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Frontiers of Optoelectronics

Front. Optoelectron.    2014, Vol. 7 Issue (2) : 121-155     DOI: 10.1007/s12200-013-0371-5
Investigation of ultra-broadband terahertz time-domain spectroscopy with terahertz wave gas photonics
Xiaofei LU1,Xi-Cheng ZHANG2,*()
1. SunEdison Inc. 501 Pearl Dr. Saint Peters, MO 63376, USA
2. The Institute of Optics, University of Rochester, Rochester, NY 14627-0186, USA
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Recently, air plasma, produced by focusing an intense laser beam to ionize atoms or molecules, has been demonstrated to be a promising source of broadband terahertz waves. However, simultaneous broadband and coherent detection of such broadband terahertz waves is still challenging. Electro-optical sampling and photoconductive antennas are the typical approaches for terahertz wave detection. The bandwidth of these detection methods is limited by the phonon resonance or carrier’s lifetime. Unlike solid-state detectors, gaseous sensors have several unique features, such as no phonon resonance, less dispersion, no Fabry-Perot effect, and a continuous renewable nature. The aim of this article is to review the development of a broadband terahertz time-domain spectrometer, which has both a gaseous emitter and sensor mainly based on author’s recent investigation. This spectrometer features high efficiency, perceptive sensitivity, broad bandwidth, adequate signal-to-noise ratio, sufficient dynamic range, and controllable polarization.

The detection of terahertz waves with ambient air has been realized through a third order nonlinear optical process: detecting the second harmonic photon that is produced by mixing one terahertz photon with two fundamental photons. In this review, a systematic investigation of the mechanism of broadband terahertz wave detection was presented first. The dependence of the detection efficiency on probe pulse energy, bias field strength, gas pressure and third order nonlinear susceptibility of gases were experimentally demonstrated with selected gases. Detailed discussions of phase matching and Gouy phase shift were presented by considering the focused condition of Gaussian beams. Furthermore, the bandwidth dependence on probe pulse duration was also demonstrated. Over 240 times enhancement of dynamic range had been accomplished with n-hexane vapor compared to conventional air sensor. Moreover, with sub-20 fs laser pulses delivered from a hollow fiber pulse compressor, an ultra-broad spectrum covering from 0.3 to 70 THz was also showed.

In addition, a balanced detection scheme using a polarization dependent geometry was developed by author to improve signal-to-noise ratio and dynamic range of conventional terahertz air-biased-coherent-detection (ABCD) systems. Utilizing the tensor property of third order nonlinear susceptibility, second harmonic pulses with two orthogonal polarizations was detected by two separated photomultiplier tubes (PMTs). The differential signal from these two PMTs offers a realistic method to reduce correlated laser fluctuation, which circumvents signal-to-noise ratio and dynamic range of conventional terahertz ABCD systems. A factor of two improvement of signal-to-noise ratio was experimentally demonstrated.

This paper also introduces a unique approach to directly produce a broadband elliptically polarized terahertz wave from laser-induced plasma with a pair of double helix electrodes. The theoretical and experimental results demonstrated that velocity mismatch between excitation laser pulses and generated terahertz waves plays a key role in the properties of the elliptically polarized terahertz waves and confirmed that the far-field terahertz emission pattern is associated with a coherent process. The results give insight into the important influence of propagation effects on terahertz wave polarization control and complete the mechanism of terahertz wave generation from laser-induced plasma.

This review provides a critical understanding of broadband terahertz time-domain spectroscopy (THz-TDS) and introduces further guidance for scientific applications of terahertz wave gas photonics.

Keywords terahertz spectroscopy      terahertz detection      ?broadband      gas sensor     
Corresponding Authors: Xi-Cheng ZHANG   
Issue Date: 25 June 2014
 Cite this article:   
Xiaofei LU,Xi-Cheng ZHANG. Investigation of ultra-broadband terahertz time-domain spectroscopy with terahertz wave gas photonics[J]. Front. Optoelectron., 2014, 7(2): 121-155.
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Fig.1  Schematic of experimental setup. BS: beam splitter. BBO: type-I beta barium borate. PM: parabolic mirror. PMT: photomultiplier tube. HV: high voltage modulator. Terahertz wave was generated through laser-induced plasma in air. An iris with a diameter of 10 mm was placed at a distance about 50 mm after the plasma. A high-resistivity silicon wafer was used to block the residual pump beam. The terahertz beam and probe beam were focused collinearly in the presence of a modulated bias, resulting in a second harmonic signal, which was detected by PMT
Fig.2  Schematic illustration of gas cell. Both the entrance and exit windows were made of quartz, which is relatively transparent to both fundamental and second harmonic beams. The quartz material has low absorption at the frequency below 5 THz. The electrical field was connected through an electrical feed-through at the top of gas cell and the gases were introduced through the bottom of the cell
Fig.3  Measured second harmonic intensity (I2ω) versus the probe pulse energy (Iω) at a bias field of 7.5 kV/cm, and gas pressure of 756 torr with Xe and SF6 gases. Dots are from measurements and dashed lines are quadratic fits. The deviation of the probe energy dependence above 50 μJ for Xe and 70 μJ for SF6 are consistent with the onset of intensity clamping due to plasma formation
Fig.4  Terahertz (a) waveforms and (b) spectra obtained with different probe pulse energy. Electrodes were placed around the center of plasma. Black arrows are the guides for the absorption frequency, which shows a red shift while increasing the probe pulse energy
Fig.5  Measured second harmonic intensity (I2ω) versus DC bias field (EDC) at gas pressure of (a) 100 torr and (b) 756 torr, with a probe pulse energy of 50 μJ. Dots are from measurements and dashed lines are linear fits
Fig.6  Detected second harmonic intensity (I2ω) verses third order nonlinear susceptibility (χ(3)) of gases. Red dots are experimental data and black dashed line is the quadratic fit. Y-axis is normalized with the reference signal taken with 100 torr nitrogen gas at the same experimental condition. Also, all the χ(3) are normalized with that of nitrogen
Fig.7  Pressure dependence of detected second harmonic intensity from (a) xenon; (b) propane and (c) n-butane gas at different focus condition of terahertz beam. Optical probe beam power was set to be 20 mW and bias field strength is about 8 kV/cm. The Rayleigh length of terahertz beam was controlled by an iris in terahertz beam path. Black (red) dots are from measurements without iris (with iris) condition and dashed lines are fit from analytical expression. Fitted Rayleigh lengths are zT = 0.8 mm and zT = 1.5 mm, respectively
Fig.8  2D plot of detected terahertz spectra with Xe versus pressure at different terahertz focus condition. The terahertz Rayleigh lengths without and with iris were estimated to be 0.8 and 1.5 mm, respectively. The different phase match of each frequency component results in a spectral shift toward high frequency. (a) F number= 2.4; (b) F number= 1.8
Fig.9  Pressure dependence of various frequency components with Xe sensor at (a) F number= 1.8 and (b) F number= 2.4. The probe beam power is 20 mW and bias field strength is about 8 kV/cm. Data were normalized with peak value for clarity
Fig.10  Illustration of Gouy phase shift in an ABCD system. zR and zT are the Rayleigh range of optical probe beam and terahertz beam, respectively
Fig.11  Calculated Gouy phase shift corresponding to (a)ω+ω-Ω and (b) ω+ω+Ω process during ABCD. z is the longitudinal position along beams' propagation direction. Zero position is the focus position. Rayleigh ranges of terahertz beam and optical probe beam are 0.8 and 4.8 mm, respectively. Green, red and blue curves represent the phase change of terahertz waves, optical beams and phase difference between the two, respectively
Fig.12  Measured terahertz (a) waveforms and (b) spectra at various electrodes position along z-axis using ABCD
Fig.13  Extracted phase information from measurements together with a theoretical fit. Rayleigh ranges of optical probe beam and terahertz beam are estimated to be 1.5 and 0.8 mm, respectively
Fig.14  Terahertz waveforms and spectra obtained with (a) and (d) 80 fs; (b) and (e) 50 fs ; (c) and (f) sub-20 fs laser pulses
χ0(3)/χ0(3)(N2) [63]-dk/m-1 [67]IP/eV [71]FOM/FOM(N2)
Tab.1  Properties of a few gases suitable for terahertz wave detection
Fig.15  Calculated trend of (a) and (c) dynamic range (DR); (b) and (d) signal-to-noise ratio (SNR) with respect to (a) and (b) probe pulse energy (Iω); (c) and(d) DC field strength (EDC) in ABCD system
Fig.16  Typical signal output and dark current vs. supply voltage (gain voltage) of a PMT (Courtesy Hamamatsu Photonics K.K.)
Fig.17  Comparison of (a) dynamic range (DR) and (b) signal-to-noise ratio (SNR) with respect to the gain of PMT. Red dots are measured experimental data and dashed black curves are the guide for the eye
Fig.18  Comparison of (a) dynamic range (DR) and (b) signal-to-noise ratio (SNR) with respect to bias field strength. Blacked dashed lines are the guides for the eyes
Fig.19  Schematic of balanced ABCD for terahertz waves. WP: Wollaston prism. PMT: photomultiplier tube. The polarization of each beam and the experimental coordinate are shown inside the gray circle
Fig.20  A circuit diagram of current subtractor. Current outputs from two PMTs (P1 and P2) are sent through an analogy device AD 820, which can provide a output proportional to the subtraction between P1 and P2 (Courtesy Dr. Brian Schulkin)
Fig.21  Each component measured in balanced ABCD. Waveforms are offset vertically for clarity
Fig.22  Comparison of measured dynamic ranges (DRs) between (a) conventional ABCD and (b) balanced ABCD. Background fluctuations with a 500 times magnification are shown in gray circles. Waveforms are normalized with peak values. Waveforms are obtained with a lock-in time constant of 100 ms and a total of 9 scans
Fig.23  Comparison of measured signal-to-noise ratio (SNR) between (a) conventional ABCD and (b) balanced ABCD. Terahertz spectra and noise floors are shown in red and black lines, respectively. Signals were obtained with a lock-in time constant of 100 ms and a total of 9 scans
conventional ABCDbalanced ABCD
signal (S)2Iω2ETHzEbias4A2Iω2ETHzEbias
background fluctuation (ETHz=0)2IωδIω(Ebias)20
noise (ETHz0, ?S?IωδIω)*2IωδIω[(ETHz)2+(Ebias)2+2ETHzEbias]8A2IωδIωETHzEbias
signal-to-noise ratioIωETHzEbiasδIω[(ETHz)2+(Ebias)2+2ETHzEbias]Iω2δIω
dynamic rangeETHzEbiasIωδIω
Tab.2  Theoretical comparison of signal-to-noise ratio and dynamic range between conventional ABCD and balanced ABCD
Fig.24  Schematics of hollow fiber pulse compressor used in our experiment. 35 fs second laser pulses was input into a hollow core fiber placed in a neon-filled chamber. The self-phase modulation of intense laser pulses provides a sufficient bandwidth. Output pulses are compressed down to sub-10 fs by three pairs of chirped mirrors
Fig.25  Measured spectra of output pulses from hollow-core fiber pulse compressor with various (a) input pulse energy and (b) neon gas pressure in the chamber
Fig.26  Experimental setup of terahertz ABCD with few-cycle pulses. SM: spherical mirror. PMT: photomultiplier tube. A 60%–40% ultrafast beam splitter was used to separate laser pulses into optical pump pulses and optical probe pulses. The pump pulses were focused with a spherical mirror with 150 mm effective focal length to ionize ambient air. A 1 mm thick silicon wafer was used to block the residue optical beam. The optical probe beam went through a time delay stage and focused by another spherical mirror into the detection region
Fig.27  Comparison of generated terahertz field strength with various BBO thicknesses. Electrical field strength was measured using a 100 μm GaP crystal
Fig.28  Measured (a) waveforms and (b) spectra of ultra-broadband terahertz waves generated with ultra-short pulses with different input pulse energy
Fig.29  Measured (a) waveform and (b) corresponding spectrum in ABCD with short pulses. Pulse duration is estimated to be around 15 fs
Fig.30  Illustration of double helix electrical field applied on plasma region. Laser pulses are focused to ionize air where a pair of double helix electrodes was positioned. The trajectory of electrons follows the direction of external electrical field, resulting in an elliptically polarized terahertz wave in far field. The laboratory coordinate and definition of handedness are shown in the figure
Fig.31  Temporal evolution of electrical field vector of (a) right-handed and (b) left-handed elliptically polarized and (c) linear polarized terahertz pulses. Simulated temporal evolution of electrical field vector of (d) right-handed and (e) left-handed elliptically polarized and (f) linear polarized terahertz pulses. EXP: experimental results. SIM: simulation results
Fig.32  Measured far-field terahertz waves in x (upper) and y (lower) direction at various electrodes position from pairs of (a) right-handed; (b) left-handed helical and (c) linear electrodes. The calculated far-field terahertz waves in x and y direction at various electrodes position from (d) right-handed and (e) left-handed helical and (f) linear electrodes are also shown for comparison. Black curves show the polarization trajectories of far-field terahertz radiation at position z = -20, -10, 0, 10 mm, respectively. EXP: experimental results. SIM: simulation results
Fig.33  Measured temporal evolution of electrical field vector of (a) right-handed and (b) left-handed circular polarized terahertz pulses with a HDPE Fresnel prism. The phase difference and amplitude ratio between x and y component for (c) right-handed and (d) left-handed circular polarized terahertz pulses in frequency domain; (e) phase difference and (f) amplitude ratio of elliptically polarized terahertz pulses generated from double helix electrodes are shown for comparison. EXP: experimental results. SIM: simulation results
1 Ferguson B, Zhang X C. Materials for terahertz science and technology. Nature Materials, 2002, 1(1): 26–33
doi: 10.1038/nmat708 pmid: 12618844
2 Siegel P H. Terahertz technology. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(3): 910–928
doi: 10.1109/22.989974
3 Tonouchi M. Cutting-edge terahertz technology. Nature Photonics, 2007, 1(2): 97–105
doi: 10.1038/nphoton.2007.3
4 Nuss M, Orenstein J. Terahertz time-domain spectroscopy. In: Grüner G, ed. Millimeter and Submillimeter Wave Spectroscopy of Solids. Berlin/Heidelberg: Springer, 1998, 7–50
5 Grischkowsky D, Keiding S, Exter M, Fattinger C. Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. Journal of the Optical Society of America. B, Optical Physics, 1990, 7(10): 2006–2015
doi: 10.1364/JOSAB.7.002006
6 Exter M, Fattinger C, Grischkowsky D. Terahertz time-domain spectroscopy of water vapor. Optics Letters, 1989, 14(20): 1128–1130
doi: 10.1364/OL.14.001128 pmid: 19753077
7 Yeh K L, Hoffmann M C, Hebling J, Nelson K A. Generation of 10 μJ ultrashort terahertz pulses by optical rectification. Applied Physics Letters, 2007, 90(17): 171121
doi: 10.1063/1.2734374
8 You D, Jones R R, Bucksbaum P H, Dykaar D R. Generation of high-power sub-single-cycle 500-fs electromagnetic pulses. Optics Letters, 1993, 18(4): 290–292
doi: 10.1364/OL.18.000290 pmid: 19802113
9 Bartel T, Gaal P, Reimann K, Woerner M, Elsaesser T. Generation of single-cycle THz transients with high electric-field amplitudes. Optics Letters, 2005, 30(20): 2805–2807
doi: 10.1364/OL.30.002805 pmid: 16252781
10 Hirori H, Doi A, Blanchard F, Tanaka K. Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3. Applied Physics Letters, 2011, 98(9): 091106
doi: 10.1063/1.3560062
11 Sell A, Leitenstorfer A, Huber R. Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm. Optics Letters, 2008, 33(23): 2767–2769
doi: 10.1364/OL.33.002767 pmid: 19037420
12 Cao J C. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Physical Review Letters, 2003, 91(23): 237401
doi: 10.1103/PhysRevLett.91.237401 pmid: 14683214
13 Gaal P, Reimann K, Woerner M, Elsaesser T, Hey R, Ploog K H. Nonlinear terahertz response of -type GaAs. Physical Review Letters, 2006, 96(18): 187402
doi: 10.1103/PhysRevLett.96.187402 pmid: 16712394
14 Danielson J R, Lee Y S, Prineas J P, Steiner J T, Kira M, Koch S W. Interaction of strong single-cycle terahertz pulses with semiconductor quantum wells. Physical Review Letters, 2007, 99(23): 237401
doi: 10.1103/PhysRevLett.99.237401 pmid: 18233409
15 Shen Y, Watanabe T, Arena D A, Kao C C, Murphy J B, Tsang T Y, Wang X J, Carr G L. Nonlinear cross-phase modulation with intense single-cycle terahertz pulses. Physical Review Letters, 2007, 99(4): 043901
doi: 10.1103/PhysRevLett.99.043901 pmid: 17678365
16 Su F H, Blanchard F, Sharma G, Razzari L, Ayesheshim A, Cocker T L, Titova L V, Ozaki T, Kieffer J C, Morandotti R, Reid M, Hegmann F A. Terahertz pulse induced intervalley scattering in photoexcited GaAs. Optics Express, 2009, 17(12): 9620–9629
doi: 10.1364/OE.17.009620 pmid: 19506611
17 Jewariya M, Nagai M, Tanaka K. Ladder climbing on the anharmonic intermolecular potential in an amino acid microcrystal via an intense monocycle terahertz pulse. Physical Review Letters, 2010, 105(20): 203003
doi: 10.1103/PhysRevLett.105.203003 pmid: 21231227
18 Kuehn W, Gaal P, Reimann K, Woerner M, Elsaesser T, Hey R. Coherent ballistic motion of electrons in a periodic potential. Physical Review Letters, 2010, 104(14): 146602
doi: 10.1103/PhysRevLett.104.146602 pmid: 20481951
19 Kampfrath T, Sell A, Klatt G, Pashkin A, Mahrlein S, Dekorsy T, Wolf M, Fiebig M, Leitenstorfer A, Huber R. Coherent terahertz control of antiferromagnetic spin waves. Nature Photonics, 2011, 5(1): 31–34
doi: 10.1038/nphoton.2010.259
20 Lein? S, Kampfrath T, Volkmann K, Wolf M, Steiner J T, Kira M, Koch S W, Leitenstorfer A, Huber R. Terahertz coherent control of optically dark paraexcitons in Cu2O. Physical Review Letters, 2008, 101(24): 246401
doi: 10.1103/PhysRevLett.101.246401 pmid: 19113639
21 Huber R, Tauser F, Brodschelm A, Bichler M, Abstreiter G, Leitenstorfer A. How many-particle interactions develop after ultrafast excitation of an electron-hole plasma. Nature, 2001, 414(6861): 286–289
doi: 10.1038/35104522 pmid: 11713523
22 Kaindl R A, Carnahan M A, H?gele D, L?venich R, Chemla D S. Ultrafast terahertz probes of transient conducting and insulating phases in an electron-hole gas. Nature, 2003, 423(6941): 734–738
doi: 10.1038/nature01676 pmid: 12802330
23 Günter G, Anappara A A, Hees J, Sell A, Biasiol G, Sorba L, De Liberato S, Ciuti C, Tredicucci A, Leitenstorfer A, Huber R. Sub-cycle switch-on of ultrastrong light-matter interaction. Nature, 2009, 458(7235): 178–181
doi: 10.1038/nature07838 pmid: 19279631
24 Hu B B, Zhang X C, Auston D H, Smith P R. Free-space radiation from electrooptic crystals. Applied Physics Letters, 1990, 56(6): 506–508
doi: 10.1063/1.103299
25 Han P Y, Zhang X C. Free-space coherent broadband terahertz time-domain spectroscopy. Measurement Science & Technology, 2001, 12(11): 1747–1756
doi: 10.1088/0957-0233/12/11/301
26 Huber R, Brodschelm A, Tauser F, Leitenstorfer A. Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz. Applied Physics Letters, 2000, 76(22): 3191–3193
doi: 10.1063/1.126625
27 Kübler C, Huber R, Tubel S, Leitenstorfer A. Ultrabroadband detection of multi-terahertz field transients with GaSe electro-optic sensors: approaching the near infrared. Applied Physics Letters, 2004, 85(16): 3360–3362
doi: 10.1063/1.1808232
28 Auston D H. Picosecond optoelectronic switching and gating in silicon. Applied Physics Letters, 1975, 26(3): 101–103 doi:10.1063/1.88079
29 Mourou G, Stancampiano C V, Antonetti A, Orszag A. Picosecond microwave pulses generated with a subpicosecond laser-driven semiconductor switch. Applied Physics Letters, 1981, 39(4): 295–296
doi: 10.1063/1.92719
30 Fattinger C, Grischkowsky D. Point source terahertz optics. Applied Physics Letters, 1988, 53(16): 1480–1482
doi: 10.1063/1.99971
31 Kr?kel D, Grischkowsky D, Ketchen M B. Subpicosecond electrical pulse generation using photoconductive switches with long carrier lifetimes. Applied Physics Letters, 1989, 54(11): 1046–1047
doi: 10.1063/1.100792
32 Shen Y C, Upadhya P C, Linfield E H, Beere H E, Davies A G. Ultrabroadband terahertz radiation from low-temperature-grown GaAs photoconductive emitters. Applied Physics Letters, 2003, 83(15): 3117–3119
doi: 10.1063/1.1619223
33 Fill E, Borgstr?m S, Larsson J, Starczewski T, Wahlstr?m C G, Svanberg S. XUV spectra of optical-field-ionized plasmas. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1995, 51(6): 6016–6027
doi: 10.1103/PhysRevE.51.6016 pmid: 9963341
34 Hamster H, Sullivan A, Gordon S, White W, Falcone R W. Subpicosecond, electromagnetic pulses from intense laser-plasma interaction. Physical Review Letters, 1993, 71(17): 2725–2728
doi: 10.1103/PhysRevLett.71.2725 pmid: 10054760
35 Forestier B, Houard A, Durand M, Andre Y B, Prade B, Dauvignac J Y, Perret F, Pichot C, Pellet M, Mysyrowicz A. Radiofrequency conical emission from femtosecond filaments in air. Applied Physics Letters, 2010, 96(14): 141111
doi: 10.1063/1.3378266
36 Cook D J, Hochstrasser R M. Intense terahertz pulses by four-wave rectification in air. Optics Letters, 2000, 25(16): 1210–1212
doi: 10.1364/OL.25.001210 pmid: 18066171
37 Thomson M D, Blank V, Roskos H G. Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields. Optics Express, 2010, 18(22): 23173–23182
doi: 10.1364/OE.18.023173 pmid: 21164658
38 Wu Q, Zhang X C. Free-space electro-optics sampling of mid-infrared pulses. Applied Physics Letters, 1997, 71(10): 1285–1286
doi: 10.1063/1.119873
39 Jepsen P U, Winnewisser C, Schall M, Schyja V, Keiding S R, Helm H. Detection of THz pulses by phase retardation in lithium tantalate. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1996, 53(4): R3052–R3054
doi: 10.1103/PhysRevE.53.R3052 pmid: 9964764
40 Nahata A, Auston D H, Heinz T F, Wu C. Coherent detection of freely propagating terahertz radiation by electro-optic sampling. Applied Physics Letters, 1996, 68(2): 150–152
doi: 10.1063/1.116130
41 Vagelatos N, Wehe D, King J S. Phonon dispersion and phonon densities of states for ZnS and ZnTe. Journal of Chemical Physics, 1974, 60(9): 3613–3618
doi: 10.1063/1.1681581
42 Kleinman D A, Spitzer W G. Infrared lattice absorption of GaP. Physical Review, 1960, 118(1): 110–117
doi: 10.1103/PhysRev.118.110
43 Gupta S, Frankel M Y, Valdmanis J A, Whitaker J F, Mourou G A, Smith F W, Calawa A R. Subpicosecond carrier lifetime in GaAs grown by molecular beam epitaxy at low temperatures. Applied Physics Letters, 1991, 59(25): 3276–3278
doi: 10.1063/1.105729
44 Prabhu S S, Ralph S E, Melloch M R, Harmon E S. Carrier dynamics of low-temperature-grown GaAs observed via THz spectroscopy. Applied Physics Letters, 1997, 70(18): 2419–2421
doi: 10.1063/1.118890
45 Kono S, Tani M, Sakai K. Coherent detection of mid-infrared radiation up to 60 THz with an LT-GaAs photoconductive antenna. Iee P-Optoelectron, 2002, 149(3): 105–109
doi: 10.1049/ip-opt:20020262
46 Liu J, Zhang X C. Terahertz-radiation-enhanced emission of fluorescence from gas plasma. Physical Review Letters, 2009, 103(23): 235002
doi: 10.1103/PhysRevLett.103.235002 pmid: 20366153
47 Liu J, Zhang X C. Plasma characterization using terahertz-wave-enhanced fluorescence. Applied Physics Letters, 2010, 96(4): 041505
doi: 10.1063/1.3291676
48 Liu J, Dai J, Chin S L, Zhang X C. Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases. Nature Photonics, 2010, 4(9): 627–631
doi: 10.1038/nphoton.2010.165
49 Clough B, Liu J, Zhang X C. Laser-induced photoacoustics influenced by single-cycle terahertz radiation. Optics Letters, 2010, 35(21): 3544–3546
doi: 10.1364/OL.35.003544 pmid: 21042344
50 Liu J, Clough B, Zhang X C. Enhancement of photoacoustic emission through terahertz-field-driven electron motions. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2010, 82(6 Pt 2): 066602
doi: 10.1103/PhysRevE.82.066602 pmid: 21230746
51 Dai J, Xie X, Zhang X C. Detection of broadband terahertz waves with a laser-induced plasma in gases. Physical Review Letters, 2006, 97(10): 103903
doi: 10.1103/PhysRevLett.97.103903 pmid: 17025819
52 Karpowicz N, Dai J, Lu X, Chen Y, Yamaguchi M, Zhao H, Zhang X C, Zhang L, Zhang C, Price-Gallagher M, Fletcher C, Mamer O, Lesimple A, Johnson K. Coherent heterodyne time-domain spectrometry covering the entire “terahertz gap”. Applied Physics Letters, 2008, 92(1): 011131
doi: 10.1063/1.2828709
53 Nahata A, Heinz T F. Detection of freely propagating terahertz radiation by use of optical second-harmonic generation. Optics Letters, 1998, 23(1): 67–69
doi: 10.1364/OL.23.000067 pmid: 18084414
54 Cook D J, Chen J X, Morlino E A, Hochstrasser R M. Terahertz-field-induced second-harmonic generation measurements of liquid dynamics. Chemical Physics Letters, 1999, 309(3–4): 221–228
doi: 10.1016/S0009-2614(99)00668-5
55 Lu X, Karpowicz N, Zhang X C. Broadband terahertz detection with selected gases. Journal of the Optical Society of America. B, Optical Physics, 2009, 26(9): A66–A73
doi: 10.1364/JOSAB.26.000A66
56 Lu X, Zhang X C.Terahertz wave gas photonics: sensing with gases. Journal of Infrared, Millimeter and Terahertz Waves, 2011, 32(5): 562–569
57 Lu X, Karpowicz N, Chen Y, Zhang X C. Systematic study of broadband terahertz gas sensor. Applied Physics Letters, 2008, 93(26): 261106
doi: 10.1063/1.3056119
58 Kleinman D A, Ashkin A, Boyd G D. Second-harmonic generation of light by focused laser beams. Physical Review, 1966, 145(1): 338
59 Ward J F, New G H C. Optical third harmonic generation in gases by a focused laser beam. Physical Review, 1969, 185(1): 57
60 Karpowics N. Physics and utilization of terahertz gas photonics. In: Physics. Rensselaer Polytechnic Institute, Troy, NY, 2009, 124
61 Finn R S, Ward J F. DC-induced optical second-harmonic generation in the inert gases. Physical Review Letters, 1971, 26: 285–289
62 Becker A, Akozbek N, Vijayalakshmi K, Oral E, Bowden C M, Chin S L. Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas. Applied Physics. B, Lasers and Optics, 2001, 73(3): 287–290
doi: 10.1007/s003400100637
63 Shelton D P. Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm. Physical Review A, 1990, 42(5): 2578–2592 PMID:9904326
doi: 10.1103/PhysRevA.42.2578
64 Boyd R W. Nonlinear Optics. Burlington, MA: Academic Press, 2008
65 Hermann J P, Ducuing J. Third-order polarizabilities of long-chain molecules. Journal of Applied Physics, 1974, 45(11): 5100–5102
doi: 10.1063/1.1663197
66 Rustagi K C, Ducuing J. Third-order optical polarizability of conjugated organic-molecules. Optics Communications, 1974, 10(3): 258–261
doi: 10.1016/0030-4018(74)90153-9
67 Korff S, Breit G. Optical dispersion. Reviews of Modern Physics, 1932, 4(3): 471–503
doi: 10.1103/RevModPhys.4.471
68 Gouy L G. Sur la propagation anomale des ondes. Compt. Rendue Acad. Sci. Paris, 1890, 111: 33
69 Gouy L G. Sur une propriete nouvelle des ondes lumineuses. C. R. Acad. Sci. Paris, 1890, 110: 1251
70 Ruffin A B, Rudd J V, Whitaker J F, Feng S, Winful H G. Direct observation of the Gouy phase shift with single-cycle terahertz pulses. Physical Review Letters, 1999, 83(17): 3410–3413
doi: 10.1103/PhysRevLett.83.3410
71 Lide D R, ed. CRC Handbook of Chemistry and Physics. 86th ed. Boca Raton: CRC-Press, 2005
72 Wu Q, Zhang X C. Free-space electro-optics sampling of mid-infrared pulses. Applied Physics Letters, 1997, 71(10): 1285–1286
doi: 10.1063/1.119873
73 Naftaly M, Dudley R. Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers. Optics Letters, 2009, 34(8): 1213–1215
doi: 10.1364/OL.34.001213 pmid: 19370121
74 Bigio I J, Ward J F. Measurement of the hyperpolarizability ratio χyyyy(-2ω; 0, ω, ω)/χyyxx(-2ω; 0, ω, ω) for the inert gases. Physical Review A, 1974, 9(1): 35–39
doi: 10.1103/PhysRevA.9.35
75 Ward J F, Bigio I J. Molecular second- and third-order polarizabilities from measurements of second-harmonic generation in gases. Physical Review A, 1975, 11(1): 60–66
doi: 10.1103/PhysRevA.11.60
76 Ward J F, Miller C K. Measurements of nonlinear optical polarizabilities for twelve small molecules. Physical Review A, 1979, 19(2): 826–833
doi: 10.1103/PhysRevA.19.826
77 Xie X, Dai J, Zhang X C. Coherent control of THz wave generation in ambient air. Physical Review Letters, 2006, 96(7): 075005
doi: 10.1103/PhysRevLett.96.075005 pmid: 16606102
78 Kim K Y, Glownia J H, Taylor A J, Rodriguez G. Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields. Optics Express, 2007, 15(8): 4577–4584
doi: 10.1364/OE.15.004577 pmid: 19532704
79 Kim K Y, Taylor A J, Glownia J H, Rodriguez G. Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions. Nature Photonics, 2008, 2(10): 605–609
doi: 10.1038/nphoton.2008.153
80 Karpowicz N, Zhang X C. Coherent terahertz echo of tunnel ionization in gases. Physical Review Letters, 2009, 102(9): 093001
doi: 10.1103/PhysRevLett.102.093001 pmid: 19392516
81 Silaev A A, Vvedenskii N V. Residual-current excitation in plasmas produced by few-cycle laser pulses. Physical Review Letters, 2009, 102(11): 115005
doi: 10.1103/PhysRevLett.102.115005 pmid: 19392210
82 Kre? M, L?ffler T, Thomson M D, D?rner R, Gimpel H, Zrost K, Ergler T, Moshammer R, Morgner U, Ullrich J, Roskos H G. Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy. Nature Physics, 2006, 2(5): 327–331
doi: 10.1038/nphys286
83 Jones D J, Diddams S A, Ranka J K, Stentz A, Windeler R S, Hall J L, Cundiff S T. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science, 2000, 288(5466): 635–639
doi: 10.1126/science.288.5466.635 pmid: 10784441
84 Paulus G G, Grasbon F, Walther H, Villoresi P, Nisoli M, Stagira S, Priori E, De Silvestri S. Absolute-phase phenomena in photoionization with few-cycle laser pulses. Nature, 2001, 414(6860): 182–184
doi: 10.1038/35102520 pmid: 11700551
85 Ferrari F, Calegari F, Lucchini M, Vozzi C, Stagira S, Sansone G, Nisoli M. High-energy isolated attosecond pulses generated by above-saturation few-cycle fields. Nature Photonics, 2010, 4(12): 875–879
doi: 10.1038/nphoton.2010.250
86 Paul P M, Toma E S, Breger P, Mullot G, Augé F, Balcou P, Muller H G, Agostini P. Observation of a train of attosecond pulses from high harmonic generation. Science, 2001, 292(5522): 1689–1692
doi: 10.1126/science.1059413 pmid: 11387467
87 Strickland D, Mourou G. Compression of amplified chirped optical pulses. Optics Communications, 1985, 56(3): 219–221
doi: 10.1016/0030-4018(85)90120-8
88 Nisoli M, De Silvestri S, Svelto O. Generation of high energy 10 fs pulses by a new pulse compression technique. Applied Physics Letters, 1996, 68(20): 2793–2795
doi: 10.1063/1.116609
89 Nisoli M, De Silvestri S, Svelto O, Szip?cs R, Ferencz K, Spielmann C, Sartania S, Krausz F. Compression of high-energy laser pulses below 5 fs. Optics Letters, 1997, 22(8): 522–524
doi: 10.1364/OL.22.000522 pmid: 18183254
90 Matsubara E, Yamane K, Sekikawa T, Yamashita M. Generation of 2.6 fs optical pulses using induced-phase modulation in a gas-filled hollow fiber. Journal of the Optical Society of America. B, Optical Physics, 2007, 24(4): 985–989
doi: 10.1364/JOSAB.24.000985
91 Hauri C P, Kornelis W, Helbing F W, Heinrich A, Couairon A, Mysyrowicz A, Biegert J, Keller U. Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation. Applied Physics. B, Lasers and Optics, 2004, 79(6): 673–677
doi: 10.1007/s00340-004-1650-z
92 Couairon A, Franco M, Mysyrowicz A, Biegert J, Keller U. Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient. Optics Letters, 2005, 30(19): 2657–2659
doi: 10.1364/OL.30.002657 pmid: 16208932
93 Kane D J, Trebino R. Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating. Optics Letters, 1993, 18(10): 823–825
doi: 10.1364/OL.18.000823 pmid: 19802285
94 Johnson F A. Lattice absorption bands in silicon. Proceedings of the Physical Society, London, 1959, 73(2): 265–272
doi: 10.1088/0370-1328/73/2/315
95 Shan J, Dadap J I, Heinz T F. Circularly polarized light in the single-cycle limit: The nature of highly polychromatic radiation of defined polarization. Optics Express, 2009, 17(9): 7431–7439
doi: 10.1364/OE.17.007431 pmid: 19399121
96 L?ffler T, Jacob F, Roskos H G. Generation of terahertz pulses by photoionization of electrically biased air. Applied Physics Letters, 2000, 77(3): 453–455
doi: 10.1063/1.127007
97 Roskos H G, Thomson M D, Kre? M, L?ffler T. Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications. Laser Photonics Rev, 2007, 1(4): 349–368
doi: 10.1002/lpor.200710025
98 Houard A, Liu Y, Prade B, Tikhonchuk V T, Mysyrowicz A. Strong enhancement of terahertz radiation from laser filaments in air by a static electric field. Physical Review Letters, 2008, 100(25): 255006
doi: 10.1103/PhysRevLett.100.255006 pmid: 18643672
99 Blanchard F, Sharma G, Ropagnol X, Razzari L, Morandotti R, Ozaki T. Improved terahertz two-color plasma sources pumped by high intensity laser beam. Optics Express, 2009, 17(8): 6044–6052
doi: 10.1364/OE.17.006044 pmid: 19365426
100 Babushkin I, Kuehn W, K?hler C, Skupin S, Bergé L, Reimann K, Woerner M, Herrmann J, Elsaesser T. Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases. Physical Review Letters, 2010, 105(5): 053903
doi: 10.1103/PhysRevLett.105.053903 pmid: 20867920
101 Liu Y, Houard A, Prade B, Mysyrowicz A, Diaw A, Tikhonchuk V T. Amplification of transition-Cherenkov terahertz radiation of femtosecond filament in air. Applied Physics Letters, 2008, 93(5): 051108
doi: 10.1063/1.2965612
102 Chen Y P, Wang T J, Marceau C, Théberge F, Chateauneuf M, Dubois J, Kosareva O, Chin S L. Characterization of terahertz emission from a dc-biased filament in air. Applied Physics Letters, 2009, 95: 101101
doi: 10.1063/1.3224944
103 Dai J, Karpowicz N, Zhang X C. Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma. Physical Review Letters, 2009, 103(2): 023001
doi: 10.1103/PhysRevLett.103.023001 pmid: 19659200
104 Wen H D, Lindenberg A M. Coherent terahertz polarization control through manipulation of electron trajectories. Physical Review Letters, 2009, 103(2): 023902
doi: 10.1103/PhysRevLett.103.023902 pmid: 19659205
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