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Photocurrent and its THz pulse generation from shaped two-color femtosecond laser pulses interaction with gas-plasma are investigated numerically. An opaque filter is used to block some frequency components of the dispersed laser pulse to generate a new shaped pulse. Although the filter decreases the pump laser energy, this method can generate broad, tunable THz pulses. It is found that the width and the position of the filter affect the THz pulse directly because this method generates a different laser pulse shape. In addition, THz generation is also a periodic function of the second harmonic pulse phase.
© 2014 Optical Society of America
1. Introduction
Two-color femtosecond laser pulses (fundamental pulse and its second harmonic) interaction with gas/air-plasma has been used to generate strong and broadband terahertz (THz) radiation [1–3]. Until now several models have been proposed to describe this ultrafast phenomenon, including photocurrent model [4] and four-wave mixing [5, 6]. In the two-color laser scheme, the laser beam is focused to ionize the gas atoms which produce plasma, and then the free electrons are accelerated in the broken laser field to produce a current. This current oscillates with the laser pulse and emits THz wave. Because the two-color pulses break the symmetry of the laser field, it can produce a large net current [7]. Some parameters that affect THz generation from this photocurrent have been investigated, including laser power [8], laser wavelength [9], focusing conditions [10, 11], gas species [12], and gas density distribution [13]. Borodin et al have demonstrated that both the photocurrent and the nonlinear polarization of neutrals contribute the THz generation [14].
During the process of photocurrent production, free electrons are accelerated by the laser field to form a current. So, the photocurrent is directly affected by the laser pulse shape. This means it is possible to change and control THz pulses generation by the interaction of shaped laser pulses with gas-plasma. Over the past decade, pulse shaping technologies, such as spatial light modulator and acousto-optic modulator, have allowed to generate complicated ultrafast optical waveforms [15, 16]. It is noted that shaped femtosecond laser pulses have also been used to generate narrow, tunable THz wave by optical rectification [17, 18]. Yamaguchi et al have demonstrated experimentally that a shaped laser pulses can optimize THz generation from gas-plasma by using a phase-only pulse shaper [19]. In this paper, THz generation from shaped two-color femtosecond laser pulses interaction with gas-plasma is studied numerically using the photocurrent model, with the aim of generating a broad, tunable THz wave source for resonant and nonresonant THz wave-matter interaction [20].
2. Theory model and simulations
The most successful and widely adopted approach for pulse shaping is achieved by spatial masking of the spatially dispersed optical frequency spectrum [15, 16]. This approach requires that the laser pulse be dispersed by a diffraction grating, which separates its frequency components spatially, and then its spectrum is spatially modulated. After the pulse is modulated by using a mask, another grating is used to combine all the frequency components into a single pulse to obtain a shaped output pulse. In practice, a so-called 4f arrangement is widely used, because of its simple setup and freedom from temporal dispersion [21]. In the 4f arrangement, the input pulses are dispersed by the first grating, and then the beam is collimated by the first lens. The first grating is located at the focal plane of the first lens. Then the second lens, which is 2f away from the first lens, focuses the beam on the second grating, which combines all the frequency components to form a single pulse. The distance between these two gratings is 4f, and the modulator is set between these two lenses, hence it is called 4f arrangement. From the point of view of frequency domain, the output of this approach is the product of the input signal and a frequency response function: Eout(ω) = Ein(ω)H(ω). After modulation, the pulse time waveform can be obtained by Fourier transform. In order to implement a desired filtering function, both a phase and an amplitude mask are needed. A filter function can also modulate the phase or the amplitude, either separately or simultaneously. For example, an opaque mask with several isolated slits is used to filter certain frequency components of the pulse, and a pulse trains or square pulses are then obtained [22].
After the laser pulse is dispersed by the grating, its frequency components are spatially distributed. Then, if an opaque filter blocks some components of the spectrum, the new pulse shape is generated after the compression by the second grating. So, this method offers a simple way to change the laser pulse profile. Figure 1(a) shows a normal femtosecond laser pulse with 800nm central wavelength and its shaped pulse, and (b) gives their frequency spectra, respectively. Here, an opaque filter blocks 3nm bandwidth of laser spectrum in spatial. The actual width of the filter can be decided by the angular dispersion of the grating and the focal lens. So it can be adjusted according to the actual setup in experiment.
Fig. 1 Normal femtosecond laser pulse and its shaped pulse time waveforms (a), and their frequency spectra (b).
After the laser pulse is shaped by a filter using the 4f system, this new pulse can form a new two-color laser pulses scheme with a thin β-BBO crystal. The ionization rate, wi, of the gas atoms induced by the laser field is calculated using the Ammosov-Delone-Krainov ionization theory (where i = 1, 2,..., represents the ionization order) [7]. Then the free electrons are accelerated to produce a transverse current in the laser field. According to the photocurrent model [4, 7], the transverse current is given by
where e and m are the electron charge and mass, respectively, Elaser is the laser field, and ni is the ionized atom density. Based on the ADK ionization theory and Eq. (1), the currents at any time generated from laser interaction with gas atoms are calculated. This photocurrent oscillates and produces a nonlinear polarization which then generates a THz wave pulse [4, 8]. So, the THz yield is the time derivative of this current: [8].In our simulations, after the laser pulse is shaped the pulse profile is numerically fitted and then the resultant second harmonic pulse is calculated. The second harmonic pulse is assumed to have a similar pulse shape to the fundamental pulse while with doubled frequency and smaller amplitude. Here, the second harmonic conversion ratio from the fundamental pulse is set to 7% of the laser energy. The mixing field, fundamental pulse and second harmonic pulse, ionizes the gas atoms and accelerate the free electrons. The laser intensity is 1014 W/cm2, the fundamental pulse central wavelength is 800 nm, and the input pulse shape has a Gaussian shape with a duration of 100 femtosecond FWHM (Full width at half maximum).The gas atom is set nitrogen. Figure 2(a) is the total two-color laser field from a normal laser pulse (black) and a shaped laser pulse (red). The shaped laser pulse has the same profile as Fig. 1 red line shows. Figure 2(b) is the photocurrents induced by them. Because the filter in the laser beam blocks some laser energy, the laser field becomes smaller as shown in Fig. 2(a). So it induces the photocurrent weak. However, the photocurrents oscillate in both conditions with some difference. This produces the THz emission differently somewhere. Figure 3(a) gives the THz time waveforms from a normal and several shaped pulses. The filter is set to 1nm, 2nm, and 3nm, respectively. Figure 3(b) gives the frequency spectra of them. As Fig. 3(b) shows, the THz pulses cover the whole THz range and extend to the mid-infrared. But their most power is in the THz range. It can be seen that because the pump laser pulse shapes are changed, the resultant THz wave pulses are tuned. This is because the laser pulse shapes determine the photocurrent generation, so the THz pulse from this transient current is changed. The filter blocks some laser pulse frequency components, therefore when the filter width increases, the laser pulse energy decreases. As a result, the THz wave becomes weaker. The power generation law is shown in Fig. 3(c). The frequency spectrum of a Gaussian laser pulse is also a Gaussian distribution. So when the filter becomes broader, it blocks more laser pulse energy. As a result, there is less laser pulse energy to generate THz pulse. Therefore, the width of the filter used in the 4f system has a disadvantage that it wastes some laser energy. So an optimal width of the filter is needed to choose in factual using.
Fig. 2 Total two-color laser pulse field (a) and their photocurrents (b).The other parameters are given in the text.
Fig. 3 When the laser pulse is shaped, the resultant THz pulse is changed. (a) shows THz waveforms from a normal and some shaped pulses with filtered bandwidths of 1nm, 2nm, and 3nm, (b) gives their frequency spectra, and (c) depicts the THz wave generation law from shaped pulse.
It is also found that if a filter is moved transversely in the dispersed laser pulse, the generated THz pulses are also changes. Here, a 3nm-wide filter is used in the 4f system, and it can be seen that the THz pulse is tuned when this filter is moved. Figure 4(a) shows some THz spectra generated from the laser pulses with the filter at different positions, and (b) shows the relation of the THz amplitude and the filter position. The curve symmetry is at the laser’s central wavelength 800nm. Compared to the results shown in Fig. 3(b), moving the filter can generate similar results, while the filter blocks less laser energy.
Fig. 4 By moving a filter transversely in the dispersed laser pulse, the resultant THz pulse is tuned. (a) gives the THz frequency spectra with the filter at different positions, and (b) is the THz amplitude yield as a function of filter position.
Photocurrent [7] and THz generation [1] from the laser pulses are altered when the phase difference between the fundamental pulse and the second harmonic pulse changes. There is a similar phenomenon for the shaped laser pulses. When the shaped laser pulse has a shape as represented by the red line in Fig. 1(a), the generated THz wave as a function of the second harmonic pulse phase is shown in Fig. 5. It is found that the THz generation from shaped laser pulses is also a periodic function of this phase. This is because free electrons are accelerated to different velocities when this phase changes. So, the phase change induces a change of photocurrent and consequently THz generation is affected. Even if the laser pulse has been shaped by a spatial modulator, the mechanism for photocurrent production and its THz generation is not altered. It is noted that THz generation is also the function of this phase difference according to the four-wave mixing [23] and it can be used to control the THz generation.
3. Summary
In conclusion, the photocurrent and its THz generation from shaped two-color femtosecond laser pulses interaction with gas-plasma are investigated numerically. It is found that the THz wave pulse is tuned and changed by moving an opaque mask within the spatially dispersed laser pulse. This is because the mask changes the amplitude of some frequency components of the dispersed laser pulses, and new shaped pulses are generated. As a result, the photocurrents produced by these shaped pulses and their THz generation are affected. It is also found that the THz wave is a periodic function of the second harmonic pulse phase, which is the same as the normal two-color scheme. This method offers a simple way to tune and change THz generation from laser gas/air-plasma interaction.
Acknowledgements
Hai-Wei Du acknowledges the support from the Foreign Postdoctoral Researcher Program of RIKEN, Japan.
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