Scattering Matrix Method Applied to Photonic Crystals
Scattering Matrix method deal with collections of objects having different electromagnetic parameters or different shapes. The method of fictitious sources is a versatile and reliable method to deal with many scattering problems. It relies upon a simple idea: the electromagnetic field in the various domains of the diffracting structure can be expressed as a combination of fields radiated by suitable electromagnetic sources. The chapter provides useful theoretical tools to understand and design the properties of devices based on photonic crystals. It summarises the properties of the propagating Bloch modes in infinite photonic crystals and pay special attention to the propagation of energy. The chapter considers two-dimensional photonic crystals made of a finite number of dielectric cylinders placed in a vacuum. It reviews the properties of the allowed electromagnetic propagating modes in the infinite photonic crystal. The chapter shows that the interfaces of the slice are perpendicular to the y-axis.