Recently, some scholars have proposed inverted pin beam (IPB) with a Bessel-like shape and found that compared with Bessel beam (BB), pin beam (PB), and Gaussian beam (GB), IPB have a lower scintillation index during moderate to strong atmospheric turbulence transmission. Although IPBs have a superior anti-turbulence ability in long-distance transmission, the characteristic of the gradually increasing beam width during transmission will result in lower received power in the far field. Therefore, we propose nonuniformly correlated inverted pin beam (NUCIPB), which can further reduce the light intensity fluctuations and other perturbation effects caused by atmospheric turbulence and improve the received power in a certain range of the far field by introducing self-focusing characteristics with the assistance of nonuniform correlation modulation.

Based on the coherent mode decomposition and random phase screen methods, a numerical simulation model of NUCIPB transmitting in atmospheric turbulence is built, and the light intensity evolution characteristics of the beam transmitting through free space and turbulent atmosphere are simulated and analyzed. The aperture averaged scintillation index, beam wander, and beam broadening are employed to evaluate the beam quality affected by atmospheric turbulence. On this basis, the average bit error rate (BER) of the system is calculated when the beams are adopted as a space optical communication link, and the transmission and communication performances of the NUCIPB, IPB, PB, BB, and GB are compared in the same conditions.

The light intensity evolution during free space transmission of IPB and NUCIPB shows that the trend of spot size variations for NUCIPB and IPB is identical, but the intensity distribution of NUCIPB is more uniform. Meanwhile, NUCIPB also show the characteristics of Bessel-like distribution in the paraxial region. The difference is that it will degenerate into a Gaussian-like distribution after a certain distance, and the attenuation degree of light intensity along the axis increases significantly lower than that of IPB with the increasing transmission distance (Figs. 1?5). The fluctuation degree of light intensity for all beams increases with the rising transmission distance and turbulence intensity, and the corresponding communication performance also degrades gradually. The comparison of the two sizes of receiving apertures indicates that an increase in the receiving aperture can significantly reduce the scintillation index and the communication BER. Under strong turbulence and Ra=0.10m, compared with GB, the scintillation index of BB, PB, IPB and NUCIPB decreases by 55.1%, 16.8%, 67.2%, and 78.0% respectively after atmospheric turbulence transmission of 10 km, and the BER also decreases by 50.7%, 12.6%, 63.4%, and 78.5% respectively (Figs. 8 and 13). The optical power in the two receiving apertures gradually decreases with the increasing transmission distance, and the greater turbulence intensity leads to a faster decline rate. The power in the bucket (PIB) of BB is greatly affected by the aperture size and NUCIPB will have self-focusing characteristics compared with IPBs during the transmission. In the case of strong turbulence and Ra=0.10m, the PIB of NUCIPB at the focusing position will increase by nearly 38.6% compared with IPB (Fig. 9). Meanwhile, the beam spreading degree of NUCIPB after 10 km transmission in strong turbulence is 38.4%, 13.7%, 22.6%, and 5.1% lower than that of GB, BB, PB, and IPB respectively (Fig. 10). In terms of the degree of beam wander, NUCIPB have a certain advantage in weak to moderate turbulence for long-distance transmission (Fig. 11).

We propose and construct NUCIPB, and build an atmospheric turbulence transmission model based on the coherent mode decomposition and the random phase screen methods. The transmission and communication characteristics of NUCIPB are simulated, and compared with GB, BB, PB, and IPB, the simulation results show that as the transmission distance and turbulence intensity increase, the intensity fluctuations of all beams continually intensify, causing gradual degradation of corresponding communication performance. A comparison between two sizes of receiving apertures reveals that increasing the receiving aperture size can significantly reduce intensity scintillation and decrease the communication BER. Under strong turbulence and Ra=0.10m, compared with GB, the scintillation index of BB, PB, IPB, and NUCIPB decreases by 55.1%, 16.8%, 67.2%, and 78% respectively after 10 km atmospheric turbulence transmission, and the BER also decreases by 50.7%, 12.6%, 63.4%, and 78.5% respectively. Additionally, the optical power in the two receiving apertures gradually decreases with the increasing transmission distance, and the greater turbulence intensity leads to a faster decline rate. The PIB of BB is greatly affected by the aperture size and NUCIPB will have self-focusing characteristics compared with IPB in the transmission process. Under strong turbulence and Ra=0.10m, the PIB of NUCIPB at the focusing position will increase by nearly 38.6% compared with IPB. Meanwhile, with the rising transmission distance, beam spreading becomes more severe. There is little difference between beam spreading in weak and moderate turbulence intensity. Compared with GB, BB, PB, and IPB, the beam spreading of NUCIPB after 10 km is reduced by 38.4%, 13.7%, 22.6%, and 5.1% respectively. In terms of the degree of beam wander, NUCIPB have certain advantages in long-distance transmission under weak to moderate turbulence, but with the rising turbulence intensity, there is little difference between NUCIPB and IPB. Compared with fully coherent IPB, NUCIPB perform better in reducing the negative effects caused by turbulence, such as light intensity fluctuations, beam wander, and beam spreading. Meanwhile, due to the introduction of self-focusing characteristics, NUCIPB surpass IPB in far-field energy focusing within a specific transmission range, which can improve the far-field energy receiving efficiency. Although the current research is entirely based on simulation calculations to explore the performance of NUCIPB in atmospheric turbulence channels, we can further employ digital micro-mirror devices (a modulation rate of 17 kHz) and programmable lithium niobate SLMs (a modulation rate able to reach 5 MHz and 1.6 GHz respectively) with high modulation rates to construct NUCIPB and experimentally verify the feasibility of NUCIPB for free space optics (FSO) communication.