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.

Along with the generation of extreme-ultraviolet and soft x-ray radiation, gas ionization by an intense few-cycle laser pulse can also induce the generation of low-frequency terahertz waves. The latter is caused by the excitation of a residual quasi-dc current in the produced plasma by the electric field of the laser pulse. We describe this phenomenon using the quantum-mechanical approach based on solving the 3D time-dependent Schrödinger equation. We calculate the dependences of the residual-current density on the carrier-envelope phase, duration, and intensity of the few-cycle laser pulse, and find optimal conditions for high-efficiency realization of the studied phenomenon.

Frolov, M. V.; Manakov, N. L.; Popov, A. M.; Tikhonova, O. V.; Volkova, E. A.; Silaev, A. A.; Vvedenskii, N. V.; and Starace, Anthony F., "Analytic theory of high-order-harmonic generation by an intense few-cycle laser pulse" (2012 We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of abovethreshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number N of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov et al. [Phys. Rev. A 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both N and the CEP φ of an N -cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large N , and begins to form, as N increases, in the energy region beyond the HHG plateau cutoff.

Ultrafast strong-field ionization is shown to be accompanied by atypical multiwave mixing with the number of mixed waves defined by the dependence of the ionization rate on the field strength. For two-color laser pulses of various frequency ratios, this results in the excitation of a free-electron current at laser combination frequencies and possibly in the excitation of the zero-frequency (residual) current responsible for terahertz (THz) generation in a formed plasma. The high-order nature of ionization-induced wave mixing may cause THz generation with uncommon laser frequency ratios (such as 2:3 and 3:4) to be virtually as effective as that with the commonly used frequency ratio of 1:2.

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