M.Sc Thesis

M.Sc StudentDaniel Aronovich
SubjectThe Nonlinear Hyperlens: Modelling Linear Nonlinear
Cylinderical Metal-Dielectric Multilayers at
the Nanoscale
DepartmentDepartment of Electrical Engineering
Supervisor Professor Bartal Guy


            The emerging field of Plasmonics and Metamaterials utilizes nano-scale metal-dielectric composites at dimensions much smaller than the wavelength of light, to obtain extraordinary electromagnetic properties not existing in naturally occurring materials. One family of these composites is the metal-dielectric periodic structures with periods of 10s of nanometres - much smaller than the wavelength of visible light.

            Past research of such media had already shown negative refraction, far field imaging (Hyperlens) and nonlinear effects at sub-wavelength scale. The Optical Hyperlens was studied extensively in the past few years owing to its capability of  conveying Subwavelength information into the far field while overcoming the diffraction limit, thereby showing great promise in real-time nanoscale optical imaging and sensing. 

In this work we model and investigate wave propagation in cylindrically-symmetric subwavelength metal-dielectric multilayers. First, we propose performance improvement of the hyperlens by relaxing the SPP resonance condition and utilizing self-focusing nonlinearity, e.g., using dielectric layers with high Kerr-type nonlinearity, to counteract the diffraction. We refer to this device as the Nonlinear Hyperlens and show that the operation frequency range of the device can be extended and longer propagation distance can be achieved, improving further the device resolution. The sub-wavelength propagation in such nonlinear medium is simulated using a self-developed nonlinear beam propagation method (NL-BPM) in cylindrical coordinates that is applicable for any non-paraxial propagation along the radial direction.

We next present an analytical method for accurate modelling of wave propagation in cylindrically-symmetric sub-wavelength metal-dielectric multilayers. Utilizing a Cylindrical Transfer Matrix Method, we compute the Amplitude Transfer Function of Cylindrical Hyperlens, simulate the exact field distribution and propagation for a given source and compare it to the Effective Hyperbolic Medium.  We investigate the conditions under which the effective medium approximation (EMT), which is often used to analyse such systems, is valid and show that in cylindrical configuration not only the size of the unit cell compared to the wavelength is futile to the validity of the EMT, but also that the ratio of the inner radius to the unit cell plays an important role.