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Light guiding properties of the photonic waveguides highly depend on the geometrical parameters once the material platform is decided, such as silicon-on-insulator technology. Uniform index profile can be engineered to obtain Bragg gratings operating in the wavelength or sub-wavelength scales. The standard index modulation of waveguides as in the Bragg gratings gives rise to band gap appearance that provides various types of light filtering features. Besides, the light propagation at the band edges can be tailored to manipulate the group velocity of optical signals. However, highly dispersive nature of band gap edges causes serious pulse distortions. Overcoming this problem by means of limited parameter search and trial-and-error method is a highly challenging design problem since it would be very time consuming to find a suitable structure. To obtain different spectral characteristics for the index guided mode traveling in silicon waveguide and alter the mode’s dispersion property, we propose an inverse design approach based on topology optimization. By appropriately defining figure of merits in the spectral domain, complex index modulation of short length multimode waveguide sections provides sharp filtering features that are ripple-free and accompanied with large group index values (>15.0) over a certain bandwidth at telecom wavelengths (1550 nm). The generated CMOS compatible non-intuitive geometries inside the waveguide structures were fabricated with the standard optical lithography steps and they can be applied to different photonic applications such as optical computing, spectroscopy, and sensing.
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