Frequency-dissymmetric nonlinear sideband generation in a photonic crystal fibre

Abstract

Summary form only given. Generation of correlated photon pairs by spontaneous parametric four-wave mixing (FWM) in photonic crystal fibres (PCF) opens the way for many applications, particularly for fibre-based quantum communication devices. In degenerate FWM, two pump photons at frequency ωρ are annihilated to produce simultaneously a signal photon at ωs and an idler photon at ωi, such as ωs + ωi = 2ωp (energy conservation). This process occurs with high efficiency only if the phase-matching condition (i.e. momentum conservation) is satisfied [1].The group-velocity dispersion (GVD) of the silica-core PCF used in our experiments (fig.1.a, inset) has been experimentally determined by a time-of-flight measurement for wavelengths from 740 nm to 930 nm. The result is consistent with the analytical calculation provided by Saitoh and Koshiba [2]. Particularly, we estimate the zero-dispersion wavelength of the PCF: λZDW = 834 nm. From this GVD measurement, we deduce the phasematching curve given in fig.1.a, on which we note that there is a vertical asymptote at λp - 832 nm. Thus, FWM should not be observed if the pump wavelength λp is lower than this limit value. Our experimental observations are very different from this prediction. Indeed, by injecting inside the fundamental mode of a 1.3-m-long PCF hyperbolic secant picosecond pulses (with an intensity-FWHM duration of about 2 ps) at λinj = 815 nm with a 80-MHz repetition rate, we actually observe a spontaneous parametric FWM phenomenon (with sidebands generated around 925 nm and 745 nm), and moreover with a clear frequency dissymmetry with respect to the injected pulse frequency (ωinj = 2ππc/λinj) (fig.1.b): generated signal and idler frequencies ωs and ωi do not satisfy ωs + ωi = 2ωinj.A systematic study of this frequency-dissymmetric phenomenon shows that it occurs only when the injected pulse peak power (Pinj) is higher than a threshold value Pth, and that Pth increases when λinj decreases from λZDW. This variation of Pth as a function of λinj can be understood by considering the key role played by self-phase modulation (SPM) in the observed phenomenon. Indeed, the frequency-dissymmetric signal and idler waves are generated only when the spectral broadening (due to SPM) of the injected pulses is sufficient to reach a threshold wavelength λth (i.e. a threshold frequency ωth) of the order of 832 nm. This value corresponds to the position of the vertical asymptote in the phase-matching curve. Finally, we observe that ωs + ωi - 2ωth when Pinj Pth. All these observations highlight the fact that, when the injected pulse peak power Pinj is high enough, spectral broadening by SPM is sufficient to get a part of the injected pulse spectrum higher than the threshold value λth, and thus this part of the spectrum can play the role of pump in an efficient FWM process (i.e. with the phasematching condition satisfied). It is important to note that this phenomenon advantageously presents an extension of the spectral range on which an efficient FWM process can occur: instead of being restricted to injected pulse wavelengths higher than the zero-dispersion wavelength λZDW of the fibre (or at least, higher than a threshold wavelength λth of the order of λZDW), experimenters can work with lower wavelengths, providing the availability of a high enough peak power and/or interaction length to sufficiently broaden (by SPM) the injected pulse spectrum.