Abstract

We establish a one-to-one mapping between the local phase slip and the spatial position near the focus by scanning a thin jet along the propagation direction of laser beams. The measurement shows that the optimal phase of terahertz can be utilized to characterize in situ the spatially dependent relative phase of the two-color field. We also investigate the role of the Gouy phase shift on terahertz generation from two-color laser-induced plasma. The result is of critical importance for phase-dependent applications of two-color laser-field, including high-order harmonic and terahertz generation.

© 2016 Optical Society of America

1. Introduction

Since it was first demonstrated by Cook et. al. [1] in 2000, terahertz (THz) radiation from two-color laser-induced plasma has been extensively studied [2–8], due to its broad-bandwidth, easy implementation and high efficiency. Several models, including four-wave mixing [1] and transient photo-current [9, 10], have been proposed to explain the underlying physical mechanism. In this intense THz generation scheme, the relative phase between the fundamental and second-harmonic laser fields, as a phase-gating, is extremely critical for THz generation [11–14]. The question of determining the value of the optimal phase, which maximizes THz radiation, has to be addressed. This problem was solved very recently by a synchronous measurement of high-order harmonics and THz generation [15–17].

However, THz pulses are usually generated from air plasma in the laser focus. As is well known, the Gouy phase shift (GPS) is introduced [18] while the electromagnetic wave passes through its focus. This phase shift has important consequences in the optical range of the electromagnetic spectrum. It also provides us an empirically adjustable quantity in some phase-dependent researches such as controlling the chemical reactions [19], reshaping the electromagnetic pulses [20,21], optimizing THz detection efficiency [22] and measurement precision [23], and so on. In principle, the GPS ϕGouy [24] of a continuous Gaussian wave, is related to the wavelength λ and beam waist w0 by

ϕGouy=arctan(zλπw02),
which indicates the z-dependent GPS of the two color lasers causes a relative phase slip over the Rayleigh range. Although it is discovered more than one hundred years ago, the experimental evidence of the GPS relied for years on interference measurements. Recently, the first non-interferometric observation of the GPS has been reported by the polarity reversal of focused single-cycle THz pulses [25]. Indeed, the details of the phase change in the focus depend on the spatial profile of the laser beam and the focusing geometry. The GPS of complex laser beams and ultrashort pulses cannot be easily calculated based on Eq. (1). Efforts are still being made to precisely measure and control the spatial variation of the GPS in the whole focal region. The so-called stereo-ATI (above-threshold-ionization) scheme is used to determine the evolution of the carrier-envelope phase in the focus of few-cycle laser pulses [26]. The ion imaging is performed to characterize in situ the GPS of an annular beam for further high-precision attosecond measurements [27].

In this paper, we demonstrate the first experimental determination of the evolution of the relative phase in the focus of the two-color laser pulses by means of THz generation. This is important because this method can be applied to complex beam profiles and realized simultaneously with strong field experiment. By scanning the thin gas jet through the focus, we demonstrate directly that THz generation from long gas plasma is the superposition of that from sliced gas medium. We also investigate the phase averaging effect on THz generation in air plasma.

2. Experimental details

Figure 1 shows the experimental setup. 25 fs laser pulses with the energy of 1.6 mJ centered at 790 nm from a 1 kHz Ti:sapphire system (Femtopower Compact PRO; Femtolasers Produktion GmbH) are split into two arms as the pump and probe beams. The pump beam is frequency doubled by a type-I β-barium borate (β-BBO), after which temporally separated two color lasers with orthogonal polarizations are thus formed. To make their polarization parallel, a special dual-wavelength waveplate (DWP) is employed, which introduces a phase retardation of λ/2 for fundamental, and λ for the second-harmonic. A wire grid polarizer (WGP) after the DWP further eliminates the residual fundamental laser fields with different polarization. The α-BBO is used to make the two-color field temporally overlap with each other. A pair of fused-silica wedges are adopted to finely control the relative phase between the two-color laser field. The two color laser pulses are focused by a spherical mirror (SM) with a focal length of 200 mm onto a gas jet to generate THz. The jet with 50 μm inner diameter is placed in a vacuum chamber pumped down to 10−5 mbar. The generated THz waves are focused by a hole-drilled off-axis parabolic mirror (PM) onto a 1 mm thick (110)-cut ZnTe crystal, which is shined on by the delayed probe beam for electro-optic sampling (EOS) detection. The two-color laser beams after the gas jet propagate through another β-BBO crystal to frequency double the residual fundamental laser and the resulted second harmonic will interfere with the second harmonic components in the two-color field.

 figure: Fig. 1

Fig. 1 Schematic diagram of the experimental setup. DWP: dual-wavelength plate; WGP: wire grid polarizer; SM: spherical mirror; PM: parabolic mirror; PBS: polarizing beam splitter.

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The interference of second-harmonics measured by Detector 2 is used to monitor the shift of the relative phase between two-color fields [28]. Varying the relative phase between fundamental and second-harmonic fields by inserting one of the wedges, the modulation of second-harmonic is recorded at a high vacuum (∼ 10−5mbar) as shown with red squares in Fig. 2(a). When a gas jet with 50 μm diameter and 3 bar backing pressure is inserted into the focus, the measured intensity interference is shown as blue dots in Fig. 2(a). There is no significant difference between the two cases. Therefore, the dispersion introduced by the thin gas jet can be neglected.

 figure: Fig. 2

Fig. 2 (a) The interference signal of second-harmonic measured with (blue dots) and without (red squares) gas jet. (b)The modulation of THz intensity versus the relative phase between the two-color laser fields. Red dots are the experiment data and the black line is the fitted curve. The zero point of relative phase is chosen arbitrarily in both figures.

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The relative phase can control the THz intensity finely in the linearly-polarized two-color field. The total laser field is expressed as E(t) = Eω cos(ωt) + E2ω cos(2ωt + ϕ), where the Eω and E2ω are the fundamental and the second-harmonic amplitudes respectively, ϕ is the relative phase composed of two controllable parts ϕd and ϕG, ϕ = ϕdϕG. The dispersion-induced relative phase ϕd is related to the wedge insertion Δ, ϕd(Δ) = 2ϕωϕ2ω = 2ω (nωn2ω)Δ/c, where nω and n2ω are the refractive indices of the fused silica and c is the speed of light in vacuum, the GPS-induced relative phase ϕG is z-dependent along the propagation of two color lasers, ϕG(z) = 2ϕGouy(ω, z) − ϕGouy(2ω, z). We place the gas jet at the focus of two color lasers (ϕG = 0), and record THz waveform varying the relative phase ϕd. The resolution of the relative phase ϕd is 0.04π according to the period of the second harmonic. The modulation of THz intensity is illustrated in Fig. 2(b). The experimental data (red dots) can be well fitted by a cosine function in the form of ITHzAcos2(ϕϕd0), where ITHz is the THz intensity, A is the modulation depth, ϕd0 is the measured optimal phase which maximizes the THz intensity by inserting the optical wedge. At different jet positions z along the laser propagation, ϕd0(z)=ϕ0+ϕG(z), where ϕ0 is the absolute value of the optimal phase which can be calibrated by the intrinsic attochirp of different high-order even harmonics [15, 16].

3. Results and discussion

3.1. GPS in THz generation with two color laser fields

We can establish the mapping between the GPS-induced relative phase ϕG and the jet position, if we calibrate the optimal phase ϕ0 and record the measured optimal phase ϕd0. Scanning the thin gas jet through the focus with a step of 0.5 mm along the propagation direction, we maximize THz intensity varying the relative phase by inserting one of the optical wedges. Figure 3(a) shows the measured THz yield at optimal phase when the gas jet lies in different positions. Since the stronger laser field can ionize gaseous atoms more efficiently and produce larger photocurrent, the THz intensity peaks at the focus and decreases symmetrically in the Rayleigh region as indicated in Fig. 3(a). This solves the difficulty in finding the exact focus in practical experiment. Figure 3(b) presents the relationship between the measured optimal phase ϕd0 and the jet position, which agrees well with the calculated GPS-induced relative phase ϕG. The results show that the change of the measured optimal phases at different gas jet positions depends mainly on the Gouy phase, which indicates that the absolute optimal phase is constant when gas jet moves. So we can use the measured optimal phase ϕd0 to measure the relative phase slippage of two-color laser. It also opens up the possibility of measuring the relative phase of two-color field by using the optimal phase ϕ0.

 figure: Fig. 3

Fig. 3 (a) The THz yield at optimal phase varies with the gas jet position. The red dots is the measured THz intensity and the black line guides the eyes. The fundamental laser intensities at the focus is estimated to be ∼ 1.8 × 1014W/cm2. (b) The dispersion-induced relative phase ϕd varies with the jet position to maximize THz intensity. The red dots is the experimental ϕd at different z-position along the propagation of two color lasers. The black line is the calculated relative phase ϕG induced by the GPS.

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In order to further inspect the influence of other factors on the optimal phase, we fix the jet at the focus (ϕG = 0) and record the dispersion-induced relative phase ϕd under different pump intensities and the ratios of two color lasers. The laser intensity is changed from the minimum, which can deliver detectable THz radiation, to the maximum, which is estimated about 1.8 × 1014W/cm2 by the cutoff of the high-order harmonic generation [29]. It is found that the optimal phases of THz remain approximately constant as shown in Fig. 4(a). The ratios of two color pulses are changed by using BBO crystals with various thicknesses while the laser intensity is maximum. Figure 4(b) shows the optimal phases have little shift while the intensity ratios changed from 0.1% to 25%. The additional phase shift caused by the BBO thickness can be compensated by adjusting the insertion of the wedge, which makes sure the modulation of second-harmonic is the same in every measurement. The zero points in both Figs. 4(a) and 4(b) are measured with the low intensity of two-color laser-filed whose ratio is about 5% to eliminate the effect of plasma and produce measurable THz radiation. It is worth noting that the optimal phase of THz is robust against the laser intensities and the intensity ratios of second-harmonic to fundamental pulses, which agrees well with the soft-collision theory [15,17] under the experimental conditions. Figures 4(a) and 4(b) indicate that the optimal phase of THz generation will be a good tool to calibrate and monitor the relative phase of two-color laser-field.

 figure: Fig. 4

Fig. 4 The optimal phase measured in different fundamental laser intensities (a) and intensity ratios (b). The reference phase (zero point) is chosen that in the low laser intensity.

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3.2. GPS effect for long gas medium

For long gas medium, the measured THz waveform can be considered as a coherent superposition of THz waveform from different slices along the propagation direction. We move the gas jet along the laser propagation direction at fixed ϕd, and record THz waveforms for all z-positions. Figure 5(a) shows the contour of THz waveforms when the jet lies at the different positions along the Rayleigh range with two specific relative phase delays ϕd1 and ϕd2. Since the phase changes by π in the propagation through the focus, virtually all possible relative phase are available moving the thin gas jet. There always exists at least one position where the relative phase is optimal for THz yield. The relative phase ϕd1 is set optimum at the focus in the left of Fig. 5(a). The amplitude of THz electric field peaks at the focus and decreases symmetrically due to the GPS and decreased laser intensity when the gas jet moves away from the focus. It’s not easy to decouple the effect of the Gouy phase shift from the laser intensity variation on the THz yield in the whole focal region. In order to manifest the phase gating effect, we compare THz yield in the same laser intensity but at another relative phase delay ϕd2. The phase-gating can turn off THz radiation at the laser focus completely and the coupling effect between the laser intensity and the GPS reproduces the maximal THz yield in the 1.5 mm as shown in the right of Fig. 5(a).

 figure: Fig. 5

Fig. 5 (a) THz waveforms measured at different jet positions along the propagation of laser beams. The THz intensity at the focus is maximum in the left while minimum in the right, corresponding to different relative phases ϕd1 and ϕd2. (b) The phase dependence of THz generation from the thin jet at the focus (left), from the coherent superposition of different thin jet positions near the focus (middle), and from low-pressure argon in a chamber (right).

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The THz waveform detected by EOS contains not only the amplitude information, but also the phase information. Therefore, it is possible to combine a THz wave by a coherent superposition of THz waves measured at all z-positions with the same ϕd. Figure 5(b) shows that the phase dependence of combined THz (middle) is the same as that measured at the focus (left). The same phase dependence is obtained for the low-pressure gas as shown in the right of Fig. 5(b), since the dispersion of the plasma and neutral atoms can be ignored when the pressure of argon in the chamber is about 10−2 mbar. Our experiment promotes to the intense research on spatiotemporal dynamics of THz generation in gases [4, 5, 21].

We consider the THz waveform from a long gas medium as the coherent superposition of many gas slices of a cylindrical source to understand the phase-dependence of THz emission. In the far field, the length of the THz source is much shorter than the propagation distance and the detected THz electric field E⃗(r⃗, Ω) can be expressed as

E(r,Ω)eikriΩtreiϕ(0)zA(z,Ω)eiΔϕ(z)eikcosθdz,
where A⃗(z, Ω) is the local THz electric field with frequency Ω generated from the gas slice at position z, ϕ(0) is the relative phase of the two-color field at the focus, Δϕ(z) is the relative phase difference between the position z and the focus, k is the wave number of THz, r⃗ is the position of THz detection, and θ is the propagation angle between THz and laser.

In low-pressure gas cell, the laser intensity distribution is symmetric about the focus, which leads to the symmetric amplitude of THz, A⃗(−z, Ω) = A⃗(z, Ω). The phase Δϕ(z) introduced only by GPS is antisymmetric, Δϕ(−z) = −Δϕ(z). According to Eq. (2), THz waveforms obtained with the superposition of symmetric slices before and after the focus will have the same phase as that generated from the focus. Therefore, Fig. 5(b) shows the same phase dependence between THz generated from the long gas medium and the gas jet at the focus.

While increasing the pressure in the chamber, the dispersion of plasma and neutral gasous atoms cannot be neglected any more. The dispersion will break the antisymmetric phase distribution induced by GPS gradually, and the symmetric THz amplitude will also be broken down. In this condition, A⃗(−z, Ω) ≠ A⃗(z, Ω), Δϕ(−z) ≠ −Δϕ(z). The integral in the Eq. (2) cannot carry out to be a real number again. When we fill argon in the chamber with a higher pressure (∼ 10mbar), the measured THz waveforms for various relative phase are shown in the Fig. 6(a). The amplitude of THz radiation cannot be reduced to zero as the black line presented in the Fig. 6(a), even if we adjust the relative phase of two-color field carefully. Figure 6(b) shows the modulation of THz intensity detected by the thermal detector, which is characterized with a noticeable background due to the phase slippage near the focus.

 figure: Fig. 6

Fig. 6 THz waveforms (a) and intensity (b) vary with the relative phase of two-color fields. The phase-gating cannot turn off the THz radiation completely due to the relative phase slippage along the long gas plasma. This phase slippage results in the non-zero amplitude of THz radiation at any relative phase as shown with black line in (a) and noticeable background as shown in (b).

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The GPS also can change the ellipticity of THz generation. As discussed in [11, 30], when either one of the two color pulses is elliptically or circularly polarized, the polarization of THz wave is very close to linear polarization, and the polarization direction of the THz will rotate while varying the relative phase of two color lasers. In order to display the effect of GPS more intuitively, the linearly-polarized fundamental laser is replaced by the circularly polarized, and its second-harmonic is elliptically polarized with an ellipticity of about 5/11. Here, the ellipticity is defined as e = EMinor_axis/EMajor_axis. The THz waveforms are recorded by a polarization-sensitive air-biased-coherent-detection system [31], Fig. 7(a) depicts the rotation of THz polarization generated at the focus when the relative phase is changed by the insertion of one glass wedge. Since the GPS leads to the spatial variation of relative phase in the whole focal region, the direction of linearly polarized THz in the plasma varies with the position. In low pressure, the laser intensity is symmetric and the relative phase is antisymmetric with respect to the focus. The coherent superposition of THz waveforms from different plasma slices produces linearly polarized THz radiation according to Eq. (2). Due to the dispersion of the plasma and neutral atoms in high pressure, the antisymmetric phase distribution of GPS is broken and THz waves are not out-of phase from the symmetric plasma slices before and after the focus. This effect is more remarkable in high pressure. Thus, the elliptically polarized THz wave can be produced from the coherent superposition in high pressure. Figure 7(b) shows the increase of THz ellipticity with gas pressure. This also indicates that precise control of the spatial phase distribution can be a simple tool to manipulate the THz ellipticity.

 figure: Fig. 7

Fig. 7 THz generation driven by the circularly polarized two-color field. (a) The polarization of THz waveforms rotate with the relative phase of two-color fields when the gas jet is placed at the focus. (b) The ellipticity of THz wave increases with the higher gas pressure.

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4. Conclusion

In conclusion, we present the first full and unambiguous investigation on the effect of Gouy phase in air-plasma THz generation. Our results show that the optimal phase of THz is robust enough to measure in situ the value of the relative phase in the phase-sensitive two-color experiments. By means of the THz phase meter, we establish a one-to-one mapping between the Gouy phase slippage and the spatial THz generation in the focus. We find that the phase averaging in air plasma decreases the modulation depth and increases the ellipticity of THz radiation in linearly and circularly polarized two-color field, respectively. These findings contribute to the attempt to characterize the distribution of THz electric field within the plasma filament. We envision that the approach outlined here will serve to characterize the phase variation of more complex beam profile and open up doors for the observation of ultrafast electron dynamics by means of THz generation as well as high-precision attosecond studies.

Acknowledgments

This work is supported by the National Basic Research Program (973 Program) of China (Grant No. 2013CB922203), and the National Natural Science Fund of China (Grant Nos. 11374366, 11474359, 11574396 and 11404400). Z. L. and D. Z. acknowledge support through the National Natural Science Fund of China (Grant No. 61490694).

References and links

1. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25(16), 1210–1212 (2000). [CrossRef]  

2. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993). [CrossRef]   [PubMed]  

3. 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, 245002 (2007). [CrossRef]   [PubMed]  

4. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010). [CrossRef]   [PubMed]  

5. Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012). [CrossRef]   [PubMed]  

6. Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013). [CrossRef]  

7. N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014). [CrossRef]   [PubMed]  

8. P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015). [CrossRef]   [PubMed]  

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

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

11. 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, 023001 (2009). [CrossRef]   [PubMed]  

12. Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015). [CrossRef]   [PubMed]  

13. L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014). [CrossRef]  

14. J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009). [CrossRef]  

15. D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012). [CrossRef]  

16. Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013). [CrossRef]  

17. W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015). [CrossRef]  

18. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010). [CrossRef]  

19. R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007). [CrossRef]   [PubMed]  

20. S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23(5), 385–387 (1998). [CrossRef]  

21. Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012). [CrossRef]   [PubMed]  

22. H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012). [CrossRef]  

23. P. Kuzel, H. Nemec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010). [CrossRef]   [PubMed]  

24. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001). [CrossRef]  

25. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999). [CrossRef]  

26. F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004). [CrossRef]   [PubMed]  

27. N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurents,” Opt. Lett. 35, 3312–3314 (2010). [CrossRef]   [PubMed]  

28. A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991). [CrossRef]  

29. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994). [CrossRef]   [PubMed]  

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

31. Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012). [CrossRef]  

References

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  1. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25(16), 1210–1212 (2000).
    [Crossref]
  2. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
    [Crossref] [PubMed]
  3. 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, 245002 (2007).
    [Crossref] [PubMed]
  4. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
    [Crossref] [PubMed]
  5. Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
    [Crossref] [PubMed]
  6. Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
    [Crossref]
  7. N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
    [Crossref] [PubMed]
  8. P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
    [Crossref] [PubMed]
  9. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605–609 (2008).
    [Crossref]
  10. K. Y. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas 16, 056706 (2009).
    [Crossref]
  11. 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, 023001 (2009).
    [Crossref] [PubMed]
  12. Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
    [Crossref] [PubMed]
  13. L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
    [Crossref]
  14. J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009).
    [Crossref]
  15. D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
    [Crossref]
  16. Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
    [Crossref]
  17. W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
    [Crossref]
  18. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).
    [Crossref]
  19. R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007).
    [Crossref] [PubMed]
  20. S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23(5), 385–387 (1998).
    [Crossref]
  21. Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
    [Crossref] [PubMed]
  22. H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012).
    [Crossref]
  23. P. Kuzel, H. Nemec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010).
    [Crossref] [PubMed]
  24. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001).
    [Crossref]
  25. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
    [Crossref]
  26. F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
    [Crossref] [PubMed]
  27. N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurents,” Opt. Lett. 35, 3312–3314 (2010).
    [Crossref] [PubMed]
  28. A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
    [Crossref]
  29. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
    [Crossref] [PubMed]
  30. H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009).
    [Crossref] [PubMed]
  31. Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
    [Crossref]

2015 (3)

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

2014 (2)

L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
[Crossref]

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

2013 (2)

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

2012 (5)

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

2010 (4)

N. Shivaram, A. Roberts, L. Xu, and A. Sandhu, “In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurents,” Opt. Lett. 35, 3312–3314 (2010).
[Crossref] [PubMed]

P. Kuzel, H. Nemec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18(15), 15338–15348 (2010).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).
[Crossref]

2009 (4)

J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009).
[Crossref]

K. Y. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas 16, 056706 (2009).
[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, 023001 (2009).
[Crossref] [PubMed]

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

2008 (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. Photon. 2, 605–609 (2008).
[Crossref]

2007 (2)

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, 245002 (2007).
[Crossref] [PubMed]

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007).
[Crossref] [PubMed]

2004 (1)

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

2001 (1)

2000 (1)

1999 (1)

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
[Crossref]

1998 (1)

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

1993 (1)

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

1991 (1)

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Alexandrov, L. N.

L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
[Crossref]

Babushkin, I.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Bai, Y.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Balcou, P.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Baltuska, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Barge, V. J.

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007).
[Crossref] [PubMed]

Bergé, L.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Cabrera-Granado, E.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Chen, W.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Chudinov, A. N.

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Cook, D. J.

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Dai, J.

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, 023001 (2009).
[Crossref] [PubMed]

J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009).
[Crossref]

Du, X.

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Elsaesser, T.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Emelin, M. Y.

L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
[Crossref]

Falcone, R. W.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

Feng, S.

Gildenburg, V. B.

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, 245002 (2007).
[Crossref] [PubMed]

Glownia, J. H.

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

Gordon, R. J.

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007).
[Crossref] [PubMed]

Gordon, S.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Hamster, H.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

He, H.

H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012).
[Crossref]

Hellwarth, R. W.

Herrmann, J.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Hochstrasser, R. M.

Huang, Y.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

Husakou, A.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Kadlec, C.

Kadlec, F.

Kapitzky, Y. E.

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Karpowicz, N.

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, 023001 (2009).
[Crossref] [PubMed]

Kim, K. Y.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

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

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

Köhler, C.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Korytin, A. I.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

Kostin, V. A.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

Krausz, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Kuehn, W.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Kurihara, T.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

Kuzel, P.

L’Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Li, C.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Li, R.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Lindenberg, A. M.

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

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Liu, J.

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Liu, P.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Lu, H.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Lü, Z.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

Martínez, P.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Meng, C.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Minami, Y.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

Morgner, U.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Murzanev, A. A.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

Nakajima, M.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

Nemec, H.

Oh, T. I.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

Paulus, G. G.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Reimann, K.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Roberts, A.

Rodriguez, G.

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

Rudd, J. V.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
[Crossref]

Ruffin, A. B.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
[Crossref]

Ryabikin, M. Y.

L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
[Crossref]

Sandhu, A.

Shivaram, N.

Shulginov, A. A.

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Silaev, A. A.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

Skupin, S.

P. Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Song, L.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Stepanov, A. N.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

Suemoto, T.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

Sullivan, A.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

Sun, L.

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

Taylor, A. J.

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

Visser, T. D.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).
[Crossref]

Vvedenskii, N. V.

N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, “Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse,” Phys. Rev. Lett. 112, 055004 (2014).
[Crossref] [PubMed]

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, 245002 (2007).
[Crossref] [PubMed]

Walther, H.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Wang, X.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

Wen, H.

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

Whitaker, J. F.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
[Crossref]

White, W.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725–2728 (1993).
[Crossref] [PubMed]

Winful, H. G.

Woerner, M.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Wolf, E.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).
[Crossref]

Xu, L.

Xu, R.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Xu, Z.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Yamaguchi, K.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

You, Y. S.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

Yuan, J.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Zel’Dovich, B. Y.

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Zeng, Z.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Zhang, D.

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

Zhang, X.-C.

H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012).
[Crossref]

J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009).
[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, 023001 (2009).
[Crossref] [PubMed]

Zhang, Z.

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

Zhao, J.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

Zhao, Z.

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref] [PubMed]

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Zhou, Z.

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

Appl. Phys. Lett. (4)

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[Crossref]

J. Dai and X.-C. Zhang, “Terahertz wave generation from gas plasma using a phase compensator with attosecond phase-control accuracy,” Appl. Phys. Lett. 94, 021117 (2009).
[Crossref]

H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett. 100, 061105 (2012).
[Crossref]

Z. Lü, D. Zhang, C. Meng, L. Sun, Z. Zhou, Z. Zhao, and J. Yuan, “Polarization-sensitive air-biased-coherent-detection for terahertz wave,” Appl. Phys. Lett. 101, 081119 (2012).
[Crossref]

J. Chem. Phys. (1)

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127, 204302 (2007).
[Crossref] [PubMed]

J. Phys. B At. Mol. Opt. Phys. (2)

Z. Lü, D. Zhang, C. Meng, X. Du, Z. Zhou, Y. Huang, Z. Zhao, and J. Yuan, “Attosecond synchronization of terahertz wave and high-harmonics,” J. Phys. B At. Mol. Opt. Phys. 46, 155602 (2013).
[Crossref]

L. N. Alexandrov, M. Y. Emelin, and M. Y. Ryabikin, “Coulomb effects in directional current excitation in the ionization of gas by a two-color laser field,” J. Phys. B At. Mol. Opt. Phys. 47, 204028 (2014).
[Crossref]

Nat. Photon. (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. Photon. 2, 605–609 (2008).
[Crossref]

Opt. Commun. (1)

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Opt. Quant. Electron. (1)

A. N. Chudinov, Y. E. Kapitzky, A. A. Shulginov, and B. Y. Zel’Dovich, “Interferometric phase measurements of average field cube Eω2E2ω*,” Opt. Quant. Electron. 23, 1055–1060 (1991).
[Crossref]

Phys. Plasmas (1)

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

Phys. Rev. A (2)

W. Chen, Y. Huang, C. Meng, J. Liu, Z. Zhou, D. Zhang, J. Yuan, and Z. Zhao, “Theoretical study of terahertz generation from atoms and aligned molecules driven by two-color laser fields,” Phys. Rev. A 92, 033410 (2015).
[Crossref]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (13)

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

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulses,” Phys. Rev. Lett. 83, 3410–3413 (1999).
[Crossref]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[Crossref] [PubMed]

Y. Bai, L. Song, R. Xu, C. Li, P. Liu, Z. Zeng, Z. Zhang, H. Lu, R. Li, and Z. Xu, “Waveform-controlled terahertz radiation from the air filament produced by few-cycle laser pulses,” Phys. Rev. Lett. 108, 255004 (2012).
[Crossref] [PubMed]

D. Zhang, Z. Lü, C. Meng, X. Du, Z. Zhou, Z. Zhao, and J. Yuan, “Synchronizing terahertz wave generation with attosecond bursts,” Phys. Rev. Lett. 109, 243002 (2012).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the experimental setup. DWP: dual-wavelength plate; WGP: wire grid polarizer; SM: spherical mirror; PM: parabolic mirror; PBS: polarizing beam splitter.
Fig. 2
Fig. 2 (a) The interference signal of second-harmonic measured with (blue dots) and without (red squares) gas jet. (b)The modulation of THz intensity versus the relative phase between the two-color laser fields. Red dots are the experiment data and the black line is the fitted curve. The zero point of relative phase is chosen arbitrarily in both figures.
Fig. 3
Fig. 3 (a) The THz yield at optimal phase varies with the gas jet position. The red dots is the measured THz intensity and the black line guides the eyes. The fundamental laser intensities at the focus is estimated to be ∼ 1.8 × 1014W/cm2. (b) The dispersion-induced relative phase ϕd varies with the jet position to maximize THz intensity. The red dots is the experimental ϕd at different z-position along the propagation of two color lasers. The black line is the calculated relative phase ϕG induced by the GPS.
Fig. 4
Fig. 4 The optimal phase measured in different fundamental laser intensities (a) and intensity ratios (b). The reference phase (zero point) is chosen that in the low laser intensity.
Fig. 5
Fig. 5 (a) THz waveforms measured at different jet positions along the propagation of laser beams. The THz intensity at the focus is maximum in the left while minimum in the right, corresponding to different relative phases ϕ d 1 and ϕ d 2. (b) The phase dependence of THz generation from the thin jet at the focus (left), from the coherent superposition of different thin jet positions near the focus (middle), and from low-pressure argon in a chamber (right).
Fig. 6
Fig. 6 THz waveforms (a) and intensity (b) vary with the relative phase of two-color fields. The phase-gating cannot turn off the THz radiation completely due to the relative phase slippage along the long gas plasma. This phase slippage results in the non-zero amplitude of THz radiation at any relative phase as shown with black line in (a) and noticeable background as shown in (b).
Fig. 7
Fig. 7 THz generation driven by the circularly polarized two-color field. (a) The polarization of THz waveforms rotate with the relative phase of two-color fields when the gas jet is placed at the focus. (b) The ellipticity of THz wave increases with the higher gas pressure.

Equations (2)

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ϕ Gouy = arctan ( z λ π w 0 2 ) ,
E ( r , Ω ) e i k r i Ω t r e i ϕ ( 0 ) z A ( z , Ω ) e i Δ ϕ ( z ) e i k cos θ d z ,

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