Abstract

In the past decade we have witnessed remarkable advances associated with the frequency stabilization of the comb present in the output of a mode-locked femtosecond laser. While proving itself to be fantastically successful in its role as the “gears” of optical atomic clocks, the optical frequency comb has further evolved into a valuable tool for a wide range of applications, including ultraviolet and infrared spectroscopy, frequency synthesis, optical and microwave waveform generation, astronomical spectrograph calibration, and attosecond pulse generation, to name a few. In this review, I will trace several of these developments while attempting to offer perspective on the challenges and opportunities for frequency combs that might lie ahead in the next decade.

© 2010 U.S. Government

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2010 (11)

Z. Chang and P. Corkum, “Attosecond photon sources: the first decade and beyond,” J. Opt. Soc. Am. B 27, B9-B17 (2010).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37-40 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41-45 (2010).
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C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104, 070802 (2010).
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J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtoseond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
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B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hansch, and N. Picque, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55 (2010).
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T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16-L20 (2010).
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A. J. Benedick, G. Chang, J. R. Birge, L. Chen, A. G. Glenday, C. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175-19184 (2010).
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F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for infrared astronomical spectrograph calibration,” Rev. Sci. Inst. 81, 063105 (2010).
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W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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S. Grop, P.-Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46, 420-421 (2010).
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2009 (8)

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331-3340 (2009).
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E. Ivanov and M. E. Tobar, “Low phase-noise sapphire crystal microwave oscillators: Current status,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 263 (2009).
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D. Braje, L. Hollberg, and S. A. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
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M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170-fs, 1.5-μm solid-state laser oscillator,” Appl. Phys. B 99, 401-408(2009).
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D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87Rubidium,” Phys. Rev. A 80, 053806 (2009).
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M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition rate multiplication,” Opt. Lett. 34, 872-874 (2009).
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A. Bartels, D. Heinecke, and S. A. Diddams, “10 GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
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I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351 (2009).
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2008 (9)

S. A. Meyer, J. A. Squier, and S. A. Diddams, “Diode-pumped Yb:KYW femtosecond laser frequency comb with stabilized carrier-envelope offset frequency,” European Physics Journal D 48, 19 (2008).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Appl. Phys. B 91, 397-414 (2008).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
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K. -K. Ni, S Ospelkaus, M. H. G. de Miranda, A. Pe'er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, “A high phase-space density gas of polar molecules,” Science 322, 231-235 (2008).
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C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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 cms−1,” Nature 452, 610-612 (2008).
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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 T. Udem, “Laser frequency combs for astronomical observations,” Science 23, 1335 (2008).
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D. Braje, M. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57-66 (2008).

2007 (10)

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D'Odorico, M. Fischer, T. W. Hansch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839 (2007).
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S. Osterman, S. Diddams, M. Beasley, C. Froning, L. Hollberg, P. MacQueen, V. Mbele, and A. Weiner, “A proposed laser frequency comb-based wavelength reference for high-resolution spectroscopy,” Proc. SPIE 6693, 66931G (2007).
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Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1, 463-467 (2007).
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N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase×32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865-867 (2007).
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A. Pe'er, E. A. Shapiro, M. C. Stowe, M. Shapiro, and J. Ye, “Precise control of molecular dynamics with a femotosecond frequency comb,” Phys. Rev. Lett. 98, 113004 (2007).
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S. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with spectrally-resolved modes of a femtosecond laser frequency comb,” Nature 445, 627 (2007).
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P. Fendel, S. D. Bergeson, Th. Udem, and T. W. Hänsch, “Two-photon frequency comb spectroscopy of the 6 s-8 s transition in cesium,” Opt. Lett. 32, 701-703 (2007).
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P. Del'Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214-1217 (2007).
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N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B 24, 1756-1770 (2007).
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R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, “Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function,” Opt. Express 15, 9090-9095 (2007).
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2006 (5)

K. Kim, S. A. Diddams, P. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3 μm femtosecond optical frequency comb using spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. 31, 277-279 (2006).
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T. W. Hänsch, “Nobel lecture: Passion for precision,” Rev. Mod. Phys. 78, 1297 (2006).
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J. L. Hall, “Nobel lecture: Defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279 (2006).
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M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599 (2006).
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T. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011-1013(2006).
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2005 (8)

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105 (2005).
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V. Gerginov, C. E. Tanner, S. A. Diddams, A. Bartels, and L. Hollberg, “High resolution spectroscopy with a femtosecond laser frequency comb,” Opt. Lett. 30, 1734-1736 (2005).
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P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science 309, 749-752 (2005).
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K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
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J. J. McFerran, E. N. Ivanov, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 36-37 (2005).
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A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. Oskay, and L. Hollberg, “Femtosecond laser based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667-669 (2005).
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R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
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Ch. Gohle, Th. Udem, J. Rauschenberger, R. Holzwarth, M. Herrmann, H. A. Schussler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234-237 (2005).
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2004 (5)

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542-1544 (2004).
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B. Washburn, S. Diddams, N. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jørgensen, “A self-referenced, erbium fiber laser-based frequency comb in the near infrared,” Opt. Lett. 29, 252-254 (2004).
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L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303, 1843 (2004).
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A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063 (2004).
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S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318 (2004), and references therein.
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2003 (6)

T. M. Fortier, D. J. Jones, and S. T. Cundiff, “Phase stabilization of an octave-spanning Ti:sapphire laser,” Opt. Lett. 28, 2198-2200 (2003).
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F. Tauser, A. Leitenstorfer, and W. Zinth, “Amplified femtosecond pulses from an Er:fiber system: Nonlinear pulse shortening and self-referencing detection of the carrier-envelope-phase evolution,” Opt. Express 11, 594-600 (2003).
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N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944- 946 (2003).
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K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003).
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J. N. Ames, S. Ghosh, R. S. Windeler, A. L. Gaeta, and S. T. Cundiff, “Excess noise generation during spectral broadening in microstructured fiber,” Appl. Phys. B 77, 279 (2003).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611 (2003).
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J. L. Hall, “Optical frequency measurement: 40 years of technology revolutions,” IEEE J. Sel. Top. Quantum Electron. 6, 1136 (2000).
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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 modelocked lasers and direct optical frequency synthesis,” Science 288, 635 (2000).
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A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740-743 (2000).
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J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air--silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25-27 (2000).
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S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102 (2000).
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M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, Th. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, “Measurement of the hydrogen 1S-2S transition frequency by phase coherent comparison with a microwave cesium fountain clock,” Phys. Rev. Lett. 84, 5496-5499 (2000).
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T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the cesium D-1 line with a mode-locked laser,” Phys. Rev. Lett. 823568-3571 (1999).
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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, 881-883 (1999).
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H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327 (1999).
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Ames, J. N.

J. N. Ames, S. Ghosh, R. S. Windeler, A. L. Gaeta, and S. T. Cundiff, “Excess noise generation during spectral broadening in microstructured fiber,” Appl. Phys. B 77, 279 (2003).
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Angelow, G.

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740-743 (2000).
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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 T. Udem, “Laser frequency combs for astronomical observations,” Science 23, 1335 (2008).
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Arcizet, O.

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A. Bartels, D. Heinecke, and S. A. Diddams, “10 GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
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D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87Rubidium,” Phys. Rev. A 80, 053806 (2009).
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T. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011-1013(2006).
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L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105 (2005).
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V. Gerginov, C. E. Tanner, S. A. Diddams, A. Bartels, and L. Hollberg, “High resolution spectroscopy with a femtosecond laser frequency comb,” Opt. Lett. 30, 1734-1736 (2005).
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A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. Oskay, and L. Hollberg, “Femtosecond laser based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667-669 (2005).
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L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303, 1843 (2004).
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Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1, 463-467 (2007).
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I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351 (2009).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37-40 (2010).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41-45 (2010).
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Nature (7)

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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611 (2003).
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Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233 (2002).
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S. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with spectrally-resolved modes of a femtosecond laser frequency comb,” Nature 445, 627 (2007).
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Ch. Gohle, Th. Udem, J. Rauschenberger, R. Holzwarth, M. Herrmann, H. A. Schussler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234-237 (2005).
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Opt. Commun. (1)

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Opt. Lett. (19)

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K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
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K. Kim, S. A. Diddams, P. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3 μm femtosecond optical frequency comb using spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. 31, 277-279 (2006).
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T. M. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, “Phase coherent link from optical to microwave frequencies via the broadband continuum from a 1 GHz Ti:sapphire femtosecond oscillator,” Opt. Lett. 27, 1842-1844 (2002).
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R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbüldt, K. Gäbel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376-1378 (2001).
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B. Washburn, S. Diddams, N. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jørgensen, “A self-referenced, erbium fiber laser-based frequency comb in the near infrared,” Opt. Lett. 29, 252-254 (2004).
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T. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011-1013(2006).
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M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition rate multiplication,” Opt. Lett. 34, 872-874 (2009).
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Phys. Rev. A (2)

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87Rubidium,” Phys. Rev. A 80, 053806 (2009).
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J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtoseond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008).
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R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
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M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, Th. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, “Measurement of the hydrogen 1S-2S transition frequency by phase coherent comparison with a microwave cesium fountain clock,” Phys. Rev. Lett. 84, 5496-5499 (2000).
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Proc. SPIE (1)

S. Osterman, S. Diddams, M. Beasley, C. Froning, L. Hollberg, P. MacQueen, V. Mbele, and A. Weiner, “A proposed laser frequency comb-based wavelength reference for high-resolution spectroscopy,” Proc. SPIE 6693, 66931G (2007).
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Rev. Sci. Inst. (1)

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for infrared astronomical spectrograph calibration,” Rev. Sci. Inst. 81, 063105 (2010).
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Science (11)

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 23, 1335 (2008).
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Figures (7)

Fig. 1
Fig. 1

Frequency comb evolutionary tree.

Fig. 2
Fig. 2

Time-frequency interpretation of the output of the mode-locked laser. The frequency modes ν n = n f r + f o of the mode-locked laser are essentially a series of cw oscillators tightly locked in phase that coherently add to form a short pulse at a period T, which is the inverse of the repetition rate. The carrier-envelope offset frequency f o is measured via the heterodyne between the second harmonic ( × 2 ) of the infrared and visible comb components. For simplicity, f o is shown with the value of zero, such that every pulse is identical. The repetition rate (mode spacing) f r can be measured with a fast photodiode and compared or phase-locked to a microwave reference ν r.f. . Alternatively, mode N of the comb can be heterodyned with an external cw laser at frequency ν opt . Active feedback to the frequency comb can force the comb mode to oscillate in phase with the cw laser, and as the other modes are already locked in phase via the mode-locking mechanism, f r assumes the value of f r = ( ν opt + f o ) N .

Fig. 3
Fig. 3

Spectra of early and more recent frequency combs. (a) Spectrum of first mode-locked laser operating near 633 nm , as measured with a scanning Fabry-Perot etalon. The mode spacing is 56 MHz . Reprinted with permission from L. E. Hargrove, R. L. Fork, and M. A. Pollack, Appl. Phys. Lett. 5, p. 4-5. Copyright 1964, American Institute of Physics. (b) A portion of the 20 GHz frequency comb generated by mode-filtering the output of a frequency-stabilized 1 GHz frequency comb [38]. The lower part of the figure is the grey-scale “fringes” of the comb as recorded with a grating spectrometer and CCD camera. The upper part of the figure shows a line out of a portion of the CCD image. The modes are spectrally separated by 20 GHz and spatially dispersed by about 100  microns per mode. Central wavelength is 960 nm . (c) Spectral envelope of some common optical frequency combs generated with different laser sources. (i) 10 GHz Ti:Saph [39], (ii) 1 GHz broadband Ti:Saph [37], (iii) 180 MHz Yb:KYW [26], (iv) 100 MHz Er:fiber [20].

Fig. 4
Fig. 4

Record of improvement of precise frequency measurements in the optical and terahertz frequency domains over time. The y-axis is the base-ten logarithm of the fractional uncertainty Uc = σ ν o , where σ is the standard uncertainty and ν o is the carrier frequency. A distinction is made between frequencies less than and greater than 100 THz , which is somewhat arbitrarily defined as the beginning of the “optical” domain. Note that there were just a few measurements at frequencies greater than 100 THz prior to 1990, and it was not until the introduction of the femtosecond laser frequency comb around 2000 that the rate at which optical frequencies were measured truly accelerated and became commonplace. The circled points are a few noteworthy measurements: (i) The first measurement of an optical frequency involving a femtosecond laser frequency comb [55]. (ii) The most accurate measurement of an optical frequency standard, which is presently the ratio of the frequencies of two Al + quantum logic clocks with combined uncertainty of 2.5 × 10 17 . The evaluated inaccuracy of one of the Al + clocks is a factor of 3 smaller at 8.6 × 10 18 [63]. The residual fractional uncertainty of the frequency comb in the comparison of optical frequency standards and the construction of an optical clock is at or below 1 × 10 19 .

Fig. 5
Fig. 5

Three different spectroscopy approaches using femtosecond laser frequency combs. (a) Fluorescence detection. (b) Spectrally dispersed detection with a high resolution imaging spectrometer based on a VIPA (virtually-imaged phased array) disperser. (c) Dual comb multi-heterodyne spectroscopy with a point detector and high-speed data acquisition. In all cases, what is depicted as a vapor cell could in fact be atoms or molecules in a beam, trap, or other gas phase sample. In principle, liquids and solids could also be studied in a similar fashion.

Fig. 6
Fig. 6

Concept of an astronomical spectrograph calibrated by a femtosecond laser frequency comb. The atomically-referenced comb spectrum enters the spectrograph offset from the star light such that it appears below the dispersed stellar spectrum. In reality a fiber-fed spectrograph is preferable to reduce pointing errors. The optimum spacing of the comb lines is one every 3–4 resolution elements [86], amounting to 30 GHz for a visible spectrograph with resolving power of 60,000.

Fig. 7
Fig. 7

(a) Comparison of measured and projected phase noise on the 10 GHz signal generated from a few sources. (i) measured commercial sapphire oscillator [94], (ii) measured research sapphire oscillator [95], (iii) measured cryogenic sapphire oscillator [96], (iv) projected phase noise for a frequency comb locked to a cw laser that is stabilized to a high-finesse reference cavity [97, 98, 100]. (v) dashed line is the projected white noise floor given by photodetector shot noise. (b) General approach to line-by-line pulse shaping with an optical frequency comb. The different comb elements are spatially/spectrally dispersed and directed to a modulator array, where individual comb lines are modified in amplitude and phase. The modes are then re-combined to form an optical field with user-defined spectral and temporal characteristics.

Tables (1)

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Table 1 List Of Self-Referenced Frequency Combs, Including Some Key Parameters a

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