Ultra wide-band （UWB） filter is designed from defected ground structure of conducting plane or PEC （perfect electric conductor） with complimentary split ring resonator （DGS-CSRR）. From Simulation results, the transmission bandwidth （BW） and fractional bandwidth （FBW） UWB at10dB below the transmission power are2.48GHz and27.46%respectively. These results have already been greater than the minimum requirement set by the Federal Communications （FCC） of USA. The frequency dependent of DGS-CSRR of macroscopic properties permittivity （ε） and permeability （μ） of UWB resonator are are derived from the law of kinematic motions of free electrons of metals and Maxwell’s equations under the influence of external electromagnetic field forming Drude-Lorentz harmonic oscillator. Drude-Lorentz mode harmonic oscillator helps to track down the resonance frequency of UWB oscillator around which both ε and μ become simultaneously negative values. This scenario would bring unique properties of the materials, which do not exist naturally forming a special classification called metamaterial or double material of negative refractive index （NIM） material. UWB made from such materials have attracted a great interest in both academic and industry in the past few years for applications in short range wireless mobile systems. This is due to the potential advantages of UWB transmission such as low power, high rate, immunity multi-path propagation and low interference.On the other hand under optical frequency regime, the interaction of light with free electrons in gold and silver nano-structure can give rise to collective excitations commonly known as surface plasmons. Plasmons provide a powerful means of confining light between the metal and the dielectric interfaces, which intern they can generate intense local electromagnetic fields and significantly amplify the signal derived from an analytical techniques from weak signals due to Raman scattering. With plasmon pho-tonic signals can be manipulated on the nano-scale, enabling integration with electronics. Furthermore the optica; responses of various geometrical gold or silver nano-shell with silica core are investigated by finite difference time domain （FDTD） method. This method provides a convenient, symmetric, and general approach for calculating the optical responses of nono-structural of arbitrary symmetry and geometry to an incident light wave. Properties such as optical extinction cross-section （the sum of absorption and scattering cross-section）, surface plasmon resonances （SPR） including longitudinal and surface plasmon resonances, enhancement of local electric field （ELEF） are extracted and dealt with this method. The method is widely applied to uniform and non uniform gold and silver nano-shells with silica dielectric cores, aggregated or colloidal number of various shapes and size of gold and silver nano-particles inside silica dielectric medium. It is also applied for optical characterization of naked and silica-coated gold and silver nano-particles inside a polymer. Eventually the results show that defects and sharper edges of nano-particles of various forms and arrangements are significantly affecting the enhancement of the electric field for amplifying the weak signals called raman scattering. Latter on this assists the development of surface-enhanced Raman scattering （SERS）. SERS provides a sensitive metod for detecting trace levels of wide range of chemical and bioechmical compound absorbed on anno-structured plasmonic Au/Ag nano-particles surfaces.