Abstract

We study adiabatic mode transformations in photonic-crystal integrated circuits composed of a triangular lattice of holes etched into a planar waveguide. The taper relies on the manufacture of holes with progressively-varying dimensions. The variation synthesizes an artificial material with a gradient effective index. Calculations performed with a three-dimensional exact electromagnetic theory yield high transmission over a wide frequency range. To evidence the practical interest of the approach, a mode transformer with a length as small as λ/2 is shown to provide a spectral-averaged transmission efficiency of 92% for tapering between a ridge waveguide and a photonic crystal waveguide with a one-row defect.

© 2002 Optical Society of America

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References

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Appl. Phys. Lett.

M. Palamaru and Ph. Lalanne, �Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion," Appl. Phys. Lett. 78, 1466-69 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdr� and U. Oesterle, �Low-loss channel waveguides with two-dimensional photonic crystal boundaries,� Appl. Phys. Lett. 77, 2813-15 (2000).
[CrossRef]

Electron. Lett.

Z. Weissman and A. Hardy, "2-D mode tapering via tapered channel waveguide segmentation," Electron. Lett. 28, 1514-1516 (1992).
[CrossRef]

IEEE J. Quantum Electron.

Ph. Lalanne, �Electromagnetic analysis of photonic crystal waveguides operating above the light cone,� to be published in IEEE Journal of Quantum Electronics

J. Computational. Phys.

J. P B�renger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational. Phys. 114, 185-200 (1994).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Nature

T. F. Krauss, R. M. De La Rue and S. Brand, �Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,� Nature 383, 699-702 (1996).
[CrossRef]

Opt. Lett.

Other

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

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Figures (7)

Fig. 1.
Fig. 1.

Tapering with artificial materials between two different PC waveguides. Gray zones correspond to a high refractive-index material. The specific case of a W1–W3 mode conversion is illustrated for a triangular lattice of air holes.

Fig. 2.
Fig. 2.

Geometries considered for testing the taper principle. The lower ridge waveguides are assumed to be illuminated by the fundamental TE00 mode with a unit intensity. Ri and Ti denote the reflected and the transmitted intensities, respectively. (a) situation with tapers. To lower computational loads, only two different holes H1 and H2 are considered for the gradual variation. (b) situation without taper used as a reference. For both situations, the total length of the PC circuit is 18a.

Fig. 3.
Fig. 3.

Cross section of a slice used for the computation. Perfect Matched Layers are used at the boundary of the unit cell. The example corresponds to a slice of a W1 waveguide.

Fig. 4.
Fig. 4.

Convergence performance of the present method.

Fig. 5.
Fig. 5.

Periodic waveguides associated to the taper segments. The horizontal line shows the z-plane location of the Bloch-mode profiles shown in Fig. 7.

Fig. 6.
Fig. 6.

Numerical results for the transmission (top) and reflection (bottom) spectra of the geometries shown in Fig. 2. The wavelength range covers the full band-gap spectral region. Circles : T2, squares : T1. The horizontal line indicate the spectral domain of interest.

Fig. 7.
Fig. 7.

Bloch-mode profiles for the different taper sections for λ = 0.9 μm. The effective indices (real parts) are given in parentheses. The horizontal dashed lines correspond to the stack interfaces cover/core/substrate. (a), (b), (c) and (d) correspond to the W3, WH1, WH2 and W1 waveguides. The profiles are obtained at longitudinal locations indicated by the horizontal solid lines in Fig. 5.

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