Abstract

The photonic crystal structure with parallelogram lattice, capable of bending a self-collimated wave with free angles and partial bandgap reflection, is presented. The equifrequency contours show that the direction of the collimation wave can be turned by tuning the angle between the two basic vectors of the lattice. Acute, right, and obtuse angles of collimating waveguide bends have been realized by arc lattices of parallelogram photonic crystals. Moreover, partial bandgap reflection of the parallelogram lattice photonic crystals is validated from the equifrequency contours and the projected band structures. A waveguide taper based on this partial bandgap reflection is also designed and proved to have above 85% transmittance over a very wide operating bandwidth of 180nm.

© 2008 Optical Society of America

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References

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  1. A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, “All-silicon omnidirectional mirrors based on one-dimensional photonic crystals,” Appl. Phys. Lett. 82, 3227-3229 (2003).
    [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]
  7. Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341-1343 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (1)

2005 (1)

S. G. Lee, S. S. Oh, J. E. Kim, H. Y. Park, and C. S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

2004 (2)

2003 (6)

C. Chen, A. Sharkawy, D. Pustai, S. Shi, and D. Prather, “Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides,” Opt. Express 11, 3153-3159 (2003).
[CrossRef] [PubMed]

X. Yu, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, “All-silicon omnidirectional mirrors based on one-dimensional photonic crystals,” Appl. Phys. Lett. 82, 3227-3229 (2003).
[CrossRef]

Y. Akahane, T. Asano, and B. S. Song, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944-947 (2003).
[CrossRef]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

2002 (1)

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

2000 (3)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402-1411 (2000).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

1996 (1)

H. Hirayama, “Novel surface emitting laser diode using photonic band-gap crystal cavity,” Appl. Phys. Lett. 69, 791-793 (1996).
[CrossRef]

Appl. Phys. Lett. (7)

H. Hirayama, “Novel surface emitting laser diode using photonic band-gap crystal cavity,” Appl. Phys. Lett. 69, 791-793 (1996).
[CrossRef]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

M. Qiu and B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal,” Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

S. G. Lee, S. S. Oh, J. E. Kim, H. Y. Park, and C. S. Kee, “Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett. 87, 181106 (2005).
[CrossRef]

X. Yu, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

A. Bruyant, G. Lérondel, P. J. Reece, and M. Gal, “All-silicon omnidirectional mirrors based on one-dimensional photonic crystals,” Appl. Phys. Lett. 82, 3227-3229 (2003).
[CrossRef]

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

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Nature (London) (1)

Y. Akahane, T. Asano, and B. S. Song, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944-947 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (2)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the parallelogram lattice PC.

Fig. 2
Fig. 2

(a) Brillouin zone of the rectangular lattice PC and (b) band structure along the high symmetry points.

Fig. 3
Fig. 3

Equifrequency contours of parallelogram lattice PCs with various values of θ and b: (a) θ = 90 ° , b = 2 a ; (b) θ = 120 ° , b = 2 a ; (c) θ = 120 ° , b = 2.4 a .

Fig. 4
Fig. 4

(a) Definition of the incident angle α and (b) projected band structure of the parallelogram lattice PC.

Fig. 5
Fig. 5

Field distributions in the self-collimated waveguide bends with various bend angles: (a) φ = 30 ° , (b) φ = 60 ° , (c) φ = 90 ° , (d) φ = 120 ° .

Fig. 6
Fig. 6

Bend efficiencies of the waveguide bends with various bend angles.

Fig. 7
Fig. 7

(a) Field distribution in the convex field-size converter and (b) the transmittance of the converter.

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