Abstract

The propagation of 120-fs laser pulses through nonlinear waveguides with embedded high-contrast, two-dimensional photonic crystals was studied. Each AlGaAs waveguide fabricated upon a GaAs substrates contained a region of deeply etched air holes in a triangular lattice to form the photonic crystal. In transmission, a photonic bandgap was formed with a short-wavelength photonic bandedge at 925 nm from a 270-nm period lattice in the Γ–K orientation. Pulse propagation was highly nonlinear, with both strong optical limiting and spectral narrowing. These effects arose from the waveguide rather than from the photonic crystal. Nonlinear effects were simulated theoretically, with good agreement with the data, by consideration of the effects of two-photon absorption and self-phase modulation on chirped incident pulses.

© 2002 Optical Society of America

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References

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  1. T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
    [CrossRef]
  2. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 μm wavelengths,” Opt. Lett. 26, 286–288 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. B. J. Eggleton, C. Martijn de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
    [CrossRef] [PubMed]
  7. N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen, and R. I. Laming, “Experimental observation of nonlinear pulse compression in nonuniform Bragg gratings,” Opt. Lett. 22, 1837–1839 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
    [CrossRef] [PubMed]
  11. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7, p. 240.
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    [CrossRef]
  13. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
    [CrossRef]
  14. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, Oxford, 1997), Chap. 3, pp. 98–104.
  15. R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
    [CrossRef]

2001 (1)

1999 (2)

T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in an AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
[CrossRef]

1997 (3)

1996 (2)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

B. J. Eggleton, C. Martijn de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
[CrossRef] [PubMed]

1994 (2)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

1993 (1)

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

1990 (2)

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

H. Q. Le, H. K. Choi, and C. A. Wang, “Measurement of the two-photon absorption coefficient in a GaAs/AlGaAs quantum well laser,” Appl. Phys. Lett. 57, 212–214 (1990).
[CrossRef]

Aitchison, J. S.

P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in an AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Broderick, N. G. R.

Choi, H. K.

H. Q. Le, H. K. Choi, and C. A. Wang, “Measurement of the two-photon absorption coefficient in a GaAs/AlGaAs quantum well laser,” Appl. Phys. Lett. 57, 212–214 (1990).
[CrossRef]

Chow, E.

Colas, E.

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

De La Rue, R. M.

T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in an AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Eggleton, B. J.

Fox, A. M.

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Grousson, R.

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Huttner, B.

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Ibsen, M.

Joannopoulos, J. D.

Johnson, S. G.

Kang, J. U.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Kapon, E.

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

Krauss, T. F.

T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in an AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Laming, R. I.

Lavallard, P.

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Le, H. Q.

H. Q. Le, H. K. Choi, and C. A. Wang, “Measurement of the two-photon absorption coefficient in a GaAs/AlGaAs quantum well laser,” Appl. Phys. Lett. 57, 212–214 (1990).
[CrossRef]

Lin, S. Y.

Martijn de Sterke, C.

Millar, P.

Oliver, M. K.

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

Pate, M. A.

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Planel, R.

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Richardson, D. J.

Roberts, J. S.

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Roblin, M. L.

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Ryan, J. F.

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Slusher, R. E.

Smith, P. W. E.

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

Stegeman, G. I.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Taverner, D.

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

Voliotis, V.

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Wang, C. A.

H. Q. Le, H. K. Choi, and C. A. Wang, “Measurement of the two-photon absorption coefficient in a GaAs/AlGaAs quantum well laser,” Appl. Phys. Lett. 57, 212–214 (1990).
[CrossRef]

Wendt, J. R.

Appl. Phys. Lett. (2)

H. Q. Le, H. K. Choi, and C. A. Wang, “Measurement of the two-photon absorption coefficient in a GaAs/AlGaAs quantum well laser,” Appl. Phys. Lett. 57, 212–214 (1990).
[CrossRef]

J. S. Aitchison, M. K. Oliver, E. Kapon, E. Colas, and P. W. E. Smith, “Role of two-photon absorption in ultrafast semiconductor optical switching devices,” Appl. Phys. Lett. 56, 1305–1307 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
[CrossRef]

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

Nature (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

A. M. Fox, B. Huttner, J. F. Ryan, M. A. Pate, and J. S. Roberts, “Evaluation of GaAs/Al0.3Ga0.7As multiple quantum-well waveguides for pulsed squeezed light generation,” Phys. Rev. A 50, 4415–4418 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

Semicond. Sci. Technol. (1)

R. Grousson, V. Voliotis, P. Lavallard, M. L. Roblin, and R. Planel, “Determination of excitonic properties in GaAs/Ga1−xAlxAs quantum wells by optical waveguiding experiments,” Semicond. Sci. Technol. 8, 1217–1225 (1993).
[CrossRef]

Other (2)

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 7, p. 240.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, Oxford, 1997), Chap. 3, pp. 98–104.

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Figures (6)

Fig. 1
Fig. 1

(a) Optical microscope image of the top view of the sample. Channel waveguides of 2-µm width can be seen entering and exiting the photonic crystal region. The top waveguide contains a 36-period photonic crystal, the middle waveguide contains no photonic crystal and is termed a blank waveguide, and the bottom waveguide is an 18-period photonic crystal. (b) Scanning-electron microscope image of a similar photonic crystal sample. In this case the 210-nm Γ–M lattice of air holes can be seen clearly.

Fig. 2
Fig. 2

Spectra of 120-fs laser pulses centered at wavelengths from 910 to 935 nm after transmission through a waveguide containing an 18-period, 270-nm lattice spacing, Γ–K photonic crystal. The laser power was 0.08 mW. Inset, transmission spectrum of the photonic crystal obtained from the transmitted pulse spectra.

Fig. 3
Fig. 3

Laser output intensity transmitted through a blank waveguide versus input intensity when the laser was tuned to 920-nm center wavelength. The curve is a fit to relation (1) for the parameters given in Table 1 below.

Fig. 4
Fig. 4

(a) Spectra of 120-fs laser pulses centered at 920 nm transmitted through a waveguide containing an 18-period, 270-nm lattice spacing, Γ–K photonic crystal as a function of increasing laser power. (b) Spectra of pulses centered at 920 nm transmitted through the blank waveguide.

Fig. 5
Fig. 5

Schematic showing the direction of light propagation through the waveguides and the distinct regions considered in the theoretical model.

Fig. 6
Fig. 6

Theoretical prediction of the shaping of a chirped laser pulse spectrally centered at 920 nm after the pulse has passed through (a) a nonlinear photonic crystal waveguide and (b) a blank waveguide.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in Fitting the Transmission Data in Fig. 3 and 4

Equations (7)

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

Ioutco exp(-αz)β[1-exp(-αz)]α+1ciIin,
C(ω, t)=a(ω)exp[i(ωt)]×expiΩ(ω)t-λ24πcDΩ(ω)2z,
E(t)= C(ω, t)dω
ΔΦ(t)=2πlλ[n2I(t)],
Eout(t)=Ein(t)exp[iΔΦ(t)],
Eout(t)=Ein(t)exp-αl2,
Eout(t)=Ein(t)[1-βlEin(t)Ein*(t)],

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