Abstract

We have developed a general analytic description of polarized light pulses and explored the properties of circularly polarized single-cycle pulses. The temporal evolution of the electric-field vector of such spectrally broad pulses, which may be described in terms of a Hilbert transform relationship, differs significantly from the well-known behavior of quasi-monochromatic radiation. Single-cycle circularly polarized pulses have been produced and characterized experimentally in the terahertz spectral region.

© 2009 Optical Society of America

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    [PubMed]
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    [CrossRef] [PubMed]
  8. R. A. Cheville, R. W. McGowan, and D. Grischkowsky, "Time resolved measurements which isolate the mechanisms responsible for terahertz glory scattering from dielectric spheres," Phys. Rev. Lett. 80, 269-272 (1998).
    [CrossRef]
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  22. The definition of polarized radiation introduced in this paper may be extended to statistical fields through the use of the coherence matrix. The criterion for a fully polarized field is then, in the terminology of Born and Wolf [1], that the complex degree of coherence of the two field components at zero time delay attains its maximum value, |?xy(? = 0)| = 1. This criterion also constitutes the natural generalization of existing treatment of quasi-monochromatic radiation.
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  24. The complex parameter ? = ey?/ex can be related to the standard parameters of the polarization ellipse. If we denote the angle of the azimuth of the major axis by ? and the ellipticity parameter by ?, then ?= (tan ?+i tan ?) /(1-i tan ? tan ?) .
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  29. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2007 (1)

2006 (4)

2005 (2)

R. Shimano, H. Nishimura, and T. Sato, "Frequency tunable circular polarization control of terahertz radiation," Jpn. J. Appl. Phys. 44, L676-L678 (2005).
[CrossRef]

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

2004 (1)

K. L. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

2003 (2)

U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
[CrossRef] [PubMed]

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

2000 (2)

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

1999 (3)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[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]

Q. Chen and X. C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 74, 3435-3437 (1999).
[CrossRef]

1998 (2)

R. A. Cheville, R. W. McGowan, and D. Grischkowsky, "Time resolved measurements which isolate the mechanisms responsible for terahertz glory scattering from dielectric spheres," Phys. Rev. Lett. 80, 269-272 (1998).
[CrossRef]

J. Bromage, S. Radic, G. P. Agrawal, C. R. Stroud, P. M. Fauchet, and R. Sobolewski, "Spatiotemporal shaping of half-cycle terahertz pulses by diffraction through conductive apertures of finite thickness," J. Opt. Soc. Am. B 15, 1399-1405 (1998).
[CrossRef]

1997 (2)

T. J. Bensky, G. Haeffler, and R. R. Jones, "Ionization of Na Rydberg atoms by subpicosecond quarter-cycle circularly polarized pulses," Phys. Rev. Lett. 79, 2018-2021 (1997).
[CrossRef]

L. A. Nafie, "Infrared and Raman vibrational optical activity: Theoretical and experimental aspects," Annu. Rev. Phys. Chem. 48, 357-386 (1997).
[CrossRef] [PubMed]

1996 (2)

Q1. A. Nahata and T. F. Heinz, "Reshaping of freely propagating terahertz pulses by diffraction," IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

1994 (1)

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

1990 (1)

1985 (1)

Agrawal, G. P.

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Amer, N.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Auston, D. H.

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Backus, S.

Baltuska, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Bensky, T. J.

T. J. Bensky, G. Haeffler, and R. R. Jones, "Ionization of Na Rydberg atoms by subpicosecond quarter-cycle circularly polarized pulses," Phys. Rev. Lett. 79, 2018-2021 (1997).
[CrossRef]

Bromage, J.

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Chen, Q.

Q. Chen and X. C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 74, 3435-3437 (1999).
[CrossRef]

Cheung, K. P.

Cheville, R. A.

R. A. Cheville, R. W. McGowan, and D. Grischkowsky, "Time resolved measurements which isolate the mechanisms responsible for terahertz glory scattering from dielectric spheres," Phys. Rev. Lett. 80, 269-272 (1998).
[CrossRef]

Clarke, J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

De Silvestri, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Fauchet, P. M.

Feng, S.

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]

Flammini, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Gagnon, E.

Gallmann, L.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Gallot, G.

Gohle, C.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Grischkowsky, D.

Haeffler, G.

T. J. Bensky, G. Haeffler, and R. R. Jones, "Ionization of Na Rydberg atoms by subpicosecond quarter-cycle circularly polarized pulses," Phys. Rev. Lett. 79, 2018-2021 (1997).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Hangyo, M.

Hansch, T. W.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Hattori, R.

Heinz, T. F.

Q1. A. Nahata and T. F. Heinz, "Reshaping of freely propagating terahertz pulses by diffraction," IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Hentschel, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Hirota, Y.

Holzwarth, R.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Hurlbut, W. C.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Jamison, S. P.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Jones, R. R.

T. J. Bensky, G. Haeffler, and R. R. Jones, "Ionization of Na Rydberg atoms by subpicosecond quarter-cycle circularly polarized pulses," Phys. Rev. Lett. 79, 2018-2021 (1997).
[CrossRef]

Kanda, N.

Kapteyn, H. C.

Keiding, S. R.

Keller, U.

U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
[CrossRef] [PubMed]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Konishi, K.

Krausz, F.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Kuwata-Gonokami, M.

Lee, Y. S.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Lew, D. J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Ludwig, F.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Lytle, A. L.

Masson, J. B.

Matuschek, N.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

McGowan, R. W.

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

R. A. Cheville, R. W. McGowan, and D. Grischkowsky, "Time resolved measurements which isolate the mechanisms responsible for terahertz glory scattering from dielectric spheres," Phys. Rev. Lett. 80, 269-272 (1998).
[CrossRef]

Merchant, P.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Mittleman, D. M.

K. L. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

Murnane, M. M.

Nafie, L. A.

L. A. Nafie, "Infrared and Raman vibrational optical activity: Theoretical and experimental aspects," Annu. Rev. Phys. Chem. 48, 357-386 (1997).
[CrossRef] [PubMed]

Nahata, A.

Q1. A. Nahata and T. F. Heinz, "Reshaping of freely propagating terahertz pulses by diffraction," IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Nemeth, D. T.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Nishimura, H.

R. Shimano, H. Nishimura, and T. Sato, "Frequency tunable circular polarization control of terahertz radiation," Jpn. J. Appl. Phys. 44, L676-L678 (2005).
[CrossRef]

Nisoli, M.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Norris, T. B.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Norton, B. J.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Orenstein, J.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Parks, B.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Paul, A.

Poletto, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Radic, S.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

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]

Sandhu, A. S.

Sansone, G.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Sato, T.

R. Shimano, H. Nishimura, and T. Sato, "Frequency tunable circular polarization control of terahertz radiation," Jpn. J. Appl. Phys. 44, L676-L678 (2005).
[CrossRef]

Scrinzi, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Shimano, R.

R. Shimano, H. Nishimura, and T. Sato, "Frequency tunable circular polarization control of terahertz radiation," Jpn. J. Appl. Phys. 44, L676-L678 (2005).
[CrossRef]

Sobolewski, R.

Spielman, S.

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

Stagira, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Steinmeyer, G.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Stroud, C. R.

Sutter, D. H.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Tani, M.

Thomann, I.

Udem, T.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Velotta, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Villoresi, P.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Vozzi, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Wang, K. L.

K. L. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

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]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Winful, H. G.

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]

Yakovlev, V. S.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Zhang, X. C.

Q. Chen and X. C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 74, 3435-3437 (1999).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

L. A. Nafie, "Infrared and Raman vibrational optical activity: Theoretical and experimental aspects," Annu. Rev. Phys. Chem. 48, 357-386 (1997).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Q. Chen and X. C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 74, 3435-3437 (1999).
[CrossRef]

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, and T. B. Norris, "Generation of terahertz pulses with arbitrary elliptical polarization," Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Q1. A. Nahata and T. F. Heinz, "Reshaping of freely propagating terahertz pulses by diffraction," IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

R. Shimano, H. Nishimura, and T. Sato, "Frequency tunable circular polarization control of terahertz radiation," Jpn. J. Appl. Phys. 44, L676-L678 (2005).
[CrossRef]

Nature (3)

K. L. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
[CrossRef] [PubMed]

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (4)

S. Spielman, B. Parks, J. Orenstein, D. T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D. J. Lew, "Observation of the quasi-particle Hall-effect in superconducting YBa2Cu3O7-8," Phys. Rev. Lett. 73, 1537-1540 (1994).
[CrossRef] [PubMed]

T. J. Bensky, G. Haeffler, and R. R. Jones, "Ionization of Na Rydberg atoms by subpicosecond quarter-cycle circularly polarized pulses," Phys. Rev. Lett. 79, 2018-2021 (1997).
[CrossRef]

R. A. Cheville, R. W. McGowan, and D. Grischkowsky, "Time resolved measurements which isolate the mechanisms responsible for terahertz glory scattering from dielectric spheres," Phys. Rev. Lett. 80, 269-272 (1998).
[CrossRef]

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]

Science (3)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Other (7)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7 ed. (Cambridge Univ. Press, 1999).
[PubMed]

S. Huard, Polarization of Light (Wiley, New York, 1997).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).

D. Grischkowsky, in Frontiers in Nonlinear Optics, H. Walther, N. Koroteev, and M. O. Scully Eds. (Institute of Physics, Philadelphia, 1992), pp. 196-227.

The definition of polarized radiation introduced in this paper may be extended to statistical fields through the use of the coherence matrix. The criterion for a fully polarized field is then, in the terminology of Born and Wolf [1], that the complex degree of coherence of the two field components at zero time delay attains its maximum value, |?xy(? = 0)| = 1. This criterion also constitutes the natural generalization of existing treatment of quasi-monochromatic radiation.

L. Mandel and E. Wolf, Introduction to the Theory of Fourier Integrals (Cambridge Univ. Press, Cambridge, New York, 1995).

The complex parameter ? = ey?/ex can be related to the standard parameters of the polarization ellipse. If we denote the angle of the azimuth of the major axis by ? and the ellipticity parameter by ?, then ?= (tan ?+i tan ?) /(1-i tan ? tan ?) .

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Figures (3)

Fig. 1.
Fig. 1.

Right column: Parametric plots of the electric-field vector E⃗(t) of left CP pulses with x-components given by Ex(t) = E 0 exp(-t 2/τ 2)sin(ω 0 t) and the corresponding Ey (t) calculated by the Hilbert transform of Eq. (7). Panels (a), (b), and (c) correspond to decreasing normalized pulse durations of ω 0 τ= 60, 3.5, and 2, respectively. Left column: Time dependence of the angular speed θ̇(t) of the electric-field vector E⃗(t) for the corresponding pulses, plotted for times when the field amplitude exceeds 0.1% of its peak values.

Fig. 2.
Fig. 2.

Experimental setup for the generation of CP THz radiation through the use of a Fresnel rhomb. Ti:Sapphire (Ti:S) laser pulses are split into two beams by a beam splitter (BS). One arm of the beam is delayed using a time-delay stage (TDS), focused into a ZnTe THz emitter (E), collimated by a parabolic mirror (PM) prior to injection into the Fresnel rhomb (FR), and refocused by a second PM into a second ZnTe crystal for electro-optic sampling (EOS) system. The second arm of the laser beam is used for detection in a differential detection (DET) scheme. (P, A) and (P′, A′) are the polarizer and analyzer for the optical probe and the THz radiation, respectively. The inset is a schematic representation of the Fresnel rhomb arranged to transform linearly polarized pulses to CP pulses.

Fig. 3.
Fig. 3.

(a) Time dependence of the electric-field vector, its two orthogonal components Ex (t) and Ey (t), and the parametric plot of the field components for a left CP THz pulse generated in the experiment (symbols). The solid lines correspond to the time dependence of the electric-field vector, the y-component of which is calculated from the experimental waveform for Ex (t) by the Hilbert-transform relation of Eq. (7).

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

E ( t ) = E x ( t ) x ̂ + E y ( t ) y ̂ = Re { e ̂ E ( ω ) e iωt }
E ( t ) = Re 0 e ̂ ( ω ) E ( ω ) e iωt .
E ( t ) = Re { e ̂ E ˜ ( t ) } ,
E ˜ ( t ) = 0 dωE ( ω ) e iωt
E x ( t ) = ( ζ E y ( t ) + ζ H [ E y ( t ) ] ) / ς 2 ,
E y ( t ) = ζ E x ( t ) ζ H [ E x ( t ) ] )
H [ f ( t ) ] = 1 π PV f ( t ) dt t t ,
E x ( t ) = H [ E y ( t ) ]
E y ( t ) = ± H [ E x ( t ) ] ,
E x ( t ) = ε ( t ) sin [ ω 0 t + φ ( t ) ]
ε ( t ) = ε ( t ) e ( t )
E y ( t ) ε ( t ) cos ( ω 0 t + φ ( t ) ) .
θ ˙ ( t ) = ω 0 + φ ˙ ( t )
E x ( t ) = E 0 exp ( t 2 / τ 2 ) sin ( ω 0 t )
θ ˙ ( t ) = [ E ˙ y ( t ) E x ( t ) E y ( t ) E ˙ x ( t ) ] / [ E x 2 ( t ) + E y 2 ( t ) ] .

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