1. Introduction

Free-space optical communication (FSOC) has attracted extensive attention recently among the telecommunication community for both high capacity ground to satellite transmission link and last-mile applications [1, 2], thanks to the great progress on components developed for fiber-optic communication systems such as high power erbium-doped fiber amplifiers (EDFAs), narrow linewidth semiconductor lasers, and coherent receivers [3–7].At the receive side of such a system the free-space propagating light beam must be firstly coupled into a fiber before being processed. However, wave-front aberration of the propagating beam induced by atmosphere turbulence greatly degrades the fiber coupling efficiency for free-space propagating light beam [8, 9], and consequently impacts the BER performance of the receivers seriously. Therefore, improving the fiber coupling efficiency for free-space light beam in the presence of atmospheric turbulence is one of the most significant issues for FSOC system.

In the past few decades, the fiber coupling efficiency with single mode fiber (SMF) and multimode fiber (MMF) for free-space light beam has been widely investigated theoretically and experimentally [6, 10–13]. Because of the small core diameter of ~10 μm, the fiber coupling efficiency with SMF is difficult to be improved in the presence of atmospheric turbulence, even assisted with adaptive optics (AO) technology. The coupling efficiency with MMF which can hold several hundred modes is effectively improved due to its large core diameter of more than 50 μm [14]. However, the MMF is hardly compatible with the current SMF-based optic communication technology, especially for coherent detection. Recently, fiber-optic communication based on few mode fiber (FMF) with a relatively large core diameter of ~20 μm which can support a small number of modes is proposed and rapidly developed with larger capacity and higher speed compared with SMF-based communication systems. Few mode fiber devices such as mode multiplexer/de-multiplexers, few mode amplifiers and mode couplers are commercial available [15–17] which might further promote their applications in FSOC system. So it is necessary to investigate the FMF coupler efficiency under turbulence. However, the FMF coupling efficiency for free-space light beam in the presence of atmospheric turbulence has not been investigated till now.

In this paper, the FMF coupling efficiency for free-space light beam in case of various turbulence is investigated theoretically and experimentally for the first time so far as our known. Both simulation and experimental results show that, compared with SMF, the coupling efficiencies for a 2-mode fiber (2MF, holding LP01 and LP11 modes) and a 4-mode fiber (4MF, holding LP01, LP11, LP21 and LP02 modes) are improved by ~4 dB and ~7 dB respectively in the presence of moderate and strong turbulence.

2. Modeling for free-space to FMF coupling

The schematic diagram for free-space to FMF coupling is depicted in Fig. 1. A gauss beam with mode field diameter of 7 mm and wavelength of 1550 nm is firstly passed through a turbulence phase screen generated with Fourier Transform method [18] according to modified Von Karman turbulence model [19]. The beam field and phase screen are characterized by 255⨉255 matrices, and the ratio D/r₀ is introduced to characterize the effect of turbulence on FSO beams, where D is the diameter of transmitting beams, r₀ is atmospheric coherence length parameter (Fried parameter) [20]. Then, after propagation, the beam distorted by atmosphere turbulence is focused using a lens with diameter of 9 mm and focal length of 18 mm before coupled into a coil of SMF or FMF. In this scheme Fresnel diffraction integral method [21] is used to perform beam propagation and focus. The free space to FMF coupling efficiency is calculated using Eq. (1) and (2)

 

Fig. 1 Schematic modeling for free-space to FMF coupling.

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Where m is the numbers of modes held by FMF, α is the loss induced by receiving aperture, η_i is coupling efficiency of the i-th mode in FMF. U₀ represents the optical field in the focal plane and U_i depicts the normalized i-th mode profile of FMF. For 2MF, which holds LP01 mode and two degenerate LP11 mode named LP11a and LP11b, m equals to 3; For 4MF, which holds LP01 mode, LP02 mode, degenerated LP11 modes and two degenerated LP21 modes named LP21a and LP21b, m is 6. For SMF, m equals to 1, since only fundamental mode (LP01) is excited. In this paper, three kinds of fibers are adopted in simulation and experiment. The first one is a standard G.652 SMF with fundamental mode diameter of 9 μm. The second one is a 2MF with core diameter of 18 μm and fundamental mode diameter of 15.6 μm. The last one is a 4MF whose core diameter is 24 μm and fundamental mode diameter is 18.2 μm. All the normalized mode profiles in these fibers are shown in Fig. 1.

3. Experimental setup

Figure 2 shows the experimental setup for fiber coupling. The output of a polarization-maintained-fiber pigtailed laser with optical power of 0 dBm, wavelength centered at 1550 nm, is collimated by a fiber collimator whose output beam diameter is 7 mm. Then the beam is reflected and distorted by a phase-only spatial light modulation (SLM) with 1920 × 1080 pixels, the size for each pixel is 8 um × 8 um. Each pixel has 256 grayscales corresponding to phase modulation depth ranges from 0 to 2π. The generated atmospheric turbulence phase screens are combined with a blazed grating before loading on SLM to separate diffracted beam from the reflected one. Then the distorted beam is split by a 50:50 beam splitter (BS). One is detected by an infrared camera (CCD) to measure the intensity distribution, the other is collimated by a zoom collimator with focal length of 18 mm and aperture of 9 mm before coupled into the fibers as mentioned in section 2. A fiber pigtailed power meter (PM) is used to measure the output power from the fibers. The output spots (point B in Fig. 2) is collimated by a collimator with focal length of 8.18 mm and measured by CCD.

 

Fig. 2 Experimental setup. SLM: spatial light modulation, BS: 50:50 beam splitter, CCD: infrared camera, PM: power meter. The focal length for collimator is 37.13 mm, 18 mm for collimator 2 and 8,18 mm for collimator 3. Point A is next to the front of collimator 2, and point B is at the output end of fiber.

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4. Results and discussion

Figure 3 shows the simulated and measured beam intensity distributions before collimator (point A in Fig. 2) and after the fibers (point B in Fig. 2) with D/r₀ = 0 (without turbulence), 1.03 and 4.12, the corresponding turbulence phase screens are also presented. It can be seen that, the output of SMF is always gauss shaped LP01 mode with and without turbulence. The output beam spots from FMFs are combination of LP01 and LP02 modes even with absent of turbulence. This is due to the small size of the focused beam coupling into fiber. Since the focused beam size is much smaller than that of FMFs, LP01 and LP02 are excited in the FMFs. It can also be seen that LP11 and LP21 modes appear in the presence of turbulence. When turbulence get stronger, the output spot of SMF is much darker than that of the FMFs.

 

Fig. 3 Phase screens with various value of D/r₀ and the corresponding beam spots.

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Figure 4 shows the simulated and measured average output power and relative standard deviation (RSD) for 3 kinds of fibers in case of various turbulences. 100 random phase-screens are used for each turbulence strength. When there is no turbulence, diameter of collimator2 is larger than that of the received beams, it can be observed that the received power for SMF and FMF is almost the same. With increase of turbulence strength, the received power for 4MF and 2MF get higher than that for SMF. When D/r₀>10 (moderate and strong turbulence), the received power for 2MF and 4MF is improved by 4 dB and 7 dB over SMF respectively. The simulation results agree well with the experiment regardless of the insert loss induced by beam splitter (3 dB) and SLM (4 dB).

 

Fig. 4 (a) Average receiving power of each fiber in different turbulent strength; (b) Relative standard deviation (RSD) of received power in both simulation and experiment.

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Since 100 random phase screens are utilized in simulation and experiment for each turbulence strength, the power fluctuation evaluated by the relative standard deviation (RSD) of received power is described in Fig. 4(b). It is shown that as turbulence strength increases, relative fluctuation of the received power increases. When D/r₀>10, the RSD of received power with SMF, 2MF and 4MF are stable around 1.06, 0.70 and 0.54, respectively. The RSD with 2MF and 4MF are about 66% and 51% of RSD with SMF. The experimental RSD are obviously higher than simulating results when D/r₀<10 due to the power fluctuation of the experimental light source and the off-axis error.

Figure 5 shows the measured received power distribution for 100 random turbulence phase-screens and with three kinds of fibers for D/r₀ = 1.03, 4.12, and 16.4. The intrinsic loss of the experimental link without turbulence is 11.2 dB, 12.1 dB and 12.8 dB with a coil of 4MF, 2MF and SMF, respectively. It can be seen in Fig. 5(a) that the output power of 4MF fluctuates between −12 dBm to −10 dBm, while the output power of 2MF and SMF range from −14 dBm to −11 dBm and −17 dBm to −11dBm respectively. When D/r0 = 4.12, as Fig. 5(b) shows, near 50% of the received power by 4MF is distributed in 2 dB range, while neither the 2MF nor the SMF has the concentrate trends in received power. For D/r0 = 16.4, most of the received power for 4MF fluctuates from −32 dBm to −23 dBm, while −38 dBm to −26 dBm for 2MF, −50 to −29 dBm for SMF as shown in Fig. 5(c). If the receiver sensitivity of −35 dBm is assumed, the outage probabilities of SMF, 2MF and 4MF are 65%, 19% and 2%.

 

Fig. 5 Experimental power distribution for 100 random phase-screens with (a) D/r₀ = 1.03, (b) D/r₀ = 4.12, and (b) D/r₀ = 16.4.

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It has been shown that the coupling efficiency increases when the mode numbers of FMF get higher, especially when turbulence get stronger. Actually, the coupling efficiency with MMF outperforms FMF due to its large core diameter of more than 50μm. However, the fibers holding too many modes cannot be used for large capacity and high speed communication subject to the serious mode coupling and modal dispersion [15]. Therefore, a four mode fiber might be a good choice for performance improvement of FSOC system.

5. Conclusions

In conclusion, we compared the coupling efficiency of FSO systems with a coil of SMF, 2MF or 4MF in case various turbulence strength. Both simulation and experimental results show that compared with SMF, the coupling efficiency for 2MF and 4MF are improved by ~4 dB and ~7 dB respectively in the presence of medium moderate and strong turbulence. Relative standard deviation of received power is also investigated for 100 turbulence phase screens. Compared with SMF, the RSD with 4MF and 2MF is reduced by at least 49% and 34% under various turbulence.