Negative index materials are a subclass of metamaterials which are materials having properties that are not found in nature. Present day research regarding metamaterials indicates that they possess remarkable behavior. This thesis is focused on a metamaterial-based photonic directional coupler employing a negative index material (NIM) in one of its waveguides while the other waveguide consists of a positive index material (PIM). A NIM-PIM directional coupler (DC) exhibits optical feedback even without any actual traditional resonator structure. This feedback exists because of the NIM employed in one of the structure\u27s waveguides. The ability of a NIM-PIM DC to propagate light in the backward direction indicates the possible use of NIM-PIM DC for any optical component requiring optical feedback. We seek to study, for the first time, a laser based on a NIM-PIM DC. Coupled-mode equations and corresponding solutions have been devised for an active NIM-PIM DC in which optical gain is introduced. An analysis of the transmittivity and reflectivity for the case of a resonator-type optical amplifier has been carried out. Lasing behavior of an active NIM-PIM directional coupler has also been investigated for the first time. We do so using two approaches: the transmittivity and the transcendental eigenvalue equation which we derive for the first time. Throughout the thesis, a distributed feedback (DFB) resonator and standard PIM-PIM DC have been detailed for comparison. Our equations and solutions are general enough to consider a range of optical gain configurations. In particular, we study three important cases of NIM optical gain: 1) equal to PIM gain; 2) zero gain; 3) negative gain, i.e. loss. The results show that that it is possible to achieve lasing with a NIM-PIM DC similar to that of an a DFB laser if the same amount of gain is introduced in both of its waveguides. It is also possible for the device to lase in the case of gain in the PIM waveguide and no gain in the NIM waveguide. The more practical case involving loss in the NIM waveguide has also been investigated and found to naturally exhibit the much sought-after case of single mode lasing operation. Thus, this research lays the foundation for a new kind of single-mode laser
