Active photonic systems with balanced gain and loss

In the age of information technology one of the main challenges for researches and engineers is to increase the efficiency of transmitting and processing of information. During long distance transmission, a carrier signal can experience attenuation and distortion. To restore and amplify the signal, active photonic systems are widely used. At the same time, all physical systems have losses, which are usually considered a negative effect and should be avoided. However, it was recently shown that if losses and gain in a system are mutually balanced, it demonstrates unique properties, which are not typical to conservative systems. The structure symmetry imposes specific mode geometry, which can facilitate non-reciprocal transmission, selective mode suppression or amplification, and optical switching through phase transition, with applications in lasers and nonlinear optics. In this thesis, we study several active photonic systems with balanced gain and loss and demonstrate how these systems can be used for signal amplification, filtering and lasing. We also suggest a surface nanoscale fiber resonator with specially designed shapes that allow reflectionless signal transmission, as well as generation of optical frequency combs of tiny spacing in a nonlinear regime. Chapter 1 provides a comprehensive introduction to active photonic systems with balanced gain and loss. Here we discuss the concept of PT-symmetric systems, an overview of some pioneering works on the topic and describe mode properties of basic geometries. We also explain basic principles of light transmission through a so-called Surface Nanoscale Axial Photonic (SNAP) fiber resonator and discuss its possible applications. Chapter 2 focuses on PT-symmetric and pseudo Hermitian structures composed of coupled waveguides. It is shown, that when incorporated into a chain of conservative waveguides, PT symmetric dimer and trimer couplers can substantially amplify transmitted and reflected signals. Chapter 3 proposes a PT symmetric fiber laser composed of two coupled ring cavities with gain and loss. It performs analytical and numerical mode analysis taking into account gain saturation in one case and power dependent phase modulators in another case. We predict laser bistability in the PT-symmetric regime in contrast to a symmetry-broken single-mode operation. Chapter 4 explores signal transmission through the SNAP fiber resonator where the shape is designed in a special way providing reflectionless signal propagation. It reveals that reflectionless modulations can realize control of a transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk. Chapter 5 develops a theory of frequency comb generation in SNAP bottle microresonators, employing the nonlinear interaction of whispering gallery modes which are confined along an optical fiber with nanoscale radius variation. It was predicted that a SNAP microresonator with a few-mm radius can generate frequency combs of sub-GHz spectral spacing. It was shown that special engineering of the SNAP radius profile can be used to compensate nonlinearity induced dispersion. Chapter 6 concludes the thesis and provides an outlook to the research works that can be extended from the results in this thesis. Appendix A is devoted to nonlinear mode interactions in SNAP fiber resonators. The detailed derivation of the general model describing multi-mode interactions is presented for a nonlinear, dispersive media. For the particular case of self-action of one azimuthal mode, we present some physical estimates of the considered system and show that nonlinear effects can potentially be observed in experiment