Introduction
The rapid increasing demand for data traffic coming from the Internet of Things (IOT), cloud services, online game, video and business etc., is driving the modern optical communication systems, including the short-reach optical interconnect systems, to increase the transmission data rate and capacity timely [1]. In general, there are technologically numerous methods to meet the bandwidth and density requirements of short-reach datacenter optical interconnect. Under the consideration of the most important concerns of low cost and high integration on the short reach optical interconnection systems, the optical spatial division multiplexing (SDM), which is regarded as the last unexplored physical dimension to improve the capacity of optical communication [2–4], has been studied recently. And the SDM-based architecture could provide best cost-performance tradeoff depend on the network load and data center (DC) size [5].
SDM-based technologies are involved the use of fiber bundle with multiple parallel optical fibers together, coupled or uncoupled multi-core fiber (MCF), and few-mode or multi-mode fiber (FMF/MMF). The later one is also categorized as the mode division multiplexing (MDM) technology because the multiple orthogonal fiber modes are used as the individual channels to transmit optical signal. MDM technique has been demonstrated in short-reach optical interconnects by means of mode-group (MG) multiplexing [6,7], linearly polarized modes (LPMs) multiplexing [8,9], orbital angular momentum (OAM) multiplexing [10–12], and vector modes (VMs) multiplexing [13–16]. In general, VMs are the eigenmodes supported by the optical fiber with spatially inhommogeous states of polarization (SOP). As one kind of VMs, the cylindrical vector beams (CVBs), whose SOP is cylindrically symmetric, has been studied in various research fields. But, the data transmission based on VM over optical fiber has not been demonstrated widely so far. Recently, 4 × 10 Gb/s CVB-based (the order of±2) multiplexing transmission with the on-off keying (OOK) signal over 5-km link FMF has been demonstrated [17]. Researchers also use compact, integrated optics to realize the 2 × 20 Gb/s eigenmode multiplexing communication in 2-km circular optical fiber [18]. However, most of these newly employed MDM transmissions are based on the coherent detection which is not the best choice for the short-reach optical interconnects.
In this paper, we review the demonstrations of VM-based MDM (VMDM in briefly) transmission over free-space optical link and 4-mode FMF with the aim to improve the data rate and transmission capacity. The beam quality of VM generated using q-plate (QP) as well as the induced mode crosstalk have been analyzed. And the VMDM transmissions have been demonstrated by using the modulation of direct-detection (DD) orthogonal-frequency-division-multiplexing (OFDM) without multiple-input multiple-output (MIMO) digital signal processing (DSP).
In Section 2, we discuss the VM generation and characterization used in VMDM transmission systems. We introduce the QPs that used to realize the basic CVBs (TE and TM modes) generation and higher-order mode conversion based on conventional phase plates. In Section 3, we describe the VMDM transmission experiments in free-space optical link with DD-OFDM modulation. The demonstrations have been implemented for a two-mode 120 Gb/s quadrature phase shift keying (QPSK) transmission over 80 cm and a four-mode 95.16 Gb/s transmission over 20 cm respectively with direct detection. In Section 4, we show the transmission experiment performed on a four-mode FMF supporting four linearly polarized modes which correspond to seven fiber vector eigenmodes. A modal decomposition scheme based on polarization grating is used to analyze the mode inter-coupling and the variation of spatial and polarization distribution when the CVBs propagate in the few-mode fiber. By using the eigenmode of TM01 and TE01, the 95.16 Gb/s over 5 m four-mode FMF and 47.58 Gb/s over 10 0m four-mode FMF transmissions have been realized with the DD-OFDM technology. Note that there is no MIMO processing in these vector-mode-based demonstrations. Finally, the conclusions are made in the end of the paper.
Vector mode generation and characterization
Like the other MDM transmission systems, the mode converter used to realize the VM generation in the VMDM-DD-OFDM system is also one kind of the key components. Currently, many methods including fiber-based and liquid-crystal-based can be used to realize VM conversion. Here we describe the QPs which are passive liquid crystal optical devices used as the mode converter. QP can change the spatial distribution of the SOP of a homogenous polarized optical field. To perform the VMDM-DD-OFDM transmission, the properties of the used QP should be measured first. And then, the characterization of the generated VMs has been implemented subsequently.
Properties measurement of q-plates
In general, the optical axis orientation a of QP in the x-y plane can be assumed to be given as followswhere (r, j) stands for the points on the transverse plane. q is the topological charge and a0 a constant offset angle. Here, the QPs with q = 1/2 fabricated by Arcoptix company are used to do the demonstration. The Jones matrix of QP can be described as Js [19]
The output optical-field of a linearly polarized light after passing through the QP can be expressed as Eout = JsEin. Then the different polarization patterns can be obtained. Figure 1(a) shows the schematic diagram of the QPs characterization. The wavelength and power of the input continuous-wave (CW) light are about 1549.994 nm and power of 12.5 dBm respectively. Then the light is collimated by the lens (L), fed into the QP to realize the VM conversion after filtered by the linear polarizer (LP), and detected by (i) the spatial optical power meter (SOPM) and (ii) common OPM respectively. At the same time, the charge-coupled device (CCD) camera (iii) is used to capture the intensity profiles of generated VMs [14].
Fig.1 (a) Schematic setup for q-plate (QP) characterization by using (i) spatial optical power meter (SOPM), (ii) common OPM, and (iii) charged-coupled device (CCD) camera. L: lens; LP: linear polarizer. And the normalized power vs. applied Vb based on (b) SOPM and (c) OPM. ROR: regular operational region; POR: partial operational region and NOR: non-operational region [14] |
The measured power of QPs by SOPM (i) and OPM (ii) have been shown in Figs. 1(b) and 1(c), respectively. Obviously, the performances of QPs have a good agreement with each other. The QP insertion loss is around 5 dB. But, the optical power shows an abrupt variation when Vb>1.2 V. This meant that a large portion of input laser has not been converted to the VMs. The insets show the captured intensity profiles when Vb equaling to 0.1, 2.0 and 4.2 V respectively. It can be observed that the higher-order VMs can be realized under the regular operation region (ROR), while no VM can be generated within the non-operational region (NOR). As a result, a few VMs with lower pureness will be found when Vb biased in the partial operational region (POR).
Vector mode generation and characterization
TE01 and TM01 modes characterization
The characterization of VMs generated by the two QPs is shown as follows. With the use of Jones vector, the SOP of VMs can be expressed as [19]
where l =±1,±2,…, and g = 0, p/2. For example, Jones vector (cosjsinj)T and (- sinjcosj)T stand for the radially (TM01 mode) and azimuthally (TE01 mode) polarized optical fields, respectively. These two typical VMs can be generated by QPs with proper bias voltage. To characterize them, the intensity profiles captured by CCD camera are used to identify the polarization distribution with rotating the LP to a specific angle. The bias voltage Vb was set to 0 V based on the previous measurement. The characterization results of the generated TE01 and TM01 modes are shown in Fig. 2. A rotation of ~ 45° of the direction can be observed that would be induced by the constant offset a0 of QPs. In addition, the crosstalk between the two CVBs has been measured in terms of a mode isolation (MI) which is>20 dB.
Higher-order vector modes characterization
Besides the basic 1st-order eigenmodes of TE01 and TM01, there are other CVB modes, such as HE21e and HE21o modes, can be used to build the VMDM systems. Here, we perform the arbitrary VM conversion by using a few q-plate (QPs) and half-wave plates (HWPs).
The higher-order Poincaré sphere model based VM transformations have been shown in Fig. 3 [20]. q and f are the colatitude and azimuth angles over the sphere (q ∈ [0, p], f ∈ [0, 2p]). Then, an arbitrary SOP can be described as belowwhere and represent left and right-circular polarized components corresponding to north and south poles on the sphere, respectively. l and j are the order and azimuthal angle of Poincaré spheres. The point located at equators in Figs. 3(b), 3(c) and 3(d) stand for the SOPs with inhomogeneous linear polarization. Then these SOPs can be described as below
Thus, C (cosj sinj)T and D (sinj-cosj)T shown in Fig. 3(b) stand for the radial and azimuthal CVB modes, respectively. Except for C and D, the other points of the equator stand for the generalized CVB modes which are a linear superposition of them. With the assumption of a0 = 0, the general transformation of VMs can be described as below
The experimental used to validate CVB mode conversion is illustrated in Fig. 4. Here, the beam waist of input laser source (l = 1550 nm, power= 12.5 dBm) is collimated to ~2.1 mm before passing the linear polarizer.
Figure 5(A1) / (A2)−(E1) / (E2) show the intensity profiles at the different locations (A, B, C, D and E) labeled in Fig. 4. The TM01 /TE01 modes are first converted by QP1 following an HWP1 with fast axis at p/2, and subsequently transformed into HE21e/ HE21o modes. The inset 4(i) is used to show the inverse process of Eq. (6). Namely, HE21e/ HE21o modes will be converted to TM01 /TE01 modes by HWP2. Accordingly, inset 4(ii) shows that HE21e/ HE21o modes will be transformed to higher-order VMs if HWP2 was replaced with QP2. Figure 5(b1)/ (b2)−(e1)/ (e2) depict the SOPs of the four typical CVBs. Thus, the demonstration shows that the various VMs have been effectively converted by using the simple setup.
Figure 6 indicates the experimental results of modal isolation in between these VMs. It can be observed that a maximum MI of -10.3 dB between these mode channels induced by the QPs and other impact factors.
VMDM-DD-OFDM transmission in free-space optical link
In this section, we perform the high-speed VMDM-based free-space optical (FSO) transmission with high-order modulation formats.
Two-mode VMDM transmission
Fig.7 Experimental setup for VMDM-based optical transmission in FSO link. IM: intensity modulator; AWG: arbitrary waveform generator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SMF: single mode fiber; PBS: polarization beam splitter; TOF: tunable optical filter; VOA: variable optical attenuator; PD: photo-detector; OSC: oscilloscope [14] |
The demonstration of two-mode VMDM transmission is shown in Fig. 7 [14]. The wavelength, linewidth and power of the used external cavity laser (ECL) at the transmitter are 1549.994 nm,<100 kHz and 14.5 dBm respectively. An arbitrary waveform generator (AWG, Tektronix AWG 70002A) with a 25 Gs/s sampling rate is used to generate the electrical OFDM signal of Vpp ((peak-to-peak voltage) ~ 1 V. Then, an intensity modulator (IM, Photoline MX-LN-40) with the half-wave voltage and bias voltage of 3.4 and 1.9 V respectively is used to realize the optical OFDM modulation before amplified by the EDFA1. Other parameters used in the experiment are can be found in Ref. [14]. After VM division multiplexing by QP1 and transmission over FSO link, the optical OFDM signal is mode de-multiplexed by QP2 and PBS. Insets (i)−(iv) show the intensity profiles of the points A, B and C labeled in Fig. 7. Then, the transmitted signal is pre-amplified by another Erbium-doped fiber amplifier (EDFA) and then filtered by a tunable optical filter (TOF). At optical receiver, a PD (u2t XPDV2120R, 3-dB bandwidth of 50 GHz) is used to realize the optical-to-electrical (O/E) conversion adjusted by a variable optical attenuator (VOA). Then the real-time oscilloscope (OSC, LecroyLabMaster 10-36Zi) is used to sample the yield electrical signal which would be processed off-line. And the electrical spectrum of this signal shown in inset (v). Then the off-line digital signal processing (DSP) is used to further process the received signal. The total raw bit rate of this two-mode demonstrateion is 120.12 Gbit/s.
The measured bit-error-ratio (BER) performances are shown in Fig. 8(a). The power penalty between the single VM channel and “back to back” (B2B) transmission is found to be ~1.88 dB. And only 0.55 dB power penalty is induced when the two VMs are transmitted simultaneously. Figure 8(b) shows the constellations of the demodulated OFDM/32QAM signals corresponding to the cases shown in Fig. 8(a) with the received power of - 14 dBm.
Four-mode VMDM transmission
The demonstration of four-mode VMDM-DD-OFDM transmission over FSO link is shown in Fig. 9 [20]. The basic configuration of the experiment is the same with Fig. 7 except the parts of generation and demodulation of the higher-order VMs. At transmitter, the optical carrier with wavelength of 1550 nm is modulated by a QPSK-OFDM signal generated as the same way in Section 3.1. After amplified by EDFA, the output optical signal is split into two branches via an optical coupler (OC) and then converted to TE01 and TM01 modes through QP1. Afterwards, the optical signals are split by a non-polarizing 50:50 beam splitters (NPBS). One part is converted into HE21e/ HE21o with an HWP (b = p/2). Thereafter, four VMs have been combined by the other NPBS. According to the parameters in Ref. [20], the aggregate raw bit rate of this experiment is 95.16 Gb/s. The intensity profile of the multiplexed four VMs is shown in inset (a) of in Fig. 9.
Fig.9 Schematic of four-mode VMDM demonstration. Intensity profiles of (a) the 4 multiplexed VMs, (b) the demultiplexed HE21e and HE21o channels, (c) the un-demultiplexed TE01 and TM01 modes, (d) the demultiplexed VMs of TE01 and TM01 modes, and (e) the un-demultiplexed HE21e and HE21o modes [20] |
At receiver side, VM demultiplexing is realized via two steps after ~ 20 cm FSO transmission. The first step, HWP2 (b = p/2) is used (dotted-rectangle in Fig. 9), HE21e/ HE21o will be converted to the fundamental mode. Figure 9(b) shows the intensity profile of the demultiplexed VMs. But, TE01 and TM01 modes will be converted to higher-order VMs which cannot be guided by SMF. Figure 9(c) shows the intensity profile of the un-demultiplexed higher-order VMs. The second step, HWP2 is removed from the optical path, only TE01 and TM01 modes will be demodulated. Figures 9(d) and 9(e) show the intensity profiles of the case respectively. Then PBS is used to split two demodulated channels.
The transmission performances are shown in Fig. 10(a). When the two channels of TE01 and TM01, or HE21e/ HE21o are propagated, power penalties of 0.8 and 0.75 dB, or 1.1 and 1.25 dB will be induced under the forward error correction (FEC) threshold of 3.8 × 10-3. But, the power penalties will be 3.5, 3.35, 4.1 and 4.1 dB for TE01, TM01, HE21e/HE21o channels, respectively when they transmitted simultaneously.
Multichannel two-mode VMDM transmission
In this section, we shown the demonstration of VMDM in combination of WDM shown as in Fig. 11 [21]. At the transmitter, an optical frequency comb generator (OFCG) (OptoComb WTAS-02) is used to generate the desired multiple wavelengths with a wavelength interval of ~ 0.2 nm. A wavelength selective switch (WSS, Waveshaper 4000S) is used to shape the performance of the desired channels. The optical spectrum of the 20 WDM channels covering 4 nm range is shown in inset (ii).
Like the same procedure implemented in the previous experiment, after amplified by an EDFA, the optical carriers are launched into the IM and modulated by a QPSK-OFDM signal generated by the AWG. Then the optical beam is split into two parts with an OC and combined by a PBS to realize the TE01 (Ch1) and TM01 modes (Ch2) conversion via QP, respectively.
The mode crosstalk of two VMs at five different wavelengths (within the range from 1548 to 1552 nm) are shown in Fig. 12(a). It can be observed that the maximum MI is around -17 dB between 2 channels. Figure 12(b) shows the measured BER performances. Obviously, the multichannel error-free transmission has realized under the FEC threshold of 3.8 × 10-3.
DD-OFDM transmission in few-mode fiber link
In principle, the VMs are the eigenmode of the optical fiber and can be converted using the fiber-based devices and then propagated through optical fibers with good performance [22]. Thus, we perform the extension of VMDM-DD-OFDM transmission over the few-mode fiber link [23]. According to the property of VM, a non-separable coupling will be involved in between the spatial and polarization degrees of freedom. This coupling will induce the mode crosstalk between different VMs. To analyze the crosstalk, we first perform the mode performance characterization.
Crosstalk measurement during fiber propagation
Fig.13 (a) Experiment setup for CVB performance characterization. FMF: four-mode few-mode fiber; PC-FMF: polarization controller fabricated by four-mode fiber; PG: polarization grating; QWP: quarter-wave plate. (i) Intensity profile of converted VM by QP. (b) Power ratio between the two basic states with transmission over different distances. (c) (ii) and (iii) are the intensity profiles of the two orthogonal states after 5 m FMF propagation; (iv) and (v) the interference patterns corresponding to the (ii) and (iii), respectively. (d) Index profile of the used FMF |
Figure 13(a) shows the schematic of CVB mode performance characterization. As described in previous sections, the radially polarized VM TM01 (inset (i)) has been converted by QP and then launched into the 4-mode FMF link. Figure 13(d) shows the index profile of the used 4-mode FMF with a core diameter of 9.5 mm, a cladding diameter of 125 mm. Meanwhile, the index of the fiber core and cladding are 1.449 and 1.444 respectively. Thus, the VMs of HE11, TE01, TM01, HE21, HE12, EH11 and HE31 at 1550 nm wavelength can be guided by the FMF. The polarization grating (PG) is used to split the two basic states with the opposite order from the output beams. To illustrate the influence of the non-separable coupling, we take the characterization of TM01 mode as an example. According to Eq. (4), a pure TM01 mode can be generated if the IL and IR part have the same scale. The respective power in different cases of transmission have been measured as shown in Fig. 13(b). It can be observed that the pureness of the TM01 mode is not very high. Therefore, the scale of the two components of TM01 mode becomes further imbalanced after transmission over the FMF. Figures 13(c)-(ii) and 13(c)-(iii) show the intensity profiles of two parts after transmission over 5 m FMF. At last, we use a quarter-wave plate (QWP) to compete the interference with Gaussian beam. These interference patterns have been shown in Figs. 13(c)-(iv) and 13(c)-(v).
Tab.1 Modal isolation (dB) for CVBs transmission over the used FMF. |
| vector modes | 5 m FMF | 100 m FMF | ||
|---|---|---|---|---|
| TE01 | TM01 | TE01 | TM01 | |
| TE01 | 0 | 18.5 | 0 | 13.7 |
| TM01 | 16.8 | 0 | 12.5 | 0 |
The measured modal isolation between CVBs channels (TE01 and TM01) is shown in Table 1, in which the respective minimum MIs are about 16.8 dB after transmitting over 5 m FMF and 12.5 dB over 100 m FMF. Based on the MI results, the VMDM-DD-OFDM transmissions over FMF link with different distance and modulation formats have been performed respectively.
Two-mode VMDM transmission
We perform the VMDM-DD-OFDM transmission over FMF link shown in Fig. 14 [23]. The ECL (1550 nm, 16 dBm) at transmitter is launched into an intensity modulator to realize the QPSK-OFDM signal modulation as abovementioned. The process of signal generation and mode conversion are the same as the previous sections. The intensity profiles of the fundamental mode and CVBs are shown in insets (i) and (ii). And a PC-FMF is adopted to adjust the polarization and intensity pattern of the channels at the end of the FMF. For instance, inset (iii) shows the intensity pattern after transmission over 100 m FMF. Then, the output beams are converted to the fundamental mode via QP2 as shown in inset (iv). At last, the two orthogonal mode channels are separated by the PBS. Similarly, the optical signals are received by a photo-detector at receiver as usual, and the yielded electrical signal is then sampled via real-time OSC and the off-line DSP is used to recovery the transmitted information.
Figure 15 shows the measured BER performance for the VMDM transmission over FMF. For 16QAM-OFDM signal transmission, it can be observed that there are 1.7, 1.9 dB power penalties between B2B and 5 m FMF respectively under the FEC threshold of 3.8 × 10-3. However, for QPSK transmission, only 0.6 and 0.55 dB power penalties are observed after transmission over 100 m FMF. Meanwhile, the received power is much lower than that of 16QAM transmission.
Conclusion
In conclusion, the vector-mode-based mode division multiplexing transmission systems over free-space optical link and few-mode fiber have been reviewed. We use the commercial QP as the VM converter to realize the generation of cylindrical vector beams and then implement the MDM transmission over short-reach optical link. By using the DD-OFDM technology, we achieved the high-speed VMDM transmission without the MIMO digital signal processing. Thus, both the FSO and FMF experimental transmission results show that the VM-based MDM technique has the potential in optical interconnects such as datacenter or high-performance computing.