Abstract

We propose the concept of a photonic band-gap (PBG) prism based on two-dimensional PBG structures and realize it in the millimeter-wave spectral regime. We recognize the highly nonlinear dispersion of PBG materials near Brillouin zone edges and utilize the dispersion to achieve strong prism action. Such a PBG prism is very compact if operated in the optical regime, ~20 μm in size for λ ~ 700 nm, and can serve as a dispersive element for building ultracompact miniature spectrometers.

© 1996 Optical Society of America

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References

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  1. E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 67, 3380 (1991).
    [CrossRef] [PubMed]
  2. J. Martorell, N. M. Lawandy, Opt. Commun. 78, 169 (1990).
    [CrossRef]
  3. See, for example, J. P. Dowling, C. M. Bowden, J. Mod. Opt. 41, 345 (1994).
    [CrossRef]
  4. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322 (1993); P. R. Villeneuve, M. Piche, Phys. Rev. B 46, 4969 (1992).
    [CrossRef]
  5. S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
    [CrossRef]
  6. See, for example, E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), pp. 129–131.
  7. See, for example, B. D. Guenther, Proc. SPIE 2145, 120 (1994).
    [CrossRef]

1996 (1)

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

1994 (2)

See, for example, B. D. Guenther, Proc. SPIE 2145, 120 (1994).
[CrossRef]

See, for example, J. P. Dowling, C. M. Bowden, J. Mod. Opt. 41, 345 (1994).
[CrossRef]

1993 (1)

1990 (1)

J. Martorell, N. M. Lawandy, Opt. Commun. 78, 169 (1990).
[CrossRef]

1989 (1)

E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Arjavalingam, G.

Bowden, C. M.

See, for example, J. P. Dowling, C. M. Bowden, J. Mod. Opt. 41, 345 (1994).
[CrossRef]

Brommer, K. D.

Dowling, J. P.

See, for example, J. P. Dowling, C. M. Bowden, J. Mod. Opt. 41, 345 (1994).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Guenther, B. D.

See, for example, B. D. Guenther, Proc. SPIE 2145, 120 (1994).
[CrossRef]

Hecht, E.

See, for example, E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), pp. 129–131.

Hietala, V. M.

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

Joannopoulos, J. D.

Lawandy, N. M.

J. Martorell, N. M. Lawandy, Opt. Commun. 78, 169 (1990).
[CrossRef]

Lin, S. Y.

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

Lyo, S. K.

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

Martorell, J.

J. Martorell, N. M. Lawandy, Opt. Commun. 78, 169 (1990).
[CrossRef]

Meade, R. D.

Rappe, A. M.

Robertson, W. M.

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Zajac, A.

See, for example, E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), pp. 129–131.

Zaslavsky, A.

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

S. Y. Lin, V. M. Hietala, S. K. Lyo, A. Zaslavsky, Appl. Phys. Lett. 68, 3233 (1996).
[CrossRef]

J. Mod. Opt. (1)

See, for example, J. P. Dowling, C. M. Bowden, J. Mod. Opt. 41, 345 (1994).
[CrossRef]

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

Opt. Commun. (1)

J. Martorell, N. M. Lawandy, Opt. Commun. 78, 169 (1990).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); E. Yablonovitch, T. J. Gmitter, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Proc. SPIE (1)

See, for example, B. D. Guenther, Proc. SPIE 2145, 120 (1994).
[CrossRef]

Other (1)

See, for example, E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), pp. 129–131.

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Figures (5)

Fig. 1
Fig. 1

Schematics of (a) PBG dispersion, f versus k, of a PBG material, showing the linear and nonlinear regimes as well as the PBG; (b) the corresponding index of refraction, neff, plotted as a function of frequency f; (c) a 2-D triangular array. The arrows indicate directions of light propagation. δ is the angle of the deviation.

Fig. 2
Fig. 2

Schematic of our PBG prism transmission measurement setup.

Fig. 3
Fig. 3

Transmission spectra of EM waves as a function of frequency f through a bandpass filter (a) with no prism in the beam path (as a reference) and (b) with a PBG prism present. The incident angle is θi = 60°, and the angle of deviation is δ = 46.5°.

Fig. 4
Fig. 4

Plot of δ versus θi at f = 99 GHz. The filled circles are experimental data, and the curve is a least-squares fit to Eq. (1) with a single fitting parameter, neff = 1.57.

Fig. 5
Fig. 5

Plot of the measured neff as a function of f for a 2D triangular lattice structure with a0 = 0.81 mm and d = 0.305 mm. As expected, neff increases rapidly as f approaches the band edge of the fundamental TM band gap.

Equations (1)

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δ = θ i + sin 1 { ( sin α ) [ n 2 sin 2 θ i ] 1 / 2 sin θ i cos α } α .

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