# Temporal and spectral compression of pulses in fibers with a running refractive index wave

It is known that when a light pulse propagates through anoptical fibre, in which a running refractive-index wave(RRIW) is generated, one can observe the effects that are absent both in homogeneous fibres and in fibres with a static inhomogeneity or periodicity. The authors of Refs studied the effects related to a change in polarisation and carrier frequency offset of quasi-monochromatic wave packets under the RRIW influence. Pulsed regimes of light propagation in optical fibres with a RRIW are characterised by a several-fold increase in the pulse power with a corresponding reduction of its duration. However, despite the abovesaid, current publications (except for a relatively small number of papers; see e.g.) lack a detailed examination of the possibility of the control of the frequency modulation rate and the spectral width of pulses interacting with a RRIW.

In this paper we investigate the conditions for temporal and spectral compression of frequency-modulated (FM) Gaussian pulses propagating in a fibre with a RRIW. It is shown that such a fibre can be characterised by a strong pulse frequency modulation at a constant linear velocity. This fact can be used for the subsequent strong spectral or temporal compression. We present analytical expressions for the dependences of duration, spectral width and initial rate of frequency modulation of a (chirp) pulse on the distance travelled along the fibre. Based on the numerical analysis we have studied the behaviour of these characteristics by changing the coefficient of the refractive-index modulation and other parameters of the RRIW. To modulate pulses with their subsequent compression in dispersing elements (optical fibres or diffraction gratings) one can use not only fibres, but also planar structures.

The analysis performed in this paper shows that optical fibres with a RRIW synchronised (by the propagation velocity) with the pulse launched into the optical fibre can be used for strong frequency modulation of the corresponding pulses at a small (less than 10 cm) length of the waveguide modulator. In this case, even at this length of the fibre, one can obtain a considerable spectral broadening of the pulse (by 1 – 3 orders of magnitude, up to \(\Delta \omega ={{10}^{14}}\ {{\text{s}}^{-1}}\) inclusive) at a virtually ideal preservation of the chirp linearity.

The latter circumstance, in turn, makes possible the subsequent strong pulse compression (temporary compression) by 1 – 3 orders up to subpicosecond and femtosecond values (in the optical range). On the other hand, the corresponding waveguide modulators (such as fibre and planar ones) can be used for the spectral compression of initially frequency-modulated broadband pulses.

The set of appropriate techniques (both spectral and temporal compression) can be successfully used in CPA for amplification of frequency-modulated pulses in the highpower subpicosecond and femtosecond laser systems.