Abstract

An analysis of the polarization of terahertz (THz) radiation from a laser-induced plasma source is presented. THz emission is achieved by mixing a laser pulse with its second harmonic after focusing through a β-BaB2O4 (β-BBO) crystal. Numerical calculations, based on the nonlinear four-wave mixing model and the microscopic polarization model, are compared with experimental results. The main focus lies on the study of the dependence of THz polarization on the polarization and relative phase of the incident fundamental and second-harmonic pulses. We show that the modulation of the fundamental pulse by the BBO crystal has to be taken into account in order to describe experimental observations. By including the finite extension of the plasma and considering cross- and self-phase modulation of the two-color pump pulse, we are able to explain the observed ellipticity of the THz pulse as well as the orientation of the polarization axis.

© 2009 Optical Society of America

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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]

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” Phys. Rev. Lett. 102, 115005 (2009).
[CrossRef] [PubMed]

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

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

2008 (7)

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[CrossRef]

H.-C. Wu, J. Meyer-ter-Vehn, and Z.-M. Sheng, “Phase-sensitive terahertz emission from gas targets irradiated by few-cycle laser pulses,” New J. Phys. 10, 043001 (2008).
[CrossRef]

P. Bejot, Y. Petit, L. Bonacina, J. Kasparian, M. Moret, and J.-P. Wolf, “Ultrafast gaseous 'half-wave plate',” Opt. Express 16, 7564-7570 (2008).
[CrossRef] [PubMed]

A. Houard, Y. Liu, B. Prade, and A. Mysyrowicz, “Polarization analysis of terahertz radiation generated by four-wave mixing in air,” Opt. Lett. 33, 1195-1197 (2008).
[CrossRef] [PubMed]

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

2007 (6)

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

C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47-189 (2007).
[CrossRef]

M. D. Thomson, M. Kress, T. Loeffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349-368 (2007).
[CrossRef]

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]

Y.-H. Chen, S. Varma, I. Alexeev, and H. M. Milchberg, “Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry,” Opt. Express 15, 7458-7467 (2007).
[CrossRef] [PubMed]

2006 (4)

H. Zhong, N. Karpowicz, and X.-C. Zhang, “Terahertz emission profile from laser-induced air plasma,” Appl. Phys. Lett. 88, 261103 (2006).
[CrossRef]

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

2005 (4)

T. Bartel, P. Gaal, K. Raimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805-2807 (2005).
[CrossRef] [PubMed]

A. Dreyhaupt, S. Winnerl, T. Dekorsky, and M. Helm, “High-intensity terahertz radiation from microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

T. Löffler, T. Hahn, M. Thomson, F. Jacob, and H. G. Roskos, “Large-area electro-optic ZnTe terahertz emitters,” Opt. Express 13, 5353-5362 (2005).
[CrossRef] [PubMed]

A. M. Bystrov, N. V. Vvedenskii, and V. B. Gildenburg, “Generation of terahertz radiation upon the optical breakdown of a gas,” JETP Lett. 82, 753-757 (2005).
[CrossRef]

2004 (4)

S. V. Golubev, E. V. Suvorov, and A. G. Shalashov, “On the possibility of terahertz wave generation upon dense gas optical breakdown,” JETP Lett. 79, 361-364 (2004).
[CrossRef]

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quantum Electron. 40, 175-182 (2004).
[CrossRef]

J. Faure, J. Van Tilborg, R. A. Kaindl, and W. P. Leemans, “Modelling laser-based table-top THz sources: optical rectification, propagation and electro-optic sampling,” Opt. Quantum Electron. 36, 681-697 (2004).
[CrossRef]

M. Kress, T. Loeffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett. 29, 1120-1122 (2004).
[CrossRef] [PubMed]

2001 (1)

2000 (4)

A. Gürtler, C. Winnewisser, H. Helm, and P. U. Jepsen, “Terahertz pulse propagation in the near field and the far field,” J. Opt. Soc. Am. A 17, 74-83 (2000).
[CrossRef]

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

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

1999 (2)

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

1998 (1)

R. Kersting, J. N. Heyman, G. Strasser, and K. Unterrainer, “Coherent plasmons in n-doped GaAs,” Phys. Rev. B 58, 4553-4559 (1998).
[CrossRef]

1997 (1)

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, “Few-cycle thz emission from cold plasma oscillations,” Phys. Rev. Lett. 79, 3038-3041 (1997).
[CrossRef]

1995 (2)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73-75 (1995).
[CrossRef] [PubMed]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

1994 (1)

H. Hamster, A. Sullivan, S. Gordon, and R. W. Falcone, “Short-pulse terahertz radiation from high-intensity-laser-produced plasmas,” Phys. Rev. E 49, 671-677 (1994).
[CrossRef]

1993 (3)

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]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, “Generation of high-power sub-single-cycle 500-fs electromagnetic pulses,” Opt. Lett. 18, 290-292 (1993).
[CrossRef] [PubMed]

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

1992 (1)

P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, “Computational modeling of femtosecond optical solitons from Maxwell's equations,” IEEE J. Quantum Electron. 28, 2416-2422 (1992).
[CrossRef]

1991 (1)

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25-27 (1991).
[CrossRef]

1990 (1)

D. P. Shelton, “Nonlinear-optical susceptibilities of gases at 1064 and 1319 nm,” Phys. Rev. A 42, 2578-2592 (1990).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. QE-22, 1013-1014 (1986).
[CrossRef]

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377-382 (1981).
[CrossRef]

1977 (1)

B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. U.S.A. 74, 1765-1766 (1977).
[CrossRef] [PubMed]

1972 (1)

1966 (2)

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

1962 (1)

L. S. Frost and A. V. Phelps, “Rotational excitation and momentum transfer cross sections for electrons in H2 and N2 from transport coefficients,” Phys. Rev. 127, 1621-1633 (1962).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Alexeev, I.

Auston, D. H.

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25-27 (1991).
[CrossRef]

Bakker, H. J.

Bartel, T.

Becker, A.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Bejot, P.

Blanchard, F.

Bonacina, L.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Braun, A.

Bucksbaum, P. H.

Bystrov, A. M.

A. M. Bystrov, N. V. Vvedenskii, and V. B. Gildenburg, “Generation of terahertz radiation upon the optical breakdown of a gas,” JETP Lett. 82, 753-757 (2005).
[CrossRef]

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Chang, R. S. F.

Châteauneuf, M.

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

Chen, M.

M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
[CrossRef]

Chen, Y.

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Chen, Y.-H.

Chien, C.-Y.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Chin, S. L.

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

Clement, T. S.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Comtois, D.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Cook, D. J.

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

Couairon, A.

C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47-189 (2007).
[CrossRef]

Dai, J.

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]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

D'Amico, C.

C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

Daranciang, D.

H. Wen, D. Daranciang, H. Navirian, and A. M. Lindenberg, “Nonlinear THz interactions with matter: application to semiconductors and ferroelectrics,” presented at the International Workshop on Optical Terahertz Science and Technology (OTST 2009), Santa Barbara, California, March 7-11, 2009, paper SuD4.

Darrow, J. T.

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25-27 (1991).
[CrossRef]

Dekorsky, T.

A. Dreyhaupt, S. Winnerl, T. Dekorsky, and M. Helm, “High-intensity terahertz radiation from microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Desparois, A.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Djeu, N.

Dörner, R.

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
[CrossRef]

Dreyhaupt, A.

A. Dreyhaupt, S. Winnerl, T. Dekorsky, and M. Helm, “High-intensity terahertz radiation from microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Du, D.

Dubois, J.

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

Durand, M.

Y. Liu, A. Houard, M. Durand, B. Prade, and A. Mysyrowicz, “Observation of Maker fringes in the terahertz radiation generated by 2-color laser field inside a long femtosecond filament,” presented at the International Workshop on Optical Terahertz Science and Technology (OTST 2009), Santa Barbara, California, March 7-11, 2009, paper SuE97.

Dykaar, D. R.

Eden, S.

Elsaesser, T.

Engquist, B.

B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. U.S.A. 74, 1765-1766 (1977).
[CrossRef] [PubMed]

Ergler, T.

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
[CrossRef]

Falcone, R. W.

H. Hamster, A. Sullivan, S. Gordon, and R. W. Falcone, “Short-pulse terahertz radiation from high-intensity-laser-produced plasmas,” Phys. Rev. E 49, 671-677 (1994).
[CrossRef]

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]

Faure, J.

J. Faure, J. Van Tilborg, R. A. Kaindl, and W. P. Leemans, “Modelling laser-based table-top THz sources: optical rectification, propagation and electro-optic sampling,” Opt. Quantum Electron. 36, 681-697 (2004).
[CrossRef]

Fay, A. T.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1997).

Franco, M.

C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

Freude, W.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quantum Electron. 40, 175-182 (2004).
[CrossRef]

Frost, L. S.

L. S. Frost and A. V. Phelps, “Rotational excitation and momentum transfer cross sections for electrons in H2 and N2 from transport coefficients,” Phys. Rev. 127, 1621-1633 (1962).
[CrossRef]

Fujii, M.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media,” IEEE J. Quantum Electron. 40, 175-182 (2004).
[CrossRef]

Gaal, P.

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]

A. M. Bystrov, N. V. Vvedenskii, and V. B. Gildenburg, “Generation of terahertz radiation upon the optical breakdown of a gas,” JETP Lett. 82, 753-757 (2005).
[CrossRef]

Gimpel, H.

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
[CrossRef]

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. Photonics 2, 605-609 (2008).
[CrossRef]

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

Golubev, S. V.

S. V. Golubev, E. V. Suvorov, and A. G. Shalashov, “On the possibility of terahertz wave generation upon dense gas optical breakdown,” JETP Lett. 79, 361-364 (2004).
[CrossRef]

Goorjian, P. M.

P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, “Computational modeling of femtosecond optical solitons from Maxwell's equations,” IEEE J. Quantum Electron. 28, 2416-2422 (1992).
[CrossRef]

Gordon, S.

H. Hamster, A. Sullivan, S. Gordon, and R. W. Falcone, “Short-pulse terahertz radiation from high-intensity-laser-produced plasmas,” Phys. Rev. E 49, 671-677 (1994).
[CrossRef]

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]

Gornik, E.

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, “Few-cycle thz emission from cold plasma oscillations,” Phys. Rev. Lett. 79, 3038-3041 (1997).
[CrossRef]

Gürtler, A.

Hagness, S. C.

P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, “Computational modeling of femtosecond optical solitons from Maxwell's equations,” IEEE J. Quantum Electron. 28, 2416-2422 (1992).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Hahn, T.

Hamster, H.

H. Hamster, A. Sullivan, S. Gordon, and R. W. Falcone, “Short-pulse terahertz radiation from high-intensity-laser-produced plasmas,” Phys. Rev. E 49, 671-677 (1994).
[CrossRef]

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]

Helm, H.

Helm, M.

A. Dreyhaupt, S. Winnerl, T. Dekorsky, and M. Helm, “High-intensity terahertz radiation from microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Heyman, J. N.

R. Kersting, J. N. Heyman, G. Strasser, and K. Unterrainer, “Coherent plasmons in n-doped GaAs,” Phys. Rev. B 58, 4553-4559 (1998).
[CrossRef]

Hochstrasser, R. M.

Houard, A.

A. Houard, Y. Liu, B. Prade, and A. Mysyrowicz, “Polarization analysis of terahertz radiation generated by four-wave mixing in air,” Opt. Lett. 33, 1195-1197 (2008).
[CrossRef] [PubMed]

C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

Y. Liu, A. Houard, M. Durand, B. Prade, and A. Mysyrowicz, “Observation of Maker fringes in the terahertz radiation generated by 2-color laser field inside a long femtosecond filament,” presented at the International Workshop on Optical Terahertz Science and Technology (OTST 2009), Santa Barbara, California, March 7-11, 2009, paper SuE97.

Jackson, J. D.

J. D. Jackson, Klassische Elektrodynamik, 2nd ed. (Walter de Gruyter, 1983).

Jacob, F.

Jepsen, P. U.

Jiang, Z.

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Johnston, T. W.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Jones, R. R.

Joseph, R. M.

P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, “Computational modeling of femtosecond optical solitons from Maxwell's equations,” IEEE J. Quantum Electron. 28, 2416-2422 (1992).
[CrossRef]

Kaindl, R. A.

J. Faure, J. Van Tilborg, R. A. Kaindl, and W. P. Leemans, “Modelling laser-based table-top THz sources: optical rectification, propagation and electro-optic sampling,” Opt. Quantum Electron. 36, 681-697 (2004).
[CrossRef]

Karpowicz, N.

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

H. Zhong, N. Karpowicz, and X.-C. Zhang, “Terahertz emission profile from laser-induced air plasma,” Appl. Phys. Lett. 88, 261103 (2006).
[CrossRef]

Kasparian, J.

P. Bejot, Y. Petit, L. Bonacina, J. Kasparian, M. Moret, and J.-P. Wolf, “Ultrafast gaseous 'half-wave plate',” Opt. Express 16, 7564-7570 (2008).
[CrossRef] [PubMed]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

Kato, K.

K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. QE-22, 1013-1014 (1986).
[CrossRef]

Kauffmann, H. F.

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, “Few-cycle thz emission from cold plasma oscillations,” Phys. Rev. Lett. 79, 3038-3041 (1997).
[CrossRef]

Kersting, R.

R. Kersting, J. N. Heyman, G. Strasser, and K. Unterrainer, “Coherent plasmons in n-doped GaAs,” Phys. Rev. B 58, 4553-4559 (1998).
[CrossRef]

R. Kersting, K. Unterrainer, G. Strasser, H. F. Kauffmann, and E. Gornik, “Few-cycle thz emission from cold plasma oscillations,” Phys. Rev. Lett. 79, 3038-3041 (1997).
[CrossRef]

Kieffer, J.-C.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Kim, K. Y.

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

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

Korn, G.

Kress, M.

M. D. Thomson, M. Kress, T. Loeffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349-368 (2007).
[CrossRef]

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
[CrossRef]

M. Kress, T. Loeffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett. 29, 1120-1122 (2004).
[CrossRef] [PubMed]

La Fontaine, B.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Leemans, W. P.

J. Faure, J. Van Tilborg, R. A. Kaindl, and W. P. Leemans, “Modelling laser-based table-top THz sources: optical rectification, propagation and electro-optic sampling,” Opt. Quantum Electron. 36, 681-697 (2004).
[CrossRef]

Lindenberg, A. M.

H. Wen, D. Daranciang, H. Navirian, and A. M. Lindenberg, “Nonlinear THz interactions with matter: application to semiconductors and ferroelectrics,” presented at the International Workshop on Optical Terahertz Science and Technology (OTST 2009), Santa Barbara, California, March 7-11, 2009, paper SuD4.

Liu, W.

Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
[CrossRef]

Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
[CrossRef] [PubMed]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Liu, X.

Liu, Y.

A. Houard, Y. Liu, B. Prade, and A. Mysyrowicz, “Polarization analysis of terahertz radiation generated by four-wave mixing in air,” Opt. Lett. 33, 1195-1197 (2008).
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Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
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M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
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B. La Fontaine, F. Vidal, Z. Jiang, C.-Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615-1621 (1999).
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A. Houard, Y. Liu, B. Prade, and A. Mysyrowicz, “Polarization analysis of terahertz radiation generated by four-wave mixing in air,” Opt. Lett. 33, 1195-1197 (2008).
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C. D'Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, and A. Couairon, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[CrossRef] [PubMed]

Y. Liu, A. Houard, M. Durand, B. Prade, and A. Mysyrowicz, “Observation of Maker fringes in the terahertz radiation generated by 2-color laser field inside a long femtosecond filament,” presented at the International Workshop on Optical Terahertz Science and Technology (OTST 2009), Santa Barbara, California, March 7-11, 2009, paper SuE97.

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M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases,” Phys. Rev. E 78, 046406 (2008).
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M. D. Thomson, M. Kress, T. Loeffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349-368 (2007).
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M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
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T. Löffler, T. Hahn, M. Thomson, F. Jacob, and H. G. Roskos, “Large-area electro-optic ZnTe terahertz emitters,” Opt. Express 13, 5353-5362 (2005).
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M. Kress, T. Loeffler, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett. 29, 1120-1122 (2004).
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Silaev, A. A.

A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” Phys. Rev. Lett. 102, 115005 (2009).
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F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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Stewart, K. R.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
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Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
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S. V. Golubev, E. V. Suvorov, and A. G. Shalashov, “On the possibility of terahertz wave generation upon dense gas optical breakdown,” JETP Lett. 79, 361-364 (2004).
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K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
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K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577-4584 (2007).
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1997).

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Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, Y. Zhang, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission in the forward direction of a femtosecond laser filament in air,” Appl. Phys. Lett. 93, 231116 (2008).
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Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
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F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
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Thomson, M. D.

M. D. Thomson, M. Kress, T. Loeffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349-368 (2007).
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M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
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M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nat. Phys. 20, 327-331 (2006).
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F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pépin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418-433 (2000).
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A. A. Silaev and N. V. Vvedenskii, “Residual-current excitation in plasmas produced by few-cycle laser pulses,” Phys. Rev. Lett. 102, 115005 (2009).
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Woerner, M.

Wolf, J.-P.

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H.-C. Wu, J. Meyer-ter-Vehn, and Z.-M. Sheng, “Phase-sensitive terahertz emission from gas targets irradiated by few-cycle laser pulses,” New J. Phys. 10, 043001 (2008).
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Y. Zhang, Y. Chen, C. Marceau, W. Liu, Z.-D. Sun, S. Xu, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Non-radially polarized THz pulse emitted from femtosecond laser filament in air,” Opt. Express 16, 15483-15488 (2008).
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Appl. Phys. B (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

Appl. Phys. Lett. (6)

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Figures (6)

Fig. 1
Fig. 1

Schematic of experimental setup.

Fig. 2
Fig. 2

(a) Projection of the THz transient from (b) onto the x y plane (solid curve) and the fitted ellipse (dashed curve). The ellipticity and polarization orientation of the single-cycle pulse is clearly visible. (b) Reconstruction of the temporal evolution of the THz electric field vector for a typical THz transient from the plasma filament. Pol, polarization.

Fig. 3
Fig. 3

THz peak amplitude in x and y directions as a function of distance between the BBO crystal and focus for the four-wave mixing model and the microscopic polarization model. Both models are normalized to their respective peak value for better comparison. The vertical lines represent the position used in our experiment. (a) The BBO crystal leads to an elliptically polarized fundamental pulse. In this case, both models predict maximum amplitudes for similar values of d. (b) The influence of the BBO was neglected. In this case, both fundamental and second-harmonic pulses are linearly polarized and the phase dependence of both models is shifted by 90° with respect to each other.

Fig. 4
Fig. 4

Dependence of x and y components of THz peak amplitude (solid and dashed curves) on the relative angle between fundamental and second-harmonic polarization for (a) the four-wave mixing model and (b) the microscopic polarization model. Both models are normalized to their respective peak value for better comparison. The dotted vertical lines represent the angle used in our experiment.

Fig. 5
Fig. 5

Effect of a finite length of the plasma filament on (a) the orientation and (b) ellipticity for the four-wave mixing model (dashed curve) and the microscopic polarization model (solid curve). Also shown is the orientation and ellipticity of the fundamental (dashed–dotted curve) and second-harmonic pulses (dotted curve).

Fig. 6
Fig. 6

Normalized projection of the measured transient from Fig. 2a together with the projection of the resulting THz pulse for a filament length of 3 mm calculated with the four-wave mixing model.

Equations (48)

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n 2 I = ρ ( I ) e 2 λ 2 8 π 2 c 2 ϵ 0 m ,
γ = 2 π c e λ E 0 2 U O 2 m
ρ ( t ) t = W ( t ) ( ρ O 2 ρ ( t ) ) ,
τ e e = τ e i = 16 π ϵ 0 2 m ( k B T e ) 3 2 3 e 4 ρ e ln Λ 330 fs
τ b = ( σ b ρ at 3 k B T e m ) 1 = 550 fs .
E ω ( t ) = 1 2 E 0 [ cos ( α ) x ̂ sin ( α ) y ̂ ] e i ω t e t 2 T 0 2 + c.c. ,
E 2 ω ( t ) = 1 2 E 2 ω [ cos ( β ) x ̂ sin ( β ) y ̂ ] e i 2 ω t e 2 t 2 T 0 2 + c.c. ,
E 2 ω = i η E 0 sin 2 ( β α ) .
δ t = 0 for E ω x ,
δ t = L BBO c ( n o ω n e ω ) for E ω y ,
δ t = L BBO c ( n e 2 ω n e ω ) for E 2 ω x ,
δ t = L BBO c ( n o 2 ω n e ω ) for E 2 ω y .
n o 2 = 2.7359 + 0.01878 λ 2 0.01822 0.01354 λ 2 ,
n e 2 = 2.3753 + 0.01224 λ 2 0.01667 0.01516 λ 2 ,
1 n e 2 ( θ c ) = sin 2 ( θ c ) n e 2 + cos 2 ( θ c ) n o 2 .
ϕ = 2 ω c d ( n air 2 ω n air ω ) π 2 .
n = 1 + ( 8060.51 + 2480990 λ 2 132.274 λ 2 1 + 17455.7 λ 2 39.32957 λ 2 1 ) × 10 8 ,
E THz ( z ) = 1 4 π ϵ 0 1 c 2 z 2 t 2 V P d 3 r .
V P d 3 r = c π w 0 2 T 0 P .
P i = ϵ 0 j k l m n o χ i j k l ( 3 ) E j ( ω m ) E k ( ω n ) E l ( ω o ) ,
χ x x y y ( 3 ) = χ y y x x ( 3 ) ,
χ x y x y ( 3 ) = χ y x y x ( 3 ) ,
χ x y y x ( 3 ) = χ y x x y ( 3 ) ,
χ x x x x ( 3 ) = χ y y y y ( 3 ) = χ x x y y ( 3 ) + χ x y x y ( 3 ) + χ x y y x ( 3 ) .
χ x x y y ( 3 ) = χ x y x y ( 3 ) = χ x y y x ( 3 ) = 1 3 χ x x x x ( 3 ) .
P x = 1 2 ϵ 0 χ x x x x ( 3 ) ( 3 4 E x 2 ω E ¯ x ω E ¯ x ω + 1 4 E x 2 ω E ¯ y ω E ¯ y ω + 1 2 E y 2 ω E ¯ x ω E ¯ y ω + c.c. ) ,
P y = 1 2 ϵ 0 χ x x x x ( 3 ) ( 3 4 E y 2 ω E ¯ y ω E ¯ y ω + 1 4 E y 2 ω E ¯ x ω E ¯ x ω + 1 2 E x 2 ω E ¯ y ω E ¯ x ω + c.c. ) ,
2 P ( t ) t 2 + 1 τ eff P ( t ) t + ω 0 2 P ( t ) = e 2 m ρ ( t ) E ( t ) .
2 P ( t ) t 2 = e 2 m ρ ( t ) E ( t ) ,
2 P ( t ) t 2 + 1 τ eff P ( t ) t + ω 0 2 P ( t ) = 0 ,
v ( t , t 0 ) = t 0 t e m E ( t ) d t ,
P ( t ) = e t ρ ( t 0 ) v ( t , t 0 ) d t 0 ,
P ( t ) = j 0 Ω sin ( Ω t ) e t 2 τ eff ,
n ω ( ρ ) = n ω 2 ρ 2 e 2 ϵ 0 m ω 2
n 2 ω ( ρ ) = n 2 ω 2 ρ 2 e 2 4 ϵ 0 m ω 2
P x ω = 3 8 χ x x x x ( 3 ) ϵ 0 ( E x ω E x ω E ¯ x ω + 2 3 E x ω E x ω E ¯ y ω + 1 3 E y ω E y ω E ¯ x ω ) + c.c. ,
P y ω = 3 8 χ x x x x ( 3 ) ϵ 0 ( E y ω E y ω E ¯ y ω + 2 3 E y ω E y ω E ¯ x ω + 1 3 E x ω E x ω E ¯ y ω ) + c.c. ,
P x 2 ω = 3 4 χ x x x x ( 3 ) ϵ 0 ( E x 2 ω E x ω E ¯ x ω + 1 3 E x 2 ω E y ω E ¯ y ω + 1 3 E y 2 ω E x ω E ¯ y ω + 1 3 E y 2 ω E y ω E ¯ x ω ) + c.c. ,
P y 2 ω = 3 4 χ x x x x ( 3 ) ϵ 0 ( E y 2 ω E y ω E ¯ y ω + 1 3 E y 2 ω E x ω E ¯ x ω + 1 3 E x 2 ω E y ω E ¯ x ω + 1 3 E x 2 ω E x ω E ¯ y ω ) + c.c.
E THz = j N E j e i n THz ω ( L z j ) c d z ,
D ω = ϵ 0 n ω 2 ( ρ ) E ω + P ω ,
D 2 ω = ϵ 0 n 2 ω 2 ( ρ ) E 2 ω + P 2 ω .
T ( ω ) = E det ( ω ) E in ( ω ) = w in ( ω ) w det ( ω ) ,
w det = 2 c f focus ω w in ( ω ) ,
E det THz ( t ) = F 1 [ exp ( T 0 2 ω 2 8 ) F [ E det ( t ) ] ] ,
Δ I I = ω n 3 r 41 L 2 c E det THz ( cos γ sin 2 ϕ + 2 sin γ cos 2 ϕ ) ,
E x = A 0 [ cos ( t ) cos ( ϕ 0 ) + e sin ( t ) sin ( ϕ 0 ) ] ,
E y = A 0 [ cos ( t ) sin ( ϕ 0 ) + e sin ( t ) cos ( ϕ 0 ) ] ,

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