With the manufacture of nano-scale features in the last ten years, it is possible to do optical experiments on features as small as a tenth/hundredth wavelength. It turns out that the experimental data cannot be explained by classical diffraction theories. Thus, it is necessary to develop new methods or use existing approaches which are effective in other fields, to solve problems in photonics. We use finite difference time domain (FDTD), to study transmission properties of sub-wavelength slits in a metallic film. By doing simulations on periodic and single slits, we confirm that the TE mode has a cutoff while a TM mode always has a propagating mode in the small apertures. Then we find that the transmittance is minimum when the array period is equal to the wavelength of surface plasmon polariton (SPP) at normal incidence. In fact, the SPP-like waves exist in both periodic and isolated slits, and they help the transmittance of small apertures. In order to establish the role of SPP in the transmission mechanism, it is necessary to single out each mode from the total fields. We developed Bloch mode method (BMM) to calculate the amplitudes of the lowest N orders, and the amplitudes tell us which one is dominant (not including the guided mode) at high and low transmission. BMM converges very fast and it is more accurate than FDTD since it does not suffer from numerical dispersion. Both methods can resolve the Wood anomaly and SPP anomaly; however, FDTD converges very slowly at the SPP resonance and oscillates around the value obtained through BMM at the Wood anomaly. BMM is not sensitive to material types, incident angles, and anomalies; it will be a useful tool to investigate similar problems.

Metamaterials attracted significant attention in recent years due to their potential to create novel devices that exhibit specific electromagnetic properties. In this thesis, we investigated transmission and propagation properties of novel metamaterial structures. Electromagnetic properties of metamaterials are characterized and the resonance mechanism of Split Ring Resonator (SRR) structure is investigated. Furthermore, a recent lefthanded metamaterial structure for microwave regime called Fishnet-type metamaterial is studied. We demonstrated the left-handed transmission and negative phase velocity in Fishnet Structures. Finally, we proposed and successfully demonstrated novel approaches that utilize the resonant behavior of SRR structures to enhance the transmission of electromagnetic waves through sub-wavelength apertures at microwave frequency regime. We investigated the transmission enhancement of electromagnetic waves through a sub-wavelength aperture by placing SRR structures in front of the aperture and also by changing the aperture shape as SRR-shaped apertures. The incident electromagnetic wave is effectively coupled to the sub-wavelength aperture causing a strong localization of electromagnetic field in the sub-wavelength aperture. Localized electromagnetic wave gives rise to enhanced transmission from a single sub-wavelength aperture. The proposed structures are designed, simulated, fabricated and measured. The simulations and experimental results are in good agreement and shows significant enhancement of electromagnetic wave transmission through sub-wavelength apertures by utilizing proposed novel structures. Radius (r) of the sub-wavelength aperture is approximately twenty times smaller than the incident wavelength (r/&amp / #955 / ~0.05). This is the smallest aperture size to wavelength ratio in the contemporary literature according to our knowledge.