cos 2 sin
1.5 The Characteristics of THz Generated by Laser Induced Plasma by Four Wave Mixing
1.5 The Characteristics of THz Generated by Laser Induced Plasma by Four Wave Mixing
With the coming of the amplified laser system, one can easily reach pulse energy sufficient to ionize atoms and molecule in ambient air in the focused beam. If it is in an ambient air at 1 atm pressure, a plasma can be generated with a length of a few millimeter and a diameter of up to 100 μm can be produced by a 1 kHz Ti:Sapphire amplified laser system with pulse energies in the few hundreds of micro-joule regime.
plasma 100 μm-thick BBO
Lens, f=20cm
Figure 1-7 : Schematic of the laser induced plasma setup used for THz generation
Following the approach of Cook et al.[10], we construct a setup of terahertz time domain spectroscopy system with laser induced plasma to generate terahertz. Figure 1-7 is the illustration of terahertz generation setup, we employed 1kHz Ti:sapphire laser system (Spitfire) at 800nm with maximum pulse energy of 2 , pulse duration 50fs. We focus the pluses through a
J m
100 mμ thick type-I β-barium borate (BBO) crystal with a lens (f=20 ), which has been phase matched for second harmonic generation (SHG), placed at an adjustable distance from the focus point. The generated terahertz is detected by free space EO sampling with 1 thick ZnTe crystal. The terahertz time domain electric field is shown in Figure 1-8, and its corresponding frequency domain spectrum is depicted in the inset.
cm
mm
Figure 1-8 : The THz time domain waveform inset: its corresponding frequency domain
First, we rotate the BBO crystal against the beam axis which means varying the angle between fundamental beam (ω ) and second harmonic beam (2ω ). But during the experiment we found that there was terahertz which generated from the BBO crystal.
By use of a teflon to block the laser beam behind BBO, we can measure the terahertz radiation from the BBO crystal, see Figure 1-9. The solid line is theoretically expected sin ( )4 α of the SHG efficiency. The terahertz generated from BBO was identified as optical rectification of fundamental beam. The terahertz radiation from BBO reach maximum when SHG efficiency is zero. Figure 1-10 show the terahertz signal generated by four wave mixing that is numerically subtracted the signal generated by BBO because the THz signal from BBO will overlap the signal from plasma. We can see that the maximum signal is at the angle ±40° to the maximum SHG efficiency (45° and 225 ) °
0 50 100 150 200 250 300 350 400
Figure 1-9 : Terahertz radiation from BBO versus its azimuthal angle
0 50 100 150 200 250 300 350 400
Figure 1-10 : Terahertz radiation from plasma versus the azimuthal angle of BBO
Four wave mixing predicts that the generated THz signal is proportional to the third order nonlinearity, electric field of second harmonic wave, the square of electric field of fundamental wave and their relative phase ϕ.
(3) 2
2 sin( )
ETHz ∝χ E Eω ω ϕ (22) We can change the phase by varying the distance d between BBO and the focus point.
The phase shift ϕ
Figure 1-11 shows that terahertz amplitude is varied by adjusting the distance from BBO to focus point. The moving range only from 4.9 to 6.3 is due to the damage threshold of BBO and its dimension area. The pump beam size is larger than BBO dimension area when the distance is larger than 6.4cm, and close to the damage threshold of BBO crystal when the distance less than 4.9 .
cm
Figure 1-11 : THz amplitude versus the distance from BBO to focus point
The blue-solid line is the theoretical fitting. Changing the distance d is not only altering the relative phase but also changing the SHG efficiency and the beam spot size on the BBO crystal. The SHG power conversion efficiency [11] is defined as
2
Figure 1-12 : THz amplitude versus laser pulse energy
We measured the THz signal intensity with varying the laser pulse energy before the BBO crystal, The results are shown in Figure 1-12, while the BBO angle was set at 185 and the distance ° d =4.7cm.
Using the relation
2
E2ω ∝Eω ∝Iω (26) Eq. (22) has quadratic dependence
(3) 2
ETHz ∝χ Iω (27) The pulse energy below 300 Jμ can be fitted well with Eq. (27), but the THz signal falls below the fitted quadratic curve in the higher pulse energies portion. It may be likely due to the defocusing of the laser beam by the plasma and reduces the effective peak intensity. In addition, at larger plasma volumes, phase mismatch and THz absorption effects are more likely to become significant. [12]
Reference
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APL_vol67_p3523_1995
[10] D. J. Cook, Intense terahertz pulses by four-wave rectification in air, OL_25_1210_2000
[11] Photonics 6ed, Yariv and Yeh
[12] Markus Kress, Torsten Löff ler, Susanne Eden, Mark Thomson, and Hartmut G. Roskos, Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves, OPTICS LETTERS / Vol. 29, No. 10 / May 15, 2004