Abstract

We theoretically analyze the nonlinear phase shifts induced by cascaded χ2:χ2 processes in one-dimensional photonic bandgap structures. We find that the enhancement of the density of modes near the band edge, coupled with a suitable choice of relative phase mismatch, leads to a remarkable new effect: The relative phase shift of the fundamental field on transmission can be of the order of π over a distance of 7 µm, with input intensities of the order of only 10 MW/cm2.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds. feature on development and applications of materials exhibiting photonic bandgaps, J. Opt. Soc. Am. B 10, 279–359 (1993).
  2. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
    [CrossRef] [PubMed]
  3. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
    [CrossRef]
  4. M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
    [CrossRef]
  5. M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
    [CrossRef]
  6. J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
    [CrossRef]
  7. R. De Salvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, H. Vanherzeele, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [CrossRef]
  8. A. V. Balakin, D. Boucher, V. A. Bushev, N. I. Koroteev, B. I. Mantsyzov, P. Masselin, I. A. Ozheredov, and A. P. Shurinov, Opt. Lett. 24, 793 (1999).
    [CrossRef]
  9. Courtesy of the Société de Production et Recherches Appliquées, www.sopra-sa.com/indices.htm .
  10. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), pp. 765–766.

1999 (1)

1998 (2)

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

1996 (1)

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

1993 (1)

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds. feature on development and applications of materials exhibiting photonic bandgaps, J. Opt. Soc. Am. B 10, 279–359 (1993).

1992 (1)

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), pp. 765–766.

Balakin, A. V.

Bendickson, J. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Bloemer, M. J.

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Boucher, D.

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Bushev, V. A.

Cole, J. D.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

De Salvo, R.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Flynn, R. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Hagan, D. J.

Haus, J. W.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

Kalocsai, A. G.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

Koroteev, N. I.

Leavitt, R. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Ledbetter, H. S.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

Mantsyzov, B. I.

Masselin, P.

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), pp. 765–766.

Ozheredov, I. A.

Reinhardt, S. B.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Scalora, M.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Sheik-Bahae, M.

Shurinov, A. P.

Stegeman, G.

Theimer, J.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

Tocci, M. D.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Viswanathan, R.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

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

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds. feature on development and applications of materials exhibiting photonic bandgaps, J. Opt. Soc. Am. B 10, 279–359 (1993).

Opt. Lett. (2)

Phys. Rev. A (2)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, Phys. Rev. A 56, 3166 (1997).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, Phys. Rev. A 57, 2120 (1998).
[CrossRef]

Phys. Rev. E (1)

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Phys. Rev. Lett. 73, 1368 (1994).
[CrossRef] [PubMed]

Other (2)

Courtesy of the Société de Production et Recherches Appliquées, www.sopra-sa.com/indices.htm .

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart & Winston, New York, 1976), pp. 765–766.

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

Normalized intensity Uω,N-12 of (a) the eigenmode for the fundamental frequency (FF) field tuned at the N-1th peak of transmittance near the first band edge and (b) the eigenmode for the SH field tuned at the first resonance near the second-order band edge for the 30-period structure described in the text. The layer thicknesses are chosen to be a=93 nm Al2O3 and b=154 nm Al30%Ga70%As. Inset, schematic representation of the 1-D, finite N-period structure.

Fig. 2
Fig. 2

DOM (in units of 1/c) for the multilayer stack in Fig. 1. ω0 is the frequency corresponding to a wavelength of 895 nm.

Fig. 3
Fig. 3

Variation of the nonlinear phase of the FF field ΔΦωNL versus the input FF intensity. The structure is the same as in Fig. 1.

Equations (7)

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

d2Aω/dz2+kω2Aω=-λαAω*A2ω,d2A2ω/dz2+k2ω2A2ω=-2λαAω2,
d2Ajω/dz02+kjω2z0Ajω=0, j=1,2,
|jω,mj=expimjπNΛz0Ujω,mjz0,mj=1,2,,N-1,N+1,,2N-1,2N+1,,
dA˜ω/dz=iωρωγωA˜2ωA˜ω*,
dA˜2ω/dz=iωρ2ωγ2ω*A˜12,
dA˜ω/dz=iσωA˜2ωA˜1ω* expiπNΛz,
dA˜2ω/dz=iσ2ωA˜ω2 exp-iπNΛz,

Metrics