We investigate for the first time, both experimentally and theoretically, low-frequency terahertz (THz) emission from the ambient air ionized by a two-color femtosecond laser pulse containing, besides the fundamental-frequency main field, a weak additional field tunable near the frequency of the half harmonic. By controlling the mutual polarization and the powers of the main and additional fields, we determine the dependences of the THz power and polarization on the parameters of the two-color pulse. We also discover the resonantlike dependence of the THz yield on the frequency detuning of the additional field. The analytical formulas obtained using the model of the free-electron residual current density give an excellent agreement with the experimental results.

It is found that dissipative types of stable soliton structures can exist in nonlinear optical media with broadband gain and group-velocity dispersion (GVD). These structures resemble ionization or combustion waves and are essentially self-accelerating pulses with a stationary-envelope form and a permanently shifting wave spectrum. Contrary to the conservative solitons, the dissipative ones exist for any sign of GVD. Being an attractor in the development of arbitrary initial distributions, the dissipative structures cause the fundamental Schrodinger solitons to disappear in the course of evolution in weakly nonconservative systems. PACS number(s): 42.50.Rh, 42.81. Dp, 42.65.ReRecent progress in developing ultrashort-laser techniques attracts the interest of studying interaction between powerful optical pulses and broadband active media. This problem is of particular importance for the dynatnics of femtosecond laser generators [1], amplifiers of supershort pulses [2], and nonlinear active optical fibers [3]. A common theoretical aspect in these applications is the long-term evolution of wave packets in dispersive active media that exhibits simultaneously both conservative and dissipative nonlinearities.It is we11 known that the propagation of wave pulses in a lossless and dispersive dielectric medium with its self-action incorporated is described by the nonlinear Schrodinger (NLS) equation, which normally includes the conservative cubic nonlinearity of the refractive index. The interplay between nonlinearity and group-velocity dispersion (GVD) then may lead to soliton generation [4] or quasishockwave formation [5]. On the other hand, in two-level optical media solitons of induced transparency can be formed due to the nonconservative character of the resonant light-matter interaction [6]. Specific nonconservative mechanisms of soliton generation, caused by a delicate balance between saturable absorption and amplification and/or transverse phase modulation and gain inhomogeneity, play an important role in the passively modelocked short-pulse laser operation [1,7,8].The purpose of the present paper is to show that the long-term evolution of a wave pulse propagating in a nonlinear two-level optical medium containing broadband gain elements results in the formation of new types of single soliton structures (named here dissipative opti-

We report on the first experimental observation of graphene optical emission induced by the intense THz pulse. P-doped CVD graphene with the initial Fermi energy of about 200 meV was used, optical photons was detected in the wavelength range of 340-600 nm. Emission started when THz field amplitude exceeded 100 kV/cm. For THz fields from 200 to 300 kV/cm the temperature of optical radiation was constant, while the number of emitted photons increased several dozen times. This fact clearly indicates multiplication of electron-hole pairs induced by an external field itself and not due to electron heating. The experimental data are in a good agreement with the theory of Landau-Zener interband transitions. It is shown theoretically that Landau-Zener transitions are possible even in the case of heavily doped graphene because the strong THz field removes quasiparticles from the region of interband transitions during several femtoseconds, which cancels the Pauli blocking effect. *oladyshkin@gmail.comThe nonlinear optical properties of graphene are currently actively investigated in view of their prospective use in plasmonics, optoelectronics, and photonics [1]. The specific features of gapless dispersion of Dirac fermions, including the so-called Dirac cones, make graphene a unique material. In the neighborhood of the Dirac point, fermions have a massless dispersion law up to energies of order 1.5 eV and high Fermi velocity 8 F 10 cm/s  , thus providing ultrahigh nonlinear susceptibility (both quadratic and cubic) of graphene in the infrared and terahertz ranges [2][3][4][5][6][7][8][9][10]. The interaction of graphene with terahertz radiation is presently arousing particular interest from the viewpoint of various applications [11]. Terahertz video pulses are also used for studying relaxation processes in graphene [12,13].An interesting effectthe THz-pulse-initiated carrier multiplication (CM) was studied experimentally in [12]. This effect was attributed in [12] to impact ionization (II), i.e., to interband reverse Auger recombination. At the same time, according to the theoretical results obtained in [14] within the framework of the 2D Fermi-liquid model, the Auger processes have low efficiency in the region of the linear dispersion law 1 ; consequently, in the simulation made in [12] the Auger resonances were broadened "artificially" within the framework of the numerical scheme 2 . The CM effect was also observed in the case of optical pumping [13,[16][17][18][19][20][21][22], when the contribution of the reverse Auger 1 The situation is different for graphene in magnetic field (see, e.g., [15]). 2 The authors of [12] assumed that dislocations could be a possible physical mechanism of such broadening.relaxation to the formation of electron population in the conducting band did not exceed 5-10% [17].It is worth noting that the ballistic (directly initiated by the field) interband transitions were neglected in [12] in view of the small photon energy as compared to the typical kinetic energy of fermions in doped graphe...

We observe enhanced second-harmonic generation in monolayer graphene in the presence of an ultra-strong terahertz field pulse with a peak amplitude of 250 kV/cm. This is a strongly nonperturbative regime of light-matter interaction in which particles get accelerated to energies exceeding the initial Fermi energy of 0.2 eV over a timescale of a few femtoseconds. The secondharmonic current is generated as electrons drift through the region of momenta corresponding to interband transition resonance at an optical frequency. The resulting strongly asymmetric distortion of carrier distribution in momentum space gives rise to an enhanced electric-dipole nonlinear response at the second harmonic. We develop an approximate analytic theory of this effect which accurately predicts observed intensity and polarization of the second-harmonic signal. arXiv:1812.10192v1 [cond-mat.mes-hall] 26 Dec 2018 E 0 (t) as a parameter [11]. For a weak low-frequency field the perturbation of an originally isotropic distribution is localized mainly near the Fermi surface. In this case the parameter of anisotropy is expressed through a low-frequency Drude current J Dr . The resulting nonlinear response obtained by perturbations turns out to be proportional to the magnitude of J Dr (see [11]). The magnitude of the SH current J 2ω scales aswhere J Dr = e 2 τ Dr |µ| 4 E 0 , τ Dr is the relaxation time of a DC current, µ is chemical potential,E ω is the electric field amplitude of an optical pumping at frequency ω. Equation (1) is valid when the perturbation of electron distribution at Fermi surface is small.

Second harmonic generation and two-photon luminescence from colloidal gold nanoparticles in the 980–1300 nm wavelength range of exciting femtosecond radiation were investigated experimentally. The measured polarization and spectral characteristics of the second harmonic and two-photon luminescence demonstrate that the observed nonlinear optical signal is determined by the dimers constituting several percent of the total nanoparticle number.