Precision in optics has always been a challenge, which has persistently demanding new methods of design. Achieving a high performance imaging system with a compact form factor such as AR/VR displays, cameras and microscopes requires extra degrees of freedom. Recently, emerging science like freeform conformal meta-optics, which is an integrated technology of metamaterials combined with freeform optical surface profiles, offers lighter, simple and more compact assemblies. We propose a new inverse synthesis method based on the Dirac distribution of the E-M fields at an arbitrary interface and come up with with an extension of the Generalized Sheet Transition Conditions (GSTCs) valid for any arbitrary surface which we called Conformal-GSTCs (or C-GSTCs in short). We model the CGSTCs using a three dimensional FDTD method and demonstrate the validity of our modelling technique by numerically implementing the scheme for optical devices such as lenses and deflectors using home made parallel FDTD codes. We have used our numerical simulations to study the effect of the shape of the metasurface interface on the performances of metalenses. These performances were numerically characterized using standard methods of optics such as the Full Wave at Half Maximum (FWHM), Point Spread Function (PSF) or optical aberrations calculation through Zernike polynomial analysis. Our numerical implementation can serve as a tool to design freeform meta-optics, and can help in evaluating and optimizing the optical response of complex freeform optical assemblies.On the other direction, we have come up with certain characterization techniques to measure the phase data experimentally by using an in-house experimental set up. The measured phase data is processed for the evaluation of the susceptibilities. The transmitted field data arising from the metaoptical devices are computed numerically using Fourier beam propagation methods with the help of measured susceptibilities. Finally, the performance of the optical devices such as metalenses and deflectors are studied and reported. This technique could help in characterizing optical devices without the need of much complicated tools & devices in experimental labs, which could save a huge amount of resources.We have developed a full vectorial mesoscopic model to investigate the light-metasurface interaction. In this method, we obtain the distributed form of the susceptibilities from the geometric design of the metasurface by the lattice representation of nano-antennas, an approach which is similar to the concept of solid state physics. We obtain an analytical expression for the propagation of the field through the metasurface by solving Maxwell's equations for a given susceptibility function. We prove that the transmitted co-polarized beam alone acquires a global phase associated with the antenna response. Contrarily to the co-polarization beam, the transmitted cross-polarized beam is influenced by both PB and propagation phases. We extend this phase phenomenon to a general situation by decomposing the arbitrary polarization of a normally incident light in circular basis, showing that each eigenstate acquires an opposite extra phase delay due to the topological phase retardation associated with the PB phase. The diffractive properties of topological phase gradient metasurfaces are analyzed in depth via the analytical derivations, and the results are verified with optical measurements. The other physical mechanisms such as the universal principles of co-polarization and cross-polarization transmission, and the coexistence of the zero and nonzero phase gradient leading to the ordinary and generalized Snell’s law, are illustrated using the present framework. Our model an initiative to develop an intuitive understanding of topological and functional beam splitters for future applications in quantum optics and quantum information protocols.