# Temperature-Insensitive Imaging Properties of a Broadband Terahertz Nonlinear Quantum Cascade Laser
## 3 Results and Discussion  
Figure 3a-d show the THz beam patterns from our THz NL-QCL at temperatures ranging from 297 K to 160 K. To map the 2D far-field emission patterns of the devices, we used a set-up consisting of two motorized XY translation stages [26]. As shown in Figure 3a-d, the THz beam patterns at each temperature showed Gaussian-like shapes that are favorable for THz imaging applications. Figure 4a-d depict the line profiles extracted from Figure 3a-d along the horizontal broken lines corresponding to the fast axis. Figure 4e-h depict the line profiles extracted from Figure 3a-d along the vertical broken lines corresponding to the slow axis. From the horizontal and vertical profiles, the beam full-width at half-maximum (FWHM) values were 17.9 mm, 17.7 mm, 18.7 mm and 18.8 mm along the fast axis (Figure 4a-d, respectively), and similarly 21.9 mm, 22.4 mm, 22.9 mm and 23.5 mm along the slow axis (Figure 4e-h, respectively), for which the corresponding divergence angles were estimated to be 17.3\({}^{\circ}\), 17.1\({}^{\circ}\), 18.0\({}^{\circ}\) and 18.1\({}^{\circ}\) for the fast axis, and 21.0\({}^{\circ}\), 21.5\({}^{\circ}\), 22.0\({}^{\circ}\) and 22.5\({}^{\circ}\) for the slow axis, respectively. We found that both the output direction of the THz beam and the divergence angle were insensitive to the operating temperature. Figure 3: Far-field profiles from THz NL-QCL at: (**a**) 297 K, (**b**) 240 K, (**c**) 200 K and (**d**) 160 K.  
Figure 2: THz transmission imaging system. Figure 5a shows a photograph of a stainless-steel test object, whose thickness was 0.3 mm. As shown in Figure 5a, the test object had 0.5 mm-wide stripes. We obtained THz images of the test object with the THz NL-QCL (100 \(\times\) 180 pixels, 0.2 mm steps). Figure 5b-d show THz images of the test object obtained by the imaging system equipped with the THz NL-QCL, in which the QCL device was operated at 240 K, 200 K and 160 K (Figure 5b-d, respectively). We found that the THz images were well-resolved despite the changing operating temperature. For further investigation, we acquired line profiles of the terahertz intensity along the horizontal axis and vertical axis from Figure 5b-d. In a previous work, the results of the modulation depth of the test object (line pair pattern having 0.5 mm-wide stripes) were over 20%. According to the 20% modulation threshold criterion, the spatial resolution was better than 0.5 mm [26]. Therefore, we evaluated imaging quality using a profile of stripe of 0.5 mm. Figure 6 illustrates the method of extracting line profiles from the THz images. As shown in Figure 6, we highlighted two areas including 3 \(\times\) 21 pixels (\(X_{ij}\) and \(Y_{ij}\), \(i\) = 1, 2, \(3,j\) = 1, 2,..., 21). From the pixels, we could obtain three profiles corresponding to three groups of 1 \(\times\) 21 pixels along the horizontal direction (\(X_{1,1}\)-\(X_{2,21}\), \(X_{2,1}\)-\(X_{2,21}\) and \(X_{3,1}\)-\(X_{3,21}\)). Then, we obtained three profiles corresponding to three groups of 1 \(\times\) 21 pixels along the vertical direction (\(Y_{1,1}\)-\(Y_{2,21}\), \(Y_{2,1}\)-\(Y_{2,21}\) and \(Y_{3,1}\)-\(Y_{3,21}\)). From three profiles along the horizontal direction and vertical direction, we calculated the average line profile and standard deviation for the horizontal direction and vertical direction. Figure 7a-f shows line profiles of THz images for the horizontal direction and vertical direction obtained with the THz NL-QCL at 240 K, 200 K and 160 K, respectively. The insets show the profiles of the non-normalized intensity without error-bars: \(X_{2,1}\)-\(X_{2,21}\) and \(Y_{2,1}\)-\(Y_{2,21}\). These profiles were almost consistent with each other despite the changing operating temperature. This is attributable to the temperature-insensitivity of the imaging properties; that is, both the output direction and divergence angle of the beam were not influenced by the operating temperature.