Wavefront shaping to focus a scattered beam

In Fig. 1a, an indoor use case for the CAO-Tx is depicted. From the access point (the CAO-Tx depicted in Fig. 1a), the narrow light beams with user data are sent to the wireless terminals. Usually, user data are transmitted from an information server to an access point via an indoor fiber network. In some cases, a direct high-speed connection between the CAO-Tx and the terminal can be established via a line-of-sight (LOS) path. However, when the direct pathway is obstructed, the light can instead be directed to a diffuse reflection ceiling or wall to establish an indirect NLOS pathway to the device (right example: diffuse reflection in Fig. 1). However, the light incident on the diffuse reflecting object will be scattered in many different directions, as shown in Fig. 1b. Therefore, the OWC detector at a large distance from the diffuse reflector will only collect a small amount of the diffused light.

Fig. 1 a Indoor use case of the coherent array optical transmitter. In the absence of a direct LoS path, diffusely reflected light can be focused to the OWC detector of the wireless device. b Basic principles of wavefront shaping: a diffuse reflecting surface is illuminated with a flat wavefront, and the light is randomly scattered in all directions. Only a small fraction of the light reaches the detector. c By means of an SLM, the phases of different segments of the incident light are modulated to maximize the intensity at the detector Full size image

To overcome this problem, the CAO-Tx includes an SLM, allowing control over the phase of field E a , which is incident on the diffuse reflecting surface. We subdivide the SLM into N different segments, which are all separately controlled. Now, the scattered field reaching the OWC detector of the device can be described by:

$$E_b = \mathop {\sum }\limits_a^N t_{ba}E_a$$ (1)

where t ba is an element of the scattering matrix T, connecting the N number of incident field segments E a to the detected field E b . Here, all elements of the matrix T are assumed to be random complex variables, and as a result, all scattered waves t ba E a will have a random phase20,25. All of these randomly scattered waves interfere, forming a complex intensity pattern known as a speckle pattern.

Assuming that the scattering material does not change during the optimization, we can modulate the phase of E a to optimize the intensity at the detector. To maximize the intensity \(|E_b|^2\), we use the stepwise sequential wavefront-shaping algorithm20,25, where the phases of all of the incident field segments are modulated between 0 and 2π in a stepwise fashion. As a result, the intensity measured at the detector will vary as a function of θ a , the phase of a single input segment a:

$$I_b\left( {\theta _a} \right) \equiv \left| {E_b} \right|^2 = \left| {E_{ref} + t_{ba}E_ae^{i\theta _a}} \right|^2$$ (2)

with reference field \(E_{ref} \equiv \mathop {\sum }

olimits_{a{\prime}

e a}^N t_{ba{\prime}}E_{a{\prime}}\). The intensity at the detector is maximized when E ref and \(t_{ba}E_ae^{i\theta _a}\) are in phase, i.e., \(\theta _a = arg(E_{ref}) - arg(t_{ba}E_a).\) This procedure is repeated for all input field segments, and finally the optimized phase of all incident field segments is applied to the SLM, resulting in an enhancement of the light intensity at the position of the detector (see Fig. 1c). To enhance the light intensity at a different detector position, the algorithm is performed again to find the new ideal phase pattern.

The diffusely reflected light can be focused to any location in the room as long as the OWC detector is capable of measuring the intensity of the SLM-modulated light during the optimization process. The scattered light can be focused on multiple detectors simultaneously by superimposing multiple ideal phase patterns on the SLM20,25. The theoretical intensity enhancement at the detector is independent of the properties of the scattering material. The only limiting factor is the signal-to-noise ratio (SNR) at the receiver26. The losses of the diffuse link over large distances can be compensated by optimizing for a larger number of SLM segments since the intensity enhancement increases linearly with N20. Once the diffuse link with required optical power is obtained using the proposed CAO-Tx, high-speed OWC signals can be transmitted to the receiver.

The non-line-of-sight optical wireless link

We proceed to describe the 30-Gbit/s indoor non-line-of-sight beam reconfigurable optical wireless communication system enabled by the CAO-Tx method. Figure 2 depicts the experimental setup and detailed parameters. To match the trend of well-established wireless standards such as IEEE 802.11ac (Wi-Fi) and ITU IMT-Advanced LTE (4G), the widely used orthogonal frequency-division multiplexing (OFDM) signal is adopted. In our experiment, an electrical 30-Gbit/s OFDM signal is generated by an arbitrary waveform generator (AWG). The digital signal processing flow and parameters can be found in S1 in the Supplementary Information. This OFDM signal is then modulated onto an optical carrier via an optical transmitter including an extra cavity laser and an optical IQ modulator. The signal details are presented in the section “Materials and methods”. The optical signal is amplified via an Erbium-doped Fiber Amplifier (EDFA-1). A 1-km bend-insensitive single-mode fiber is used to emulate indoor applications. Afterward, a polarization controller (PC-1) is used to align the polarization of the optical signal to the polarization axis of the SLM before a collimator. The collimated Gaussian beam is then incident on the SLM (HOLOEYE, PLUTO Phase Only SLM; see S4 in the Supplementary Information for more details). The angle between the incident beam and the reflected beam is 45°. To match the size of the Gaussian beam, 1024 × 1024 pixels are activated, which are further grouped into segments of 128 × 128 pixels, yielding a total of 8 × 8 segments. All pixels in a segment are simultaneously modulated from 0 to 2π in increments of π/4. After the phase modulation of these segments, a lens (f = 200 mm) focuses the modulated beam onto a diffuse reflection barrier, which emulates the rough surface (ceiling or wall) in an indoor scenario. Here, two types of scattering samples are tested: a) a Thorlabs polystyrene screen (EDU-VS1/M); b) a sandblasted aluminum film. The angle between the SLM-modulated beam and the normal of the barrier is −22.5°, and we define the principal reflection angle as +22.5° (i.e., the angle of reflection equals the angle of incidence).

Fig. 2: Schematic drawing of the experimental setup. AWG: arbitrary waveform generator; EDFA: Erbium-doped Fiber Amplifier; PC: polarization controller; SLM: spatial light modulator; OLO: optical local oscillator BPD: Balanced Photodiodes; VOA: variable optical attenuator; ADC/DAC: analog-to-digital converter/digital-to-analog converter; DPO: digital phosphor oscilloscope Full size image

To collect the diffusely reflected optical signal, the light is coupled into a fiber using a collimator. The receiving fiber is mounted on a movable stage, allowing the receiving angle and distance to be varied. An optical power meter is used to provide feedback for the wavefront-shaping algorithm to enhance the light intensity at the receiving fiber. The received optical signal is pre-amplified via a second EDFA (EDFA-2) before it is detected by an optical coherent receiver. Finally, the detected signal is sampled by a real-time oscilloscope operating at a 50-GSa/s sampling rate. The sampled signal is then processed through an offline digital signal-processing algorithm, and the binary signal is ultimately recovered.

Enhancement of received power

To evaluate the effectiveness of CAO-Tx, we compare cases with and without wavefront shaping. We use the optical power arriving at the receiver (see Fig. 3) as a figure of merit. The enhancement of the received power induced by wavefront shaping is shown in Fig. 3. First, the optimization experiment is performed on the polystyrene screen. To explore the performance of the focusing and the large-scale beam steering (direction tuning), the optical power is measured at a 43-cm distance for an angle ranging from −15° to 45° (offset to the principal reflection angle, similarly hereinafter). Each measurement is performed at 3 different spots on the diffuse reflector, and the results are shown in Fig. 3a. It can be seen that the reflected power slightly decreases with the angle, with a 4-dB half-angular range of ~30°. Through this range, the intensity enhancement remains approximately constant, as expected theoretically, and an average gain of 14 dB is achieved. It can be seen that the initial power fluctuates strongly as the spot on the diffuse reflector is changed. This effect is due to the random speckle distribution of the scattered light. The optimized power does not suffer from this effect, and indeed, the optimized power is largely independent of the position of the spot on the diffuse reflector.

Fig. 3 a, b The measured power versus various reflection angles before and after wavefront shaping by using the THORLABS standard diffuse sample and the sandblasted aluminum, respectively; c the measured power versus various distances before and after wavefront shaping Full size image

Similar measurements are also performed on the sandblasted aluminum film. The distance between the diffuse reflector and the optical receiver is fixed at 0.11 m. The optical power is measured at an angular offset ranging from −17° to 17°. Each measurement is performed at four different spots on the diffuse reflector. Before wavefront shaping, the received power at the 0° offset intensely fluctuates from −59.1 dBm to −43.9 dBm. In contrast, the received power can always be enhanced to a relatively stable level (1.5-dB fluctuation). An 11.7-dB average enhancement is observed (from −51.5 dBm to −39.8 dBm). When the receiver is located at a dark point (−59.1 dBm), a maximum gain of 18.3 dB could be obtained. This result proves that, even when the receiver is located at a dark spot, the wavefront-shaping algorithm can effectively focus the diffusely reflected light to the receiving collimator. A similar focus enhancement is obtained for other angles, in which the power after wavefront shaping is optimized to ~−42.8 ± 0.8 dBm for a −10° offset and ~−43.8 ± 1.2 dBm for a 10° offset.

Additionally, the distance between the reflector and the receiver is varied from 0.11 m to 1.5 m while keeping the receiver angle fixed at 0°. The measured power-to-distance curves are depicted in Fig. 3c. Again, we notice that, although the signal power decreases with distance, the signal enhancement obtained by wavefront shaping remains approximately constant.

The experimental results of these two diffuse materials prove the effectiveness of power enhancement in a diffuse link achieved by wavefront shaping. Because ceilings and walls are generally diffuse reflectors15, this method is expected to be effective as well. Compared with the isotropically scattering polystyrene screen (enhanced power: ~−60 dBm@0.43 m in Fig. 3a), the received power of the sandblasted aluminum has a ~18-dB improvement (~−42.2 dBm@0.44 m in Fig. 3c). Although the angular coverage becomes narrower, the received power is much higher. Therefore, we use the sandblasted aluminum reflector in our data transmission experiment. The detailed scattering response of the two diffuse reflection materials can be found in S2 in the Supplementary Information.

Record data rate over a diffused link

In this experiment, we demonstrate a diffuse NLOS link enabled by CAO-Tx. A record 30-Gbit/s data rate is achieved in a diffused optical wireless communication system. Figure 4a presents the normalized optical spectra (normalized to the same noise level) before and after wavefront shaping to show the optical SNR improvement. The spectrum of the optical back-to-back (OBTB) case without the free-space link serves as a reference with 43.12-dB normalized peak power. The peak values of the spectra before and after wavefront shaping are 3.50 dB and 22.92 dB with a 19.42-dB improvement.

Fig. 4 a The measured optical spectra; b the measured Q factor as a function of the received power; c, d the RF spectra before (OBTB) and after wavefront shaping Full size image

To evaluate the transmission performance of the CAO-Tx link, we measure the Q factor as a function of the received power by adjusting the VOA as shown in Fig. 4b. Here, the Q factor is defined as the electrical SNR27. The 8 × 8 segments are further divided into 16 × 16 segments to achieve a higher power gain for the transmission. Compared to the incident power to the reflector (~10 dBm), the diffuse reflection sample in our experiment introduces a >60-dB loss (−50.9 dBm at the received collimator) at 0° offset, which greatly reduces power efficiency. After the wavefront shaping, the power can be enhanced to −29.9 dBm with a 20.9-dB gain. When the angle is shifted to ± 10°, the power is enhanced from −54.40 dBm and −52.10 dBm to −34.50 dBm and −34.78 dBm, respectively. Except for the curve of the default OBTB case (13.7 dBm after fiber), two more reference curves are measured for the OBTB cases, but with the power (after fiber) attenuated to −29.9 dBm (0°) and −34.5 dBm (±10°). We assess power penalties at the forward error correction (FEC) threshold of 3.8 × 10−3 (Q = 15.17 dB). The power penalties between the focusing cases and their references (Reference 0° and Reference ±10°) are less than 1.5 dB. This suggests that the diffuse NLOS link does not introduce notable impairment. The power penalty between the case of 0° and the cases of ±10° is 8 dB, which is the same as the penalty between the OBTB case and the cases of Reference ±10°. The 4.6-dB power difference results in an 8-dB power penalty when the received power is low (~−30 dBm). This suggests that the improvement of received power by CAO-Tx is critically important for diffuse NLOS links. Moreover, the received RF spectra generated from the digital Fourier transform of the sampled OFDM signal for the OBTB case (without the free-space link) and the diffuse focused case are shown in Fig. 4c, d, respectively. For wireless communication, a significant limit in the NLOS scenario is frequency fading, as depicted in the inset in Fig. 4d. Typical frequency spectra with (w/) and without (w/o) fading are located on the left side and the right side, respectively. In a fading spectrum, the faded parts usually cause serious inter-symbol interference in the time domain. Such interference plays a major role for system performance degradation, rather than the low received power28,29,30. Compared with the OBTB case (shown in Fig. 4c), no frequency fading is found for the focusing case (shown in Fig. 4d). This absence of frequency fading can be attributed to the limited illuminated area on the diffuse reflector, causing negligible multiple path delays. The shaped wavefront is projected to a spot with a diameter of ~1.5 mm. Consequently, the time delay between the shortest and longest path from the transmitter cannot exceed 10 ps. For the OFDM signal used in our experiment, its cyclic prefix length is 1.333 μs, which is much larger than the maximum time delay (10 ps). Therefore, inter-symbol interference is not a limiting factor in the proposed system. Detailed analysis of the link performance is presented in S3 in the Supplementary Information.