Abstract

Experimental measurements of the second-harmonic-generation intensity in centrosymmetric photonic crystals indicate that the efficiency of this quadratic nonlinear process increases as the angle subtended by a reciprocal lattice vector and the second-harmonic field wave vector also increases. This behavior is explained by the use of a simple theoretical model based on second-harmonic generation from a lattice of nonlinear bilayers that confirms the surface character of this nonlinear process in this type of material.

© 1998 Optical Society of America

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References

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  1. J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
    [CrossRef]
  2. J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
    [CrossRef]
  3. R. W. J. Hollering and W. J. O. V. Tesselink, “Angular dependence of optical second-harmonic generation in molecular monolayers,” Opt. Commun. 79, 224 (1990).
    [CrossRef]
  4. N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970).
    [CrossRef]
  5. J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319 (1994).
    [CrossRef]
  6. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 25, p. 480.
  7. The coupling coefficient or the directly related Bragg bandwidth in the case of an fcc lattice of spherical particles was derived by R. J. Spry and D. J. Kosan, “Theoretical analysis of the crystalline colloidal array filter,” Appl. Spectrosc. 40, 782 (1986).
    [CrossRef]
  8. T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), Chap. 5.

1997

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
[CrossRef]

1994

J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319 (1994).
[CrossRef]

1990

R. W. J. Hollering and W. J. O. V. Tesselink, “Angular dependence of optical second-harmonic generation in molecular monolayers,” Opt. Commun. 79, 224 (1990).
[CrossRef]

1986

1970

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

Bloembergen, N.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

Corbalán, R.

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
[CrossRef]

J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319 (1994).
[CrossRef]

Hollering, R. W. J.

R. W. J. Hollering and W. J. O. V. Tesselink, “Angular dependence of optical second-harmonic generation in molecular monolayers,” Opt. Commun. 79, 224 (1990).
[CrossRef]

Kosan, D. J.

Martorell, J.

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
[CrossRef]

J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319 (1994).
[CrossRef]

Sievers, A. J.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

Spry, R. J.

Tesselink, W. J. O. V.

R. W. J. Hollering and W. J. O. V. Tesselink, “Angular dependence of optical second-harmonic generation in molecular monolayers,” Opt. Commun. 79, 224 (1990).
[CrossRef]

Vilaseca, R.

J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
[CrossRef]

Appl. Phys. Lett.

N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Appl. Phys. Lett. 70, 702 (1997).
[CrossRef]

Appl. Spectrosc.

Opt. Commun.

R. W. J. Hollering and W. J. O. V. Tesselink, “Angular dependence of optical second-harmonic generation in molecular monolayers,” Opt. Commun. 79, 224 (1990).
[CrossRef]

J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319 (1994).
[CrossRef]

Phys. Rev. A

J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Phys. Rev. A 55, 4520 (1997).
[CrossRef]

Other

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 25, p. 480.

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), Chap. 5.

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Figures (5)

Fig. 1
Fig. 1

Reflected SH intensity from eight crystals with different lattice spacing. The circular dots correspond to the experimental values measured for eight crystals with Laue resonances at (a) 12°, (b) 15.5°, (c) 16.7°, (d) 19.5°, (e) 22°, (f) 29.7°, (g) 34.3°, and (h) 36.2° (the dashed curve is only a guide for the eye).

Fig. 2
Fig. 2

Bragg-reflection band for one of the colloidal crystals. The circular dots correspond to the experimental values measured for crystal (c) of Fig. 1, and the solid curve is the theoretically calculated Bragg-reflection band for a crystal made of 500 bilayers as the ones shown in the inset of the figure. The inset corresponds to a section of three bilayers of the periodic structure considered in the theoretical analysis. The index of the dark layers where the NL molecules are adsorbed is n1, and the index of the surrounding material is n0.

Fig. 3
Fig. 3

Reflected maximum SH intensity from the same eight crystals of Fig. 1. The circular dots correspond to the experimentally measured values, while the solid squares represent the values for maximum SH intensity obtained from the numerical calculation with the bilayer model described in the text.

Fig. 4
Fig. 4

Reflected SH intensity from a crystal of plane bilayers as a function of the number of layers. This numerical result was obtained considering a 5% dispersion in the length of the nonlinear slab and an effective absorption coefficient of 46 cm-1 for the SH and 3.6 cm-1 for the fundamental in the model.

Fig. 5
Fig. 5

Reflected SH intensity for crystal (f) of Fig. 1. The experimental values measured are represented in circular dots (the dashed curve is only a guide for the eye), and the solid curve is the reflected SH intensity obtained from the theoretical model for a 2500 bilayer crystal with the parameters measured from the passive properties of the crystal (f).

Equations (1)

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2E2ω-(E2ω)-c2 2E2ωt2=μ0 2PNLt2,

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