Chaotic laser can effectively ameliorate the problem of insufficient security of optical communications due to its noise-like and high-bandwidth characteristics.1^–3 However, there are three key challenges in secure optical communications based on the chaotic laser: (i) because of the limited bandwidth of the chaotic laser, their security performance will degrade significantly in high-speed optical communications; (ii) the current rate of chaotic optical communication systems is mostly in tens of Gb/s, thus failing to satisfy the actual communication needs of hundreds of Gb/s; and (iii) the existing methods of chaotic optical communication do not take into account the spatial expansion of chaotic laser, which is difficult to support multidimensional superior security and high-density storage. Therefore, there is an urgent demand to develop a technology that combines spatial modes with chaotic lasers to achieve high-security and massive-capacity optical communications.

Numerous efforts have been dedicated to the development of enhanced bandwidth4^–10 and expanded capacity11^–16 in the chaotic laser empowered communication systems. It has been shown, for the former, that the use of extra optical injection,4^,5 tunable optical feedback,6^,7 efficacious postprocessing,8^,9 etc. enables to boost the safety of information. However, the realization of increased bandwidth with these strategies is at the cost of cumbersome chaotic laser structure, which is not beneficial to real optical communication applications. For the latter, by leveraging orthogonal frequency-division multiplexing,11 polarization-division multiplexing,12 and wavelength-division multiplexing,14 it permits one to effectively enlarge capacity of the chaotic secure optical communication systems. Yet, these methods only allow capacity in tens of Gb/s, impeding extremely large capacity optical communication. It is thus highly desired to incorporate a fire-new dimension into the chaotic laser, which can not only enhance the security of the optical communication system but also impressively improve the communication capacity. Over the past decade, spatial orbital angular momentum (OAM), which is carried by optical vortices with the helical transverse phase structure of $e^{il\varphi }$ ($\varphi$ is the transverse azimuthal angle, and $l$ is the topological charge), has aroused unprecedented research enthusiasm in optical communication,17^–25 optical manipulation,26 optical trapping,27^,28 optical storage,29 optical detection,30^,31 and high-resolution imaging.32^,33 Particularly in optical communication, the OAM offers a promising prospect on account of its additional confidentiality, infinite orthogonal modes, environmental insensitivity, and good compatibility. Therefore, an interesting question arises: whether it is possible to fuse temporal chaotic laser with spatial OAM to realize high-security and massive-capacity optical communication?

Here, we introduce a conceptual paradigm to yield orbital angular momentum configured chaotic laser (OAM-CCL), which can be used to achieve a high-security and large-capacity optical communication system. Specifically, on the one hand, it is found that the OAM-CCL-based communication system still maintains the high security even at low optical signal-to-noise ratio (OSNR, 20 dB) and complete eavesdropping. On the other hand, by utilizing 11 orbital angular momentum modes, the OAM-CCL-based communication system is theoretically expected to realize a communication rate of $100\mathrm{Gb}/\mathrm{s}$. It means that the potential degrees of freedom ($>100$) of the system still allow a higher communication capacity ($>100\mathrm{Gb}/\mathrm{s}$) with a bit error ratio (BER) below the forward error correction (FEC). Moreover, the robustness of the OAM-CCL-based communication system to misalignment is revealed. Finally, we validate the conceptual paradigm of the OAM-CCL-based communication system. In brief, all the above superiorities indicate that the OAM-CCL-based communication system not only alleviates the drawback that the security of the traditional OAM communication system cannot be fully guaranteed but also solves the issue of limited transmission capacity in traditional chaotic secure optical communication. Our study will help promote the application of chaotic lasers in multidimensional, high-security, massive-capacity, and robust optical communication.

In order to tackle the shortcomings of the traditional chaotic laser, we propose a conceptual paradigm of OAM-CCL, as shown in Fig. 1(a). After OAM configured, the wavefront of the chaotic laser becomes a helical structure, and the temporal properties of the chaotic signal are preserved. Thus the OAM-CCL can be used as a broadband chaotic laser source driving a pair of lasers to generate synchronous masking signals for communication in free space. The OAM-CCL is schematically shown in Fig. S1 in the Supplementary Material. The OAM-CCL possesses the following characteristics: (i) it is difficult to eavesdrop in free space, providing additional security. (ii) It can be spatial quadrature multiplexed with other OAM beams, bringing additional freedom to the optical communication system, similar to Fig. 1(b).

The schematic diagram of the communication system based on OAM-CCL is shown in Fig. 2. An all-optical feedback chaotic laser ${\mathrm{SL}}_{\mathrm{D}}$ with a wavelength of 1550 nm generates a high-bandwidth chaotic laser as the driving chaotic source.34 The driving chaotic signal is split into two parts: one part is injected into the laser ${\mathrm{SL}}_{\mathrm{T}}$ to generate an encrypted chaotic signal $E_{\mathrm{ch}}(t)$, whereas the other part is sent to the receiver and injected into ${\mathrm{SL}}_{\mathrm{R}}$ to generate a synchronous chaotic signal $E_{\mathrm{ch}}^{\prime }(t)$.35 Continuous-wave lasers ${\mathrm{SL}}_1-{\mathrm{SL}}_{10}$ are modulated to produce $10\mathrm{Gb}/\mathrm{s}$ nonzeroing on–off keying signals $E_n(t)$, respectively. After that, the information signals are masked as encrypted signals $E_n^{\mathrm{enc}}(t)=E_n(t)+a{E}_{\mathrm{ch}}(t)$. Note that due to the presence of the attenuator the masking coefficients differ from channel to channel, avoiding the possibility of the eavesdropper removing the chaotic signal by simple differencing.

Then the encrypted signals are coupled from single-mode fibers to free space via collimators that can be described as Eq. (S1) in the Supplementary Material. After the construction of spatial light modulators, the beams carrying the encrypted signals is, respectively, converted into vortex beams of OAM $\pm 3$, OAM $\pm 5$, OAM $\pm 7$, OAM $\pm 9$, and OAM $\pm 11$, as shown in Eq. (S2) in the Supplementary Material. Similarly, the driving chaotic signal is also converted from a Gaussian beam to an OAM $+1$ beam, multiplexed with other encrypted signals through beam splitters and transmitted to the receiver via free space, which can be described as Eq. (S3) in the Supplementary Material. At the receiver, the multiplexed OAM beams are subjected to an opposite topological charge and filtered to demultiplexing, the optical field can be expressed as Eq. (S4) in the Supplementary Material. The demultiplexed driving chaotic signal will be injected into the laser ${\mathrm{SL}}_{\mathrm{R}}$ to generate synchronous chaotic signal $E_{\mathrm{ch}}^{\prime }(t)$. The demultiplexed encrypted signals are differenced from the synchronous chaotic signal to recover information signals $E_n^{\prime }(t)=E_n^{\mathrm{en}{\mathrm{c}}^{\prime }}(t)-a_n^{\prime }{E}_{\mathrm{ch}}^{\prime }(t)$.

The commonly driven chaotic synchronization mechanism is used in the OAM-CCL-based communication system.36^,37 This scheme has the advantages of simplicity, robustness, fast synchronization, and suitability for multichannel encryption. When the driving chaotic signal is injected into a pair of parameter matching slave lasers with a certain intensity, the two slave lasers will produce highly synchronous chaotic signals for encryption and decryption. We use Eqs. (S5)–(S7) in the Supplementary Material to describe the complex chaotic synchronization dynamics and stable spatial modes in the OAM-CCL optical communication system.

The OAM-CCL-based communication system inherits the security of traditional chaotic secure optical communication. Figure 3 shows the simulation results of the OAM-CCL-based communication system in the time domain. Figure 3(a) shows the time waveform of the chaotic lasers ${\mathrm{SL}}_{\mathrm{D}}$, ${\mathrm{SL}}_{\mathrm{T}}$, and ${\mathrm{SL}}_{\mathrm{R}}$. The synchronization coefficient of the two slave lasers ${\mathrm{SL}}_{\mathrm{R}}$ and ${\mathrm{SL}}_{\mathrm{T}}$ is 0.976, and the synchronization coefficient between the driving laser ${\mathrm{SL}}_{\mathrm{D}}$ and the slave laser ${\mathrm{SL}}_{\mathrm{T}}$ is 0.763, which means that attackers cannot use the driving chaotic signal for decryption, ensuring the security of the system. The effective bandwidths (80% energy) for driving and masking chaotic signal are 11.73 and 13.35 GHz, respectively. Figure 3(b) shows the variation of the power spectrum of the information signal before and after encryption with $\rho =0.187$. The masking coefficient $\rho$ is defined as the ratio of the amplitude of the information signal to the amplitude of the chaotic signal.38 The encrypted signal exhibits a noticeably flat power spectrum, indicating effective masking of the information signal by the chaotic signal. In Fig. 3(c), the impact of different masking coefficients on the BER is shown for both legitimate and illegitimate decryption at an OSNR of 20 dB. It can be seen that even if the signal is completely eavesdropped, the system still achieves secure communication within a masking coefficient range of 0.31 to 0.56. In Fig. 3(d), the BER for legitimate decryption of the system is presented. It can be observed that increasing the masking coefficient enhances the system’s tolerance to noise, but it may reduce the system’s security level.

In addition to the conventional temporal domain security discussed above, the OAM-CCL communication system also demonstrates remarkable resistance against eavesdropping in the spatial domain. These outcomes are elucidated further in Sec. S5 of the Supplementary Material. We substantiate this eavesdropping resilience by constructing an eavesdropping channel. Our results indicate that compared to the free-space optical communication system, Eve’s eavesdropping on the OAM-CCL-based communication system for high-quality interception requires a larger size and positioning closer to the optical axis. In this case, Eve’s interception of the beam at such a close position will cause Bob’s alarm.

For the OAM-CCL-based communication system, the limit value of communication rate $C_{\lim }$ can be described as Eq. (S9) in the Supplementary Material. The parameters $C_{\max }$ and DoF determine the value of $C_{\lim }$, which represents the system single-mode maximum rate and the system degree of freedom, respectively. $C_{\max }$ is related to the bandwidth of the chaotic carrier and masking coefficient.39 Figure S6 in the Supplementary Material shows the relationship between a single-mode information rate and BER for the system with different masking coefficients at OSNR = 20 dB. The relationship between the mode number and the system capacity of the system with different masking coefficients is shown in Fig. 4(a). It is clear that the communication rate increases in proportion to the mode number.

Theoretically, OAM modes have infinite degrees of freedom, but in practice, because of the divergence nature of OAM beams, the degrees of freedom of the system are limited under finite physical conditions. Here, we modify the study result of Sawan et al.40 and considering the beam limitation by the transmitter, define the DoF for the OAM-CCL-based communication system: $$\mathrm{DoF}\triangleq \underset{{\omega }_0}{\max }\#\{{\mathrm{LG}}_p^l|r_p^l(0)\le R_T,1-\frac{R_R^2}{z^2+z_R^2}\le \mathcal{P}\},$$(1)where #{} represents the size of a set, $r_p^l$ indicates the beam size,41$R_T$ denotes the transmitter radius, and $R_R$ denotes the receiver radius. $\mathcal{P}$ is the paraxial estimator, and it is the ratio of the true power crossing a transverse area obtained using the Helmholtz and paraxial equations. 42 The paraxial estimator not only can be used to indicate the validity of paraxial approximation of the beam but also the beam divergence. The higher-order OAM modes have a smaller paraxial estimator, so the paraxial estimator can be used as an important parameter for defining the DoF. Equation (1) defines a degree of freedom as the set of all LG modes that satisfy a beam emission size smaller than the emitter size and an estimate of the beam evening axis at the receiving end greater than the reference value. The paraxial estimator and beam size are calculated as shown in Sec. S13 in the Supplementary Material.

Figure 4(b) shows the relationship between transmission distance and DoF for different initial beam waists, as the transmission distance increases, the DoF tends to decrease. At close range ($<345\mathrm{m}$), the smaller the initial beam waist is, the higher the DoF in the system is, and the opposite is true at long range. And the receiver size plays a role in constraining the degrees of freedom, as depicted in Fig. S7 in the Supplementary Material. Therefore, in order to ensure the freedom of the system, the appropriate transmitter size, receiver size, and initial beam waist radius should be selected depending on the communication distance.

In practical applications, mechanical vibrations and wind variations can cause minor displacements or jitters, which may cause misalignment between the transmitter and receiver. Such a misalignment leads to a decrease in orthogonality between OAM modes,43^–47 thus giving rise to a deterioration of chaotic synchronization and communication quality in the OAM-CCL-based communication system. The basic forms of misalignment include angular error and displacement error between the transmitter and the receiver, shown as Fig. S10 in the Supplementary Material.

By adjusting the basic parameters, we find that the OAM-CCL-based communication system exhibits robustness to misalignment. Figure 5(a) shows the variation of the synchronization coefficient when displacement error and angle error occur simultaneously. Figure 5(b) shows the BER variation with a mode spacing of 2 under the presence of displacement error and angular error, when $\rho =0.187$, ${\omega }_0=2\mathrm{cm}$. Beyond that, we have also investigated the change in system performance when displacement and angular errors occur independently, and the specific results are shown in Figs. S11–S14 in the Supplementary Material. We find that the larger the beam waist is, the more robust the system is to displacement error, and the less robust it is to angular error. Larger mode space can reduce the crosstalk between modes, but it may increase the overall power loss of the system. Therefore, the choice of initial beam waist and mode space should be carefully considered in the system design.

As a conceptual illustration, we built a prototype system of OAM-CCL-based communication system, as shown in Fig. 6. The prototype system is used to simulate image transfer experiment, and the simulations together confirmed the above conclusions, as detailed in Sec. S11 in the Supplementary Material. More interestingly, the OAM-CCL, as a new type of hybrid laser, is in a position to realize the coupling of temporal chaotic laser and spatial OAM in an all-optical way, which means that more dimensions can be fused together. For example, it is theoretically possible to incorporate up to 256 polarization dimensions to the OAM-CCL using commercially available spatial light modulators, and we predict that the security of the OAM-CCL-based communication system will be further improved48 (legal $\mathrm{BER}<10^{-4}$ and illegal $\mathrm{BER}\gg \mathrm{FEC}$), and the system capacity can theoretically reach the order of $66.56\mathrm{Tb}/\mathrm{s}$33 (26 OAM × 256 Pol.), while the requirements of the system on the environment to be more loosened. In addition, we simulate the communication performance of the system under turbulent conditions, details of which are given in Fig. S16 in the Supplementary Material. The results show that the system still performs well under the moderately turbulent condition, meaning that the system has the potential to be used in a variety of environments, such as underwater and atmospheric.

In order to improve the robustness of chaotic synchronization, we use the commonly driven chaotic synchronization mechanism as the core of the encryption and decryption mechanism in the OAM-CCL-based communication system. Interestingly, the OAM modes allow the OAM-CCL-based communication system to have multiple channels, so we can use different channels to transmit the driving chaotic signal and the encrypted signal, respectively, reducing the interference between each other, thus improving the quality of chaotic synchronization.

So far, the OAM-CCL-based communication system is in its infancy. Its practical implementation still faces several significant challenges, including beam divergence, alignment issues, atmospheric turbulence, and the lack of standardized protocol and interface. Therefore, in future endeavors, it is crucial to integrate the OAM-CCL-based communication with beam shaping technology,49 adaptive optics technology,50 and a tracking and capture system51 to overcome the challenges posed by divergence, misalignment, and turbulence. Furthermore, there is a pressing necessity to formulate communication protocol standards aimed at augmenting interoperability and compatibility between the OAM-CCL-based communication system and the established optical communication infrastructure.

Our team has done extensive preliminary research on chaotic secure communication and OAM light beams, respectively. The former mainly includes long-range chaotic synchronization,52 chaotic lasers for high-speed classical key distribution,53 and coherent chaotic optical communication.37 The latter mainly consists of OAM generation,54 manipulation,29 and application.30^,31^,33 These above achievements have laid a solid foundation for the experimental realization of OAM-CCL and OAM-CCL-based communication systems. As a result, we believe it is reasonable to use the conceptual paradigm of OAM-CCL to establish a superior-security, massive-capacity, high-fidelity, and robust optical communication.

To conclude, we have theoretically presented and experimentally verified a new conceptual paradigm for the generation of OAM-CCL supporting access to high-security and massive-capacity optical communications. To achieve this, we first leverage the spatial light modulator to encode the OAM of the chaotic laser, and then regard it as an ultrabandwidth source to drive synchronous mask for communicating in free space. It is shown that the use of OAM-CCL carrying 11 vortex modes enables to succeed in achieving a versatile optical communication system, which features a total transmission capacity of $100\mathrm{Gb}/\mathrm{s}$ and a bit error rate below the FEC threshold $3.8\times {10}^{-3}$. In addition, such an OAM-CCL-based communication system is nearly immune to the 3D misalignment within the prescribed argument scopes. It is worth mentioning that the OAM modes allow the OAM-CCL system to have multiple channels, so it is well suited to the commonly driven chaotic synchronization mechanism.

Compared to the existing communication technologies (traditional free-space optical communication or chaotic optical communication), our proposed system is primarily distinguished by both high security and massive capacity. On the one hand, the fusion of temporal chaotic signal and spatial OAM beam ensures the multidimensional encryption of the OAM-CCL-based communication system, making it difficult to eavesdrop, separate, and decrypt. On the other hand, because of the engagement of spatial OAM modes, the OAM-CCL-based communication system is shown to exhibit unlimited storage capacity and superior compatibility in principle. As a result, it is expected to potentially achieve Pb/s capacity by combining with techniques, such as wavelength division multiplexing, advanced modulation, and fractional OAM, although we only show a $100\mathrm{Gb}/\mathrm{s}$ level in this article as a fundamental illustration. In addition, in order to further improve the antimisalignment ability of the OAM-CCL-based communication system, we may resort to some additional techniques, such as power adaptive compensation, demasking power matching, and a tracking system, thus forecasting that the misalignment error rate will drop to a lower level. Beyond that, the OAM-CCL-based communication system is based on an all-optical feedback chaotic laser, which means that it is easy to integrate into large-scale high-rate optical communication networks. The conceptual paradigm for OAM-CCL provides a feasible idea for high-security, large-capacity, and robust optical communications.

Yanwei Cui received his BS degree in measurement and control technology and instrumentation from Qingdao University of Science and Technology, Qingdao, China, in 2021. He is currently pursuing his MS degree in instrument science and technology at Taiyuan University of Technology, Taiyuan, China. His research interests include information security and chaotic secure communication.

Jianguo Zhang received his BS degree in automation, his MS degree in detection technology and automatic equipment, and his PhD in circuit and system from Taiyuan University of Technology, Taiyuan, China, in 2002, 2005, and 2013, respectively. He is currently an associate professor at the Key Laboratory of Advanced Transducers and Intelligent Control System of Taiyuan University of Technology. His research interests include information security technology, deep learning, and hardware implementation of neural networks.

Zhongquan Nie is an associate research fellow of the College of Advanced Interdisciplinary Studies at the National University of Defense Technology, Changsha, China. He obtained his PhD in physics in 2015 from Harbin Institute of Technology, Harbin, China. His research fields include structure vector light field control, all-optical magnetic recording/storage, interaction between light and matter, and femtosecond laser direct writing. He has published 70 papers in journals, such as Light: Science and Applications, Science Advances, Opto-Electronic Advances, Light: Advanced Manufacturing, and Advanced Photonics Nexus.

Anbang Wang received his BS degree in applied physics and his PhD in electronic circuits and systems from Taiyuan University of Technology, Taiyuan, China, in 2003 and 2014, respectively. He is currently a professor at the School of Information Engineering of Guangdong University of Technology, Guangzhou, China. His research interests include laser dynamics, wideband chaos generation, optical time-domain reflectometry, random bit generation, and secure communications.

Yuncai Wang received his BS degree in semiconductor physics from Nankai University, Tianjin, China, in 1986, and his MS and PhD degrees in physics and optics from Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, China, in 1994 and 1997, respectively. He is currently the deputy director of the Advanced Institute of Photonic Technology at the Guangdong University of Technology. His research interests include nonlinear dynamics of semiconductor lasers and chaotic secure communication.