Abstract

We have experimentally measured the birefringence in bulk two-dimensional hexagonal photonic crystals in transparent spectral regions above and below the fundamental band gap. Data is presented for structures with different numbers of layers and two different air-filling fractions. We have used these data to design a photonic crystal quarter waveplate and provide independent experimental demonstrations of its operation.

© 2002 Optical Society of America

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References

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  1. E. Yablonovitch, �??Photonic crystals,�?? J. Mod. Opt. 41, 173 (1994).
    [CrossRef]
  2. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, D. C. Allan, �??Single-mode photonic band gap guidance of light in air,�?? Science 285, 1537 (1999).
    [CrossRef] [PubMed]
  4. S. Mingaleev and Y. Kivshar, �??Nonlinear photonic crystals toward all-optical technologies,�?? Opt. & Phot. News 13, 48 (2002).
    [CrossRef]
  5. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, �??Three-dimensional control of light in a twodimensional photonic crystal slab,�?? Nature 407, 983 (2000).
    [CrossRef] [PubMed]
  6. R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel applications of photonic band-gap materials - Low-loss bends and high Q-cavities,�?? J. Appl. Phys. 75, 4753 (1994).
    [CrossRef]
  7. T. A. Birks, P. J. Roberts, P. St. J. Russel, D. M. Atkin and T. J. Shepherd, �??Full 2-D photonic bandgaps in silica/air structures,�?? Electron. Lett. 31, 1941 (1995).
    [CrossRef]
  8. S. G. Johnson, J. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751 (1999).
    [CrossRef]
  9. E. Ozbay, in Photonic Band Gap Materials, C. M. Soukoulis, ed. (Kluwer, Amsterdam, 1996), p. 41.
    [CrossRef]
  10. J. M. Hickmann, D. Solli, C. F. McCormick, R. Plambeck, and R. Y. Chiao, �??Microwave measurements of the photonic band gap in a two-dimensional photonic crystal slab,�?? J. Appl. Phys. 92, 6918 (2002).
    [CrossRef]
  11. S. Foteinopoulou, A. Rosenberg, M M. Sigalas, and C. M. Soukoulis, �??In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,�?? J. Appl. Phys. 89, 824 (2001).
    [CrossRef]
  12. H. A. Macleod, Thin-film Optical Filters, (Hilger, London, 1969).
  13. D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, �??Experimental observation of superluminal group velocities in bulk two-dimensional photonic band gap crystals,�?? to appear in IEEE J. Sel. Top. Quantum Electron. (2003).
    [CrossRef]
  14. R. W. Ditchburn, Light, 3rd ed., (Interscience, New York, 1976), Appendix XIX B.
  15. C. Kittel, Introduction to Solid State Physics, 7th ed., (Wiley, New York, 1996), Chap. 11.
  16. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, �??Highly birefringent photonic crystal fibers,�?? Opt. Lett. 25, 1325 (2000).
    [CrossRef]
  17. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, �??Highly birefringent index-guiding photonic crystal fibers,�?? IEEE Phot. Tech. Lett. 13, 588 (2001).
    [CrossRef]
  18. C. Kerbage, P. Steinvurzel, P. Reyes, P. S.Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, �??Highly tunable birefringent microstructured optical fiber,�?? Opt. Lett. 27, 842 (2002).
    [CrossRef]
  19. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, �??Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,�?? Science 293, 1123 (2001).
    [CrossRef] [PubMed]
  20. R. E. Slusher, S. Spalter, B. J. Eggleton, S. Pereira, and J. E. Sipe, �??Bragg-grating-enhanced polarization instabilities,�?? Opt. Lett. 25, 749 (2000).
    [CrossRef]
  21. S. Pereira, J. E. Sipe, R. E. Slusher, and Stefan Sp¨alter, �??Enhanced and suppressed birefringence in .ber Bragg gratings,�?? J. Opt. Soc. Am. B 19, 1509 (2002).
    [CrossRef]
  22. L. Li, �??Two-dimensional photonic crystals: Candidate for waveplates,�?? Appl. Phys. Lett. 78, 3400 (2001).
    [CrossRef]
  23. D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, �??Experimental demonstration of photonic crystal waveplates,�?? to appear in Appl. Phys. Lett. (February 03, 2003).
  24. AIP Handbook, 3rd ed., edited by D. E. Gray (McGraw-Hill, New York, 1972), p. 5-132.

Appl. Phys. Lett. (2)

L. Li, �??Two-dimensional photonic crystals: Candidate for waveplates,�?? Appl. Phys. Lett. 78, 3400 (2001).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, �??Experimental demonstration of photonic crystal waveplates,�?? to appear in Appl. Phys. Lett. (February 03, 2003).

Electron. Lett. (1)

T. A. Birks, P. J. Roberts, P. St. J. Russel, D. M. Atkin and T. J. Shepherd, �??Full 2-D photonic bandgaps in silica/air structures,�?? Electron. Lett. 31, 1941 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, �??Experimental observation of superluminal group velocities in bulk two-dimensional photonic band gap crystals,�?? to appear in IEEE J. Sel. Top. Quantum Electron. (2003).
[CrossRef]

IEEE Phot. Tech. Lett. (1)

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, �??Highly birefringent index-guiding photonic crystal fibers,�?? IEEE Phot. Tech. Lett. 13, 588 (2001).
[CrossRef]

J. Appl. Phys. (3)

J. M. Hickmann, D. Solli, C. F. McCormick, R. Plambeck, and R. Y. Chiao, �??Microwave measurements of the photonic band gap in a two-dimensional photonic crystal slab,�?? J. Appl. Phys. 92, 6918 (2002).
[CrossRef]

S. Foteinopoulou, A. Rosenberg, M M. Sigalas, and C. M. Soukoulis, �??In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,�?? J. Appl. Phys. 89, 824 (2001).
[CrossRef]

R. D. Meade, A. Devenyl, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel applications of photonic band-gap materials - Low-loss bends and high Q-cavities,�?? J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

J. Mod. Opt. (1)

E. Yablonovitch, �??Photonic crystals,�?? J. Mod. Opt. 41, 173 (1994).
[CrossRef]

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

Nature (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, �??Three-dimensional control of light in a twodimensional photonic crystal slab,�?? Nature 407, 983 (2000).
[CrossRef] [PubMed]

Opt. Lett. (3)

Opt. Phot. News (1)

S. Mingaleev and Y. Kivshar, �??Nonlinear photonic crystals toward all-optical technologies,�?? Opt. & Phot. News 13, 48 (2002).
[CrossRef]

Phys. Rev. B (1)

S. G. Johnson, J. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Science (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, D. C. Allan, �??Single-mode photonic band gap guidance of light in air,�?? Science 285, 1537 (1999).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, �??Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,�?? Science 293, 1123 (2001).
[CrossRef] [PubMed]

Other (5)

R. W. Ditchburn, Light, 3rd ed., (Interscience, New York, 1976), Appendix XIX B.

C. Kittel, Introduction to Solid State Physics, 7th ed., (Wiley, New York, 1996), Chap. 11.

AIP Handbook, 3rd ed., edited by D. E. Gray (McGraw-Hill, New York, 1972), p. 5-132.

E. Ozbay, in Photonic Band Gap Materials, C. M. Soukoulis, ed. (Kluwer, Amsterdam, 1996), p. 41.
[CrossRef]

H. A. Macleod, Thin-film Optical Filters, (Hilger, London, 1969).

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Figures (5)

Fig. 1.
Fig. 1.

Experimentally measured TM (green line) and TE (blue line) indices of refraction for hexagonal crystals with 16 layers and AFFs 0.60 (a) and 0.32 (b). The curves are shown on both sides of the fundamental band gap (shaded areas).

Fig. 2.
Fig. 2.

Experimentally measured differences between the indices of refraction (purple solid lines) for 4- (a), 8- (b), and 16-layer (c) crystals with AFF 0.60. Data are shown on both sides of the fundamental TM and TE band gap (shaded areas). First (red dashed lines), second (green dotted lines), third (blue short dashed line), and fourth (cyan short dotted line) order quarter wave condition (QWC) curves are also displayed.

Fig. 3.
Fig. 3.

Experimentally measured differences in the indices of refraction (solid lines) for 4- (a), 8- (b), and 16-layer (c) crystals with AFF 0.32. Data are shown on both sides of the fundamental TM and TE band gap (shaded areas). First (red dashed lines), second (green dotted line), and third (blue short dashed line) order quarter waveplate condition (QWC) curves are also displayed.

Fig. 4.
Fig. 4.

Experimentally measured power transmission vs. frequency with the receiver horn oriented at 0°, 45°, 90°, and 135° from the transmitter horn; for 4- (a), 8-(b), and 16-layer (c) crystals with AFF 0.60. At 0°, the receiver horn antenna is perpendicular to the optic axis of the crystal.

Fig. 5.
Fig. 5.

Experimentally measured amplitude transmission at 17.4 GHz vs. horn rotation angle, for an 8-layer crystal with AFF 0.60. The horns are rotated together with a fixed angle between them of 0 (closed green squares) and 90° (open blue circles). Also plotted are the functions 1 2 sin 2 θ and cos 4 θ + sin 4 θ .

Equations (5)

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n ( ω ) = 1 + c Δ ϕ ω L ,
L = [ 2 + ( N 1 ) 3 ] r ,
Δ n ( ω ) = π c ω L ( m + 1 2 )
E E 0 = cos 4 θ + sin 4 θ
E E 0 = 1 2 sin 2 θ

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