Abstract

For optimal sensitivity in electric field measurements, electro-optic (EO) crystals are typically selected based on their EO coefficients and dielectric constants. However, the conventional figure of merit yields sensitivity predictions regarding EO materials that are inconsistent with experimental data. In this Letter, we demonstrate that depolarization effects, which are often ignored, can dramatically enhance responsivity depending on the shape and orientation of the EO crystal. For optimal sensitivity, these effects are best exploited in longitudinal EO sensors, where they yield an optical modulation depth that increases quadratically with crystal length.

© 2012 Optical Society of America

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References

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  1. A. Garzarella, S. B. Qadri, and D. H. Wu, Appl. Phys. Lett. 94, 221113 (2009).
    [CrossRef]
  2. S. Chadderdon, R. Gibson, R. H. Selfridge, S. M. Schultz, W. C. Wang, R. Forber, J. Luo, and A. K. Y. Jen, Appl. Opt. 50, 3505 (2011).
    [CrossRef]
  3. F. Cecelja, M. Bordovsky, and B. Balachandran, in Proceedings of the IEEE Conference on Precision Electromagnetic Measurements (IEEE, 1998), pp. 639–640.
  4. A. Garzarella, S. B. Qadri, D. H. Wu, and R. J. Hinton, Appl. Opt. 46, 6636 (2007).
    [CrossRef]
  5. R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
    [CrossRef]
  6. C. H. Lee, Microwave Photonics (CRC Press, 2007), p. 119.
  7. A. Garzarella, S. B. Qadri, T. J. Wieting, D. H. Wu, and R. J. Hinton, Opt. Lett. 32, 964 (2007).
    [CrossRef]
  8. A. F. Kip, Fundamentals of Electricity and Magnetism, 2nd ed. (McGraw-Hill, 1969), pp. 150–151.
  9. J. Venermo and A. Sihvola, J. Electrostat. 63, 101 (2005).
    [CrossRef]
  10. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, 1971), pp. 224–230.

2011 (1)

2009 (1)

A. Garzarella, S. B. Qadri, and D. H. Wu, Appl. Phys. Lett. 94, 221113 (2009).
[CrossRef]

2007 (2)

2005 (1)

J. Venermo and A. Sihvola, J. Electrostat. 63, 101 (2005).
[CrossRef]

1987 (1)

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Balachandran, B.

F. Cecelja, M. Bordovsky, and B. Balachandran, in Proceedings of the IEEE Conference on Precision Electromagnetic Measurements (IEEE, 1998), pp. 639–640.

Bordovsky, M.

F. Cecelja, M. Bordovsky, and B. Balachandran, in Proceedings of the IEEE Conference on Precision Electromagnetic Measurements (IEEE, 1998), pp. 639–640.

Cecelja, F.

F. Cecelja, M. Bordovsky, and B. Balachandran, in Proceedings of the IEEE Conference on Precision Electromagnetic Measurements (IEEE, 1998), pp. 639–640.

Chadderdon, S.

Clark, W. W.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Cory, W. K.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Forber, R.

Garzarella, A.

Gibson, R.

Hinton, R. J.

Jen, A. K. Y.

Kip, A. F.

A. F. Kip, Fundamentals of Electricity and Magnetism, 2nd ed. (McGraw-Hill, 1969), pp. 150–151.

Lee, C. H.

C. H. Lee, Microwave Photonics (CRC Press, 2007), p. 119.

Luo, J.

Miller, M. J.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Neurgaonkar, R. R.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Oliver, J. R.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Qadri, S. B.

Schultz, S. M.

Selfridge, R. H.

Sharp, E. J.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Sihvola, A.

J. Venermo and A. Sihvola, J. Electrostat. 63, 101 (2005).
[CrossRef]

Venermo, J.

J. Venermo and A. Sihvola, J. Electrostat. 63, 101 (2005).
[CrossRef]

Wang, W. C.

Wieting, T. J.

Wod, G. L.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

Wu, D. H.

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, 1971), pp. 224–230.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Garzarella, S. B. Qadri, and D. H. Wu, Appl. Phys. Lett. 94, 221113 (2009).
[CrossRef]

J. Cryst. Growth (1)

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, W. W. Clark, G. L. Wod, M. J. Miller, and E. J. Sharp, J. Cryst. Growth 84, 629 (1987).
[CrossRef]

J. Electrostat. (1)

J. Venermo and A. Sihvola, J. Electrostat. 63, 101 (2005).
[CrossRef]

Opt. Lett. (1)

Other (4)

A. F. Kip, Fundamentals of Electricity and Magnetism, 2nd ed. (McGraw-Hill, 1969), pp. 150–151.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, 1971), pp. 224–230.

C. H. Lee, Microwave Photonics (CRC Press, 2007), p. 119.

F. Cecelja, M. Bordovsky, and B. Balachandran, in Proceedings of the IEEE Conference on Precision Electromagnetic Measurements (IEEE, 1998), pp. 639–640.

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Figures (3)

Fig. 1.
Fig. 1.

Transients from 5mm×5mm×60mm KD*P and LN sensors placed under a pulsed electric field generated in a TEM cell. Both sensors were biased with 6 mW of laser power at 1550 nm. In spite of its lower EO coefficient and larger dielectric constant, the KD*P sensor yielded a substantially larger signal due to depolarization effects.

Fig. 2.
Fig. 2.

Markers: responsivity data of (a) LN and (b) KD*P sensors as a function of L. Fit 1: theoretical responsivity assuming Eint=Eext/εj, fit 2: theoretical responsivity assuming Eint=Eext/εj. The good agreement between fit 2 and the data indicates depolarization effects in the sensor responsivity.

Fig. 3.
Fig. 3.

Calculated ε3 based on the depolarization factors of the LN and KD*P crystals used in Fig. 2. Minimum and maximum values reflect the thin rod and planar limits illustrated in the inset, respectively. Due to their different orientations in the electric field (longitudinal versus transverse), peak responsivity occurs for large L in KD*P and for small L in LN.

Equations (2)

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ϕEO=πLλΔ(ni3rij)Eint,
εj=1+Njχj,

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