# Frequency Division Multiplexing of Terahertz Waves Realized by Diffractive Optical Elements
## 3 Results
### Multiplexing with Frequency Division  
Measurements presented in the previous subsection have been supplemented with a simple parallel data transmission experiment. Results shown above prove that the THz radiation with different frequencies is focused and redirected at different angles by the designed structures. Therefore, they can be used to multiplex THz channels in the frequency division. To visualize such functionality, THz radiation with two different carrier frequencies has been coupled into a common optical path by a semitransparent mirror (beam splitter). Combined signals illuminated the designed multiplexing DOE, where the signals have been spatially separated. The photograph of the optical setup with the beam paths marked with red and blue lines is presented in Figure 8.  
Two independent signals with the frequencies of \(\
u_{1}=300\) GHz and \(\
u_{2}=330\) GHz have been modulated with the frequencies of \(\omega_{1}=6\) Hz and \(\omega_{2}=24\) Hz, respectively. In the common path (before DOE), two separate signals and their combination have been measured. Results are presented in Figure 9 in the form of time domain waveforms as well as the corresponding Fourier transforms.  
Blue and orange waveforms correspond to the \(\
u_{1}\) and \(\
u_{2}\) signals, respectively, and have been measured with only a single emitter turned on. The green waveform, on the other hand, has been observed with both transmitters operating. It can be seen that the broadband detector integrates both signals and the obtained waveform is a sum of both modulation frequencies. It can be observed even more clearly in the Fourier spectra of the recorded waveforms, where both modulation frequencies appear in the joined power spectral density (PSD) dependence. Higher modulation frequencies visible for the 300 GHz beam (with \(\omega_{1}=6\) Hz) are a numerical artifact connected with the finite length of the transformed time domain waveform resulting in the presence of higher harmonics of the original modulation frequency \(\omega_{1}\).  
Figure 8: The optical setup used for verification of the spatial separation of signals with frequencies of 300 GHz and 330 GHz. E1 and E2—emitters, C—collimator, FM—focusing mirror, M—flat mirror, BS—beam splitter, PM—parabolic mirror, DOE—designed structure, D1 and D2—detector positions.  
Analogous measurements have also been performed in the positions D1 and D2 marked in Figure 8. It is assumed that \(\
u_{1}\) frequency should be focused in the D1 position, while \(\
u_{2}\) in D2. Results are presented in Figure 10.  
In all charts, the blue, orange, and green lines denote, respectively, signals with the \(\
u_{1}\), \(\
u_{2}\), and both frequencies combined. It can be noticed that, in the D1 position, only the \(\omega_{1}\) modulation frequency is detected, while, in the D2 position, only the \(\omega_{2}\) modulation frequency is registered. In both cases, when only the opposing transmitter is turned on, no modulation can be observed in the time domain waveform. Corresponding Fourier transforms also prove it, as the corresponding power spectral distributions are flat. This experiment, although simple, shows that the designed structures can be successfully used for simultaneous data transmission of more than one signal within a common optical path. Multiplexing and demultiplexing of signals differing in the carrier frequency can be performed with the proposed DOEs.  
Figure 9: **(a)** Reference results of signals registered in the common path (before DOE). The intensity registered in time domain for frequencies of \(v_{1}=300\) GHz and \(v_{2}=330\) GHz with rectangular modulation of \(\omega_{1}=6\) Hz and \(\omega_{2}=24\) Hz measured in the single optical path before signals separation—both sources are on (green), only a 300 GHz source is on (blue) and only a 330 GHz source is on (orange); **(b)** the power spectral densities for modulated signal frequencies \(v_{1}\) and \(v_{2}\) obtained by Fourier Transform.