Abstract

A fundamental 1×2 beam splitter based on directional coupling of flexible optical waveguides is presented. The coupling and transmission characteristics of the beam splitter are investigated by using the plane wave expansion method and finite-difference time-domain method, respectively. Calculated results indicate that, for this beam splitter, without any structural optimization, near-complete transmission is observed within a wide frequency band. Combining the fundamental 1×2 beam splitter with flexible optical waveguides, we construct a simple and compact 1×4 beam splitter. Those beam splitters are expected to be applied to highly dense photonic integrated circuits.

© 2011 Optical Society of America

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    [CrossRef]
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2010

2009

2008

B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93, 181107(2008).
[CrossRef]

2007

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

P. Luan and K. Chang, “Periodic dielectric waveguide beam splitter based on co-directional coupling,” Opt. Express 15, 4536–4545 (2007).
[CrossRef] [PubMed]

2006

Z. Li, Y. Zhang, and B. Li, “Terahertz photonic crystal switch in silicon based on self-imaging principle,” Opt. Express 14, 3887–3892 (2006).
[CrossRef] [PubMed]

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

2004

2003

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003).
[CrossRef]

2002

2001

1995

T. Rasmussen, J. K. Rasmussen, and J. H. Povlsen, “Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,” J. Lightwave Technol. 13, 2069 (1995).
[CrossRef]

1993

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Abrishmian, M. S.

Arakawa, Y.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

Asakawa, K.

Baba, T.

A. Sakai, T. Fukazawa, and T. Baba, “Low loss ultra-small branches in a silicon photonic wire waveguide,” IEICE Trans. Electron. E85-C, 1033–1038 (2002).

Carlsson, N.

Chang, K.

Chen, B.

Chen, H.

Chu, T.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

Cuesta, F.

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003).
[CrossRef]

de Miguel, J. L.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Djavid, M.

Fallahi, M.

Fan, S.

Ferreras, A.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Fukazawa, T.

A. Sakai, T. Fukazawa, and T. Baba, “Low loss ultra-small branches in a silicon photonic wire waveguide,” IEICE Trans. Electron. E85-C, 1033–1038 (2002).

Ghaffari, A.

Gomez-Salas, E.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, 2000).

Haus, H. A.

Hernandez-Gil, F.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Ikeda, N.

Inoue, K.

Ishida, S.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

Jiang, X. Q.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kawai, N.

Kim, H. J.

Kristensen, M.

Krüger, A. C.

Lee, E. H.

Lee, H. S.

Lee, S. G.

Li, B.

Li, Z.

Liao, Q. H.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

Liu, T.

Liu, Z.

B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93, 181107(2008).
[CrossRef]

Luan, P.

Malureanu, R.

Manolatou, C.

Mansuripur, M.

Marti, J.

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003).
[CrossRef]

Martinez, A.

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003).
[CrossRef]

Moon, K. M.

O, B. H.

Park, I.

Park, S. G.

Povlsen, J. H.

T. Rasmussen, J. K. Rasmussen, and J. H. Povlsen, “Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,” J. Lightwave Technol. 13, 2069 (1995).
[CrossRef]

Rasmussen, J. K.

T. Rasmussen, J. K. Rasmussen, and J. H. Povlsen, “Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,” J. Lightwave Technol. 13, 2069 (1995).
[CrossRef]

Rasmussen, T.

T. Rasmussen, J. K. Rasmussen, and J. H. Povlsen, “Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,” J. Lightwave Technol. 13, 2069 (1995).
[CrossRef]

Rodriguez, F.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

Sakai, A.

A. Sakai, T. Fukazawa, and T. Baba, “Low loss ultra-small branches in a silicon photonic wire waveguide,” IEICE Trans. Electron. E85-C, 1033–1038 (2002).

Sugimoto, Y.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, 2000).

Tang, T.

Wang, M. H.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

Wang, Z.

B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93, 181107(2008).
[CrossRef]

Yamada, H.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

Yang, J. Y.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

Yu, T. B.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

Zakharian, A. R.

Zeng, S.

Zhang, M.

Zhang, Y.

Appl. Opt.

Appl. Phys. Lett.

B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93, 181107(2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1371–1379 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Ferreras, F. Rodriguez, E. Gomez-Salas, J. L. de Miguel, and F. Hernandez-Gil, “Useful formulas for multimode interference power splitter/combiner design,” IEEE Photon. Technol. Lett. 5, 1224–1227 (1993).
[CrossRef]

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003).
[CrossRef]

IEICE Trans. Electron.

A. Sakai, T. Fukazawa, and T. Baba, “Low loss ultra-small branches in a silicon photonic wire waveguide,” IEICE Trans. Electron. E85-C, 1033–1038 (2002).

J. Lightwave Technol.

T. Rasmussen, J. K. Rasmussen, and J. H. Povlsen, “Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,” J. Lightwave Technol. 13, 2069 (1995).
[CrossRef]

T. Liu, A. R. Zakharian, M. Fallahi, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. 22, 2842–2846 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

T. B. Yu, M. H. Wang, X. Q. Jiang, Q. H. Liao, and J. Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A: Pure Appl. Opt. 9, 37–42 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, 2000).

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Figures (4)

Fig. 1
Fig. 1

(a) Dispersion curves of TE modes in the flexible waveguide. A schematic drawing of the flexible waveguide is shown in the inset. a denotes the lattice constant of the 1D PC. n 1 = 1.6 , n 2 = 4.6 , n 0 = 1 , h 1 = 0.75 a , h 2 = 0.25 a , and h 0 = 2.75 a . The solid line in the inset is E y field distributions at A ( 0.1007 [ 2 π / a ] , 0.21 [ 2 π c / a ] ). The frequency ranges of ORB TE , 0.151 0.281 [ 2 π c / a ] and of PBG for normal incidence 0.145 0.281 [ 2 π c / a ] are indicated as two dotted lines, respectively. (b) The dispersion curves of TE modes in the three-channel flexible waveguide with the interval of d = 4 a . A schematic drawing of the three-channel flexible waveguide is shown in the inset. The other parameters are the same as those in Fig. 1a. The E y field distributions at B ( 0.1098 [ 2 π / a ] , 0.21 [ 2 π c / a ] ), C ( 0.1007 [ 2 π / a ] , 0.21 [ 2 π c / a ] ), and D ( 0.0900 [ 2 π / a ] , 0.21 [ 2 π c / a ] ) are shown in the inset, respectively.

Fig. 2
Fig. 2

(a) Schematic drawing of the fundamental 1 × 2 beam splitter based on flexible photonic crystal waveguides. (b) The coupling length L c with different interval d in the 1 × 2 beam splitter.

Fig. 3
Fig. 3

(a) For the 1 × 2 beam splitter with d = 4 a and L c = 25.30 a as shown in Fig. 2a, the frequency range of high transmittance band is 0.2059 0.2125 [ 2 π c / a ] . The distributions of E y at normalized frequency 0.21 [ 2 π c / a ] is shown in the inset. (b) For the 1 × 2 beam splitter with d = 5 a and L c = 45.27 a as shown in Fig. 2a, the frequency range of high transmittance band is 0.1986 0.2032 [ 2 π c / a ] . The distributions of E y at normalized frequency 0.20 [ 2 π c / a ] is shown in the inset.

Fig. 4
Fig. 4

(a) Schematic drawing of the 1 × 4 beam splitter, which is composed of three fundamental 1 × 2 beam splitters with L c , d = 4 a = 25.30 a and two groups of 180 ° arc flexible waveguides with curved radius R = 9 a . (b) The distributions of E y at normalized frequency 0.21 [ 2 π c / a ] in the 1 × 4 beam splitter.

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