Demonstration of Magnetism in Thin Films at Optical Frequencies

Abstract

Obtaining a non-unity value for magnetic permeability, �= 1, at optical frequencies is typically associated with subwavelength arrays of structured materials known as metamaterials, this is achieved by the shaping of current densities into circulating currents that can give rise to magnetic multipoles.

Such magnetic responses can enable the design of new devices at optical frequencies utilizing phenomena normally restricted to radio and micro-wave frequencies such as s-polarized Brewster angles, negative refraction lenses and transverse electric surface waves. However, given that these magnetic responses are confined to complex and difficult to fabricate metamaterials, there is limited demonstration of these phenomena, and fewer direct applications. Therefore, the demonstration and application of these magnetic responses in simpler systems, such as thin films, is of great interest, and is the focus of this work.

In this thesis, we derive an angle dependent multipole decomposition model, allowing us to decompose the reflection and transmission spectra of a subwavelength SiN thin film in terms of electric and magnetic multipoles. We then devise an experiment to verify these predictions across visible and near-infrared frequencies. Showing that well known phenomena, such as Fabry Perot modes and p-polarized Brewster angles can only exist if one includes magnetic responses by accounting for magnetic dipoles, quadrupoles and octupoles.

We identify Fabry Perot modes as arising from the destructive interference, in the direction of reflection, between even and odd parity multipoles, which include both electric and magnetic responses, regardless of polarization or mode order.

The p-polarized Brewster angle is identified as resulting from the direction of reflection and electric dipole moment aligning, resulting in zero reflection. This is in agreement with literature, however, we demonstrate an additional, previously unobserved condition to observe the Brewster angle, the destructive interference between electric and magnetic multipoles.

We notice the possibility of additional Brewster angles associated with electric and magnetic multipoles other than the electric dipole, which arise from the alignment between the direction of reflection and the associated multipole moment. These new Brewster angles are hidden in the reflection spectra of our thin film, as the destructive interference between remaining multipoles is absent, but it is not possible to accurately model reflection without these hidden Brewster angles. We suggest several cases where metamaterials may be capable of supporting these new Brewster angles and demonstrate methodologies to unambiguously identify them.

Next we explore how to quantify the effective permittivity and permeability of thin films arising from these multipoles, by evaluating how these multipoles polarize our thin films. We demonstrate how the presence of spatial dispersion, the wavevector dependence of the electric permittivity can arise from either all magnetic multipoles or from electric multipoles that are not the electric dipole. Spatial dispersion plays a vital role in magnetic responses at optical frequencies, given that it is typically understood as being inseparable from magnetic permeabilities at optical frequencies.

Next we move to study thin films that are significancy larger than the wavelength of the incident light, by exploring the reflection of a 50 �m thick film of SiO2. We demonstrate how spatial dispersion may be identified by the dispersion relation of the Fabry Perot mode in cases when multipole decomposition is difficult to practically use.

Having demonstrated how thin films may support magnetic responses through magnetic multipoles and higher order electric multipoles, we then move to demonstrate an application of the magnetic response. We modify the response of a low loss Fabry Perot resonator consisting of 1200 nm of PMMA by depositing it on a thin film of 1 nm Ti and 40 nm Au. Through eigenmode analysis we demonstrate the existence of several modes that arise from the coupling between the Fabry Perot mode in the PMMA cavity and a transverse electric surface plasmon in the metal layers.

A transverse surface wave is identified by two features in the structure. Firstly, the asymmetric Fano lineshapes, which are associated with coupled modes, which were observed in both measurement and model. Secondly, eigenmode analysis identifies a strong magnetic field enhancement along the direction of propagation of the mode, which is a feature unique to transverse electric surface plasmon modes. Simulations introducing an air spacer layer in between the Au and PMMA layers shows this TE surface wave as am evanescent mode confined to the interface between the Au and air layers. However we propose further work to unambiguously identify this surface wave as a surface plasmon in measurements.