I5 December 1999 OPTICS COMMUNICATIONS ELSEVIER Optics Communications 172 (1999) 59-68 www.elsevier.com/1ocate/optcom Measuring the frequency of light with mode-locked lasers ’ J. Reichert *, R. Holzwarth, Th. Udem, T.W. Hksch Max-Planck-Institutflir Quantenoptik, Hans-Kopfermann-Str. I, 85748 zyxwvutsrqponmlkjihgfedcbaZYXWVUT G arc hing , G e rm any Received 1 July 1999; received in revised form 20 August 1999; accepted 1 September 1999 zyxwvutsrqponmlkjihgfedcbaZ Abstract We have stabilized the modes of a comb of optical frequencies emitted by a mode-locked femtosecond-laser and used it as a ruler to measure differences of up to 45.2 THz between laser frequencies in a new type of frequency chain. Directly converting optical to radio frequencies, we have used it for an absolute frequency measurement of the IS-2s transition in the hydrogen atom. Here, an intuitive model of the comb’s properties is given and essential techniques for its stabilization and efficient detection of beat signals are presented. 0 1999 Elsevier Science B.V. All rights reserved. Keywords: Frequency comb; Femtosecond laser; Frequency chain; Optical frequency measurement In recent years, we have witnessed dramatic progress in the development of optical frequency standards based on trapped ions [l] and narrow spectral lines of neutral atoms such as the hydrogen lS-2s transition [2]. Having the potential to reach accuracies far beyond the current state of the art cesium atomic clocks [3], the missing part of future atomic clocks still remains a precise, reliable ‘clock- work’, converting frequencies in the optical range of several hundred Terahertz to radio frequencies. In the past, phase coherent comparisons between optical and radio frequencies have been performed with the few harmonic frequency chains that reach all the way up to the visible or the UV region [2,4,5]. A promising approach for a new type of frequency chain is the determination of an optical frequency j ’ Corresponding author. E-mail: reichert@mpq.mpg.de ’ We dedicate this article to Marlan 0. Scully on occasion of his 60th birthday. by measuring a frequency interval in the optical region. For example, the interval Af = 2f-f=f between zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML f and its second harmonic 2f could be measured. Optical frequency interval dividers [6,7] that allow the phase coherent bisection of arbitrarily large frequency differences can reduce that interval. These dividers generate the sum frequency of the two input laser frequencies in a nonlinear crystal and phase-lock the second harmonic of a third laser to it. This forces the fundamental frequency of the third laser to oscillate at the precise center of the interval. If y1 such dividers are cascaded the initial frequency gap is reduced by a factor 2”. The simplicity and reliability of such a new frequency chain depends critically on the capability to directly measure large optical frequency differences, avoiding the need for a large number of frequency interval dividers. While we have demonstrated a 5 stage frequency interval divider chain about two years ago [2], in recent experiments we have used the comb of modes emitted by a mode-locked femtosecond-laser to OO30-4018/99/$ see front matter 0 1999 Elsevier Science B.V. All rights reserved. PIl: s0030-4018(99)0049 l-5