Adaptive free-space optical communications through turbulence using self-healing Bessel beams

We present a scheme to realize obstruction- and turbulence-tolerant free-space orbital angular momentum (OAM) multiplexing link by using self-healing Bessel beams accompanied by adaptive compensation techniques. Compensation of multiple 16-ary quadrature amplitude modulation (16-QAM) data carrying Bessel beams through emulated atmospheric turbulence and obstructions is demonstrated. The obtained experimental results indicate that the compensation scheme can effectively reduce the inter-channel crosstalk, improve the bit-error rate (BER) performance, and recuperate the nondiffracting property of Bessel beams. The proposed scheme might be used in future high-capacity OAM links which are affected by atmospheric turbulence and obstructions.

studying the performance of Bessel beam multiplexing link through atmospheric turbulence and compensation block.
In this paper, we propose an obstruction-and turbulence-tolerant FSO OAM multiplexing link by using self-healing Bessel beams assisted by adaptive compensation techniques. A spatial light modulator (SLM) loaded with Kolmogorov phase mask added by an obstruction phase mask is used to simultaneously emulate atmospheric turbulence and obstruction in the laboratory environment. By measuring the phase distortions of a probe Gaussian beam through a wavefront sensor (WFS), correction masks are created and loaded to another SLM to compensate the distortions of multiplexed Bessel beams. Using this scheme, we experimentally demonstrate compensation of multiple Bessel beams through emulated atmospheric turbulence and obstruction. The compensation effects on inter-channel crosstalk and bit-error rate (BER) performance of a two Bessel beams multiplexing system each carrying a 10-Gbaud (40-Gbit/s) 16-ary quadrature amplitude modulation (16-QAM) data are studied. Figure 1 shows the block diagram of turbulence compensation for distorted Bessel beam propagation links. Two cases are considered here: (i) compensation for a distorted link with only atmospheric turbulence ( Fig. 1(a)); (ii) compensation for a distorted link with both atmospheric turbulence and obstruction ( Fig. 1(b)). In the first case, only phase distortions caused by atmospheric turbulence are studied. A phase screen is used to emulate the atmospheric turbulence in the laboratory environment. The field just after the phase screen, i.e. the near field, has almost the same intensity profile as input Bessel beam but distorted phases. After diffraction transmission, the far field becomes distorted, losing the characteristics of the Bessel beam. In order to recover the Bessel beam, an adaptive compensation unit is introduced to correct the phase distortions. While for the second case, both phase distortions caused by atmospheric turbulence and obstructions are considered. Due to the self-healing property of Bessel beam, it could be reconstructed itself after encountering a partial obstruction. However, the atmospheric turbulence will destroy the nondiffracting property, resulting in distorted beam profiles. Fortunately, after turbulence compensation, the self-healing property can still be recuperated.

Experimental setup. The experiment setup for demonstrating compensation of distorted multiplexed
Bessel beams is illustrated in Fig. 2. The transmitter block is used to generate 10-Gbaud (40-Gbit/s) 16-QAM signal at a wavelength of 1550 nm. The signal is then split into three paths and fed into three collimators, generating three collimated Gaussian beams (the beam radius of path I and II is about 2 mm). One beam (path I) is launched to SLM-1 loaded with a hologram phase mask to create one Bessel beam with topological charge l = 3. The second beam (path II) is injected to SLM-2 and converted to another Bessel beam with topological charge l = 5. Bessel beams are generated by holographic axicon masks 22 . The propagation-invariant distance of generated Bessel beam is about 0.74 m. And the distance between SLM-1 and SLM-3 is about 0.36 m. It is noteworthy that path II is turned on only when studying the impact of crosstalk on the BER of multiplexed Bessel beams. The third Gaussian beam (path III) after expansion is used as the probe beam for phase distortion sensing and required correction-mask retrieval. Then the beams are sent to a turbulence emulator (SLM-3) loaded with pseudo-random phase masks that follow the Kolmogorov spectrum statistics 23 . The distorted beams exiting from SLM-3 are imaged onto the wavefront corrector (SLM-4) loaded with correction masks for turbulence compensation. In order to obtain the correction mask, the probe Gaussian beam firstly passes through the link. A small portion of the probe beam reflected by SLM-4 is imaged onto a Shack-Hartmann WFS (HASO from Imagine Optic Inc.) by using a 4f lens system for phase distortion detection. Then a feedback controller dynamically feeds SLM-4 with the appropriate correction masks according to difference between target phase and measured phase. The correction mask obtained from the probe Gaussian beam is then used to compensate the multiplexed Bessel beams. A probe beam is adopted as the reference of phase distortion sensing due to the fact that it is hard to directly measure the wavefront distortion of an OAM beam having doughnut shape (i.e. null intensity at the beam center) with Shack-Harman WFS. Note that probe beam and multiplexed Bessel beams could be separated by using different polarizations or wavelengths 20,21 . After wavefront correction, the multiplexed Bessel beams are then sent to SLM-5 loaded with changeable phase mask for demultiplexing followed by coherent detection.
We use pseudo-random phase masks that follow the Kolmogorov spectrum statistics to emulate atmospheric turbulence characterized by the Fried coherence length r 0 24 . An example of Kolmogorov turbulence phase mask with r 0 = 1 mm is shown in Fig. 3. The emulated propagation distance through atmosphere is 1 km. Moreover, to simultaneously emulate atmospheric turbulence and obstruction with single phase mask, an obstruction phase mask is added to the turbulence phase mask, as depicted in Fig. 3. The obstruction phase mask has transparent area and block area. The block area is actually blazed grating with small period which can diffract the input beam to a specific direction. However, the transparent area will not affect the direction of the input beam. When the grating period is small enough, limited by the size of optical elements, such beam will be obstructed. Moreover, for a more realistic situation, obstruction can be emulated by a real opaque object, while the SLM is only used to emulate atmospheric turbulence.

Experimental results
We first transmit the probe Gaussian beam through a random turbulence realization with r 0 = 1 mm and use the adaptive close-loop to generate the corresponding correction mask. Then the correction mask is used to compensate the wavefront distortions of Bessel beams from charge l = 0 to charge l = 6. For the case with only turbulence, the measured field profiles of various Bessel beams with and without compensation are shown in Fig. 4(a-c). From the figures, one can see that the distorted Bessel beams are efficiently compensated. For the case with strip obstruction and turbulence, the measured near and far field profiles are displayed in Fig. 4(d-g). The  impact of the obstruction can be seen from the near field profiles just after the turbulence-obstruction phase mask (Fig. 4(d)). Bessel beams can reconstruct themselves after traveling a distance, as shown in Fig. 4(e). However, from Fig. 4(f), one can find that the self-healing property will be distorted by atmospheric turbulence. By using the compensation, the self-healing property can be recuperated, as displayed in Fig. 4(g). Figure 5 shows the measured power distributions over different channels when only Bessel beam l = 3 is transmitted. Both cases without obstruction (Fig. 5(a-c)) and with strip obstruction (Fig. 5(d-f)), under a random turbulence realization, with and without compensation are measured. The wavefront distortion caused by turbulence may lead to power leakage from a specific Bessel beam to the neighboring channels, causing inter-channel crosstalk, as shown in Fig. 5(b,e). Figure 5(d) shows the measured power distributions of various channels with strip obstruction. Owing to the self-healing property of Bessel beams, the inter-channel crosstalk caused by the strip obstruction is not obvious, but it may induce some power loss. After compensation, the measured results are depicted in Fig. 5(c,f). From the power distributions, one can find that without compensation, the power is spread among neighboring channels, whereas with compensation, the received power is better confined to the Bessel channel l = 3. Moreover, the self-healing property can be recuperated, as shown in Fig. 5(f).
Moreover, we measured the near and far filed intensity profiles of Bessel beams passing through a more complicated random emulated obstruction which consists of a number of randomly distributed circular block area as shown in Fig. 6(a). From Fig. 6(b-d), it can be seen that the self-healing property can also be recuperated through adaptive compensation.
Finally, we measure the BER performance of 10-Gbaud (40-Gbit/s) 16-QAM signals over multiplexed Bessel channels with a random turbulence realization. Path I is used to transmit data-carrying Bessel beam l = 3.   Meanwhile, path II is also turned on to transmit data-carrying Bessel beam l = 5 to investigate the crosstalk effects. The measured BERs and constellations for Bessel channel l = 3, with and without compensation are shown in Fig. 7. Both cases with and without obstruction are measured. When only channel l = 3 passes through the system, the turbulence just cause received power fluctuation but no crosstalk. Therefore, the power penalty is very small. When both channel l = 3 and l = 5 are turned on, due to the strong crosstalk caused by turbulence, the BER values do not decease with the increase of optical signal-to-noise ratio (OSNR), and cannot be below the forward error correction (FEC) limit of 3.8e-3. After compensation, the BERs could achieve the FEC limit with small OSNR penalties compared to the cases without turbulence. For the case without obstruction, after compensation the measured crosstalk from channel l = 5 to l = 3 is reduced from − 3.3 dB to − 21.2 dB. For the case with obstruction, the measured crosstalk is reduced from − 2.1 dB to − 17.5 dB.

Discussion
We have experimentally demonstrated an OAM-carrying Bessel beam multiplexing link for adaptive FSO communications through turbulence. By using the self-healing property, it is possible to establish obstruction-free FSO OAM communication links. However, strong atmospheric turbulence may distort the phase and intensity of Bessel beam causing inter-channel crosstalk and impairing the nondiffracting property. To realize obstructionand turbulence-tolerant OAM FSO links, adaptive compensation approach has been introduced to the Bessel multiplexing system. Using a SLM loaded with Kolmogorov phase mask added by an obstruction phase mask, we simultaneously emulate atmospheric turbulence and obstruction in the laboratory environment. The atmospheric turbulence compensation scheme is similar to that scheme for LG beams, using a beacon beam to measure wavefront aberrations. Due to the phase distortion and obstruction are at the same plane, therefore, the compensation scheme can be also used for Bessel beams with obstruction. However, for a more complicated situation, obstruction may also cause phase distortions, and some improved methods should be used to compensate the turbulence. The compensation effects on inter-channel crosstalk and BER performance of a two Bessel beams multiplexing system each carrying a 10-Gbaud (40-Gbit/s) 16-QAM data are demonstrated. The obtained experimental results indicate that the compensation scheme can effectively suppress inter-channel crosstalk, improve the BER performance, and recuperate the nondiffracting property of Bessel beams. The proposed scheme might see potential applications in future high-capacity OAM links which are affected by atmospheric turbulence and obstructions. where L 0 is called the outer scale, l 0 is called the inner scale, and r 0 is the Fried coherence length.