Phys. Rev. Lett. 76, pp. 18-21, 1996.
[2] H. R. Telle, D. Meschede and T. W. Hänsch, “Realization of a New Concept for Visible Frequency Division: Phase Locking of Harmonic and Sum Frequencies," Opt. Lett. 15, pp. 532-534, 1990.
[3] J. N. Eckstein, A. I. Ferguson and T. W. Hänsch, “High-Resolution Two-Photon Spectroscopy with Picosecond Light Pulses,” Phys. Rev. Lett. 40, pp. 847-850, 1978.
[4] Th. Udem, J. Reichert, R. Holzwarth and T. W. Hänsch, “Accurate Measurement of Large Optical Frequency Differences with a Mode-Locked Laser,” Opt. Lett. 24, pp. 881-883, 1999.
[5] 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, pp. 635-639, 2000.
[6] 鄭王曜、施宙聰 “2005年諾貝爾物理獎得主-漢希(T. W. Hänsch)與霍爾(J. L. Hall),” 物理雙月刊 28, pp. 15-21, 2006.
[7] O. Svelto, “Principles of Lasers,” 4th Edition, Kluwer Academic/Plenum Publishers, 1998.
[8] U. Keller, W. H. Knox, G. W. 'tHooft, H. Roskos, T. K. Woodward, J. E. Cunningham, D. L. Sivco and A. Y. Cho, “Coupled-Cavity Resonant Passive Mode-locked Solid-State Lasers,” Advance Solid State Lasers 10, pp. 115-119, 1991.
[9] B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” 2nd Edition, Wiley Interscience, 2007.
[10] S. T. Cundiff, J. Ye and J. L. Hall, “Optical Frequency Synthesis Based on Mode-Locked Lasers,” Rev. of Sci. Inst. 72, pp. 3749-3771, 2001.
[11] 李明翰 “飛秒光頻梳的改進” 國立清華大學碩士論文, 2008.
[12] J.-C. Diels and W. Rudolph, “Ultrashort Laser Pulse Phenomena,” 2nd Edition, Academic Press, 1996.
[13] R. Szipocs and K. Ferencz, “Chirped Multilayer Coatings for Broadband Dispersion Control in Femtosecond Lasers,” Opt. Lett. 19, pp. 201-203, 1994.
[14] T. Brabec and F. Krausz, “Intense Few-Cycle Laser Fields: Frontiers of Nonlinear Optics,” Rev. Mod. Phys. 72, pp. 545-591, 2000.
[15] Th. Udem, R. Holzwarth and T. W. Hänsch, “Optical Frequency Metrology,” Nature 416, pp. 233-237, 2002.
[16] G. P. Agrawal, “Non linear Fiber Optics,” 3rd Edition, Academic Press, 2001.
[17] J. L. Hall, L. Hollberg, T. Saer and H. G. Robinson, “Optical Heterodyne Saturation Spectroscopy,” Appl. Phys. Lett. 39, pp. 680-682, 1981.
[18] J. H. Shirley, “Modulation Transfer Processes in Optical Heterodyne Saturation Spectroscopy,” Opt. Lett. 7, pp. 537-539, 1982.
[19] Demtröder, “Laser Spectroscopy,” 4th Edition, Springer, 2008.
[20] F.-L. Hong, J. Ishikawa, A. Onae and H. Matsumoto, “Rotation Dependence of the Excited-State Electric Quadrupole Hyperfine Interaction by High-Resolution Laser Spectroscopy of 127I2,” J. Opt. Soc. Am. B 18, pp.1416-1422, 2001.
[21] 方惠梅 “碘分子穩頻雷射之研究” 國立交通大學博士論文, 2004.
[22] F.-L. Hong, J. Ishikawa, T.-H. Yoon, L.-S. Ma, J. Ye and J. L. Hall, “Portable 12-Stabilized Nd:YAG Laser for Wavelength Standards at 532 nm and 1064 nm.,” SPIE 3477, pp. 2-10, 1998.
[23] G. Grynberg and B. Cagnac, “Doppler-Free Multiphotonic Spectroscopy,” Rep. Prog. Phys. 40, pp. 791-841, 1997.
[24] M. Bellini, A. Bartoli and T. W. Hänsch, “Two-Photon Fourier Spectroscopy with Femtosecond Light Pulses,” Opt. Lett. 22, pp. 540-542, 1997.
[25] E. Jaatinen, D. J. Hopper and J. Back, “Residual Amplitude Modulation Mechanisms in Modulation Transfer Spectroscopy that Use Electro-Optic Modulators,” Meas. Sci. Technol. 20, pp. 1-8, 2009.
[26] R. Felder, “Practical Realization of the Definition of the Metre, Including Recommended Radiations of Other Optical Frequency Standards (2003),” Metrology 42, pp. 322-325, 2003.
[27] 陳宥寰 “腔內式822 nm銫原子穩頻半導體雷射” 國立中山大學碩士論文, 2009.
[28] D. A. Steck, “Cesium D. line Data,” http://george.ph.utexas.edu/~dsteck/ alkalidata/cesiumnumbers.pdf
[29] D. J. Jones, T. M. Fortier and S. T. Cundiff, “Highly Sensitive Detection of the Carrier-Envelope Phase Evolution and Offset of Femtosecond Mode-Locked Oscillators,” J. Opt. Soc. Am. B 21, pp. 1098-1103, 2004.
[30] V. Tsatourian, H. S. Margolis, G. Marra, D. T. Reid and P. Gill1, “Common-Path Self-Referencing Interferometer for Carrier-Envelope Offset Frequency Stabilization with Enhanced Noise Immunity,” Opt. Lett. 35, pp. 1209-1211, 2010.