The optical spectroscopy techniques have been used to investigate left-handed behavior of metamaterials as well as the electron-bosonic spectral functions (or Bosonic spectra) of high-transition-temperature superconductors (or high-Tc superconductors) in the research work of this thesis. The periodic double-ring split-ring resonator (SRR) array was one of the first proposed magnetic metamaterials which could give rise to a negative magnetic permeability (μ<0). In the traditional design of negative index metamaterials, the SRR arrays were combined with continuous metallic wires that provide a negative electric permittivity (∊<0). However, the requirement of an unbroken electrical connection between unit cells would be challenging in building contoured devices. In our study, we carefully examine the electromagnetic properties of the double-ring SRR arrays on silicon substrates in the mid-infrared frequency regime experimentally and numerically. For light at normal incidence, we observe that an electric resonance in the outer ring and a magnetic resonance in the inner ring exist at similar frequencies in one of our samples, which suggests that the double-ring SRR array could have simultaneous a negative permittivity and a negative permeability, or a left-handed behavior. Our conjectures are confirmed by the numerical simulations. We also propose a new left-handed metamaterial composed of two single-ring SRRs in each unit cell. The left-handed behaviors in our designs originate from the SRR structure itself only and therefore, there are no metallic continuous wires involved compared to the conventional left-handed SRR metamaterials. The high-Tc superconductor samples studied here are highly under-doped YBa2Cu3O6.35 (YBCO6.35), nearly optimally doped monolayer HgBa2CuO4+ઠ (Hg1201), Zn- and Ni- doped Bi2Sr2CaCu2O8+ઠ (Bi2212) single crystals. We experimentally determine the optical constants of the samples and numerically extract the electronboson spectral functions from the optical scattering rate by either an analytic formula or a maximum entropy inversion technique. We find that the bosonic mode obtained from the optical data is consistent with a peak in the q-averaged susceptibility seen in the magnetic neutron scattering studies. The comparisons of the bosonic spectra between YBCO6.35 and YBCO6.50, monolayer Hg1201 and trilayer Hg1223 (HgBa2Ca2Cu3O8+ઠ), Zn-doped and Ni-doped Bi2212 characterize the variation of the bosonic spectra with the hole concentration, Tc as well as the magnetic and nonmagnetic atom substitution. / Thesis / Doctor of Philosophy (PhD)