The field of metamaterials is driven by fascinating and far-reaching theoretical visions,

such as perfect lenses, invisibility cloaking, and enhanced optical nonlinearities. However,

losses have become the major obstacle towards real world applications in the optical regime.

Reducing the losses of optical metamaterials becomes necessary and extremely important.

In this thesis, two approaches are taken to reduce the losses. One is to construct an

indefinite medium. Indefinite media are materials where not all the principal components of the permittivity and permeability tensors have the same sign. They do not need the resonances to achieve negative permittivity. So, the losses can be comparatively small. To obtain indefinite media, three-dimensional (3D) optical metallic nanowire media with different structures are designed. They are numerically demonstrated that they are homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. Negative group refraction and pseudo focusing are observed.

Another approach is to incorporate gain into metamaterial nanostructures. The nonlinearity

of gain is included by a generic four-level atomic model. A computational scheme

is presented, which allows for a self-consistent treatment of a dispersive metallic photonic

metamaterial coupled to a gain material incorporated into the nanostructure using the finite difference time-domain (FDTD) method. The loss compensations with gain are done for various structures, from 2D simplified models to 3D realistic structures. Results show the losses of optical metamaterials can be effectively compensated by gain. The effective gain coefficient of the combined system can be much larger than the bulk gain counterpart, due to the strong local-field enhancement.