High-resolution broadband spectroscopy with a resonator-based phase modulator

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In the method proposed, an ultrashort laser pulse is transmitted through a dispersive element (optical fiber) and a waveguide (or bulk) Fabry-Perot resonator with an incorporated waveguide (or bulk) phase modulator. If the pulse bandwidth is much greater than the modulation frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> =N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</sup> FSR (N is an integer), the output pulse spectrum has two periods: one of them equals to the FSR and the second one is Λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> =1/(2πβ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Lf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ), where β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and L are the group velocity dispersion coefficient and length of the dispersive element, respectively. In our simulations, these periods were chosen to be equal. The modulated pulse is transmitted through the sample and recorded by a photodiode and an oscilloscope. The pulse spectrum is scanned by simultaneous variations of the value and delay, t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , of the voltage applied to the modulator. The calculated output pulse spectrum within the FSR is shown in Fig.1 for the input pulse width W=100 fs, FSR=1.905 GHz, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> =6FSR=11.43 GHz, β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> L =7.309 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</sup> 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-21</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , the modulation index A=2.2 π and the finesse of the resonator (with no modulation) F=72. Unlike conventional Fabry-Perot interferometers, the system spectral response can consist of multiple peaks and this increases signal-to-noise ratio. Such a spectral response is taken into account in data processing. The simulations show that our system is equivalent to a conventional Fabry-Perot resonator with a finesse of ≈1900 and a resolution of ≈1 MHz but much more stable against random variations of the resonator parameters.