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.