PHASE MATCHING FOR DIFFERENCE FREQUENCY GENERATION USING NANOSTRUCTURED METAMATERIALS
The mid-IR frequency region is highly intriguing due to its transition response to gas molecules. To date, this region has provided numerous applications, such as gas detection, atmospheric monitoring, and environmental trace for toxic vapors. In general, mid-IR frequency sources are more complex to make compared to visible and near-IR sources. To generate mid-IR frequencies from visible or near-IR frequencies, difference frequency generation (DFG) of optical nonlinear frequency conversion is used. This can be done through a material with relatively high nonlinear properties, such as gallium arsenide (GaAs). GaAs is a crystal of semiconductor materials with a broad mid-IR transparency region. The further development of technology has made GaAs the optimal choice for mid-IR generation. However, one major drawback in using DFG is phase velocity mismatching between interacting waves, which results from optical frequency conversion. Phase-mismatch essentially degrades the conversion efficiency. The anisotropic properties of some nonlinear crystals can overcome the phase-mismatch using birefringent phase matching (BPM). Unfortunately, because GaAs is an isotropic crystal, its lack of anisotropic properties prevents the use of BPM with GaAs. Modifications to the GaAs crystal are thus required through the addition of another material, rendering the modified crystal anisotropic. If metallic nanowires of silver (Ag) are embedded in GaAs, the composite structure is characterized as a metamaterial with anisotropic properties. The structure is optically characterized by full wave simulation using the finite difference time domain (FDTD) method to compute the refractive indices from the scattering parameters (S-parameters) in order to investigate it for phase matching. The resultant phase-matched mid-IR frequencies are broad and tunable from 2.8 µm to 11 µm. The tuning is performed by varying the pump and the signal wavelength. A structure of GaAs with periodic arrays of longitudinal nanoholes is investigated for phase matching. The refractive indices of the structure are determined from the S-parameters using FDTD simulation. The longest wavelength achieved is 16.2229 μm and the shortest is 3.2961 μm. The results of the FDTD simulation are compared with results obtained from the effective medium theory, using the Maxwell Garnett model. The comparison shows excellent agreement.