1. Introduction

Miscellaneous physical dimensions of a light beam, such as time, polarization, frequency, amplitude and phase, have been fully exploited to increase transmission capacity. By using those physical dimensions, multiplexing techniques such as wavelength-division multiplexing (WDM), time-division multiplexing (TDM), and polarization-division multiplexing (PDM) and advanced modulation techniques such as m-ary phase-shift keying (m-PSK) and m-ary quadrature amplitude modulation (m-QAM) have achieved great success in the past decades [1–4]. However, the well-established techniques have almost reached their scalability limits, and it is highly desired to find additional dimensions to address the coming capacity crunch. Recently, space that is considered as the only known physical dimension left to exploit in optical transport has attracted much attention for the next multiplicative capacity growth for optical communication [5, 6]. Space based communication technique, also known as space-division multiplexing (SDM), can be realized through multiple-input multiple-output (MIMO) transmission, employing spatially orthogonal modes or spatial positions to increase the multiplexing channels. SDM is applicable for optical communications in both free space and guided waves. In fiber optical communications, few-mode fiber (FMF) or multi-mode fiber (MMF) and multi-core fiber (MCF) are known as two typical SDM strategies for achieving the high-capacity and high-energy-efficiency data transmission [7–9]. SDM technique is also used in silicon nanophotonic integrated devices to enhance the capacity of an optical interconnect link [10]. More recently, orbital angular momentum (OAM) beam, has also attracted great attention for its possible use in both free-space and fiber SDM communication systems [11–17].

OAM beam can be described in the spatial phase form of $\text{exp}(il\phi )$ ($l=0,\pm 1,\pm 2,\dots$), where $l$ is the topological charge number and $\phi$ refers to the azimuthal angle [18]. Coaxially propagating OAM beams with different $l$ states are intrinsically orthogonal and can be efficiently separated, making it possible to use OAM beam to increase the capacity of communication systems. Generally, there are two different approaches to employ OAM beams with different $l$ states in communications applications. The first one is to use OAM beams as carriers of different data streams, which has been widely employed in most of the recent works [11–13]. The second way, also called OAM encoding, employs N OAM states as N possible values of data symbols [19–23]. Using OAM beams as information carriers for SDM in communication systems have been seeing a lot of huge progress. Pbit/s scale capacity has been achieved by employing OAM SDM together with WDM [13]. Although the concept of OAM encoding is firstly introduced to OAM communication, its development is not very fast. One of the major limitations is that there is no fast switching device between different OAM states, which is necessary to achieve a high data rate. Fortunately, with the rapid development of optoelectronic devices technology, the limitation is likely to be overcome. New OAM modulation and generation techniques are continuously proposed [24–27], providing the possibility for realization of high speed OAM switching. By using integrated photonic circuits with thermal tuning, the rate of switching OAM modes has been reduced to about 20 us [28]. Moreover, nano-to-picosecond switching times are also possible by using carrier injection to tune the integrated photonic devices. Therefore, in the near future, tuning rate may not be a major limiting factor. In addition to improve the tuning speed, another approach to improve the capacity of an OAM encoding system is to increase the number of OAM states used for encoding. Although states of OAM beams are unlimited in theory, the available states may be limited by actual situations, such as generation of OAM beams with large topological charge numbers. Moreover, large-tuning-range, high-speed switching and detecting technology of OAM states are also relatively difficult to realize. Therefore, the number of available states used for encoding might be a main limitation of OAM encoding techniques in the future. In this scenario, a laudable goal would be to find a scalable way to facilitate the increase of capacity of OAM encoding system with a small number of OAM states in optical communications, especially in optical interconnects applications.

The key metric of optical interconnects should be transmission capacity density rather than transmission capacity itself, due to the implementation of interconnects is fundamentally limited by available space [29]. Therefore, increasing the space utilization efficiency of OAM based interconnects is also very important.

In this paper, we propose a high-base OAM encoding/decoding scheme for optical interconnects by employing multiple OAM arrays to encode information. Through optimizing the use of space dimension (spatially orthogonal modes and spatial positions), one can easily implement large-scale OAM encoding/decoding with less OAM beams [30]. Using OAM array with 4 spatial locations each with 5 or 6 possible OAM beams, we experimentally demonstrate 625-element and 1296-element high-base OAM array encoding/decoding link for optical interconnects. Both direct OAM detection and simultaneous multi-OAM demodulation method are used for decoding the OAM array. Moreover, the influence of atmospheric turbulence is also evaluated in the experiment.

2. Concept and principle

When using OAM states for symbol encoding, the amount of bit information carried by one symbol is determined by the number of OAM beams N used for encoding. The encoding efficiency can be improved ${\text{ Log}}_2\text{N}$ times compared to binary encoding. However, the number of practically available OAM beams might be limited as aforementioned. To facilitate the efficiency of OAM encoding with a small number of OAM states, an improvement encoding scheme is desired. An effective way to enhance the encoding efficiency is the combination of multiple communication dimensions, which can directly give rise to multiplicative growth of information capacity. The space dimension is a special degree of freedom that has two approaches to increase the transmission capacity, i.e. using spatially orthogonal modes and spatial positions. These two approaches can be also combined, allowing up to two orders of magnitude capacity increase. A typical example is the few-mode multicore fiber used in fiber-based SDM system [8]. In a similar way, OAM encoding can also be realized by making full use of the space dimension, i.e. using OAM array for information encoding. The concept and principle of the OAM array encoding/decoding for optical interconnects is shown in Fig. 1. Several OAM beams are placed in different spatial positions, forming an OAM beam array. By changing the values of OAM beams at different spatial positions, one can get different OAM array permutations (states). One OAM array state represents a symbol code, and the number of total states is Nⁿ, where N is the number of OAM beams used for encoding and n is the number of spatial locations of OAM array. As an example shown in Fig. 1, N is assumed to be 2 ($l=1,2$), and n is assumed to be 4 (position I, II, III, IV), and the number of total state is 2⁴ = 16. Compared to the use of one OAM state at a single spatial position as one symbol code, the number of base symbols of OAM array encoding is improved by $16/2=8$ times. The source shown in Fig. 1 is a light source array, which could be fiber array source, multicore fiber, or integrated photonic laser array. The modulator is used to encode incoming information onto OAM array states, i.e. generating different OAM array within different time slots. The light source array and modulator can also be integrated together by using photonic integration technology. After modulation, the signal sequence is transformed into OAM array sequence. For instance, four OAM array states of the sequence are depicted in Fig. 1. Finally, a demodulator is used to decode the OAM array sequence and recover the signal.

 

Fig. 1 Concept of OAM encoding/decoding with multiple OAM array states for optical interconnects. Several OAM beams are placed in different spatial positions, forming an OAM beam array. The data sequence is encoded to OAM array sequence. Each OAM array state represents a data symbol value.

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3. Experimental setup

OAM beams can be directly detected, which does not require optical demodulation owing to the fact that the radius of intensity rings of OAM beams are depended on the topological charge l. It has been shown that the radius of the primary intensity ring dependents on the topological charge, $r_l\propto {(l+1)}^{1/2}$ [31]. OAM beams could be received by direct detection through circular concentric photodetector (PD) arrays [32]. We first explore the performance of OAM array encoding/decoding with direct detection method.

Shown in Fig. 2(a) is the experimental setup for demonstration of OAM array encoding/decoding with direct detection scheme. The laser beam at 1550 nm is split into four paths (I, II, III, IV) relatively delayed with fibers, and coupled to free space by four collimators to generate collimated Gaussian beams (3-mm beam size). Four Gaussian beams with different horizontal and vertical optical axes (I and II are above III and IV, I and III are on the left of II and IV) are combined by three beam splitters to form a four-beam Gaussian beam array. The intensity profiles of the generated Gaussian beam array are depicted in Fig. 2(b). A spatial light modulator (SLM) is used as a signal modulator to encode information onto OAM arrays, i.e. generating OAM array sequence according to the incoming signal sequence. To generate OAM arrays, the phase mask loaded onto SLM with 1920$\times$1080 pixel resolution is divided into four parts with each part corresponding to an Gaussian beam of the input Gaussian beam array. As an example, a phase mask used to generate OAM $l_1=1,l_{\text{ II}}=5,l_{\text{III}}=9,l_{\text{IV}}=13$ is shown in Fig. 2(c), and the intensity profile of the generated OAM array is also illustrated on Fig. 2(c). In this experiment we chose OAM $l=1,5,9,13,17$ for encoding, so the number of total OAM array states is 5⁴ = 625, i.e. the number of symbol base is 625. For decoding, we use a camera as the detector to record intensity distributions and then recover the information from the collected images through a computer.

 

Fig. 2 (a) Experimental setup of OAM array encoding/decoding with direct detection method for optical interconnects. OC: optical coupler; PC: polarization controller; Col.: collimator; Pol.: polarizer; BS: beam splitter; SLM: spatial light modulator. (b) Intensity profiles during the generation of Gaussian beam array. (c) Phase mask loaded onto SLM for OAM array generation and intensity profile of generated OAM array. (d) Detected value of the input OAM array.

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4. Experimental results

4.1 OAM array encoding/decoding with direct detection method

First, we characterize the radii of different OAM beams. Four positions are fixed with the same topological charge $l$. The measured intensity profiles of OAM array with $l=1,5,9,13,17$ are shown in Fig. 3(a). One can clearly see that, the larger the topological charge $l$ is, the larger the radius r is. The radius value of each order OAM can be achieved from normalized intensities along x direction, as shown in Fig. 3(b). These values will be used as the judgment to distinguish different OAM states. It should be noted that OAM beams expand with the increase of propagation distance due to the diffraction effect. Therefore, for a specific propagation distance, one must select a reasonable interval (distance between adjacent OAM beams in an OAM array) that large enough to avoid beam overlap. Then we test the performance of the encoding/decoding system for optical interconnects by transmitting data signals through it. We randomly generate 100000-bit binary data and encode the binary data with 625 base symbol. After encoding/decoding transmission, all the data is well received without error symbol. Some typical intensity profiles of the OAM array states during the data transmission are displayed in Fig. 4.

 

Fig. 3 Intensity profiles of different OAM array states with $l_i=1, 5,9, 13, 17 (i=\text{I}, \text{II}, \text{III},\text{IV})$. The four positions are fixed with the same OAM. (b) Normalized intensities of OAM $l=1, 5,9, 13, 17$ along x direction.

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Fig. 4 Typical intensity profiles of different OAM array states for optical interconnects by OAM array encoding/decoding with direct detection method.

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4.2 OAM array encoding/decoding with simultaneous multi-OAM demodulation method

Using direct detection method, we have successfully realized OAM array encoding and decoding. However, the direct detection method may be limited in some situations. With increase of number of OAM beams and decrease of spacing of OAM orders, the distinguishing ability of direct detection method may become worse. Moreover, the direct detection method cannot be used to distinguish OAM beams with the same $\left|l\right|$ but opposite sign due to their identical beam size. Therefore, the direct detection method is suitable for small number and large spacing OAM array encoding/decoding. To increase the number of OAM beams used for OAM array encoding/decoding, OAM demodulation scheme could be employed.

We used the method proposed in our previous work [33], to realize to realize simultaneous multi-OAM demodulation with a complex phase mask. Two groups of six OAM beams (two groups: $l=\pm 9,\pm 10,\pm 11$ and $l=\pm 9,\pm 12,\pm 15$) are used in this experiment. The two groups of tests are to analyze the effect of different spacing of OAM order on the performance of the system. Additional SLM (SLM2) loaded with complex phase mask is used as the demodulator to realize simultaneous multi-OAM demodulation, as shown in Fig. 5. The encoding part is the same as the direct detection experiment. SLM1 is still used for OAM array generation. The CCD camera is also used as the detector. The receiving plane is still divided into four parts with each part further divided into six small areas. As an example of OAM array decoding process with simultaneous multi-OAM demodulation scheme, shown in Fig. 6 are the complex phase mask loaded onto the demodulation SLM and the intensity profiles of OAM array ($l_{\text{ I}}=11,l_{\text{II}}=9,l_{\text{III}}=11,l_{\text{IV}}=-11$) before and after demodulation. From Fig. 6, one can clearly see that four OAM beams of the OAM array can be successfully back converted to Gaussian-like beams and steered to the desired locations. From the recorded intensity profiles of OAM array demodulation, the value of each OAM in the OAM array can be easily distinguished by filtering out the central bright spot and discriminating its positionInitially, the demodulated position of each OAM in the OAM array should be determined, which will be used for discriminating the received OAM values. We then study the performance of the encoding/decoding system for optical interconnects by transmitting 10000 data symbols through the system. After decoding, the received symbols of both two groups of experiments ($l=\pm 9,\pm 10,\pm 11$ and $l=\pm 9,\pm 12,\pm 15$) are well recovered without seeing any error symbols. Some examples of the demodulated intensity profiles of OAM array states are depicted in Fig. 7, from which one can find that all the transmitted OAM arrays can be well back converted and received.

 

Fig. 5 Experimental setup for OAM array encoding/decoding with with simultaneous multi-OAM demodulation method. OC: optical coupler; PC: polarization controller; Col.: collimator; Pol.: polarizer; BS: beam splitter; SLM: spatial light modulator.

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Fig. 6 The complex phase mask array loaded onto the demodulation SLM and the intensity profiles of OAM array ($l_{\text{ I}}=11,l_{\text{II}}=9,l_{\text{III}}=11,l_{\text{IV}}=-11$) before and after demodulation

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Fig. 7 Typical demodulated intensity profiles of OAM array states for optical interconnects by OAM array encoding/decoding with simultaneous multi-OAM demodulation method. (a) Corresponding to the first group of six OAM beams with $l=\pm 9,\pm 10,\pm 11$. (b) Corresponding to the second group of six OAM beams with $l=\pm 9,\pm 12,\pm 15$.

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4.3 Performance of OAM array encoding/decoding with atmospheric turbulence

Inorder to estimate the system performance under outside disturbance. Performance of OAM array encoding/decoding with atmospheric turbulence is also studied. Atmospheric turbulence can distort the helical phase fronts of OAM beams, which could induce OAM discrimination problem [34, 35]. We use a pseudo-random phase screen mask obeying Kolmogorov spectrum statistics and featured by its correlation length $r_0$ to emulate the turbulence [36, 37], as shown in Fig. 8(b). The turbulence phase mask is added to the OAM array generation phase mask [Fig. 8(a)]. When using OAM array phase mask with turbulence [Fig. 8(c)] for OAM array encoding, the helical phase structures of OAM beams are distorted, resulting in the aberration of intensity profiles of OAM array states. For instance, the intensity profiles of OAM array states before and after demodulation for $r_0=3 mm$ and $1 mm$ are displayed in Figs. 8(d)-(g). One can clearly see that the turbulence can cause fluctuation of location of central bright spot of the demodulated beam, or even worse, there is no central bright spot at the center of the demodulated beam. The strong aberration of the demodulated beam may cause OAM detection problem leading to serious bit error rate. In the experiment, for each sending OAM array symbol, the system can randomly generate a turbulence mask with a specific $r_0$ and add it to the OAM array generation phase mask to emulate time-varying atmospheric turbulence. The measured bit-error rate (BER) and symbol-error rate (SER) curves for two groups of OAM array encoding/decoding ($l=\pm 9,\pm 10,\pm 11$ and $l=\pm 9,\pm 12,\pm 15$) with different correlation length $r_0$ are shown in Fig. 9. The BER values are a little smaller than the SER values, which can be explained with the fact that some bits consisted in an error symbol might be correct. For the first group of OAM array encoding/decoding ($l=\pm 9,\pm 10,\pm 11$), when $r_0$ is larger than 6 mm, the measured BER is less than 1e-3. For the second group of OAM array encoding/decoding ($l=\pm 9,\pm 12,\pm 15$), the BER is less than 1e-3 while the when $r_0$ is larger than 3 mm. The second group shows better performance against the turbulence due to the larger spacing of OAM orders compared to the first group. However, larger spacing may decrease the number of OAM beams used for encoding. To guarantee the available OAM number, adaptive optical compensation method could be used for the case of small spacing OAM beams with strong atmospheric turbulence [34, 35].

 

Fig. 8 (a) OAM array generation phase mask. (b) Simulated atmosphere turbulence phase mask. (c) OAM array generation phase mask with atmosphere turbulence. (d)(e) Turbulent intensity profiles of OAM array before and after demodulation with $r_0=3 mm$. (f)(e) Turbulent intensity profiles of OAM array before and after demodulation with $r_0=1 mm$.

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Fig. 9 Bit-error rate (BER) and symbol-error rate (SER) curves for two groups of OAM array encoding/decoding for optical interconnects (first group: $l=\pm 9,\pm 10,\pm 11$; second group: $l=\pm 9,\pm 12,\pm 15$).

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In order to further intuitively show the performance of the optical interconnects system with turbulence, we use OAM array states composed by $l=\pm 9,\pm 12,\pm 15$ for encoding transmission of a grayscale image. The original image with 256 different grayscale values has 150$\times$150 pixels, as shown in Fig. 10(a). Each pixel needs 8 bits to represent it, and the number of total bits is $150\times 150\times 8=180000$. The used OAM array has 1296 states. After encoding the symbol length is 16929, which is reduced by 10.63 times compared to the original binary data. For the case without turbulence, the image can be well recovered without error bit. When the correlation lengths $r_0$ of turbulence phase masks are 3 and 1 mm, the recovered images are depicted in Figs. 10(b) and (c), respectively. The BER values for $r_0=3$ and 1 mm are about 1.2e-3 and 0.14, respectively. From Figs. 10(b) and (c), one can find that strong turbulence might cause significant distortion to the transmitted data information.

 

Fig. 10 (a) Original image with 256 different grayscale values and 150 × 150 pixels. (b)(c) Recovered image after optical interconnects when the correlation lengths $r_0$ of turbulence phase masks are 3 and 1 mm, respectively.

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5. Discussion and conclusion

These proof-of-concept experiments demonstrate the OAM array encoding and decoding scheme to effectively increase the number of bits information encoded in a single symbol code. Through the comprehensive utilization of the spatially orthogonal modes and spatial positions, one can greatly improve the information content of a single symbol with a relatively small number of OAM states. OAM array encoding/decoding with direct detection method and simultaneous multi-OAM demodulation method are considered. The influence of atmospheric turbulence is also evaluated. Although, the encoding speed is not high in these experiments (about 0.6s per symbol), further improvements such as high-speed integrated OAM transmitters, might lead to the use of OAM array as an effective and fast way to encode information.

For communication systems such as optical interconnects, security is a one important issue. G. Gibson, et al. has pointed out that OAM encoding can inherently enhance the communication security, which does not depend on mathematical or quantum-mechanical encryption methods [19]. When using OAM array for encoding, the security might be further improved. The OAM array will be more sensitive for angular restriction, a lateral shift or angular misalignment of the measurement axis. Only when each OAM in the array is correctly detected, the data information carried by an OAM array can be well recovered. Moreover, since there are lots of symbol states, the mathematical encoding can be very complicated, which is also advantageous for improving the security of optical interconnects.

Component and system integration is expected to effectively reduce the cost and energy consumption [6]. SDM with few-mode fibers, multi-core fibers and few-mode multi-core fibers have been introduced to increase the transmission capacity and decrease the cost per bit. Similar to few-mode multi-core fibers, using OAM array for information encoding/decoding transmission is expected to effectively improve the system integration and reduce the cost.

Besides, component integration is not only beneficial to reduce the cost and energy consumption but also helpful for size-limited application environments, for instance, data centers or computer backplanes where high-interconnection density is highly desired. OAM array could be easily generated and modulated by integrated devices [24, 25, 28], so it is expected that the OAM array communication might also facilitate optical interconnects among integrated chips (i.e. chip-scale optical interconnects), which could improve the interconnection density of data centers or computer backplanes. Moreover, the modulation speed of integrated devices has the potential to be very high.

In conclusion, we propose and experimentally demonstrate an OAM array communication system for optical interconnects. By employing OAM array state to encode information, the information content of a single symbol can be greatly improved with a small number of OAM beams. Using OAM array with 4 spatial locations each with 5 possible OAM beams, a 625-element OAM encoding/decoding communication link for optical interconnects is demonstrated with direct OAM detection method. Moreover, using OAM array with 4 spatial locations each with 6 possible OAM beams and simultaneous multi-OAM detection method, a 1296-element high-base OAM encoding/decoding communication link for optical interconnects under atmospheric turbulence is also evaluated. The proposed OAM array communication scheme for optical interconnects might inspire wide optical communications applications exploiting the space dimension of light beams.