Abstract

We model a backward mirrorless optical parametric oscillator in a fragmented GaN waveguide consisting of a sequence of submicronic periodically poled elements separated by uniformly polarized connection sections representing stitching errors. We find that the generated coherent phase of the backscattered wave locks the phases of the forward propagating waves in such a way that the dynamics is nonintuitivelly as efficient as for a uniform quasi-phase-matched waveguide. The best coherence transfer to the backward wave, obtained for perfect group-velocity matching of the forward propagating waves, requires a nanoscale poled periodicity, which is achieved in GaN through epitaxy.

© 2013 Optical Society of America

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  1. S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
    [CrossRef]
  2. Y. I. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
    [CrossRef]
  3. C. Canalias and V. Pasiskevicius, Nat. Photonics 1, 459 (2007).
    [CrossRef]
  4. V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
    [CrossRef]
  5. G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
    [CrossRef]
  6. G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
    [CrossRef]
  7. A. Picozzi and M. Hælterman, Phys. Rev. Lett. 86, 2010 (2001).
    [CrossRef]
  8. A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
    [CrossRef]
  9. C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
    [CrossRef]
  10. A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
    [CrossRef]
  11. C. Montes, W. Grundkötter, H. Suche, and W. Sohler, J. Opt. Soc. Am. B 24, 2796 (2007).
    [CrossRef]
  12. A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
    [CrossRef]
  13. S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
    [CrossRef]
  14. S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
    [CrossRef]
  15. M. Monerie, IEEE J. Quantum Electron. 18, 535 (1982).
    [CrossRef]
  16. C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
    [CrossRef]
  17. C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
    [CrossRef]
  18. X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
    [CrossRef]

2012

2011

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
[CrossRef]

2008

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

2007

2005

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

2004

C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
[CrossRef]

2003

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

2002

A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
[CrossRef]

2001

A. Picozzi and M. Hælterman, Phys. Rev. Lett. 86, 2010 (2001).
[CrossRef]

1997

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

1996

Y. I. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

1982

M. Monerie, IEEE J. Quantum Electron. 18, 535 (1982).
[CrossRef]

1966

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Aschieri, P.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
[CrossRef]

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

Bhardwaj, M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

Brault, J.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

Canalias, C.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

C. Canalias and V. Pasiskevicius, Nat. Photonics 1, 459 (2007).
[CrossRef]

Chowdhury, A.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

Chua, S. J.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

de Micheli, M.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

Ding, Y. I.

Y. I. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

Gallo, K.

C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
[CrossRef]

Ginovart, F.

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

Grandjean, N.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Grundkötter, W.

Hælterman, M.

A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
[CrossRef]

A. Picozzi and M. Hælterman, Phys. Rev. Lett. 86, 2010 (2001).
[CrossRef]

Harris, S. E.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Khurgin, J. B.

Y. I. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

Laurell, F.

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

Leroux, M.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

Lim, G. C.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

Liu, W.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

Massies, J.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Mikhailov, A.

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

Monerie, M.

M. Monerie, IEEE J. Quantum Electron. 18, 535 (1982).
[CrossRef]

Montes, C.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
[CrossRef]

C. Montes, W. Grundkötter, H. Suche, and W. Sohler, J. Opt. Soc. Am. B 24, 2796 (2007).
[CrossRef]

C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
[CrossRef]

A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
[CrossRef]

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

Ng, F. L.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

Ng, H. M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

Pasiskevicius, V.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

C. Canalias and V. Pasiskevicius, Nat. Photonics 1, 459 (2007).
[CrossRef]

Pezzagna, S.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Picozzi, A.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
[CrossRef]

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
[CrossRef]

A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
[CrossRef]

A. Picozzi and M. Hælterman, Phys. Rev. Lett. 86, 2010 (2001).
[CrossRef]

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

Sohler, W.

Strömqvist, G.

G. Strömqvist, V. Pasiskevicius, C. Canalias, P. Aschieri, A. Picozzi, and C. Montes, J. Opt. Soc. Am. B 29, 1194 (2012).
[CrossRef]

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

Suche, H.

Vennéguès, P.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Wang, X. C.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

Weimann, N. G.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

Wieck, A. D.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Appl. Phys. Lett.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, Appl. Phys. Lett. 83, 1077 (2003).
[CrossRef]

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Appl. Surf. Sci.

X. C. Wang, G. C. Lim, F. L. Ng, W. Liu, and S. J. Chua, Appl. Surf. Sci. 252, 1492 (2005).
[CrossRef]

IEEE J. Quantum Electron.

M. Monerie, IEEE J. Quantum Electron. 18, 535 (1982).
[CrossRef]

Y. I. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

J. Appl. Phys.

S. Pezzagna, J. Brault, M. Leroux, J. Massies, and M. de Micheli, J. Appl. Phys. 103, 123112 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

C. Canalias and V. Pasiskevicius, Nat. Photonics 1, 459 (2007).
[CrossRef]

Opt. Commun.

C. Montes, A. Picozzi, and K. Gallo, Opt. Commun. 237, 437 (2004).
[CrossRef]

Phys. Rev. A

G. Strömqvist, V. Pasiskevicius, C. Canalias, and C. Montes, Phys. Rev. A 84, 023825 (2011).
[CrossRef]

Phys. Rev. E

A. Picozzi, C. Montes, and M. Hælterman, Phys. Rev. E 66, 056605 (2002).
[CrossRef]

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, Phys. Rev. E 55, 1086 (1997).
[CrossRef]

Phys. Rev. Lett.

A. Picozzi and M. Hælterman, Phys. Rev. Lett. 86, 2010 (2001).
[CrossRef]

Proc. SPIE

V. Pasiskevicius, C. Canalias, G. Strömqvist, and F. Laurell, Proc. SPIE 6875, 687508 (2008).
[CrossRef]

C. Montes, P. Aschieri, and A. Picozzi, Proc. SPIE 8011, 801136 (2011).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Group velocity for the z-polarized waves in GaN as function of the wavelength, calculated from the Sellmeier expansions in [14] with a particular profile of the refractive index of the guide [15]. The triangles mark the configuration of perfectly matched pump and idler group velocities (|vpvi|=0), and are labeled P for the pump, S for the signal, and I for the idler.

Fig. 2.
Fig. 2.

Quasi-phase-matching is obtained by a phase-reversal sequence of the ferroelectric domains with a grating periodicity ΛQPM. The segmented backward MOPO is composed by a train of PP GaN elements separated by uniformly polarized connection sections ε˜ representing stitching errors.

Fig. 3.
Fig. 3.

Stochastic pumped MOPO (segmented in 64 elements). (a) Incoherent pump spectrum fitted by a Gaussian envelope of FWHM Δνp(L)=4.40THz, (b) backward signal spectrum with Δνs(0)=18.18GHz, and (c) forward idler spectrum with a Gaussian fitting of FWHM Δνi(L)=3.31THz. The coherence gain attains Δνp/Δνs=242.

Equations (1)

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(t+vpx+γp+iβptt)Ap=σp(x)AsAi,(tvsx+γs+iβstt)As=σs(x)ApAi*,(t+vix+γi+iβitt)Ai=σi(x)ApAs*,

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