OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 15130–15143
« Show journal navigation

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


View Full Text Article

Acrobat PDF (2528 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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.

© 2010 OSA

1. Introduction

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

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

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

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

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

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

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

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

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

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]

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

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

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.

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
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.
. 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 (RV) of RV = 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.

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

3.2 Pressure dependence

The pressure dependence (Fig. 3(b) and Fig. 4
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.
) 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

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.

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
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.
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

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

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]

] and directional photocurrent [14

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]

] 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

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

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.

4. Photocurrent model and discussion

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

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

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]

,17

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

,21

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

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

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
Et=c×B4πJ,
(1)
Bt=c×E,
(2)
Jt=e2mneE,
(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 ne(x,t) is calculated by summing over the number density of ions Nj(x,t) with charge state j
ne=jjNj.
(4)
The ion densities are found by integrating a system of rate equations assuming a stepwise ionization process
N0t=W1N0,
(5)
Njt=WjNj1Wj+1Nj,
(6)
NZmaxt=WZmaxNZmax1,
(7)
where, Wj 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

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]

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

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=1.61ωauZ2neff(10.87Z3neff4EauE)2neff1.5exp(23Z3neff3EauE),
(8)
where ωau 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 neff is found by equating the ionization potential Ip of the ion or neutral atom with(Z2/neff2)IpH where Z is the residual charge state and Ip H is the ionization potential of hydrogen (Ip H = 13.6 eV)

neff=ZIp13.6  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).
Ey=Bz=E800+E400,=2ηoIωsin(ωt)exp(βt2/τω2)+2ηoI2ωsin(ωt+θ)exp(β(t+Δt)2/τ2ω2),
(10)
where, β = 2ln2 and ηo is the free-space intrinsic impedance (376.6 Ω). The optical pulsewidths are given by τω and τ 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 Nj(x,t) (j ≠ 0) and n e(x,t) are also computed.

In Fig. 6
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, Iω = 5 × 1014 W/cm2, I = 1014 W/cm2, and τω = τ = 40 fs.
we show a sample calculation for Ar (ZAr = 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: Iω = 5 × 1014 W/cm2, I = 0.2 Iω, τω = τ = 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.

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)
Fig. 7 Computed THz spectral power for Ar gas (L = 500 μm) as the (a) input intensity (Iω = 5 × 1014, 1015, 5 × 1015, and 1016 W/cm2) and (b) neutral gas pressure (P = 50,100,200,500, and 700 Torr) are varied.
is a plot of the integrated THz power spectrum for various input intensities: Iω = 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
Fig. 8 Computed THz spectral power for 500 Torr (L = 500 μm) of Ne, Ar, Kr, and Xe gas at an input intensity of Iω = 1015 W/cm2.
is a plot of the THz power spectrum calculated for neon, argon, krypton, and xenon for an input intensity of Iω = 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

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

,28

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.

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

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]

,12

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

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,
Δkneut=(2ω/c)(nω(P)n2ω(P)),
(14)
where, n ω(P) and n (P) are the pressure dependent indices of the gas. Using the indices of refraction from [25

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]

,29

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

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

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]

] 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
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.
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,
Δkp= 2kωk2ω34ωp2cω,
(15)
where, the ω and 2ω wave vector magnitudes and indices are: k ω = nωω/c, k = 2nω/c, nω = (1-ω p 22)½, and n = (1-ωp 2/(2ω)2)½. The plasma frequency is ωp = (n ee2mε0)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 ℓp = 2π/|Δk p|≈40 μm and 26 μm. Since the plasma length is L > ℓp, 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 ℓp = 1240 μm and 809 μm for argon and xenon, respectively. When L < ℓp, plasma slippage is less severe, but THz output is compromised because the photocurrent is diminished from lack of liberated electrons.

5. Conclusions

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited