| Summary: | The first part of the presented thesis begins by developing the lasing mode theory of a structurally chiral laser and highlighting the possibilities for a structurally chiral laser to lase both left and right circularly polarised light, as well as within the photonic bandgap. The discoveries are utilised in order to develop the lasing mode theory of a chiral distributed Bragg reflector laser, which consists of structurally chiral mirrors and a uniform lasing cavity, as well as of a hybrid chiral laser, which consists of structurally chiral mirrors with a contrahanded structurally chiral lasing cavity. Applications towards more efficient 3D projectors as well as 3D displays are discussed. The second part of the thesis develops the theory of transformation optics from first principles using differential geometry. The rigorously constructed structure is manipulated in order to examine the effects of a transformation on the refractive index. The analysis reveals the existence of a refractive index ellipsoid, which encodes the complete transformation and can be used to intuitively grasp the effects of any given transformation on light rays travelling inside the transformation optics device. The refractive index ellipse is calculated for the well known cylindrical cloak as well as for a new type of twist deformation, providing insights into the inner workings of these devices.
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