# Off-Axis Diffractive Optics for Compact Terahertz Detection Setup
## 2 Design and Modeling
Next the side part of this lens, placed 60 mm from the center and with the diameter of 75 mm, has been cut. In this way, the original focal point is located 100 mm behind the lens plane and 22.5 mm up from its edge, lying outside of the  
Figure 2: Two concepts of designing off-axis lens—analytical equation (a) and re-propagation of ideal focal spot (b). Subimages (**a.1,a.2**) show the phase distributions of the whole lens designed with the analytical equation in the non-paraxial approach and its part taken for image reconstruction, respectively. The theoretical focal spot obtained from the cut-out lens can be seen in (**a.3**). The phase distribution obtained after back-propagation of the predefined focal spot is shown in the subfigure (**b.1**) (assuming also Gaussian shape illumination resulting from the divergence of the used radiation source). The image reconstructed using this method is presented in (**b.2**). The same focal plane can be seen in wider scale in the subimage (**b.3**). contour of the lens. As it can be seen, this lens focuses radiation in the desired position with a good efficiency, but the spot is relatively big and elongated. Second approach based on re-propagation of the optical field is shown in Figure 2b. The ideal focal spot (diffraction-limited intensity distribution with flat phase) is defined in the focal plane. The assumed background of the defined focal spot is not perfectly black, but in the very dark grey shade. It allows the preservation of the information about the phase distribution without affecting the result in any significant way. Then, light is propagated backward to the lens plane and a shifted circular aperture with 75 mm in diameter is cut from the obtained phase distribution (Figure 2(b.1)). It can be seen that after back-propagation at a distance of 100 mm such a defined phase distribution of light diverges only to a certain diameter. This diameter is insufficient to properly describe off-axis structure with the described above geometrical parameters. As a result, the majority of the lens area is relatively flat and only its top part is active and works as intended. Nevertheless, the focal spot with dimensions smaller than in the first case (using analytical equation) is obtained (Figure 2(b.2)). However, its intensity is much lower due to the fact that most of the energy is not redirected and forms an unwanted bright region in the middle of the structure. This non-diffracted zeroth order can be seen at the bottom of intensity distribution shown in the Figure 2(b.3)). The third approach is a combination of previous two cases. The light is propagated back and forth from the lens plane to the focal plane in an iterative algorithm (similar to Gerchberg-Saxton [19] or ping pong [20] algorithms). In the lens plane, the calculated amplitude is overwritten with the amplitude of the incident plane wave, while the amplitude of the ideal focal spot is defined in the focal plane. The phase distribution obtained in the lens plane defines the optimized off-axis lens. The algorithm converges fast and in just a few iterations the output light field distribution matches with the desired one well. The phase distributions in the lens plane and the intensity distributions in the focal plane for first three iterations are shown in Figure 3.  
In the first step, the light is focused by the lens created according to the analytical equation as in the first method. Then the amplitude distribution is replaced by ideal point distribution as in the second method. The amplitude was modified but the phase distribution was maintained as calculated after propagation. Next the light field was propagated back to the lens plane. The new lens is illuminated once more with initial plane wave distribution and the second iteration of algorithm begins. As it can be seen, the second focal spot is already significantly smaller than the first one, but still noticeably elongated.