1. Introduction

In recent years, exponentially increasing demand for transmission capacity is the driving force for research in high-capacity optical transmission systems. High-capacity systems have achieved capacities up to 100 Tb/s by employing time-, wavelength-, polarization-division multiplexing, and multilevel modulations [1–4]. However, transmission capacity is rapidly approaching its fundamental limit [5]. One of the key techniques in achieving ultra-high-capacity optical communications is known as space-division multiplexing (SDM), which employs the spatial modes of light as information carriers [6]. SDM has been showing promise in both free-space and fiber-based optical communications [7–10]. So far, there have been lots of works on SDM with orbital angular momentum (OAM) beams, Bessel beams, and linearly-polarized (LP) modes commonly used to describe fiber modes [11–13]. In principle, OAM beam is a helically phased beam comprising an azimuthal phase term exp(ilφ), possessing an OAM of lℏ per photon, where l is referred to topological charge and φ is the azimuthal angle [14,15]. Multiplexing employing OAM modes provides a potential alternative way of SDM to alleviate the emerging capacity crunch.

Spatial modes have been predominately used for the method of SDM where each spatial mode serves as an independent data channel [16–20]. However, spatial modes can also be used for spatial mode encoding/decoding where each spatial mode serves as a different data state. In 2004, Gibson et al. demonstrated the transfer of data information encoded as OAM modes of a light beam to enhance the security of data transmission [21]. They showed that the information encoded by OAM modes was resistant to eavesdropping in the sense that any attempt to sample the beam away from its axis would be subject to an angular restriction and a lateral offset, both of which result in inherent uncertainty in the measurement. After that, many works followed using spatial modes encoding/decoding for information transfer in free space to achieve long-distance, high speed data transmission [22–25]. In 2014, M. Krenn et al. demonstrated free space OAM modes encoding/decoding through 3 km of strong turbulence over the city of Vienna [26]. Besides, data encoding at 20 Gbit/s using OAM modes was reported by A. J. Willner et al. in 2015 [27]. Meanwhile, vector modes were also used to encode data for optical communication in free space [28]. In more recent experiment, spatial mode coding using Laguerre-Gaussian (LG) modes in 1.5 m gradient-index fiber (GIF) was reported [29]. However, many short haul optical communication systems (e.g. data centers) need km-scale fiber transmission. In this scenario, a laudable goal would be to encode information using spatial modes in optical fibers for km-scale data information transfer.

In this paper, we propose a simple method to transfer image using 4 spatial modes (LP₀₁, LP_11a, LP_11b and OAM_-1) and 2 OAM modes (OAM₊₁ and OAM_-1) encoding/decoding in km-scale FMF, respectively. We experimentally demonstrate 1.1 km FMF data transmission of three grayscale images. A zero bit-error rate (BER) is observed during the transfer of 3 grayscale images, which shows favorable fiber link communication performance using the spatial modes of fiber encoding/decoding. Moreover, we also experimentally demonstrate 10-km FMF image transmission using 4 modes encoding/decoding. The measured BER is 4.8828e-04.

2. Concept and principle of spatial modes encoding/decoding in FMF

Figure 1(a) illustrates the concept and principle of data encoding/decoding for image transfer using 4 modes (LP₀₁, LP_11a, LP_11b and OAM_-1) and 2 OAM modes in a FMF communication system. First of all, we extract the gray value (0-255) of each pixel from the grayscale image with 8 bits information, and then convert it to 4 quaternary numbers. Then, each quaternary number corresponds to a spatial mode in FMF (e.g. 0→LP₀₁, 1→LP_11a, 2→LP_11b and 3→OAM_-1). Note that for a two OAM modes encoding/decoding system, one pixel from the grayscale image will be converted to 8 binary numbers (e.g. 0→OAM₊₁ and 1→OAM_-1). When the quaternary number sequence is encoded, each quaternary number can find its corresponding phase pattern which is used to generate the desired mode from a Gaussian beam. The above spatial mode encoding/decoding scheme is similar with quadrature amplitude modulation (QAM). We can take 4 spatial modes encoding/decoding as 4-QAM. Moreover, the 2 OAM modes encoding/decoding scheme, which use only the phase distribution of the spatial modes, can be taken analogous to binary phase shift keying (BPSK).

 

Fig. 1 Concept and principle of spatial modes encoding/decoding for image transfer. (a) Grayscale images convert into quaternary numbers and binary numbers; (b) Principle of 4 spatial modes encoding/decoding in FMF

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Here, we take 4 spatial modes encoding/decoding as an example to illustrate the working principle, which is shown in Fig. 1(a). At the transmitter side, we first extract the gray value (0-255) of each pixel from the grayscale image, and then convert it to 4 quaternary numbers. When the quaternary number sequence is encoded, each quaternary number can find its corresponding phase pattern which is used to generate the desired mode from a Gaussian beam. After encoding, the quaternary number sequence is transferred to time-varying spatial mode sequence in free space and then coupled into FMF for transmission. At the receiver side, the mode sequence is recorded by a camera for analyses. The 4 transmitted spatial modes have different intensity distribution. Thus, by measuring the intensity distribution of different spatial modes, one can decode the data sequence. To distinguish different spatial modes conveniently, we set two cross lines (e. g. x-axis and y-axis) at the center of each recorded intensity profile. Then we can get the intensity distribution along each line. By counting the peaks of two intensity distribution lines, one can easily find out the recorded spatial mode. For LP₀₁, the two intensity distributions each has a single peak. For LP_11a, the x-axis intensity distribution has two peaks and the y-axis intensity distribution has no peaks. For LP_11b, the x-axis intensity distribution has no peaks and the y-axis intensity distribution has two peaks. For OAM_-1, the x-axis and y-axis two intensity distributions both have two peaks. Hence, it is possible to distinguish all 4 modes simply through the recorded output intensity distributions. At last, one can easily reconstruct the transmitted image with the received data sequence. For 2 OAM modes encoding/decoding scheme, we cannot distinguish between two OAM modes from their intensity distribution. Thus, we record the interferograms of the OAM modes with Gaussian mode to decode the mode sequence.

3. Experimental setup

The experimental setup is shown in Fig. 2. The light comes from the laser with a wavelength of 1550 nm and a linewidth of ~1 kHz, and passes through a polarization controller (PC) to adjust its polarization. Then the light is sent to a collimator to generate a Gaussian beam. A polarizer (Pol.) and a half-wave plate (HWP) are used to adjust the polarization of the input Gaussian beam along with the working direction of polarization-sensitive spatial-light modulator (SLM). SLM loads different phase patterns with grating to generate different spatial modes. After modulated by the SLM, the light is expanded by two lenses (L1 (f = 100 mm) and L2 (f = 200 mm)). Then the expanded light is focused by a 10X objective lens with a focal length f = 20 mm and coupled into the FMF.

 

Fig. 2 Experimental setup of spatial modes encoding/decoding for image transmission in 1.1-km FMF. Col.: collimator; Pol.: polarizer; HWP: half-wave plate; SLM: spatial light modulator; L1: f = 100 mm lens; L2: f = 100 mm lens; OL: Objective Lens; FMF-PC: few-mode fiber polarization controller.

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We use two inline few mode fiber polarization controllers (FMF-PCs) to adjust the output mode of FMF in agreement with the input mode. By appropriately adjusting the FMF-PCs to minimize the mode coupling, one can get the corresponding output OAM modes with high quality. Such phenomenon might be briefly explained as follows. In the experiments, we are able to control mode coupling in the FMF by using FMF-PCs. The use of FMF-PCs is somehow equivalent to mitigating mode coupling using multiple-input-multiple-output (MIMO) digital signal processing (DSP). One can change the transmission matrix of the FMF until it is approximately diagonal by adjusting the FMF-PC. A diagonal transmission matrix means little mode coupling. Here, we measure the mode crosstalk between the transmitted modes in a traditional way. We use “inverse mask” to convert the transmitted modes into Gaussian-like beams, and couple them into a single mode fiber (SMF) to detect the power. The measured fiber modes transmission matrix for 4 spatial modes encoding/decoding case is shown in Fig. 3. Seen from the matrix, we can found that the crosstalk between LP₁₁ and OAM_-1 is about −4 dB, which is because OAM modes are not orthogonal to LP modes. Thus, we cannot decode the 4 modes by using the “inverse mask”. In our experiment, we distinguish the 4 modes (LP₀₁, OAM_-1, LP_11a, and LP_11b) from their intensity distribution, as shown in Fig. 1(b). To distinguish different spatial modes conveniently, we set two cross lines (x-axis and y-axis) at the center of each recorded intensity profile. By counting the peaks of two intensity distribution lines, one can easily find out the recorded spatial mode. Hence, it is possible to distinguish all 4 modes simply through the recorded output intensity distributions. Moreover, for 2 OAM modes encoding/decoding, the measured crosstalk between the 2 OAM modes is about −16.5 dB.

 

Fig. 3 Measured fiber modes transmission matrix for 4 spatial modes encoding/decoding case.

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After 1.1-km FMF transmission, the light is collimated by another 10X objective lens. The total coupling and transmission loss is estimated to be around 2.75 dB. Then the light passes through L2 and L1, and is reflected by a mirror. For 4 spatial modes encoding/decoding, we only need to use a HAMAMATSU InGaAs camera to record the intensity distribution of the output light beam. For 2 OAM modes encoding/decoding, it is impossible to distinguish the 2 modes with only the intensity distribution. Due to the difference phase distribution of the 2 OAM modes, we can distinguish between 2 OAM modes with the interferograms. Thus, a reference Gaussian beam is required to interfere with the output OAM beam to get the interferograms. So, we use an optical coupler to divide the light into two parts. One is sent into the system to generate spatial modes, the other is used as the reference Gaussian beam as shown in the dashed box in Fig. 2. The camera we used in the experiments has a resolution of 320x256 pixels. For the 4 spatial modes encoding/decoding case, we use two cross lines in the recorded image, which contains 576 (320 + 256) pixels. For the 2 OAM modes encoding/decoding case, we use two parallel lines in the recorded image, which contains 512 (256 + 256) pixels. The bit error rate (BER) is measured by counting all the received data sequence, and comparing with the transmitted data sequence. When the received data is the same with the transmitted data, the BER is zero. The similarity of the transmitted and received images is also quantified by the BER. When the BER is zero, the transmitted and received images are the same.

To encode data information with spatial modes for image transmission, we need to extract the gray value of each pixel from the grayscale image, and then convert it to symbol sequence. Each symbol in the symbol sequence is corresponding to its specific phase pattern for generating specific spatial mode. When the symbol sequence changes over time, the phase pattern loaded onto SLM keeps switching and transforms the symbol sequence into the spatial modes sequence. After km-scale FMF transmission, the spatial mode sequence is recorded by a camera. Then, the transmitted spatial mode sequence is decoded to symbol sequence. At last, we reconstruct the transmitted image with the decoded symbol sequence.

4. Fiber characterization

The employed 1.1-km FMF in the experiment is a conventional circular core optical fiber with a step index profile, which is shown in Fig. 4. The radii of the fiber core and cladding are r_core = 6.35 $\text{μm}$ and r_cladding = 62.5$\text{μm}$, respectively. The relative refractive index difference ($\text{Δ}=(n_1-n_2)/n_2$) between the fiber core ($n_1$) and cladding ($n_2$) is $\text{Δ}$ = 0.377%. The normalized frequency V of the fiber is 3.23. The designed and fabricated FMF supports six eigenmodes in total ($H{E}_{11}^{even}$,$H{E}_{11}^{odd}$,$T{E}_{01}$,$T{M}_{01}$, $H{E}_{21}^{even}$, $H{E}_{21}^{odd}$). Those six eigenmodes are divided into two mode groups with relatively large effective refractive index difference (>2.3X10⁻³) between mode group 0 ($H{E}_{11}^{even}, H{E}_{11}^{odd}$) and mode group 1 ($T{E}_{01}, T{M}_{01}, H{E}_{21}^{even}, H{E}_{21}^{odd}$). One can get right OAM modes and LP modes through proper linear combinations of eigenmodes in the mode group 1. By appropriately adjusting the inline FMF-PC, one can get the corresponding output modes in good agreement with the input modes with high quality.

 

Fig. 4 (a) Cross-section view of the FMF. (b) Relative refractive index profile of the FMF. (c) Supported six eigenmodes in two mode groups of the FMF.

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5. Experimental results

Firstly, we demonstrate the image transmission using 4 spatial modes (LP₀₁, LP_11a, LP_11b and OAM_-1) in a 1.1-km FMF. We encode 3 grayscale images (64x64 pixels, 64x48 pixels and 64x26 pixels). Here, we take the 64x64 pixels Lena gray image as an example. We first extract the gray value (0-255) of each pixel from the image which has 8 bits information, and then convert it to 4 quaternary numbers. Hence, the 64 × 64 pixels Lena gray image can be converted to a quaternary number sequence with 16384 quaternary numbers. We map the quaternary number sequence to 4 spatial modes sequence by switching the corresponding phase pattern loaded onto the SLM. The experimental results are shown in Fig. 5.The first line of Fig. 5 shows the experimental results of LP₀₁ mode transmission. The simple grating phase pattern is used to generate LP₀₁ mode. From the detected pattern, we can find that the x-axis and y-axis intensity distributions both have only one peak. So the data is decoded as 0. The second line of Fig. 5 shows the experimental results of LP_11a mode transmission. From the detected intensity distributions, we notice that the x-axis intensity distribution has two peaks and y-axis no peak, which indicates the transmitted data of 1. The third line of Fig. 5 shows the experimental results of LP_11b mode transmission. We can see that the x-axis intensity distribution has no peak and y-axis two peaks, which indicates the transmitted data of 2. The last line of Fig. 5 shows the experimental results of OAM_-1 mode transmission. We can easily find that the x-axis and y-axis intensity distributions both have two peaks, which indicates the transmitted data of 3. From the recorded experimental results, the 4 spatial modes after 1.1-km FMF transmission can be clearly identified. Thus, we can realize long distance high performance image transmission.

 

Fig. 5 Experimental results for image transmission using 4 spatial modes (LP₀₁, LP_11a, LP_11b and OAM_-1) in 1.1-km FMF. From left side to right side, it depicts the transmitted data, phase patterns for mode generation, generated mode intensity profiles, detected mode intensity profiles, x/y intensity distribution of the detected mode, and the receiced data.

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The transmitted and received 3 grayscale images are shown in Fig. 6. Figures 6(a)-6(c) are transmitted images. The resolution of Figs. 6(a)-6(c) is 64X64 pixels, 64X48 pixels and 64X26 pixels, respectively. Figures 6(d)-6(f) are received images. One can clearly see that the received image exactly recovers the transmitted one, which confirms the successful image transmission using the 4 spatial modes encoding/decoding in FMF. Moreover, a zero BER is observed, which shows favorable performance of the image transmission link.

 

Fig. 6 The transmitted and received 3 grayscale images using 4 modes (LP₀₁, LP_11a, LP_11b and OAM_-1) encoding/decoding. (a)-(c) Transmitted images. (d)-(f) Received images. (a)(d) 64X64 pixels. (b)(e) 64X48 pixels. (c)(f) 64X26 pixels.

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Furthermore, we use two OAM modes (OAM₊₁ and OAM_-1) encoding/decoding in FMF to transmit image. The experimental results are shown in Fig. 7. Because the intensity distributions of OAM₊₁ and OAM_-1 are the same, as shown in Fig. 7(b), we cannot distinguish them using the previous method. One approach is to record the interferograms when an OAM beam and a Gaussian beam interfere with a small angle, which is shown in Fig. 7(c). By determining the direction of the fork interferograms, one can distinguish the two OAM modes. As shown in Figs. 7(d) and 7(e), we plot the intensity distributions along two lines (L1 and L2) in each of the interferograms. When comparing the intensity distributions along L1 and L2, one can find that L2 has more peaks than L1 with the input mode of OAM₊₁. On the other hand, L1 has more peaks than L2 with the input mode of OAM_-1. Thus, we can easily distinguish the two OAM modes. By using this method, we encode a 64x64 pixels Lena gray image with two OAM modes in FMF, as shown in Fig. 8(a). We first extract the gray value (0-255) of each pixel (8 bits) from the image, and then convert it to 8 binary numbers. Hence, the 64 × 64 pixels Lena gray image can be converted to a binary number sequence with 32768 binary numbers. We map the binary number sequence to two OAM modes sequence by switching the corresponding phase pattern loaded onto the SLM, as shown in Fig. 7(a). After 1.1-km FMF transmission, we record the fork interferograms and reconstruct the transmitted image. Figure 8(b) plots the received image. The BER performance is assessed showing zero error among all received binary numbers. The obtained results indicate successful implementation of OAM modes encoding/decoding in FMF with favorable transmission performance.

 

Fig. 7 Experimental results for image transmission using two OAM modes (OAM₊₁ and OAM_-1) in 1.1-km FMF. (a) Phase pattern for mode generation; (b) Intensity profiles of the transmitted modes. (c) Interferograms for the transmitted modes with Gaussian mode. (d) and (e) Intensity distribution in two line of the interferograms.

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Fig. 8 Experimental results for image transmission using two OAM modes (OAM₊₁ and OAM_-1) in 1.1-km FMF.

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6. Discussion

In our experiments, 1.1-km fiber is employed to realize spatial modes encoding/decoding, which could be used for the relatively short-reach optical communications (e.g. data centers). For several kilometres of propagation, random linear mode coupling might influence the communication performance of mode encoding/decoding. The mode coupling can be covered by using automatic polarization controller feedback–based correction techniques [9]. Polarization controller feedback–based correction techniques are commonly used in conventional polarization-division multiplexed systems. Moreover, we also measure the 4 modes encoding/decoding (LP₀₁, OAM_-1, LP_11a, and LP_11b) in a 10-km few-mode fiber. In the experiment, we transmitted an image “A”, which is shown in Fig. 9(a). The received image is depicted in Fig. 9(b). The calculated BER is 4.8828e-04.

 

Fig. 9 Experimental results of 4 modes encoding/decoding in 10-km FMF.

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In addition, all the spatial modes are at one polarization in our experiments. The presented encoding/decoding method could also be done in a single mode fiber using two polarizations, by using a polarization beam splitter (PBS) or polarization beam displacing prism (PBDP) to separate two polarizations. Moreover, it is challengeable and also of great importance to extend the proposed approach to a higher number of fiber modes for encoding/decoding. Remarkably, by using digital image processing technique in special fibers, which can support a large number of modes, one could potentially extend the number of the fiber modes used for data encoding/decoding. In recent years, many new fibers which can support tens of eigenmodes have been designed and fabricated, such as multimode fiber [30], supermode fiber [31], hollow-core high-index-ring fiber [32],and multi-core multi-ring fiber [33,34]. By using these special fibers, higher number fiber modes encoding/decoding might be achieved. Moreover, digital image processing technology with adaptive pattern recognition algorithm can also be used to detect a large number of transmitted modes by distinguishing different mode intensity profiles [26].

Remarkably, it is important to minimize the mode coupling among different modes for spatial modes encoding/decoding. In our experiments, two FMF-PCs are employed to make transmission channel matrix of the fiber to be diagonal and minimize the mode coupling. When the FMF-PCs are not aligned correctly, which means the transmission channel matrix is not diagonal and mode coupling exists, the transmitted images will be indiscernible. Figure 10 illustrates the experimental result, when the FMF-PCs are not aligned correctly. The calculated BER is 0.6874. Moreover, to avoid mode coupling, we can use specially designed optical fiber (e.g. elliptical-core few-mode fiber) [35,36], which can reduce the mode coupling between the transmitted modes. Thus, the FMF-PCs can be eliminated.

 

Fig. 10 Experimental results of 4 modes encoding/decoding when the polarization controllers were not aligned correctly.

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Moreover, the commonly used SLMs are slow to respond with the best switching rates of the order of 100 Hz. In our experiments, the data rate is 10 bit/s for 4 mode encoding/decoding and 5 bit/s for 2 OAM modes encoding/decoding. For high speed mode encoding/decoding, we can use SLMs combining with high speed optical switch. By using this technic, 20 Gbit/s modes encoding/decoding has been realized in free space communications [27].

7. Conclusion

In summary, we present simple methods for image transmission using 4 modes (LP₀₁, LP_11a, LP_11b and OAM_-1) and 2 modes (OAM₊₁ and OAM_-1) encoding/decoding in FMF, respectively. We experimentally demonstrate 1.1-km FMF image transmission using both 4 modes encoding/decoding and 2 modes encoding/decoding. A zero BER is observed during the information transfer of 3 grayscale images. The obtained results indicate successful implementation of optical fiber communication link based on spatial modes encoding/decoding with favorable transmission performance. Moreover, we also experimentally demonstrate 10-km FMF image transmission using 4 modes encoding/decoding.