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Ascertainment of photonic stopband absolute topological character requires information regarding the Bloch eigenfunction spatial distribution. Consequently, the experimental investigations predominantly restrict themselves to the bulk-boundary correspondence principle and the ensuing emergence of topological surface state. Although capable of establishing the equivalence or inequivalence of bandgaps, the determination of their absolute topological identity remains out of its purview. The alternate method of reflection phase-based identification also provides only contentious improvements owing to the measurement complexities pertaining to the interferometric setups. To circumvent these limitations, we resort to the Kramers-Kronig amplitude-phase causality considerations and propose an experimentally conducive method for bandgap topological character determination directly from the parametric reflectance measurements. Particularly, it has been demonstrated that in case of one-dimensional photonic crystals, polarization-resolved dispersion measurements suffice in qualitatively determining bandgap absolute topological identities. By invoking the translational invariance of the investigated samples, we also define a parameter Differential Effective Mass that encapsulates bandgap topological identities and engenders an experimentally discernible bandgap classifier.

In this thesis, we explore random lasing from a system comprising of amplifying microresonators. Using Monte-Carlo simulation, we investigate the diffusive propagation of light in an amplifying medium with randomly suspended resonant scatterers. The simulation shows that a more efficient and stable coherent random lasing can be achieved with monodisperse scatterers having amplification in the intra-scatterer region. To realize that experimentally, the array of amplifying microdroplets is created using a vibrating orifice droplet generator. The degree of randomness is tuned by varying the size and spacing between the droplets. Upon optical excitation, coherent random lasing is observed in the longitudinal direction of the array. By making the droplets monodisperse, we realized amplifying periodic-on-average random superlattice (aPARS) system. The statistical study of the lasing wavelengths from aPARS droplet array shows that the lasing peaks occur only within a specific interval of wavelengths. Using spectral mode-matching, we restrict the frequency fluctuation of modes within ~ 1.2 nm. The calculation based on the transfer matrix method shows that experimentally observed lasing peaks arise from the perturbed band-edge states of the underlying periodic system. The spatial intensity distribution of the lasing modes in droplet array confirms its Anderson-localized nature. We also consider the microdroplet array as a direct-coupled active chain of spherical microcavities and examine the ability of gain to overcome the bending and other radiative losses., Comment: 142 pages, 60 figures, PhD Thesis