Abstract

A coupler-type optical filter in 2D photonic crystal (PhC) with square lattice of dielectric rods in air is presented. The reduced-index and increased-index waveguides of filter have dispersion curves with opposite slopes to realize contra-directional coupling, and the point of anti-crossing is designed below the light line to avoid vertical radiation. The filter has a broad operable bandwidth due to the absence of mini stop bands. The transmission properties are analyzed using coupled modes theory (CMT) and simulated using the finite-difference time-domain (FDTD) method. The results show that a filtering bandwidth of 4 nm can be achieved in the range of 1500∼1600 nm, and over 83% drop coefficient is obtained.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. J. Joannopoulos, R, Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995)
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    [CrossRef]
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    [CrossRef]
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  13. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely Large Group-Velocity Dispersion of Line-defect Waveguides in Photonic Crystal Slabs,�?? Phys. Rev. Lett. 87, 253902, (2001).
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Appl. Phys. Lett. (2)

Min Qiu, Mikael Mulot, Marcin Swillo, Srinivasan Anand, Bozena Jaskorzynska, and Anders Karisson, �??Photonic crystal optical filter based on contra-directional waveguide coupling,�?? Appl. Phys. Lett. 83, 5121-5123, (2003).
[CrossRef]

Min Qiu, �??Effective method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,�?? Appl. Phys. Lett. 81, 1163-1165, (2002).
[CrossRef]

Electron. Lett. (1)

M. Tokushima, and H. Yamada, �??Photonic crystal line defect waveguide directional coupler,�?? Electron. Lett. 37, 1454-1455 (2001)
[CrossRef]

IEEE J. Lightwave Technol. (2)

Jin Hong, and WeiPing Huang, �??Contra-directional Coupling in Grating-Assisted Guided-Wave Devices,�?? IEEE J. Lightwave Technol. 10, 873-881 (1992)
[CrossRef]

Masanori Koshiba, �??Wavelength Division Multiplexing and Demultiplexing With Photonic Crystal Waveguide Couplers,�?? IEEE J. Lightwave Technol. 19, 1970-1975 (2001)
[CrossRef]

IEEE J. Quantum Electron. (1)

Sergey Kuchinsky, Vladislav Y. Golyatin, Alexander Y. Kutikov, Thomas P. Pearsall, and Dusan Nedeljkovic, �??Coupling Between Photonic Crystal Waveguides,�?? IEEE J. Quantum Electron. 38, 1349-1352 (2002)
[CrossRef]

Opt. Commun. (1)

Turan Erdogan, �??Optical add�??drop multiplexer based on an asymmetric Bragg coupler,�?? Opt. Commun. 157, 249-264, (1998).
[CrossRef]

Opt. Express (3)

Photonics and Nanostructures (1)

Min Qiu, and Marcin Swillo, �??Contra-directional coupling between two-dimensional photonic crystal waveguides,�?? Photonics and Nanostructures, 1, 23-30, (2003).
[CrossRef]

Phys. Rev. B (1)

Steven G. Johnson, Pierre. R. Villeneuve, Shanhui Fan, and J. D. Joannopoulos, �??Linear waveguides in photonic-crystal slabs,�?? Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Phys. Rev. E (1)

Steven G. Johnson, Peter Bienstman, M. A. Skorobogatiy, Mihai Ibanescu, Elefterios Lidorikis, and J. D. Joannopoulos, �??Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,�?? Phys. Rev. E 66, 066608-5758 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely Large Group-Velocity Dispersion of Line-defect Waveguides in Photonic Crystal Slabs,�?? Phys. Rev. Lett. 87, 253902, (2001).
[CrossRef] [PubMed]

Other (2)

H. A. Haus, waves and fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, USA, 1985)

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

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Figures (6)

Fig. 1.
Fig. 1.

The structure of optical filter based on contra-directional waveguide coupling in 2D PhC with square lattice of dielectric rods. The two waveguides are formed by reducing and increasing the radius of one row of rods respectively.

Fig. 2.
Fig. 2.

The band structures of (a) W1 waveguide and (b) W2 waveguide. The PhC is a square lattice of dielectric rods in air. The radius of rods in bulk is 0.20 a, and the waveguide W1 (W2) is form by reducing (increasing) the radius of a row of dielectric rods to 0.10 a (0.25 a).

Fig. 3.
Fig. 3.

(a) The band structure of the optical filter, or the band structure for the coupled W1 and W2 waveguides. (b) The band structure near the anti-crossing point (encircled region of part a).

Fig. 4.
Fig. 4.

Normalized transmission spectra at different output ports for the 200 a long coupler-type filter. The port numbers correspond to those in Fig. 1.

Fig. 5.
Fig. 5.

(a) The coupling coefficient as a function of the radius of the rods between W1 and W2 PhC waveguide. The other parameters of filter maintain unchanged. (b) Normalized transmission spectra at different output ports for the 100 a long coupler-type filter, and the radius of the rods between W1 and W2 PhC waveguides is tuned to 0.23 a.

Fig. 6.
Fig. 6.

(a) The band structure when the radius of W2 PhC waveguide decreases from 0.25 a to 0.24 a. The point of anti-crossing occurs close to the band edge. (b) The band structure near the anti-crossing point (encircled region of part a).

Equations (8)

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d α + d z = j β + α + + κ α ,
d α d z = j β α + κ * α + ,
α + = ( A + e γ z + A e + γ z ) e j β + + β 2 z ,
α = ( B + e γ z + B e + γ z ) e j β + + β 2 z ,
γ κ 2 ( β + β 2 ) 2 = κ 2 ( ( d β + d ω d β d ω ) ( ω ω 0 ) ) 2 κ 2 δ 2 ,
D ( l ) = [ sinh γ l ( γ / κ * ) cosh γ l + ( j δ / κ * ) sinh γ l ] 2 ,
Δ λ = 2 λ 0 2 κ π ( β + ω β ω ) = 2 λ 0 2 κ π ( c v g + c v g ) ,
D ( l ) = tanh 2 ( κ l ) = ( e κ l e κ l e κ l + e κ l ) 2 .

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