Abstract

We theoretically investigate an all-optical isolator under arbitrary linearly polarized fundamental wave (FW) input in an optical superlattice (OSL). The scheme is based on simultaneously phase matching the first-order Type I (oo-e) quasi-phase-matching (QPM) second-harmonic generation (SHG) process and higher-order Type 0 (ee-e) QPM SHG process in an OSL with a defect inserted in an asymmetrical position. Simulation results show that the contrast ratio of the all-optical isolator can maintain close to 1 under arbitrary linearly polarized FW. Thus, an all-optical isolator based on an OSL that is not sensitive to the direction of linear polarization can be realized. We also show that, with the defect in a strong asymmetry position, the length of the defect can be designed flexibly to maintain a high contrast ratio. Additionally, if the length of the OSL is longer, the nonreciprocal response can be realized for low optical intensities.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2011

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]

2010

2009

S. C. Kumar, G. K. Samanta, and M. Ebrahim-Zadeh, “High-power, single-frequency, continuous-wave second-harmonic-generation of ytterbium fiber laser in PPKTP and MgO:sPPLT,” Opt. Express 17, 13711–13726 (2009).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

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

2008

2007

2006

2005

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Bistable isolator action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

2002

2001

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

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

2000

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]

1999

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

K. Gallo and G. Assanto, “All-optical isolator based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[CrossRef]

1997

S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

1984

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

Amemiya, T.

Arie, A.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

Assanto, G.

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

K. Gallo and G. Assanto, “All-optical isolator based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[CrossRef]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Brener, I.

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

Byun, Y. T.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

Canalias, C.

Cha, M.

Chen, X.

Chen, Y.

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]

Chou, M. H.

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

Dekker, P.

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]

Du, Y.

Ebrahim-Zadeh, M.

Edwards, G. J.

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

Fan, S. H.

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

Fedotov, V. A.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Bistable isolator action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Fejer, M. M.

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

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

Fradkin-Kashi, K.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

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 isolator in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

K. Gallo and G. Assanto, “All-optical isolator based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[CrossRef]

Hai, P. N.

He, J.

Hu, X.-K.

Johnston, B.

Kivshar, Y.

Kivshar, Yu. S.

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Bistable isolator action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Kumar, S. C.

Kumar, S. Chaitanya

Kurimura, S.

Laurell, F.

Lawrence, M.

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

Lee, S.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

Lee, W. Y.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

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]

Liao, J.

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

Lin, X.-W.

Liu, Z.

Lu, F.

Lu, Y.-Q.

Mathew, M.

Ming, N.

Mizumoto, T.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

Nakano, Y.

Ok, S. H.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

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]

Parameswaran, K. R.

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

Pasiskevicius, V.

Peale, D.

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

Plum, E.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

Qian,

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]

Q. Wang, F. Xu, Z.-Y. Yu, X.-S. Qian, X.-K. Hu, Y.-Q. Lu, and H.-T. Wang, “A bidirectional tunable optical isolator based on periodically poled LiNbO3,” Opt. Express 18, 7340–7346(2010).
[CrossRef] [PubMed]

Qin, Y.

Ro, J. H.

Roh, J. W.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

Rosenman, G.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

Saltiel, S.

Samanta, G. K.

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Bistable isolator action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Shimizu, H.

Song, X.-S.

Taira, T.

Tanaka, M.

Urenski, P.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

Wang, H.

Wang, H.-T.

Wang, Q.

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]

Withford, M.

Woo, D. H.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[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]

X.-S.,

Xu, F.

Yang, J. S.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

Yokoyama, M.

Yu, N. E.

Yu, Z. F.

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

Yu, Z.-Y.

Zhang, C.

Zhang, J.

Zheludev, N. I.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

Zhu, S.

Zhu, Y.

Appl. Opt.

Appl. Phys. Lett.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94, 131901 (2009).
[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]

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

Electron. Lett.

I. Brener, M. H. Chou, D. Peale, and M. M. Fejer, “Cascaded χ(2) wavelength converter in LiNbO3 waveguides with counterpropagating beams,” Electron. Lett. 35, 1155–1157 (1999).
[CrossRef]

IEEE Trans. Magn.

J. S. Yang, J. W. Roh, S. H. Ok, D. H. Woo, Y. T. Byun, W. Y. Lee, T. Mizumoto, and S. Lee, “An integrated optical waveguide isolator based on multimode interference by wafer direct bonding,” IEEE Trans. Magn. 41, 3520–3522 (2005).
[CrossRef]

J. Appl. Phys.

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. B

Nat. Photon.

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

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

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

Phys. Rev. E

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Bistable isolator action in left-handed periodic structures,” Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Phys. Rev. Lett.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[CrossRef] [PubMed]

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001).
[CrossRef]

Science

S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Required fabrication periods versus the temperature for phase-matched Type I (black solid curve), and fifth- (red dashed–dotted curve) and seventh- (blue dashed curve) order Type 0 QPM SHG at 1064 nm .

Fig. 2
Fig. 2

Schematic diagram of the all-optical isolator under arbitrary linearly polarized FW input. Λ is the period of grating. A defect is introduced at x = L 1 with a length δ L .

Fig. 3
Fig. 3

Transmission in both directions and the contrast ratio under an arbitrary linearly polarized FW based on (a) simultaneously phase-matched first-order Type I and seventh-order Type 0 SHG processes, and (b) simultaneously phase-matched first-order Type I and fifth-order Type 0 SHG processes.

Fig. 4
Fig. 4

Evolution of two-wave coupling of the SHG processes inside the crystal under two different linearly polarized FW. (a)  P y / P = 0.2 ; the FW propagates from left to right. (b)  P y / P = 0.2 ; the FW propagates from right to left. (c)  P y / P = 0.8 ; the FW propagates from left to right. (d)  P y / P = 0.8 ; the FW propagates from right to left.

Fig. 5
Fig. 5

Contrast ratio influenced by the position and length of the defect under an arbitrary linearly polarized FW. (a)  δ L = 0.4 Λ , L 1 / L = 0.1 (black solid curve), 0.2 (red dashed curve), 0.25 (blue dotted curve), 0.3 (olive dashed–dotted curve). (b)  L 1 / L = 0.1 , δ L = 0.2 Λ (black solid curve), 0.4 Λ (red dashed curve), 0.6 Λ (blue dotted curve), 0.8 Λ (olive dashed–dotted curve). The inset shows the details of (b).

Fig. 6
Fig. 6

Contrast ratio influenced by the input FW intensity under an arbitrary linearly polarized FW while L = 4 cm , L 1 / L = 0.1 , δ L = 0.2 Λ . The black solid, red dashed, blue dotted, and olive dashed–dotted curves correspond to I = 20 MW / cm 2 , 40 MW / cm 2 , 60 MW / cm 2 , and 80 MW / cm 2 . The inset shows the details of the curves corresponding to I = 40 MW / cm 2 , 60 MW / cm 2 , and 80 MW / cm 2 .

Fig. 7
Fig. 7

Contrast ratio versus the polarization state of the FW and the input intensity for different crystal lengths. (a)  L = 2 cm , (b)  L = 4 cm , (c)  L = 6 cm , and (d)  L = 8 cm . In these figures, L 1 / L = 0.1 and δ L / Λ = 0.4 .

Equations (2)

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d A 1 y ( x ) d x = i σ 1 A 2 z A 1 y * exp ( i Δ k 1 x ) , d A 1 z ( x ) d x = i σ 2 A 2 z A 1 z * exp ( i Δ k 0 x ) , d A 2 z ( x ) d x = i σ 1 A 1 y A 1 y exp ( i Δ k 1 x ) i σ 2 A 1 z A 1 z exp ( i Δ k 0 x ) ,
A j ξ = n j ω j E j ξ , σ 1 = g 2 d 31 c ω 1 2 ω 2 n 1 z 2 n 2 z , σ 2 = g 2 d 33 c ω 1 2 ω 2 n 1 z 2 n 2 z ,

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