Abstract

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation and because PC-based waveguides may be integrated into optical interferometers. We propose a novel tunable PC waveguide Mach–Zehnder interferometer based on nematic liquid crystals and investigate its interference properties numerically by using the finite-difference time-domain method. We can change the refractive indices of liquid crystals by rotating the directors of the liquid crystals. Then we can control the phase of light propagation in a PC waveguide Mach-Zehnder interferometer. The interference mechanism is a change in the refractive indices of liquid-crystal waveguides. The novel interferometer can be used either as an optically controlled on–off switch or as an amplitude modulator in optical circuits.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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Appl. Phys. Lett. (4)

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O�??Brien, P. D. Dapkus, and W. K. Marshall, �??Two-dimensional photonic crystal Mach�??Zehnder interferometers,�?? Appl. Phys. Lett. 84, 460-462 (2004).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, �??Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,�?? Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Y. Shimoda, M. Ozaki, and K. Yoshino, �??Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,�?? Appl. Phys. Lett. 79, 3627-3629 (2001).
[CrossRef]

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, �??Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,�?? Appl. Phys. Lett. 83, 3236-3238 (2003).

Electron. Lett. (1)

T. Baba, N. Fukaya, and J. Yonekura, �??Observation of light propagation in photonic crystal optical waveguides with bends,�?? Electron. Lett. 35, 654-656 (1999).
[CrossRef]

IEEE Microwave Wireless Compon. Lett. (1)

M. Koshiba, Y. Tsuji, and Saski, �??High-performance absorbing boundary conditions for photonic crystal waveguide simulations,�?? IEEE Microwave Wireless Compon. Lett. 11, 152-154 (2001).
[CrossRef]

J. Appl. Phys. (3)

H. Takeda and K. Yoshino, �??Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,�?? J. Appl. Phys. 92, 5958-5662 (2002).

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, �??Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,�?? J. Appl. Phys. 91, 922-929 (2002).
[CrossRef]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel application of photonic band gap materials: low-loss bends and high-Q cavities,�?? J. Appl. Phys. 75, 4753-4755 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (3)

H. Takeda and K. Yoshino, �??Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,�?? Opt. Commun. 219, 177-182 (2003).
[CrossRef]

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagüe, B. Beche, H. Porte, R. Warno, and M. Karpierz, �??Highly unbalanced GaAlAs-GaAs integrated Mach�??Zehnder interferometer for coherence modulation at 1.3 µm,�?? Opt. Commun. 167, 67-79 (1999).
[CrossRef]

E. Centeno and D. Felbacq, �??Guiding waves with photonic crystals,�?? Opt. Commun. 160, 57-60 (1999).
[CrossRef]

Phys. Rev. B (1)

H. Takeda and K. Yoshino, �??Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,�?? Phys. Rev. B 67, 073106 (2003).
[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]

Phys. Solid State (1)

A. V. Zakharov and L. V. Mirantsev, �??Dynamic and dielectric properties of liquid crystals,�?? Phys. Solid State 45, 183-188 (2003).
[CrossRef]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).

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

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Photonic band structure for the triangular array of dielectric columns. Inset, the Brillouin zone.

Fig. 2.
Fig. 2.

PC waveguide Mach–Zehnder interferometer with path-length differences of (a) 0 and (b) 4a. Inset, lattice constant a and radius of rods r.

Fig. 3.
Fig. 3.

Electric field patterns observed in the frequency domain of the PC waveguide Mach–Zehnder interferometer with path-length differences of (a) 0 and (b) 4a.

Fig. 4.
Fig. 4.

PC waveguide Mach–Zehnder interferometer with LCs. Shaded regions, parts infiltrated with LC waveguides. Diagram at lower left, director of a LC.

Fig. 5.
Fig. 5.

Dispersion relations of guided modes in the PC waveguide with a nematic LC at ϕ=0°, 45°, 90°. Shaded regions, projected band structures of the perfect crystals.

Fig. 6.
Fig. 6.

The refractive index profile of cross-section AA of Fig. 4 with phases (a) ϕ 1=0 °, ϕ 2=0 ° and (b) ϕ 1=0 °, ϕ 2=90 °.

Fig. 7.
Fig. 7.

Transmission spectrum for the structure in Fig. 4 with input wavelength λ=1.42 µm and variable rotation angle ϕ 2.

Fig. 8.
Fig. 8.

Calculated rotation angle ϕ as a function of normalized voltage. V th is the threshold voltage.

Fig. 9.
Fig. 9.

Electric field patterns observed in the frequency domain of the tunable PC waveguide Mach–Zehnder interferometer with LCs at ϕ 2=0 °, ±45 °, ±90 °.

Equations (5)

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× [ 1 ε ( r ) × H ( r ) ] = ( ω c ) 2 H ( r ) ,
ε xx ( r ) = ε o ( r ) sin 2 ϕ + ε e ( r ) cos 2 ϕ ,
ε zz ( r ) = ε o ( r ) cos 2 ϕ + ε e ( r ) sin 2 ϕ ,
ε xz ( r ) = ε zx ( r ) = [ ε e ( r ) ε o ( r ) ] cos ϕ sin ϕ ,
ϕ d = 2 π λ [ n e ( ϕ 2 ) n e ( ϕ 1 ) ] L LC ,

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