Abstract

Modulating signal with polarization modulator (PolM) is the simplest method for polarization shift keying (PolSK) in free space optical communication. However, this method has an intrinsic drawback on degree of polarization (DOP) reduction for the existence of polarization mode dispersion (PMD) in PolM. In this work, we analyze this change of DOP and its influence on PolSK using coherency matrix. We demonstrate that the decrease of DOP after PolM will generate extra loss and bit error ratio (BER) for PolSK communication, while this loss and BER will aggravate with the increase of laser linewidth and PolM length. For a practical PolSK system, laser linewidth should be less than 0.008nm.

© 2015 Optical Society of America

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References

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  1. S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
    [Crossref]
  2. S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
    [Crossref]
  3. J. Zhang, S. Ding, H. Zhai, and A. Dang, “Theoretical and experimental studies of polarization fluctuations over atmospheric turbulent channels for wireless optical communication systems,” Opt. Express 22(26), 32482–32488 (2014).
    [Crossref] [PubMed]
  4. X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Condition for Gaussian Schell-model beam to maintain the state of polarization on the propagation in free space,” Opt. Express 17(20), 17888–17894 (2009).
    [Crossref] [PubMed]
  5. W. C. Cox, B. L. Hughes, and J. F. Muth, “A polarization shift-keying system for underwater optical communication,” in proceedings of IEEE OCEANS 2009, MTS/IEEE Biloxi - Marine Technology for Our Future: Global and Local Challenges (IEEE, 2009), pp. 1–4.
  6. S. Trisno and C. C. Davis, “Performance of free space optical communication systems using polarization shift keying modulation,” Proc. SPIE 6304, 63040V (2006).
    [Crossref]
  7. X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
    [Crossref]
  8. X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with direct detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009).
    [Crossref]
  9. J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
    [Crossref]
  10. H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).
  11. K. Mochizuki, “Degree of polarization in jointed fibers: the Lyot depolarizer,” Appl. Opt. 23(19), 3284–3288 (1984).
    [Crossref] [PubMed]
  12. M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
    [Crossref]
  13. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999), Chap. 10.
  14. J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
    [Crossref]
  15. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [Crossref]
  16. U. Schlarb and K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B Condens. Matter 48(21), 15613–15620 (1993).
    [Crossref] [PubMed]
  17. D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
    [Crossref]
  18. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
    [Crossref]
  19. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997).
    [Crossref] [PubMed]
  20. M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
    [Crossref]
  21. J. G. Proakis and M. Salehi, Digital Communications, 5th expanded ed. (McGraw-Hill Higher Education, 2007), Chap. 4.
  22. Photline Technologies, “Polarization Switches,” http://www.photline.com/product/Modulators//Polarization_Switches/

2014 (1)

2013 (1)

M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
[Crossref]

2009 (2)

2008 (1)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

2007 (1)

H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).

2006 (2)

S. Trisno and C. C. Davis, “Performance of free space optical communication systems using polarization shift keying modulation,” Proc. SPIE 6304, 63040V (2006).
[Crossref]

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

2004 (1)

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

1997 (1)

1995 (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

1993 (1)

U. Schlarb and K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B Condens. Matter 48(21), 15613–15620 (1993).
[Crossref] [PubMed]

1992 (1)

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[Crossref]

1984 (2)

K. Mochizuki, “Degree of polarization in jointed fibers: the Lyot depolarizer,” Appl. Opt. 23(19), 3284–3288 (1984).
[Crossref] [PubMed]

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

1982 (1)

J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
[Crossref]

1976 (1)

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
[Crossref]

1966 (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[Crossref]

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

Benedetto, S.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[Crossref]

Betzler, K.

U. Schlarb and K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B Condens. Matter 48(21), 15613–15620 (1993).
[Crossref] [PubMed]

Bull, J. D.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Buller, G. S.

H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).

Dang, A.

Davis, C. C.

S. Trisno and C. C. Davis, “Performance of free space optical communication systems using polarization shift keying modulation,” Proc. SPIE 6304, 63040V (2006).
[Crossref]

Ding, S.

Domanski, A. W.

M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
[Crossref]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Edwin, R. P.

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
[Crossref]

Fairburn, M.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

Gaudino, R.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

Ghanipour, P.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Gordeev, H. Y.

H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).

Gordon, K. J.

H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).

Hobden, M. V.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[Crossref]

Jaeger, N. A. F.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Jundt, D. H.

Kato, H.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Kimura, T.

J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
[Crossref]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Liao, C.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Liu, C.

Liu, S.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Liu, X.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Lu, Y.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Machida, S.

J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
[Crossref]

Makowski, P. L.

M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
[Crossref]

Mochizuki, K.

Poggiolini, P.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[Crossref]

Redek, M.

M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
[Crossref]

Reid, A.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

Riccius, H. D.

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
[Crossref]

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

Sakai, J.

J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
[Crossref]

Schlarb, U.

U. Schlarb and K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B Condens. Matter 48(21), 15613–15620 (1993).
[Crossref] [PubMed]

Smith, D. S.

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
[Crossref]

Sun, Y.

Tang, Z.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Trisno, S.

S. Trisno and C. C. Davis, “Performance of free space optical communication systems using polarization shift keying modulation,” Proc. SPIE 6304, 63040V (2006).
[Crossref]

Warner, J.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[Crossref]

Yao, Y.

Zhai, H.

Zhang, J.

Zhao, F.

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Zhao, X.

Appl. Opt. (1)

Appl. Phys. B-Lasers. (1)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B-Lasers. 91(2), 343–348 (2008).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Sakai, S. Machida, and T. Kimura, “Degree of polarization in anisotropic single-mode optical fiber: theory,” IEEE J. Quantum Electron. 18(4), 488–495 (1982).
[Crossref]

IEEE J. Sel. Areas Comm. (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct Detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

IEEE Trans. Commun. (1)

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[Crossref]

J. Opt. Commun. Netw. (1)

J. OPTICS-UK (1)

M. Redek, P. L. Makowski, and A. W. Domanski, “Influence of ambient temperature variations on the performance of Lyot depolarizers,” J. OPTICS-UK 15(10), 105704 (2013).
[Crossref]

Opt. Commun. (2)

H. Y. Gordeev, K. J. Gordon, and G. S. Buller, “Tunable electro-optic polarization modulator for quantum key distribution applications,” Opt. Commun. 234(1–6), 203–210 (2007).

D. S. Smith, H. D. Riccius, and R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17(3), 332–335 (1976).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Phys. Lett. (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[Crossref]

Phys. Lett. A (1)

X. Liu, Z. Tang, C. Liao, Y. Lu, F. Zhao, and S. Liu, “Polarization states encoded by phase modulation for high bit rate quantum key distribution,” Phys. Lett. A 358(5-6), 386–389 (2006).
[Crossref]

Phys. Rev. B Condens. Matter (1)

U. Schlarb and K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B Condens. Matter 48(21), 15613–15620 (1993).
[Crossref] [PubMed]

Proc. SPIE (2)

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communication systems,” Proc. SPIE 5577, 133–143 (2004).
[Crossref]

S. Trisno and C. C. Davis, “Performance of free space optical communication systems using polarization shift keying modulation,” Proc. SPIE 6304, 63040V (2006).
[Crossref]

Other (4)

W. C. Cox, B. L. Hughes, and J. F. Muth, “A polarization shift-keying system for underwater optical communication,” in proceedings of IEEE OCEANS 2009, MTS/IEEE Biloxi - Marine Technology for Our Future: Global and Local Challenges (IEEE, 2009), pp. 1–4.

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999), Chap. 10.

J. G. Proakis and M. Salehi, Digital Communications, 5th expanded ed. (McGraw-Hill Higher Education, 2007), Chap. 4.

Photline Technologies, “Polarization Switches,” http://www.photline.com/product/Modulators//Polarization_Switches/

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of PolSK modulation using two orthogonal linearly polarized lasers.

Fig. 2
Fig. 2

Schematic diagram of PolSK modulation using phase modulator.

Fig. 3
Fig. 3

Schematic diagram of PolSK system using polarization modulator.

Fig. 4
Fig. 4

DOP of PolSK signal and depolarization loss versus laser linewidth.

Fig. 5
Fig. 5

BER versus laser linewidth.

Fig. 6
Fig. 6

DOP of PolSK signal versus PolM length.

Fig. 7
Fig. 7

Depolarization loss versus PolM length.

Fig. 8
Fig. 8

BERversus PolM length.

Equations (27)

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

J=[ J xx J xy J yx J yy ]=[ E x E x * E x E y * E y E x * E y E y * ]
P= I pol I tot = 1 4detJ tr J 2
E(t)= 1 π 0 υ(ω)exp(jωt)dω
υ(ω)={ E(t)exp(jωt)dt;ω0 0ω<0
E 0 = 1 2 [ E 0 (t) E 0 (t) ]
E 0 (t)= 1 π 0 υ 0 (ω)exp(jωt)dω
I 0 =trJ=tr E 0 · E 0 * = 1 π 2 0 | υ 0 (ω) | 2 dω
E a =[ E x (t) E y (t) ]=[ exp[ jφ(t) ] 2 π 0 υ 0 (ω)exp{ (j(ω ω 0 )[ t( d β x dω )L ] }dω 1 2 π 0 υ 0 (ω)exp{ (j(ω ω 0 )[ t( d β y dω )L ] }dω ]
D=detJ=det E 0 · E 0 * = 1 4 ( I 0 2 | S 1 | 2 )
S 1 = 1 π 2 0 | υ 0 (ω) | 2 exp[ j(ω ω 0 )δ τ g L ]dω
δ τ g = d β x dω d β y dω d[ ( n x n y )| k | ] d(c| k |) = 1 c [ ( n x n y )λ d( n x n y ) dλ ]
P= | S 1 | I 0 =| γ |
| υ 0 (ω) | 2 =exp[ ( ln2 ) ω ω 0 δω ]
δω= 2πc λ 2 δλ
γ=exp[ ( δωδ τ g L 2 ln2 ) 2 ]=exp[ ( πcδλδ τ g L λ 2 ln2 ) 2 ]
P=exp[ ( πcδλδ τ g L λ 2 ln2 ) 2 ]
U= R u ( t FR | E x (t) | 2 t FR | E y (t) | 2 )={ R u ( t FR I 0 0 )=+ R u t FR I 0 =+ R u I R | E x (t) || E y (t) | R u ( 0 t FR I 0 )= R u t FR I 0 = R u I R | E x (t) |<| E y (t) |
B ER = 1 2 erfc( | U | 2 σ n )= 1 2 erfc( S N 2 )
erfc(z)= 2 π z exp( t 2 )dt
U dep ={ R u { [ P I R + (1P) I R 2 ] (1P) 2 I R }=+P| U |,| E x (t) || E y (t) | R u { (1P) 2 I R [ P I R + (1P) I R 2 ] }=P| U |,| E x (t) |<| E y (t) |
L dep = U U dep U =1P
B ERd = 1 2 erfc( | U dep | 2 σ n )= 1 2 erfc( P S N 2 )
n i = A i1 + A i2 + B i1 (T T 0 )(T+ T 0 +546) λ 2 [ A i3 + B i2 (T T 0 )(T+ T 0 +546) ] 2 + B i3 (T T 0 )(T+ T 0 +546) A i4 λ 2
n x = 4.9048+ 1.1775× 10 13 λ 2 4.7533× 10 14 2.7153× 10 10 λ 2
n x = 4.5820+ 0.9921× 10 13 λ 2 4.4479× 10 14 2.1940× 10 10 λ 2
L OPD =( n x n y )L
L CO = λ 2 δλ

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