The study of optical phenomena related to the strong electromagnetic response of noble metals (silver (Ag) and gold (Au) being most popular) over the last couple of decades has led to the emergence of a fast growing research area called plasmonics named after 'surface plasmons' which are electron density waves that propagate along the interface of a metal and a dielectric medium. Surface plasmons are formed by the coupling of light to the electrons on the metal surface subject to the fulfillment of certain physical conditions and they are bound to the metal surface. Depending on whether the metallic medium is a continuous film or a structure having dimensions less than or comparable to the wavelength of the exciting light, propagating or localized surface plasmons can be excited. The structure can be either a hole or an arbitrary pattern in a metal film, or a metallic particle. An array of subwavelength structures can behave as an effective homogeneous medium to incident light and this is the basis of a new class of media known as metamaterials. Metallic metamaterials enable one to engineer the electromagnetic response to  incident light and provide unconventional optical properties like negative refractive index as one prominent example. Metamaterials exhibiting negative index (also called negative index materials (NIMs)) open the door for super resolution imaging  and development of invisibility cloaks. However, the only problem affecting the utilization of plasmonic media to their fullest potential is the intrinsic loss of the metal, and it becomes a major issue especially at visible-near infrared (NIR) frequencies. The frequency of the surface plasmon is the same as that of the exciting light but its wavelength could be as short as that of X-rays. This property allows light of a given optical frequency to be conned into very small volumes via subwave lengthmetallic structures, that can be used to develop ecient sensors, solar cells, antennas and ultrasensitive molecular detectors to name a few applications. Also, interaction of surface plasmons excited in two or more metallic subwavelength structures in close proximity inuences the far-eld optical properties of the overall coupled system. Some eects of plasmonic interaction in certain coupled particles include polarization conversion, optical activity and transmission spectra mimicking electromagnetically-induced transparency (EIT) as observed in gas based atomicsy stems. In this thesis, we mainly focus on the optical properties of square arrays of certain plasmonic structures popularly researched in the last decade. The structures considered are as follows: (1) subwavelength holes of a composite hole-shape providing superior near-eld enhancement such as two intersecting circles (called' double hole') in an optically thick Au/Ag lm, (2) double layer shnets, (3) subwavelength U-shaped particles and (4) rectangular bars. The entire work is based on electromagnetic simulations using time and frequency domain methods. Au/Ag lms with periodic subwavelength holes provide extraordinarily high transmission of light at certain wavelengths much larger than the dimension of the perforations or holes. The spectral positions of the maxima depend on the shape of the hole and the intra-hole medium, thereby making such lms function as a refractive index sensor in the transmission mode. The sensing performance of the double-hole geometry is analyzed in detail and compared to rectangular holes. Fishnet metamaterials are highly preferred when it comes to constructing a NIM at optical frequencies. A shnet design that theoretically oers a negative refractive index with least losses at telecommunication wavelengths (1.4 1.5 microns) is presented. U-shaped subwavelength metallic particles, in particular single-slit split-ring resonators (SSRRs), provide a large negative response to the magnetic eld of light at a specic resonance frequency. The spectral positions of the structural resonances of the U-shaped particle can be found from its array far field transmission spectrum at normal incidence. An effort is made to clarify our understanding of these resonances with the help of localized surface plasmon modes excited in the overall particle. From an application point of view, it is found that a planar square array of SSRRs eectively functions as an optical half-wave waveplate at the main resonance frequency by creating a polarization in transmission that is orthogonal to that of incident light. A similar waveplate eect can be obtained purely by exploiting the near-eld interaction of dierently oriented neighbouring SSRRs. The physical reasons behind polarization conversion in dierent SSRR-array systems are discussed. A rectangular metallic bar having its dipolar resonance in the visible-NIR is called a nanoantenna, owing to its physical length in the order of nanometers. The excitation of localized surface plasmons, metal dispersion and the geometry of the rectangular nanoantenna make an analytical estimation of the physical length of the antenna from the desired dipolar resonance dicult. A practical map of simulated resonance values corresponding to a variation in geometrical parameters of Au bar is presented. A square array of a coupled plasmonic system comprising of three nanoantennas provides a net transmission response that mimicks the EIT effect. The high transmission spectral window possesses a peculiar dispersion profile that enables light with frequencies in that region to be slowed down. Two popular designs of such plasmonic EIT systems are numerically characterized and compared. / <p>QC 20121017</p>