Abstract

The manipulation of the polarization properties of light in guided media is crucial in many classical and quantum optical systems. However, the capability of current technology to finely define the state of polarization of particular wavelengths is far from the level of maturity in amplitude control. Here, we introduce a light-by-light polarization control mechanism with wavelength selectivity based on the change of the phase retardance by means of stimulated Brillouin scattering. Experiments show that any point on the Poincaré sphere can be reached from an arbitrary input state of polarization with little variation of the signal amplitude (<2.5  dB). Unlike other Brillouin processing schemes, the degradation of the noise figure is small (1.5 dB for a full 2π rotation). This all-optical polarization controller can forge the development of new polarization-based techniques in optical communication, laser engineering, sensing, quantum systems, and light-based probing of chemical and biological systems.

© 2020 Chinese Laser Press

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References

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2018 (1)

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

2017 (2)

2014 (1)

2013 (1)

2012 (3)

2011 (2)

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

2010 (1)

2009 (2)

2008 (3)

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

2006 (1)

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett. 18, 208–210 (2006).
[Crossref]

2001 (1)

2000 (1)

1998 (1)

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[Crossref]

1991 (1)

F. Heismann and M. S. Whalen, “Broadband reset-free automatic polarisation controller,” Electron. Lett. 27, 377–379 (1991).
[Crossref]

Astar, W.

Bao, X.

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[Crossref]

Barozzi, M.

Bennink, R. S.

Botvinick, E.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Bowman, R.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Boyd, R. W.

Carter, G. M.

Casas-Bedoya, A.

Chao Chen, C. L.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Chaudhari, C.

Chen, L.

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[Crossref]

Chen, M. C.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Chenato, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

Chin, S.

Choi, D. Y.

Cirigliano, M.

DeLong, A.

Derickson, D.

D. Derickson, Fiber Optica Test and Measurement (Prentice Hall, 1998), Chap. 6.

Eggleton, B. J.

Eyal, A.

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

Fang, Y. Q.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Fatome, J.

Ferrario, M.

Fisher, R. A.

Galtarossa, A.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

Heebner, J. E.

Heismann, F.

F. Heismann and M. S. Whalen, “Broadband reset-free automatic polarisation controller,” Electron. Lett. 27, 377–379 (1991).
[Crossref]

Huang, H. L.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Jiang, X.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Keen, S.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Kito, C.

Koch, B.

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

Kozlov, V. V.

Lahoz, F. J.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett. 18, 208–210 (2006).
[Crossref]

Lantz, E.

Leach, J.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Li, L.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Li, W.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Liao, M.

Liu, N. L.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Liu, Y.

Loayssa, A.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett. 18, 208–210 (2006).
[Crossref]

Lu, C. Y.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Luo, Y. H.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Luther-Davies, B.

Madden, S. J.

Mahmood, T.

Maillote, H.

Marazzi, L.

Marpaung, D.

Martelli, P.

Martinelli, M.

Matsumoto, M.

Menyuk, C. R.

Millot, G.

Mirvoda, V.

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

Misumi, T.

Mitchell, A.

Morin, P.

Morrison, B.

Nguyen, D. M.

Nguyen, T. G.

Noé, R.

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

Nuño, J.

Ohishi, Y.

Padgett, M.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Pagani, M.

Palmieri, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

Pan, J. W.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Pitois, S.

Preece, D.

D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express. 16, 15897–15902 (2008).
[Crossref]

Primerov, N.

Qin, G.

Ren, G.

Rogers, A.

A. Rogers, Polarization in Optical Fibers (Artech House, 2008).

Sandel, D.

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

Santagiustina, M.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

Shmilovitch, Z.

Stiller, B.

Su, Z. E.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Suzuki, T.

Sylvestre, T.

Thevenaz, L.

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

Tur, M.

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

Ursini, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

Vannucci, A.

Vidal, B.

Vu, K.

Wabnitz, S.

Wang, X. L.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Whalen, M. S.

F. Heismann and M. S. Whalen, “Broadband reset-free automatic polarisation controller,” Electron. Lett. 27, 377–379 (1991).
[Crossref]

Yan, X.

Yao, X. S.

X. S. Yao, “Fiber squeezer polarization controller with low activation loss,” US patentUS6480637 (November12, 2002).

X. S. Yao, “Fiber devices based on fiber squeezer polarization controllers,” US patentUS6493474 (December10, 2002).

Zadok, A.

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

Zarifi, A.

Zhang, J.

X. L. Wang, Y. H. Luo, H. L. Huang, M. C. Chen, Z. E. Su, C. L. Chao Chen, W. Li, Y. Q. Fang, X. Jiang, J. Zhang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Zilka, E.

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

Electron. Lett. (2)

F. Heismann and M. S. Whalen, “Broadband reset-free automatic polarisation controller,” Electron. Lett. 27, 377–379 (1991).
[Crossref]

B. Koch, R. Noé, V. Mirvoda, and D. Sandel, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47, 813–814 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett. 18, 208–210 (2006).
[Crossref]

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Chenato, and L. Ursini, “Polarized Brillouin amplification in randomly birefringent and unidirectionally spun fibers,” IEEE Photon. Technol. Lett. 20, 1420–1422 (2008).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[Crossref]

Opt. Express (8)

M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17, 947–955 (2009).
[Crossref]

M. Liao, C. Chaudhari, G. Qin, X. Yan, C. Kito, T. Suzuki, Y. Ohishi, M. Matsumoto, and T. Misumi, “Fabrication and characterization of a chalcogenide tellurite composite microstructure fiber with high nonlinearity,” Opt. Express 17, 21608–21614 (2009).
[Crossref]

J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express 18, 15311–15317 (2010).
[Crossref]

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[Crossref]

A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21602–21707 (2008).
[Crossref]

M. Pagani, D. Marpaung, D. Y. Choi, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Tunable wideband microwave photonic phase shifter using on-chip stimulated Brillouin scattering,” Opt. Express 22, 28810–28818 (2014).
[Crossref]

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[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. (a) Concept of the nonlinear polarization controller based on two independently controlled variable elements: a circular retarder and a linear retarder. The SOP of an incoming optical signal at f0 with, for example, linear polarization at 45º (Jones vector [1/2(1,1)]T) is altered by a pair of pump signals, gain and loss, respectively, at f0fp and f0+fp with circular polarization for the circular retarder, and a second pair of pump at f0fp and f0+fp with linear polarization for the linear retarder. Inset: phase response of the all-optical polarization-dependent SBS all-pass filter. (b) Magnitude of the frequency response of the all-optical polarization-dependent SBS all-pass filter. Combined gain + loss response (green), natural SBS gain response (blue solid), and loss response (blue dotted). (c) Polarization rotation on the Poincaré sphere for the ideal circular retarder. (d) Polarization rotation on the Poincaré sphere for the ideal linear retarder.
Fig. 2.
Fig. 2. Block diagram of a nonlinear all-optical polarization controller made of one circular retarder plus one linear retarder. HNLF, highly nonlinear fiber; OC, optical circulator; ISO, isolator; VOA, variable optical attenuator; PC, polarization controller; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; PA, polarization analyzer.
Fig. 3.
Fig. 3. Experimental results for a 0.16 mW input signal with linear polarization at 45º (Jones vector [1/2(1,1)]T). (a) (Left) Retardance induced as a function of pump power for the circular retarder: experiment (solid orange) and theory (dotted orange); (right) evolution of the signal degree of polarization (DOP) for the circular retarder as a function of pump power. (b) Poincaré sphere representation of the evolution of the output signal polarization over a circular retarder for an input signal. (c) Rotation of the signal SOP induced by the Brillouin-based circular and linear retarders.
Fig. 4.
Fig. 4. (a) (Left) Retardance induced as a function of pump power for the circular (blue solid) and linear (red solid) retarders for input signal with linear SOP at 45º (Jones vector [1/2(1,1)]T). (Right) Variation of the output signal power versus pump power. (b) Sphere’s rotation angle for input signal with ellipticity of ±0.5 (Jones vector [1/2(1,ejπ4)]T, [1/2(1,ejπ4)]T). (c) Control of the retardance bandwidth; (blue) single pump configuration; (red) multitone pump configuration. (d) Comparison of the change of the noise figure for the proposed method (blue) and polarization pulling (orange).
Fig. 5.
Fig. 5. Retardance versus pump power for a Brillouin circular retarder for signals of 0.63 mW (dotted black), 0.16 mW (dotted red), 0.08 mW (dotted green), and 0.04 mW (dotted blue).
Fig. 6.
Fig. 6. Variation of the insertion loss of the polarization controller as a function of pump power for signals with different input power at the HNLF.
Fig. 7.
Fig. 7. Temporal stability of the signal SOP at the output of the polarization controller. (a) Stokes parameters of the signal output with linear SOP at 135° as a function of time: S1 (blue solid curve), S2 (red solid curve), and S3 (yellow solid curve). Stokes parameters are normalized to S0. (b) (Red) signal SOP without SBS; (blue) signal SOP with SBS polarization conversion.
Fig. 8.
Fig. 8. Block diagram of a nonlinear all-optical polarization controller used to measure noise. HNLF, highly nonlinear fiber; OC, optical circulator; ISO, isolator; VOA, variable optical attenuator; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; PA, polarization analyzer; ES, electrical spectrum analyzer; VNA, vector network analyzer.

Tables (1)

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Table 1. Standard Deviation of Stokes Parameters from Fig. 7(a)

Equations (5)

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φmax/min=ζg0PpLeff2AeffΔvB(fpυB)(fpυB)2+(ΔvB2)2,
Γ=2φmax2φmin=g0PpLeff3AeffΔvB(fpυB)(fpυB)2+(ΔvB2)2.
JSBS=M2M1=(GminAmin·[cos(Γ22)jsin(Γ22)·cos(2δ)]GmaxAmax·jsin(Γ22)·sin(2δ)GminAmin·jsin(Γ22)·sin(2δ)GmaxAmax·[cos(Γ22)jsin(Γ22)·cos(2δ)])(GminAmincos(Γ1/2)GmaxAmaxsin(Γ1/2)GminAminsin(Γ1/2)GmaxAmaxcos(Γ1/2)),
SP(f)=SESA(f)|meaSESA(f)|thSESA(f)|calRINcal(f)Pcal22qimeaR2[W2Hz].
NF=PsSP(f)+2GPshv2hvGPs2,