光頻率標準對於基礎研究或是工業應用，都是十分重要的，例如，物理常數的定義、精細光譜量測、測量學、光鐘與光通訊系統。隨著光通訊市場的迅速成長，研發了許多重要的技術，特別一提的是，多波長多工系統。這種在同一光纖同時傳遞多道雷射光的技術，使得光通訊頻寬倍數成長。頻率量測就變的非常重要。

原子與分子的吸收譜線可以提供頻率標準，來當作光通道的校準。鎖定在線寬窄、沒有都普勒背景的吸收譜線，可以有極高的頻率穩定性、精確性、重複性。我們利用銣原子雙光子吸收譜線上的頻率標準在760 nm，建立了一光通訊的頻率標準在1520 nm，其精確度達 10-11。也同時建立了一頻率標準在碘分子吸收譜線的超精細結構上在近紅外光的波段。

但是利用原子與分子的吸收譜線來建立的頻率標準，受限於某些特定頻率。而且也只有一些適合波長的雷射可以當頻率標準光源。雖然利用原子與分子的吸收譜線來建立的頻率標準，設計與組裝都比較容易，但是只受限於特定波長。隨著鎖模雷射與光子晶體光纖的發展，讓我們可以製作出飛秒光頻梳系統。將飛秒鎖模雷射的脈衝光，打入光子晶體光纖中，讓飛秒雷射的頻寬放大到一個光頻上的八度音，而輸出光的光頻可以看成是一幾乎涵蓋可見光範圍的寬頻光源，而且其中的頻率譜線是具有像梳子般的等距光頻率。飛秒光頻梳可以看成是一個 “光頻率尺”，可以用來量測任何光的頻率，只要光頻率落在飛秒光頻梳的光譜中。我們架設一飛秒光頻梳系統，將鎖模雷射的重複頻率與外差頻率鎖定。我們的飛秒光頻梳系統的準確度可以達到 10-11。

Optical frequency standards are important for fundamental research, such as physical constants definitions, frequency metrology, precision optical spectroscopy, and industrial applications, such as optical communication system and optical clock. With the rapid growth of optical communication market, the numerous and important techniques are developed, especially high-density wavelength-division multiplexing (WDM). The WDM system provides multi-channel optical transmissions at single optical fiber. The calibration of channel allocation becomes important.

Atomic and molecular absorption lines provide wavelength references that are essential for the calibration of channel allocation. Locking to narrow Doppler-free lines is required for greater frequency stability, accuracy, and reproducibility. We set up the frequency standards for optical communication system based on rubidium 5S-7S two-photon absorptions at 760 nm for optical communication system. The accuracy is 10-11. And we lock the laser frequency on the hyperfine structure of iodine spectroscopy at near infrared.

But the frequency standards based on atomic and molecular absorption lines are limited to some specific frequencies. Although the frequency standards based atomic and molecular absorption lines are not difficult to set up, the flexibility is limited. With the progresses of the mode-locked laser and photonic crystal fiber, the frequency comb from visible to near infrared region is realized. The output pulse of the femtosecond laser is launched into a photonic crystal fiber and, as a result, a narrow frequency comb of mode-locked laser pulse is extended into a "comb" of equally spread, very broad light sources that cover almost all the visible spectrum. It is like a “frequency ruler” to measure any unknown frequency at optical region. We set up the femtosecond comb system for the absolute frequency measurement from visible to near infrared and stabilize the repetition frequency and the offset frequency. The frequency jitter of the stabilized repetition frequency is 4 mHz. The frequency fluctuation of the offset frequency is 11 mHz when it is locked. It provides the accuracy of the optical frequency measurements up to the 10-11 level.

Reference for Chapter 1:

[1] M. Ohtsu, ed., “Frequency Control of Semiconductor Lasers”, John Wiley & Sons, Inc. (1996)
[2] A. Danielli, P. Rusian, A. Arie, M.H Chou, and M. M. Fejer, “Frequency stabilization of a frequency-doubled 1556-nm source to the 5S1/2→5D5/2 two-photon transitions of rubidium”, Optics Letters 25, 905 (2000)
[3] H. C. Chui, Y. W. Liu, R. V. Rossuev, M. M. Fejer, S. Y. Shaw, and J. T. Shy, “Frequency-stabilized 1520 nm diode laser on rubidium 5S1/2 → 7S1/2 two-photon absorption”, accepted by Applied Optics.
[4] H. C. Chui, M. S. Ko, Y. W. Liu, T. Lin, J. T. Shy, S. Y. Shaw, R. V. Roussev, and M. M. Fejer, “Iodine-stabilization of a 1520-nm diode laser”, CMH6, Conference on Laser and Electro-Optics 2004, San Francisco
[5] S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs”, Review of Modern Physics, 75, 325 (2003).
[6] V. Mahal, A. Arie, M. A. Arbore, and M. M. Fejer, “Quasi phase-matched frequency doubling of a 1560-nm diode laser and locking to the rubidium D2 absorption lines”, Optics Letters, 21, 1217 (1996).
[7] Krishnan R. Parameswaran, Roger K. Route, Jonathan R. Kurz, Rostislav V. Roussev, Martin M. Fejer, Masatoshi Fujimura, “Highly efficient second-harmonic generation in buried waveguides formed by annealed and reverse proton exchange in periodically poled lithium niobate,” Optics Letters, 27, 179 (2002)
[8] S. Gerstenkorn, J. Verges, and J. Chevillard, “Atlas du Spectre d’Absorption de la Molecule d’Iode 11.000–14.000 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1982); S. Gerstenkorn, and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14.000–15.600 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1978); S. Gerstenkorn, and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14.800–20.000 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1978).
[9] R. Klein and A. Arie, “Observation of iodine transitions using the second and third harmonics of a 1.5-□m laser,” Applied Physics B 75, 79 (2002)
[10] A. Bartels, T. Dekorsy, and H. Kurz, “Femtosecond Ti:sapphire ring laser with a 2-GHz repetition rate and its application in time-resolved spectroscopy”, Optics Letter, 24, 996 (1999)
[11] D. J. Jones, Scott A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis Science”, 288,635 (2000)
[12] T. Udem, R. Holzwarth and T. W. Hänsch, “Optical frequency metrology”, Nature, 416, 233 (2002)
[13] R. Kaarls, “Evolving Needs for Metrology in Trade, Industry and Society and the Role of the BIPM”, Bureau International des Poids et Mesures (BIPM), Paris, France (2003).
[14] Yan-Rung Lin, “Tunable Mid-IR Difference Frequency Generation Source and Precise Spectroscopy of Helium Hydride Molecular Ion HeH+”, PhD Dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2001)

Reference for Chapter 2:

[1] M. Ohtsu, ed., “Frequency Control of Semiconductor Lasers”, John Wiley & Sons, Inc. (1996)
[2] F. Ducos, J. Honthaas, and O. Acef, “Development of an optical frequency comb around 1556 nm referenced to an Rb frequency standard at 778 nm,” European Physics Journal-Applied Physics 20, 227 (2002).
[3] M. de Labachelerie, K. Nakagawa, Y. Awaji, and M. Ohtsu, “High frequency-stability laser at 1.5 □m using Doppler-free molecular lines”, Optics Letters 20, 572 (1995).
[4] G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, “Frequency stabilization of a 1.54 □m Er–Yb laser against Doppler-free 13C2H2 lines,” Optics Communications, 209, 411 (2002).
[5] Y. Awaji, M. de Labachelerie, M. Ohtsu, H. Sasada, “Optical frequency measurement of the H12C14 N Lamb-dip-stabilized 1.5 □m diode laser”, Optics Letters, 20, 2024(1995).
[6] V. Mahal, A. Arie, M. A. Arbore, and M. M. Fejer, “Quasi phase-matched frequency doubling of a 1560-nm diode laser and locking to the rubidium D2 absorption lines”, Optics Letters, 21, 1217 (1996).
[7] A. Bruner, A. Arie, M.A. Arbore, and M.M. Fejer, “Frequency stabilization of a diode laser at 1540 nm by locking to sub-Doppler lines of potassium at 770 nm,” Applied Optics 37, 1049 (1998)
[8] C. Svelto, F. Ferrario, A. Arie, M.A. Arbore, and M.M. Fejer, “Frequency Stabilization of a Novel 1.5-□m Er–Yb Bulk Laser to a 39K Sub-Doppler Line at 770.1 nm,” IEEE Journal of Quantum Electronics 37, 505 (2001)
[9] M. Poulin, C. Latrasse, N. Cyr, and M. Tetu, “An absolute frequency reference at 192.6 THz (1556 nm) based on a two-photon absorption line of rubidium at 778 nm for WDM communication systems”, IEEE Photonics Technology Letters, 9, 1631 (1997).
[10] A. Danielli, P. Rusian, A. Arie, M.H Chou, and M. M. Fejer, “Frequency stabilization of a frequency-doubled 1556-nm source to the 5S1/2→5D5/2 two-photon transitions of rubidium”, Optics Letters 25, 905 (2000).
[11] M. S. Ko, and Y. W. Liu, “The first observation of rubidium 5S1/2→7S1/2 two-photon transitions with a diode laser,” accepted by Optics Letters
[12] H. C. Chui, Y. W. Liu, J. T. Shy, S. Y. Shaw, R. Roussev, and M. M. Fejer “Frequency-stabilized 1520 nm diode laser on rubidium 5S1/2 → 7S1/2 two-photon absorption,” Accepted by Applied Optics.
[13] R. Kaarls, “Evolving Needs for Metrology in Trade, Industry and Society and the Role of the BIPM”, Bureau International des Poids et Mesures (BIPM), Paris, France (2003)
[14] Krishnan R. Parameswaran, Roger K. Route, Jonathan R. Kurz, Rostislav V. Roussev, Martin M. Fejer, Masatoshi Fujimura, “Highly efficient second-harmonic generation in buried waveguides formed by annealed and reverse proton exchange in periodically poled lithium niobate,” Optics Letters, 27, 179 (2002)
[15] ITU-T Recommendation G. 694.1, “Spectral grids for WDM applications: DWDM frequency grid”, International Telecommnuication Union, Jun. 2002
[16] F. S. pavone, P. Cancio, M. inguscio, R. U. Martinelli, R. J. Menna, “Linewidth and tuning characteristics of a mirror-extended cavity distributed-feedback 1.65-□m diode laser,” Applied Physics Letters, 60, s249, 1995.
[17] S. Gerstenkorn, J. Verges, and J. Chevillard, “Atlas du Spectre d’Absorption de la Molecule d’Iode 11.000–14.000 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1982); S. Gerstenkorn, and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14.000–15.600 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1978); S. Gerstenkorn, and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14.800–20.000 cm-1,” Laboratoire Aime Cotton, CNRS, Orsay, France (1978).
[18] W. Y. Cheng, H. Y. Chang, Y. R. Lin, J. T. Shy, T. Lin, Y. K. Chen, M. H. Chou, and M. M. Fejer, “Iodine-stabilized 1534 nm diode laser for optical fiber communication,” in Conference on Precision Electromagnetic Measurements 2000 (CPEM 2000), digest 2000, Sydney, Australia, p.205
[19] R. Klein and A. Arie, “Observation of iodine transitions using the second and third harmonics of a 1.5-□m laser,” Applied Physics B 75, 79 (2002)
[20] Yan-Rung Lin, “Tunable Mid-IR Difference Frequency Generation Source and Precise Spectroscopy of Helium Hydride Molecular Ion HeH+”, PhD Dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2001)
[21] A. Bartels, T. Dekorsy, and H. Kurz, “Femtosecond Ti:sapphire ring laser with a 2-GHz repetition rate and its application in time-resolved spectroscopy”, Optics Letter, 24, 996 (1999)
[22] S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs”, Review of Modern Physics, 75, 325 (2003).
[23] H. C. Chui, M. S. Ko, J. L. Peng, R. H. Ann, Y. W. Liu, and J. T. Shy, “Absolute frequency measurement of rubidium 5S1/2→7S1/2 two-photon transition with self-reference femtosecond laser”, Submitted to Optics letters.

Reference for Chapter 3:

[1] J. L. Hall, “Optical Frequency Measurement: 40 Years of Technology Revolutions”, IEEE Journal of Selected Topics in Quantum Electronics, 6, 1136 (2000).
[2] J. L. Hall, J. Ye, S. A. Diddams, L. S. Ma, S. T. Cundiff, and D. J. Jones, “Ultrasensitive Spectroscopy, the Ultrastable Lasers, the Ultrafast Lasers, and the Seriously Nonlinear Fiber: A New Alliance for Physics and Metrology”, IEEE Journal of Quantum Electronics, 37, 1482 (2001)
[3] S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs”, Review of Modern Physics, 75, 325 (2003).
[4] D. J. Jones, Scott A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis Science”, 288,635 (2000)
[5] A. Bartels, T. Dekorsy, and H. Kurz, “Femtosecond Ti:sapphire ring laser with a 2-GHz repetition rate and its application in time-resolved spectroscopy”, Optics Letter, 24, 996 (1999)
[6] R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses”, Physics Review Letters, 24, 592 (1970)
[7] See the websites of Crystal Fibre A/S (http://www.crystal-fibre.com/) and Blazephotonics, inc (http://www.blazephotonics.com/)
[8] J. C. Knight, “photonic crystal fibers”, Nature 424, 847 (2003)
[9] G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers”, Optics Express 10, 1083 (2002)
[10] S. A. Diddams, Th. Udem, K. R. Vogel, C. W. Oates, E. A. Curtis, R. S. Windeler, A. Bartels, J. C. Bergquist, and L. Hollberg, “A compact femtosecond-laser-based optical clockwork”, in Laser Frequency Stabilization , Standards, Measurements, and Applications, Proceeding of SPIE 4269, 77 (2001)
[11] J.-C. Diels, and W. Rudolph, “Ultrashort laser pulse phenomena”, Academic Press, inc (1996)
[12] K. M. Hilligsøe, H. N. Paulsen, J. Thøgersen, S. R. Keiding, and J. J. Larsen, “Initial steps of supercontinuum generation in photonic crystal fibers”, Journal of Optical Society of America B 20, 1887 (2003)
[13] http://www.gigaoptics.de/
[14] T. M. Fortier, D. J. Jones, J. Ye, and S. T. Cundiff, “Highly Phase Stable Mode-Locked Lasers”. IEEE Journal OF Selected Topics in Quantum Electronics, 9, 1002 (2003)
[15] S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, S. Bize, E. A. Curtis, J. C. Bergquist, and L Hollberg, “Design and Control of Femtosecond Lasers for Optical Clocks and the Synthesis of Low-Noise Optical and Microwave Signals”, IEEE Journal OF Selected Topics in Quantum Electronics, 9, 1072 (2003)
[16] A. Bartels, C.W. Oates, L. Hollberg and S.A. Diddams, “Sub-hertz stabilization of femtosecond laser frequency combs”, CMW7, Conference on Laser and Electro-Optics 2004, San Francisco
[17] Yan-Rung Lin, “Tunable Mid-IR Difference Frequency Generation Source and Precise Spectroscopy of Helium Hydride Molecular Ion HeH+”, PhD Dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2001)
[18] H. C. Chui, Y. W. Liu, J. T. Shy, S. Y. Shaw, R. Roussev, and M. M. Fejer “Frequency-stabilized 1520 nm diode laser on rubidium 5S1/2 → 7S1/2 two-photon absorption,” Accepted by Applied Optics.

Reference for Chapter 4:

[1] Yan-Rung Lin, “Tunable Mid-IR Difference Frequency Generation Source and Precise Spectroscopy of Helium Hydride Molecular Ion HeH+”, PhD Dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2001)
[2] M. S. Ko and Y. W. Liu, “Observation of rubidium 5S1/2→7S1/2 two-photon transitions with a diode laser”, Accepted by Optics Letters.
[3] H. C. Chui, Y. W. Liu, J. T. Shy, S. Y. Shaw, R. Roussev, and M. M. Fejer “Frequency-stabilized 1520 nm diode laser on rubidium 5S1/2 → 7S1/2 two-photon absorption,” Accepted by Applied Optics.
[4] S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs”, Review of Modern Physics, 75, 325 (2003).
[5] S. A. Diddams, Th. Udem, K. R. Vogel, C. W. Oates, E. A. Curtis, R. S. Windeler, A. Bartels, J. C. Bergquist, and L. Hollberg, “A compact femtosecond-laser-based optical clockwork”, in Laser Frequency Stabilization , Standards, Measurements, and Applications, Proceeding of SPIE 4269, 77 (2001)
[6] S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, S. Bize, E. A. Curtis, J. C. Bergquist, and L Hollberg, “Design and Control of Femtosecond Lasers for Optical Clocks and the Synthesis of Low-Noise Optical and Microwave Signals”, IEEE Journal OF Selected Topics in Quantum Electronics, 9, 1072 (2003)
[7] A. Arie, and R. L. Byer, “Laser heterodyne spectroscopy of 127I2 hyperfine structure near 532 nm”, Journal of Optical society of America B 10, 1990 (1993).
[8] T. J. Quinn, ‘‘Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),’’ Metrologia 40, 103–133 (2003)
[9] See the manufacturer’s website http://www.lwecorp.com/
[10] T. J. Kane, and R. L. Byer, “Monolithic, unidirectional single-mode Nd:YAG ring laser”, Optics Letters, 10, 65 (1985)
[11] See the manufacturer’s website http://www.hcphotonics.com/
[12] Wang-Yau Cheng, “Frequency Measurements on 543 nm He-Ne Lasers and the Hyperfine Spectrum of Iodine Molecule on 543 nm Wavelength”, PhD dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan (1999)
[13] H. C. Chui, M. S. Ko, J. L. Peng, R. H. Ann, Y. W. Liu, and J. T. Shy, “Absolute frequency measurement of rubidium 5S1/2→7S1/2 two-photon transition with self-reference femtosecond laser”, Submitted to Optics letters
[14] G. Grynberg and B. Cagnac, “Doppler-free multiphotonic spectroscopy”, Report of Progress Physics, 40, 791(1977).
[15] M. J. Snadden, A. S. Bell, E. Riis, A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb”, Optical communications 125, 70. (1996)
[16] E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms”, Review of Modern Physics 49, 31 (1977).

Reference for Chapter 5:

[1] B. Bodermann, M. Klug, U. Winkelho_, H. Kn¨ockela, and E. Tiemann, “Precise frequency measurements of I2 lines in the near infrared by Rb reference lines”, European Physics Journal D 11, 213 (2000)
[2] Yan-Rung Lin, “Tunable Mid-IR Difference Frequency Generation Source and Precise Spectroscopy of Helium Hydride Molecular Ion HeH+”, PhD Dissertation, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2001)
[3] Hsin-Chih Wang, “Single-frequency Continuous-wave Periodically Poled Lithium Niobate Optical Parametric Oscillator”, Master Thesis, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan. (2003).