Abstract

We study disorder-induced propagation losses of guided modes in photonic crystal slabs with line-defects. These losses are treated within a theoretical model of size disorder for the etched holes in the otherwise periodic photonic lattice. Comparisons are provided with state-of-the-art experimental data, both in membrane and Silicon-on-Insulator (SOI) structures, in which propagation losses are mainly attributed to fabrication imperfections. The dependence of the losses on the photon group velocity and the useful bandwidth for low-loss propagation are analyzed and discussed for membrane and asymmetric as well as symmetric SOI systems. New designs for further improving device performances are proposed, which employ waveguides with varying channel widths. It is shown that losses in photonic crystal waveguides could be reduced by almost an order of magnitude with respect to latest experimental results. Propagation losses lower than 0.1 dB/mm are predicted for suitably designed structures, by assuming state-of-the-art fabrication accuracy.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  31. L. C. Andreani, �??Photonic bands and radiation losses in photonic crystal waveguides,�?? Physica Status Solidi B 234, 139 (2002).
    [CrossRef]
  32. L. C. Andreani and M. Agio, �??Intrinsic diffraction losses in photonic crystal waveguides with line defects,�?? Appl. Phys. Lett. 82, 2011�??2013 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  34. M. Galli, D. Bajoni, M. Patrini, G. Guizzetti, D. Gerace, L. C. Andreani, M. Belotti, and Y. Chen, �??Single-mode versus multi-mode behavior in Silicon photonic crystal waveguides measured by attenuated total reflectance,�?? submitted to Phys. Rev. B.
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    [CrossRef]
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    [CrossRef]

Appl. Phys. Lett. (6)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. .M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, and C. Jouanin, �??Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,�?? Appl. Phys. Lett. 76, 532 (2000).
[CrossRef]

K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, �??Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model,�?? Appl. Phys. Lett. 77, 1617�??1619 (2000).
[CrossRef]

M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, and M. Solja�?i�?, �??Effect of a photonic band gap on scattering from waveguide disorder,�?? Appl. Phys. Lett. 84, 3639�??3641 (2004).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, �??Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,�?? Appl. Phys. Lett. 82, 1661�??1663 (2003).
[CrossRef]

B. Cluzel, D. G´erard, E. Picard, T. Charvolin, V. Calvo, E. Hadji, and F. de Fornel, �??Experimental demonstration of Bloch mode parity change in photonic crystal waveguide,�?? Appl. Phys. Lett. 85, 2682�??2684 (2004).
[CrossRef]

L. C. Andreani and M. Agio, �??Intrinsic diffraction losses in photonic crystal waveguides with line defects,�?? Appl. Phys. Lett. 82, 2011�??2013 (2003).
[CrossRef]

Bell. Syst. Tech. J. (1)

D. Marcuse, �??Mode conversion caused by surface imperfections of a dielectric slab waveguide,�?? Bell. Syst. Tech. J. 48, 3187 (1969).

IEEE J. Quantum Electron. (3)

L. C. Andreani and M. Agio, �??Photonic bands and gap maps in a photonic crystal slab,�?? IEEE J. Quantum Electron. 38, 891�??898 (2002).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, �??Structural tuning of guiding modes of line-defect waveguides of Silicon-on-Insulator photonic crystal slabs,�?? IEEE J. Quantum Electron. 38, 736�??742 (2002).
[CrossRef]

See papers in IEEE J. Quantum Electron. 38, Feature section on Photonic Crystal Structures and Applications, edited by T. F. Krauss and T. Baba, pp.724�??963 (2002).
[CrossRef]

IEEE Photon. Techn. Lett. (2)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, �??Out-of-plane scattering in photonic crystal slabs,�?? IEEE Photon. Techn. Lett. 13, 565�??567 (2001).
[CrossRef]

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, �??Size influence on the propagation loss induced by side-wall roughness in ultra-small SOI waveguides,�?? IEEE Photon. Techn. Lett. 16, 1661�??1663 (2004).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (1)

K. Yamada, H. Morita, A. Shinya, and M. Notomi, �??Improved line-defect structures for photonic-crystal waveguides with high group velocity,�?? Opt. Commun. 198, 395�??402 (2001).
[CrossRef]

Opt. Express (6)

M. Skorobogatiy, G. Bégin, and A. Talneau, �??Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,�?? Opt. Express 13, 2487�??2502 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2487">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2487</a>.
[CrossRef] [PubMed]

S. J. McNab, N. Moll, and Yu. A. Vlasov, �??Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,�?? Opt. Express 11, 2927�??2939 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927</a>.
[CrossRef] [PubMed]

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, and K. Inoue, �??Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length,�?? Opt. Express 12, 1090�??1096 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090</a>.
[CrossRef] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H.-Y. Ryu, �??Waveguides, resonators and their coupled elements in photonic crystal slabs,�?? Opt. Express 12, 1551�??1561 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551</a>.
[CrossRef] [PubMed]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, and R. Baets, �??Basic structures for photonic integrated circuits in Silicon-on-insulator,�?? Opt. Express 12, 1583�??1591 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1583">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1583</a>.
[CrossRef] [PubMed]

Yu. A. Vlasov and S. J. McNab, �??Losses in single-mode silicon-on-insulator strip waveguides and bends,�?? Opt. Express 12, 1622�??1631 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622</a>.
[CrossRef] [PubMed]

Opt. Lett. (2)

Opt. Quant. Electron. (1)

F. P. Payne and J. P. R. Lacey, �??A theoretical analysis of scattering loss from planar optical waveguides,�?? Opt. Quant. Electron. 26, 977�??986 (1994).
[CrossRef]

Phot. Nanostruct. (1)

L. C. Andreani, D. Gerace, and M. Agio, �??Gap maps, diffraction losses and exciton-polaritons in photonic crystal slabs,�?? Phot. Nanostruct. 2, 103�??110 (2004).
[CrossRef]

Phys. Rev. B (4)

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. Qiu, �??Band gap effects in asymmetric photonic crystal slabs,�?? Phys. Rev. B 66, 033103 (2002).
[CrossRef]

T. Ochiai and K. Sakoda, �??Nearly free-photon approximation for two-dimensional photonic crystal slabs�?? Phys. Rev. B 64, 045108 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

M. Notomi, K. Yamada, A. Shinya, J. 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]

S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486�??2489 (1987).
[CrossRef] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, �??Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,�?? Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett.` (1)

E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059�??2062 (1987).
[CrossRef] [PubMed]

Physica Status Solidi B (1)

L. C. Andreani, �??Photonic bands and radiation losses in photonic crystal waveguides,�?? Physica Status Solidi B 234, 139 (2002).
[CrossRef]

Other (4)

M. Galli, D. Bajoni, M. Patrini, G. Guizzetti, D. Gerace, L. C. Andreani, M. Belotti, and Y. Chen, �??Single-mode versus multi-mode behavior in Silicon photonic crystal waveguides measured by attenuated total reflectance,�?? submitted to Phys. Rev. B.

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

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001).

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer, Dordrecht, 2002).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic pictures of systems under study in the present work. (a) Line-defect along the Γ-K direction for the unperturbed and disordered triangular lattices in the (x,y) plane; the effect of a random variation of holes radii has been exaggerated. Light gray holes represent the fundamental cell to be repeated with supercell periodicity in a square lattice. The main symmetry directions of the triangular lattice, Γ-K and Γ-M, are also defined. (b) Vertical guiding structures considered in this work: (from left to right) the air-clad, the asymmetric SiO2-clad, and the symmetric SiO2-clad photonic crystal waveguides.

Fig. 2.
Fig. 2.

Calculated photonic dispersion of TE-like modes in a W1.0 waveguide realized in a d=220 nm thick Silicon membrane patterned with a triangular lattice of air holes (r/a=0.275, lattice constant a=400 nm), and out-of-plane propagation losses corresponding to the σ kz =-1 defect mode for different values of the disorder parameter. The low-loss single-mode frequency window is highlighted.

Fig. 3.
Fig. 3.

Calculated photonic mode dispersion of a W0.7 PhC waveguide realized in a d=220 nm thick SOI system patterned with a triangular lattice of air holes (r/a=0.275, lattice constant a=400 nm), and out-of-plane propagation losses corresponding to the σ kz =-1 defect mode. The low-loss frequency range is highlighted.

Fig. 4.
Fig. 4.

Calculated photonic dispersion of TE-like modes in air-clad PhC waveguides of channel widths (a) W=1.1·√3a, (b) W=1.3·√3a and (c) W=1.5·√3a, realized in a d=220 nm thick Silicon membrane patterned with a triangular lattice of air holes (r/a=0.275, lattice constant a=400 nm), and corresponding out-of-plane propagation losses related to the σ kz =-1 defect mode below the light line. Highlighted regions correspond to the single-mode low-loss propagation range.

Fig. 5.
Fig. 5.

Calculated photonic dispersion and propagation losses of guided modes in reduced-width PhC waveguides realized in a SOI structure, as schematically represented in Fig. 1(b) (picture in the middle), for different widths of the waveguide channel. Parameters are: d/a=0.5, r/a=0.26, a=400 nm. The highlighted spectral region on the right refers to the σ kz =-1 defect mode with the largest low-loss propagation bandwidth (W0.65 waveguide).

Fig. 6.
Fig. 6.

Calculated photonic dispersion and related propagation losses of TE-like modes in PhC waveguides realized in a Silicon core sandwiched between SiO2 claddings and with SiO2 in the patterned holes, as schematically represented in Fig. 1(b) (picture on the right). Parameters are: d/a=0.5, r/a=0.26, a=400 nm. (a) Reduced-width waveguides, and (b) increased width waveguides. The spectral regions of the σ kz =-1 defect mode with the lowest propagation losses (W0.7 and W1.1 waveguides, respectively) in the single-mode frequency window are also highlighted.

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