This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods are appropriate for problems where the power is to be maximized or minimized at a few frequencies, without regards on the detailed profile of the optical pulse or the need of large amount of frequency samplings. The design of slow light couplers connecting ridge waveguides and the photonic crystal waveguides is showcased here. It is demonstrated both numerically and experimentally that the optimized couplers could improve the coupling efficiency prominently. With more focus on the time-domain optimization method, the thesis discusses extensively the design of pulse-shaping filters, which greatly exploits the benefits of time-domain methods. Finite-difference time-domain method is used here as the modeling basis for the inverse problem. Filters based on both one-dimensional gratings and two-dimensional planar structures are designed and different issues regarding local minima, black and white design, minimum lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses.
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Hvam, Jørn Märcher, Lavrinenko, Andrei, Sigmund, Ole