Femtosecond Laser Frequency Combs

As recognized by the 2005 Nobel Prize in Physics, frequency combs based on femtosecond lasers are immensely powerful tools for a wide range of applications. The precise spectral and temporal qualities of stabilized frequency combs have applications in optical clocks based on atomic references [1], femtosecond stability timing distribution systems [2], tests of quantum mechanics and fundamental physical constants, astrophysical spectrograph calibration [3, 4], high harmonic generation or soft x-ray generation, and atomic and molecular spectroscopy [5] to name only a few.

Frequency combs are fundamentally based on mode-locked laser technology, which has been available since the 1970’s. The fundamental shift was the development first of microstructure fibers that allowed tremendous coherent broadening of the output spectrum from mode-locked lasers [6]. However, the broader range of applications has come with the maturing of mode-locked Ti:sapphire lasers [7] and chirped mirror technology for dispersion control [8], as well as impressive advances in Er:fiber laser technology [9]. Currently, frequency combs directly obtained from femtosecond lasers cover a wavelength range from 0.6 µm to 2 µm. Other wavelength ranges may be achieved via frequency conversion of an available comb, a nonlinear optical process that guarantees the transfer of accuracy and stability of the initial comb.

Figure 1—The output from a mode locked laser is a periodic sequence of pulses of light due to the mode locking mechanism. The time between pulses is the pulse repetition period, and the time required for the underlying carrier wave to replicate its position under the pulse envelope is the carrier-envelope offset period.

Figure 2—The optical spectrum of the train of pulses is a periodic sequence of bright spectral lines. The spacing between the features is the inverse of the pulse repetition period, and is inversely related to the length of the optical cavity. If we extend the periodic spacing of the lines to the origin, we will find a small offset from zero, the frequency of which will be the inverse of the carrier-envelope offset period. Ti:sapphire based femtosecond lasers can have spectral bandwidths exceeding several hundred terahertz, more than one octave.

Controlling the absolute frequency of each component of the output spectrum from the mode locked laser is the defining aspect of a frequency comb. The output spectrum from the comb is described by the spacing between the individual frequency components, ƒ_rep, as well as the offset of those components from zero frequency, ƒ₀. Knowing and controlling these two frequencies, allows all other frequencies generated from the laser to be simply defined as, ƒ = ƒ₀ + Νƒ_rep. This control can be achieved in various ways, and should be tailored to the expected manner in which the comb will be used for best results.

Figure 3—Transforming a Ti:sapphire femtosecond laser into a frequency comb. In this particular type of construction, the top half of the diagram corresponds to the stabilization scheme necessary for controlling the pulse repetition rate. The lower right corner contains the optics necessary for control of the offset frequency [10].

One of the more recently proposed applications for frequency comb technology is the calibration of astronomical spectrographs [4]. Highly precise and highly accurate calibration of astronomical spectrographs is necessary to enable astronomers to use the radial velocity method to search for planets outside our solar system and to unravel other cosmological mysteries. In this method, astronomers monitor the light emitted from stars to observe a slight periodic shift in the emitted spectrum caused by the motion of the star induced by an orbiting planet. In this application, both the accuracy and precision of the frequency comb will be utilized to enable searches for earth-like planets and solar systems.

Figure 4 - For calibrating astrophysical spectrographs, the ideal calibration spectrum is one which contains many bright, evenly spaced features, each with a very well known frequency. The plot above is the output of a frequency comb based on a 1GHz Ti:sapphire laser whose output spectrum has been filtered to pass only every 40th component of the output spectrum. This allows resolution of individual spectral lines from the comb by the spectrograph, while preserving the precision and stability necessary for high quality calibration [3].

References:

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2. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator. Optics Letters, 2007. 32(9): p. 1044-1046.

3. 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, 2008. 452(7187): p. 610-612.

4. M. T. Murphy, T. 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. Monthly Notices of the Royal Astronomical Society, 2007. 380(2): p. 839-847.

5. 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, 2006. 311(5767): p. 1595-1599.

6. M. Bellini and T. W. Hansch, Phase-locked white-light continuum pulses: toward a universal optical frequency-comb synthesizer. Optics Letters, 2000. 25(14): p. 1049-1051.

7. R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, Generation of 5-fs pulses and octave-spanning spectra directly from a Ti : sapphire laser. Optics Letters, 2001. 26(6): p. 373-375.

8. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, Design and fabrication of double-chirped mirrors. Optics Letters, 1997. 22(11): p. 831-833.

9. I. Hartl, T. R. Schibli, A. Marcinkevicius, D. C. Yost, D. D. Hudson, M. E. Fermann, and J. Ye, Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 X 10(14) W/Cm-2 peak intensity at 136 MHz. Optics Letters, 2007. 32(19): p. 2870-2872.

10. A. Benedick, D. Tyurikov, M. Gubin, R. Shewmon, I. Chuang, and F. X. Kärtner, “Compact, Ti:sapphire based methane-stabilized optical molecular frequency comb and clock,” Optics Letters 2009. 34:(14), p. 2168-2170.