Abstract

Periodic intensity variations as a function of incident and azimuthal angles were observed upon rotating a face-centered-cubic photonic crystal with respect to a linearly polarized microwave beam. These intensity variations also depended on the radiation frequency. We have studied propagating wavelengths that were smaller than, comparable with, and larger than the crystallographic pitches. It is suggested that the observed transmission variations arise from the combination of a periodic structure with transverse confinement of the propagating wave. Such diffraction configurations may permit spatial filtering techniques with subwavelength periodic structures.

© 2002 Optical Society of America

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References

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  1. T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
    [CrossRef]
  2. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
    [CrossRef]
  3. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  4. H. Grebel, J. L. Graziani, S. Vijayalakshmi, L. Shacklette, K. Stengel, L. Eldada, R. Norwood, and J. Yardley, “Self-imaging chirp holographic optical waveguides,” Appl. Opt. 36, 9391–9395 (1997).
    [CrossRef]
  5. J. M. Tobias and H. Grebel, “Self-imaging in photonic crystals in a subwavelength range,” Opt. Lett. 24, 1660–1662 (1999).
    [CrossRef]
  6. S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
    [CrossRef]
  7. S. C. Tsay and H. Grebel, “Transverse holographic optical interconnect design,” Appl. Opt. 33, 6747–6749 (1994).
    [CrossRef] [PubMed]
  8. S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
    [CrossRef]
  9. M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
    [CrossRef]
  10. J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 293, 49–57 (1994).

2001

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

1999

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

J. M. Tobias and H. Grebel, “Self-imaging in photonic crystals in a subwavelength range,” Opt. Lett. 24, 1660–1662 (1999).
[CrossRef]

1998

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

1997

1995

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

1994

1987

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Ajgaonkar, M.

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

Atkins, D. M.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

Birks, T. A.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

Brewitt-Taylor, C. R.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Dimond, P.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Dorsinville, R.

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

Eldada, L.

Enoch, S.

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Fixter, G.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Graziani, J. L.

Grebel, H.

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

J. M. Tobias and H. Grebel, “Self-imaging in photonic crystals in a subwavelength range,” Opt. Lett. 24, 1660–1662 (1999).
[CrossRef]

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

H. Grebel, J. L. Graziani, S. Vijayalakshmi, L. Shacklette, K. Stengel, L. Eldada, R. Norwood, and J. Yardley, “Self-imaging chirp holographic optical waveguides,” Appl. Opt. 36, 9391–9395 (1997).
[CrossRef]

S. C. Tsay and H. Grebel, “Transverse holographic optical interconnect design,” Appl. Opt. 33, 6747–6749 (1994).
[CrossRef] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Laight, A.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Lederer, P.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Maystre, D.

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Norwood, R.

Pendry, J. B.

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 293, 49–57 (1994).

Roberts, P. J.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

Russell, P. St. J.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

Shacklette, L.

Shepard, T. J.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

Stengel, K.

Tapster, P. R.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Tobias, J. M.

Tsay, S. C.

Vijayalakshmi, S.

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

H. Grebel, J. L. Graziani, S. Vijayalakshmi, L. Shacklette, K. Stengel, L. Eldada, R. Norwood, and J. Yardley, “Self-imaging chirp holographic optical waveguides,” Appl. Opt. 36, 9391–9395 (1997).
[CrossRef]

White, C. W.

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

Yaglioglu, G.

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

Yardley, J.

Youngs, I. J.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

Zhang, Y.

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Ajgaonkar, Y. Zhang, H. Grebel, and C. W. White, “Nonlinear optical properties of a coherent array of sub-micron SiO2 spheres (opal) embedded with Si nanoparticles,” Appl. Phys. Lett. 75, 1532–1534 (1999).
[CrossRef]

S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Dorsinville, and C. W. White, “Nonlinear dispersion properties of sub-wavelength photonic crystals,” Appl. Phys. Lett. 78, 1, 1754–1756 (2001).
[CrossRef]

Electron. Lett.

T. J. Shepard, C. R. Brewitt-Taylor, P. Dimond, G. Fixter, A. Laight, P. Lederer, P. J. Roberts, P. R. Tapster, and I. J. Youngs, “3D microwave photonic crystals: novel fabrication and structures,” Electron. Lett. 34, 787–788 (1998).
[CrossRef]

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkins, and T. J. Shepard, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995).
[CrossRef]

J. Mod. Opt.

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 293, 49–57 (1994).

Opt. Commun.

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Experimental coordinates. A close-packed fcc structure comprised of spherical media was rotated with respect to the incident angle θ and azimuthal angle ϕ. Microwave and laser radiation propagated along the x axis at an incident angle θ, with respect to the crystal-face normal.

Fig. 2
Fig. 2

Contour plots of transmitted intensity (dBm) at the self-imaging point as a function of incident and azimuthal angles at (a) f=5 GHz, (b) f=10 GHz, (c) f=15 GHz.

Fig. 3
Fig. 3

Contour plots of transmitted intensity variations (dBm) as a function of radiation frequency and azimuthal angles at a given incident angle; (a) θ=0°, (b) θ=10°, (c) θ=25°.

Fig. 4
Fig. 4

Transmission through a sample with four layers. The arrows indicate the position of the peaks. The sphere diameter was 31 mm. (a) Incident angle θ is (a) 0°, (b) 10° (close to the magic angle), (c) 15°.

Fig. 5
Fig. 5

Experimental results for artificial opal; λ=0.532 µm, D=0.300 µm. The structure consists of 40 layers with an approximate total thickness of 10 µm. The data are normalized to a reference signal.

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