Enhancement of THz Generation by Two-Color TW Laser Pulses in a Low-Pressure Gas

Abstract

We identify experimental conditions for efficient generation of THz pulses by high power near IR laser radiation: 2 TW, 30 fs, 800-nm laser pulses with their second harmonic were slightly focused in a low-pressure gas cell in such a way to avoid multiple filamentation and excessive ionization. This two-color scheme yields a microjoule level of THz pulses which is two orders of magnitude higher than the signal generated in the atmosphere of ambient air.

Appendix

To reconstruct the total THz spectrum from the data of transmitted energy with different filters, the following method was developed: Full THz spectrum was represented by model curve S(f), which goes down to zero in the microwave and infrared spectrum ranges, with adjustable spectral width Δ, and slopes (b for microwave edge, g for infrared edge), with area normalized to unity.

$$ S(f)=\frac{f^b\exp \left[-{\left(\frac{f}{\Delta }\right)}^g\right]}{\underset{0}{\overset{\infty }{\int }}{f}^b\exp \left[-{\left(\frac{f}{\Delta }\right)}^g\right]\mathrm{df}}\kern1em $$

(A1)

where b, g, Δ are fitting parameters for a particular experimental data.

The signal detected after transmission through the particular filter should be equal to the integral of the product of S(f) and transmission filter S_m(f)_i spectra (see A6, A7 below) over the used frequency range. Parameters of function S(f) were fitted by total error minimization with N filters:

$$ \delta =\sum \limits_{i=1}^N{\left({T}_{e_i}-{\int}_0^{\infty }S(f)\cdotp {S}_m{(f)}_i\cdotp \mathrm{d}f\right)}^2 $$

(A2)

where i is the filter number, ${T}_{e_i}$ is the filter transmitted signal in the experiment (normalized to unfiltered THz signal). For the models in Figs. 2, 3, and 4 we used: b = 0.6; g = 1.8; Δ = 2 THz.

For a quality description of pressure and energy dependence of THz energy next simplified model was used:

Electron concentration is simulated as:

$$ {N}_e(p)={N}_e\frac{p}{p_0}, $$

(A3)

where N_e = 1 × 10¹⁶cm⁻³, p₀—atmospheric pressure. To fit THz energy dependence on Fig. 4b, we used Ф(I)~I, and N_e~I that is not true in general.

Plasma transmission spectrum is calculated as:

$$ T\left(f,p,L,I\right)=\exp \left[\frac{2\pi f}{c}L\ \mathit{\operatorname{Im}}\left[{\left[1-\frac{\frac{N_e\left(p,I\right)\cdotp {e}^2}{m_e\cdotp {\varepsilon}_0}}{{\left(2\pi f\right)}^2-i\cdotp \nu \left(2\pi f\right)}\right]}^{0.5}\right]\right]\kern1.25em $$

(A4)

To fit our experimental data, we used $\nu =0.1\frac{\mathrm{THz}}{2\uppi},L=10\mathrm{cm}$.

THz pulse energy after plasma and filters absorption is calculated as:

$$ {U}_{\mathrm{THz}}=\frac{Ne{\left(p,I\right)}^2\cdotp {I}^2\cdotp I}{N_0^2{I_0}^3}\cdotp \underset{0}{\overset{\infty }{\int }}S(f)\cdotp T\left(f\cdotp THz,p,L,I\right)\cdotp {T}_{\mathrm{filter}}\left(f,d\right)\mathrm{df}\kern1em $$

(A5)

where I is laser intensity at 800 nm, I₀ = 3 × 10¹³ W/cm². The fraction before the integral describes proportionality of THz signal to the carrier concentration, to the intensity of the fundamental radiation and to intensity of second harmonic.

Filter transmissions T_filter(f,d) were calculated by Fresnel formulas for a plane-parallel plate. The absorption coefficient for PMMA was approximated as

$$ {\alpha}_{\mathrm{pmma}}(f)=\frac{f^2\cdotp 7.39+4.4\cdotp f}{2} $$

(A6)

where f- is in THz. For silicon with conductivity 0.3 Ω × cm, its permittivity was calculated as:

$$ {\varepsilon}_{Si}(f)=11.9-\frac{{\left(2\pi \cdotp 2.33 THz\right)}^2}{{\left(2\pi f\right)}^2+i\left[1.17\cdotp THz\cdotp \left(2\pi \right)\right]2\pi f}\kern0.75em $$

(A7)

here, 2.33 THz is plasma frequency, which depends on the doping level, for other used silicon filters with conductivity 0.9 and 1.1 Ω cm, it was 1.13 and 2.55 THz, respectively. The thickness of PMMA and Si filters used for Figs. 3b and 4b data was d = 2.5 mm, and d = 270 μm respectively.