Study of new oscillator schemes based on exceptional points of degeneracy

The aim of this thesis is to introduce a new concept of distributed radiating and oscillating device by investigating and manipulating some dispersive properties of particular periodic structures based on planar technology. Floquet-Bloch modes describe the propagation of electromagnetic waves in periodic transmission lines. Two-port periodic guiding structures allow the occurrence of regular band edge (RBE), that is a fundamental class of exceptional point of degeneracy (EPD). Under these special dispersion conditions, both the two system eigenvectors and eigenvalues coalesce. This represents a standing wave where energy is not flowing through the periodic circuit. A description of the wide range of applications in which dispersive degeneracy conditions have crucial importance is presented. As an example the reader will notice how it is possible to have better control of beam and directivity in fast travelling wave radiators, to allow the design of high Q-factor and high spectral purity oscillators and obtain sensors with enhanced sensitivity. After a basic introduction to radio frequency and microwave oscillators, leaky wave antennas and to the basis of the periodic structures mathematical model, the attention is eventually focused on the general transmission line theory of exceptional points of degeneracy. For these structures, the central concept of gain (introduced by active devices) and loss (ohmic and radiation) balance is presented, pointing out how symmetries are involved in determining whether or not an EPD can exist. As a final result of the study, two microstrip ladder oscillators schemes based on regular band edge are proposed. Microstrip lines, interdigitated capacitors and non-linear active devices are conveniently arranged in asymmetric and folded structures able to provide a stable oscillation, high spectral purity, high loaded Q-factor, ability to radiate at the oscillation frequency along with a simple design. Finally, a last chapter presents some considerations about the possibility of having oscillation in looped ladder structures. Where the behaviour of an infinitely long periodic structure is reproduced, EPD can be ideally retrieved by providing gain. Operating near such special degeneracy conditions further improvements appear, leading to potential performance enhancement in a broad variety of microwave and optical devices.