# Sub-Terahertz Computer Generated Hologram with Two Image Planes
## 3 Methods  
The set of simulation parameters was imposed mainly by the available apparatus and materials. The design wavelength (DWL) was set to 1760 \(\upmu\)m and was dictated by the accessible source and detector. The frequency multiplier from Virginia Diodes Inc. (at a working range of 140-220 GHz) was used as a source of radiation (the maximum of spectral power distribution fell at around 1760 \(\upmu\)m). Detection was carried out also with a Schottky diode from Virginia Diodes Inc. (with a working range of 140-220 GHz). The detector was attached to the set of motorized stages, allowing scanning in all three directions (a span of 0-15 cm). Furthermore, a relatively long wavelength was chosen to ensure a high quality manufacturing of the hologram structure (shown in Figure 4) and to assure low attenuation. Additionally, for this wavelength, the refractive index of polyamide 12 (PA12) was established (with a Teraview TPS Spectra 3000 spectrometer under conditions of low humidity, not exceeding 0.5%) as equal to 1.59 (while the absorption coefficient \(\alpha=1\,\mathrm{cm}^{-1}\)). From the optical point of view and accounting for the wide range of highly-absorptive materials for THz radiation,  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Setup** & **FWHM x/y (mm)** & \(z_{1}\) (mm) & \(z_{1}+z_{2}\) (mm) & \(M_{1}\) & \(M_{2}\) \\ \hline Setup A & 102/114 & 190 & 480 & 1.27 & 1.65 \\ Setup B & 93/96 & 140 & 270 & 0.95 & 0.93 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Incident beam parameters (full width at half maximum (FWHM)) for A and B setups. Reconstructed image parameters: distance from the hologram to a particular image and magnifications of the images formed.  
Figure 3: X and Y cross-sections of the measured illuminating beam in the case of Setup A.  
such a value of absorption coefficient is relatively low. PA12 is a material often used for 3D printers, which together with the high resolution of the 3D printer (compared to DWL), allowed printing the simulated hologram. The available 3D printer imposed a sampling of 39 \(\upmu\)m (we assumed a voxel size of 117 \(\upmu\)m to assure good quality of printing and the possibility to print structures with a thickness varying from 0 to almost 3 mm). Such a value was sufficient due to the millimeter-size antenna used during the experiment and was necessary only to create a proper file for manufacturing. In order to reduce the neighbor effect, to weaken the impact of boundaries in the simulations carried out, and to fit the designed image, the calculation matrix size was established to be 8192 px by 8192 px. It has to be noted that with the image sampling of 117 \(\upmu\)m and the real size of the hologram equal to 10 cm, its size in pixels was equal to 855 px by 855 px. All simulations were carried out using LightSword software (based on the modified convolution propagation method) in version 6.4.9. Structures were printed with the EOS P 396 printer. It is a selective laser sintering printer providing a layer thickness of 0.12 mm (for PA12) and a standard accuracy of \(\pm\)0.3% with a lower limit at \(\pm\)0.3 mm.  
The sizes of the images obtained (Figure 5) in comparison with the hologram size (Figure 4) were bigger. Here, it should be underlined that we can test whether reconstruction from a relatively small hologram (approximately 57 wavelengths) will provide enough information to obtain a reasonable quality image.  
Figure 5 illustrates the amplitude distributions of the designed objects. Then, the images obtained as a result of simulations, at first, with plane wave illumination assumed, are shown in the lower row of Figure 5. In all distributions, a hologram area is marked with a red square.  
Additionally, a set of simulations for a larger number of objects was carried out. We have demonstrated that using such simulation parameters, we can create a hologram consisting of 4 different simple objects.