Abstract

A specific class of planar photonic crystals is investigated that provides a condensed matter combining the properties of planar multilayer stacks and two-dimensional photonic crystals in order to achieve large partial bandgaps in the eigenstate spectrum. These gaps are larger than the directionally dependent and polarization-dependent partial gaps of photonic crystal slabs. Full in-plane gaps are demonstrated numerically. Strong dispersion, waveguide confinement, high Q-cavities, and alternative photonic signal processing are feasible with these structures.

© 2003 Optical Society of America

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References

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Appl. Phys. Lett. (2)

S. G. Johnson and J. D. Joannopoulos, �??Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,�?? Appl. Phys. Lett. 77, 3490-3492 (2000).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, �??Design of three-dimensional photonic crystals at submicron lengthscales,�?? Appl. Phys. Lett. 65, 1466-1468 (1994).
[CrossRef]

J. Vac. Sci. Technol. B (1)

E. Kuramochi, M. Notomi, T. Tamamura, T. Kawashima, S. Kawakami, J. Takahashi, and C. Takahashi, �??Drilled alternating-layer structure for three-dimensional photonic crystals with a full band gap,�?? J. Vac. Sci. Technol. B 18, 3510-3513 (2000).
[CrossRef]

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, �??Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,�?? Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (7)

Opt. Quantum Electron. (1)

S. Kawakami, E. Kuramochi, M. Notomi, T. Kawashima, J. Takahashi, C. Takahashi, and T. Tamamura, �??A new fabrication technique for photonic crystals: nanolithography combined with alternating-layer deposition,�?? Opt. Quantum Electron. 34, 53-61 (2002).
[CrossRef]

Phys. Rev. B. (4)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B. 60, 5751-5758 (1999).
[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]

T. Søndergaard and K. H. Dridi, �??Energy flow in photonic crystal waveguides,�?? Phys. Rev. B. 61, 15688-15696 (2000).
[CrossRef]

Z. Y. Li and Y. Xia, �??Omnidirectional absolute band gaps in two-dimensional photonic crystals,�?? Phys. Rev. B. 64, 153108-153112 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

K. M. Ho, C. T. Chan, and C. M. Soukoulis, �??Existence of a photonic gap in periodic dielectric structures,�?? Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, �??Photonic band structure: the face-centered-cubic case employing nonspherical atoms,�?? Phys. Rev. Lett. 67, 2295-2298 (1991).
[CrossRef] [PubMed]

Science (5)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, �??Full three-dimensional photonic bandgap crystals at nearinfrared wavelengths,�?? Science 289, 604-606 (2000).
[CrossRef] [PubMed]

O. Toader and S. John, �??Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,�?? Science 292, 1133-1135 (2001).
[CrossRef] [PubMed]

Y. Fink, J.N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, �??An all-dielectric coaxial waveguide,�?? Science 289, 415-419 (2000).
[CrossRef] [PubMed]

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, �??Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,�?? Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Other (1)

J. D. Joannopoulos, R .D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

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Figures (5)

Fig. 1.
Fig. 1.

Multilayer stacks of 2D photonic crystals that exhibit large bandgaps in their mode spectrum (from left to right MS2DPC1 and MS2DPC2). MS2DPC1 is made of a 1D dielectric multilayer stack of alternating planar layers A and B filled with materials A and B, respectively, in which a 2D crystal lattice of cylindrical holes is etched and where the holes might be filled with material C. MS2DPC2 is made of a 2D crystal lattice of cylindrical pillars grown in a background material C. These pillars are made of a 1D dielectric multilayer stack of alternating planar layers with materials A and B.

Fig. 2.
Fig. 2.

Projected band diagrams for all polarization states and dependency of the bandgap on the normalized kz component of the propagation vector for a specific MS2DPC1 design (relevant kz values belong to the interval [0;0.5Λ/Λ z ]). This structure has a triangular lattice of air holes, nA =4.6, nB =4.1, nC =1, r 0/Λ=0.475 with Λz/Λ=0.5 and tAz z=1- tBz z=0.8. The light blue region represents modes for which electromagnetic radiation is allowed in the bulk MS2DPC1 structure, while the dark cyan region represents forbidden modes where electromagnetic radiation is not allowed in the bulk MS2DPC1 structure. The region hatched with dark lines is denoted R 1, and will be the subject of a discussion in a later paragraph.

Fig. 3.
Fig. 3.

Band diagram for kz =0 for all polarization states of the specific MS2DPC of Fig. 2 near the gap. The eigenstates are clearly polarized in this window of the spectrum, and are categorized into the P 1 and the P 2 polarization types.

Fig. 4.
Fig. 4.

Regions of forbidden modes for states with E E z < 0.1 resulting from filtering the band diagrams with energy constraints for the MS2DPC1 structure with D=2r 0=0.95Δ and D=2r 0=0.8Λ. Other parameter values are the same as those for the structure of Fig. 2. The light grey region is the RFM for D=0.95Λ with respect to SiO 2 defects, while the dark grey region is the RFM for D=0.8Λ with respect to SiO 2 defects. The upper region hatched with lines with positive slope is the RFM for D =0.95Λ with respect to air defects, while the lower region hatched with lines with negative slope is the RFM for D=0.8Λ with respect to air defects.

Fig. 5.
Fig. 5.

Bandgap regions for states with E E z < 0.1 (P 1) together with the air line and the SiO 2 line for severalmaterial systems (A,B) with (Ge,Si) (filled square symbols), (Si,SiN) (open square symbols), (Si,SiO 2) (filled circle symbols), (SiN,SiN) (Si-rich SiN with index 2.35, and SiN with index 2.1) (open circle symbols), and (SiN,SiO 2) (filled triangle symbols), in a MS2DDPC where nC =1, r 0/Λ=0.41, Λ z /Λ=0.4, and tAz z =1-tBz z =0.5. In parentheses we write the index contrasts of the respective material systems.

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