1 Department of Photonics Engineering, Technical University of Denmark2 Department of Electromagnetic Systems, Technical University of Denmark3 Rector’s office, Administration, Technical University of Denmark
From the work carried out within the ph.d. project two topics have been selected for this thesis, namely emission of radiation by sources in dielectric microstructures, and planar photonic crystal waveguides. The work done within the first topic, emission of radiation by sources in dielectric microstructures, will be presented in the part I of this thesis consisting of the chapters 2-5. An introductions is given in chapter 2. In part I three methods are presented for calculating spontaneous and classical emission from sources in dielectric microstructures. The first method presented in chapter 3 is based on the Fermi Golden Rule, and spontaneous emission from emitters in a passive dielectric microstructure is calculated by summing over the emission into each electromagnetic mode of the radiation field. This method is applied to investigate spontaneous emission in a two-dimensional photonic crystal and photonic crystal microcavity. In chapter 4 a general theory based on a Green's tensor formalism is put forward for spontaneous emission in active dielectric microstructures, and an example is given whre the method is applied to a fiber amplifier. The Green's tensor in chapter 4 is constructed a a summation over a biorthogonal set of electromagnetic modes. An alternative method based on a Lippmann-Schwinger type integral equation is presented in chapter 5 for the construction of the Green's tensor and calculation of emission of radiation by sources. The integral equation approach is applied to calculate near fields and far fields generated by a dipole emitter in finite-sized dielectric disks. A collection of results obtained within the second topic, planar photonic crystal waveguides, are presented in part II of this thesis consisting of the chapters 6-10. Chapter 6 contains a further introduction to the topic planar photonic crystal waveguides. Chapter 7 contains fundamental research on the electromagnetic energy flow and the number of guided modes versus waveguide width and frequency for two-dimensional photonic crystal waveguides. In chapter 8 it is shown how two-dimensional calculations for infinite-height photonic crystal waveguides can be used to obtain guidelines for the design of leakage-free finite-height planar photonic crystal waveguidse. Guidelines are obtained by comparing the two-dimensional calculations to dispersion relations for the media above and below the finite-height waveguide. In chapter 9 both a two-dimensional and three-dimensional theoretical analysis is presented for a photonic crystal waveguide based on the semiconductor-on-insulator materials system. The chapter 10 addresses the design of planar photonic crystal waveguides that support leakage-free guidance of light over a large bandwidth.