Abstract

We theoretically investigate the electro-optic coupling in an optical superlattice of linear chirped-periodically poled lithium niobate. It is found that the electro-optic coupling in such optical superlattice can work in a wide wavelength range. Some of examples, with bandwidths of 20, 40, 80, 120nm, are demonstrated. The way to determine the electric field for perfect conversion between o- and e-ray and the method using apodized crystals of tanh profile to reduce the ripples are shown. As one of its applications, one kind of broadband Solc-type bandpass filter in optical communication range is proposed.

©2010 Optical Society of America

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References

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  1. Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31(11), 1093–1128 (1999).
    [Crossref]
  2. K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82(22), 3841–3843 (2003).
    [Crossref]
  3. L. Arizmendi, “Photonic applications of Lithium Niobate,” Phys. Status Solidi A 201(2), 253–283 (2004).
    [Crossref]
  4. Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
    [Crossref]
  5. C. S. Kee, Y. L. Lee, and J. Lee, “Electro- and thermo-optic effects on multi-wavelength Šolc filters based on x(2) nonlinear quasi-periodic photonic crystals,” Opt. Express 16(9), 6098–6103 (2008).
    [Crossref] [PubMed]
  6. 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(21), 2115–2117 (2003).
    [Crossref] [PubMed]
  7. Y. H. Chen and Y. C. Huang, “Actively Q-switched Nd:YVO4 laser using an electro-optic periodically poled lithium niobate crystal as a laser Q-switch,” Opt. Lett. 28(16), 1460–1462 (2003).
    [Crossref] [PubMed]
  8. M. Charbonneau-Lefort, M. M. Fejer, and B. Afeyan, “Tandem chirped quasi-phase-matching grating optical parametric amplifier design for simultaneous group delay and gain control,” Opt. Lett. 30(6), 634–636 (2005).
    [Crossref] [PubMed]
  9. M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
    [Crossref] [PubMed]
  10. H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
    [Crossref]
  11. H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
    [Crossref] [PubMed]
  12. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, 2003), Chap. 17.
  13. C. H. von Helmolt, “Broadband single-mode TE/TM convertors in LiNbO3: a novel design,” Electron. Lett. 22(3), 155–156 (1986).
    [Crossref]
  14. O. Eknoyan, W. K. Burns, R. P. Moeller, and N. J. Frigo, “Broadband LiTaO3 guided-wave TE-TM mode converter,” Appl. Opt. 27(1), 114–117 (1988).
    [Crossref] [PubMed]
  15. W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
    [Crossref]
  16. G. Zheng, H. Wang, and W. She, “Wave coupling theory of Quasi-Phase-Matched linear electro-optic effect,” Opt. Express 14(12), 5535–5540 (2006).
    [Crossref] [PubMed]
  17. L. D. Landau, “Zur Theorie der Energieubertragung. II,” Phys. Soviet Union 2, 46–51 (1932).
  18. C. Zener, “Non-adiabatic Crossing of Energy Levels,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 137(833), 696–702 (1932).
    [Crossref]
  19. 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]
  20. Optoplex support, “DWDM ITU Grid Specification,” (Optoplex corporation,2010), http://www.optoplex.com/PDF/DWDM-ITU.pdf .
  21. J. Huang, X. P. Xie, C. Langrock, R. V. Roussev, D. S. Hum, and M. M. Fejer, “Amplitude modulation and apodization of quasiphase-matched interactions,” Opt. Lett. 31(5), 604–606 (2006).
    [Crossref] [PubMed]
  22. T. Umeki, M. Asobe, Y. Nishida, O. Tadanaga, K. Magari, T. Yanagawa, and H. Suzuki, “Widely tunable 3.4 μm band difference frequency generation using apodized χ(2) grating,” Opt. Lett. 32(9), 1129–1131 (2007).
    [Crossref] [PubMed]
  23. Y. L. Lee, Y. C. Noh, C. S. Kee, N. E. Yu, W. Shin, C. Jung, D. K. Ko, and J. Lee, “Bandwidth control of a Ti:PPLN Solc filter by a temperature-gradient-control technique,” Opt. Express 16(18), 13699–13706 (2008).
    [Crossref] [PubMed]

2009 (1)

2008 (4)

C. S. Kee, Y. L. Lee, and J. Lee, “Electro- and thermo-optic effects on multi-wavelength Šolc filters based on x(2) nonlinear quasi-periodic photonic crystals,” Opt. Express 16(9), 6098–6103 (2008).
[Crossref] [PubMed]

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Y. L. Lee, Y. C. Noh, C. S. Kee, N. E. Yu, W. Shin, C. Jung, D. K. Ko, and J. Lee, “Bandwidth control of a Ti:PPLN Solc filter by a temperature-gradient-control technique,” Opt. Express 16(18), 13699–13706 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

2005 (1)

2004 (1)

L. Arizmendi, “Photonic applications of Lithium Niobate,” Phys. Status Solidi A 201(2), 253–283 (2004).
[Crossref]

2003 (3)

2001 (1)

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

2000 (1)

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

1999 (1)

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31(11), 1093–1128 (1999).
[Crossref]

1988 (1)

1986 (1)

C. H. von Helmolt, “Broadband single-mode TE/TM convertors in LiNbO3: a novel design,” Electron. Lett. 22(3), 155–156 (1986).
[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]

1932 (2)

L. D. Landau, “Zur Theorie der Energieubertragung. II,” Phys. Soviet Union 2, 46–51 (1932).

C. Zener, “Non-adiabatic Crossing of Energy Levels,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 137(833), 696–702 (1932).
[Crossref]

Afeyan, B.

Arie, A.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
[Crossref] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Arizmendi, L.

L. Arizmendi, “Photonic applications of Lithium Niobate,” Phys. Status Solidi A 201(2), 253–283 (2004).
[Crossref]

Asobe, M.

Baker, K. L.

K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82(22), 3841–3843 (2003).
[Crossref]

Burns, W. K.

Carrasco, S.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Charbonneau-Lefort, M.

Chen, X.

Chen, Y.

Chen, Y. H.

Eknoyan, O.

Fejer, M. M.

Frigo, N. J.

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]

Huang, J.

Huang, Y. C.

Hum, D. S.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

J. Huang, X. P. Xie, C. Langrock, R. V. Roussev, D. S. Hum, and M. M. Fejer, “Amplitude modulation and apodization of quasiphase-matched interactions,” Opt. Lett. 31(5), 604–606 (2006).
[Crossref] [PubMed]

Jung, C.

Kee, C. S.

Ko, D. K.

Landau, L. D.

L. D. Landau, “Zur Theorie der Energieubertragung. II,” Phys. Soviet Union 2, 46–51 (1932).

Langrock, C.

Lee, J.

Lee, W. K.

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Lee, Y. L.

Lu, Y. Q.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

Magari, K.

Ming, N. B.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31(11), 1093–1128 (1999).
[Crossref]

Moeller, R. P.

Nasr, M. B.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Nishida, Y.

Noh, Y. C.

Oron, D.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
[Crossref] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Prabhudesai, V.

Roussev, R. V.

Saleh, B. E.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Sergienko, A. V.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

She, W.

She, W. L.

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Shi, J.

Shin, W.

Silberberg, Y.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
[Crossref] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Suchowski, H.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
[Crossref] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Suzuki, H.

Tadanaga, O.

Teich, M. C.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Torner, L.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Torres, J. P.

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Umeki, T.

von Helmolt, C. H.

C. H. von Helmolt, “Broadband single-mode TE/TM convertors in LiNbO3: a novel design,” Electron. Lett. 22(3), 155–156 (1986).
[Crossref]

Wan, Z. L.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

Wang, H.

Wang, Q.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[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]

Xi, Y. X.

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

Xia, Y.

Xie, X. P.

Yanagawa, T.

Yu, N. E.

Zener, C.

C. Zener, “Non-adiabatic Crossing of Energy Levels,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 137(833), 696–702 (1932).
[Crossref]

Zheng, G.

Zhu, Y.

Zhu, Y. Y.

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31(11), 1093–1128 (1999).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82(22), 3841–3843 (2003).
[Crossref]

Y. Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[Crossref]

Electron. Lett. (1)

C. H. von Helmolt, “Broadband single-mode TE/TM convertors in LiNbO3: a novel design,” Electron. Lett. 22(3), 155–156 (1986).
[Crossref]

Opt. Commun. (1)

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31(11), 1093–1128 (1999).
[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. Rev. A (1)

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008).
[Crossref]

Phys. Rev. Lett. (1)

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Phys. Soviet Union (1)

L. D. Landau, “Zur Theorie der Energieubertragung. II,” Phys. Soviet Union 2, 46–51 (1932).

Phys. Status Solidi A (1)

L. Arizmendi, “Photonic applications of Lithium Niobate,” Phys. Status Solidi A 201(2), 253–283 (2004).
[Crossref]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character (1)

C. Zener, “Non-adiabatic Crossing of Energy Levels,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 137(833), 696–702 (1932).
[Crossref]

Other (2)

R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, 2003), Chap. 17.

Optoplex support, “DWDM ITU Grid Specification,” (Optoplex corporation,2010), http://www.optoplex.com/PDF/DWDM-ITU.pdf .

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Figures (5)

Fig. 1
Fig. 1 | κ | / | α | vs. | α | L for different conversion efficiency from o- to e-ray. The incident light is o-ray, and the wavelength has a perfect phase matching point at 0.5 | α | L . The insert in (a) is a curve for 100% conversion.

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Fig. 2
Fig. 2 Numerical simulations of electro-optic coupling covering 40nm in LCPLNs with different lengths. (a) 2cm, α = 4.4 × 10 − 7 μ m − 2 , Ey = 1.52kV/mm; (b) 3cm, α = 2.9 × 10 − 7 μ m − 2 , Ey = 1.24kV/mm; (c) 4cm, α = 2.2 × 10 − 7 μ m − 2 , Ey = 1.08kV/mm; (d) 5cm,. α = 1.8 × 10 − 7 μ m − 2 , Ey = 0.96kV/mm.

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Fig. 3
Fig. 3 Numerical simulations of conversion efficiency of broadband electro-optic coupling in LCPLN with FWHM 20nm, 80nm and 120nm, respectively. The length of LCPLN is 2cm. Solid line: 1540-1560nm; dash line: 1510-1590nm; dotted line: 1490-1610nm.

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Fig. 4
Fig. 4 |f 1(x)| corresponding respectively to unapodized LCPLN (D(x) = 0.5) and an apodized LCPLN with tanh profile (a = 3).

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Fig. 5
Fig. 5 Ripples reduction by using the apodized LCPLNs with tanh profile (a = 3).

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Equations (10)

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

d d x A 1 ( x ) = − i κ ( x ) A 2 ( x ) exp [ i φ ( x ) ] − i v ( x ) A 1 ( x ) ,
d d x A 2 ( x ) = − i κ * ( x ) A 1 ( x ) exp [ − i φ ( x ) ] .
λ 1 = 2 π K 0 ( n o 1 − n e 1 ) ,   λ 2 = 2 π K 0 − α L ( n o 2 − n e 2 ) ,   λ 0.5 = 2 π K 0 − 0.5 α L ( n o − n e ) .
Δ λ = λ 2 − λ 1 ≈ ε λ 0.5 ,
K 0 = − Δ k ( λ 1 ) ,   K 0 − α L = − Δ k ( λ 2 ) ,   α L = Δ k ( λ 2 ) − Δ k ( λ 1 ) .
η = 1 − exp ( − 2 π | κ | 2 | α | ) ,   ( | α | L → ∞ ) .
f 0 ( x ) = 2 D ( x ) − 1 ,   f 1 ( x ) = 1 i π { 1 − cos [ 2 π D ( x ) ] + i sin [ 2 π D ( x ) ] } ,
D ( x ) = 1 2 tanh ( 2 a x L ) ( 0 ≤ x < L 2 ) ,   D ( x ) = 1 2 tanh [ 2 a ( L − x ) L ] ( L 2 ≤ x ≤ L ) ,
Δ λ ≈ γ ε λ 0.5 ,
K 0 − 1 2 ( 1 − γ ) α L = − Δ k ( λ 1 ) ,   K 0 − 1 2 ( 1 + γ ) α L = − Δ k ( λ 2 ) ,   γ α L = Δ k ( λ 2 ) − Δ k ( λ 1 ) ,

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