Free-space optical communication, which uses a laser as an information carrier, is a wireless communication technology that is widely used in various communication systems. Owing to sufficient parametric dimensions, a series of new technologies have been developed to enhance optical communication capacity based on light field modulation. However, in recent years, with the exhaustion of these traditional dimensional resources and the advent of the big data era, optical communication is once again facing the challenge of a capacity crisis. In response, spatial structures (modes) of light fields are gradually being developed to address the growing capacity bottlenecks. For example, vortex beams carrying orbital angular momentum (OAM) have become an important breakthrough for sustainable capacity expansion of optical communications because their spatial modes are a new degree of freedom in constructing a high-dimensional Hilbert space. Consequently, various methods have emerged to encode information using the azimuthal order of OAM modes. Besides the azimuthal order multiplexing of OAM modes, the radial index and the vector modes are also used to achieve further information capacity enhancement. Although the spatial modes obtained based on the transverse modulation of light fields have fully demonstrated their feasibility in classical and quantum communications, another important spatial dimension of the light field, that is, the longitudinal dimension, has not been exploited for information encoding and decoding. Herein, we propose a dielectric metasurface for longitudinally modulating the superposition state of OAM modes and demonstrate the capability of these modulated light fields in information-encoding scenarios. The metasurface consists of tetratomic macropixels, which enable spin-dependent complex amplitude modulation of the transmitted field because of polarization-dependent interference and can produce a 5×5 light beam array with each beam channel presenting longitudinally variant superposition states of 0 to 15 orders. By introducing longitudinal modulation, the mode capacity of individual channels can be increased exponentially, depending on the number of longitudinal segments in the superposition state of the OAM modes.

The longitudinal encoding and decoding principles are shown in Fig. 1(a). The information from Bob at the transmitter is compiled into multiple superposition states composed of two OAM modes with topological charges of l₁ and l₂ according to the American Standard Code for Information Interchange (ASCII). As the superposition state presents the intensity distribution as the shape of |l₁-l₂| petals, it is characterized by the azimuthal order |l₁-l₂|. These superposition states are then loaded into light beams with longitudinal on-demand transformations for spatial transmission. Alice at the receiver side can obtain the correct information by measuring the superposition modes in different transmission planes, such as z₁, z₂, and z₃, and by decoding the correct sequence of operations. Figure 1(b) shows the codec table corresponding to the ASCII codes and the superposition states with azimuthal orders varying from 0 to 15. Moreover, a spatial array structure can be introduced to increase the parallel transmission rate of information.

An optical frozen wave was used to realize the longitudinal modulation of the OAM modes, and a tetratomic macro-pixel dielectric metasurface was designed to experimentally generate such a light field array with encoded information. The tetratomic macro-pixel is shown in Fig. 2(a), which considers the intrinsic relationship and interaction between the optical responses of rectangular meta-atoms and can achieve complex amplitude modulation because of polarization-dependent interference. According to this principle, the transmission phases φ_0A and φ_0B and rotation angles θ_A and θ_B of the meta-atoms A and B in a tetratomic pixel can be obtained by combining equations (3) and (8). The transmission fields of rectangular nanopillars with different lengths and widths were scanned under the conditions of height H₀=590 nm and period P₀=400 nm to find 17 different geometries, of which the transmitted phases φ₀ linearly increased as shown in Fig. 2(b).

As an example, the message Northwestern Polytechnical University is used to demonstrate the longitudinally encoding capability of this specially structured light field. According to the ASCII hexadecimal code elements, the letters and spaces in the message are transformed into 74 superposition states, which are then divided into a 5×5 beam array. The longitudinal variation of each beam channel contains three segments, which are located at propagation distances of z=0-0.4 mm, 0.4-0.8 mm, and 0.8-1.2 mm, respectively. Because the superposition state in each beam channel can change three times along the longitudinal dimension, the total mode capacity of the beam array is expanded to 16³. The simulated and measured intensity distributions of beam arrays in z₁=0.1 mm, z₂=0.5 mm, and z₃=0.9 mm planes are shown in Fig. 3. The experimental measurements are consistent with that of the simulations. Therefore, the correct message can be obtained by decoding two hexadecimal digits in a Z-shaped sequence starting from the first line in z₁. It should be noted that this method requires the measurement of the light field modes in three different planes for decoding. In this study, a longitudinal scanning method is used. However, to improve the decoding efficiency, a split-plane imaging approach can also be used to obtain the light-field distribution in three longitudinal planes simultaneously by splitting the light twice and then imaging different longitudinal planes. In addition, according to the propagation characteristics of light waves, if the complex amplitude information of the light field is measured in a single plane, the complex amplitude distributions of other planes can be obtained by numerical calculations, and the light field patterns of multiple longitudinal planes can then be obtained.

In this study, a dielectric metasurface that can independently control the amplitude and phase of two light fields is proposed. Flexible modulation of the OAM modes of the beam array in the longitudinal dimension is achieved using the spectral modulation principle of frozen waves. Using these longitudinally modulated light fields, exponential expansion of the mode capacity is experimentally realized to enhance the mode capacity of free-space optical communication. The longitudinal dimensional coding and decoding functionality verified in this study is expected to be a breakthrough in the capacity improvement of free-space optical communication.