Circuit Complexity Introduction


The description given above is very brief, and shows the fact that we are able to study (by means of numerical techniques) just a very limited range of various optical components. On the other hand, a more complex optical circuit can be somehow divided into smaller elements or units of single straight and curved waveguides. The elements are mostly some basic, indispensable, well-known, and also well- understood photonic ingredients such as curvilinear directional couplers (e.g. four port coupler), branching and combining waveguides, various bent waveguides and several kinds of tapers. Of course, all these waveguiding structures can be efficiently simulated by BPM.

Based on the fact that most of more advanced circuits are created by the fundamental photonic elements and we will briefly point out four categories of the photonic circuits attracting our interest. The decision criteria are obvious and they will be given for each category. This paragraph will, we hope, illustrate the principal idea of our method. Any further analysis of the presented circuits will be related and compared to practical possibilities of the BPM techniques. Since our goal is to analyze a given complex photonic circuit as efficiently as possible, we will also mention numerical analysis simplifications and improvements even for those circuits theoretically suitable just for the BPM.