# Frequency Division Multiplexing of Terahertz Waves Realized by Diffractive Optical Elements
## 1 Introduction  
Recently, the rapid development of terahertz (THz) technologies is observed [1]. Unique features of the THz waves allowed them to find applications in many fields of science [2, 3], nondestructive testing [4, 5, 6, 7], medical diagnostics [8, 9, 10] as well as telecommunication [11, 12, 13, 14]. Although the precise technologies and bands reserved for future wireless communication systems are not yet known, it is commonly believed that they will utilize terahertz frequencies [15]. One of the crucial aspects of all modern telecommunication systems is the constant demand for increasing bandwidth. It can be met by systems, in which more than one communication link can be placed in a single communication medium (which is known as multiplexing). The multiplexing methods are generally based on the launching of many signals into a single channel and their subsequent separation at the detector's side. To successfully demultiplex independently propagating signals, one must separate them in some dimension or feature space. The simplest method is to distribute signals in the space, which is known as Space Division Multiplexing (SDM) [16]. In the case ofwireless data transmission, it is often implemented in the form of so-called MIMO systems (Multiple Input Multiple Output) [17]. Multiplexing techniques based on signal division in time, polarization, modal distribution, or orbital angular momentum have also been shown and implemented in many telecommunication systems [18; 19; 20]. However, probably, the most widespread and impactful multiplexing method is based on the separation of the wavelength of electromagnetic waves. In optical fiber communication systems, it is known as Wavelength Division Multiplexing (WDM), while, in wireless transmission, the more common name is Frequency Division Multiplexing (FDM) [21]. Recently, more and more multiplexing and demultiplexing solutions are also proposed for the THz band. The natural approach is to adapt solutions known from other telecommunication systems. Therefore, the most commonly considered multiplexing methods in the THz spectral range are based on the MIMO systems [22; 23; 24; 25]. However, the first THz multiplexing solutions based on frequency division [26; 27], polarization division [26], space division [28], or orbit angular momentum division [29] are also reported. In this paper, we present a novel method of frequency division multiplexing of the THz radiation, based on the combination of two different diffractive optical elements (DOEs). Designed structures separate spatially signals coming from a single data transmission channel with respect to the carrier frequency. DOEs are optical elements that introduce a defined change in the complex amplitude of the incident radiation to obtain the intended intensity distribution in the output plane [30]. A particular case is a phase kinoform that progressively changes the phase from 0 to 2\(\pi\) and can redirect the whole radiation into a single order of diffraction [31]. According to the theory, such phase coding allows for obtaining 100% diffraction efficiency of the structure. The idea presented in this article is to combine a diffraction grating with the diffractive converging lens into a single phase DOE coded in the form of kinoform. A diffraction grating illuminated by the monochromatic radiation redirects it into \(m\) diffraction orders, according to the well-known equation:  
\[m\lambda=d\sin\alpha_{m}, \tag{1}\]  
where \(\lambda\) is the design wavelength (DWL), \(m\) is considered diffraction order, \(d\) is grating constant, and \(\alpha_{m}\) is an angle between the 0 th (main optical axis) and \(m\)th order of diffraction. One can easily notice that the change of the wavelength \(\lambda\) (that is inversely proportional to frequency) introduces a change in the diffraction angle \(\alpha_{m}\) of all orders of diffraction except 0 th. It means that the radiation of longer wavelength (smaller frequency) will be redirected farther from the optical axis within the single diffraction order.