Designing photonic structures by using an optimization algorithm

Materials in nature have different characteristical properties. One of these properties is refractive index which lead to light-matter interaction. Photonic crystals consist of dielectric materials with different refractive index values. Photonic crystals are periodically designed dielectric structures and their periodicity can be one, two, or three dimensional. One can achieve different light manipulation scenarios by using photonic crystals. The main phenomena behind the revelation of photonic crystal is the photonic band gap which means that if a frequency of an incident wave is in the frequency interval of a photonic band gap, the incident wave cannot propagate through the photonic crystal structure. Taking advantage of photonic band gaps, various photonic crystal structures can be designed. For instance, by introducing a point defect in a photonic crystal, a photonic crystal cavity structure can be designed. Another example is that by introducing a line defect in a photonic crystal, one can design a waveguide structure. Photonic crystal structures are not only designed based on photonic band gap phenomena. For example, a photonic crystal lens structure can be designed to focus an incident wave. Also, anomalous light behaviors such as self-collimation, superprism, negative refraction and slow light phenomena can be observed in photonic crystals. Besides, a bio-chemical sensor structure can be designed by using photonic crystals. In general, photonic crystals are simple and designed by hand. And it is known that complex photonic crystal structures can have high performance. However, designing complex structures with high performance based on analytical theory and an intuition approach is limited. For this reason, using an optimization algorithm to design a photonic crystal with high performance can be a good solution. Optimization algorithms are used to increase the desired property and decrease the undesired property of a system during the design process of that system. In general, optimization algorithms are created as algorithms which are inspired by nature or theory of evolution. Optimization algorithms can produce good candidate solutions for complex design problems. Since designing a photonic crystals can be a complex problem, idea of using an optimization algorithm to design a photonic crystal structures has taken great attention in recent years because a photonic crystal that is designed by using an optimization algorithm can possess very good properties. In this dissertation, various photonic crystal structures are designed by using an optimization algorithm. Differential Evolution, which is an evolutionary algorithm, is selected as an optimization algorithm in this dissertation. It is shown that Differential Evolution can produce better solutions than the other well known optimization algorithms can. By using Differential Evolution, subwavelength focusing photonic crystal lens structures are designed. And by optimizing the unit cell of a photonic crystal, photonic band gap is widened and a waveguide structure is designed. Also, cavity region of a photonic crystal cavity structure is optimized to obtain a high quality factor value. As a result of the studies in this dissertation, the designed structures are brought to the literature. Also, it is shown that Differential Evolution can be used to design photonic crystal structures and a new approach to design a photonic crystal is introduced. The obtained results are promising for the photonic crystals that will be designed in the future.