Abstract

We present pigtailed electro-optic probes that allow a simultaneous measurement of high frequency electric fields and temperature using a unique laser probe beam. This has been achieved by the development of a novel probe design associated with a fully automated servo-controlled optical bench, initially developed to stabilize the electric field sensor response. The developed electro-optic probes present a stable response in outdoors conditions over a time duration exceeding 1h, a frequency bandwidth from kHz to tens of GHz with a sensitivity of 0.7Vm1Hz1/2, and a temperature accuracy of 40mK.

© 2008 Optical Society of America

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  1. W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
    [CrossRef]
  2. S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
    [CrossRef]
  3. G. Zheng, J. Xu, L. Chen, H. Wang, and W. She, “Athermal design for the potassium titanyl phosphate electro-optical modulator,” Appl. Opt. 46, 6774-6778 (2007).
    [CrossRef] [PubMed]
  4. R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.
  5. M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
    [CrossRef]
  6. V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
    [CrossRef]
  7. R. Claverie, J.-P. Salvestrini, and M. D. Fontana, “New electro-optic sensor architecture for temperature measurements,” presented at the Instrumentation and Measurement Technology Conference, Warsaw, Poland, 1-3 May 2007.
  8. B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
    [CrossRef]
  9. G. C. Baldwin, An Introduction to Non Linear Optics (Plenum, 1969).
    [CrossRef]
  10. B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79-93 (1986).
    [CrossRef]
  11. K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
    [CrossRef]
  12. L. Levi, Applied Optics (Wiley & Sons, 1980), Vol. 2.
  13. R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).
  14. L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric-field measurements. I. Theoretical comparison among different modulation techniques,” J. Opt. Soc. Am. B 19, 2692-2703 (2002).
    [CrossRef]
  15. L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric-field measurements. II. Choice of the crystals and complete optimization of their orientation,” J. Opt. Soc. Am. B 19, 2704-2715 (2002).
    [CrossRef]
  16. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
    [CrossRef]
  17. L. Duvillaret and G. Gaborit, “Sonde électro-optique de mesure de température et de champ électromagnétique,” French patent deposit 06-52156 (2006).
  18. G. Gaborit, J.-L. Coutaz, and L. Duvillaret, “Vectorial electric field measurement using isotropic electro-optic crystals,” Appl. Phys. Lett. 90, 241118 (2007).
    [CrossRef]
  19. K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalate,” J. Appl. Phys. 80, 6561-6563 (1996).
    [CrossRef]

2007

G. Zheng, J. Xu, L. Chen, H. Wang, and W. She, “Athermal design for the potassium titanyl phosphate electro-optical modulator,” Appl. Opt. 46, 6774-6778 (2007).
[CrossRef] [PubMed]

G. Gaborit, J.-L. Coutaz, and L. Duvillaret, “Vectorial electric field measurement using isotropic electro-optic crystals,” Appl. Phys. Lett. 90, 241118 (2007).
[CrossRef]

2006

L. Duvillaret and G. Gaborit, “Sonde électro-optique de mesure de température et de champ électromagnétique,” French patent deposit 06-52156 (2006).

2004

M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
[CrossRef]

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

2002

2001

B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
[CrossRef]

2000

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
[CrossRef]

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

1996

K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalate,” J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

1995

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).

1991

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

1986

B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79-93 (1986).
[CrossRef]

1980

L. Levi, Applied Optics (Wiley & Sons, 1980), Vol. 2.

1969

G. C. Baldwin, An Introduction to Non Linear Optics (Plenum, 1969).
[CrossRef]

Abe, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Abedin, K. S.

K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalate,” J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

Achkar, J.

B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
[CrossRef]

Baldwin, G. C.

G. C. Baldwin, An Introduction to Non Linear Optics (Plenum, 1969).
[CrossRef]

Barmenkov, Y. O.

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

Baum, C. E.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

Bloom, D. M.

B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79-93 (1986).
[CrossRef]

Chen, L.

Claverie, R.

R. Claverie, J.-P. Salvestrini, and M. D. Fontana, “New electro-optic sensor architecture for temperature measurements,” presented at the Instrumentation and Measurement Technology Conference, Warsaw, Poland, 1-3 May 2007.

Coutaz, J.-L.

Duvillaret, L.

G. Gaborit, J.-L. Coutaz, and L. Duvillaret, “Vectorial electric field measurement using isotropic electro-optic crystals,” Appl. Phys. Lett. 90, 241118 (2007).
[CrossRef]

L. Duvillaret and G. Gaborit, “Sonde électro-optique de mesure de température et de champ électromagnétique,” French patent deposit 06-52156 (2006).

L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric-field measurements. II. Choice of the crystals and complete optimization of their orientation,” J. Opt. Soc. Am. B 19, 2704-2715 (2002).
[CrossRef]

L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric-field measurements. I. Theoretical comparison among different modulation techniques,” J. Opt. Soc. Am. B 19, 2692-2703 (2002).
[CrossRef]

Dyott, R. B.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).

Filippov, V. N.

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

Fontana, M. D.

R. Claverie, J.-P. Salvestrini, and M. D. Fontana, “New electro-optic sensor architecture for temperature measurements,” presented at the Instrumentation and Measurement Technology Conference, Warsaw, Poland, 1-3 May 2007.

Forber, R.

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

Gaborit, G.

G. Gaborit, J.-L. Coutaz, and L. Duvillaret, “Vectorial electric field measurement using isotropic electro-optic crystals,” Appl. Phys. Lett. 90, 241118 (2007).
[CrossRef]

L. Duvillaret and G. Gaborit, “Sonde électro-optique de mesure de température et de champ électromagnétique,” French patent deposit 06-52156 (2006).

Huang, M.-S.

M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
[CrossRef]

Ito, H.

K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalate,” J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

Katehi, L. P. B.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
[CrossRef]

Kishi, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Kolner, B. H.

B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79-93 (1986).
[CrossRef]

Levi, L.

L. Levi, Applied Optics (Wiley & Sons, 1980), Vol. 2.

Lu, M.-H.

M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
[CrossRef]

Makarov, V. V.

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

Mellouet, B.

B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
[CrossRef]

Nitsch, D.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

Ohara, T.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Prather, W. D.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

Rialland, S.

Sabath, F.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

Salvestrini, J.-P.

R. Claverie, J.-P. Salvestrini, and M. D. Fontana, “New electro-optic sensor architecture for temperature measurements,” presented at the Instrumentation and Measurement Technology Conference, Warsaw, Poland, 1-3 May 2007.

Schultz, S.

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

Selfridge, R.

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

She, W.

Shy, J.-T.

M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
[CrossRef]

Starodumov, A. N.

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

Torres, R. J.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

Tsuchiya, M.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Velasco, L.

B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
[CrossRef]

Wakana, S.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Wang, H.

Wang, W. C.

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

Whitaker, J. F.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
[CrossRef]

Xu, J.

Yamazaki, E.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

Yang, K.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
[CrossRef]

Zang, D.-Y.

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

Zheng, G.

Appl. Opt.

G. Zheng, J. Xu, L. Chen, H. Wang, and W. She, “Athermal design for the potassium titanyl phosphate electro-optical modulator,” Appl. Opt. 46, 6774-6778 (2007).
[CrossRef] [PubMed]

V. N. Filippov, A. N. Starodumov, Y. O. Barmenkov, and V. V. Makarov, “Fiber-optic voltage sensor based on a Bi12TiO20 crystal,” Appl. Opt. 9, 1389-1393 (2000).
[CrossRef]

Appl. Phys. Lett.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486-488 (2000).
[CrossRef]

G. Gaborit, J.-L. Coutaz, and L. Duvillaret, “Vectorial electric field measurement using isotropic electro-optic crystals,” Appl. Phys. Lett. 90, 241118 (2007).
[CrossRef]

IEEE J. Quantum Electron.

B. H. Kolner and D. M. Bloom, “Electro-optic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79-93 (1986).
[CrossRef]

IEEE Trans. Electromag. Compat.

W. D. Prather, C. E. Baum, R. J. Torres, F. Sabath, and D. Nitsch, “Survey of worldwide high-power wideband capabilities,” IEEE Trans. Electromag. Compat. 46, 335-344 (2004).
[CrossRef]

IEEE Trans. Instrum. Meas.

B. Mellouet, L. Velasco, and J. Achkar, “Fast method applied to the measurement of microwave power standards,” IEEE Trans. Instrum. Meas. 50, 381-384 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiber-edge electrooptic/magnetooptic probe for spectral-domain analysis of electromagnetic field,” IEEE Trans. Microwave Theory Tech. 48, 2611-2616 (2000).
[CrossRef]

J. Appl. Phys.

K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalate,” J. Appl. Phys. 80, 6561-6563 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Rev. Sci. Instrum.

M.-S. Huang, M.-H. Lu, and J.-T. Shy, “High sensitivity bulk electro-optic modulator field sensor for high voltage environments,” Rev. Sci. Instrum. 75, 5364-5366 (2004).
[CrossRef]

Other

L. Levi, Applied Optics (Wiley & Sons, 1980), Vol. 2.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

L. Duvillaret and G. Gaborit, “Sonde électro-optique de mesure de température et de champ électromagnétique,” French patent deposit 06-52156 (2006).

R. Forber, W. C. Wang, D.-Y. Zang, S. Schultz, and R. Selfridge, “Dielectric EM field probes for HPM test & evaluation,” presented at the Annual ITEA Technology Review, Cambridge, United Kingdom, 7-10 August 2007.

G. C. Baldwin, An Introduction to Non Linear Optics (Plenum, 1969).
[CrossRef]

R. Claverie, J.-P. Salvestrini, and M. D. Fontana, “New electro-optic sensor architecture for temperature measurements,” presented at the Instrumentation and Measurement Technology Conference, Warsaw, Poland, 1-3 May 2007.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: PD, photodiode; LD, laser diode; BS, nonpolarizing beam splitter; EO, electro-optic.

Fig. 2
Fig. 2

Schematic and picture (inset) of the EO probe with indication of the relative orientations of the eigen dielectric axes of the probe optical elements.

Fig. 3
Fig. 3

Single shot vertically polarized high power microwave signal measurement obtained with (a) a reference antenna, (b) the EO probe having its sensitivity vector Δ K vertically aligned, and (c) the EO probe having its sensitivity vector Δ K horizontally aligned (an artificial offset has been added for clarity).

Fig. 4
Fig. 4

Spectra of the single shot high power microwave signal (see Fig. 3) measured with a reference antenna (dotted line), the EO probe having its sensitivity vector Δ K vertically aligned (solid line), and the EO probe having its sensitivity vector Δ K horizontally aligned (dots).

Fig. 5
Fig. 5

Temporal record of the orientations of the two servo- controlled wave plates Q1 and H1 used to lock the optical system on an optimal working point during the cool down of the EO probe.

Fig. 6
Fig. 6

Folded (solid curve) and unfolded (dotted line) dephasing ϕ 0 introduced between the two eigenpolarization states inside the EO crystal during its cool down and calculated from the wave plates orientations given in Fig. 5.

Fig. 7
Fig. 7

Temperature of the EO probe calculated from the dephasing ϕ 0 plotted in Fig. 6 (solid curve) and simultaneously measured with a thermocouple (crosses). A theoretical adjustment of the EO probe temperature is also represented in dotted curve.

Equations (9)

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

P 1 2 = P inc 2 ( 1 ± ϕ E ) = P inc 2 ( 1 ± 2 π Δ K E L eff λ ) ,
M probe = M λ / 4 · R - α · ( exp ( - j Δ ϕ / 2 ) 0 0 exp ( j Δ ϕ / 2 ) ) · R α · M λ / 4 ,
M P M F = ( exp ( - j θ / 2 ) 0 0 exp ( j θ / 2 ) ) .
M system = R - φ H 1 · R λ / 2 · R φ H 1 - φ Q 1 · R λ / 4 · R φ Q 1 · M PMF · R - π / 4 · M probe · R π / 4 · M PMF .
( P 1 P 2 ) | M system . ( 0 1 ) | 2 .
P 1 2 = 1 2 { 1 ± ( cos 2 φ Q 1 cos Δ ϕ + sin ( 2 α + θ ) sin 2 φ Q 1 sin Δ ϕ ) cos ( 4 φ H 1 2 φ Q 1 ) ± cos ( 2 α + θ ) sin Δ ϕ sin ( 4 φ H 1 2 φ Q 1 ) } .
φ Q 1 = 1 2 arccos ( δ sin ϕ 0 1 cos 2 ( 2 α + θ ) cos 2 ϕ 0 ) , φ H 1 = 1 4 { 2 φ Q 1 + arctan ( cos ( 2 α + θ ) , cos 2 φ Q 1 tan ϕ 0 + sin ( 2 α + θ ) sin 2 φ Q 1 ) } ,
θ = arctan ( tan ( 4 φ H 1 - 2 φ Q 1 ) , sin 2 φ Q 1 ) - 2 α , ϕ 0 = Ψ sgn ( φ H 1 π 8 + Ψ 4 ) , with Ψ = arctan ( tan 2 ( 4 φ H 1 2 φ Q 1 ) + sin 2 2 φ Q 1 , cos 2 φ Q 1 ) ,
Δ n T = λ 2 π L crystal ϕ 0 T .

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