Abstract

We propose an optical isolator based on the electro-optic (EO) effect of periodically poled lithium niobate (PPLN). When the EO effect occurs in PPLN under a TE field, each domain serves as a half-wave plate under the quasi-phase-matching condition, and PPLN shows optical activity similar to quartz. The introduction of an additional half-domain to the normal PPLN changes the incident azimuth angle of the reflected light. As a result, the reflected light does not return to the original polarization state. Thus, the optical rotation accumulates and optical isolation occurs. The isolator can be employed for all linearly polarized light and has the advantage of being used in a weak-light system with low driving voltage and high isolation contrast.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2011 (4)

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Y. Zhang, Y. Chen, and X. Chen, “Polarization-based all-optical logic controlled-NOT, XOR, and XNOR gates employing electro-optic effect in periodically poled lithium niobate,” Appl. Phys. Lett. 99, 161117 (2011).
[CrossRef]

2009 (4)

K. Liu, J. Shi, and L. Chen, “Linear polarization-state generator with high precision in periodically poled lithium niobate,” Appl. Phys. Lett. 94, 101106 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

2007 (5)

2006 (4)

2005 (1)

T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B: Lasers Opt. 80, 193–198 (2005).
[CrossRef]

2003 (3)

2001 (2)

S. Mujumdar and H. Ramachandran, “Use of a graded gain random amplifier as an optical diode,” Opt. Lett. 26, 929–931 (2001).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

2000 (2)

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

1996 (1)

1995 (1)

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

1979 (1)

Alexander, D.

Amemiya, T.

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Baldi, P.

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Bruce Iii, J.

Chan, C. T.

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Chen, L.

K. Liu, J. Shi, and L. Chen, “Linear polarization-state generator with high precision in periodically poled lithium niobate,” Appl. Phys. Lett. 94, 101106 (2009).
[CrossRef]

Chen, X.

Y. Zhang, Y. Chen, and X. Chen, “Polarization-based all-optical logic controlled-NOT, XOR, and XNOR gates employing electro-optic effect in periodically poled lithium niobate,” Appl. Phys. Lett. 99, 161117 (2011).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117(2003).
[CrossRef]

L. Shi, L. Tian, and X. Chen, “Electro-optic chirality control in MgO:PPLN,” arXiv:1204.1174 (2012).

Chen, Y.

Chen, Y. H.

Chen, Y.-F.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Chung, J. S.

T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B: Lasers Opt. 80, 193–198 (2005).
[CrossRef]

Deogun, J.

Dotsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Fujii, A.

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Gevorgyan, A. H.

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

Gong, Q.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Hai, P. N.

Hamza, H.

Harutyunyan, M. Z.

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

Hu, X.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Huang, Y.

Huang, Y. C.

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Kakihara, K.

Kivshar, Y. S.

Koch, B.

Kono, N.

Koshiba, M.

Lan, S.

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

Li, Z.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Lin, X.-S.

Lin, Z.

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Liu, K.

K. Liu, J. Shi, and L. Chen, “Linear polarization-state generator with high precision in periodically poled lithium niobate,” Appl. Phys. Lett. 94, 101106 (2009).
[CrossRef]

Lu, Y.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Lu, Y.-Q.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Luo, C.

Matsuhisa, Y.

Ming, N.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Miroshnichenko, A. E.

Mujumdar, S.

Nakano, Y.

Osgood, R. M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

Ozaki, M.

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Pinkevych, I.

Poo, Y.

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Qian, X.-S.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Ramachandran, H.

Rudebusch, R.

Saitoh, K.

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Shi, J.

K. Liu, J. Shi, and L. Chen, “Linear polarization-state generator with high precision in periodically poled lithium niobate,” Appl. Phys. Lett. 94, 101106 (2009).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117(2003).
[CrossRef]

Shi, L.

L. Shi, L. Tian, and X. Chen, “Electro-optic chirality control in MgO:PPLN,” arXiv:1204.1174 (2012).

Shimizu, H.

Shvets, G.

G. Shvets, “Optical polarizer/isolator based on a rectangular waveguide with helical grooves,” Appl. Phys. Lett. 89, 141127 (2006).
[CrossRef]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Stegeman, G. I.

Takao, Y.

Tanaka, M.

Tian, L.

L. Shi, L. Tian, and X. Chen, “Electro-optic chirality control in MgO:PPLN,” arXiv:1204.1174 (2012).

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Treviño-Palacios, C. G.

Wan, Z.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Wang, Q.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Wang, T. J.

T. J. Wang and J. S. Chung, “Wavelength-tunable polarization converter utilizing the strain induced by proton exchange in lithium niobate,” Appl. Phys. B: Lasers Opt. 80, 193–198 (2005).
[CrossRef]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
[CrossRef]

Wu, H.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Wu, R.-x.

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Wu, S.-T.

Wu, W.-Q.

Xi, Y.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Xia, Y.

Xu, F.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Yang, H.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Yang, Y.

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Yeh, P.

Yokoyama, M.

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Yu, Z.-Y.

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

Zhang, J.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Zhang, X.

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Zhang, Y.

Y. Zhang, Y. Chen, and X. Chen, “Polarization-based all-optical logic controlled-NOT, XOR, and XNOR gates employing electro-optic effect in periodically poled lithium niobate,” Appl. Phys. Lett. 99, 161117 (2011).
[CrossRef]

Zhou, H.

Zhou, K.-F.

Zhou, Y.

Zhu, Y.

Zuhlke, C.

Adv. Funct. Mater. (1)

X. Hu, Z. Li, J. Zhang, H. Yang, Q. Gong, and X. Zhang, “Low-Power and high-contrast nanoscale all-optical diodes via nanocomposite photonic crystal microcavities,” Adv. Funct. Mater. 21, 1803–1809 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (1)

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Appl. Phys. Lett. (9)

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[CrossRef]

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K. Liu, J. Shi, and L. Chen, “Linear polarization-state generator with high precision in periodically poled lithium niobate,” Appl. Phys. Lett. 94, 101106 (2009).
[CrossRef]

Y. Zhang, Y. Chen, and X. Chen, “Polarization-based all-optical logic controlled-NOT, XOR, and XNOR gates employing electro-optic effect in periodically poled lithium niobate,” Appl. Phys. Lett. 99, 161117 (2011).
[CrossRef]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

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[CrossRef]

J. Appl. Phys. (1)

X.-S. Qian, H. Wu, Q. Wang, Z.-Y. Yu, F. Xu, Y.-Q. Lu, and Y.-F. Chen, “Electro-optic tunable optical isolator in periodically poled LiNbO3,” J. Appl. Phys. 109, 053111 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
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Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
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Opt. Express (4)

Opt. Lett. (6)

Phys. Rev. E (1)

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[CrossRef]

Phys. Rev. Lett. (1)

Y. Poo, R.-x. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Other (1)

L. Shi, L. Tian, and X. Chen, “Electro-optic chirality control in MgO:PPLN,” arXiv:1204.1174 (2012).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental verification of the optical rotation in PPLN by the EO effect. The input wavelength of light is 1542 nm, and the experiment was conducted at a temperature of 20°C. The PPLN used in our experiment is MgO doped and 3.6 cm long. The period of the domain structure is 19.7 μm, with a duty cycle of 1.

Fig. 2.
Fig. 2.

Polarization evolution process of light in HPPLN. Y and Z represent the principal axes of the index ellipsoid, and P represents the polarization state of light. The incident light satisfies the QPM condition.

Fig. 3.
Fig. 3.

Schematic diagram of the optical isolator based on the EO effect of HPPLN. A positive half-domain is added to the normal PPLN to form HPPLN. Under the QPM condition, each domain serves as a half-wave plate, and the half-domain serves as a quarter-wave plate.

Fig. 4.
Fig. 4.

(a) Theoretical transmittance of the incident light (solid curve) and reflected light (dashed curve) and (b) isolation contrast as a function of the external electric field. The QPM wavelength is 1550 nm.

Equations (3)

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θγ51E/[(1/ne)2(1/no)2],
{dAo/dx=iκAeeiΔβxdAe/dx=iκ*AoeiΔβx,
{Ao(L)=cos(|κ|L)Ao(0)sin(|κ|L)Ae(0)Ae(L)=cos(|κ|L)Ae(0)+sin(|κ|L)Ao(0).

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