Abstract

Light passing through a photonic crystal can undergo a negative or a positive refraction. The two refraction states can be functions of the contrast index, the incident angle and the slab thickness. By suitably using these properties it is possible to realize very simple and very efficient optical components to route the light. As an example we present a passive device acting as a polarizing beam splitter where TM polarization is refracted in positive direction whereas TE component is negatively refracted.

© 2005 Optical Society of America

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References

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  1. J.D. Joannopulos, R.D. Mead, J.N. Winn, Photonic crystal: Molding the flow of light, Princeton University Press (Princeton, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals, Springer Verlag (2001).
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10 096-099 (1998).
    [CrossRef]
  4. M. Notomi. "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
    [CrossRef]
  5. F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner and U. Gösele, �??Large birefringence in twodimensional silicon photonic crystals,�?? Phys. Rev. B 63, 161101 (2001).
    [CrossRef]
  6. Lijun Wu, M. Mazilu, J.-F. Gallet and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106, (2005).
    [CrossRef]
  7. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney and M. Mansuripur, �??Design of a Compact Photonic- Crystal-Based Polarizing Beam Splitter,�?? IEEE Photonics Technol. Lett., 17, 1435-1437 (2005).
    [CrossRef]
  8. C. Y. Luo, S. G. Johnson and J. D. Joannopoulos. "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
    [CrossRef]
  9. E. Cubukcu, K. Aydin, et al. "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
    [CrossRef] [PubMed]
  10. J. B. Pendry and D. R. Smith. "Reversing light with negative refraction,�?? Physics Today 57, 37-43 (2004).
    [CrossRef]
  11. S Anantha Ramakrishna, �??Physics of negative refractive index materials,�?? Rep. Prog. Phys. 68, 449�??521 (2005).
    [CrossRef]
  12. V. Mocella, "Negative refraction in Photonic Crystals: thickness dependence and Pendellösung phenomenon," Opt. Express 13, 1361-1367 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1361">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1361</a>.
    [CrossRef] [PubMed]
  13. B. W. Battermann, H. Cole, �??Dynamical diffraction theory of X rays by perfect crystals,�?? Rev. Mod. Phys. 36, 681-717 (1964).
    [CrossRef]
  14. P.P. Ewald, �??Crystal optics for visible light and X rays,�?? Rev. Mod. Physics 37, 46-56 (1965).
    [CrossRef]
  15. G.S. Agarwal, D. N. Pattanyak, E. Wolf, "Electromagnetic field in spatially dispersive media," Phys. Rev. B, 10, 1447-1475 (1974).
    [CrossRef]
  16. K. Henneberger, "Additional Boundary Condition: an historical mistake," Phys. Rev. Lett. 80, 2889-2892, (1998).
    [CrossRef]
  17. J.J. Hopefield, D.G. Thomas, �??Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,�?? Phys. Rev. 123, 563-572 (1963).
    [CrossRef]

Appl. Phys. Lett. (2)

C. Y. Luo, S. G. Johnson and J. D. Joannopoulos. "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

Lijun Wu, M. Mazilu, J.-F. Gallet and T. F. Krauss, "Dual lattice photonic-crystal beam splitters," Appl. Phys. Lett. 86, 211106, (2005).
[CrossRef]

IEEE Photonics Technol. (1)

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney and M. Mansuripur, �??Design of a Compact Photonic- Crystal-Based Polarizing Beam Splitter,�?? IEEE Photonics Technol. Lett., 17, 1435-1437 (2005).
[CrossRef]

Nature (1)

E. Cubukcu, K. Aydin, et al. "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. (1)

J.J. Hopefield, D.G. Thomas, �??Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,�?? Phys. Rev. 123, 563-572 (1963).
[CrossRef]

Phys. Rev. B (4)

G.S. Agarwal, D. N. Pattanyak, E. Wolf, "Electromagnetic field in spatially dispersive media," Phys. Rev. B, 10, 1447-1475 (1974).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10 096-099 (1998).
[CrossRef]

M. Notomi. "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

F. Genereux, S. W. Leonard, H. M. van Driel, A. Birner and U. Gösele, �??Large birefringence in twodimensional silicon photonic crystals,�?? Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

K. Henneberger, "Additional Boundary Condition: an historical mistake," Phys. Rev. Lett. 80, 2889-2892, (1998).
[CrossRef]

Physics Today (1)

J. B. Pendry and D. R. Smith. "Reversing light with negative refraction,�?? Physics Today 57, 37-43 (2004).
[CrossRef]

Rep. Prog. Phys. (1)

S Anantha Ramakrishna, �??Physics of negative refractive index materials,�?? Rep. Prog. Phys. 68, 449�??521 (2005).
[CrossRef]

Rev. Mod. Phys. (1)

B. W. Battermann, H. Cole, �??Dynamical diffraction theory of X rays by perfect crystals,�?? Rev. Mod. Phys. 36, 681-717 (1964).
[CrossRef]

Rev. Mod. Physics (1)

P.P. Ewald, �??Crystal optics for visible light and X rays,�?? Rev. Mod. Physics 37, 46-56 (1965).
[CrossRef]

Other (2)

J.D. Joannopulos, R.D. Mead, J.N. Winn, Photonic crystal: Molding the flow of light, Princeton University Press (Princeton, 1995).

K. Sakoda, Optical Properties of Photonic Crystals, Springer Verlag (2001).

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

When the incoming wavelength is larger than the lattice period of the PhC the medium can be considered homogeneous and the dispersion surfaces are spheres (a). When the wavelength decreases the spheres approach one another and a Bragg gap appears (b). The conservation of the tangential component of the wavevector in the external medium, k i , determines the wavevectors in the PhC: P 1 O , P 2 O , P 1 H , P 2 H (c).

Fig. 2.
Fig. 2.

Dispersion (equi-frequency) surface for an air hole square lattice PhC in silicon (ε=11.9), r/a=0.195, in two adjacent Brillouin zones along the ΓX direction for TM polarization (E along the holes’ axis). By increasing the normalized frequency from 0.06 to 0.1848, the dispersion surfaces intersect over the lower 0-band (a). In such a case the upper 1-band has to be considered as well to get the complete dispersion surface, where the Bragg gap 2π/λ0 occurs (b).

Fig. 3.
Fig. 3.

Band diagram of the PhC of Fig. 2 for TM polarization (a). The regions along the XM direction, where many wavevectors are allowed for a given frequency, are highlighted in gray and labeled as α-β-γ. The dispersion surfaces corresponding to a frequency in region β (b) and region γ (c) show the overlap of different bands.

Fig. 4.
Fig. 4.

Band diagram for TM and TE polarization referring to the same PhC as in Fig. 2, along the XM direction (a). Λ0 /a as a function of ωn (b). The difference between the two polarization states is apparent.

Fig. 5
Fig. 5

(2.42 Mb) Movie versus time of FDTD simulation for TM (a) and TE polarization (b). The incident wave (λ=1.55 μm) has a Gaussian profile with 4 μm FWHM and impinges at an angle 20.57° over a PhC square lattice of air holes in silicon with r/a=0.195, a=0.64 μm. The grid size in calculation is 15 nm, in x and z direction.

Fig. 6.
Fig. 6.

The power flows of the refracted beams and of the reflected beam as a function of the wavelength for TE (a) and TM (b) polarization.

Equations (4)

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k 2 = k 2 k = ( ω c ) 2 ε ˜ ( k , ω )
I + max t = 2 m Λ 0 2
I max t = ( 2 m i ) Λ 0 2 m = 1,2
t = 2 m Λ 0 TE 2 = ( 2 m 1 ) Λ 0 TM 2

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