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Photonic crystal waveguides with semi-slow light and tailored dispersion properties

Lars H. Frandsen, Andrei V. Lavrinenko, Jacob Fage-Pedersen, and Peter I. Borel

Open Access Open Access

Abstract

We demonstrate a concept for tailoring the group velocity and dispersion properties for light propagating in a planar photonic crystal waveguide. By perturbing the holes adjacent to the waveguide core it is possible to increase the useful bandwidth below the light-line and obtain a photonic crystal waveguide with either vanishing, positive, or negative group velocity dispersion and semi-slow light. We realize experimentally a silicon-on-insulator photonic crystal waveguide having nearly constant group velocity ~c 0/34 in an 11-nm bandwidth below the silica-line.

©2006 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. (a) Typical band diagram showing the normalized frequencies versus normalized wavevectors for a single-line defect 2D photonic crystal waveguide supporting an even (solid) and odd (dashed) mode in the bandgap. The inset of the graph sketches the supercell used in the plane wave expansion calculation. (b) Group velocity v g in units of the speed of light in vacuum, c 0, versus wavevector k z (black), calculated by using Eq. (1). The group velocity dispersion parameter β 2 obtained from Eq. (2) (red). (c) Modal field distributions in a W1 PhCW for the wavevectors marked by a red, yellow, and green square in (a) and (b).

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Fig. 2.
Fig. 2. Movement of the even PBG mode when changing the diameter (a) D 1 of the first row and (b) D 2 of the second row of holes in a W1 PhCW. Bulk holes have diameter D=0.60Λ.

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Fig. 3.
Fig. 3. (a). Band diagram for different even PBG modes in a 3D W1 PhCW where the diameter D 1/D 2 of the first/second row of holes have been changed according to the legend, relative to the bulk diameter D=222 nm. (b) Corresponding calculated group indices (bottom) and group velocity dispersion parameter β 2 (top, left and right) for the modes plotted in (a).

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Fig. 4.
Fig. 4. Scanning electron micrograph of a perturbed photonic crystal waveguide. The diameter D 1/D 2 has been decreased/increased compared to the diameter D of the bulk holes.

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Fig. 5.
Fig. 5. (a). 3D band diagram (left) and transmission spectrum (right) for a perturbed 500-µm PhCW with ΔD1=-60 nm and ΔD2=+10 nm. The even PBG mode (solid black) gives rise to two transmission peaks: one located above (dotted red) and one located below (dotted green) the silica-line (violet). (b) Measured (black), 2D FDTD (blue) and 3D PWE (red) calculated group index for the perturbed PhCW. The measured propagation loss is also plotted (green).

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

v g = d ω d k = c 0 n g ,
β 2 = d 2 k d ω 2 = d n g d ω 1 c 0 .
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