Efficient Carrier Envelope Offset Locking for a Frequency Comb by Modifying a Collinear f-to-2f Interferometer

Efficient Carrier Envelope Offset Locking for a Frequency Comb by Modifying a Collinear f -to-2f Interferometer
　
Atsushi Ishizawa, Tadashi Nishikawa, and Hidetoshi Nakano
Optical Science Laboratory
　The development of the mode-locked laser has contributed to our ability to control of the carrier envelope offset (CEO), which is the absolute phase slip between laser pulses. The mode-locked laser also contains various frequency components in the hundred of terahertz region. These regularly spaced components are called a "frequency comb". By controlling the phase and amplitude of individual comb lines, it would be possible to synthesize an optical field waveform directly like an electric pulse waveform can, which would contribute to the control of laser-matter interactions.
　We need a CEO-locked frequency comb with more than a 10-GHz repetition rate in order to resolve each mode of the frequency comb with an arrayed-waveguide grating. The problem is that the pulse energy decreases as the repetition rate increases. We therefore need to achieve CEO locking with a small and high-repetition-rate device with low pulse energy. Recently, we demonstrated a CEO-locked frequency comb with 230-pJ fiber coupling pulse energy [1]. To generate an octave-bandwidth spectrum in a nonlinear fiber and of the second harmonic in an f -to-2f interferometer with low pulse energy, we used a tellurite photonic crystal fiber (PCF) and a periodically poled LiNbO₃ ridge waveguide, respectively. However, we had to use a pulse energy of about 1 nJ because the coupling efficiency of the output of the laser to the PCF. To solve this problem, we propose a method for modifying the optical components in a collinear f -to-2f interferometer. We use angled V-groove splicing between the tellurite PCF and a high-NA fiber to increase coupling efficiency into the tellurite PCF. In addition, we set up the collinear f -to-2f interferometer with the minimum number of optics without an additional dispersion compensation fiber in order to reduce connection and propagation losses. Using our method, we have demonstrated a CEO-locked frequency comb at telecommunications wavelengths with 500-pJ pulse energy, which breaks the previous record of 600 pJ [2] and is, to the best of our knowledge, the lowest pulse energy ever achieved for CEO locking [3]. We believe that our method is useful for lower pulse energy and for long-term stability due to the simple setup.
[1] A. Ishizawa et al., Opt. Express 16 (2008) 4706.
[2] I. Hartl et al., Opt. Express 13 (2005) 6490.
[3] A. Ishizawa et al., CLEO/IQEC 2009, Baltimore, U.S.A. (May 2009).
　

Fig. 1. Experimental setup for the CEO locking with low pulse energy.
SMF: single-mode fiber. TEC: thermally expanded core.
　

Fig. 2. (a) Self-referencing beat signal of the 250-MHz laser. f₀: CEO frequency. f_r: repetition rate of the laser. (b) The phase difference between the beat signal and local oscillator.

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