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Orbital angular momentum holographic multicasting for switchable and secure wireless optical communication links

Baoli Li, Hang Su, Weijia Meng, Ke Cheng, Haitao Luan, Min Gu, and Xinyuan Fang

Open Access Open Access

Abstract

The physical dimension of orbital angular momentum (OAM) states of light has been successfully implemented as information carrier in wireless optical communication (WOC) links. However, the current OAM data coding strategies in WOC are mainly limited to the temporal domain, rarely involving the degree of freedom of spatial domain to transmit an image directly. Here, we apply OAM holographic multiplexing technology for spatial information encoding in WOC links. Further, we demonstrate the new concept of OAM holographic multicasting, wherein a beam-steering grating has been utilized for information decoding. To distribute the OAM multiplexing information appropriately in the receiving terminal, the beam-steering grating with controllable topological charges and amplitude weighting coefficients of each diffraction order in the spatial frequency domain has been designed. An iterative algorithm has been introduced to obtain the intensity uniformity >98% at target diffraction orders. As such, this scheme experimentally allows four separate users to receive independent images, which can be switched by modulating the topological charges of the beam-steering gratings at each diffraction order. In addition, this leads to a beam-steering grating-encrypted WOC links, wherein the information can only be decoded by the grating phase with 7 pre-set spatial frequency components. Our results mark a new parallel decoding paradigm of OAM multiplexing holography, which opens up the door for future high-capacity and high-security all-optical holographic communications.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Wireless optical communication (WOC) exploits optical carrier to transfer information from one point to another through an unguided channel [1]. Recently, stimulated by a rapidly increasing number of wireless terminal devices that require high information capacity, WOC has attracted significant attention in both academic and industrial fields [2]. Therein, the indoor WOC using near infrared or visible light for communication within a building owns the advantages of electromagnetic interference immunity and huge spectrum resources [3]. To establish high-security and high-capacity WOC links predominately required in the processes of data transmission, the coding of theoretically unlimited orthogonal orbital angular momentum (OAM) states of light beams have been emerged as a promising scheme [4,5]. Distinctive OAM states provide another optical dimension to multiplex the information, boosting the data rate and the spectral efficiency [6–9]. Up to now, the OAM data coding strategies in WOC relies mainly in the temporal domain, and rarely uses the spatial domain as a degree of freedom to transmit an image directly [10,11].

Holography offers a powerful tool to manipulate three-dimensional (3D) optical wavefronts [12], enabling numerous ground-breaking applications, e.g., imaging [13], display [14], encryption [15,16], and optical neural networks [17]. With the development of 5 G and 6 G technology, ultra-high data transmission speed provides the possibility for holographic communications [18]. In the holographic communication system, the information is encoded and compressed into a bit stream for transmission, and the object is reconstructed after decoding at the terminal [19]. In the recent years, OAM has been implemented as an information carrier in holography [20], resulting in the concept of OAM holography wherein each pixel of the image can be encoded with well-defined OAM states. Combined with various linear or nonlinear micro/nano photonic devices, the ultrahigh bandwidth holograms in the OAM division, or OAM-multiplexing hologram, enable the high-security encryption [21,22], optical-addressable display [23,24], individual control of nonlinear harmonic waves [25,26] and so on [27]. However, to apply the mechanism of OAM multiplexing holography in spatial-domain WOC, beam-steering technology should be developed to decode the OAM multiplexing hologram with proper directivity and flexibility.

In this paper, we propose and experimentally demonstrate a new concept of OAM holographic multicasting that a beam-steering grating has been utilized for information decoding. After a beam steering grating with uniform amplitude distribution and different topological charges in each diffraction order (lg1, lg2, and lg3), the same holographic information encoded in a specific OAM channel (l0) can be duplicated into various OAM channels (l0 + lg1, l0 + lg2, l0 + lg3 in Fig. 1(a)), which is termed as OAM holographic multicasting. When distinctive images are encoded with different OAM states and transmitted coaxially in the WOC link, different users can selectively receive distinctive images from the same information by manipulating the grating (Fig. 1(b)). Notably, the information at the receiving terminal can be switched when the topological charges of beam-steering grating are modulated (Fig. 1(c)). Moreover, our scheme leads to an application of a beam-steering grating-encrypted WOC links, wherein the information can only be decoded by the beam-steering grating with specific Fourier spectrum comprising amplitude distributions, spatial frequencies and topological charges. In the experiment, an iterative algorithm has been introduced to obtain the beam-steering grating with a uniformity >98% of target diffraction orders. We further show four separate users to receive independent images after a 4-meter transmission. Finally, a beam-steering grating with 7 Fourier components can be utilized as a key to decrypt the information, which is spatially split into 7 parts encoded with pre-set OAM states.

 figure: Fig. 1.

Fig. 1. Conceptual illustration of OAM holographic multicasting in the application of WOC links. (a) Schematic of OAM holographic multicasting. (b) Encoding and decoding mechanisms in the WOC link. (c) Switching of images by reconfiguring the beam-steering gratings. (d) A beam-steering grating-encrypted holographic decoding.

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2. Design and characterization of a beam-steering grating

To design a beam-steering grating for OAM holographic multicasting, the topological charge (l) and the amplitude of each diffraction order should be controlled in the spatial frequency domain. As such, the transmission function f (φ) of such grating can be expressed as

$$f(\varphi )= \sum\limits_m {{A_{{l_m}}}\exp ({i{l_m}\varphi } )\exp ({i{g_m}} )} ,$$
where lm and Alm denote the topological charge and the amplitude weighting coefficient of the elementary grating function gm, respectively. Obviously, f (φ) appears in a complex-amplitude form normally.

To achieve an approximate form for the phase-only grating function g(φ), which can be defined as

$$g(\varphi )= \exp [{ip(\varphi )} ],$$
where p(φ) can be expressed as:
$$p(\varphi )= \textrm{Re} \left\{ { - i\ln \left[ {\sum\limits_{m = 1}^N {{B_{{l_m}}}} \exp ({i{l_m}\varphi } )\exp ({i{g_m}} )} \right]} \right\},$$
where Blm is a decisive factor for p(φ), Re{} denotes the symbol of “real part”. Expanding the grating function g(φ) into Fourier series:
$$g(\varphi )= \sum\limits_{m ={-} \infty }^\infty {{C_{{l_m}}}} \exp ({i{l_m}\varphi } )\exp ({i{g_m}} ),$$
where the decomposition coefficient Clm can be expressed as:
$${C_{{l_m}}} = \frac{1}{{2\pi }}\int_0^{2\pi } {g(\varphi )} \exp ({ - i{l_m}\varphi } )\exp ({ - i{g_m}} )d\varphi .$$

Limited by the phase-only spatial light modulator (SLM) in our experiment, the optimizing algorithm introduced below is adopted to ensure the phase-only transmission function g(φ) and the original function f(φ) are approximately consistent. Firstly, ηm, the diffraction efficiency of the grating at m-order, is defined as

$${\eta _m} = \frac{{{C_{{l_m}}}}}{{{C_l}}},$$
where Cl represents the total energy, ${C_l} = \frac{1}{{2\pi }}\int_0^{2\pi } {g(\varphi )} \exp ({ - i{l_m}\varphi } )d\varphi $.

Afterwards, another parameter U can be utilized to evaluate the diffraction efficiency and uniformity among different diffraction orders simultaneously, which can be expressed as

$$U = 1 - \frac{{{\eta _\textrm{m}}(\max ) - {\eta _\textrm{m}}(\min )}}{{{\eta _\textrm{m}}(\max ) + {\eta _\textrm{m}}(\min )}}.$$

Here, ηm (max) and ηm (min) represent the maximum and minimum values of ηm, respectively.

The flow chart to obtain the phase-only beam-steering grating function is shown in the Fig. 2(a) below. As an initiation of the process, we set the decisive factor Blm = Alm and the iteration counter n = 0. According to Eqs. (2)–(7)), ηm and U can be calculated. When the iteration counter n is less than the pre-set number N, the phase-only grating g(φ) is optimized through continuously updating the Blm.

$$\begin{aligned} |{B_{{l_m}}^{\prime}} |&= |{{B_{{l_m}}}} |+ \beta ({|{{A_{{l_m}}}} |- |{{C_{{l_m}}}} |} ),\\ B_{{l_m}}^{\prime} &= \frac{{|{B_{{l_m}}^{\prime}} |}}{{|{{C_{{l_m}}}} |}}\ast {C_{{l_m}}}. \end{aligned}$$

 figure: Fig. 2.

Fig. 2. Design of the beam-steering grating. (a) Flow chart of the phase-only beam-steering grating function. (b) Phase distribution (1024 × 1024 pixels) of a grating with three main elementary grating functions. (c) The distribution in spatial frequency domain of grating shown in Fig. 2(b). (d) The theoretical and experimental results of intensity distributions of each diffraction order.

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Here, || denotes the symbol of the “amplitude part”. And β is a constant representing the update rate. Finally, a phase-only beam-steering grating function featuring different topological charges in different diffraction orders with high efficiency and high uniformity can be obtained.

Without losing generality, a beam-steering grating function with three main elementary grating functions in Fig. 2(b) has been designed. When illuminated by the Gaussian beams, exceeding 92% of the incident energy concentrates on the target diffraction orders, wherein the topological charges of each order are l = -1, l = 0 and l = 1, respectively (Fig. 2(c)). To further illustrate the uniformity of the beam-steering function, the experimental intensity ratio of the three diffraction orders is 1:0.94:1, suggesting a parameter U of 0.970 (Fig. 2(d)).

3. OAM holographic multicasting

The schematic diagram of the experimental setup for OAM holographic multicasting in a WOC link is shown in Fig. 3(a). A 632.8 nm beam from a He-Ne laser, passed through a half-wave plate (HWP) in combination with a polarization beam-splitter (PBS), which is used to continuously adjust the laser power. Through a beam expansion system consisting of 50-mm (Lens 1) and 400-mm (Lens 2) focal-length convex lenses, the light beam illuminated on the first SLM (Hamamatsu, X13138). To implement the OAM as the holographic information carrier for transmission, the OAM-encoded hologram is designed after a superposition of a vortex phase with a topological charge len and OAM-preserved hologram. Notably, the OAM-preserved hologram is obtained through an iterative Fourier transformation of the image after proper sampling (Fig. 3(b)) [20]. To construct a 4-meter WOC system, two SLMs were placed at double focal length in front and back of Lens 3, wherein the OAM-encoded hologram in Fig. 3(b) and the beam-steering grating in Fig. 2(b) are loaded on SLM1 and SLM 2 (Holoeye, GAEA-2-VIS-036), respectively. Finally, a CCD camera (Lumenera, Lt29059C) is used to record the received holographic patterns in the spatial frequency domain. The OAM property of the received holographic information can be duplicated onto three OAM channels, which is revealed by the distinctive intensity distributions and the astigmatic transformation patterns of enlarged pixels in the reconstructed images (Fig. 3(c)) [28]. Herein, due to the OAM conservation law, the topological charges lm,I of the image pixels at different diffraction order m are determined by the topological charge lm at different diffraction order of the beam steering grating and the encoded vortex phase plate, lm,I = lm + len. Moreover, due to the uniform Fourier coefficients of the beam-steering grating, the intensity of the received image can also be divided approximately equally, which is illustrated by analyzing the intensities of the nine pixels in the dotted boxes in Fig. 3(c). In comparison to the original received image with a parameter U of 0.910, the parameters U to characterize the uniformities of the images after holographic multicasting are 0.948, 0.959 and 0.960, respectively (Fig. 3(d)).

 figure: Fig. 3.

Fig. 3. Experimental setup and OAM holographic multicasting results. (a) Experimental setup for OAM holographic multicasting in a 4-meter WOC link. (b) Design of an OAM-encoded hologram. (c) Holographic multicasting images. Insets: astigmatic transformation pattern of nine selected pixels. (d) The intensity distributions of the selected pixels of the original image and the multicasting images at each diffraction order.

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4. Multi-channel switchable dynamic holographic WOC

Distinctive images can be encoded with different helical phase plates, resulting in the design of OAM-multiplexing hologram which can be loaded on SLM1 in Fig. 3(a). As such, a beam-steering grating with the equal amplitude weighting coefficients and inverse topological charges at different diffraction orders for holographic multicasting could be utilized in multi-channel holographic WOC. At each diffraction order, only the image encoded with an inverse helical mode index (len = -lm) can be converted into the Gaussian mode with a stronger intensity distribution in each pixel of a holographic image due to OAM conservation. Through manipulating the topological charges at the diffraction orders of the beam steering grating, the holographic images in WOC can be further switched.

Specifically, ten image frames are extracted from ‘rotating windmill’, ‘waxing and waning of the moon’, ‘rotary stick’ and ‘changing numbers’ videos in our experiment. And the image frames of each video were sampled and superposed with vortex phase plates (herein, len = -4, -2, 2, 4), leading to OAM-encoded holograms. Through superposing the OAM-encoded holograms of the image frames of distinctive videos, a time sequential OAM-multiplexing holograms are obtained (Fig. 4(a)). A beam-steering grating function with topological charges at different diffraction order lm = 4, 2, -2, -4 is shown in the left upper panel of Fig. 4(b). By analyzing the intensity distributions in the spatial frequency domain (left lower panel of Fig. 4(b)), the experimental uniformity of the beam steering grating as high as U = 0.989 can be given. As such, each frame can be distributed almost equally in the four-channel dynamic holographic WOC (Fig. 4(c)). Notably, by manipulating the beam steering grating loaded on SLM 2 in Fig. 3(a), the topological charges of each diffraction order can be controlled. As such, the dynamic videos in different WOC information channels can be switched. In such OAM holographic multicasting-based WOC link, the communication rate determined by the OAM pixel numbers of each transmitted image N*N and the diffraction order M of the beam-steering grating, is M*N*N*2(binary image in our experiments). In Fig. 4, the communication time is mainly determined by refreshing time of the spatial light modulator (∼1/60 s). As such, the final communication rate here is 4*13*13*2*60 bit/s = 81.12 kilobits/s.

 figure: Fig. 4.

Fig. 4. Demonstration of multi-channel switchable dynamic holographic WOC. (a) The design of time sequential OAM-multiplexing holograms. (b) A beam-steering grating function with four diffraction orders. (c) The reconstructed images of a four-channel dynamic holographic images.

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5. Beam-steering grating-encrypted high-security WOC

This scheme can be further applied in the beam-steering grating-encrypted WOC link for the transmission of a single image (Fig. 5). Here, we take the image of the Oriental Pearl TV Tower (OPTT) as an example to prove this concept. Firstly, the image of OPTT was divided into seven parts with equal size. As a data preprocessing process, the OAM-preserved hologram of each part was numerically designed after sampling. Then, the complex superposition of these holograms encoded with helical phase plates (lencoding = -6, -4, -2, 0, 2, 4, 6) results in an OAM-multiplexing hologram. The seven parts, as an OAM-multiplexing hologram, was then transmitted in a 4-meter distance coaxially. Each part of the image can be reconstructed by using incident OAM decoding beams with an inverse helical mode index, ldecoding, of 6, 4, 2, 0, -2, -4, -6, respectively. In order to reconstruct the seven parts simultaneously, we specially designed a beam-steering grating, which has a helical mode index of 6, 4, 2, 0, -2, -4, -6 in each diffraction order in the spatial frequency domain. Notably, in order to match the original OPTT pattern, the spacing between diffraction orders was carefully designed through controlling the spatial frequency of the grating function in the iterative processes. In addition, we used mode filtering arrays for re-rendering in order to reduce the noises in each pattern from the crosstalk OAM channels [20]. Finally, the OPTT image with 7*10*10*2 = 1.4 kilobits data can be seen as shown in the right lower panel in Fig. 5. Obviously, if the beam-steering grating comprising proper topological charges and spatial frequencies is not available, the reconstructed image cannot be decoded.

 figure: Fig. 5.

Fig. 5. The flowchart of beam-steering grating-encrypted high-security WOC link.

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6. Conclusion

In summary, the new concept of OAM holographic multicasting has been proposed and applied in WOC link with the help of a beam-steering fork grating. The uniformities of the grating after iterative optimizations for holographic multicasting are >0.98, laying the foundation of duplication of the spatial information into distinctive OAM information channels. In addition, the versatile technique, OAM multiplexing holography is applied in spatial WOC to boost information capacity. The multi-channel holographic information is broadcast to all diffractive orders of the beam-steering grating. At each diffraction order, only the information encoded with an inverse helical mode index (len = -lm) can be converted into the Gaussian mode due to OAM conservation. By further manipulating the topological charge distribution of the beam-steering grating, the user-received holographic image is switchable. Furthermore, this leads to a high-security information encryption WOC link, wherein the encrypted information can only be decoded by the beam-steering grating comprising 7 particular topological charges and spatial frequency. Our proposed OAM holographic multicasting technique provides a novel way to decode the OAM multiplexing hologram with good directivity and flexibility, opening up the future all-optical high-capacity and high-security OAM-based holographic communications.

Funding

National Natural Science Foundation of China (62005164, 62005166); Natural Science Foundation of Shanghai (23ZR1443700); Young Elite Scientist Sponsorship Program by CAST (20220042); Shanghai Rising-Star Program (20QA1404100); Science and Technology Commission of Shanghai Municipality (21DZ1100500); National Key Research and Development Program of China (2022YFB2804301).

Acknowledgments

We acknowledge the support from the Shanghai Municipal Science and Technology Major Project, and Shanghai Frontiers Science Center Program (2021–2025 No. 20). "Chen Guang" project (20CG54) supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation.

Disclosures

The authors declare no conflicts of interest.

Data availability

All data needed to evaluate the conclusions in the paper are available in the main text.

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Data availability

All data needed to evaluate the conclusions in the paper are available in the main text.

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Figures (5)
Fig. 1.
Fig. 1. Conceptual illustration of OAM holographic multicasting in the application of WOC links. (a) Schematic of OAM holographic multicasting. (b) Encoding and decoding mechanisms in the WOC link. (c) Switching of images by reconfiguring the beam-steering gratings. (d) A beam-steering grating-encrypted holographic decoding.

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Fig. 2.
Fig. 2. Design of the beam-steering grating. (a) Flow chart of the phase-only beam-steering grating function. (b) Phase distribution (1024 × 1024 pixels) of a grating with three main elementary grating functions. (c) The distribution in spatial frequency domain of grating shown in Fig. 2(b). (d) The theoretical and experimental results of intensity distributions of each diffraction order.

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Fig. 3.
Fig. 3. Experimental setup and OAM holographic multicasting results. (a) Experimental setup for OAM holographic multicasting in a 4-meter WOC link. (b) Design of an OAM-encoded hologram. (c) Holographic multicasting images. Insets: astigmatic transformation pattern of nine selected pixels. (d) The intensity distributions of the selected pixels of the original image and the multicasting images at each diffraction order.

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Fig. 4.
Fig. 4. Demonstration of multi-channel switchable dynamic holographic WOC. (a) The design of time sequential OAM-multiplexing holograms. (b) A beam-steering grating function with four diffraction orders. (c) The reconstructed images of a four-channel dynamic holographic images.

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Fig. 5.
Fig. 5. The flowchart of beam-steering grating-encrypted high-security WOC link.

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

f ( φ ) = ∑ m A l m exp ⁡ ( i l m φ ) exp ⁡ ( i g m ) ,
g ( φ ) = exp ⁡ [ i p ( φ ) ] ,
p ( φ ) = Re { − i ln ⁡ [ ∑ m = 1 N B l m exp ⁡ ( i l m φ ) exp ⁡ ( i g m ) ] } ,
g ( φ ) = ∑ m = − ∞ ∞ C l m exp ⁡ ( i l m φ ) exp ⁡ ( i g m ) ,
C l m = 1 2 π ∫ 0 2 π g ( φ ) exp ⁡ ( − i l m φ ) exp ⁡ ( − i g m ) d φ .
η m = C l m C l ,
U = 1 − η m ( max ) − η m ( min ) η m ( max ) + η m ( min ) .
| B l m ′ | = | B l m | + β ( | A l m | − | C l m | ) , B l m ′ = | B l m ′ | | C l m | ∗ C l m .
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