PHYSICAL REVIEW A 92, 033856 (2015) Extreme self-compression along with superbroad spectrum up-conversion of few-cycle optical solitons in the ionization regime A. V. Kim,A. G. Litvak, V. A. Mironov, and S. A. Skobelev Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov st, 603950 Nizhny Novgorod, Russia and University of Nizhny Novgorod, 23 Gagarin Ave, 603950 Nizhny Novgorod, Russia (Received 3 April 2015; published 30 September 2015) A regime of extreme self-compression of optical solitons to single-cycle duration with further shortening along with superbroad spectrum up-shifting is revealed when the Kerr nonlinearity and ionization process are independently controlled. This results in efficient optical-pulse compression as a whole towards extremely short single-cycle pulses at essentially shorter wavelengths, which may open a new way to generate optical pulses with durations of hundreds of attoseconds in the ultraviolet domain. DOI: 10.1103/PhysRevA.92.033856 PACS number(s): 42.65.Jx, 42.50.−p I. INTRODUCTION The concept of optical solitons have played an important role in the recent development of nonlinear optics. Two re- markable applications of soliton dynamics are supercontinuum generation and laser-pulse self-compression down to single- cycle duration [1–3]. Recently, the concept of conventional optical solitons was extended to few-cycle pulses for which the traditional envelope approach is not valid [4,5]. Of course, there are earlier examples in optical physics where the wave equation for the real laser field is treated in the context of solitons or extremely short pulses, but most of them deal with light propagation in two-level systems [6–8] or Raman-active [9] media. From a practical point of view, producing tunable few- cycle pulses of high energies is still a formidable task in contemporary laser physics. Whereas in the infrared range, such pulses can be generated at particular wavelengths by conventional solid-state systems, e.g., based on Ti:sapphire or optical parametric chirped-pulse-amplification technologies. No analogous techniques are available in the optical and ultraviolet domains. Nevertheless, for high-energy pulses there are a number of nonlinearities that can be employed for pulse shortening; for instance, the relativistic nonlinearity or plasma effects (see Refs. [10–12]). Here, we pay particular attention to the ionization nonlinearity that has a strong impact on pulse propagation dynamics. The fundamental issue of this interaction follows from the fast ionization of atoms strongly modifying the index of refraction, even on a timescale less than the optical period. This leads to a number of interesting nonlinear phenomena such as ionization instabilities [13,14], frequency blueshifting [15,16], high-order harmonics, and ter- ahertz generation [17,18]. It is also important to emphasize that the ionization nonlinearity is able by itself to ensure essential self-frequency up-shifting and pulse self-compression [19,20]. Based on these effects a new way of reaching petawatt-class pulses of few-cycle duration was recently proposed [21]. With the advent of gas-filled hollow-core photonic fibers (HC-PCF), nonlinear fiber optics where the Kerr nonlinearity together with the ionization nonlinearity can be self-consistently employed, brings new opportunities for controlling the spectrum and pulse evolution [22]. In particular, in Refs. [23–25] soliton blueshifting as well as self-compression effects are discussed based on the conventional compression scheme which allows shortening pulses even to single-cycle duration. However, the most intriguing question is the following: can we expect further shortening of a single-cycle pulse as a whole? In this paper we show that, in media with independent control of the Kerr and ionization nonlinearities, such as a mixture of two gases with noticeably differing ionization potentials, there may occur extreme pulse compression. Detailed analysis shows that this could open a new way to generate pulses with durations of hundreds of attoseconds in the ultraviolet domain having energy efficiency up to forty percent, which is much higher than attainable with available methods. The gas with a higher potential (and a higher density) provides the Kerr nonlinearity and thus keeps the soliton as a stable structure, whereas the second ionizing gas provides frequency up-shifting. A waveguide system is proposed to be used to control the wave velocity dispersion. In this case, the soliton self-compression regime consists of two qualitatively different consecutive stages. In the first stage, the soliton pulse is compressed conventionally, when the process evolves adiabatically matching the soliton relations (see, e.g., Ref. [26]). However, the extreme compression occurs in the second stage, when a few-cycle soliton becomes actually a single-cycle soliton with an ultrabroad spectrum. We show that, in this stage, the process of further self-compression is strongly accelerated along with superbroad spectrum up- conversion, keeping the single-cycle soliton as a whole entity. II. BASIC EQUATIONS AND FEW-CYCLE SOLITONS For an adequate analysis of the extreme self-compression of laser pulses in a waveguide filled with a mixture of two gases with noticeably differing ionization potentials we should refer directly to the description of the self-action dynamics of the electromagnetic field in a medium within a wide spectral range based on the wave equation ∂ 2 zz E − 1 c 2 ∂ 2 tt E = 4π c 2 ∂ 2 tt P , (1) where ∂ i =z,t stands for the respective derivatives, c is the speed of light, and P (E ) is the polarization response of the medium. In the case of a resonant interaction of the laser radiation with matter, when the signal frequency is close to the resonant transition frequency, the polarization response of the medium P can be defined based on a two-level-system model [6–8]. 1050-2947/2015/92(3)/033856(8) 033856-1 ©2015 American Physical Society