## 3 Results
### Experimental Considerations  
#### 3.3.1 Near Field vs. Far Field  
The electromagnetic field of an antenna is commonly described as evolving from the near field region, where the angular distribution of the field varies with distance from the antenna, to the far field region, where the angular distribution is distance-independent. The near-field region may be further divided into the reactive and radiative regions. The reactive near field region decays rapidly with distance from the antenna, and becomes negligible compared with the radiative component within one wavelength distance from  
Figure 4: Normalized angular beam profiles of the PIN diode emitter for frequencies between 100 GHz and 1 THz at 50 GHz intervals, measured at a distance of 60 mm from the emitter for: (**a**) H-plane orientation and (**b**) E-plane orientation. All profiles are normalised for ease of comparison.  
the antenna. Within the radiative near field region, the distances from an observation point to two arbitrary antenna elements will generally be different, so that the relative phase and amplitude of their contributions to the field will be different. As the observation point moves further away from the antenna, the relative differences in distances between antenna elements to the observation point will decrease, and so the contributions of separate antenna elements will become more equal. Hence, in the far field, the antenna appears as a point source, and the angular distribution of the emitted field becomes independent of the distance from the antenna. Therefore, it is necessary to ensure that antenna beam profiles are measured in the far field.  
The commonly used criterion for the distance from the antenna at which its radiation is considered to be far-field, \(L_{\text{far}}\), may be calculated from [42]:  
\[\text{For }D<\frac{\lambda}{2}\,\ L_{far}>2\lambda=\ \frac{2c}{f}, \tag{1}\]  
\[\text{For }D>\frac{\lambda}{2}\,\ L_{far}\ >\ \frac{2D^{2}}{\lambda}=\ \frac{2D^{2}f}{c}, \tag{2}\]  
where \(D\) is the emitter aperture and \(\lambda\) is the radiation wavelength. Equation (2) is sometimes referred to as the Fraunhofer distance. This is defined as the distance between a radiating point source and a receiving antenna of aperture \(D\) such that the spherical wavefront of the source varies by no more than \(\pi/8\) radians over the entire antenna aperture. These limits for the far field distance are somewhat arbitrary, and so it is preferable to measure the beam profiles at a distance greater than that suggested by Equations (1) and (2). Figure 5 shows this distance for frequencies between 100 GHz and 1 THz for radiation travelling through both air and silicon, as calculated from Equation (2).  
In the case of the PIN diode THz emitter, the aperture is the size of the bow-tie antenna, which is 1 mm. The emitter is mounted on a hyper-hemispherical Si lens having a diameter of 10 mm. The overall combined thickness of the silicon lens and InP chip is approximately 6.5 mm [32]. As the wavelength of the radiation is shorter in silicon (\(\lambda_{\text{Si}}=\lambda_{0}/n_{\text{Si}}\) where \(n_{\text{Si}}=3.42\) is the refractive index of silicon), the far field distance in silicon is longer. It can be seen from Figure 5 that at frequencies above 300 GHz, the near-field region extends beyond the silicon lens boundary. Figure 4a,b shows peak broadening and an increase in small features in both the E- and H- plane profiles beginning at 300 GHz to 400 GHz and continuing up to 1 THz. This could indicate that the near-field extending beyond the lens has a significant effect on the profile. As stated previously, all profile measurements shown in this paper were recorded at a distance of 60 mm from the antenna; thus, they are well within the far field region for all frequencies measured.  
Figure 5: The far field distance, as given by Equation (2), for frequencies between 100 GHz and 1 THz for radiation travelling through air and silicon.