Generation of tuneable and ultrahigh repetition rate by fractional Talbot effect in frequency-shifted feedback lasers

Abstract

Summary form only given. We present an experimental demonstration of a novel technique for the generation of Fourier transform-limited pulses at tuneable and possibly ultrahigh repetition rates, limited only by the spectral bandwidth of the laser. Our proposal is based on a frequency shifted feedback (FSF) laser injected with a single-mode laser. Recall that a FSF laser consists in a laser cavity with an internal frequency shifter (usually an acousto-optics frequency shifter or AOFS): each time a photon makes a roundtrip in the cavity, its frequency is increased by twice the frequency of the acoustic wave in the AOFS (in the case of a linear cavity). When seeded with a single-mode laser, the output of the FSF laser consists in a frequency comb with a mode spacing equal to the shift frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> : the frequency of the n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> mode is f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> = f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> + nf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is the frequency of the seed laser. However contrary to mode-locked frequency combs where all modes share the same phase, the phases of the modes at the output of the FSF laser are quadratic with n and are given by πn(n+1)f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is the free spectral range of the FSF cavity [1]. Early numerical simulations predicted the generation of Fourier transform-limited pulses when the frequency shift per roundtrip and the cavity free spectral range are in the ratio of two integers, that is f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = p/q, p and q being coprime integers [2]. In this case the repetition rate is equal to qf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (=pf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ). We demonstrated experimentally this property for large values of p and q, by implementing a FSF dye cavity seeded with a monochromatic (dye) laser. The spectral bandwidth of the comb is 150 GHz. By adjusting the length of the FSF laser cavity (i.e. f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ), we have demonstrated the generation of 6 ps pulses at a repetition rate tuneable by more than two orders of magnitude, between 240 MHz and 47 GHz, by steps of 80 MHz. This result is interpreted in terms of temporal fractional Talbot effect [3] and described analytically. A very good agreement with the experiment is obtained. In particular we characterize the phases of the optical pulses. This work offers important novel perspectives for the generation of ultrahigh repetition rates (GHz to THz) for various applications in data processing, opt-electronics, THz generation and spectroscopy of metallic nanoparticles.