Abstract

We propose in this paper a chirped-quasi-periodic structure using the projection method. This type of new structure combines the advantages of chirped and quasi-periodic structures, and can be used for both multiple quasi-phase-matching and multiple bandwidths control. Numerical simulation of second-harmonic generation performance is in good agreement with the Fourier spectrum of the structure.

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References

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  1. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
    [CrossRef]
  2. C. Zhang, H. Wei, Y. Y. Zhu, H. T. Wang, S. N. Zhu, and N. B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26(12), 899–901 (2001).
    [CrossRef]
  3. B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
    [CrossRef]
  4. A. H. Norton and C. M. de Sterke, “Aperiodic 1-dimensional structures for quasi-phase matching,” Opt. Express 12(5), 841–846 (2004).
    [CrossRef] [PubMed]
  5. Z. W. Liu, Y. Du, J. Liao, S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. T. Wang, J. L. He, C. Zhang, and N. B. Ming, “Engineering of a dual-periodic optical superlattice used in a coupled optical parametric interaction,” J. Opt. Soc. Am. B 19(7), 1676–1684 (2002).
    [CrossRef]
  6. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, “Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure,” Opt. Lett. 28(7), 558–560 (2003).
    [CrossRef] [PubMed]
  7. X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
    [CrossRef]
  8. Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
    [CrossRef]
  9. G. K. Samanta and M. Ebrahim-Zadeh, “Continuous-wave, single-frequency, solid-state blue source for the 425-489 nm spectral range,” Opt. Lett. 33(11), 1228–1230 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. G. Imeshev, “Tailoring of Ultrafast Frequency Conversion with Quasi-Phase-Matching Gratings,” Ph.D. dissertation (Stanford University, 2000).
  12. X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
    [CrossRef]
  13. R. K. P. Zia and W. J. Dallas, “A simple derivation of quasi-crystalline spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985).
    [CrossRef]
  14. A. Yariv, and P. Yeh, Optical Waves in Crystal (Wiley, 1984).

2008

G. K. Samanta and M. Ebrahim-Zadeh, “Continuous-wave, single-frequency, solid-state blue source for the 425-489 nm spectral range,” Opt. Lett. 33(11), 1228–1230 (2008).
[CrossRef] [PubMed]

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

2007

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

2006

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

2004

2003

2002

2001

1999

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

1997

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

M. A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. 22(12), 865–867 (1997).
[CrossRef] [PubMed]

1985

R. K. P. Zia and W. J. Dallas, “A simple derivation of quasi-crystalline spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985).
[CrossRef]

Arbore, M. A.

Asobe, M.

Dallas, W. J.

R. K. P. Zia and W. J. Dallas, “A simple derivation of quasi-crystalline spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985).
[CrossRef]

de Sterke, C. M.

Deng, Q. H.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Dong, B. Z.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

Du, Y.

Ebrahim-Zadeh, M.

Fejer, M. M.

Gao, Z. D.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

Gu, B. Y.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

He, J. L.

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Z. W. Liu, Y. Du, J. Liao, S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. T. Wang, J. L. He, C. Zhang, and N. B. Ming, “Engineering of a dual-periodic optical superlattice used in a coupled optical parametric interaction,” J. Opt. Soc. Am. B 19(7), 1676–1684 (2002).
[CrossRef]

Hu, X. P.

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Kung, A. H.

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

Li, M. Z.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Liao, J.

Liu, Z. W.

Lv, X. J.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Marco, O.

Ming, N. B.

Miyazawa, H.

Nishida, Y.

Norton, A. H.

Qin, Y. Q.

Samanta, G. K.

Sui, Z.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Suzuki, H.

Tadanaga, O.

Tu, S.-Y.

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

Wang, H. T.

Wei, H.

Xie, Z. D.

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Yang, G. Z.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

Zhang, C.

Zhang, Y.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

Zhao, G.

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Zhu, S. N.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

Z. W. Liu, Y. Du, J. Liao, S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. T. Wang, J. L. He, C. Zhang, and N. B. Ming, “Engineering of a dual-periodic optical superlattice used in a coupled optical parametric interaction,” J. Opt. Soc. Am. B 19(7), 1676–1684 (2002).
[CrossRef]

C. Zhang, H. Wei, Y. Y. Zhu, H. T. Wang, S. N. Zhu, and N. B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26(12), 899–901 (2001).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Zhu, Y. Y.

Zia, R. K. P.

R. K. P. Zia and W. J. Dallas, “A simple derivation of quasi-crystalline spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985).
[CrossRef]

Appl. Phys. B

X. P. Hu, G. Zhao, C. Zhang, Z. D. Xie, J. L. He, and S. N. Zhu, “High-power, blue-light generation in a dual-structure, periodically poled, stoichiometric LiTaO3 crystal,” Appl. Phys. B 87(1), 91–94 (2007).
[CrossRef]

Appl. Phys. Lett.

Z. D. Gao, S. N. Zhu, S.-Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalite,” Appl. Phys. Lett. 89(18), 181101 (2006).
[CrossRef]

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Math. Gen.

R. K. P. Zia and W. J. Dallas, “A simple derivation of quasi-crystalline spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985).
[CrossRef]

Opt. Express

Opt. Laser Technol.

X. J. Lv, Z. Sui, Z. D. Gao, M. Z. Li, Q. H. Deng, and S. N. Zhu, “Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice,” Opt. Laser Technol. 40(1), 21–29 (2008).
[CrossRef]

Opt. Lett.

Science

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Other

G. Imeshev, “Tailoring of Ultrafast Frequency Conversion with Quasi-Phase-Matching Gratings,” Ph.D. dissertation (Stanford University, 2000).

A. Yariv, and P. Yeh, Optical Waves in Crystal (Wiley, 1984).

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Figures (4)

Fig. 1
Fig. 1

Schema of the projection method to obtain a quasi-periodic structure.

Fig. 2
Fig. 2

Fourier transformation of a quasi-periodic grating.

Fig. 3
Fig. 3

Fourier transformation of the CQP grating. The inset shows the detail of G 21.

Fig. 4
Fig. 4

SHG conversion efficiency versus fundamental wavelength using reciprocal vectors G 11 (a) and G 21 (b) in a CQP structure (The initial intensity of fundamental wave is 30MW/cm 2).

Equations (14)

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G m , n = 2 π m + n τ τ D A + D B ,
τ = N A N B = d x d y tan θ .
r x ( y ) = d x ( y ) ( N ) d x ( y ) ( 1 ) d x 0 ( y 0 ) ,
d x ( y ) ( n ) = d x ( y ) ( 1 ) + n N r x ( y ) d x 0 ( y 0 ) .
D A ( ξ ) = d y ( ξ ) sin θ ,
D B ( ξ ) = d x ( ξ ) cos θ .
τ ( ξ ) = d x ( ξ ) d y ( ξ ) tan θ .
G m , n ( ξ ) = 2 π ( m cos θ d x ( ξ ) + n sin θ d y ( ξ ) ) = 2 π ( m cos 2 θ D B ( ξ ) + n sin 2 θ D A ( ξ ) ) .
{ G m 1 , n 1 ( ξ ) = 2 π ( m 1 cos 2 θ D B ( ξ ) + n 1 sin 2 θ D A ( ξ ) ) , G m 2 , n 2 ( ξ ) = 2 π ( m 2 cos 2 θ D B ( ξ ) + n 2 sin 2 θ D A ( ξ ) ) ,
{ D A ( ξ ) = 2 π sin 2 θ ( m 2 n 1 m 1 n 2 ) m 2 G m 1 , n 1 ( ξ ) m 1 G m 2 , n 2 ( ξ ) , D B ( ξ ) = 2 π cos 2 θ ( m 2 n 1 m 1 n 2 ) n 1 G m 2 , n 2 ( ξ ) n 2 G m 1 , n 1 ( ξ ) .
{ G 1 , 1 ( ξ ) = 2 π ( cos 2 θ D B 0 + sin 2 θ D A 0 ) , G 2 , 1 ( ξ ) = 2 π ( 2 cos 2 θ D B 0 + sin 2 θ D A 0 ) + ξ L / 2 L / 2 δ G .
{ D A ( ξ ) = 1 / ( 1 D A 0 δ G ( ξ L / 2 ) π L sin 2 θ ) , D B ( ξ ) = 1 / ( 1 D B 0 + δ G ( ξ L / 2 ) π L cos 2 θ ) .
{ d E 1 / d x = i ω 1 d 33 f ( x ) n 1 c E 2 E 1 * exp ( i d k x ) , d E 2 / d x = i 2 ω 2 d 33 f ( x ) n 2 c E 1 2 exp ( i d k x ) ,
f ( x ) = { 1 w h e n x i s i n t h e p o s i t i v e d o m a i n , 1 w h e n x i s i n t h e n e g a t i v e d o m a i n .

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