The terahertz polarization pulse shaping

Summary form only given. The polarization pulse shaping, that is, the manipulation of the direction and timing of electromagnetic fields, has played a pivotal role in handling the interactions between strong pulsed light fields and matter, such as in increasing multiphoton ionization yield, optical gating for higher harmonic generation, and photoassisted asymmetric synthesis of chiral molecules. Recent advances in terahertz technologies have extended the scope of these studies to terahertz frequency ranges. The shaping of the temporal trajectories of terahertz vector fields could substantially increase the degree of freedom of such nonlinear interactions. However, to date, the methods for terahertz polarization pulse shaping have been limited to combining terahertz waves generated by multiple laser pulses, and their flexibility is far behind the Fourier-synthesis based shaping techniques available for optical frequencies which can actively control numerous parameters necessary to generate tailored pulses.In this paper, we experimentally demonstrate the generation of arbitrary terahertz vector waveforms via conversion from polarization-shaped laser pulses designed on the basis of the polarization selection rules for optical rectification in a threefold crystal. The terahertz electric field generated through the optical rectification process is described as a linear response to the intensity envelope of the fundamental laser pulse, which is well described by the instantaneous Stokes parameters (ISPs), Si(t) (i = 0 to 3) [1]. When the light propagates along a threefold axis of a nonlinear optical crystal, the polarization selection rule for the optical rectification becomes very simple [2]. For example, when the excitation laser pulse propagates along a threefold [111] axis of GaP, the generated terahertz is described as follows: ETHz ] ∞ x (t) = ETHz y (t) 0 S1(τ) ] α(t - τ) -S2(τ) dτ. The coordinates are taken as x II - 110], y II [112], z II [111] in GaP. The function α(t) is the impulsive response determined by the strength of second-order nonlinear response, absorption of terahertz waves by the crystal, and phase matching conditions. According to Eq. (1), one can generate terahertz waves with arbitrary Ex(t) and Ey(t), if S1(t) and S2(t) can be tuned arbitrarily. For this purpose, we build a Fourier-synthesis based optical pulse shaper with a liquid-crystal spatial light modulator [3]. This pulse shaper can modulate the phases of the two cross linearly polarized components for each frequency. We developed an explicit method to design these phases required to achieve desired S1(t) and S2(t) by this pulse shaper. For example, Fig. 1 shows an experimentally obtained electric field trajectory of a circularly polarized terahertz pulse. To achieve this, we rotated the trajectory of [S1(t),S2(t)] vector in the (S1,S2) plane, which means that the polarization azimuth of the incident laser rotates in time. Owing to the direct design of the parameters of the pulse shaper, we have achieved to control not only just the polarization state of the terahertz pulse, but also other various parameters such as its central frequency, bandwidth, and spectral phases.