Abstract

Phase shift exceeding π2 at 1THz is demonstrated by using electrically controlled birefringence in a homeotropically aligned nematic liquid crystal (E7) cell, 570μm in thickness. The driving voltage required for a phase shift of 90° is 125V (rms). We demonstrate that the phase shifter works as an electrically switchable quarter-wave plate at 1THz. The device can also be used as an electrically tuned phase compensator around the quarter-wave point near 1THz.

© 2006 Optical Society of America

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References

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  1. D. Grischkowsky, S. R. Keiding, M. V. Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
    [CrossRef]
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  3. D. Mittleman, Sensing with THz Radiation (Springer, 2002).
  4. I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
    [CrossRef]
  5. R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
    [CrossRef]
  6. T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
    [CrossRef]
  7. K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
    [CrossRef]
  8. T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
    [CrossRef] [PubMed]
  9. R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
    [CrossRef]
  10. C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
    [CrossRef]
  11. C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).
  12. T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
    [CrossRef]
  13. F. J. Kahn, Appl. Phys. Lett. 22, 386 (1973).
    [CrossRef]
  14. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, 1983).
  15. S. Chandrasekhar, Liquid Crystal, 2nd ed. (Cambridge, 1992).
    [CrossRef]
  16. C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, Opt. Express 13, 3921 (2005).
    [CrossRef] [PubMed]
  17. E. Hecht, Optics, 3rd ed. (Addison Wesley-Longman, 1998).
  18. K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
    [CrossRef]

2005 (1)

2004 (4)

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

2003 (2)

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

2002 (1)

B. Ferguson and X.-C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

2000 (2)

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
[CrossRef]

1993 (1)

K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
[CrossRef]

1990 (1)

1980 (1)

K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[CrossRef]

1973 (1)

F. J. Kahn, Appl. Phys. Lett. 22, 386 (1973).
[CrossRef]

Baumgärtner, S.

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Liquid Crystal, 2nd ed. (Cambridge, 1992).
[CrossRef]

Chen, C.-Y.

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

Dawson, P.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, 1983).

Exter, M. V.

Fattinger, C.

Feldmann, J.

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Ferguson, B.

B. Ferguson and X.-C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Grischkowsky, D.

Hangyo, M.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison Wesley-Longman, 1998).

Hecker, N. E.

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Hein, G.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

Hempel, M.

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Hsieh, C.-F.

C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, Opt. Express 13, 3921 (2005).
[CrossRef] [PubMed]

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

Kahn, F. J.

F. J. Kahn, Appl. Phys. Lett. 22, 386 (1973).
[CrossRef]

Keiding, S. R.

Kersting, R.

R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
[CrossRef]

Kleine-Ostmann, T.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

Koch, M.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Lackner, A. M.

K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
[CrossRef]

Lagerwall, S. T.

K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[CrossRef]

Libon, I. H.

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Lim, K. C.

K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
[CrossRef]

Lin, Y.-F.

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

Margerum, J. D.

K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
[CrossRef]

Mittleman, D.

D. Mittleman, Sensing with THz Radiation (Springer, 2002).

Miyamaru, F.

Pan, C.-L.

C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, Opt. Express 13, 3921 (2005).
[CrossRef] [PubMed]

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

Pan, R.-P.

C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, Opt. Express 13, 3921 (2005).
[CrossRef] [PubMed]

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

Pierz, K.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, 1983).

Skarp, K.

K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[CrossRef]

Stebler, B.

K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[CrossRef]

Strasser, G.

R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
[CrossRef]

Tanaka, M.

Tani, M.

Tsai, T.-R.

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

Unterrainer, K.

R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
[CrossRef]

Wang, C.-H.

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

Zhang, X.-C.

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003).
[CrossRef] [PubMed]

B. Ferguson and X.-C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, Appl. Phys. Lett. 84, 3555 (2004).
[CrossRef]

K. C. Lim, J. D. Margerum, and A. M. Lackner, Appl. Phys. Lett. 62, 1065 (1993).
[CrossRef]

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, Appl. Phys. Lett. 83, 4497 (2003).
[CrossRef]

F. J. Kahn, Appl. Phys. Lett. 22, 386 (1973).
[CrossRef]

Electron. Lett. (1)

R. Kersting, G. Strasser, and K. Unterrainer, Electron. Lett. 36, 1156 (2000).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wirel. Compon. Lett. 14, 77 (2004).
[CrossRef]

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

Mol. Cryst. Liq. Cryst. (2)

K. Skarp, S. T. Lagerwall, and B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[CrossRef]

R.-P. Pan, T.-R. Tsai, C.-Y. Chen, C.-H. Wang, and C.-L. Pan, Mol. Cryst. Liq. Cryst. 409, 137 (2004).
[CrossRef]

Nat. Mater. (1)

B. Ferguson and X.-C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Opt. Express (2)

C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, Opt. Express 12, 2630 (2004).

C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, Opt. Express 13, 3921 (2005).
[CrossRef] [PubMed]

Other (4)

E. Hecht, Optics, 3rd ed. (Addison Wesley-Longman, 1998).

D. Mittleman, Sensing with THz Radiation (Springer, 2002).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, 1983).

S. Chandrasekhar, Liquid Crystal, 2nd ed. (Cambridge, 1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic drawing of the electrically switched NLC λ 4 plate. The THz wave propagation and polarization directions are z and y, respectively.

Fig. 2
Fig. 2

Temporal waveforms of the THz pulse transmitted through the NLC cell at various driving voltages. The inset is the closeup from 14 to 16 ps .

Fig. 3
Fig. 3

Phase shift as a function of driving voltage for four frequencies. The solid curves are from the theoretical prediction.

Fig. 4
Fig. 4

Transmittance of the device as it was rotated about the THz beam propagation axis. The solid curve is the transmittance for an ideal λ 4 plate.

Equations (4)

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

δ ( V ) = 0 d 2 π f c Δ n eff ( V , z ) d z ,
Δ n eff = ( cos 2 θ n o 2 + sin 2 θ n e 2 ) 1 2 n o ,
z d = V th π V 0 θ ( 1 + q sin 2 θ sin 2 θ m sin 2 θ ) 1 2 d θ ,
V V th = 2 π 0 θ m ( 1 + q sin 2 θ sin 2 θ m sin 2 θ ) 1 2 d θ .

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