2.6.5      Metamaterial prism illumination with Gaussian beam

We present an interesting application of Gaussians beam to the analysis of left handed materials (LHM), also called metamaterials. The example ..\Materials\Metamaterial/Prism/prism.pro introduces a triangular prism composed of LHM with the Drude dispersive model applied for both electric and magnetic material properties. More information about dispersive media models may be found in A brief description of basic examples for dispersive media analysis in QW-3D.

Fig. 2.6.5-1 Scenario of the prism.pro example.

Fig. 2.6.5-1presents the considered scenario. The prism is located in the open-air region. We have set one plane wave wall above the prism to illuminate it with the 2D Gaussian beam (see Fig. 2.6.5-2). The settings on Incident degrees imply that the beam propagates in the XY-plane (Theta= 90) along the –Y direction (Phi= -90) and its electric field is Z-polarised (Polarisation= 0) Under Beam 2D we see that the angle of variation for the beam is 90 degrees. This means that the beam has no phase shift along the Z-axis. We may therefore reduce the model to the 2D one (one layer in Z- direction with electric boundary conditions at the bottom and top).

Fig. 2.6.5-2 Gaussian beam parameters in the prism.pro example.

We may notice that the neck of the Gaussian beam is set at NeckY=700 mm, which is about 120 mm above the prism, whereas the illumination is exactly perpendicular to the upper face of the prism. When the prism is made of a classical right handed material (RHM), the beam is 45 degrees bent from the wedged face of the prism.

We adjust the dispersive model of the prism material to obtain the real part of the relative permittivity (permeability) close to ε_r’ = -1 (μ_r’ = -1) at the excitation frequency f = 10.6 GHz. Fig. 2.6.5-3presents those parameters, whereas the Fig. 2.6.5-4shows this Drude model around the frequency of our interest.

Fig. 2.6.5-3 Material parameters of the metamaterial in theprism.pro example.

Fig. 2.6.5-4 Complex permittivity (permeability) of the metamaterial in the prism.pro example.

Run the simulation and invoke the 2D/3D Fields Distribution window (using  button in 2D/3D Fields tab of QW-Simulator). Fig. 2.6.5-5shows the envelope of the Poynting vector (button in Envelopetab) in a decibel scale. For classical right handed materials, with positive e_r’, the beam would refract towards the left side of the scenario. Since e_r’ = -1 and illumination angle is 45 degrees, the beam refracts exactly at the right angle.

We observe another interesting phenomenon. The original neck of the illumination beam is above the prism. We may notice that the neck is reconstructed in the refracted beam, at the same distance from the prism edge. This phenomenon cannot be achieved with right handed materials and justifies current interest in the left handed ones.

Fig. 2.6.5-5 Envelope in decibel scale of the Poynting vector in the prism.pro example.