Abstract

We have characterized a two-wave mixing adaptive interferometer based on dc-biased photorefractive CdTe:Ge crystal at 1.06 and 1.55 μm. Excellent performance is shown at both wavelengths by demonstration of high sensitivity for measurement of small displacements and high cutoff frequency at low intensity. We have achieved a considerable reduction of the undesired low-frequency response using controlled heating of the crystal, which ensures depopulation of corresponding traps. The experimental data are used for measurement of the real and imaginary parts of the coupling constant, as well as the dielectric relaxation time of the crystal and the mobility-lifetime product of the free charge carriers.

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  1. P. Delaye, A. Blouin, D. Drolet, L. A. de Montmorillon, G. Roosen, and J. P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B 14, 1723–1734 (1997).
    [CrossRef]
  2. L. A. de Montmorillon, P. Delhaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” in Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, 2002), pp. 213–282.
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  4. A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
    [CrossRef]
  5. K. Shcherbin, “High photorefractive gain at counterpropagating geometry in CdTe:Ge at 1.064 μm and 1.55 μm,” Appl. Opt. 48, 371–374 (2009).
    [CrossRef]
  6. L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
    [CrossRef]
  7. J. Frejlich, Photorefractive Materials (Wiley-Interscience, 2006).
  8. K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
    [CrossRef]
  9. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).
  10. D. T. F. Marple, “Refractive index of ZnSe, ZnTe and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
    [CrossRef]
  11. K. Tada and M. Aoki, “Linear electro-optic properties of ZnTe at 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).
  12. K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
    [CrossRef]
  13. T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
    [CrossRef]
  14. A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
    [CrossRef]
  15. K. Shcherbin and M. B. Klein, “Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm,” Opt. Commun. 282, 2580–2585 (2009).
    [CrossRef]
  16. M. B. Klein and K. Shcherbin, “Optical homodyne interferometer,” U.S. patent 8,149,421 (3April2012).

2010

T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
[CrossRef]

2009

A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
[CrossRef]

K. Shcherbin and M. B. Klein, “Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm,” Opt. Commun. 282, 2580–2585 (2009).
[CrossRef]

K. Shcherbin, “High photorefractive gain at counterpropagating geometry in CdTe:Ge at 1.064 μm and 1.55 μm,” Appl. Opt. 48, 371–374 (2009).
[CrossRef]

2002

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

2001

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

1997

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

P. Delaye, A. Blouin, D. Drolet, L. A. de Montmorillon, G. Roosen, and J. P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B 14, 1723–1734 (1997).
[CrossRef]

1990

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1971

K. Tada and M. Aoki, “Linear electro-optic properties of ZnTe at 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).

1964

D. T. F. Marple, “Refractive index of ZnSe, ZnTe and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
[CrossRef]

Aoki, M.

K. Tada and M. Aoki, “Linear electro-optic properties of ZnTe at 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).

Blouin, A.

Briat, B.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

de Montmorillon, L. A.

P. Delaye, A. Blouin, D. Drolet, L. A. de Montmorillon, G. Roosen, and J. P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B 14, 1723–1734 (1997).
[CrossRef]

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

L. A. de Montmorillon, P. Delhaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” in Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, 2002), pp. 213–282.

Delaye, P.

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

P. Delaye, A. Blouin, D. Drolet, L. A. de Montmorillon, G. Roosen, and J. P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B 14, 1723–1734 (1997).
[CrossRef]

Delaye, Ph.

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

Delhaye, P.

L. A. de Montmorillon, P. Delhaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” in Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, 2002), pp. 213–282.

dos Santos, T. O.

T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
[CrossRef]

Drolet, D.

Farid, B.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

Frejlich, J.

T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
[CrossRef]

J. Frejlich, Photorefractive Materials (Wiley-Interscience, 2006).

Garmire, E. M.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Kamshilin, A. A.

A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).

Klein, M. B.

K. Shcherbin and M. B. Klein, “Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm,” Opt. Commun. 282, 2580–2585 (2009).
[CrossRef]

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

M. B. Klein and K. Shcherbin, “Optical homodyne interferometer,” U.S. patent 8,149,421 (3April2012).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Kulchin, Y. N.

A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
[CrossRef]

Launey, J. C.

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Marple, D. T. F.

D. T. F. Marple, “Refractive index of ZnSe, ZnTe and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
[CrossRef]

Millerd, J.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Monchalin, J. P.

Odoulov, S.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

Odoulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Paivasaari, K.

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

Partovi, A.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Petrov, M. P.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).

Ramaz, F.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

Romashko, R. V.

A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
[CrossRef]

Roosen, G.

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

P. Delaye, A. Blouin, D. Drolet, L. A. de Montmorillon, G. Roosen, and J. P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B 14, 1723–1734 (1997).
[CrossRef]

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

L. A. de Montmorillon, P. Delhaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” in Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, 2002), pp. 213–282.

Shcherbin, K.

T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
[CrossRef]

K. Shcherbin and M. B. Klein, “Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm,” Opt. Commun. 282, 2580–2585 (2009).
[CrossRef]

K. Shcherbin, “High photorefractive gain at counterpropagating geometry in CdTe:Ge at 1.064 μm and 1.55 μm,” Appl. Opt. 48, 371–374 (2009).
[CrossRef]

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

M. B. Klein and K. Shcherbin, “Optical homodyne interferometer,” U.S. patent 8,149,421 (3April2012).

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Steier, W. H.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Stepanov, S. I.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).

Tada, K.

K. Tada and M. Aoki, “Linear electro-optic properties of ZnTe at 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).

Trivedi, S. B.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

von Bardeleben, H. J.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

Ziari, M.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Appl. Opt.

Appl. Phys. B

T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99, 701–707 (2010).
[CrossRef]

Appl. Phys. Lett.

A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μm in CdTe:V,” Appl. Phys. Lett. 57, 846–848 (1990).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

J. Appl. Phys.

D. T. F. Marple, “Refractive index of ZnSe, ZnTe and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
[CrossRef]

A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105, 031101 (2009).
[CrossRef]

L. A. de Montmorillon, Ph. Delaye, J. C. Launey, and G. Roosen, “Novel theoretical aspects on ultrasonic detection and implementation of a sensor with an optimum sensitivity,” J. Appl. Phys. 82, 5913–5922 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

K. Tada and M. Aoki, “Linear electro-optic properties of ZnTe at 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).

Opt. Commun.

K. Paivasaari, A. A. Kamshilin, P. Delaye, and G. Roosen, “Reduction of the space-charge field in photorefractive crystals,” Opt. Commun. 213, 357–366 (2002).
[CrossRef]

K. Shcherbin and M. B. Klein, “Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm,” Opt. Commun. 282, 2580–2585 (2009).
[CrossRef]

Opt. Mater.

K. Shcherbin, S. Odoulov, F. Ramaz, B. Farid, B. Briat, H. J. von Bardeleben, P. Delaye, and G. Roosen, “Charge transfer in photorefractive CdTe:Ge at different wavelengths,” Opt. Mater. 18, 151–154 (2001).
[CrossRef]

Other

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).

J. Frejlich, Photorefractive Materials (Wiley-Interscience, 2006).

M. B. Klein and K. Shcherbin, “Optical homodyne interferometer,” U.S. patent 8,149,421 (3April2012).

L. A. de Montmorillon, P. Delhaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” in Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, 2002), pp. 213–282.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup: M, mirrors; BS, beamsplitter; EOM, electro-optic modulator.

Fig. 2.
Fig. 2.

Amplitude of output intensity modulation ΔI normalized to the average signal intensity ISA as a function of phase-modulation frequency measured at λ=1.06μm (a) and λ=1.55μm (b); Λ=30μm, I=140mW/cm2, and E0=6kV/cm.

Fig. 3.
Fig. 3.

Cutoff frequency as a function of grating spacing measured at λ=1.06μm (squares) and λ=1.55μm (diamonds) with E0=8kV/cm and I=85mK/cm2 for both wavelengths; the solid lines represent the best fit of Eq. (4) to experimental data with τdi=100μs, LE=2.2μm for 1.06 μm and τdi=110μs, LE=2.6μm for 1.55 μm.

Fig. 4.
Fig. 4.

Imaginary coupling constant as a function of applied field measured at λ=1.06μm (squares) and λ=1.55μm (diamonds) for Λ=30μm and I=140mW/cm2; solid lines represent linear fit to experimental dependences.

Fig. 5.
Fig. 5.

Amplitude of the signal intensity modulation normalized to that at high frequencies as a function of phase-modulation frequency measured at different temperatures; λ=1.55μm, Λ=40μm, I=80mW/cm2, and E0=8kV/cm.

Equations (8)

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

ΔI=ΔIsat2πfτSC1+(2πfτSC)2,
fC=1312πτSC.
τSC=τdi(1+K2LD2)2+K2LE2(1+K2LD2),
fC=1312πτdi(1+K2LE2).
IS(t)=IS0exp(αd)[exp(2γd)+2exp(γd)sin(γd)φ(t)],
γ=πn3reffλiE0ED1+ED/EqiE0/Eq,
γ=iπn3reffλE0.
δrel=exp(αd/2)|sin(γd)|.

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