Group velocity dispersion manipulation in integrated waveguides

Abstract

The ability to arbitrarily control the chromatic dispersion in CMOS-compatible waveguides should strengthen the viability of this technology, particularly for nonlinear devices on a chip [1]. Here we report on a systematic investigation of group velocity dispersion engineering in channel and rib waveguides with a silicon nitride core (Si <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> ). The dispersion control is done by including three cladding layers: the first two are thin (<400nm) and are made of silica (SiO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ) or Si <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> with refractive indices that can be varied up to 3% with respect to an average value. All this is embedded in a silica cladding. Up to eight parameters can be tuned for dispersion optimization: height and width of the core, thickness and refractive index of the first two claddings, and the type of waveguide (rib or channel). The details of the waveguides under investigation are shown in the inset of Figure 1(a). We have two goals: 1) finding the flattest possible dispersion irrespective of its absolute value, and 2) finding the flattest and lowest dispersion. Figure 1 shows the results after optimizing the eight parameters for the rib and channel waveguide. The flattest dispersion (solid line) is found for the waveguide that includes a silica layer as the first cladding: over a bandwidth of 1000 nm (1350–2450nm) the dispersion is −68 ± 0.6 ps/nm-km. This result demonstrates that appropriate engineering in integrated waveguides produces flattened dispersion profiles comparable as those in photonic crystal fibres [2]. When the silica layer is not included, the flattest dispersion is anomalous (+45 ± 1.5 ps/nm-km) and spans over 700 nm (dotted line). If the goal is having flat and zero dispersion, again the structure with a silica cladding layer (dashed line) provides the best result (2 +/- 2 ps/nm-km over 900 nm). On the other hand the other structure provides flat and low dispersion over 500 nm (dot-dashed line). We analyzed what is the main requirement to have ultra-flat dispersion and we observed that the first silica layer allows for a large control of the dispersion flatness and its absolute value. On the other hand, having a rib waveguide or changing the layers refractive indices by a few % can flatten the dispersion, but will not allow for an arbitrary control. This indicates, that it is necessary to have a certain amount of refractive index contrast in order to modify at a great extent the dispersion.