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Abstract
Structured electromagnetic (EM) waves have been explored in various frequency regimes to enhance the capacity of communication systems by multiplexing multiple co-propagating beams with mutually orthogonal spatial modal structures (i.e., mode-division multiplexing). Such structured EM waves include beams carrying orbital angular momentum (OAM). An area of increased recent interest is the use of terahertz (THz) beams for free-space communications, which tends to have: (a) larger bandwidth and lower beam divergence than millimeter-waves, and (b) lower interaction with matter conditions than optical waves. Here, we explore the multiplexing of THz OAM beams for high-capacity communications. Specifically, we experimentally demonstrate communication systems with two multiplexed THz OAM beams at a carrier frequency of 0.3 THz. We achieve a 60-Gbit/s quadrature-phase-shift-keying (QPSK) and a 24-Gbit/s 16 quadrature amplitude modulation (16-QAM) data transmission with bit-error rates below 3.8 × 10−3. In addition, to show the compatibility of different multiplexing approaches (e.g., polarization-, frequency-, and mode-division multiplexing), we demonstrate an 80-Gbit/s QPSK THz communication link by multiplexing 8 data channels at 2 polarizations, 2 frequencies, and 2 OAM modes.
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1. Introduction
Structured electromagnetic waves with spatially tailored amplitude and phasefronts have gained much interest partially due to their unique beam structures [1,2]. One type of structured wave is an optical vortex beam carrying orbital angular momentum (OAM) [1,3]. Typically, OAM beams can be described as follows: (a) the phasefront of a wave “twists” in a helical fashion as it propagates; (b) the number of 2${\boldsymbol \pi }$ phase shifts in the azimuthal direction defines the OAM “charge,” ${\boldsymbol l}$, forming a set of orthogonal modal values; and (c) the intensity has a ring shape with a central null [3–5]. OAM can be considered as a subset of the Laguerre Gaussian (LG) modal basis with two spatial modal indices (i.e., azimuthal (${\boldsymbol l}$) and radial (${\boldsymbol p}$)) [6]. As the fundamental mode in the LG modal basis, the Gaussian mode (${\boldsymbol l}$=0 and ${\boldsymbol p}$=0) has a Gaussian-shaped spatial intensity distribution and a planar phase front, which carries zero amount of OAM [6].
This orthogonality property of OAM beams is important for communications applications [6]. Indeed, multiple independent data-carrying beams each with a different OAM value can be multiplexed at a transmitter aperture, spatially co-propagate, and be demultiplexed at a receiver aperture with little inherent crosstalk [6–8]. This approach is known as mode-division-multiplexing (MDM) and is a subset of space-division-multiplexing [6]. This simultaneous transmission of multiple data streams can increase both the system data capacity and spectral efficiency (i.e., bits/sec/Hz), and it has been demonstrated in the optical domain for both free-space and fiber systems [6–8]. Although much work focused on optical beams [4–10], it was clear that beams across different types of electromagnetic and mechanical waves can be structured to carry OAM [11–18]. Indeed, the multiplexing of OAM beams was shown in these regimes, including microwaves, millimeter waves, and acoustic waves [11–15]. Although beam multiplexing is conceptually similar in different frequency regimes, the physical challenges can be quite different.
In terms of other frequency ranges, an area of increased interest is the use of terahertz (THz) beams to facilitate higher-capacity, free-space communication systems [19–29]. This application of THz beams is motivated partially by the following issues: (a) as compared to millimeter waves, THz has more usable spectrum for communications and has lower beam divergence for longer-distance transmission [29]; and (b) as compared to optical waves, THz generally has a lower interaction with matter and is less affected by deleterious conditions (e.g., atmospheric turbulence, rain, and fog) [22,30]. Therefore, there could be significant interest in utilizing multiplexing of OAM data beams in the THz domain.
One challenge of implementing OAM-based THz communications is the need for efficient generation of high-data-rate THz beams [21]. Recently, both electronics- and/or photonics-based approaches have been demonstrated for single-beam THz free-space communications [20–23,31]. Another challenge is producing a THz OAM data beam and multiplexing it with other OAM data beams. Although structured THz beams that carry OAM have been shown [16–18], there have been few reports on THz OAM beams that carry high-speed data, much less that are multiplexed together. A laudable goal would be to explore the multiplexing of data-carrying THz OAM beams, as well as show its compatibility with other multiplexing approaches [32–35].
In this article, we experimentally explore the multiplexing of multiple THz data-carrying OAM beams for high-capacity communications in the ∼0.3-THz frequency band. In our experiments, each data channel carried by a THz Gaussian beam is initially generated by a photonics-based approach, which mixes two lasers in a high-speed photodiode (PD). Each OAM beam is generated by propagating the THz Gaussian beam through a spiral phase plate (SPP), which imparts a helical phase front to the incoming beam. After propagation through a ∼0.3-m free-space link, the OAM beam is detected at the receiver using an inverse SPP that converts the desired OAM beam back to a Gaussian-like beam. After being captured by the receiver's antenna, the THz channel is down-converted to an intermediate frequency (IF) for data recovery. We first study a THz link with two multiplexed THz OAM beams (${\boldsymbol l} ={+} 1$ and ${\boldsymbol l} ={-} 2$ or ${\boldsymbol l} ={+} 1$ and ${\boldsymbol l} ={+} 3$) at the same polarization and 0.3-THz carrier frequency. We achieve a 60-Gbit/s quadrature-phase-shift-keying (QPSK) and a 24-Gbit/s 16 quadrature amplitude modulation (16-QAM) data transmission with bit-error rates (BER) below 3.8×10−3. Finally, to show the compatibility of THz-based OAM multiplexing with other multiplexing approaches (e.g., polarization and frequency), we demonstrate an 80-Gbit/s QPSK THz communication link by multiplexing 8 data channels (5-Gbaud QPSK per channel) on 2 polarizations (X and Y pol.), 2 frequencies (0.3 and 0.310 THz), and 2 OAM modes (${\boldsymbol l}$=+1 and ${\boldsymbol l}$=+3).
2. Concept and experimental setup for THz links utilizing multiplexing of OAM beams
In general, the data capacity and spectral efficiency of THz links could be increased through the multiplex and simultaneous transmission of multiple and independent data channels [20,21,29,36]. Traditional multiplexing methods include (a) frequency-division multiplexing (FDM), where each data channel is located at a different THz frequency, thereby increasing the data capacity by a factor of the number of transmitted channels [21,29,37], and (b) polarization-division multiplexing (PDM), which can double the data capacity by transmitting two independent data channels on two orthogonal polarizations of the THz carrier wave. Moreover, PDM also doubles the spectral efficiency since the two multiplexed channels occupy the same frequency [20,36]. Figure 1 shows a potential high-capacity THz free-space communication link where OAM multiplexing is utilized to increase the data capacity and spectral efficiency. In such a link, combining PDM, FDM, and OAM multiplexing, 2×M×N data channels (2 PDM × M FDM × N OAM-muxed) are transmitted coaxially and simultaneously between a single transmitter and receiver aperture pair. Compared to the case of transmitting a single beam carrying a single data channel, the data capacity could be increased by a factor of 2×M×N, and the spectral efficiency could be enhanced by a factor of 2×N. Here, we experimentally explore and demonstrate such a THz communication scheme in a laboratory environment through a 0.3-m free-space link using the ∼0.3-THz frequency band, a THz transmission window of recent interest partially due to low atmospheric losses [21,22].
Fig. 1. A scheme of high-capacity THz wireless communication links where OAM multiplexing is utilized to further increase the data capacity and spectral efficiency. By combining OAM multiplexing with polarization division multiplexing (PDM) and frequency division multiplexing (FDM), 2×M×N data channels (2 PDM × M FDM × N OAM-muxed) are transmitted simultaneously between a single transmitter and receiver aperture pair. Compared to the case of transmitting a single beam carrying a single data channel, the data capacity could be increased by a factor of 2×M×N, and the spectral efficiency could be enhanced by a factor of 2×N.
Figure 2(a) shows the conceptual diagram for generation, transmission, and detection of a THz data channel carried by a single OAM beam. At the transmitter (Tx), the data channel is firstly generated in the optical domain by modulating a continuous wave (CW) laser (Laser 1) and subsequently converted to the THz domain through photomixing with another frequency-offset CW laser (Laser 2) in a PD. The carrier frequency ${{\boldsymbol f}_{{\boldsymbol THz}}}$ of the generated THz data channel is determined by the frequency spacing ${\boldsymbol \varDelta f}$ between the two lasers (${{\boldsymbol f}_{{\boldsymbol THz}}} = {\boldsymbol \varDelta f}$) [22,28,34,38]. By changing the ${\boldsymbol \varDelta f}$, the carrier frequency of the THz beam could be flexibly and widely tuned [22]. We choose such a photonics-based approach in our scheme because (i) it enables a high-speed amplitude and phase modulation (e.g., QAM) with a high spectral efficiency [21–23], and (ii) the flexible tunning of the carrier frequency facilitates our explorations of the bandwidth performance of the system; (iii) Moreover, another unique feature of the photonics-based approach is its possibility to easily enable multi-frequency-carrier transmission by adding optical laser lines [20–22,37].
Fig. 2. A schematic overview of THz communication links using OAM multiplexing. (a) The generation, transmission, and detection of a data-carrying THz OAM beam in different frequency domains, including (i) data channel generation in the optical domain, (ii) OAM generation/detection, (de)multiplexing, and transmission in the THz domain, and (iii) data channel detection and recovery in the intermediate frequency (IF) domain. A THz data channel is generated by mixing two lasers (one data-modulated laser (Laser 1) and one continuous wave (CW) laser (Laser 2)) in a photodiode (PD) at the transmitter. The data-carrying THz OAM beam is generated by using a spiral phase plate (SPP). At the receiver, a corresponding conjugated SPP converts the incoming OAM beam back to a Gaussian-like beam that is captured by the receiver’s antenna, and a frequency downconverter is used to convert the THz data signal to an IF frequency for data recovery. LO: local oscillator. (b) The schematic diagram of a THz OAM-multiplexed communication link using two OAM beams each carrying an independent data channel. Two THz OAM beams with different OAM orders (${l_1}$ and ${l_2}$) are generated by SPPs, spatially multiplexed using a THz beam splitter (BS), and coaxially propagate simultaneously. (c) A schematic diagram of a THz link combining PDM, FDM, and OAM multiplexing. THz FDM channels are generated by mixing wavelength-division multiplexed (WDM) channels (two channels located on different wavelengths) with a CW laser. PDM is achieved by combining two beams with different polarizations using a THz polarization beam splitter (PBS). The approaches for the generation, multiplexing, and detection of OAM beams are the same as those shown in (b).
After the photomixing, the generated data-carrying THz Gaussian beam (${\boldsymbol l} = 0$) is transmitted to free space using an antenna. A THz-OAM beam with a specific OAM order (${\boldsymbol l} = {{\boldsymbol l}_1}$) is generated by propagating the THz Gaussian beam through a specifical SPP, which imparts the correct spatial helical phasefront to transform the incoming Gaussian beam to an OAM beam of charge ${\boldsymbol l}$ at a prescribed frequency, ${{\boldsymbol f}_{{\boldsymbol SPP}}}$ [4,17]. The SPP is defined by its thickness, as shown in Eq. (1), which varies azimuthally according to [13,18]
Based on this concept of generation, transmission, and detection for a single THz OAM data channel, we propose a system-type diagram for a THz OAM-multiplexed communication link using two OAM beams, as shown in Fig. 2(b). At the Tx, two THz emitters generate and emit two THz Gaussian beams with each beam carrying an independent data channel (Ch1 or Ch2) at the same THz carrier frequency ${{\boldsymbol f}_{{\boldsymbol THz}}} = 0.3$ THz. Specifically, we use a PIN-PD-based THz emitter with an integrated silicon lens to generate each THz channel on a single linear polarization [39,40]. Two THz OAM beams with different OAM orders (${{\boldsymbol l}_1}$ and ${{\boldsymbol l}_2}$) are generated by SPPs with the appropriate designs, and then spatially multiplexed using a THz beamsplitter (BS), and coaxially propagate together towards the Rx. Before reaching the Rx antennas, the received OAM beams are split into two copies, where each copy is mode-wise demultiplexed and converted into a Gaussian-like beam by an SPP with a design inverse to that of the generating SPP. In our experiment, only one antenna and one down-converter are used so that the multiplexed THz OAM data channels are handled one at a time, each after being treated by its corresponding inverse SPP. Down-conversion and DSP processing complete the data recovery. The detailed experimental setup, devices’ information, and DSP procedures are provided in Supplement 1 (see Section 1 and Fig. S1(a) for more details).
Additionally, more data channels could be simultaneously transmitted by combining PDM, FDM, and OAM multiplexing in a THz link, as shown in Fig. 2(c). At the Tx, THz FDM channels located at the spectral vicinity of 0.3 THz are firstly generated by mixing optical wavelength-division multiplexed (WDM) data channels with a CW laser in the PIN-PD-based THz emitter. Since the frequency spacing between each WDM channel and the CW laser is different, each WDM channel is independently converted to a different THz carrier frequency [22,33]. Subsequently, PDM is achieved by combining two FDM-modulated THz beams with different linear polarizations using two THz polarization beam splitters (PBS). After FDM and PDM, we use two SPPs designed for 0.3 THz to transform the two multiple frequencies, doubly polarized outputs to OAM beams. Finally, OAM multiplexing is again performed by a THz BS. At the Rx, the received OAM beams are mode-demultiplexed using conjugated SPPs and each converted Gaussian-like beam is polarization demultiplexed using a PBS. Following down-conversion to the IF domain, the FDM channels are separated by digital filtering using DSP. With only two available THz emitters, OAM multiplexing is achieved by power splitting the frequency- and polarization-multiplexed channels and decorrelating them for the two OAM modes in our experiments (see Section 1 and Fig. S1(b) of Supplement 1 for more details). We note that, for the generation and detection of each OAM beam, FDM and PDM data channels share the same SPP. Although the fabricated SPP is polarization-independent and can spatially modulate the beams on both polarizations, it would introduce undesired (imperfect) helical OAM phase front when the carrier frequencies are different from the SPPs’ designed frequency (${{\boldsymbol f}_{{\boldsymbol THz}}} \ne {{\boldsymbol f}_{{\boldsymbol SPP}}}$) according to Eq. (1). Such frequency-sensitive spatial modulations of SPPs can probably limit the bandwidth of the system, which will be discussed in the following sections.
3. Performance of THz OAM beams’ generation and detection
To verify the characteristics of the generated OAM beams, we measure the normalized beam intensity profiles and interferograms for a Gaussian beam (${\boldsymbol l}$=0) and OAM beams with ${\boldsymbol l}$=+1, -2, and +3, as shown in Figs. 3(a) and 3(b). To capture the profiles, the Rx (without SPPs) is attached to a 2-dimensional (2-D) translation stage with a scanning resolution of 0.25 cm, and the output IF power at each scanning location is recorded by an electrical spectrum analyzer. Ring-shaped spatial power distributions are observed in the measured normalized intensity profiles for all ${\boldsymbol l}$≠0 beams. Compared to the simulation results, the experimentally generated OAM beams have distorted beam profiles and patterns. We believe the experimental degradation could be due to the following: (i) the emitted beam from the PIN-PD-based THz emitter is not a “pure” Gaussian beam (i.e., not a single Gaussian mode) such that it is not converted to a “pure” OAM beam with a perfect ring-shaped intensity profile [39], and (ii) due to the fabrication errors of the SPPs, the SPPs may not induce a perfect helical phase change on the input beam, thereby reducing the purity of the output OAM beams [13]. To increase the quality of generated OAM beams, one may consider: (i) utilizing a THz emitter (e.g., with an antenna supporting a single Gaussian mode [18]) that could potentially provide a high-purity Gaussian beam as the input to the SPPs, and (ii) increasing the resolution for the fabricated SPPs. Interferograms are generated by interfering the generated OAM beams with a coaxial Gaussian beam using BSs [13]. The number of rotating arms and the rotating direction (clockwise or counterclockwise direction) shown in the interferograms correspond to the mode order of the relevant OAM beams and their signs. The simulated OAM beam intensity profiles and interferograms are also shown in Figs. 3(a) and 3(b). We find that the measured profiles and interferograms are matched with the simulation results.
Fig. 3. Characterization of generated OAM beams at 0.3 THz. Experimentally measured and simulated (a) normalized intensity profiles and (b) interferograms of the Gaussian and generated OAM beams. The interferograms are generated by interfering with the generated beams with a Gaussian beam. (c) Experimentally measured power distribution on different OAM components (OAM spectra) for the generated beams. The power values are measured by recording IF power when using different SPPs to receive the beams at the receiver. All power values are normalized to the received power without SPPs at both Tx and Rx.
To evaluate the modal purities of the generated OAM beams, we measure their OAM spectra (the power contents of different OAM modal components in the examined beam) [6]. This is accomplished by recording the received IF power at the output of different SPPs. As shown in Fig. 3(c), there are power leakages to other undesired modes, and the maximum power leaked to undesired modes is ∼10-dB lower than that of the desired mode, which is probably due to that the imperfect Gaussian beam emitted from the THz emitter is not being converted to a “pure” OAM beam through the SPP. Compared to the Gaussian beam (without SPPs at both Tx and Rx), we observe an increase in the Gaussian-to-OAM conversion power loss with the mode order of $|{\boldsymbol l} |$ (e.g., ∼7-dB loss for OAM ${\boldsymbol l}$=+3). This might be due to following reasons: (i) the generated beam through an SPP is a superposition of LG modes with the same azimuthal index ${\boldsymbol l}$ but a range of radial indices ${\boldsymbol p}$ [4,41], and (ii) the beams with a larger $|{\boldsymbol l} |$ have larger divergence and might experience more severe truncation by the limited-size receiver aperture [42], also contributing to stronger power coupling to other ${\boldsymbol p}$ modes and larger power loss [43]. We also simulate such mode conversion power loss and find that the simulated and measured results follow a similar trend for different values of $|{\boldsymbol l} |$ (see Sections 2 and Fig. S2 of Supplement 1 for more details)
4. Data transmission performance of the THz link using two multiplexed OAM beams
With the imperfect generation of the OAM beams (power leakages to other undesired modes), there would be modal crosstalk when two OAM channels are multiplexed. We measure the modal crosstalk between two multiplexed OAM channels (${\boldsymbol l}$=+1 and ${\boldsymbol l}$=+3), where the OAM channel ${\boldsymbol l}$=+1 is generated by THz Emitter 1 and the OAM channel ${\boldsymbol l}$=+3 is generated by THz Emitter 2. In our experiment, we measure the crosstalk by transmitting different OAM beams (${\boldsymbol l} ={+} 1$ or ${\boldsymbol l} ={+} 3$) at the Tx and measuring received IF power when inverse SPPs (${\boldsymbol l} ={-} 1$ or ${\boldsymbol l} ={-} 3$) are used for receiving corresponding OAM modes at the Rx. As shown in the crosstalk matrix in Fig. 4(a), the four measured IF power values are normalized to the maximum value, which is detected when transmitting and receiving OAM ${\boldsymbol l} ={+} 1$. Compared to the maximum value, ∼2.8-dB less power is measured when transmitting and receiving OAM ${\boldsymbol l} ={+} 3$. This might be due to that, for larger OAM orders, there could be: (i) larger Gaussian-to-OAM and OAM-to-Gaussian conversion loss through SPPs [4,41], and (ii) more beam truncation by the limited-size receiver aperture [43], as we have discussed in Section 3. For the sake of simplification, we measure the normalized crosstalk at the frequency of 0.3 THz for each channel by transmitting a CW THz wave instead of a modulated signal. The CW THz waves emitted by two THz emitters are generated by mixing two CW lasers with the same input optical power. The results show a ∼-19.6-dB modal crosstalk between ${\boldsymbol l}$=+1 and ${\boldsymbol l}$=+3. Compared to the measured crosstalk (∼-23.6-dB) between ${\boldsymbol l}$=+1 and ${\boldsymbol l}$=-2 (see Section 3 and Fig. S3(a) of Supplement 1), the worse crosstalk between ${\boldsymbol l}$=+1 and =+3 might be due to their close mode spacing [44]. To show the optical-to-THz and THz-to-IF conversion efficiency, we also measured the received IF power under different total input optical power for these two THz transmitters (without SPPs at both Tx and Rx) (see Section 4 and Fig. S4 of Supplement 1 for more details).
Fig. 4. Experimental results for a THz OAM-multiplexed communication link using two OAM beams ($l$=+1 and $l$=+3). (a) Measured channel crosstalk between two multiplexed OAM channels ($l$=+1 and $l$=+3). The values shown in the crosstalk matrix are received IF power when transmitting and receiving different OAM modes. The measured power is normalized to the maximum value in the crosstalk matrix. Two cases are considered with different modulation formats and signal baud rates. Case1 is a 15-Gbaud QPSK signal per channel and Case2 is a 3-Gbaud 16-QAM signal per channel. The optical spectrum at the THz transmitter and electrical spectrum after down conversion at the receiver for (b) the 15-Gbaud QPSK signal and (c) the 3-Gbaud 16-QAM signal. The EVMs and constellation diagrams of the received (d) 15-Gbaud QPSK signal under a signal-to-noise ratio (SNR) of ∼13.5 dB and (e) 3-Gbaud 16-QAM signal under an SNR of ∼16.5 dB. The bit error rate (BER) performance of each data channel for the (f) 15-Gbaud QPSK signal and (g) 3-Gbaud 16-QAM signal.
We subsequently evaluate the data transmission performance in a THz OAM-multiplexed transmission link using two OAM beams. Two cases with different modulation formats and signal baud rates are considered. Case 1 is a 15-Gbaud QPSK signal per channel (total data rate of 60 Gbit/s = 2 channels×15 Gbaud/channel×2 bits/symbol) and Case 2 is a 3-Gbaud 16-QAM signal per channel (total data rate of 24 Gbit/s = 2 channels×3 Gbaud/channel×4 bits/symbol). Figures 4(b) and 4(c) show the optical spectra at the Tx, as well as the electrical spectra at the IF band after the down-conversion at the Rx for Case 1 and Case 2, respectively. For both cases, the frequency spacing (${\boldsymbol \varDelta f} = 0.3{\boldsymbol \; THz}$) between the optical data channel and the CW laser determines the carrier frequency (${{\boldsymbol f}_{{\boldsymbol THz}}} = {\boldsymbol \varDelta f}$) of the generated THz data channel, and the down-converted IF (${{\boldsymbol f}_{{\boldsymbol IF}}} = {{\boldsymbol f}_{{\boldsymbol THz}}} - {{\boldsymbol f}_{{\boldsymbol LO}}} = 15.6{\boldsymbol \; GHz}$) is related to the frequency (${{\boldsymbol f}_{{\boldsymbol LO}}}$) of the LO, which is a 12-time frequency multiplied electrical radio frequency source with a frequency of ${{\boldsymbol f}_{{\boldsymbol RF}}} = 23.7{\boldsymbol \; GHz}$.
The performance of each data channel is evaluated by calculating its error vector magnitudes (EVMs) [45] and BER at the Rx. Figures 4(d) and 4(e) show the EVM and data constellation diagrams of received QPSK and 16-QAM signals when multiplexing OAM ${\boldsymbol l}$=+1 and ${\boldsymbol l}$=+3. We can find larger EVMs and more blurred constellations induced by the crosstalk when the two OAM channels are multiplexed. The BER performance of each data channel is shown in Figs. 4(f) and 4(g) for Case 1 and Case 2, respectively. BERs are measured under different received signal-to-noise ratios (SNRs) of the data channels. In our experiment, the received SNR is defined as the ratio of the desired data signal power to the noise power level measured in the IF regime at the Rx. We set different SNR values by varying the input optical power of the THz Tx, which changes the power of the transmitted THz channels at the output of the Tx as well as the corresponding down-converted IF data signal detected by the Rx [46]. As shown in Figs. 4(f) and 4(g), for different signal modulation formats and baud rates, the BER performance for all channels could reach below the 7% hard decision-forward error correction (HD-FEC) limit [47]. In order to analyze the penalty induced by OAM generation/detection and multiplexing, we compared the BER performance of each data channel carried by (i) a single Gaussian beam, (ii) a single OAM beam without multiplexing, and (iii) such a beam with multiplexing. Specifically, compared to the single Gaussian channel, the case of the single OAM channel (without multiplexing and crosstalk) shows a similar BER performance. When multiplexing ${\boldsymbol l}$=+1 and ${\boldsymbol l}$=+3, the SNR penalty induced by the channel crosstalk is ∼1.5 dB for 15-Gbaud QPSK channels. Compared to the BER performance of the QPSK signals, 16-QAM data channels suffers a larger channel crosstalk-induced SNR penalty of up to ∼2 dB, as shown in Fig. 4(g). We also measure BER performance for another multiplexed OAM mode set (${\boldsymbol l}$=+1 and ${\boldsymbol l}$=-2) and find smaller crosstalk-induced SNR penalty (∼0.8 dB for Case 1 and ∼1.8 dB for Case 2) due to the lower crosstalk between two modes (see Section 4 and Fig. S4 of Supplement 1 for more details).
In our experiment, the baud rate of the 16 QAM signal (3 Gbaud) is smaller than the baud rate of the QPSK signal (15 Gbaud), due to the limited transmitted THz power and received SNR. In addition, we note that, although the transmitted THz power could be increased by increasing the total input optical power (see Section 4 and Fig. S4 of Supplement 1), the BER performance may become worse with a larger input optical power in the experiment, which could be due to the saturation of the THz emitter [24,48] and nonlinearities of the THz amplifier and down-converter [49,50] (see Section 5 and Fig. S5 of Supplement 1 for more details).
In addition, given that the SPPs are frequency-dependent devices for OAM generation and detection [4], we also investigate the bandwidth performance of the system (see Section 6 and Fig. S6 of Supplement 1 for more details). We experimentally vary the THz carrier frequency within the range of 0.27-0.33 THz by tuning the frequency spacing ${\boldsymbol \varDelta f}$ between the two lasers. To generate and detect OAM beams for different carrier frequencies, we use the same SPPs that are designed for 0.3 THz. BER performance is measured for 15-Gbaud QPSK channels carried by different OAM beams at a different carrier frequency. The measured BERs of all channels could be achieved below the 7% HD-FEC limit for different carrier frequencies in the range of 0.27-0.33 THz, which indicates that our system could cover a bandwidth of ∼60 GHz. We note that the tuning frequency range (0.27-0.33 THz) is mainly limited by the bandwidth of the THz amplifier and down converter in our experiment.
5. Demonstration of a THz link combining PDM, FDM, and OAM multiplexing
To show the compatibility of the different multiplexing approaches (PDM, FDM, and MDM) for THz communications, we combine 2 polarizations (X and Y pol.), 2 frequencies (0.3 and 0.310 THz), and 2 OAM modes (${\boldsymbol l} ={+} 1$ and ${\boldsymbol l} ={+} 3$) in an 8-channel-multiplexed THz link. Each data channel carries a 5-Gbaud QPSK signal. Figure 5(a) shows the normalized crosstalk between channels with different polarizations, frequencies, and OAM modes. The results indicate that the channel crosstalk between different polarizations and OAM modes is lower than -18 dB. In addition, there is ∼-30 dB crosstalk between different frequencies. Figure 5(b) shows the input optical spectrum of the WDM data channels and received electrical spectrum of the down-converted FDM channels. Figure 5(c) shows the EVMs and data constellations of the received channel on the Y pol., 0.3-THz carrier frequency, and OAM mode of ${\boldsymbol l}$=+3 with a received SNR of 12.5 dB. Compared to the case of transmitting a single OAM channel, the data constellation becomes more blurred, and EVMs increase from 27.9% to 33.7% with OAM multiplexing, PDM, and FDM, which is due to the crosstalk between different channels. To evaluate the influence of the PDM, FDM, and OAM multiplexing on the link performance, we measure BER as a function of SNR for the data channel on Y pol., 0.3-THz carrier frequency, and OAM mode of ${\boldsymbol l}$=+3, as shown in Fig. 5(d1). In a link transmitting a single beam carrying a single data channel (without crosstalk), the data channel carried by OAM ${\boldsymbol l}$=+3 has a performance similar to that carried by a Gaussian beam. When multiplexing two OAM beams, the crosstalk from the other OAM modes (${\boldsymbol l}$=+1) would induce a ∼1-dB SNR penalty at the FEC limit. In addition, we also observe an additional ∼0.5-dB and a negligible SNR penalty caused by the crosstalk between two polarizations (PDM) and two frequencies (FDM), respectively. Figure 5(d2) shows that the measured BERs for all 8-multiplexed channels could reach the 7% HD-FEC limit and a total data capacity of 80 Gbit/s (8 channels ×5 Gbaud/channel ×2 bits/symbol = 80 Gbit/s) is demonstrated.
Fig. 5. Experimental results for an 8-channel-multiplexed sub-THz communication link combining PDM (X and Y pol.), FDM (0.3 and 0.310 THz), and OAM multiplexing ($l$=+1 and $l$=+3). (a) Measured normalized crosstalk between channels on different polarizations, frequencies, and OAM modes. (b) The optical spectrum of the WDM data channels and CW laser at the THz transmitter and received electrical spectrum of the down-converted FDM channels at the IF band. (c) The EVMs and data constellations of the received data channel on Y pol., 0.3-THz carrier frequency, and OAM mode of $l$=+3 under an SNR of ∼12.5 dB. (d1) Measured BERs as a function of SNR for the data channel on Y pol., 0.3-THz carrier frequency, and OAM mode of $l$=+3. (d2) Measured BERs for all 8-multiplexed channels under different SNRs.
6. Discussion
Our experiment was conducted under laboratory conditions with a 0.3-m link distance. However, we believe that this approach of multiplexing THz OAM beams for communication capacity enhancement could potentially be extended to longer distances.
Various factors that could impact the link distance include the following:
- Atmospheric attenuation: One challenge is the atmospheric attenuation due to THz absorption by water vapor and oxygen molecules [51]. Certain frequencies could be significantly affected by attenuation and limit distances to a few hundred meters (e.g., >100 dB/km for >0.5 THz). In our experiment, waves at ∼0.3 THz have an attenuation of ∼5 dB/km, such that several kilometers should be possible if only the loss is considered [51]. For example, there have been recent demonstrations of 1-km links using a single Gaussian beam at ∼0.3 THz [52].
- Beam divergence: In general, beam divergence tends to require larger receiver apertures as link distance increases in order to capture sufficient signal power [44]. Moreover, since the divergence of an OAM beam grows with $\left| l \right|$ [42], higher-order OAM beams would tend to require even larger receiver apertures (see Section 7 and Fig. S7 of Supplement 1 for more details). For example, we simulate a link with a transmitted OAM beam ($\left| l \right|$=+3) at 0.3 THz with a diameter of 1 m. After propagation, the beam diameter grows to ∼1.0 m at 10 m, ∼1.1 m at 100 m, and ∼5.2 m at 1 km. With a 1-m-diameter receiver aperture, the power loss due to beam divergence would be 0.2 dB at 10 m, 0.6 dB at 100 m, 35.9 dB at 1 km. In order to achieve a <20-dB and <10-dB power loss caused by divergence, the receiver aperture diameter should be >1.7 m and >2.5 m at 1 km, respectively. To save size and weight for larger apertures, one may consider potential alternatives to SPPs for THz OAM generation/detection/multiplexing, such as using antenna-array structures with multiple smaller antenna elements that have been demonstrated in optical and millimeter-wave regimes [14,53].
- Atmospheric turbulence: Especially for optical beams, atmospheric turbulence can cause random refractive-index fluctuations and distort the OAM beam’s phasefront, thus resulting in dynamic modal power coupling to other spatial modes and inter-channel crosstalk [54]. Due to a lower interaction with matter in the ∼0.3-THz regime, however, it is quite possible that atmospheric turbulence is not a critical issue and does not cause significant modal power coupling [55,56].
- Misalignment: In general, for a single-Gaussian-beam THz link, it is important to align the transmitter and receiver apertures, and lateral displacements and angular errors could hinder the recovery of the data signal power [57]. In an OAM-multiplexed THz link, such misalignment is more problematic in that it could also induce inter-channel crosstalk [44]. This is because the receiver might fail to recover the full azimuthal phase signature, leading to modal power coupling among multiplexed OAM beams [44]. Such degradation effects of misalignments could be potentially mitigated by various beam tracking approaches [57].
Funding
Office of Naval Research (N00014-16-1-2813); Defense Security Cooperation Agency (4440646262); Defense University Research Instrumentation Program (FA9550-20-1-0152); Air Force Office of Scientific Research (sub-award of FA9453-20-2-0001); Airbus Institute for Engineering Research; Qualcomm Innovation Fellowship.
Acknowledgments
This work is supported by the Vannevar Bush Faculty Fellowship sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research (N00014-16-1-2813); Defense Security Cooperation Agency (DSCA 4440646262); Airbus Institute for Engineering Research; DURIP (FA9550-20-1-0152); AFOSR (sub-award of FA9453-20-2-0001). H.Z. and R.Z. acknowledge the support of a Qualcomm Innovation Fellowship.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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