Abstract

We study the elimination of the chirp of narrowband terahertz pulses generated by chirped laser pulse beating using a laser pulse stretcher with two grating pairs that cancel out the third-order spectral phase. First, we show that positively chirped terahertz pulses can be generated using a pulse stretcher with a grating pair and internal lenses. We then combine this with a second grating pair, the spectral phase of which has the opposite sign to that of the first one. By varying the separation of the second grating pair, we experimentally verify that the chirp of the generated terahertz pulses can be eliminated.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Use of mismatched grating pairs in chirped-pulse amplification systems

Jeff Squier, Chris P. J. Barty, François Salin, Catherine Le Blanc, and Steve Kane
Appl. Opt. 37(9) 1638-1641 (1998)

Generation of narrowband terahertz radiation by an ultrashort laser pulse in a bulk LiNbO3 crystal

E. A. Mashkovich, S. A. Sychugin, and M. I. Bakunov
J. Opt. Soc. Am. B 34(9) 1805-1810 (2017)

Broadband and narrowband laser-based terahertz source and its application for resonant and non-resonant excitation of antiferromagnetic modes in NiO

O. V. Chefonov, A. V. Ovchinnikov, C. P. Hauri, and M. B. Agranat
Opt. Express 27(19) 27273-27281 (2019)

References

  • View by:
  • |
  • |
  • |

  1. M. C. Hoffmann and J. A. Fülöp, “Intense ultrashort terahertz pulses: generation and applications,” J. Phys. D: Appl. Phys. 44, 083001 (2011).
    [Crossref]
  2. J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large- area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
    [Crossref] [PubMed]
  3. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
    [Crossref]
  4. T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
    [Crossref]
  5. P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
    [Crossref] [PubMed]
  6. T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
    [Crossref]
  7. S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
    [Crossref] [PubMed]
  8. I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
    [Crossref]
  9. S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
    [Crossref] [PubMed]
  10. K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
    [Crossref]
  11. B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
    [Crossref] [PubMed]
  12. M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
    [Crossref]
  13. A. S. Weling and D. H. Auston, “Novel sources and detectors for coherent tunable narrow-band terahertz radiation in free space,” J. Opt. Soc. Am. B, 132783–2791(1996).
    [Crossref]
  14. J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
    [Crossref] [PubMed]
  15. F. Eickemeyer, R. A. Kaindl, M. Woerner, T. Elsaesser, and A. M. Weiner, “Controlled shaping of ultrafast electric field transients in the mid-infrared spectral range,” Opt. Lett. 25, 1472–1474 (2000).
    [Crossref]
  16. J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11, 2486–2496 (2003).
    [Crossref] [PubMed]
  17. S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
    [Crossref]
  18. S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
    [Crossref]
  19. T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
    [Crossref]
  20. E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
    [Crossref]
  21. I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
    [Crossref]
  22. O. E. Martinez, J. P. Gordon, and R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A 1, 1003–1006 (1984).
    [Crossref]
  23. T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
    [Crossref]
  24. M. van Exter, Ch. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopyof water vapor,” Opt. Lett. 14, 1128–1130 (1989).
    [Crossref]

2014 (1)

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

2013 (3)

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
[Crossref]

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
[Crossref]

2012 (2)

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
[Crossref] [PubMed]

2011 (5)

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

M. C. Hoffmann and J. A. Fülöp, “Intense ultrashort terahertz pulses: generation and applications,” J. Phys. D: Appl. Phys. 44, 083001 (2011).
[Crossref]

J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
[Crossref] [PubMed]

2010 (2)

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

2003 (1)

2002 (1)

2001 (1)

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

2000 (2)

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

F. Eickemeyer, R. A. Kaindl, M. Woerner, T. Elsaesser, and A. M. Weiner, “Controlled shaping of ultrafast electric field transients in the mid-infrared spectral range,” Opt. Lett. 25, 1472–1474 (2000).
[Crossref]

1998 (1)

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

1996 (1)

A. S. Weling and D. H. Auston, “Novel sources and detectors for coherent tunable narrow-band terahertz radiation in free space,” J. Opt. Soc. Am. B, 132783–2791(1996).
[Crossref]

1989 (1)

1986 (1)

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[Crossref]

1984 (1)

1969 (1)

E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

Aeppli, G.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Ahn, J.

Akiyama, H.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Allen, S. J.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Almasi, G.

Andrews, A. M.

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Aoki, H.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Aoki, T.

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
[Crossref]

Ashida, M.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Auston, D. H.

A. S. Weling and D. H. Auston, “Novel sources and detectors for coherent tunable narrow-band terahertz radiation in free space,” J. Opt. Soc. Am. B, 132783–2791(1996).
[Crossref]

Averitt, R. D.

Birnir, B.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Blanchard, F.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

Christov, I. P.

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[Crossref]

Cole, B. E.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Daikoku, M.

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Dekorsy, T.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Doi, A.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

Efimov, A. V.

Eickemeyer, F.

Elsaesser, T.

Fattinger, Ch.

Fiebig, M.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Field, R. W.

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

Field, R.W.

S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
[Crossref] [PubMed]

Fleischer, S.

S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
[Crossref] [PubMed]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

Fork, R. L.

Fülöp, J. A.

M. C. Hoffmann and J. A. Fülöp, “Intense ultrashort terahertz pulses: generation and applications,” J. Phys. D: Appl. Phys. 44, 083001 (2011).
[Crossref]

Gordon, J. P.

Greenland, P. T.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Grischkowsky, D.

Hattori, T.

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Hebling, J.

Helm, M.

J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
[Crossref] [PubMed]

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Hirori, H.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

Hoffmann, M. C.

M. C. Hoffmann and J. A. Fülöp, “Intense ultrashort terahertz pulses: generation and applications,” J. Phys. D: Appl. Phys. 44, 083001 (2011).
[Crossref]

Huber, R.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Inoue, H.

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Jauho, A. -P.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Johnsen, K.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Kaindl, R. A.

Kamada, S.

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
[Crossref]

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

Kampfrath, T.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
[Crossref]

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Katayama, I.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Kawashima, Y.

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Kawayama, I.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

King, B. T.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Kinjo, R.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Klatt, G.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Kono, J.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Kozma, I.

Krause, J.

Kuhl, J.

Leitenstorfer, A.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Lynch, S. A.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Mährlein, S.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Martinez, O. E.

Murata, S.

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
[Crossref]

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

Murdin, B. N.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Nagai, M.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Nakatsuka, H.

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Nelson, K. A.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
[Crossref]

S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
[Crossref] [PubMed]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

Noda, T.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Nordstrom, K. B.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Pashkin, A.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Pidgeon, C. R.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Redlich, B.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Sakaki, H.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Schartner, S.

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Schneider, H.

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Sell, A.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Sherwin, M. S.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Shimosato, H.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Stanley, C. R.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Stehr, D.

J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
[Crossref] [PubMed]

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Strasser, G.

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Takeda, J.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Tanaka, K.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
[Crossref]

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

Taylor, A. J.

Tomov, I. V.

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[Crossref]

Tonouchi, M.

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

Treacy, E. B.

E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

van der Meer, A. F. G.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

van Exter, M.

Vinh, N. Q.

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

Wagner, M.

J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
[Crossref] [PubMed]

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Weiner, A. M.

Weling, A. S.

A. S. Weling and D. H. Auston, “Novel sources and detectors for coherent tunable narrow-band terahertz radiation in free space,” J. Opt. Soc. Am. B, 132783–2791(1996).
[Crossref]

Williams, J. B.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Winnerl, S.

J. Krause, M. Wagner, S. Winnerl, M. Helm, and D. Stehr, “Tunable narrowband THz pulse generation in scalable large area photoconductive antennas,” Opt. Express 19, 19114–19121 (2011).
[Crossref] [PubMed]

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

Woerner, M.

Wolf, M.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Yoshida, T.

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

Zhou, Y.

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

Appl. Phys. Express (1)

S. Kamada, S. Murata, and T. Aoki, “On the Chirp of Narrowband Terahertz Pulses Generated by Photomixing with Nonlinearly Chirped Laser Pulse Pairs,” Appl. Phys. Express 6, 032701 (2013).
[Crossref]

Appl. Phys. Lett. (3)

S. Kamada, T. Yoshida, S. Murata, and T. Aoki, “The chirp-control of frequency-tunable narrowband terahertz pulses by nonlinearly chirped laser pulse beating,” Appl. Phys. Lett. 104, 101102 (2014).
[Crossref]

T. Yoshida, S. Kamada, S. Murata, and T. Aoki, “Fiber-based pulse stretcher for narrowband terahertz pulse generation with a chirped-pulse beating method,” Appl. Phys. Lett. 103, 151118 (2013).
[Crossref]

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98, 091106 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B, (1)

A. S. Weling and D. H. Auston, “Novel sources and detectors for coherent tunable narrow-band terahertz radiation in free space,” J. Opt. Soc. Am. B, 132783–2791(1996).
[Crossref]

J. Phys. D: Appl. Phys. (1)

M. C. Hoffmann and J. A. Fülöp, “Intense ultrashort terahertz pulses: generation and applications,” J. Phys. D: Appl. Phys. 44, 083001 (2011).
[Crossref]

Jpn. J. Appl. Phys. (1)

T. Hattori, Y. Kawashima, M. Daikoku, H. Inoue, and H. Nakatsuka, “Autocorrelation measurement of femtosecond optical pulses based on two-photon photoemission in a photomultiplier tube,” Jpn. J. Appl. Phys. 39, L809–L811 (2000).
[Crossref]

Nat. Photonics (2)

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
[Crossref]

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Nature (2)

P. T. Greenland, S. A. Lynch, A. F. G. van der Meer, B. N. Murdin, C. R. Pidgeon, B. Redlich, N. Q. Vinh, and G. Aeppli, “Coherent control of Rydberg states in silicon,” Nature 465, 1057–1061 (2010).
[Crossref] [PubMed]

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410, 60–63 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (5)

M. Wagner, H. Schneider, D. Stehr, S. Winnerl, A. M. Andrews, S. Schartner, G. Strasser, and M. Helm, “Observation of the Intraexciton Autler-Townes Effect in GaAs/AlGaAs Semiconductor Quantum Wells,” Phys. Rev. Lett. 105, 167401 (2010).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107, 163603 (2011).
[Crossref] [PubMed]

I. Katayama, H. Aoki, J. Takeda, H. Shimosato, M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Nagai, and K. Tanaka, “Ferroelectric Soft Mode in a SrTiO3 Thin Film Impulsively Driven to the Anharmonic Regime Using Intense Picosecond Terahertz Pulses,” Phys. Rev. Lett. 108, 097401 (2012).
[Crossref]

S. Fleischer, R.W. Field, and K. A. Nelson, “Commensurate Two-Quantum Coherences Induced by Time-Delayed THz Fields,” Phys. Rev. Lett. 109, 123603 (2012).
[Crossref] [PubMed]

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. -P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic Dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. 81, 457–460 (1998).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 (a) Schematic of the setup for generating tunable narrowband THz pulses with the chirped pulse beating method. (b) Double-pass grating pair without internal lenses. (c) Single pass grating pair with internal lenses; the schematic is drawn so that the effective perpendicular separation l < 0. The inset shows the case for l > 0. In (b) and (c), the red and blue arrows schematically show the traces of the lower and higher frequency components of the input laser pulse, respectively.
Fig. 2
Fig. 2 (a) The experimental dependence of the value of Φ L ( 2 ) on the perpendicular separation l. The black solid line represents the theoretical value of Φ L ( 2 ) as a function of l, and the blue dots show the experimental results. (b), (d) THz field waveform and (c), (e) Short-time Fourier transform, for the cases of the effective perpendicular separations l = −2.4 and 2.4 cm, respectively, with a center frequency of 0.5 THz. The black dashed lines show the theoretical values.
Fig. 3
Fig. 3 The dependence of the linewidth Δ/(2π) on the center frequency fT = ωT/(2π). Solid lines represent the theoretical value, and the dots show the experimental results. The black, blue, red, and green dots show the results for a perpendicular separation b = 20, 35, 45, and 53 cm, respectively.

Equations (8)

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

E in ( t ) = E 0 exp ( t 2 σ 2 i ω 0 t ) ,
Φ ( ω ) = Φ ( ω 0 ) + Φ ( 1 ) ( ω ω 0 ) + Φ ( 2 ) ( ω ω 0 ) 2 + Φ ( 3 ) ( ω ω 0 ) 3 .
E THz ( t ) exp ( σ 2 t 2 8 Φ ( 2 ) 2 ) cos ( θ + ω T t 3 Φ ( 3 ) ω T t 2 4 Φ ( 2 ) 2 ) ,
Δ = [ ( σ 2 Φ ( 2 ) ) 2 + ( 3 Φ ( 3 ) σ Φ ( 2 ) ) 2 ω T 2 ] 1 / 2 .
Φ NL ( 2 ) = 4 π 2 c b ω 0 3 d NL 2 { 1 [ ( 2 π c ω 0 d NL ) sin γ NL ] 2 } 3 2 ,
Φ NL ( 3 ) = Φ NL ( 2 ) ω 0 { 1 + ( 2 π c ω 0 d NL ) sin γ NL sin 2 γ NL 1 [ ( 2 π c ω 0 d NL ) sin γ NL ] 2 } ,
Φ L ( 2 ) = 2 π 2 cl ω 0 3 d L 2 { 1 [ ( 2 π c ω 0 d L ) sin γ L ] 2 } 3 2 ,
Φ L ( 3 ) = Φ L ( 2 ) ω 0 { 1 + ( 2 π c ω 0 d L ) sin γ L sin 2 γ L 1 [ ( 2 π c ω 0 d L ) sin γ L ] 2 } ,

Metrics