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Atmospheric turbulence resistant heterodyne coherent receiver of few-mode fiber

Cong Qiu, Wenqi Ma, Feng Wang, Haiyan Wang, and Guijun Hu

Open Access Open Access

Abstract

We propose and implement a free-space optical (FSO) communication system based on few-mode heterodyne detection that can effectively suppress atmospheric turbulence effects. The experimental results show that the received power gain of the FSO communication system using six-mode fibres is about 6 dB over that using SMF under moderate to strong turbulence conditions.In addition, we have built a coherent detection system for space laser communications with few-mode heterodyne detection and reception, and verified the compensation of atmospheric turbulence effects by the few-mode heterodyne detection and reception technique. Experimental results show that the proposed scheme improves the power budget by 4∼5dB over the single-mode heterodyne coherent reception scheme at BER = 3.8×10−3 under moderate to strong turbulence conditions.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

FSO communication [1] has the advantages of large bandwidth, immunity to electromagnetic interference, abundant spectrum resources and small size, which can increase the communication capacity by several orders of magnitude compared to radio frequency (RF) communication [2–4]. Traditional FSO communication systems often involve first coupling spatial light into the single-mode fibre (SMF) [5], which on the one hand allows the use of an EDFA with a pigtail to amplify and relay the received light signal to mitigate turbulence-induced deep fading; on the other hand, the more stable nature of the light signal in the fibre allows the signal light to be better focused on the smaller target surface of the detector. When the optical signal is transmitted in the atmospheric channel, atmospheric turbulence can lead to random fluctuations in the intensity and phase of the beam at the receiving end, thus causing deep fading of the optical signal coupled into the SMF, resulting in degraded performance of the laser communication system [6,7]. Currently, FSO communication mainly uses adaptive optics (AO) technology to correct the beam wavefront in order to improve the system reception performance [8,9]. However, FSO systems based on AO techniques not only increased the size, cost and implementation complexity of the system, but also required high accuracy and corresponding speed for high-speed communication at the GHz scale, resulting in a slightly inadequate communication performance of the system under strong turbulence conditions [10]. Therefore, a low-cost turbulence-compensated communication scheme is of high relevance for the implementation of FSO.

Few-mode fibre (FMF) can support multi-mode transmission of optical signals with several, dozens of orthogonal modes as independent channels and has a larger mode field area with significantly improved capability to receive spatial optical signals [11,12]. NASA in the USA demonstrated a 3.92dB reduction in coupling efficiency of the FMF compared to the SMF in a ground station-to-LEO satellite communication link.NEC demonstrated a 6.5dB improvement in the coupling characteristics of the six-mode fibre over the SMF in a 320m FSO communication link [13].In addition, FSO communication and LiDAR schemes based on the FMF to compensate for atmospheric turbulence have been proposed successively [14]. Bradley proposed and numerically analysed the performance of a frequency modulated LiDAR receiver based on multi-mode heterodyne detection. A frequency modulated LiDAR receiver with few modes proposed in the literature [15] and demonstrated that the detection probability increasing with the number of modes. Using FMF coupling, Liu proposes an FSO communication receiver based on few-mode prevention of atmospheric turbulence, achieving a 6dB performance improvement. Because of its high bandwidth utilisation, filtering characteristics and high reception sensitivity, coherent detection is the optimal promising reception scheme for FSO communications [16,17]. If the high coupling characteristics of FMF are combined with the advantages of coherent detection, coherent reception based on few modes can effectively compensate for atmospheric turbulence effects. To this end we propose an FSO communication system based on heterodyne coherent detection [18,19] of few-mode.

This paper proposes and implements a FSO communication system based on few-mode heterodyne detection that can effectively suppress atmospheric turbulence effects. By using a signal light containing multiple modes received by the FMF and another few-mode local oscillation light containing the corresponding modes to mix, and then performing photoelectric conversion, coherent detection of all modes in the received optical signal can be achieved, and the signal-to-noise ratio of the heterodyne coherent receiver can be improved. In addition, we have built an few-mode heterodyne coherent detection system for FSO communication and verified the compensation of atmospheric turbulence effects by the few-mode heterodyne detection and reception technique. Experimental results show that the proposed scheme improves the power budget by 4∼5dB over the scheme based on single-mode heterodyne coherent reception at BER = 3.8×10−3 under moderate to strong turbulence conditions.

2. Principle

FMF coupling-based FSO communication systems can improve the coupling efficiency at the receiver side and effectively combat random fading caused by atmospheric turbulence. In this paper, few-mode heterodyne detection is introduced into the field of FSO communication, and its schematic block diagram is shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Few-mode heterodyne coherent detection.

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The FMF based coupling system is shown in Fig. 2. The optical carrier is centred at 1550.14 nm with a linewidth of less than 100 kHz, the transmitting antenna is a fibre collimator with a focal length of 25.49 mm and an output beam diameter of 4.7 mm. It is subsequently modulated with a pure phase space light modulator (SLM), which simulates the phase distortion caused by atmospheric turbulence. At the receiving end, the received beam is coupled into a six-mode fibre through a coupling lens with a focal length of 18.75 mm.

 figure: Fig. 2.

Fig. 2. The receiver system based on FMF.

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The efficiency ${\eta _i}$ of the i-th mode in the FMF excited by incident light can be expressed as [20]:

$${\eta _i} = \frac{{{{\left|{\int_\infty {U_f^\ast {E_i}dB} } \right|}^2}}}{{\int_\infty {{{|{{U_f}} |}^2}dB\int_\infty {{{|{{E_i}} |}^2}dB} } }}.$$
where Uf is the electric field distribution at the focal plane B and Ei is the i-th mode distribution supported by the FMF. The total coupling efficiency of the FMF is ${\eta _F} = \sum\nolimits_{i = 1}^M {{\eta _i}}$, where M is the maximum mode number supported by the FMF. M = 1 represents a SMF that only supports LP01 mode; M = 6 represents a six-mode fiber that allows the transmission of LP01, LP11a/b, LP21a/b and LP02, where LP11a/b and LP21a/b are degenerate mode. The article [*] shows that the approximation of mode field distribution between Laguerre-Gaussian mode and LP mode is is higher than 98% for six-mode fiber.

One of the few-mode local oscillation excitation sections uses the characteristics of the non-mode selective photon lantern shown in Fig. 3 to excite a few modes in the FMF by laser light incident from a particular SMF port, resulting in the multi-mode beam in the FMF.

 figure: Fig. 3.

Fig. 3. Non-Mode-Selective Photonic Lantern.

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In the early days of coherent detection based on space mixing frequency, the received space beam was spatially mixed with a single-mode local oscillation light source through a spectroscopic prism and then directly incident to the photosensitive surface of the photodetector. Phase distortion due to atmospheric turbulence results in a mixing efficiency of less than 25%, and even with truncation of the fundamental mode local oscillation light, only 45% can be achieved [18]. Fibre-based mixers are able to improve the mixing efficiency by coupling spatial light into the fibre and mixing it stably with a multi-mode local oscillation source of a specific power distribution. The 50:50 six-mode coupler used in this paper has two arms supporting the mixing of two 6-mode beams, and its construction principle is shown in Fig. 4. Because the linear polarisation modes are orthogonal and independent of each other, the output light field expression of the ideal 3dB few-mode coupler after mixing can be analogous to the output of a single-mode coupler as

$$\begin{array}{l} {E_1} = \sum\limits_{i = 1}^M {{E_{1,i}}} = \frac{1}{{\sqrt 2 }}\sum\limits_{i = 1}^M {({{E_{S,i}} + j{E_{LO,i}}} )} ,\\ {E_2} = \sum\limits_{i = 1}^M {{E_{2,i}}} = \frac{1}{{\sqrt 2 }}\sum\limits_{i = 1}^M {({j{E_{S,i}} + {E_{LO,i}}} )} . \end{array}$$

 figure: Fig. 4.

Fig. 4. Coupler based on FMF.

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M in the Eq. (2) indicates the maximum number of modes supported by the few-mode coupler, the letter i indicates the number of the corresponding mode in the optical signal, S and LO indicate signal light and local oscillation light respectively, E1 and E2 indicate the output optical signal of port 1 and port 2 of the few-mode coupler respectively. The light signal after mixing is connected to a photodetector or balanced detection to complete the photoelectric conversion process.

In the FSO communication system, considering the heterodyne coherent detection model, the received optical signal coupled into the few-mode fiber and the few-mode local oscillation optical signal are expressed as

$${U_{\textrm{fib}}}(r,\varphi ;t) = \sum\limits_{i = 1}^M {{A_{s,i}}{E_i}} (r,\varphi ){e ^{j({{\omega_0}t + \theta } )}},$$
$${U_{LO}}(r,\varphi ;t) = \sum\limits_{i = 1}^M {{A_{L,i}}{E_i}} (r,\varphi ){e ^{j({{\omega_1}t} )}},$$
Where ${\omega _0}$ and ${\omega _1}$ denote the angular frequencies of the signal light and the local oscillation light respectively; $\theta = {\theta _s} + \phi$ denotes the phase of the signal light, where ${\theta _s}$ modulates the phase information of the signal and $\phi$ denotes the phase noise relative to the local oscillation light. ${E_i}(r,\varphi )$ denotes the mode field distribution of the i-th mode. as,As,i and AL,i denote the amplitude of the i-th mode of the signal light and the local oscillation light in the two incident arms of the mixer respectively. At this time, the signal light and the local oscillation light power can be expressed as
$${P_s} = \sum\limits_{i = 1}^M {{{|{{A_{s,i}}} |}^2} = } \sum\limits_{i = 1}^M {{P_{s,i}}} ,$$
$${P_L} = \sum\limits_{i = 1}^M {{{|{{A_{L,i}}} |}^2}} = \sum\limits_{i = 1}^M {{P_{L,i}}} ,$$
where ${P_{s,i}}$ and ${P_{s,i}}$ indicate the power of the i-th mode in the signal light and the local oscillation light respectively. Define ${a_i} = {{{P_{s,i}}} / {{P_s}}}$ as the power share of each mode in the signal light and satisfy the following conditions
$$\sum\limits_{i = 1}^N {{a_i}} = 1,\textrm{ }0 \le {a_i} \le 1,\textrm{ }i = 1,2,\ldots ,M,$$

The vector ${a} = [{a_1},{a_2},\ldots ,{a_M}]$ represents the signal optical power distribution and, similarly, ${b} = [{b_1},{b_2},\ldots ,{b_M}]$ represents the state of the local oscillation optical power distribution.

The beat frequency signal of the signal light and the local oscillation light can be expressed as the integrated ${U_{\textrm{fib}}}$ and ${U_{LO}}$

$${{I}_{beat}}(t) = \int\!\!\!\int {{U_{{\textrm fib}}}(r,\varphi ;t)U_{LO}^\ast (r,\varphi ;t)drd\varphi } .$$

Taking Eq. (3) and Eq. (4) into Eq. (8), the IF signal after photoelectric conversion and an Ideal low-pass filter is expressed as

$$\begin{array}{l} {y}(t) = \textrm {Re} [{R{I_{beat}}(t)} ]\\ = \textrm {Re} \left[ {\int\!\!\!\int {\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {R{A_{s,l}}A_{L,k}^\ast {E_l}(r,\varphi )E_k^\ast (r,\varphi ){e^{j(\Delta \omega + \theta )}}} } } drd\varphi } \right]\\ = R\sum\limits_{k = 1}^M {{A_{s,k}}A_{L,k}^\ast \cos (\Delta \omega + \theta )} , \end{array}$$
Where R denotes the photoelectric conversion efficiency and Re[.] denotes taking the real part. $\Delta \omega = {\omega _0} - {\omega _1}$, is the frequency of the IF signal. Jointly with Eq. (5), Eq. (6) and Eq. (9), the demodulated IF signal power is expressed as
$$\begin{array}{l} {{P}_{SIF}} = [{{{|{y(t)} |}^2}} ]\\ = {R^2}\sum\limits_{k = 1}^M {{A_{s,k}}A_{L,k}^\ast \sum\limits_{l = 1}^M {{A_{s,l}}A_{L,l}^\ast } } \\ = {R^2}{P_L}{P_s}\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {\sqrt {{b_k}{b_l}} \sqrt {{a_k}{a_l}} } } , \end{array}$$

In the above equation, it is generally convenient to set the power of each mode in the local oscillation light equal, namely bi = 1/M. On the one hand, studies have shown that the coupling efficiency in the higher modes of moderately strong turbulence is equally impressive, and equal local oscillation input allows full use of the energy of all optical signals in the FMF; on the other hand, turbulence leads to a coherence time of about 1 to 10 ms-1 [21], and it is clear that the design of a real-time variation of the signal optical power to match power distribution is not feasible. At this point, Eq. (10) simplifies to

$${P_{SIF}} = \frac{{{R^2}{P_L}{P_s}}}{M}\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {\sqrt {{a_k}{a_l}} } } ,$$

In coherent detection, when the local oscillation optical power is sufficiently large, the scattered particle noise due to the local oscillation light is considered to dominate and the effect of the system circuit noise can be ignored. At this point, the noise of the system can be expressed as

$$\begin{array}{ll} {P_{n}} &= qRB\int\!\!\!\int {{{|{{U_{LO}}(r,\varphi ;t)} |}^2}drd\varphi } \\ \textrm{ } &= qRB{P_L}, \end{array}$$
Where B denotes the system noise equivalent bandwidth while q denotes the electronic charge. Combining Eq. (11) with Eq. (12) yields an expression for the instantaneous SNR of the mode less coherent detection:
$$\begin{array}{l} {\gamma _{FMF}} = \frac{{{P_{SIF}}}}{{{P_{n}}}}\\ \textrm{ } = \frac{{R{P_s}}}{{qBM}}\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {\sqrt {{a_k}{a_l}} } } \\ \textrm{ } = \frac{{RAI}}{{qB}}\left\{ {\frac{{{P_s}}}{{AI}}} \right\}\left\{ {\frac{1}{M}\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {\sqrt {{a_k}{a_l}} } } } \right\}, \end{array}$$
Where A and I denote the area and normalised light intensity of the receiving aperture, while AI denotes the received optical power within the aperture. Observation of Eq. (13) shows that the first term represents the maximum SNR achievable for the signal within the received aperture, while the second term is the coupling efficiency of the FMF ${\eta _F}$ and the third term is the few-mode mixing efficiency ${\zeta _F}$. Without loss of generality,Eq. (13) is reformulated so that it contains the quantities related to the fibre coupling parameters:
$${\gamma _{FMF}} = \frac{{RAI}}{{qB}}{\eta _F}{\zeta _F},$$

The average SNR for few-mode heterodyne detection is related to the number of modes in the signal light M, the power distribution state a in the fibre and the turbulence effect. The expression for the average SNR is given by:

$$\begin{array}{ll} {{\bar{\gamma }}_F} &= E\left[ {\frac{{RAI}}{{qB}}\left\{ {\frac{{{P_s}}}{{AI}}} \right\}\left\{ {\frac{1}{M}\sum\limits_{k = 1}^M {\sum\limits_{l = 1}^M {\sqrt {{a_k}{a_l}} } } } \right\}} \right]\\ \textrm{ } &= \frac{{RA}}{{qB}}{{\bar{\eta }}_F}{{\bar{\zeta }}_F}, \end{array}$$

Similarly, the signal-to-noise ratio and the average signal-to-noise ratio for single-mode detection can be obtained as follows:

$${\gamma _{SMF}} = \frac{{RAI}}{{qB}}{\eta _s}{\zeta _s},$$
$${\bar{\gamma }_{SMF}} = \frac{{RA}}{{qB}}{\bar{\eta }_S}{\bar{\zeta }_S}.$$
Where ${\eta _s}$ and ${\zeta _s}$ denote the coupling efficiency and mixing efficiency of single-mode heterodyne receivers separately. Under the ideal condition that the polarization state of the local oscillation light and the signal light are the same, the mixing efficiency of the single-mode signal light can be considered as 100%.

3. Experiment

In order to better analyse the effects of turbulence intensity, fibre parameters and other factors on the performance of space laser communication received by FMF coupling, experiments on space laser communication based on a few-mode coherent receiver in the laboratory have been established. A diagram of the experimental principle and experimental setup for space laser communication with few-mode coherent detection is shown in Fig. 5. In Fig. 5 (a) is a block diagram of the system for few-mode coherent reception, while in Fig. 5 (b) is a block diagram of the system for single-mode coherent reception as a comparison experiment. The laser at the transmission end has a power of 10dBm, a wavelength of 1550nm and a linewidth of 100kHz, ensuring a polarization state and then feeding into a lithium niobate I/Q modulator (FTM7962EP). The random signal generator generates two PRBS electrical signals of length 211-1, which are filtered by a roll-off factor of 0.8 litre cosine filter and converted to analogue electrical signals by a DAC development board (DAC, Fujitsu LEIA-DK), before being amplified by an RF amplifier. The amplified RF drive signal controls the I/Q modulator to modulate the optical carrier, which generates 2Gbps of QPSK signal light. The signal light first passes through an attenuator for power control before passing through the transmitting antenna into the atmospheric channel, which in the laboratory is about 3 metres long in space, loading the turbulent phase information to be modulated via an SLM controlled by a PC terminal. Here the polarization controller (PC1) at the transmitter terminal with a deflector is used to regulate the polarization state of the transmitted light parallel to the horizontal axis of the SLM in order to ensure the most efficient modulation.

 figure: Fig. 5.

Fig. 5. Block diagram of the experimental system for (a) few-mode heterodyne detection (b) single-mode heterodyne detection of QPSK signals.

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After modulation by SLM the signal is reflected into an aspherical lens with a focal length of 17.5 mm and coupled to the A endpoint of a single-mode or few-mode fibre respectively. One of the arms of the laboratory-made 3 dB six-mode coupler acts as a coupling fibre to the A-terminus. A 100kHz linewidth semiconductor solid-state laser outputs 10dBm DC light, which is mode converted into six modes before being fed into the E2 port of the at few-mode coupler. A single-mode, three-ring polarization controller (PC2) is placed before the mode converter to modulate the polarization state of the local oscillating light to align its polarization state with the signal light to achieve maximum mixing efficiency. It is necessary to note that the centre frequency f2 of the local oscillating light power is modulated to 2 GHz of the centre frequency f1 of the signal light. The mixed signal is converted into an electrical signal by a multi-mode photodetector, sampled by a digital oscilloscope (Lecroy SDA11000) with a bandwidth of 7 GHz and a maximum sampling frequency of 40 GS/s, and finally processed off-line to recover the original information.

The sampled electrical signal should be digitally signal processed to recover the information carried by the signal light, after which the electrical signal is downsampled directly to 4GS/s. This is next performed by a conventional coherent optical receiver DSP. It goes through sample clock recovery, resampling, channel equalisation, frequency bias recovery and phase noise compensation, respectively. Lastly it calculates the BER of the detected signal and the probability of interruption.

4. Results and analysis

Firstly, the coupling characteristics of the FMF and SMF were measured at different turbulence intensities. The link loss of the system based on six-mode optical reception and SMF reception was 4 dB and 5.8 dB, respectively, under turbulence-free conditions. The relative turbulence intensities were Cn2 = 2.89e-14, 6.89e-14, 1.89e-13, 4.89e-13 for atmospheric refractive index structure constants D/r0 = 3.04, 5.1, 9.37 and 16.6, respectively, with larger values indicating a more severe effect of atmospheric turbulence on the propagating beam. The receiving fiber is a six-mode step fiber with a core warp of 18.5 $\mu m$, a cladding refractive index of 1.44402, and a core refractive index of 1.44979. Scatter plots of the received optical power for the few-mode fiber coupling and the single-mode fiber power are given in Fig. 6 for D/r0 = 3.04, 5.1, 9.37, and 16.6, with a transmit power of -7 dBm. At =3.04, the main floating range of coupling power for the six-mode fiber is 4 dB, while the floating range of coupling power for the single-mode fiber is greater than 12 dB. As turbulence increases, the floating ranges of coupling power for the six-mode fiber and single-mode fiber increase by 13 dB and 22 dB, respectively. However, when D/r0 = 16.6, there is no increase in the floating range of coupling efficiency of the fiber.

 figure: Fig. 6.

Fig. 6. Scatter plot of instantaneous received power for a six-mode fiber versus a single-mode fiber, where the turbulence intensity (a) D/r0 = 3.04, (b) D/r0 = 5.1, (c) D/r0 = 9.37, (d) D/r0 = 16.6

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Table 1 shows the average link loss with relative standard deviation (RSD) for the experimental system using SMF and six-mode fibre reception at several turbulence intensities. At, the link loss of the space laser communication system with FMF is reduced by 3.8 dB compared to that with SMF. The efficiency of the FMF enhancement increases with increasing turbulence, and FMF reduces the link loss by 6.6 dB compared to SMF at D/r0 = 9.37, however, the performance enhancement of FMF relative to SMF is 6 dB at D/r0 = 16.6 which is slightly lower than that at D/r0 = 9.37. This is due, on the one hand, to the dominant influence of the aperture effect of the system at saturated strong turbulence and, on the other hand, to the fact that at saturated strong turbulence a single phase screen is difficult to fully simulate the effect of atmospheric turbulence on the phase of the optical wave, which often requires the use of multiple turbulent phase screen modulations to solve the problem. The relative standard deviation measures the relative magnitude of the data fluctuations which, at times, is 37% lower for the FMF at 0.44 than for the SMF. At D/r0 = 5.1, 9.37 and 16.6, the magnitude of the fluctuations was reduced by 40%, 33% and 45.3% respectively. Therefore, the space laser communication system using six-mode fibres can greatly improve the coupling efficiency of the system and reduce the depth fading caused by turbulence.

Tables Icon

Table 1. Average Link Loss and Relative Standard Deviation for Six-mode and Single-mode Fibre Reception Systems

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To better analyse the effect of turbulence strength, coupling efficiency and mixing efficiency on the performance of the coupled heterodyne receiving system of the FMF, the few-mode pigtail was connected to the few-mode end of a photonic lantern with high mode purity, as well as measuring the individual mode distribution states of the output and calculating the ideal mixing efficiency. Figure 7(a) represents the scatter plot of the output power of each mode for different turbulence conditions. When D/r0 = 3.04, the six-mode signal optical power fluctuates from -20dBm to -40dBm, while the power is mainly concentrated in the LP01 mode. As the turbulence increases, although the overall coupling power decreases, the power distribution of each mode is relatively dispersed, with the coupling power of higher-order modes starting to increase. The ideal mixing efficiency estimated by the third term in Eq. (13) is shown in Fig. 7(b). The mixing efficiency fluctuates between 0.5 and 0.8 when D/r0 = 3.04, then between 0.7 and 1 when the turbulence increases. Corresponding average mixing efficiency estimates are shown in Table 2, D/r0 = 3.04, the average mixing efficiency is 0.67, as turbulence increases the higher-order mode coupling efficiency increases, resulting in an increase in mixing efficiency.

 figure: Fig. 7.

Fig. 7. Scatterplot of (a) the power distribution of each mode measured under different turbulence and (b) the scatterplot of the estimated few-mode mixing efficiency

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Table 2. Average mixing efficiency at different turbulence intensities

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We then measured the performance of the communication system. The constellation diagrams and corresponding BERs of the few-mode heterodyne receiver and single-mode heterodyne receiver are shown in Fig. 8 for the first four moments when the power at the transmitter is -14dBm and at weak turbulence (D/r0 = 3.04) and strong turbulence (D/r0 = 9.36). Figure 8(a) shows the BER for D/r0 = 3.04. The BERs for both the few-mode heterodyne receiver and the single-mode heterodyne receiver are less than 10-4 orders of magnitude, and the BER fluctuations in the side-by-side comparison are not significant within one order of magnitude, which is attributed to the small power fluctuations caused by turbulence in the weak turbulence case. Figure 8(b) shows the results for D/r0 = 9.36, where the enhanced turbulence leads to an increase in the BER of the system; in the vertical comparison, the BER of the few-mode heterodyne receiver is lower than that of the single-mode heterodyne receiver, e.g. the few-mode heterodyne receiver improves the performance by two orders of magnitude at the first sampling moment, and by about one order of magnitude at the third and fourth sampling moments. This indicates that the few-mode heterodyne receiver can effectively combat the deep fading caused by moderately strong turbulence. In a longitudinal comparison, the BERs of the few-mode heterodyne receivers are all lower than those of the single-mode heterodyne receivers. This shows that the few-mode heterodyne receiver can effectively combat the deep fading caused by moderately strong turbulence, which is in line with the performance analysis in the previous section.

 figure: Fig. 8.

Fig. 8. Set of constellation plots of heterodyne detection with corresponding BER for QPSK signals at turbulence intensity (a) D/r0 = 3.04 and (b) D/r0 = 9.36

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This paper will verify the effectiveness of an few-mode coherent receiver in a space laser communication system in two aspects. Firstly, the average BER of the few-mode coherent receiver is tested under a simulated turbulent channel, comparing its performance with that of a single-mode heterodyne receiver under the same conditions. At the same time, the interruption probability is an important indicator of the stability of space laser communication systems. The paper compares the interruption probability of the proposed receiver with that of a single-mode heterodyne receiver by measuring 100 repetitions of the test under typical turbulent conditions.

The performance of space laser communications has a direct impact on the power budget at the transmitter side which is directly relevant for designing systems, achieving stable space laser communications and reducing costs. For this reason, the experiments were conducted by measuring the average BER and interruption probability of the system at different transmitting powers. The sampled data was processed offline, as shown in Fig. 9, which plots the average BER of the system with respect to transmit power for atmospheric conditions D/r0 = 3.04, 5.07, 9.36 and 16.6. At D/r0 = 3.04, in the high BER region (BER = 3.8×10−3), the BER curves for the few-mode heterodyne receiver are essentially the same as those for the single-mode heterodyne receiver, where the average BER of the few-mode heterodyne receiver improves relative to the single-mode scheme as the transmit power increases. As the turbulence intensity increases to D/r0 = 5.07, 9.36 and 16.6 and the system reaches BER = 3.8×10−3, the few-mode heterodyne receiver scheme requires 3.8dB, 5.9dB and 5dB less transmit power than the single-mode heterodyne receiver scheme.Experimental results show that the use of a heterodyne receiver with FMF can effectively improve the performance of the communication system under moderate to strong turbulence conditions, as the FMF coupling can effectively mitigate the deep fading caused by turbulence.

 figure: Fig. 9.

Fig. 9. BER and transmitted power curves for space laser communication based on heterodyne detection reception. SMF denotes single-mode heterodyne receiver, FMF denotes few-mode heterodyne receiver

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Figure 10 shows the interruption probability curve for the communication system as a function of transmitted optical power. Similar to the average BER curve, the interruption probability curve for the few-mode heterodyne receiver differs slightly from that of the single-mode heterodyne receiver when D/r0 = 3.04.As in the previous section, this is mainly due to the lower coupling efficiency gain of the FMF under weak turbulence and the lower power of the excited higher-order modes, which leads to a reduction in mixing efficiency and ultimately to a small performance difference between the few-mode heterodyne receiver and the single-mode heterodyne receiver.However, when D/r0 = 5.07, 9.36 and 16.6, the proposed scheme reduces the transmit power by 4.5dB, 6.2dB and 4.8dB compared to the single-mode heterodyne receiver scheme when the interruption probability is observed to be 4×10−2 cases.

 figure: Fig. 10.

Fig. 10. Interruption probability versus transmitted power curve for space laser communication based on heterodyne detection reception. SMF denotes single-mode heterodyne receiver, FMF denotes few-mode heterodyne receiver

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5. Conclusion

This paper presents an in-depth study of FSO communication based on few-mode heterodyne reception technology, deriving the overall efficiency, mixing efficiency and coupling efficiency of the few-mode heterodyne receiver.The relationship between the distribution of the overall efficiency and the number of modes under turbulent conditions is derived, providing a theoretical basis for the design of a few-mode heterodyne receiver. In this paper, the turbulence resistance of the few-mode heterodyne receiver scheme is demonstrated in detail, with experimental analysis in terms of both BER and interruption probability. To verify the feasibility of the proposed scheme, we propose an heterodyne receiver based on the Kramers-Kronig relationship for few-mode heterodyne reception without frequency and phase locking of the local oscillation light to the signal light.Finally, an experimental system is built to verify the advantages of few-mode heterodyne reception under turbulent conditions. The proposed scheme improves the power budget by 4∼5 dB over the single-mode heterodyne receiver at BER = 3.8×10−3 under moderate to strong turbulence conditions, respectively. In terms of interruption probability, gains of 6.2dB and 4.8dB are achieved when the interruption probability is 4×10−2 and D/r0 = 9.36 and 16.6, respectively.

Funding

Department of Science and Technology of Jilin Province (20200401051GX, 20210201096GX); National Natural Science Foundation of China (62075080).

Disclosures

The authors declare there are no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

References

1. V. W. S. Chan, “Free-space optical communications,” J. Light. Technol. 24(12), 4750–4762 (2006). [CrossRef]  

2. M. L. Stevens, R. R. Parenti, M. M. Willis, J. A. Greco, F. I. Khatri, B. S. Robinson, and D. M. Boroson, “The lunar laser communication demonstration time-of-flight measurement system: overview, on-orbit performance, and ranging analysis,” Proc. SPIE 9739, 973908 (2016). [CrossRef]  

3. H. Hemmati, A. Biswas, and I. B. Djordjevic, “Deep-Space Optical Communications: Future Perspectives and Applications,” Proc. IEEE 99(11), 2020–2039 (2011). [CrossRef]  

4. D. M. Boroson and B. S. Robinson, “The Lunar Laser Communication Demonstration: NASA’s First Step Toward Very High Data Rate Support of Science and Exploration Missions,” Space Sci. Rev. 185(1-4), 115–128 (2014). [CrossRef]  

5. Y. Bian, Y. Li, E. Chen, W. Li, X. Hong, J. Qiu, and J. Wu, “Free-space to single-mode fiber coupling efficiency with optical system aberration and fiber positioning error under atmospheric turbulence,” J. Opt. 24(2), 025703 (2022). [CrossRef]  

6. Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44(23), 4946–4952 (2005). [CrossRef]  

7. J. D. Strasburg and W. W. Harper, “Impact of atmospheric turbulence on beam propagation,” Proc. SPIE 5413, 93–102 (2004). [CrossRef]  

8. M. Chen, C. Liu, and H. Xian, “Experimental demonstration of single mode fiber coupling over relatively strong turbulence with adaptive optics,” Appl. Opt. 54(29), 8722–8726 (2015). [CrossRef]  

9. S. Li and W. Jian, “Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics,” Opt. Lett. 41(7), 1482–1485 (2016). [CrossRef]  

10. D. Zheng, Y. Li, B. Li, W. Li, E. Chen, and J. Wu, “Free Space to Few-Mode Fiber Coupling Efficiency improvement with Adaptive Optics under Atmospheric Turbulence,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Th3C.2.

11. L. Tan, Y. Chen, L. Zhao, S. Yu, and J. Ma, “Optimal coupling condition analysis of free-space optical communication receiver based on few-mode fiber,” Opt. Fiber Technol. 53, 102004 (2019). [CrossRef]  

12. D. Zheng, Y. Li, E. Chen, B. Li, D. Kong, W. Li, and J. Wu, “Free-space to few-mode-fiber coupling under atmospheric turbulence,” Opt. Express 24(16), 18739–18744 (2016). [CrossRef]  

13. M. Arikawa and T. Ito, “Performance of mode diversity reception of a polarization-division-multiplexed signal for free-space optical communication under atmospheric turbulence,” Opt. Express 26(22), 28263–28276 (2018). [CrossRef]  

14. Y. Wu, S. Shao, Y. Li, X. Chen, D. Che, J. Chen, K. Du, R. Jiang, X. Huang, and D. Kan, “Multi-beam optical phase array for long-range LiDAR and free-space data communication,” Opt. Laser Technol. 151, 108027 (2022). [CrossRef]  

15. A. Fardoost, F. G. Vanani, H. Wen, and G. Li, “Few-Mode Frequency-Modulated LiDAR Receivers,” Opt. Lett. 45(11), 3127–3130 (2020). [CrossRef]  

16. Kikuchi and Kazuro, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express 8(20), 1642–1662 (2011). [CrossRef]  

17. K. N. Li, J. Ma, L. Y. Tan, S. Y. Yu, and C. Zhai, “Performance analysis of fiber-based free-space optical communications with coherent detection spatial diversity,” Appl. Opt. 55(17), 4649–4656 (2016). [CrossRef]  

18. H. Zhang, L. Liu, J. Xie, S. Zhao, C. Li, T. Wang, and J. Guo, “The performance of heterodyne detection system for partially coherent beams in turbulent atmosphere,” Opt. Commun. 356, 620–627 (2015). [CrossRef]  

19. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008). [CrossRef]  

20. .D. M. Boroson, A. Biswas, and B. L. Edwards, “MLCD: overview of NASA's Mars laser communications demonstration system,” Proc. SPIE 5338, 16–28 (2004). [CrossRef]  

21. J. Davis and W. J. Tango, “Measurement of the Atmospheric Coherence Time,” Publ. Astron. Soc. Pac. 108(723), 456–458 (1996). [CrossRef]  

Data availability

No data were generated or analyzed in the presented research.

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Figures (10)
Fig. 1.
Fig. 1. Few-mode heterodyne coherent detection.

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Fig. 2.
Fig. 2. The receiver system based on FMF.

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Fig. 3.
Fig. 3. Non-Mode-Selective Photonic Lantern.

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Fig. 4.
Fig. 4. Coupler based on FMF.

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Fig. 5.
Fig. 5. Block diagram of the experimental system for (a) few-mode heterodyne detection (b) single-mode heterodyne detection of QPSK signals.

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Fig. 6.
Fig. 6. Scatter plot of instantaneous received power for a six-mode fiber versus a single-mode fiber, where the turbulence intensity (a) D/r0 = 3.04, (b) D/r0 = 5.1, (c) D/r0 = 9.37, (d) D/r0 = 16.6

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Fig. 7.
Fig. 7. Scatterplot of (a) the power distribution of each mode measured under different turbulence and (b) the scatterplot of the estimated few-mode mixing efficiency

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Fig. 8.
Fig. 8. Set of constellation plots of heterodyne detection with corresponding BER for QPSK signals at turbulence intensity (a) D/r0 = 3.04 and (b) D/r0 = 9.36

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Fig. 9.
Fig. 9. BER and transmitted power curves for space laser communication based on heterodyne detection reception. SMF denotes single-mode heterodyne receiver, FMF denotes few-mode heterodyne receiver

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Fig. 10.
Fig. 10. Interruption probability versus transmitted power curve for space laser communication based on heterodyne detection reception. SMF denotes single-mode heterodyne receiver, FMF denotes few-mode heterodyne receiver

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Tables (2)

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Table 1. Average Link Loss and Relative Standard Deviation for Six-mode and Single-mode Fibre Reception Systems

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Table 2. Average mixing efficiency at different turbulence intensities

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Equations (17)

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η i = | ∫ ∞ U f ∗ E i d B | 2 ∫ ∞ | U f | 2 d B ∫ ∞ | E i | 2 d B .
E 1 = ∑ i = 1 M E 1 , i = 1 2 ∑ i = 1 M ( E S , i + j E L O , i ) , E 2 = ∑ i = 1 M E 2 , i = 1 2 ∑ i = 1 M ( j E S , i + E L O , i ) .
U fib ( r , φ ; t ) = ∑ i = 1 M A s , i E i ( r , φ ) e j ( ω 0 t + θ ) ,
U L O ( r , φ ; t ) = ∑ i = 1 M A L , i E i ( r , φ ) e j ( ω 1 t ) ,
P s = ∑ i = 1 M | A s , i | 2 = ∑ i = 1 M P s , i ,
P L = ∑ i = 1 M | A L , i | 2 = ∑ i = 1 M P L , i ,
∑ i = 1 N a i = 1 ,   0 ≤ a i ≤ 1 ,   i = 1 , 2 , … , M ,
I b e a t ( t ) = ∫ ∫ U f i b ( r , φ ; t ) U L O ∗ ( r , φ ; t ) d r d φ .
y ( t ) = Re [ R I b e a t ( t ) ] = Re [ ∫ ∫ ∑ k = 1 M ∑ l = 1 M R A s , l A L , k ∗ E l ( r , φ ) E k ∗ ( r , φ ) e j ( Δ ω + θ ) d r d φ ] = R ∑ k = 1 M A s , k A L , k ∗ cos ⁡ ( Δ ω + θ ) ,
P S I F = [ | y ( t ) | 2 ] = R 2 ∑ k = 1 M A s , k A L , k ∗ ∑ l = 1 M A s , l A L , l ∗ = R 2 P L P s ∑ k = 1 M ∑ l = 1 M b k b l a k a l ,
P S I F = R 2 P L P s M ∑ k = 1 M ∑ l = 1 M a k a l ,
P n = q R B ∫ ∫ | U L O ( r , φ ; t ) | 2 d r d φ   = q R B P L ,
γ F M F = P S I F P n   = R P s q B M ∑ k = 1 M ∑ l = 1 M a k a l   = R A I q B { P s A I } { 1 M ∑ k = 1 M ∑ l = 1 M a k a l } ,
γ F M F = R A I q B η F ζ F ,
γ ¯ F = E [ R A I q B { P s A I } { 1 M ∑ k = 1 M ∑ l = 1 M a k a l } ]   = R A q B η ¯ F ζ ¯ F ,
γ S M F = R A I q B η s ζ s ,
γ ¯ S M F = R A q B η ¯ S ζ ¯ S .
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