Inverse design of photonic structures with objective-first algorithm

Photonic devices are the basic elements used in the design of integrated optical circuits. Intuitive scanning of the parameter space or the use of non-intuitive optimization algorithms are the methods of photonic device design. In intuitive methods, the design is performed by examining the structural parameters such as the size and dielectric constant of the photonic structure by trial and error method. These methods require starting from a good starting point and require much simulation cost. Some search algorithms for scanning the parameter space have emerged as an alternative to the experience-based method. Considering many determinants such as efficiency and functionality in device performances, a more comprehensive and controlled design method was needed. Therefore, the inverse photonical design method, also known as objective-first method, has emerged in the literature. The objective-first inverse design algorithm is an up-to-date optimization method that has been effectively applied to many linear photonic devices in the literature. The objective-first algorithm approach the design problem as a reverse problem and eliminates the need to start from a good point. A photonic structure is designed for the purpose defined as boundary value problem in objective-first inverse design algorithm. The theoretical background of the objective-first algorithm was created by the bi- linearity proporty of the steady sate wave wave equation both the dielectric constant and the magnetic response of the structure. Due to the bi-linearity feature, the design problem is divided into two sub-problems and it reaches the best result by calculating iteratively between sub problems. The objective-first inverse design algorithm eliminates the need to strictly observe the steady state wave equation, and calculates how close to the possible design with the error parameter. As a natural result of the linearity feature, the solution set shows a continuous distribution and it is possible to convert it into constructable structures with additional binarization cost. Within the scope of this thesis, paralel plane resonator and optical filter designs have been made with the objective-first algorithm. In the parallel plane resonator design, the plane mirror conditions added to the two end sides of the cavity region and the waves reflected repeatedly to create the resonance at the targeted frequency. In the designed resonator structure dielectric mirror and cavity sections are obtained without manual adjustment. For low and high pass filters, the algorithm is optimized for multi-purpose and multi-freqency. The desired frequencies isolated in the designed filter structures are reflected from the beginning of the structure and the highest transmission is targeted at the other frequencies.