Abstract

Optical switches using two transmission properties in triangular photonic crystals infiltrated with liquid crystals (LCs) are investigated for incorporation in wave-guided structures for planar lightwave circuits. The two devices employ partial band gap and anomalous refraction, which are based on the anisotropic characteristics of LC reorientation under applied fields. These switches have been designed and their parameters have been analyzed by the plane wave and finite-difference time-domain calculations. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.27. The anomalous refraction can be modulated to deflect a light beam with a maximum deflection angle ~57° when the frequency is 0.3. The tunability induced by LCs can create a sharp switching in the photonic devices.

© 2007 Optical Society of America

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References

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  1. J.-M. Lourtioz, H. Benisty, V. Berger, J.-M Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, Berlin, 2005).
  2. M. Soljaèiæ and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).
    [CrossRef]
  3. S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, "All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74, 046603 (2006).
    [CrossRef]
  4. B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
    [CrossRef]
  5. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
    [CrossRef]
  6. 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]
  7. X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
    [CrossRef] [PubMed]
  8. B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
    [CrossRef]
  9. D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
    [CrossRef] [PubMed]
  10. S. He, Y. Jin, Z. Ruan and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New J. Phys. 7, 210 (2005).
    [CrossRef]
  11. S. John and K. Busch, "Photonic bandgap formation and tunability in certain self-organizing systems," J. Lightwave Tech. 17, 1931-1943 (1999).
    [CrossRef]
  12. I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
  13. H. Takeda and K. Yoshino, "Tunable refraction effects in two-dimensional photonic crystals utilizing liquid crystals," Phys. Rev. E 67, 056607 (2003).
    [CrossRef]
  14. D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
    [CrossRef]
  15. S. Xiong and H. Fukshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
    [CrossRef]
  16. W. Park and J.-B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
    [CrossRef]
  17. L. Feng, X.-P. Liu, J. Ren, Y.-F. Tang, Y.-B. Chen, Y.-F. Chen, and Y.-Y. Zhu, "Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents," J. Appl. Phys. 97, 073104 (2005).
    [CrossRef]
  18. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
  19. K. M. Ho, C. T. Chen, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  20. S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).
    [CrossRef]
  21. A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
    [CrossRef]

2006 (1)

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, "All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74, 046603 (2006).
[CrossRef]

2005 (3)

S. He, Y. Jin, Z. Ruan and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New J. Phys. 7, 210 (2005).
[CrossRef]

L. Feng, X.-P. Liu, J. Ren, Y.-F. Tang, Y.-B. Chen, Y.-F. Chen, and Y.-Y. Zhu, "Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents," J. Appl. Phys. 97, 073104 (2005).
[CrossRef]

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

2004 (3)

W. Park and J.-B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
[CrossRef] [PubMed]

M. Soljaèiæ and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).
[CrossRef]

2003 (5)

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
[CrossRef] [PubMed]

H. Takeda and K. Yoshino, "Tunable refraction effects in two-dimensional photonic crystals utilizing liquid crystals," Phys. Rev. E 67, 056607 (2003).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

S. Xiong and H. Fukshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

2000 (2)

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]

B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

1999 (1)

S. John and K. Busch, "Photonic bandgap formation and tunability in certain self-organizing systems," J. Lightwave Tech. 17, 1931-1943 (1999).
[CrossRef]

1997 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

1996 (1)

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chen, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Appl. Phys. B (1)

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

W. Park and J.-B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

IEEE Trans. Antennas Propagat. (1)

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).
[CrossRef]

J. Appl. Phys. (2)

L. Feng, X.-P. Liu, J. Ren, Y.-F. Tang, Y.-B. Chen, Y.-F. Chen, and Y.-Y. Zhu, "Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents," J. Appl. Phys. 97, 073104 (2005).
[CrossRef]

S. Xiong and H. Fukshima, "Analysis of light propagation in index-tunable photonic crystals," J. Appl. Phys. 94, 1286-1288 (2003).
[CrossRef]

J. Lightwave Tech. (1)

S. John and K. Busch, "Photonic bandgap formation and tunability in certain self-organizing systems," J. Lightwave Tech. 17, 1931-1943 (1999).
[CrossRef]

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

Nature Mater. (1)

M. Soljaèiæ and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004).
[CrossRef]

New J. Phys. (1)

S. He, Y. Jin, Z. Ruan and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New J. Phys. 7, 210 (2005).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (2)

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]

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

Phys. Rev. E (2)

H. Takeda and K. Yoshino, "Tunable refraction effects in two-dimensional photonic crystals utilizing liquid crystals," Phys. Rev. E 67, 056607 (2003).
[CrossRef]

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, "All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures," Phys. Rev. E 74, 046603 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

K. M. Ho, C. T. Chen, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Other (3)

J.-M. Lourtioz, H. Benisty, V. Berger, J.-M Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, Berlin, 2005).

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).

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Figures (8)

Fig. 1.
Fig. 1.

Sketch of the triangular-lattice PhC structure composed of pillars filled with the nematic LCs. The LC director n at a rotation angle Φ is parallel to the xy plane when an in-plane electric field is applied.

Fig. 2.
Fig. 2.

Calculated photonic band structure (TE polarizations) for the triangular 2D PhC infiltrated with LCs. The inset shows a view of the triangular lattice with the unit cell. The refractive index is approximated to be isotropic within the pillars when directors are oriented at random. The normalized frequencies marked for ω=0.27 and ω=0.3 are adopted to investigate the phenomena of the partial band gap and the anomalous refraction.

Fig. 3.
Fig. 3.

The CFC representation of ω(kx,ky) in the frequency range of Band II, with the contours for LC directors orientated at (a) Φ=0° and (b) Φ=90°.

Fig. 4.
Fig. 4.

Schematic diagram for the case of a normally incident Gaussian wave when the orientation of LC directors is varied by an in-plane electric field.

Fig. 5.
Fig. 5.

Theoretical spectral responses calculated from the observing point (shown in Fig. 4) by the FDTD method. The input TE-polarized light is a Gaussian modulated wave with the center wavelength λ=3.7µm corresponding to ω=0.27 for a=1µm. The LC directors are oriented at (a) Φ=0° and (b) Φ=90° to show the shift of the partial band gap when an in-plane electric field is applied in different directions.

Fig. 6.
Fig. 6.

TE-polarized transmission spectra calculated from the observing point (shown in Fig. 4) by the FDTD method. The input light is a Gaussian modulated wave with the center wavelength λ=1.55µm corresponding to ω=0.27 for a=0.4185µm. The LC directors are oriented at (a) Φ=0° and (b) Φ=90° for the “on” and the “off” states, respectively.

Fig. 7.
Fig. 7.

The CFC representation of ω(kx,ky) in the frequency range of Band II, with the contours for LC directors orientated at (a) Φ=40°and (b) Φ=-40°. The arrows stand for the group velocity vectors determined by the gradient ∇kω. These directions are selected by the solid lines, which are derived based on the conservation of the parallel wave vectors (ky=0).

Fig. 8.
Fig. 8.

FDTD simulations for the distribution of the magnetic fields. For the condition of the normal incidence with the frequency ω=0.3, the LC directors are oriented at (a) Φ=40° and (b) Φ=-40° to show the anomalous refraction effect when an in-plane electric field is applied in different directions. The arrows highlight the direction of the energy of the output wave. The refracted angle for Φ=40° (Φ=-40°) is about -29° (28°).

Equations (5)

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

× [ 1 ε ( r ) × H ( r ) ] = ( ω c ) 2 H ( r ) .
ε i , j ( r ) = G ε i , j ( G ) e j G r ( i , j = x , y ) .
ε x , x ( r ) = n o 2 ( r ) sin 2 Φ + n e 2 ( r ) cos 2 Φ ,
ε y , y ( r ) = n o 2 ( r ) cos 2 Φ + n e 2 ( r ) sin 2 Φ ,
ε x , y ( r ) = ε y , x ( r ) = [ n e 2 ( r ) n o 2 ( r ) ] sin Φ cos Φ ,

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