Abstract

We report the study of 2-D photonic-crystal waveguide arrays (PCWA) composed of <i>N</i> identical waveguides coupled evanescently with each other. The coupling properties of the waveguide modes are investigated using coupled-mode theory and finite-difference time domain method. One straightforward application of such an analysis is to route input power from a central waveguide to side waveguides. As a result, appropriate designs of PCWAs may permit the realization of efficient, compact and novel devices. For instance, we show that power dividers, switchers, and Mach–Zehnder interferometers can be feasible using <i>N</i> =3 channels. On the other hand, <i>N</i> =5 waveguides can divide the input power by 1/4 at a distance of approximately 37.2 <i>µ</i>m. Waveguide bends and Y-type junctions are used heavily for power transfer but they are prone to scattering losses; hence, lowering the transmission efficiency. They can be eliminated by means of PCWAs in the design of optical power distribution through photonic circuits.

© 2009 IEEE

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2007 (3)

H. Kurt, D. S. Citrin, "Photonic-crystal heterostructure waveguides," IEEE J. Quantum Electron. 43, 78-84 (2007).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Imaging properties of multimode photonic crystal waveguides and waveguide arrays," J. Lightw. Technol. 25, 402-409 (2007).

A. Theocharidis, T. Kamalakis, T. Sphicopoulos, "Accuracy of coupled-mode theory and mode-matching method in the analysis of photonic crystal waveguide perturbations," J. Lightw. Technol. 25, 3193-3201 (2007).

2006 (1)

2005 (3)

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Diffraction engineering in arrays of photonic crystal waveguides," Opt. Lett. 30, 2894-2896 (2005).

H. Kurt, D. S. Citrin, "Annular photonic crystals," Opt. Exp. 13, 10316-10326 (2005).

2004 (1)

I. Park, H. -S. Lee, H. -J. Kim, K. -M. Moon, S. -G. Lee, B. -H. O, S. -G. Park, E. -H. Lee, "Photonic crystal power-splitter based on directional coupling," Opt. Exp. 12, 3599-3604 (2004).

2003 (2)

A. Martinez, F. Cuesta, J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003).

M. Thorhauge, L. H. Frandsen, P. I. Borel, "Efficient photonic crystal directional couplers," Opt. Lett. 28, 1525-1527 (2003).

2002 (4)

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, D. Nedeljkovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (1)-(15) (2002).

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).

2001 (1)

A. Kaplan, S. Ruschin, "Optical switching and power control in ${\rm LiNbO}_{3}$ coupled waveguide arrays," IEEE J. Quantum Electron. 37, 1562-1573 (2001).

1998 (3)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A: R. Boyd, J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).

U. Peschel, T. Pertsch, F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998).

D. Christodoulides, R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1998).

1991 (1)

M. Plihal, A. A. Maradudin, "Photonic band structure of 2-D systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

1988 (1)

M. K. Smit, "New focusing and dispersive planar component based on an optical phased array," IEE Electron. Lett. 24, 385-386 (1988).

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).

1985 (1)

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightw. Technol. 3, 1135-1146 (1985).

1984 (1)

1983 (1)

H. Haus, L. Molter-Orr, "Coupled multiple waveguide systems," IEEE J. Quantum Electron. 19, 840-844 (1983).

1976 (1)

R. V. Schmidt, H. Kogelnik, "Electro-optically switched coupler with stepped Delta $\beta$ reversal using Ti-diffused ${\rm LiNbO}_{3}$ waveguides," App. Phys. Lett. 28, 503-506 (1976).

1974 (1)

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, "Channel optical waveguide directional couplers," App. Phys. Lett. 22, 46-47 (1973).

1972 (1)

H. Kogelnik, C. V. Shank, "Coupled wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).

App. Phys. Lett. (2)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, "Channel optical waveguide directional couplers," App. Phys. Lett. 22, 46-47 (1973).

R. V. Schmidt, H. Kogelnik, "Electro-optically switched coupler with stepped Delta $\beta$ reversal using Ti-diffused ${\rm LiNbO}_{3}$ waveguides," App. Phys. Lett. 28, 503-506 (1976).

Appl. Opt. (1)

IEE Electron. Lett. (1)

M. K. Smit, "New focusing and dispersive planar component based on an optical phased array," IEE Electron. Lett. 24, 385-386 (1988).

IEEE J. Quantum Electron. (6)

H. Haus, L. Molter-Orr, "Coupled multiple waveguide systems," IEEE J. Quantum Electron. 19, 840-844 (1983).

A. Kaplan, S. Ruschin, "Optical switching and power control in ${\rm LiNbO}_{3}$ coupled waveguide arrays," IEEE J. Quantum Electron. 37, 1562-1573 (2001).

H. Kurt, D. S. Citrin, "Photonic-crystal heterostructure waveguides," IEEE J. Quantum Electron. 43, 78-84 (2007).

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, D. Nedeljkovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

IEEE Photon. Technol. Lett. (1)

A. Martinez, F. Cuesta, J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003).

J. Appl. Phys. (1)

H. Kogelnik, C. V. Shank, "Coupled wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).

J. Lightw. Technol. (3)

A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightw. Technol. 3, 1135-1146 (1985).

A. Theocharidis, T. Kamalakis, T. Sphicopoulos, "Accuracy of coupled-mode theory and mode-matching method in the analysis of photonic crystal waveguide perturbations," J. Lightw. Technol. 25, 3193-3201 (2007).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Imaging properties of multimode photonic crystal waveguides and waveguide arrays," J. Lightw. Technol. 25, 402-409 (2007).

Opt. Exp. (2)

I. Park, H. -S. Lee, H. -J. Kim, K. -M. Moon, S. -G. Lee, B. -H. O, S. -G. Park, E. -H. Lee, "Photonic crystal power-splitter based on directional coupling," Opt. Exp. 12, 3599-3604 (2004).

H. Kurt, D. S. Citrin, "Annular photonic crystals," Opt. Exp. 13, 10316-10326 (2005).

Opt. Lett. (6)

Phys. Rev. B (1)

M. Plihal, A. A. Maradudin, "Photonic band structure of 2-D systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (1)-(15) (2002).

Phys. Rev. Lett. (4)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A: R. Boyd, J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).

Other (2)

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

A. Taflove, Computational Electrodynamics – The Finite-Difference Time-Domain Method (Artech House, 2000).

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