Abstract

In this Letter, we show experimentally for the first time, to the best of our knowledge, the possibility to observe the effect of polarization mutual action of three elliptically polarized waves, with one of them at terahertz frequency, when they propagate in the isotropic nonlinear medium. When three light pulses are propagated at frequencies ω, 2ω, and ωTHz through liquid nitrogen, we observed the rotation of the ellipse main axis and the ellipticity change. We have shown that this effect is very well described theoretically in the framework of a physical approach analogous to the self-rotation of the polarization ellipse first described in 1964 by Maker et al., but expanded for the case of multi-frequency interaction.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Excitation-wavelength dependent terahertz wave polarization control in laser-induced filament

Liangliang Zhang, Shijing Zhang, Rui Zhang, Tong Wu, Yuejin Zhao, Cunlin Zhang, and X.-C. Zhang
Opt. Express 25(26) 32346-32354 (2017)

Terahertz wave generation from liquid nitrogen

Alexei V. Balakin, Jean-Louis Coutaz, Vladimir A. Makarov, Igor A. Kotelnikov, Yan Peng, Peter M. Solyankin, Yiming Zhu, and Alexander P. Shkurinov
Photon. Res. 7(6) 678-686 (2019)

Polarization-ellipse rotation by induced gyrotropy in atomic vapors

William V. Davis, Alexander L. Gaeta, and Robert W. Boyd
Opt. Lett. 17(18) 1304-1306 (1992)

References

  • View by:
  • |
  • |
  • |

  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 2002).
  2. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2004).
  3. P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [Crossref]
  4. A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
    [Crossref]
  5. S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
    [Crossref]
  6. Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).
  7. A. A. Golubkov and V. A. Makarov, J. Mod. Opt. 37, 1531 (1990).
    [Crossref]
  8. A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
    [Crossref]
  9. S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, 1995).
  10. B. Wen, Y. Xue, B. Gu, G. Rui, J. He, and Y. Cui, Opt. Lett. 42, 3988 (2017).
    [Crossref]
  11. N. Kanda, K. Konishi, and M. Kuwata-Gonokami, Opt. Lett. 34, 3000 (2009).
    [Crossref]
  12. X.-C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017).
    [Crossref]
  13. K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
    [Crossref]
  14. M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
    [Crossref]
  15. D. J. Cook and R. M. Hochstrasser, Opt. Lett. 25, 1210 (2000).
    [Crossref]
  16. J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
    [Crossref]
  17. J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
    [Crossref]
  18. J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
    [Crossref]
  19. I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
    [Crossref]
  20. D. W. Oxtoby and S. A. Rice, Chem. Phys. Lett. 42, 1 (1976).
    [Crossref]
  21. O. Kosareva, M. Esaulkov, N. Panov, V. Andreeva, D. Shipilo, P. Solyankin, A. Demircan, I. Babushkin, V. Makarov, U. Morgner, A. Shkurinov, and A. Savel’ev, Opt. Lett. 43, 90 (2018).
    [Crossref]

2018 (1)

2017 (2)

B. Wen, Y. Xue, B. Gu, G. Rui, J. He, and Y. Cui, Opt. Lett. 42, 3988 (2017).
[Crossref]

X.-C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017).
[Crossref]

2015 (1)

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

2014 (1)

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

2012 (1)

M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
[Crossref]

2009 (1)

2000 (1)

1997 (1)

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

1990 (1)

A. A. Golubkov and V. A. Makarov, J. Mod. Opt. 37, 1531 (1990).
[Crossref]

1985 (1)

J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
[Crossref]

1982 (1)

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

1980 (1)

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

1978 (1)

I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
[Crossref]

1976 (1)

D. W. Oxtoby and S. A. Rice, Chem. Phys. Lett. 42, 1 (1976).
[Crossref]

1969 (1)

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
[Crossref]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

Alshershby, M.

M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
[Crossref]

Andreeva, V.

Babushkin, I.

Balakin, A. V.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2004).

Beattie, I. R.

I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
[Crossref]

Boucher, D.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Boyd, R. W.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

Cheng, Y.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Chu, W.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Cook, D. J.

Cui, Y.

Demircan, A.

Dolgaleva, K.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

Dorfmuller, T.

J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
[Crossref]

Esaulkov, M.

Fertein, E.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Gilson, T. R.

I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
[Crossref]

Golubkov, A. A.

A. A. Golubkov and V. A. Makarov, J. Mod. Opt. 37, 1531 (1990).
[Crossref]

Greenhalgh, D. A.

I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
[Crossref]

Grun, J. B.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
[Crossref]

Gu, B.

Hao, Z.

M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
[Crossref]

He, J.

Hochstrasser, R. M.

Kanda, N.

Konishi, K.

Koroteev, N. I.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Kosareva, O.

Kovrighin, A. I.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

Kozlov, S. A.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

Kuwata-Gonokami, M.

Lin, J.

M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
[Crossref]

Liu, W.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Lyakhov, G. A.

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

Makarov, V.

Makarov, V. A.

A. A. Golubkov and V. A. Makarov, J. Mod. Opt. 37, 1531 (1990).
[Crossref]

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Masselin, P.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Materikina, D. V.

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

McQuillan, A. K.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
[Crossref]

Mittag, U.

J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
[Crossref]

Morgner, U.

Oxtoby, D. W.

D. W. Oxtoby and S. A. Rice, Chem. Phys. Lett. 42, 1 (1976).
[Crossref]

Pakulev, A. V.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Panov, N.

Popov, S. V.

S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, 1995).

Rice, S. A.

D. W. Oxtoby and S. A. Rice, Chem. Phys. Lett. 42, 1 (1976).
[Crossref]

Rui, G.

Samios, J.

J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
[Crossref]

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Savel’ev, A.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 2002).

Shipilo, D.

Shkurinov, A.

Shkurinov, A. P.

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

Solyankin, P.

Stoicheff, B. P.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
[Crossref]

Svirko, Y. P.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, 1995).

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Wang, Z.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Wen, B.

Xu, Z.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Xue, Y.

Yakovlev, D. V.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

Zeng, B.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Zhang, X.-C.

X.-C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017).
[Crossref]

Zhang, Y.

X.-C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017).
[Crossref]

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Zhao, J.

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Zharikov, V. I.

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

Zhdanov, B. V.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

Zheludev, N. I.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, 1995).

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Chem. Phys. Lett. (1)

D. W. Oxtoby and S. A. Rice, Chem. Phys. Lett. 42, 1 (1976).
[Crossref]

J. Exp. Theor. Phys. (1)

A. V. Balakin, N. I. Koroteev, A. V. Pakulev, A. P. Shkurinov, D. Boucher, P. Masselin, and E. Fertein, J. Exp. Theor. Phys. 85, 52 (1997).
[Crossref]

J. Mod. Opt. (1)

A. A. Golubkov and V. A. Makarov, J. Mod. Opt. 37, 1531 (1990).
[Crossref]

J. Phys. D (1)

M. Alshershby, Z. Hao, and J. Lin, J. Phys. D 45, 265401 (2012).
[Crossref]

Laser Phys. Lett. (1)

J. Zhao, Y. Zhang, Z. Wang, W. Chu, B. Zeng, W. Liu, Y. Cheng, and Z. Xu, Laser Phys. Lett. 11, 095302 (2014).
[Crossref]

Mol. Phys. (1)

J. Samios, U. Mittag, and T. Dorfmuller, Mol. Phys. 56, 541 (1985).
[Crossref]

Nat. Photonics (1)

X.-C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017).
[Crossref]

Nature (1)

I. R. Beattie, T. R. Gilson, and D. A. Greenhalgh, Nature 276, 378 (1978).
[Crossref]

Opt. Acta (1)

S. A. Akhmanov, G. A. Lyakhov, V. A. Makarov, and V. I. Zharikov, Opt. Acta 29, 1359 (1982).
[Crossref]

Opt. Commun. (1)

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, Opt. Commun. 35, 92 (1980).
[Crossref]

Opt. Lett. (4)

Phys. Rev. (1)

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, Phys. Rev. 180, 61 (1969).
[Crossref]

Phys. Rev. A (1)

K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, Phys. Rev. A 92, 023809 (2015).
[Crossref]

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Other (4)

S. V. Popov, Y. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, 1995).

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 2002).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2004).

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. Experimental setup. L, lens; BS, beam splitter; M, mirror; PM, parabolic mirror; BBO, β -barium borate (BBO) crystal.
Fig. 2.
Fig. 2. System of coordinates for the polarization measurements.
Fig. 3.
Fig. 3. Rotation of the ellipse of polarization of the terahertz radiation after propagation through the LN. These measurements were done at the pulse energy of 2.5 mJ and pulse duration of 30 fs.

Equations (15)

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

M Ω ( z ) = 2 a b a 2 + b 2 = | E + ( Ω ) | 2 | E ( Ω ) | 2 | E + ( Ω ) | 2 + | E ( Ω ) | 2 ,
I n ω = ( | E + ( n ω ) | 2 + | E ( n ω ) | 2 ) / 2 ,
P i ( Ω ) = χ i j k l ( 3 ) ( Ω ; Ω , ω , ω ) E j ( Ω ) E k ( ω ) E l * ( ω ) + χ i j k l ( 3 ) ( Ω ; Ω , 2 ω , 2 ω ) E j ( Ω ) E k ( 2 ω ) E l * ( 2 ω ) = P i ( 1 ) + P i ( 2 ) .
χ i j k l ( 3 ) ( Ω ; Ω , ω , ω ) = χ 1 δ i j δ k l + χ 2 δ i k δ j l + χ 3 δ i l δ j k ,
χ i j k l ( 3 ) ( Ω ; Ω , 2 ω , 2 ω ) = χ 4 δ i j δ k l + χ 5 δ i k δ j l + χ 6 δ i l δ j k ,
E x ( n ω ) = I n ω 2 [ ( 1 M n ω ) 1 / 2 exp ( i Ψ n ω ) + ( 1 + M n ω ) 1 / 2 exp ( i Ψ n ω ) ] , E y ( n ω ) = I n ω 2 i [ ( 1 M n ω ) 1 / 2 exp ( i Ψ n ω ) + ( 1 + M n ω ) 1 / 2 exp ( i Ψ n ω ) ] ,
M n ( ω ) = | E + ( n ω ) | 2 | E ( n ω ) | 2 | E + ( n ω ) | 2 + | E ( n ω ) | 2
E ± ( Ω ) z 2 π i Ω 2 c 2 k THz [ P ± ( 1 ) ( Ω ) + P ± ( 2 ) ( Ω ) ] ,
P ± ( 1 ) ( Ω ) = I ω 2 { [ ( 2 χ 1 + χ 2 + χ 3 ) + ( χ 2 χ 3 ) M ω ] E ± ( Ω ) + ( χ 2 + χ 3 ) ( 1 M ω 2 ) 1 / 2 exp ( ± 2 i Ψ ω ) E ( Ω ) } , P ± ( 2 ) ( Ω ) = I 2 ω 2 { [ ( 2 χ 4 + χ 5 + χ 6 ) + ( χ 5 χ 6 ) M 2 ω ] E ± ( Ω ) + ( χ 5 + χ 6 ) ( 1 M 2 ω 2 ) 1 / 2 exp ( ± 2 i Ψ 2 ω ) E ( Ω ) } .
M Ω ( L ) = M 0 cos ( 2 μ L ) + ( 1 M 0 2 ) 1 / 2 sin ( 2 μ L ) cos ( 2 Ψ 0 + ν ) ,
Ψ Ω ( L ) = 1 2 arctg sin ( Ψ 0 α L ) η tg ( μ L ) sin ( Ψ 0 + α L + ν ) cos ( Ψ 0 α L ) + η tg ( μ L ) cos ( Ψ 0 + α L + ν ) + 1 2 arctg η sin ( Ψ 0 + α L ) + tg ( μ L ) sin ( Ψ 0 α L + ν ) η cos ( Ψ 0 + α L ) tg ( μ L ) cos ( Ψ 0 α L + ν ) .
α = π Ω 2 c 2 k T H [ ( 2 χ 1 + χ 2 + χ 3 ) I ω + ( χ 2 χ 3 ) M ω I ω + ( 2 χ 4 + χ 5 + χ 6 ) I 2 ω + ( χ 5 χ 6 ) M 2 ω I 2 ω ] ,
μ = π Ω 2 c 2 k T H { ( χ 2 + χ 3 ) 2 ( 1 M ω 2 ) I ω 2 + ( χ 5 + χ 6 ) 2 ( 1 M 2 ω 2 ) I 2 ω 2 + 2 ( χ 2 + χ 3 ) ( χ 5 + χ 6 ) ( 1 M ω 2 ) 1 / 2 ( 1 M 2 ω 2 ) 1 / 2 I ω I 2 ω cos 2 ( Ψ 2 ω Ψ ω ) } 1 / 2 ,
ν = arctg ( I ω cos ( 2 Ψ ω ) + β I 2 ω cos ( 2 Ψ 2 ω ) I ω sin ( 2 Ψ ω ) + β I 2 ω sin ( 2 Ψ 2 ω ) ) ,
β = ( χ 5 + χ 6 ) ( 1 M 2 ω 2 ) 1 / 2 ( χ 2 + χ 3 ) ( 1 M ω 2 ) 1 / 2 .

Metrics