No abstract

The generation of sub-optical-cycle, carrier-envelope phase-stable light pulses is one of the frontiers of ultrafast optics. The two key ingredients for sub-cycle pulse generation are bandwidths substantially exceeding one octave and accurate control of the spectral phase. These requirements are very challenging to satisfy with a single laser beam, and thus intense research activity is currently devoted to the coherent synthesis of pulses generated by separate sources. In this review we discuss the conceptual schemes and experimental tools that can be employed for the generation, amplification, control, and combination of separate light pulses. The main techniques for the spectrotemporal characterization of the synthesized fields are also described. We discuss recent implementations of coherent waveform synthesis: from the first demonstration of a single-cycle optical pulse by the addition of two pulse trains derived from a fiber laser, to the coherent combination of the outputs from optical parametric chirped-pulse amplifiers.

We study soliton pulse compression in materials with cascaded quadratic nonlinearities and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible. c 2018 Optical Society of America OCIS codes: 320.5520, 320.7110, 190.5530, 190.2620, 190.4400 Efficient soliton pulse compression is possible using second-harmonic generation (SHG) in the limit of large phase mismatch, because a Kerr-like nonlinear phase shift is induced on the fundamental wave (FW). Large negative phase shifts can be created, since the phase mismatch determines the sign and magnitude of the effective cubic nonlinearity. This induced self-defocusing nonlinearity thus creates a negative linear chirp through an effective self-phase modulation (SPM) term, and the pulse can therefore be compressed with normal dispersion. Beam filamentation and other problems normally encountered due to self-focusing in cubic media are therefore avoided. This self-defocusing soliton compressor can create high-energy few-cycle fs pulses in bulk materials with no power limit [1][2][3][4]. However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH) limits the pulse quality and compression ratio. Especially very short input pulses (< 100 fs) give asymmetric compressed pulses and pulse splitting occurs [4,5]. In this case, the system is in the nonstationary regime, and conversely when GVM effects can be neglected it is in the stationary regime [3][4][5]. Until now, the stationary regime was argued to be when the characteristic GVM length is 4 times longer than the SHG coherence length [1], while a more accurate perturbative description showed that the FW has a GVM-induced Raman-like term [4,5], which must be small for the system to be in the stationary regime [4]. However, no precise definition of the transition between the regimes exists.On the other hand, the concept of nonlocality provides accurate predictions of quadratic spatial solitons [6,7], and many other physical systems (see [8] for a review). Here we introduce the concept of nonlocality to the temporal regime and soliton pulse compression in quadratic nonlinear materials. As we shall show, GVM, the phase mismatch, and the SH group-velocity dispersion (GVD) all play a key role in defining the nonlocal behavior of the system. Two different nonlocal response functions appear naturally, one with a localized amplitude -representing the stationary regime -and one with a purely oscillatory amplitude -representing the nonstationary regime. In the presence of GVM they are asymmetric and thus give rise to a Raman effect on the compressed pulse.In the theoretical analysis we may neglect diffraction, higher-order dispersion, cubic Raman terms, and selfsteepening to get the SHG propagation equations for the FW (ω 1 ) and SH (ω 2 = 2ω 1 ) fields E 1,2 (z, t) [3, 9]:wher...

We present a soliton effect pulse compression technique that uses self-defocusing cascaded-quadratic nonlinearities, with no fundamental limit to its scalability to high pulse energies and the capability of generating few-cycle pulses with only a frequency-doubling crystal. The conditions for which group-velocity mismatch causes an acceptable perturbation to soliton compression are analyzed and underlie optimization of the compressor. Calculations predict compression to near-single-cycle durations, with compression ratios as high as 100. Initial experiments closely agree with calculations, demonstrating compression to durations under three optical cycles (12 fs) and generation of 600 nm bandwidths.

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (i.e., the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -related to the difference between the SHG and the Kerr soliton numbers -and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, which control the behaviour of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a β-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.