Abstract

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phase-matching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. M. Fejer, in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1998), pp. 375–406.
  2. V. Ricci, G. I. Stegeman, and K. P. Chan, “Poling of multilayer polymer films for modal dispersion phase matching of second-harmonic generation: effects in glass-transition temperature matching in different layers,” J. Opt. Soc. Am. B 17, 1349–1353 (2000).
    [Crossref]
  3. A. Saer Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasiphase matching in GaAs-ALAs superlatticewaveguides through bandgap tuning by use of quantum-well intermixing,” Opt. Lett. 25, 1370–1372 (2000).
    [Crossref]
  4. P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
    [Crossref]
  5. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24, 1157–1159 (1999).
    [Crossref]
  6. C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
    [Crossref]
  7. J. F. Corney and O. Bang, “Solitons in quadratic nonlinear photonic crystals,” Phys. Rev. E 64, 047601 (2001).
    [Crossref]
  8. O. Bang, C. Balslev Clausen, P. L. Christiansen, and L. Torner, “Engineering competing nonlinearities,” Opt. Lett. 24, 1413–1415 (1999).
    [Crossref]
  9. O. Bang, T. W. Graversen, and J. F. Corney, “Accurate switching intensities and optimal length scales in quasi-phase-matched materials,” Opt. Lett. 26, 1007–1009 (2001).
    [Crossref]
  10. A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media,” Opt. Lett. 23, 506–508 (1998).
    [Crossref]
  11. S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
    [Crossref]
  12. J. F. Corney and O. Bang, “Modulational instability in periodic quadratic nonlinear materials,” Phys. Rev. Lett. 87, 133901 (2001).
    [Crossref] [PubMed]
  13. J. F. Corney and O. Bang, “Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure,” J. Opt. Soc. Am. B 19, 812–821 (2002).
    [Crossref]
  14. P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
    [Crossref]

2002 (2)

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

J. F. Corney and O. Bang, “Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure,” J. Opt. Soc. Am. B 19, 812–821 (2002).
[Crossref]

2001 (4)

J. F. Corney and O. Bang, “Solitons in quadratic nonlinear photonic crystals,” Phys. Rev. E 64, 047601 (2001).
[Crossref]

O. Bang, T. W. Graversen, and J. F. Corney, “Accurate switching intensities and optimal length scales in quasi-phase-matched materials,” Opt. Lett. 26, 1007–1009 (2001).
[Crossref]

J. F. Corney and O. Bang, “Modulational instability in periodic quadratic nonlinear materials,” Phys. Rev. Lett. 87, 133901 (2001).
[Crossref] [PubMed]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

2000 (2)

1999 (2)

1998 (1)

1997 (1)

C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
[Crossref]

1995 (1)

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Aitchison, J. S.

Arnold, J. M.

Baldi, P.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Balslev Clausen, C.

C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
[Crossref]

Bang, O.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

J. F. Corney and O. Bang, “Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure,” J. Opt. Soc. Am. B 19, 812–821 (2002).
[Crossref]

J. F. Corney and O. Bang, “Modulational instability in periodic quadratic nonlinear materials,” Phys. Rev. Lett. 87, 133901 (2001).
[Crossref] [PubMed]

J. F. Corney and O. Bang, “Solitons in quadratic nonlinear photonic crystals,” Phys. Rev. E 64, 047601 (2001).
[Crossref]

O. Bang, T. W. Graversen, and J. F. Corney, “Accurate switching intensities and optimal length scales in quasi-phase-matched materials,” Opt. Lett. 26, 1007–1009 (2001).
[Crossref]

O. Bang, C. Balslev Clausen, P. L. Christiansen, and L. Torner, “Engineering competing nonlinearities,” Opt. Lett. 24, 1413–1415 (1999).
[Crossref]

A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media,” Opt. Lett. 23, 506–508 (1998).
[Crossref]

C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
[Crossref]

Bramati, A.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Brener, I.

Brown, C. T. A.

Bryce, A. C.

Carrasco, S.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

Chan, K. P.

Chinaglia, W.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Chou, M. H.

Christiansen, P. L.

Clausen, C. Balslev

Conti, C.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Corney, J. F.

De Micheli, M. P.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Delacourt, D.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Di Trapani, P.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Ebrahimzadeh, M.

Fejer, M. M.

Graversen, T. W.

Hutchings, D. C.

Johansen, S. K.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

Kilius, J.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Kivshar, Y. S.

A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media,” Opt. Lett. 23, 506–508 (1998).
[Crossref]

C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
[Crossref]

Kleckner, T. C.

Kobyakov, A.

Lederer, F.

Marsh, J. H.

Minardi, S.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Moutzouris, K.

Ostrowsky, D. B.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Papuchon, M.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Parameswaran, K. R.

Ricci, V.

Saer Helmy, A.

Stanley, C. R.

Stegeman, G. I.

V. Ricci, G. I. Stegeman, and K. P. Chan, “Poling of multilayer polymer films for modal dispersion phase matching of second-harmonic generation: effects in glass-transition temperature matching in different layers,” J. Opt. Soc. Am. B 17, 1349–1353 (2000).
[Crossref]

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Torner, L.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

O. Bang, C. Balslev Clausen, P. L. Christiansen, and L. Torner, “Engineering competing nonlinearities,” Opt. Lett. 24, 1413–1415 (1999).
[Crossref]

Trevino-Palacios, C. G.

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

Trillo, S.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Valiulis, G.

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Electron. Lett. (1)

P. Baldi, C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[Crossref]

Opt. Lett. (5)

Phys. Rev. E (1)

J. F. Corney and O. Bang, “Solitons in quadratic nonlinear photonic crystals,” Phys. Rev. E 64, 047601 (2001).
[Crossref]

Phys. Rev. Lett. (3)

C. Balslev Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).
[Crossref]

J. F. Corney and O. Bang, “Modulational instability in periodic quadratic nonlinear materials,” Phys. Rev. Lett. 87, 133901 (2001).
[Crossref] [PubMed]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).
[Crossref]

Other (1)

M. M. Fejer, in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1998), pp. 375–406.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Maximum gain versus an and en for |bn|2=1 and |c|2=2. (b) an(νn) for νn real and found from Eq. (18) (DB, solid line), from Eq. (19) with plus sign (HB+, dotted line), and Eq. (19) with minus sign (HB-, dashed line), for β˜=0, Λ=1, and κ=670.

Fig. 2
Fig. 2

MI gain for Λ=1 (dashed) and Λ=-1 (solid) calculated by Floquet theory. Crosses and diamonds show the analytic prediction (15). κ=β=670.

Fig. 3
Fig. 3

MI gain calculated by numerical simulation [(a) and dots in (b)–(d)] and by Floquet theory [solid curves in (b)–(d)]. κ=β=670 and Λ=-1.

Equations (19)

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

i E1z+12 2E1x2+χ(z)E1*E2 exp(iβz)=0,
i E2z+14 2E2x2+χ(z)E12 exp(-iβz)=0,
χ(z)=ndn exp(inκz),
E1(x, z)=nwn(x, z)exp(inκz),
E2(x, z)=nvn(x, z)exp(inκz-iβ˜z),
(Lˆ1-nκ)wn+l,mdn+m-l-swm*vl=0,
(Lˆ2-nκ)vn+l,mdn-m-l+swmwl=0,
wn(x, z)=[w¯n+n(x, z)]exp(iΛz),
vn(x, z)=[v¯n+μn(x, z)]exp(i2Λz).
(Lˆ1-nκ)n+l,mdn+m-l-s(w¯m*μl+v¯lm*)=0,
(Lˆ2-nκ)μn+2l,mdn-m-l+sw¯ml=0,
n(x, z)=δn(1)(z)exp(iνx)+δn(2)*(z)exp(-iνx),
μn(x, z)=δn(3)(z)exp(iνx)+δn(4)*(z)exp(-iνx),
δnzianbnc0-bn*-an0-c*2c*0en00-2c0-enδnMnδn,
λn2=An±An2-Bn,
An=12(|bn|2-an2-4|c|2-en2),
Bn=(anen-2|c|2)2-en2|bn|2.
νn2=-8nκ/3-4Λ+4β˜/3,
νn2=2β˜-3nκ-5Λ±(2β˜-nκ-3Λ)2+16|c|2.

Metrics