Scaling behavior of ultrafast two-color terahertz generation in plasma gas targets: energy and pressure dependence

doi:10.1364/OE.18.015130

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Scaling behavior of ultrafast two-color terahertz generation in plasma gas targets: energy and pressure dependence

George Rodriguez and Georgi L. Dakovski »View Author Affiliations

Optics Express, Vol. 18, Issue 14, pp. 15130-15143 (2010)
http://dx.doi.org/10.1364/OE.18.015130

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▸ Article Outline
– Abstract
1. Introduction
2. Experimental
3. Results
4. Photocurrent model and discussion
5. Conclusions
– References and links

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Abstract

Ultrafast terahertz emission from two-color generated laser plasma gas targets is studied using air and the noble gases (neon, argon, krypton, and xenon) as the generation media. Terahertz output pulse energy and power spectra are measured as function of gas species, gas pressure, and input pulse energy up to 6 mJ per pulse using a 40-fs 1-kHz Ti:sapphire laser system as the drive source. Terahertz pulse energies approaching 1 μJ per pulse with spectral content out to 40 THz and pulse duration of 35 fs is reported. A simple one dimensional transient photocurrent ionization model is used to calculate the spectra showing good agreement with experiments.

1. Introduction

Previous studies have demonstrated the preponderance of intense ultrafast terahertz (THz) sources based on two-color laser gas plasma targets with extremely broad bandwidths in excess of 70 THz [1

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2(10), 605–609 (2008). [CrossRef]

]. Applications ranging from nonlinear THz materials science to broadband hyperspectral detection drive the need for such sources to be optimized for output power and spectral content [2

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B18 (2008). [CrossRef]

–4

F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, “Improved terahertz two-color plasma sources pumped by high intensity laser beam,” Opt. Express 17(8), 6044–6052 (2009). [CrossRef] [PubMed]

]. Further, it would also be useful to have a source with a sufficiently high repetition rate frequency for sensitive lock-in coherent detection methods. It is desirable, from the perspective of practical THz sources for spectroscopy that these sources and their associated generation mechanisms be studied for optimal generation with peak THz fields in the multi MV/cm range and beyond. For instance, understanding spectral content, total energy in pulse, optimal gas concentration, focusing conditions, inter-pulse phase slippage, polarization control, and tunability are all parameters for consideration that affect output fidelity in these sources.

A couple of approaches exist for ultrafast two-color THz generation in gases. The first, generation via a gas filament [5

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]

–7

T.-J. Wang, J.-F. Daigle, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy THz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7(7), 517–521 (2010). [CrossRef]

] under long focus or self-channeling conditions is a useful approach for remote THz production, spectroscopic sensing, and standoff detection technologies. In this approach [8

F. Théberge, M. Châteauneuf, G. Roy, P. Mathieu, and J. Dubois, “Generation of tunable and broadband far-infrared laser pulses during two-color filamentation,” Phys. Rev. A 81(3), 033821 (2010). [CrossRef]

], the balance between ionization and Kerr self-focusing allows for long single channel propagation of optical beams and minimizes THz propagation issues associated with atmospheric water vapor absorption and beam diffraction for remote distances. The other approach [9

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15(8), 4577–4584 (2007). [CrossRef] [PubMed]

,10

H. G. Roskos, M. D. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1(4), 349–368 (2007). [CrossRef]

] is generally a short focus, near Rayleigh length limited, generation where beam convergence, plasma generation, and beam defocusing dominates THz properties. In this case, a relatively high density gas plasma is formed over a very short distance (~mm), and electrons generated at the focus give rise to an asymmetric transverse plane plasma current whose direction, and subsequent emitted THz polarization, are extremely sensitive to the relative optical phasing between the two colors at the focus [11

A. V. Balakin, A. V. Borodin, I. A. Kotelnikov, and A. P. Shkurinov, “Terahertz emission from a femtosecond laser focus in a two-color scheme,” J. Opt. Soc. Am. B 27(1), 16–25 (2010). [CrossRef]

–14

D. Dietze, J. Darmo, S. Roither, A. Pugzlys, J. N. Heyman, and K. Unterrainer, “Polarization of terahertz radiation from laser generated plasma filaments,” J. Opt. Soc. Am. B 26(11), 2016–2027 (2009). [CrossRef]

]. The work concerned in this paper focuses on this second approach. Recent work published on this topic has also focused on the details of the generation mechanism covering drive forces, complex phasing and polarization [11

–14

]. Yet, it is still desirable to have experimental results for which to stimulate model development [15

Z.-M. Sheng, H.-C. Wu, W. M. Wang, M. Chen, X. G. Dong, J. Zheng, and J. Zhang, “Simulation of high power THz emission from laser interaction with tenuous plasma and gas targets,” Comm. Comp. Phys. 4, 1258–1278 (2008).

–18

R. A. Akhmedzhanov, I. E. Ilyakov, V. A. Mironov, E. Y. Suvorov, D. A. Fadeev, and B. V. Shishkin, “Plasma mechanisms of pulsed terahertz radiation generation,” Radiophys. Quantum Electron. 52(7), 482–493 (2009). [CrossRef]

] and theoretical comparisons that extend description into the strong THz field regime where practical kilohertz based systems can be used for purposes of nonlinear THz science and spectroscopy.

The focus of this work is to present experimental results that test the scaling behavior with attention to THz temporal and spectral properties as the laser pulse energy is scaled or the gas species (and pressure) is varied. The results in this work bridge previous measurements that have been made at lower input pulse energies, smaller detected THz bandwidth, and under different gas source conditions [9

,10

,19

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56(10), 1137–1150 (2009). [CrossRef]

,20

Y. Chen, M. Yamaguchi, M. Wang, and X.-C. Zhang, “Terahertz pulse generation from noble gases,” Appl. Phys. Lett. 91(25), 251116 (2007). [CrossRef]

] with those made at higher input energies [1

]. Reports of THz output saturation at the sub-millijoule level input [10

,20

Y. Chen, M. Yamaguchi, M. Wang, and X.-C. Zhang, “Terahertz pulse generation from noble gases,” Appl. Phys. Lett. 91(25), 251116 (2007). [CrossRef]

] are in contrast with results from the multi-millijoule measurements [1

,21

V. A. Kostin and N. V. Vvedenskii, “Ionization-induced conversion of ultrashort Bessel beam to terahertz pulse,” Opt. Lett. 35(2), 247–249 (2010). [CrossRef] [PubMed]

] that observe saturation at a higher input energy fluence. Thus we are also motivated by examining in detail the THz power spectral weight shifting in constituent gases as the input energy or gas is varied. This makes it necessary to conduct measurements under detection conditions that have a large flat spectral response and without polarization sensitive components that could possibly skew the temporal or spectral signature of the emitted THz. We consider these issues, because one often is principally concerned with the useable bandwidth in the THz pulse and selective control over the output properties, namely power and spectral content.

In this paper we demonstrate that microjoule level THz pulses are readily attainable with multi-millijoule based kHz Ti:sapphire systems. We also study the scaling behavior output as variable parameters are changed: gas species (air, Ne, Ar, Kr, and Xe), gas concentration, and input pulse energy. In Section 2 we describe our experimental setup using a Michelson interferometer to measure temporal interferograms with power based measurements using a pyroelectric detector. In Section 3, results of temporal scans showing gas pressure and pulse energy dependence are presented with peak output THz pulse energy approaching 1 μJ/pulse and 40 THz. A simple 1-D plasma photocurrent fluid model (Section 4) is used to simulate results with discussion about effects from gas dependent phase delay and plasma phase slippage.

2. Experimental

The experiment is performed with an amplified Ti:sapphire laser system capable of delivering 800-nm, 40-fs, 6-mJ pulses at a 1-kHz repetition rate. Although higher pulse energies are desirable for larger production THz in both, power output and spectral content, the goal of these studies was aimed at using a high repetition rate source for application to ultrafast spectroscopy where 1-kHz based sources are more tractable for sensitive lock-in detection methods than low repetition rate based laser systems. A schematic of the experiment is shown in Fig. 1 . A variable length gas cell containing a nonlinear second harmonic crystal BBO is filled up to pressures between a few Torr and 700 Torr with various gases (Air, Ne, Ar, Kr, and Xe) for THz generation. The 800-nm laser pulse is focused by an input lens (f = 12.5 cm) which also serves as the input window to the gas cell. After traversing the BBO crystal, the fundamental (ω) and second harmonic (2ω) pulses come to an f/10 focus in the gas to form a plasma and generate THz pulses. A thin (625μm) one inch diameter silicon scatter-type filter window (Lake Shore Cryotronics, Inc.) is used to pass IR and THz radiation and filter out unwanted ω, 2ω and other wavelengths generated in the gas from other high order processes such as conical emission and continuum generation. The silicon window has excellent transmission (~50%) at wavelengths above 5μm and is specifically made for scatter rejection of the shorter wavelengths. It also serves as a gas to vacuum interface to separate the gas cell from a 2-ft diameter cylindrical top-hat type main vacuum chamber at the point of attachment to the main chamber. The main chamber can be completely evacuated to remove the air from the entire THz beam path and eliminate absorption from water vapor in air. Inside the chamber, the THz beam is recollimated and directed to a Michelson interferometer with a high sensitivity pyroelectric detector (Model SPH-45-OB, Spectrum Detector Inc.) for time-domain THz interferogram and Fourier transform power spectrum measurements. The LiTaO₃ pyroelectric detector is black coated to provide a nearly flat response throughout the visible to far infrared portion of the spectrum with a very high responsivity (R_V) of R_V = 4.5x10⁴ V/W at 5 Hz. Because the detector response time is milliseconds and significant responsivity roll off occurs at repetition rates as low as 100 Hz, the main 800-nm 1-kHz beam is chopped at frequencies between 10 and 30 Hz. Measurement of the THz spectrum is done by first recording a time-domain interferogram by scanning one arm of the Michelson interferometer using the pyroelectric detector signal detection and recording with a lock-in amplifier, and then, a numerical Fourier transform is performed on the interferogram to extract the THz power spectrum. In addition to recording an interferogram for the power spectrum, the gas species, gas pressure, and optical pulse energy were varied to study their effect on the THz pulse generated.

Fig. 1 Experimental layout showing that THz is generated by mixing the fundamental and its second harmonic laser field, generated from a frequency-doubling BBO crystal in a gas cell. A silicon filter is used filter out the THz pulse from the optical pulses. The THz interferogram is measured using Michelson interferometer located inside a vacuum chamber.

3. Results

Results for this work are separated into optical pulse energy dependence and gas pressure dependence. In both cases, THz time domain interferograms are recorded with post analysis consisting of a Fast Fourier Transform (FFT) to calculate the power spectrum of the pulse.

3.1 Energy dependence

Plotted in Fig. 2 are the THz interferograms and corresponding power spectra for (a)-(b) air, (c)-(d) neon, and (e)-(f) xenon at 800-nm optical pulse energies of 1 mJ, 2 mJ, 4, mJ, and 6 mJ. The pressure in the gas cell is kept fixed at 590 Torr (ambient pressure conditions in Los Alamos, New Mexico, USA). For a particular gas species, the data show that increasing optical pulse energy yields a monotonic increase in the amplitude of the THz pulse and a slight shifting of the spectrum to higher frequencies. The same trend is also observed for the others gases not plotted here: argon and krypton. This trend is consistent with our earlier observations [1

] where energies up 20 mJ/pulse were used with a 0.5 TW 50-fs 10-Hz 800 nm Ti:sapphire system. We also note that the data in Fig. 2 show that the heavier gases (Xe > Air > Ne) also tend to generate higher frequencies for a given pulse energy. Both of the trends observed here are consistent with increasing THz signal amplitude strength and spectral content as the plasma electron density increases from increased ionization due to more energy in the plasma or a lowered threshold for ionization based on the tunneling ionization rates for a particular gas [22

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

,23

C. W. Siders, G. Rodriguez, J. L. W. Siders, F. G. Omenetto, and A. J. Taylor, “Measurement of ultrafast ionization dynamics of gases by multipulse interferometric frequency-resolved optical gating,” Phys. Rev. Lett. 87(26), 263002 (2001). [CrossRef]

]. For the xenon case at 6 mJ in Fig. 2(e)-(f), we measure a THz interferogram as short as 35 fs (FWHM measured at the abscissa zero crossing of Fig. 2(e)) with frequency content out to 40 THz readily obtainable.

Fig. 2 Measured THz interferogram temporal waveforms and corresponding power spectra for the following gases at 800-nm optical pulse energies of 1 mJ, 2 mJ, 4 mJ, and 6 mJ: (a)-(b) air, (c)-(d) neon, and (e)-(f) xenon.

In addition to plotting the THz interferograms/waveforms, we also removed the Michelson interferometer and focused the entire THz beam on the pyroelectric detector to obtain a calibrated measure of the THz pulse energy as a function of gas species and input optical pulse energy at a fixed gas pressure of 590 Torr. Figure 3(a) is a plot of the THz output energy versus 800-nm input pulse energy. At the highest input energy (6 mJ), argon is seen to have maximum THz output of 0.88 μJ/pulse, and at 700 Torr the maximum pulse energy increases to 0.94 μJ. The values for the output energy account for a 50% transmission loss in the silicon filter. The maximum optical to THz conversion efficiency is approximately 1.5 × 10⁻⁴. Over the range of input pulse energies studied, a complex dependence of THz output is observed for the heavy gases (krypton and xenon) compared to the lighter gases (air, neon, and argon). Although at first not intuitive, a complex interdependence of THz output, gas pressure (Section 3.2 and Fig. 3(b)), and optical pulse energy is observed. At 590 Torr, argon and krypton switch between being the “best” THz producer over the range of pulse energies studied. This is evidence of the interplay between optical pulse (ω and 2ω) dephasing dynamics, gas- and plasma-induced index effects, and ionization. We address some of these subtleties in the next sections. This is evidence of the interplay between optical pulse (ω and 2ω) dephasing dynamics, gas- and plasma-induced index effects, and ionization. We address some of these subtleties in the next sections.

Fig. 3 THz output pulse energy versus (a) input 800-nm pulse energy (P = 590 Torr) and (b) pressure (E = 5.4 mJ/pulse) for the following gases: air, neon, argon, krypton, and xenon.

3.2 Pressure dependence

The pressure dependence (Fig. 3(b) and Fig. 4 ) of the THz output was also studied between the pressure range from 5 Torr to 700 Torr as the 800-nm pulse energy was fixed to 5.4 mJ. Figure 3(b) is a plot of the THz pulse energy versus pressure for air, neon, argon, krypton, and xenon. As the gas species is changed from light (neon) to heavy (xenon) mass, an undulation in the THz output versus pressure is observed. With increasing mass, the undulation frequency increases. Further, for the heaviest gases (krypton and xenon), as the pressure is increased, the THz output peaks, saturates and rolls off with increased pressure. As a result, at the highest pressure studied (P = 700 Torr), argon has the highest THz output rather than krypton or xenon even though the heavier gases have lower ionization potentials. We also note that the THz output is observed to have these characteristic undulations even if we decrease the laser pulse energy to conditions of low THz output and ionization. Since the ionization clearly relies on input laser pulse energy, we infer that these pressure induced undulations are principally due to ω and 2ω inter-pulse index-induced phase slippage occurring over the length of the neutral gas and not the plasma. Yet simultaneously, the THz output is also sensitive to the ionization, and in the cases of krypton and xenon, ionization begins to dominate and cause the THz output to saturate and eventually drop with increasing pressure. The saturation and drop is possibly due to phase slippage in the plasma or from plasma defocusing effects. For our tight focusing conditions (f/10), a plasma electron density between 5 × 10¹⁸ cm⁻³ and 5 × 10¹⁹ cm⁻³ is expected at our highest pulse energy (6 mJ). Under slightly softer focus conditions (f/20) for air at ambient pressure, we previously measured an electron density of 2 × 10¹⁸ cm⁻³ using electron diffractometry at 10 mJ of input energy [24

G. Rodriguez, A. R. Valenzuela, B. Yellampalle, M. J. Schmitt, and K.-Y. Kim, “In-line holographic imaging and electron density extraction of ultrafast ionized air filaments,” J. Opt. Soc. Am. B 25(12), 1988–1997 (2008). [CrossRef]

]. The conditions of these experiments at f/10 at 6 mJ generate a higher electron density such that plasma defocusing plays an important role in limiting the THz output.

Fig. 4 THz interferogram temporal waveforms and corresponding power spectra for the following gases at pressures between 20 Torr and 590 Torr: (a)-(b) air, (c)-(d) neon, and (e)-(f) argon.

The effects of pressure changes on the THz output are also studied for their effect on THz pulse temporal and spectral content. Plotted in Fig. 4 are the THz interferograms and corresponding power spectra for (a)-(b) air, (c)-(d) neon, and (e)-(f) argon at various pressures between 20 Torr and 590 Torr while keeping the pulse energy fixed at 6 mJ. In general, for a given individual gas species, the THz interferograms signal amplitudes increase as the gas pressure increased, indicative of increasing THz output with gas density. As the pressure is increased for a particular gas, fluctuations in the temporal waveforms lead to subtle changes in the spectral shape and frequency content of the power spectra. Although some of this is due to minute misalignment of the interferometer over the course of a data set run, the trend is clear: the amplitude of spectral components on the high frequency side increase as the pressure is increased. This is consistent with our previous paper [1

] that such an effect is caused by increasing electron density as the neutral gas available for ionization increases with pressure. In all cases, however, the amplitude of the power spectrum in THz pulse drops to below 10% of maximum at frequencies above 30 THz. Observation of higher frequencies may be inhibited by our lower laser pulse energy compared to our previous work.

Most interesting in the pressure dependent studies is the observation that the heavier gases (krypton and xenon) do not follow the trend with pressure as the lighter counterparts (neon, argon, and air). In Fig. 5 are the THz interferograms and corresponding power spectra for (a)-(b) krypton, (c)-(d) xenon for pressures between 20 Torr and 590 Torr at a fixed pulse energy fixed of 6 mJ. The THz output for these gases is seen to oscillate and quickly saturate with increasing gas pressure. Because these gases are more dispersive [25

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800 nm,” Appl. Opt. 47(27), 4856–4863 (2008). [CrossRef] [PubMed]

] than their lighter counterparts, we attribute the oscillation from two-color pressure dependent phase delay effects that introduce modulation in the THz output power. The pressure dependent indices of refraction for the ω and 2ω pulses introduce slippage that affects the ionization [9

] and directional photocurrent [14

] that is most severe for krypton and xenon. Some spectral weight shifting in the THz power spectra is observed for these gases in Fig. 5(b) and Fig. 5(d). We also note that the results here indicate that THz polarization control, such as in work reporting phase control with optical elements [12

J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett. 103(2), 023001 (2009). [CrossRef] [PubMed]

,13

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103(2), 023902 (2009). [CrossRef] [PubMed]

] can also be achieved by precise pressure control of the phasing between ω and 2ω pulses.

Fig. 5 THz interferogram temporal waveforms and corresponding power spectra for the following gases at pressures between 20 Torr and 590 Torr: (a)-(b) krypton and (c)-(d) xenon.

4. Photocurrent model and discussion

Several models exist for the calculation of the conversion of optical fields to THz radiation [10

,11

,17

K. Y. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas 16(5), 056706 (2009). [CrossRef]

,21

V. A. Kostin and N. V. Vvedenskii, “Ionization-induced conversion of ultrashort Bessel beam to terahertz pulse,” Opt. Lett. 35(2), 247–249 (2010). [CrossRef] [PubMed]

,26

V. B. Gildenburg and N. V. Vvedenskii, “Optical-to-THz wave conversion via excitation of plasma oscillations in the tunneling-ionization process,” Phys. Rev. Lett. 98(24), 245002 (2007). [CrossRef] [PubMed]

] via ionization. Yet, since we are principally concerned with the spectral power distribution of the generated THz pulse at high frequencies, we take a modest approach using a 1-D nonrelativistic electromagnetic fluid code [27

G. Rodriguez, C. W. Siders, C. Guo, and A. J. Taylor, “Coherent ultrafast MI-FROG spectroscopy of optical field ionization in molecular H₂, N₂, and O₂ ,” IEEE J. Quantum Electron. 7(4), 579–591 (2001). [CrossRef]

] to model optical pulse propagation, ionization dynamics, and THz generation process in the plane wave approximation. Using this approach, we ascribe the generated THz spectrum to the conditions of the plasma generated with spectral information imparted to the transmitted electric field through the plasma layer. This model solves Maxwell's equation and the momentum equation for the optical fields, electron density, and current

\frac{\partial E}{\partial t} = c \nabla \times B - 4 π J,

(1)

\frac{\partial B}{\partial t} = - c \nabla \times E,

(2)

\frac{\partial J}{\partial t} = \frac{e^{2}}{m} n_{e} E,

(3)

where,

E linearly polarized electric field along the y direction;
B magnetic field along the linearly z direction;
J transverse current along the y direction;

The propagation of the TE-wave is taken along the x direction for a uniform gas density of Ν ₀ and a laser plasma interaction length of L. The electron density n_e (x,t) is calculated by summing over the number density of ions N_j (x,t) with charge state j

n_{e} = \sum_{j} j N_{j} .

(4)

The ion densities are found by integrating a system of rate equations assuming a stepwise ionization process

\frac{\partial N_{0}}{\partial t} = - W_{1} N_{0},

(5)

\frac{\partial N_{j}}{\partial t} = W_{j} N_{j - 1} - W_{j + 1} N_{j},

(6)

\frac{\partial N_{Z_{\max}}}{\partial t} = W_{Z_{\max}} N_{Z_{\max} - 1},

(7)

where, W_j is the total ionization rate for the production of charge state j. The model takes into account only field ionization. For relatively low gas pressures (below 1 atm) collisional ionization is not expected to be the dominant rate mechanism [27

]. The field ionization rate W_j is given by the Ammosov-Delone-Krainov (ADK) tunneling formula [22

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

W = 1.61 ω_{au} \frac{Z^{2}}{n_{eff}} {(10.87 \frac{Z^{3}}{n_{eff}^{4}} \frac{E_{au}}{E})}^{2 n_{eff} - 1.5} \exp (- \frac{2}{3} \frac{Z^{3}}{n_{eff}^{3}} \frac{E_{au}}{E}),

(8)

where ω_au is the atomic unit of frequency 4.1 × 10¹⁶ s⁻¹ and E _au is the atomic unit of field (5.14 × 10⁹ V/cm). Z is the residual charge seen by the critical electron. The effective quantum number n_eff is found by equating the ionization potential I_p of the ion or neutral atom with

(Z^{2} / n_{eff}^{2}) I_{p H}

where Z is the residual charge state and I_p _H is the ionization potential of hydrogen (I_p _H = 13.6 eV)

n_{eff} = \frac{Z}{\sqrt{I_{p} 13.6 eV}} .

(9)

The incident input fields to the model are linearly polarized and are derived assuming a Gaussian intensity profile for each input field at 800 nm (ω) and 400 nm (2ω).

\begin{matrix} E_{y} = B_{z} = E_{800} + E_{400}, \\ = \sqrt{2 η_{o} I_{ω}} \sin (ω t) \exp (β t^{2} / τ_{ω}^{2}) \\ + \sqrt{2 η_{o} I_{2 ω}} \sin (ω t + θ) \exp (β {(t + Δ t)}^{2} / τ_{2 ω}^{2}), \end{matrix}

(10)

where, β = 2ln2 and η_o is the free-space intrinsic impedance (376.6 Ω). The optical pulsewidths are given by τ_ω and τ_2ω for 800 nm and 400 nm, respectively. The time delay between the 800 nm and 400 nm pulse is Δt which is set equal to zero for our purposes, and the relative temporal phase difference between the optical fields is θ. From the incident field, the model calculates the transmitted and reflected fields after a propagation distance L, the plasma length, assuming a uniform gas density of Ν ₀. The plasma length L is approximated by using the beam confocal parameter and is taken as 500 μm. The ion and electron densities N_j (x,t) (j ≠ 0) and n _e(x,t) are also computed.

We then compute the Fourier transform with respect to frequency, Ω, of the transmitted electric field at each position in x from x = 0 to x = L through the plasma layer from the plasma current time derivative, ∂J_y /∂t, to begin extracting spectral components in the propagated field at each step x along the propagation direction,

E_{y} (x, Ω) \propto \int_{- \infty}^{\infty} \frac{\partial J_{y} (x, t)}{\partial t} \exp (i Ω t) d t .

(11)

The THz portion of the intensity power spectrum, I _THz (Ω), is calculated by taking only those frequency components that lie in the THz range (Ω ≤ Ω_THz = 150 THz) by low pass filtering and integrating along x the propagation direction to sum for all spectral contributions along the propagation direction. We also account for THz absorption along the plasma propagation length, L.

I_{THz} (Ω) = {| \int_{0}^{L} E_{y} (x, Ω) e^{[- (L - x) / L_{a b s}]} e^{i ϕ (x, ω_{p})} d x |}^{2} (Ω \leq Ω_{THz}) .

(12)

The THz absorption length, L_abs, is related to the plasma index of refraction via the following relation,

L_{abs} (Ω) = c / [ω Im (n)] \approx 2 c (Ω^{2} + ν_{e}^{2}) / (ω_{p}^{2} ν_{e}),

(13)

where, the collision frequency, ν _e, is empirically set to mimic high pass filtering that is consistent with the experimental data that shows frequency roll off on the low side at approximately 5 THz in the measured power spectra.

In Fig. 6 we show a sample calculation for Ar (Z_Ar = 18, I _p = 15.76 eV) gas at 500 Torr where Ν ₀. = 1.61 × 10¹⁹ cm⁻³ from our simple 1-D model. Using the following parameters for input: I_ω = 5 × 10¹⁴ W/cm², I_2ω = 0.2 I_ω, τ_ω = τ_2ω = 40 fs, θ = π/2 input phase difference between the ω and 2ω fields, and L = 500 μm, we plot the input electric field, E _y(x = 0,t), the output electric field, E _y(x = L,t), and the corresponding transverse current, J _y, at these points given the plasma length L. Upon entrance into the computational grid (x = 0), the two-color transverse electric field generates a transient current derivative pulse that lags in time when compared to the peak electric field. This is consistent with the description that the current is derived from the point somewhere in the electric field pulse where the field becomes strong enough to ionize the gas. After this time point, the current oscillates during the electric field pulse duration as the photogenerated electrons quiver in response to the field. Quiver motion and current ceases when the field turns “off”. After traversing the plasma length (at the exit of the computational grid (x = L)), the electric field is seen to be modulated and distorted. The modulation and distortion increases with propagation distance and field strength as electrons in the plasma introduce losses when the index drops below the value of one.

Fig. 6 Computed transverse electric field, E _y, and corresponding current, J _y, which precedes calculation of the THz spectrum. The plots of the two-color electric field are for positions at the (a) input (x = 0) and (b) output (x = L) of the plasma length, L, with corresponding current at (c) x = 0 and (d) x = L. The calculation is for 500 Torr of Ar gas, L = 500 μm, I_ω = 5 × 10¹⁴ W/cm², I_2ω = 10¹⁴ W/cm², and τ_ω = τ_2ω = 40 fs.

Using the sample case above (500 Torr Ar, L = 500 μm), we also calculate the THz power spectrum using Eqs. (11) - (13). Figure 7(a) is a plot of the integrated THz power spectrum for various input intensities: I_ω = 5 × 10¹⁴ W/cm², 10¹⁵ W/cm², 5 × 10¹⁵ W/cm², and 10¹⁶ W/cm². Increasing the laser input intensity tends to shift the peak in the power spectrum and broaden the spectral components to the high frequency side of the peak. Similarly in Fig. 7(b), asthe pressure is varied from 50 Torr to 700 Torr, the spectrum is also observed to develop additional high frequency components as the overall THz power increases. In each case, increasing the intensity or pressure in the calculations, is accompanied with increasing overall THz output power. If we proceed to calculate the THz power spectrum for the set of noble gases studied, we observe a similar trend with increasing atomic mass. Figure 8 is a plot of the THz power spectrum calculated for neon, argon, krypton, and xenon for an input intensity of I_ω = 10¹⁵ W/cm² and gas pressure of 500 Torr. The calculation predicts that the highest THz output and largest spectral content is achieved with the heaviest atom (lowest ionization potential). It is also important to note that if material absorption in experimental setups can be minimized, detection out to 100 THz should be attainable with a 10³-10⁴ signal-to-noise (S/N) dynamic range. Such S/N dynamic range and bandwidth are achievable in electro-optic detection schemes. Much of our S/N limitation in our pyroelectric detection scheme is the slow response time of the detector that limits us to low chopping frequencies (10’s of Hertz) to minimize responsivity loss with increasing chopping frequency. Other noises sources such thermal transients and detector amplifier noise that also seem to appear at frequencies near to our chopping frequency. Time gated electro-optic approaches such as the air breakdown coherent detection (ABCD) of the Rensselaer group [19

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56(10), 1137–1150 (2009). [CrossRef]

,28

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006). [CrossRef] [PubMed]

] may be a more adequate detection approach that minimizes material absorption and still allows for full lock-in detection at high chopping frequencies. The latter approach also allow for THz field (amplitude & phase) spectral detection as opposed to a THz interferogram based power spectrum.

Fig. 7 Computed THz spectral power for Ar gas (L = 500 μm) as the (a) input intensity (I_ω = 5 × 10¹⁴, 10¹⁵, 5 × 10¹⁵, and 10¹⁶ W/cm²) and (b) neutral gas pressure (P = 50,100,200,500, and 700 Torr) are varied.

Fig. 8 Computed THz spectral power for 500 Torr (L = 500 μm) of Ne, Ar, Kr, and Xe gas at an input intensity of I_ω = 10¹⁵ W/cm².

When compared to our experimental data only partial agreement with our photocurrent model is observed. The calculated THz power spectra are consistent with the experimental measurements despite not accounting for material absorption in the THz beam path from the silicon filter or ultrathin 2-μm thick nitrocellulose beamsplitter in the interferometer in the model. The model also predicts increased THz output power with increasing intensity (pulse energy), pressure, and atomic mass. The experimental data loosely follow these trends, but in cases across atomic species, argon consistently yielded the highest THz output. In the pulse energy dependence (Fig. 3(a)), we attribute weaker krypton and xenon output to plasma defocusing and phase slippage arising from too much on-axis ionization resulting in an overall reduced THz output. The same explanation also applies to the pressure dependence results (Fig. 3(b)) where increasing gas pressure induces additional atoms that undergo ionization and subsequently produces too much plasma and reduces the on-axis laser focal intensity. Lending credence to this explanation is the low pressure data (≤ 80 Torr) from Fig. 3(b) where the THz output follows the expected trend Xe > Kr > Ar > Ne. Increasing gas pressure also results in slight changes to the observed plasma length, and absorption losses from changes in the length also may contribute to the observed THz spectra. More sophisticated multidimensional theoretical approaches are necessary to account for longitudinal and transverse spatial pulse propagation effects in the plasma.

Another factor affecting THz conversion is the proper phasing of the combined two-color field driving efficiency in the neutral gas and plasma. It has been shown in multiple papers [1

,12

,13

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103(2), 023902 (2009). [CrossRef] [PubMed]

] that the THz output is quite sensitive to the phase delay between the ω and 2ω fields and is optimal at π/2. Sensitivity to the relative phasing in the neutral gas is most evident in the pressure dependent data of Fig. 3(b). As described earlier, the large amplitude undulations in the data demonstrate the THz output efficiency that can be altered by varying the pressure for a particular gas species. The phase slippage in the neutral gas is given by,

Δ k_{neut} = (2 ω / c) (n_{ω} (P) - n_{2 ω} (P)),

(14)

where, n _ω(P) and n _2ω(P) are the pressure dependent indices of the gas. Using the indices of refraction from [25

,29

P. J. Leonard, “Refractive indices, verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14(1), 21–37 (1974). [CrossRef]

,30

E. R. Peck and D. J. Fisher, “Dispersion of argon,” J. Opt. Soc. Am. A 54(11), 1362–1364 (1964). [CrossRef]

], we calculate the pressure dependent undulation periods of 390 Torr (air), 3800 Torr (Ne), 420 Torr (Ar), 230 Torr (Kr), and 95 Torr (Xe) are expected in the power output. The calculated periods are in agreement with the data in Fig. 3(b): 400 Torr (air), 420 Torr (Ar), 185 Torr (Kr), and 100 Torr (Xe). These results are in agreement with those by [11

] under a similar pressure range where measurements on THz electric fields are twice the period to those reported here when THz power measurements are made.

The pressure dependent data reveal the relative phase delay contribution from neutral species, but intermixing of neutrals with plasma also affects the two-color phasing along the length of the plasma. This is illustrated in Fig. 9 where the THz output is plotted versus pressure for a single gas (Xe) at two different fundamental input pulse energies of 2.5 mJ and 5.4 mJ. Although the undulation periods remain relatively equal between the two cases, the higher energy case (5.4 mJ) data show the undulations decaying away with pressure more rapidly than the lower energy case (2.5 mJ). The data indicate that the plasma index significantlyalters the relative phase between the ω and 2ω fields with increasing ionization and background pressure. Phase slippage in the plasma is given by,

Δ k_{p} = 2 k_{ω} - k_{2 ω} \approx - \frac{3}{4} \frac{ω_{p}^{2}}{c ω},

(15)

where, the ω and 2ω wave vector magnitudes and indices are: k _ω = n_ωω/c, k _2ω = 2n_2ωω/c, n_ω = (1-ω _p ²/ω²)^½, and n_2ω = (1-ω_p ²/(2ω)²)^½. The plasma frequency is ω_p = (n _ee²∕mε₀)^½. We examine the plasma induced phase slippage by considering a couple of cases (Ar and Xe) with our photocurrent model. If we assume a moderate peak focal intensity of 10¹⁵ W/cm² for the ω field (2 × 10¹⁴ W/cm² for 2ω) over the pressure range studied, our photocurrent model predicts an electron density of n _e = 4.7 × 10¹⁹ cm⁻³ and 7.1 × 10¹⁹ cm⁻³ at 700 Torr for argon and xenon, respectively. The corresponding phase slippage modulation period lengths for these densities are ℓ_p = 2π/|Δk _p|≈40 μm and 26 μm. Since the plasma length is L > ℓ_p, at our experimental intensities, modulation form plasma phase slippage is significant at 700 Torr. At 20 Torr, the conditions are somewhat different. The calculated electron densities and modulation period lengths are n _e = 1.5 × 10¹⁸ cm⁻³ and 2.3 × 10¹⁸ cm⁻³ and ℓ_p = 1240 μm and 809 μm for argon and xenon, respectively. When L < ℓ_p, plasma slippage is less severe, but THz output is compromised because the photocurrent is diminished from lack of liberated electrons.

Fig. 9 Measured THz output pulse energy versus pressure for xenon (Xe) gas at two different in pulse energies of the fundamental (ω) laser field.

In recent experiments reporting on the two-color generation of broadband far-infrared light centered at 10 μm (30 THz) in a long filament, a nonlinear four wave mixing process was identified [8

]. These experiments, however, were performed under different experimental conditions using an f/60 focusing condition where a strong self focus filament channel is formed. Our experiments have peak spectral power at lower frequencies (12 THz for air at 590 Torr), and are clearly dependent on the relative phasing of the ω and 2ω fields, a condition that was not necessary for the work in Ref [8

]. Further, our f/10 focusing geometry tends to relax the condition of strong self-focusing, and instead puts us in a plasma dominated regime. Nonetheless, contribution to index variation due to the nonlinear index from neutrals via the Kerr self focus effect compared to the plasma index is also considered. If a moderate peak focal intensity of 10¹⁵ W/cm² is assumed, the Kerr induced index change, Δn_Kerr, for the stronger ω field is Δn_Kerr = 2.9 × 10⁻⁴ for air, 1.4 × 10⁻⁴ for argon, and 8.1 × 10⁻⁴ for xenon, respectively, using the nonlinear indices for these gases [31

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear index of refraction of air, N₂, and O₂ by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B 14(3), 650–660 (1997). [CrossRef]

]. For the plasma index change, we take an electron density of n _e = 10¹⁹ cm⁻³ which is lower than the photocurrent model predicts at an input intensity of 10¹⁵ W/cm² but consistent with previous electron density measurements [24

], a plasma index change value of Δn_p = 2.8 × 10⁻³ is calculated. Thus, we conclude that for the low dispersive gases (air, neon, and argon) plasma via a photocurrent dominates the THz emission process. For the heavier gases (krypton and xenon), despite being nearly fully ionized at several hundred Torr of pressure, and although the plasma term still dominates, contribution to far-infrared generation from Kerr induced four wave mixing from neutrals cannot be ruled out, especially at the highest pressures (> 500 Torr). Further studies are necessary to determine the crossover point between the competing mechanisms.

5. Conclusions

These studies focused on input energy and gas pressure effects on the scaling behavior of ultrafast THz generation in two-color plasma gas targets. We demonstrated a practical 1-kHz source with a detected THz spectrum out 40 THz and 0.94 μJ per pulse maximum at 700 Torr of argon gas. For a fixed pressure of 590 Torr (Fig. 3(a)) THz output saturation is not observed for any of the gases used up to 6 mJ of input pulse energy. However, for a fixed input pulse energy of 5.4 mJ (Fig. 3(b)), output saturation is observed for the heavier gases, krypton and xenon, and there is significant two-color phasing effects in all the gases up to 700 Torr, except for neon. In context with previous studies, it was shown that single THz pulse energies of greater than 10 μJ are attainable using the tilted wave front technique [32

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

], but the drawback is that the bandwidth is greatly reduced to a few THz, and is not conducive from the materials spectroscopy perspective for access to optical phonon transitions above 10 THz. THz pulse energies for two-color plasma based broadband sources have been demonstrated [1

] to generate >5 μJ per pulse at the detector, but at a greatly reduced repetition rate (10 Hz) due to drive laser (20 mJ) limitations. A recent experiment [4

] indicated improvement in the optical to THz conversion efficiency of 1.7 × 10⁻⁵, but still only yielded 0.14 μJ/pulse in a 3 THz bandwidth limited ZnTe electro-optic detection scheme. Our nearly flat response pyroelectric detection method includes a vacuum chamber and minimal material absorption design that is intended for maximizing detectable THz bandwidth and energy. This includes a scheme that is relatively insensitive to the THz polarization state which is known to vary as the optical phasing in the gas is changed [14

]. Our measured optical to THz pulse energy conversion efficiency is 1.5 × 10⁻⁴ with sufficient bandwidth to access up to 40 THz. Drawback to this technique, however, is loss of electric field phase information. Further, slow detector response and spurious noise limit chopping frequencies for lock-in detection to 10’s of Hz with chopping and only fair S/N. Improvement in the detection scheme should yield 1-kHz microjoule-level THz sources with bandwidth out to 100 THz.

Acknowledgements

Funding for this work is provided by the Laboratory Directed Research and Development Program at Los Alamos National Laboratory under the auspices of the Department of Energy for Los Alamos National Security LLC under contract number DE-AC52-06NA25396.

References and links

1.	K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2(10), 605–609 (2008). [CrossRef]
2.	J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B18 (2008). [CrossRef]
3.	M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26(9), A29–A34 (2009). [CrossRef]
4.	F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, “Improved terahertz two-color plasma sources pumped by high intensity laser beam,” Opt. Express 17(8), 6044–6052 (2009). [CrossRef] [PubMed]
5.	S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
6.	A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
7.	T.-J. Wang, J.-F. Daigle, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy THz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7(7), 517–521 (2010). [CrossRef]
8.	F. Théberge, M. Châteauneuf, G. Roy, P. Mathieu, and J. Dubois, “Generation of tunable and broadband far-infrared laser pulses during two-color filamentation,” Phys. Rev. A 81(3), 033821 (2010). [CrossRef]
9.	K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15(8), 4577–4584 (2007). [CrossRef] [PubMed]
10.	H. G. Roskos, M. D. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1(4), 349–368 (2007). [CrossRef]
11.	A. V. Balakin, A. V. Borodin, I. A. Kotelnikov, and A. P. Shkurinov, “Terahertz emission from a femtosecond laser focus in a two-color scheme,” J. Opt. Soc. Am. B 27(1), 16–25 (2010). [CrossRef]
12.	J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett. 103(2), 023001 (2009). [CrossRef] [PubMed]
13.	H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103(2), 023902 (2009). [CrossRef] [PubMed]
14.	D. Dietze, J. Darmo, S. Roither, A. Pugzlys, J. N. Heyman, and K. Unterrainer, “Polarization of terahertz radiation from laser generated plasma filaments,” J. Opt. Soc. Am. B 26(11), 2016–2027 (2009). [CrossRef]
15.	Z.-M. Sheng, H.-C. Wu, W. M. Wang, M. Chen, X. G. Dong, J. Zheng, and J. Zhang, “Simulation of high power THz emission from laser interaction with tenuous plasma and gas targets,” Comm. Comp. Phys. 4, 1258–1278 (2008).
16.	W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16(21), 16999–17006 (2008). [CrossRef] [PubMed]
17.	K. Y. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas 16(5), 056706 (2009). [CrossRef]
18.	R. A. Akhmedzhanov, I. E. Ilyakov, V. A. Mironov, E. Y. Suvorov, D. A. Fadeev, and B. V. Shishkin, “Plasma mechanisms of pulsed terahertz radiation generation,” Radiophys. Quantum Electron. 52(7), 482–493 (2009). [CrossRef]
19.	N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56(10), 1137–1150 (2009). [CrossRef]
20.	Y. Chen, M. Yamaguchi, M. Wang, and X.-C. Zhang, “Terahertz pulse generation from noble gases,” Appl. Phys. Lett. 91(25), 251116 (2007). [CrossRef]
21.	V. A. Kostin and N. V. Vvedenskii, “Ionization-induced conversion of ultrashort Bessel beam to terahertz pulse,” Opt. Lett. 35(2), 247–249 (2010). [CrossRef] [PubMed]
22.	M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).
23.	C. W. Siders, G. Rodriguez, J. L. W. Siders, F. G. Omenetto, and A. J. Taylor, “Measurement of ultrafast ionization dynamics of gases by multipulse interferometric frequency-resolved optical gating,” Phys. Rev. Lett. 87(26), 263002 (2001). [CrossRef]
24.	G. Rodriguez, A. R. Valenzuela, B. Yellampalle, M. J. Schmitt, and K.-Y. Kim, “In-line holographic imaging and electron density extraction of ultrafast ionized air filaments,” J. Opt. Soc. Am. B 25(12), 1988–1997 (2008). [CrossRef]
25.	A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800 nm,” Appl. Opt. 47(27), 4856–4863 (2008). [CrossRef] [PubMed]
26.	V. B. Gildenburg and N. V. Vvedenskii, “Optical-to-THz wave conversion via excitation of plasma oscillations in the tunneling-ionization process,” Phys. Rev. Lett. 98(24), 245002 (2007). [CrossRef] [PubMed]
27.	G. Rodriguez, C. W. Siders, C. Guo, and A. J. Taylor, “Coherent ultrafast MI-FROG spectroscopy of optical field ionization in molecular H₂, N₂, and O₂ ,” IEEE J. Quantum Electron. 7(4), 579–591 (2001). [CrossRef]
28.	J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97(10), 103903 (2006). [CrossRef] [PubMed]
29.	P. J. Leonard, “Refractive indices, verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14(1), 21–37 (1974). [CrossRef]
30.	E. R. Peck and D. J. Fisher, “Dispersion of argon,” J. Opt. Soc. Am. A 54(11), 1362–1364 (1964). [CrossRef]
31.	E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear index of refraction of air, N₂, and O₂ by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B 14(3), 650–660 (1997). [CrossRef]
32.	K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(260.3230) Physical optics : Ionization
(320.7120) Ultrafast optics : Ultrafast phenomena
(350.5400) Other areas of optics : Plasmas
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Ultrafast Optics

History
Original Manuscript: April 23, 2010
Revised Manuscript: June 10, 2010
Manuscript Accepted: June 28, 2010
Published: June 30, 2010

Citation
George Rodriguez and Georgi L. Dakovski, "Scaling behavior of ultrafast two-color terahertz generation in plasma gas targets: energy and pressure dependence," Opt. Express 18, 15130-15143 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-15130

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References

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2(10), 605–609 (2008). [CrossRef]
J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B18 (2008). [CrossRef]
M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26(9), A29–A34 (2009). [CrossRef]
F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, “Improved terahertz two-color plasma sources pumped by high intensity laser beam,” Opt. Express 17(8), 6044–6052 (2009). [CrossRef] [PubMed]
S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
T.-J. Wang, J.-F. Daigle, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy THz generation from meter-long two-color filaments in air,” Laser Phys. Lett. 7(7), 517–521 (2010). [CrossRef]
F. Théberge, M. Châteauneuf, G. Roy, P. Mathieu, and J. Dubois, “Generation of tunable and broadband far-infrared laser pulses during two-color filamentation,” Phys. Rev. A 81(3), 033821 (2010). [CrossRef]
K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15(8), 4577–4584 (2007). [CrossRef] [PubMed]
H. G. Roskos, M. D. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1(4), 349–368 (2007). [CrossRef]
A. V. Balakin, A. V. Borodin, I. A. Kotelnikov, and A. P. Shkurinov, “Terahertz emission from a femtosecond laser focus in a two-color scheme,” J. Opt. Soc. Am. B 27(1), 16–25 (2010). [CrossRef]
J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma,” Phys. Rev. Lett. 103(2), 023001 (2009). [CrossRef] [PubMed]
H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103(2), 023902 (2009). [CrossRef] [PubMed]
D. Dietze, J. Darmo, S. Roither, A. Pugzlys, J. N. Heyman, and K. Unterrainer, “Polarization of terahertz radiation from laser generated plasma filaments,” J. Opt. Soc. Am. B 26(11), 2016–2027 (2009). [CrossRef]
Z.-M. Sheng, H.-C. Wu, W. M. Wang, M. Chen, X. G. Dong, J. Zheng, and J. Zhang, “Simulation of high power THz emission from laser interaction with tenuous plasma and gas targets,” Comm. Comp. Phys. 4, 1258–1278 (2008).
W.-M. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima, “Strong terahertz pulse generation by chirped laser pulses in tenuous gases,” Opt. Express 16(21), 16999–17006 (2008). [CrossRef] [PubMed]
K. Y. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas 16(5), 056706 (2009). [CrossRef]
R. A. Akhmedzhanov, I. E. Ilyakov, V. A. Mironov, E. Y. Suvorov, D. A. Fadeev, and B. V. Shishkin, “Plasma mechanisms of pulsed terahertz radiation generation,” Radiophys. Quantum Electron. 52(7), 482–493 (2009). [CrossRef]
N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56(10), 1137–1150 (2009). [CrossRef]
Y. Chen, M. Yamaguchi, M. Wang, and X.-C. Zhang, “Terahertz pulse generation from noble gases,” Appl. Phys. Lett. 91(25), 251116 (2007). [CrossRef]
V. A. Kostin and N. V. Vvedenskii, “Ionization-induced conversion of ultrashort Bessel beam to terahertz pulse,” Opt. Lett. 35(2), 247–249 (2010). [CrossRef] [PubMed]
M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).
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