Abstract

The dependence of second harmonic generation conversion efficiency resulting from the position of poled regions of the second-order nonlinearity in uniform and chirped gratings in ferroelectric materials has been studied analytically and numerically. The displacement of the poled region’s position from a specific location in second-order nonlinear materials can introduce a wavelength shift in a uniform grating’s second harmonic intensity peak and strongly influences the bandwidth and ripple in the harmonic conversion response of chirped gratings. We propose that the poled regions should be located at specific positions within the single period to minimize the ripples and achieve a desired nonlinearity function, and also to significantly improve tolerance to fabrication errors.

© 2012 Optical Society of America

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References

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  1. L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
    [CrossRef]
  2. X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
    [CrossRef]
  3. G. K. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A 76, 043841 (2007).
    [CrossRef]
  4. M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
    [CrossRef]
  5. J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
    [CrossRef]
  6. F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
    [CrossRef]
  7. M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
    [CrossRef]
  8. M. Ahlawat, A. Tehranchi, C. Q. Xu, and R. Kashyap, “Ultrabroadband flattop wavelength conversion based on cascaded sum frequency generation and difference frequency generation using pump detuning in quasi-phase-matched lithium niobate waveguides,” Appl. Opt. 50, E108–E111 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
    [CrossRef]
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    [CrossRef]
  19. G.-W. Lu, S. Shinada, H. Furukawa, N. Wada, T. Miyazaki, and H. Ito, “160  Gb/s all-optical phase-transparent wavelength conversion through cascaded SFG-DFG in a broadband linear-chirped PPLN waveguide,” Opt. Express 18, 6064–6070 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. 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, 1129–1131 (2007).
    [CrossRef]
  24. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  25. T. Umeki, M. Asobe, T. Yanagawa, O. Tadanaga, Y. Nishida, K. Magari, and H. Suzuki, “Broadband wavelength conversion based on apodized χ(2) grating,” J. Opt. Soc. Am. B 26, 2315–2322 (2009).
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    [CrossRef]

2011 (1)

2010 (1)

2009 (4)

T. Umeki, M. Asobe, T. Yanagawa, O. Tadanaga, Y. Nishida, K. Magari, and H. Suzuki, “Broadband wavelength conversion based on apodized χ(2) grating,” J. Opt. Soc. Am. B 26, 2315–2322 (2009).
[CrossRef]

A. Tehranchi and R. Kashyap, “Novel designs for efficient broadband frequency doublers using singly pump-resonant waveguide and engineered chirped gratings,” IEEE J. Quantum Electron. 45, 187–194 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

2008 (3)

2007 (3)

2006 (1)

2004 (1)

S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
[CrossRef]

2003 (1)

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

2002 (1)

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

1998 (2)

G. W. Ross, M. Pollnau, P. G. R. Smith, W. A. Clarkson, P. E. Britton, and D. C. Hanna, “Generation of high-power blue light in periodically poled LiNbO3,” Opt. Lett. 23, 171–173 (1998).
[CrossRef]

V. V. Volkov and A. S. Chirkin, “Quasi-phase-matched parametric amplification of waves with low-frequency pumping,” Quantum Electron. 28, 95–96 (1998).
[CrossRef]

1997 (1)

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

1996 (1)

K. Kintaka, M. Fujimura, T. Suhara, and H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

1995 (1)

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1990 (1)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[CrossRef]

Ahlawat, M.

Asobe, M.

Baker, K. L.

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

Bosenberg, W. R.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

Britton, P. E.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Cha, M.-S.

Chirkin, A. S.

V. V. Volkov and A. S. Chirkin, “Quasi-phase-matched parametric amplification of waves with low-frequency pumping,” Quantum Electron. 28, 95–96 (1998).
[CrossRef]

Clarkson, W. A.

Fejer, M. M.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
[CrossRef]

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

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Fujimura, M.

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

K. Kintaka, M. Fujimura, T. Suhara, and H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Furukawa, H.

Gao, S.

S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
[CrossRef]

Guo, Y.

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

X. Liu, H. Zhang, and Y. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001).
[CrossRef]

Hanna, D. C.

Houe, M.

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Huang, D.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
[CrossRef]

Huang, J.

Hum, D. S.

Ito, H.

Ji, F.

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Jin, G.

S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kang, Y.-S.

Kashyap, R.

Kim, B.-J.

Kintaka, K.

K. Kintaka, M. Fujimura, T. Suhara, and H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Kitaeva, G. K.

G. K. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A 76, 043841 (2007).
[CrossRef]

Kodama, T.

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

Langrock, C.

Li, B.

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Li, Y.

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

Lim, H.-H.

Liu, X.

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

X. Liu, H. Zhang, and Y. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001).
[CrossRef]

Lu, G.-W.

Lu, R.

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Magari, K.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Miyazaki, T.

Myers, L. E.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

Nishida, Y.

Nishihara, H.

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

K. Kintaka, M. Fujimura, T. Suhara, and H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[CrossRef]

Pandiyan, K.

Pollnau, M.

Prakash, O.

Reid, D. T.

Ross, G. W.

Roussev, R. V.

Shinada, S.

Smith, P. G. R.

Suhara, T.

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

K. Kintaka, M. Fujimura, T. Suhara, and H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[CrossRef]

Sun, J.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
[CrossRef]

Suzuki, H.

Tadanaga, O.

Tehranchi, A.

Tillman, K. A.

Townsend, P. D.

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Umeki, T.

Volkov, V. V.

V. V. Volkov and A. S. Chirkin, “Quasi-phase-matched parametric amplification of waves with low-frequency pumping,” Quantum Electron. 28, 95–96 (1998).
[CrossRef]

Wada, N.

Wang, J.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
[CrossRef]

Xie, X. P.

Xu, C. Q.

Yanagawa, T.

Yang, C.

S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
[CrossRef]

Yao, J.

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Zhang, B.

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Zhang, H.

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

X. Liu, H. Zhang, and Y. Guo, “Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference frequency generation,” J. Lightwave Technol. 19, 1785–1792 (2001).
[CrossRef]

Zhang, X.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Optical phase erasure and its application to format conversion through cascaded second-order processes in periodically poled lithium niobate,” Opt. Lett. 33, 1804–1806 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (6)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[CrossRef]

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “All-optical format conversions using periodically poled lithium niobate waveguides,” IEEE J. Quantum Electron. 45, 195–205 (2009).
[CrossRef]

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

X. Liu, H. Zhang, Y. Guo, and Y. Li, “Optimal design and applications for quasi-phase-matching three-wave mixing,” IEEE J. Quantum Electron. 38, 1225–1233 (2002).
[CrossRef]

A. Tehranchi and R. Kashyap, “Novel designs for efficient broadband frequency doublers using singly pump-resonant waveguide and engineered chirped gratings,” IEEE J. Quantum Electron. 45, 187–194 (2009).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. Gao, C. Yang, and G. Jin, “Flat broad-band wavelength conversion based on sinusoidally chirped optical superlattices in lithium niobate,” IEEE Photon. Technol. Lett. 16, 557–559 (2004).
[CrossRef]

M. Fujimura, T. Kodama, T. Suhara, and H. Nishihara, “Quasi-phase-matched self-frequency-doubling waveguide laser in Nd:LiNbO3,” IEEE Photon. Technol. Lett. 12, 1513–1515 (2000).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Korea (1)

J. Phys. D (1)

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Opt. Commun. (1)

F. Ji, R. Lu, B. Li, B. Zhang, and J. Yao, “Mid-infrared tunable dual-wavelength generation based on a quasi-phase-matched optical parametric oscillator,” Opt. Commun. 282, 126–128 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (1)

G. K. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A 76, 043841 (2007).
[CrossRef]

Quantum Electron. (1)

V. V. Volkov and A. S. Chirkin, “Quasi-phase-matched parametric amplification of waves with low-frequency pumping,” Quantum Electron. 28, 95–96 (1998).
[CrossRef]

Other (1)

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

 Three supposed schemes when the poled region is in the right (Scheme I), middle (Scheme II), and left (Scheme III) of a cell. C is the center of the space region.

Fig. 2.
Fig. 2.

(a) Effect of moving a poled mark space with a duty cycle of 1/2 on the wavelength shift from left to the right side according to (b) a scheme in which, C, the central poled region, changes from Λ/4 to 3Λ/4.

Fig. 3.
Fig. 3.

 Relative wavelength shift for the three supposed structures in uniform grating according to the inset functions for change of nonlinearity: (a) asymmetric and (b) symmetric.

Fig. 4.
Fig. 4.

(a) Normalized SH intensity response for 10 mm long chirped APPLN crystal with different structures and (b) normalized bandwidth and ripple for structures I (red circles), II (green arrows), and III (blue reverse arrows).

Fig. 5.
Fig. 5.

(a) Normalized SH intensity versus the FH using the hyperbolic tangent apodized function and (b) schematic of the proposed apodized chirped grating structures in APPLN composed of several cells. The middle unpoled (dark) space between the nth and (n+1)th period changes as (Λ+nδ)(1(an+an+1/2))+δ/2(1an+1).

Fig. 6.
Fig. 6.

(a) Influence of different types of error in Structure II and (b) constant broadening error in three different structures.

Equations (5)

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dA1dz=2jω12d(z)n1cA2A1*ejΔkz,dA2dz=2jω22d(z)n2cA12ejΔkz,
A2/D=0CaΛ/2eiΔkzdzCaΛ/2C+aΛ/2eiΔkzdz+C+aΛ/2ΛeiΔkzdz.
A2/D=1Δk(i=0N14sin(ΔkaiL/2)ejΔkL(i+ai/2))2Δksin(ΔkL/2)ejΔkL/2,
A2/D=1Δk(i=0N14sin(ΔkL(1ai)/2)ejΔkL(i+1/2))2Δksin(ΔkNL/2)ejΔkNL/2.
A2/D=1Δk(n4sin(Δk(Lan1(L+n1)δ)/2)ejΔk[(n1)(L+δ)+L/2)]2sin(ΔkNL/2)ejΔk(LN+(N1))δ/2+4sin(ΔkL(1a0)/2)ejΔkL/2),

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