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Free-space optical communication with perfect optical vortex beams multiplexing
Optics Communications 427 (2018) 545–550
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Free-space optical communication with perfect optical vortex beams multiplexing Wei Shao a,b , Sujuan Huang a, *, Xianpeng Liu a , Musheng Chen a a
Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, 200072, China b School of Electronics and Information, Nantong University, Nantong, 226019, China
ARTICLE
INFO
Keywords: Perfect optical vortex Free-space optical communication Spatial light modulator
ABSTRACT We demonstrate a 2-channel orbital angular momentum (OAM) multiplexed free space optical communication (FSO) link using perfect optical vortex (POV) beams. POV beams are able to be transmitted coaxially over than 1m with the assistance of a microscope objective and normal lens. 16QAM-OFDM signals are used to measure the performance, which is also compared with the FSO link based on Laguerre–Gaussian (LG) vortex beams multiplexing in the same experimental environment. The results show that, the FSO link employing POVs multiplexing can bring a better performance to the system, which can always obtain a lower BER under the same received power; The using of POVs as carriers greatly reduces the systems’ sensitivity to the change of OAM topological charge numbers; And the constant diameter of POVs is also improve the versatility of the optical devices of different channels in the system.
1. Introduction Attention has been paid to the expansion of transmission capacity of a free-space optical communication system (FSO) since the unabated exponential growth in data traffic. To break the coming capacity crunch, it is highly desirable to exploit additional degrees of freedom for the conveyance of information, since those already well-known physical dimensions (e.g. time, frequency/wavelength, amplitude, phase, polarization) have been studied plentifully [1]. Fortunately, orbital angular momentum (OAM) offers us such a promising prospect in optical communication. It has been suggested that the infinite OAM eigenstates can enable a single photon to carry unlimited amount of information [2,3]. At macroscopic level, an OAM carrying beam could refer to any helically phased light beam, irrespective of its radial distribution [4]. In general, these beams are known as optical vortex (OV) beams. As pointed out in [5], OV beams can serve as carriers of information in FSO communication with great security advantages. However, when using the LG vortex beams as carriers [6–12], it is almost impossible to realize the above-mentioned ‘‘the infinite OAM eigenstates can enable a single photon to carry unlimited amount of information’’ in free-space. In practice, the LG vortex beam with larger topological charge can hardly be utilized. The root cause of this limitation is the nature of the LG vortex beam: The ring radius expends
with an increase of topological charge. This will bring two troubles to practical applications. On one hand, this property might be detrimental when coupling multiple vortex beams into a communication system, which contains some elements with a fixed annular index profile [13– 15]. On the other hand, it is related to the generation method of LG vortex beams. Nowadays, the spatial light modulator (SLM) technology provides the most common and convenient way to obtain the OV by its diffraction field. It is difficult to obtain the +1 diffraction order OV with a high energy efficiency and quality even if we have introduced digital blazed gratings in holograms, all of these are limited by the current SLM pixel size. For a LG vortex with a large topological charge, the situation will be even worse [16]. When the diffraction distance is constant, due to the larger diameter, we need to increase the diffraction angle to separate the various diffraction orders in the light field so as to avoid the overlapping between them, this will further deteriorate its energy efficiency and quality. And we have discussed the influence of the SLM pixel size on the OV diffraction angle and diffraction energy efficiency in detail in our related work [17]. In addition, the sidelobes of the LG vortex beam are also undesirable to the practical applications. Therefore, the ideal vortex beam should have a diameter that does not vary with the number of topological charges and is ‘‘pure’’ without sidelobes. Fortunately, the perfect vortex meets these conditions.
* Correspondence to: School of Communication and Information Engineering, Key Laboratory of Special Fiber Optics and Optical Access Networks, Shanghai University Shanghai, 200072, China. E-mail address: [email protected] (S. Huang).
https://doi.org/10.1016/j.optcom.2018.06.079 Received 15 May 2018; Received in revised form 24 June 2018; Accepted 25 June 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
W. Shao et al.
Optics Communications 427 (2018) 545–550
The concept of a perfect optical vortex (POV) beam was first proposed by Ostrovsky et al. in 2013 [18]. It is a pure aura whose dark hollow radius does not depend on topological charge. In 2014, an improved technique based on the width-pulse approximation of the Bessel function was proposed to generate POV beams [19]. In 2015, Vaity et al. derived a mathematical description of a POV beam as the Fourier transformation of a Bessel beam [20]. POV beams have successfully helped Brunet et al. to obtain better coupling efficiency with fiber with annular index profiles [21,22]. In our previous study, we firstly verified the feasibility of the POV for FSO and established a single communication link [23]. It has come to our knowledge that no more research on free-space optical communication using perfect optical vortex beams has been reported so far except for our earlier work. In this paper, we demonstrate a 2-channel OAM multiplexed free space optical communication link using POV beams. In our system, POV beams, generated by spatial light modulator loaded with phase holograms based on Bessel function, transmit coaxially over than 1m with the assistance of a microscope objective and normal lens. We compare our communication link with the traditional FSO based on LG vortex beams. 16QAM-OFDM signals are used to measure their performance. The constellations of OFDM subcarriers and the BER of system are shown respectively. And the performance comparison of these two kinds of links is given under the condition of the same receive power. 2. Theory of perfect optical vortex As mentioned earlier, the POV is a new kind of optical vortex whose diameter is independent of its topological charge. Based on the theory proposed in [19], POVs can be generated approximately through a Fourier transformation from Bessel–Gauss (BG) beams. A BG beam with the transverse distribution of complex amplitude reads [24] 𝐸(𝜌, 𝜑) = 𝐽𝑙 (𝑘𝑟 𝜌) exp(
−𝜌2 𝜔20
) exp(𝑖𝑙𝜑)
(1)
where 𝐽𝑙 is an 𝑙th order Bessel function of first kind, l is also the topological charge, 𝜔0 corresponds to the waist radius of the Gaussian beam that confines the BG beam, and 𝑘𝑟 is the radial wave vector. After BG beams passing through a Fourier lens (FL), optical fields can be written as ( ) ∞ 2𝜋 𝑘 𝑖𝑘 𝐸(𝑟, 𝜃) = 𝐸(𝜌, 𝜑)𝜌𝑑𝜌𝑑𝜑 exp − 𝑟𝜌 cos(𝜃 − 𝜑) (2) 2𝜋𝑓 𝑖 ∫0 ∫0 𝑓
Fig. 1. (a) The setup of perfect optical vortices’ generation. TL, tunable laser; Col, collimator; Pol, polarizer; HWP, half-wave plate; SLM, spatial light modulator. (b) Holograms of BG beams and perfect optical vortices by them.
When 𝜔=2f /k𝜔0 is an extremely small value, exp(2𝑟0 r/𝜔2 ) can be regarded as an approximation of Dirac 𝛿-function. Then, Eq. (6) will be highly according with the ideal model of POVs proposed by [10]. We performed numerical simulations of POVs based on the mathematical model provided by Eq. (6). For the POV, diameter is the only parameter of its physical size, so we can adjust it by setting the value of radial wave vector 𝑘𝑟 directly. In this paper, the 𝑘𝑟 value of all POVs are set as 6.3. Fig. 1(a) shows the setup of POVs generating, we firstly generate a BG beam with a controllable kr, and then convert it into a POV beam by using a FL, the CCD is placed at the focus of the FL. The results of numerical simulations and experiments are given in Fig. 1(b). It can be seen that the diameter of the POV beam does not change with the topology charge.
and this expression can be simplified as 𝐸(𝑟, 𝜃) = 𝑖𝑙−1
−𝑟2 + 𝑟20 𝜔0 2𝑟 𝑟 )𝐼𝑙 ( 0 ) exp(𝑖𝑙𝜃) exp( 𝜔 𝜔2 𝜔2
(3)
where 𝜔=2f /𝑘𝑤0 is the width of the annular ring, k =2𝜋/𝜆 is the wave vector and 𝐼𝑙 is the 𝑙th order modified Bessel function of first kind. The parameter 𝑟0, the ring radius of the perfect vortex beam, can be expressed as 𝑟0 =
𝑘𝑟 𝑓 𝜆𝑓 = √ 𝑘 𝑑 2 + 𝜆2
(4)
with 𝑘𝑟 the radial wave vector, d the axicon period and 𝜆 the wavelength. In practice, 𝑑 2 ≫ 𝜆2 , Eq. (4) can be rewritten as
3. Free space optical link based on POVs multiplexing
𝜆𝑓 (5) 𝑑 It illustrates that, the radius of a POV is determined by the wavelength, focal length of the lens, and the axicon period, and it is independent of its topological charge. Notice that, Eq. (3) shows the Fourier plane locating at the focus point of the lens. Thus, 𝑟 = 𝑟0 and 𝐼𝑙 (2𝑟0 r/𝜔2 ) can be approximated to exp(2𝑟0 r/𝜔2 ) [9]. Eq. (3) can be further simplified as 𝑟0 =
𝐸(𝑟, 𝜃) = 𝐴 exp(𝑖𝑙𝜃) exp(
2𝑟20 𝜔2
)
The 2-channel OAM (de)multiplexed free space optical link using POV beams is illustrated in Fig. 2, and the total optical length of our experimental setup is 160 cm. The collimator (Col.) converts the optical signal transmitted from a polarization maintaining fiber (PMF) to a Gaussian beam 4.6 mm in diameter. Then the Gaussian beam filtered linearly by a polarizer (Pol.) irradiates the SLM loading a phase hologram based on Bessel function to generate a BG beam. And Fourier lens is used to transform BG beams to POV beams. It should be noted that the focal points of FL-1 and FL-2 must coincide and the microscope objectives
(6) 546
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Optics Communications 427 (2018) 545–550
Fig. 2. A 2-channel OAM (de)multiplexed free space optical link using POV beams: PMF, polarization maintaining fiber; Col, collimator; Pol, polarizer; SLM, spatial light modulator; BS, beam splitter; FL, Fourier lens; MO, microscope objectives; SMF, single mode fiber. Table 1 Parameters of OFDM system.
should (MO) be placed at this common focal point. The MO and the lens behind collimate the coaxial superposition of two POV beams to transmit a certain distance. The principle and the optical setup of the demultiplexing part are same with the correspondence based on LG vortex beams. In this part of the optical link, the coaxially superimposed beams are indifferently divided into two duplications by a beam splitter (BS), and they are sent to the SLM loading the opposite topological hologram with spiral phase pattern for demodulation. The demodulated Gaussian spots are coupled into the single mode fibers (SMF) and sent to the subsequent part for further photoelectric conversion and digital signal processing. We supervise the transmission of POV beams from ‘‘MO’’ to ‘‘SLM3’’/ ‘‘SLM4’’ (the distance is 104 cm) in the link with the help of an IR CCD. Take the multiplexing of topological charge number 𝑙 = 2 and 𝑙 = 5 for example, their profiles, before propagation and after propagation, are shown in Fig. 3(a) and (b) respectively. Although the waists of POVs with different topological charge numbers have a certain width after propagated a distance in space, they still maintain a consistent relative size. The greatly different from the hybrid optical lattice formed by the LG vortex beams, their coaxial superposition is still a ring but with equally spaced breakpoints caused by phase jump. The number of breakpoints is determined by ||𝑙1 − 𝑙2 ||. This brings a biggest benefit to the receiver: there is no need to choose optical elements with different parameters for different topological charge numbers. The two figures in Fig. 3(c) are taken at the positions behind SLM-3 and SLM-4 respectively. The coaxially superimposed beams are demodulated by the spiral phase pattern holograms with opposite topological charges 𝑙 = −2 and 𝑙 = −5, and generate the corresponding Gaussian spots. The above results show that information can be correctly modulated, transmitted and demodulated in this POVs multiplexing based FSO link.
Parameters
Value
OFDM modulation format Number of effective subcarriers IFFT/FFT CP length Sampling rate of AWG Data rate Optical detector bandwidth Sampling rate of Oscilloscope
16-QAM 28 64 8 2 GS/s 3.05 Gb/s 1 GHz 2 GS/s
In the experiment, we test two groups of topological charges. One group is smaller (𝑙 = 2 and 𝑙 = 5), and the other is larger (𝑙 = 17 and 𝑙 = 20). The relevant parameters of OFDM-16QAM signals for our communication experiments are listed in Table 1. The constellation diagram of the received signal can intuitively reflect the performance difference that POVs and LG vortex beams bring to the communication system. We randomly select 4 subcarriers (3, 11, 20, 26) and display their constellations in Fig. 5, (a) and (b) are the case of multiplexing with small topological charges numbers and large topological charges numbers respectively, when the received power is −15 dBm. Different colors (blue and red) are used to distinguish the results of different signal carriers (POVs or LG vortex beams) transmitted in the FSO. When comparing the two corresponding constellation diagrams, it is not difficult to find that the profiles of the scatter distribution of the received signal under the same subcarrier are similar, but the constellation diagrams are cleaner when POVs are used as carriers. Fig. 6 shows the mean BER measurements of all subcarriers as a function of received optical power. Notice that we use logarithmic coordinates here. For smaller topology charge numbers, when the received power is greater than the FEC threshold, the advantage of the POV for the LG vortex beam is not very obvious, and the BER of the two are basically in the same order of magnitude. However, when the received power is reduced to −17 dBm, the signals transmitted by POV can still be correctly received by the system through FEC; at the same time, the BER of the LG vortex beam signal has far exceeded the FEC threshold. All above are illustrated in Fig. 6(a). While, Fig. 6(b) shows that, when the topological charges number are larger, the BER of multiplexing of POVs are generally an order of magnitude lower than LG vortex beams at any of the same received power. The comparison of graphs (a) and (b) shows that, with the increasing of LG vortex beams’ topological charge numbers, the BER of the system will deteriorate rapidly. However, the system is less sensitive to the change of the topological charge numbers when POVs are multiplexed. It can be asserted that the performance of FSO employing POVs multiplexing is better than the correspondence of LG vortex beams multiplexed FSO.
4. Experiments and results In this chapter, we test the performance of our FSO link and compare it with the traditional FSO link based on LG vortex beams multiplexing. Due to the difference in power loss of each channel between the two caused by the incompletely identical link structure, in this paper, we only compare the performance of them at the same received power. (The power loss range of each channel in LG-OV based link is 9.20–9.31 mW, and this range in POV based link is 10.36–10.43 mW). The setup of the entire experimental communication system is shown in Fig. 4. In the signal transmission section, OFDM-16QAM signals are sent to laser for electrooptical modulation by an arbitrary waveform generator (AWG). And then, data-carrying beams are transmitted to our FOS link by the polarization maintaining fibers (PMF). In FSO link, signals in two different channels will be transmitted coaxially in the form of POVs. In the signal receiving unit, the detectors obtain the spatially demodulated signals passing by single mode fibers (SMF), and an oscilloscope (OSC) is used to collect the information for digital signal processing (DSP). 547
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Optics Communications 427 (2018) 545–550
Fig. 3. POVs in propagation in the FSO link: (a) before propagation, and (b) after propagation; (c) the demodulated Gaussian spots.
Fig. 4. Experimental communication system with FSO link based on POVs (de)multiplexing.
5. Conclusions
bring a better performance to the system than the corresponding link based on LG vortex beams multiplexing; the system can always obtain a lower BER when the received power are the same. At the same time, the using of POVs as carriers greatly reduces the systems’ sensitivity to the change of OAM topological charge number, the increasing of topological charge number will not bring a rapid deterioration to the system performance. Also benefiting from the constant diameter of POVs, the system does not need to select optics with specific parameters for optical vortices with different topological charge numbers during transmission and reception; therefore, the versatility of the optical devices of different channels in the system has been significantly improved. Compared with the LG vortex beams, the characteristics of POVs can extend the range
In this paper, we have demonstrated a 2-channel OAM multiplexed free space optical communication link using POV beams. In our link, perfect vortex beams are generated by a SLM loaded with phase holograms based on Bessel function with the assistance of a FL, transmitted coaxially over than 1m with the assistance of a microscope objective and normal lens, and finally are indifferently divided into two duplications for demodulation. 16QAM-OFDM signals are used to test the performance of our link. It is also compared with the traditional FSO based on LG vortex beams multiplexing in the same experimental environment. The results show that, the FSO link employing POVs multiplexing can 548
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Optics Communications 427 (2018) 545–550
Fig. 5. Constellation diagram of subcarrier 3, 11, 20, 26, with a −15 dBm received power, (a) 𝑙 = 2 & 𝑙 = 5 (de)multiplexing and (b) 𝑙 = 17 & 𝑙 = 20 (de)multiplexing.
Fig. 6. BER measurements for demodulation of 16QAM-OFDM signals.
of multiplexing of the topological charge to a certain extent. We believe, the FSO link based on POVs multiplexing has great potential in the freespace optical communication field.
[5] G. Gibson, J. Courtial, M.J. Padgett, M. Vasnetsov, V. Pas’ko, S.M. Barnett, S. FrankeArnold, Free-space information transfer using light beams carrying orbital angular momentum, Opt. Express 12 (22) (2004) 5448–5456. [6] Z. Wang, N. Zhang, X. Yuan, High-volume optical vortex multiplexing and demultiplexing for free-space optical communication, Opt. Express 19 (2) (2011) 482– 492. [7] N. Bozinovic, P. Kristensen, S. Ramachandran, Long-range fiber-transmission of photons with orbital angular momentum, in: CLEO: Science and Innovations, Optical Society of America, 2011 (CTuB1). [8] S. Golowich, P. Kristensen, N. Bozinovic, P. Gregg, S. Ramachandran, Fibers supporting orbital angular momentum states for information capacity scaling, in: Frontiers in Optics, Optical Society of America, 2012, pp. FW2D–FW22. [9] S. Ramachandran, P. Kristensen, Optical vortex beam in fiber, Nanophotonics 2 (5–6) (2013) 455–474. [10] H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, S.J. Dolinar, 100 Tbit/s freespace data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength, Opt. Lett. 39 (2) (2014) 197–200. [11] Y. Yan, G. Xie, M.P. Lavery, H. Huang, N. Ahmed, C. Bao, A.F. Molisch, Highcapacity millimetre-wave communications with orbital angular momentum multiplexing, Nature Commun. (2014) 5.
Acknowledgments This work is supported in part by NSFC under Grant No. 61475098, Shanghai Science and the Shanghai Science and Technology Commission Research Plan under Grant No. 14440500100. References [1] I.B. Djordjevic, et al., Opt. Express 18 (13) (2010). [2] L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45 (11) (1992) 8185–8189. [3] S. Franke-Arnold, L. Allen, M. Padgett, Advances in optical angular momentum, Laser Photonics Rev. 2 (4) (2008) 299–313. [4] A.E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, J. Wang, Optical communications using orbital angular momentum beams, Adv. Opt. Photonics 7 (1) (2015) 66–106.
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Optics Communications 427 (2018) 545–550 [19] J. García, C.R. Parrao, A.S. Ostrovsky, Simple technique for the perfect vortex generation, in: Latin America Optics and Photonics Conference, Opt. Soc. Am., 2014 (LTu4A. 10). [20] P. Vaity, L. Rusch, Perfect vortex beam: Fourier transformation of a Bessel beam, Opt. Lett. 40 (4) (2015) 597–600. [21] C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, L.A. Rusch, Design, Fabrication and validation of an OAM fiber supporting 36 states, Opt. Express 22 (21) (2014) 26117–26127. [22] C. Brunet, B. Ung, L. Wang, Y. Messaddeq, S. LaRochelle, L.A. Rusch, Design of a family of ring-core fibers for OAM transmission studies, Opt. Express 23 (8) (2015) 10553–10563. [23] F. Zhu, S. Huang, W. Shao, J. Zhang, M. Chen, W. Zhang, Free-space optical communication link using perfect vortex beams carrying orbital angular momentum (OAM), Opt. Commun. 396 (2017) 50–57. [24] F. Gori, G. Guattari, C. Padovani, Bessel-Gauss beams, Opt. Commun. 64 (1987) 491–495.
[12] N. Ahmed, Z. Zhao, L. Li, H. Huang, M.P. Lavery, P. Liao, A. Almaiman, Modedivision-multiplexing of multiple Bessel-Gaussian beams carrying orbitalangularmomentum for obstruction-tolerant free-space optical and millimetre-wave communication links, Sci. Rep. (2016) 6. [13] Y. Yue, Y. Yan, N. Ahmed, J.Y. Yang, L. Zhang, Y. Ren, M. Tur, Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber, IEEE Photon. J. 4 (2) (2012) 535–543. [14] C. Brunet, B. Ung, Y. Messaddeq, S. LaRochelle, E. Bernier, L. Rusch, Design of an optical fiber supporting 16 OAM modes, in: Optical Fiber Communication Conference, Opt. Soc. Am., 2014, pp. Th2A–24. [15] P. Gregg, P. Kristensen, S. Ramachandran, Conservation of orbital angular momentum in air-core optical fibers, Optica 2 (3) (2015) 267–270. [16] L. Janicijevic, et al., Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings, J. Opt. Soc. Amer. 25 (11) (2008) 2659–2669. [17] W. Shao, S. Huang, M. Chen, X. Liu, W. Xie, Research of optical vortex’s energy efficiency and diffraction angle based on spatial light modulator, Opt. Eng. 56 (8) (2017) 086113. [18] A.S. Ostrovsky, C. Rickenstorff-Parrao, V. Arrizón, Generation of the ‘‘perfect’’ optical vortex using a liquid-crystal spatial light modulator, Opt. Lett. 38 (4) (2013) 534–536.
550
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Free-space optical communication with perfect optical vortex beams multiplexing Wei Shao a,b , Sujuan Huang a, *, Xianpeng Liu a , Musheng Chen a a
Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, 200072, China b School of Electronics and Information, Nantong University, Nantong, 226019, China
ARTICLE
INFO
Keywords: Perfect optical vortex Free-space optical communication Spatial light modulator
ABSTRACT We demonstrate a 2-channel orbital angular momentum (OAM) multiplexed free space optical communication (FSO) link using perfect optical vortex (POV) beams. POV beams are able to be transmitted coaxially over than 1m with the assistance of a microscope objective and normal lens. 16QAM-OFDM signals are used to measure the performance, which is also compared with the FSO link based on Laguerre–Gaussian (LG) vortex beams multiplexing in the same experimental environment. The results show that, the FSO link employing POVs multiplexing can bring a better performance to the system, which can always obtain a lower BER under the same received power; The using of POVs as carriers greatly reduces the systems’ sensitivity to the change of OAM topological charge numbers; And the constant diameter of POVs is also improve the versatility of the optical devices of different channels in the system.
1. Introduction Attention has been paid to the expansion of transmission capacity of a free-space optical communication system (FSO) since the unabated exponential growth in data traffic. To break the coming capacity crunch, it is highly desirable to exploit additional degrees of freedom for the conveyance of information, since those already well-known physical dimensions (e.g. time, frequency/wavelength, amplitude, phase, polarization) have been studied plentifully [1]. Fortunately, orbital angular momentum (OAM) offers us such a promising prospect in optical communication. It has been suggested that the infinite OAM eigenstates can enable a single photon to carry unlimited amount of information [2,3]. At macroscopic level, an OAM carrying beam could refer to any helically phased light beam, irrespective of its radial distribution [4]. In general, these beams are known as optical vortex (OV) beams. As pointed out in [5], OV beams can serve as carriers of information in FSO communication with great security advantages. However, when using the LG vortex beams as carriers [6–12], it is almost impossible to realize the above-mentioned ‘‘the infinite OAM eigenstates can enable a single photon to carry unlimited amount of information’’ in free-space. In practice, the LG vortex beam with larger topological charge can hardly be utilized. The root cause of this limitation is the nature of the LG vortex beam: The ring radius expends
with an increase of topological charge. This will bring two troubles to practical applications. On one hand, this property might be detrimental when coupling multiple vortex beams into a communication system, which contains some elements with a fixed annular index profile [13– 15]. On the other hand, it is related to the generation method of LG vortex beams. Nowadays, the spatial light modulator (SLM) technology provides the most common and convenient way to obtain the OV by its diffraction field. It is difficult to obtain the +1 diffraction order OV with a high energy efficiency and quality even if we have introduced digital blazed gratings in holograms, all of these are limited by the current SLM pixel size. For a LG vortex with a large topological charge, the situation will be even worse [16]. When the diffraction distance is constant, due to the larger diameter, we need to increase the diffraction angle to separate the various diffraction orders in the light field so as to avoid the overlapping between them, this will further deteriorate its energy efficiency and quality. And we have discussed the influence of the SLM pixel size on the OV diffraction angle and diffraction energy efficiency in detail in our related work [17]. In addition, the sidelobes of the LG vortex beam are also undesirable to the practical applications. Therefore, the ideal vortex beam should have a diameter that does not vary with the number of topological charges and is ‘‘pure’’ without sidelobes. Fortunately, the perfect vortex meets these conditions.
* Correspondence to: School of Communication and Information Engineering, Key Laboratory of Special Fiber Optics and Optical Access Networks, Shanghai University Shanghai, 200072, China. E-mail address: [email protected] (S. Huang).
https://doi.org/10.1016/j.optcom.2018.06.079 Received 15 May 2018; Received in revised form 24 June 2018; Accepted 25 June 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
W. Shao et al.
Optics Communications 427 (2018) 545–550
The concept of a perfect optical vortex (POV) beam was first proposed by Ostrovsky et al. in 2013 [18]. It is a pure aura whose dark hollow radius does not depend on topological charge. In 2014, an improved technique based on the width-pulse approximation of the Bessel function was proposed to generate POV beams [19]. In 2015, Vaity et al. derived a mathematical description of a POV beam as the Fourier transformation of a Bessel beam [20]. POV beams have successfully helped Brunet et al. to obtain better coupling efficiency with fiber with annular index profiles [21,22]. In our previous study, we firstly verified the feasibility of the POV for FSO and established a single communication link [23]. It has come to our knowledge that no more research on free-space optical communication using perfect optical vortex beams has been reported so far except for our earlier work. In this paper, we demonstrate a 2-channel OAM multiplexed free space optical communication link using POV beams. In our system, POV beams, generated by spatial light modulator loaded with phase holograms based on Bessel function, transmit coaxially over than 1m with the assistance of a microscope objective and normal lens. We compare our communication link with the traditional FSO based on LG vortex beams. 16QAM-OFDM signals are used to measure their performance. The constellations of OFDM subcarriers and the BER of system are shown respectively. And the performance comparison of these two kinds of links is given under the condition of the same receive power. 2. Theory of perfect optical vortex As mentioned earlier, the POV is a new kind of optical vortex whose diameter is independent of its topological charge. Based on the theory proposed in [19], POVs can be generated approximately through a Fourier transformation from Bessel–Gauss (BG) beams. A BG beam with the transverse distribution of complex amplitude reads [24] 𝐸(𝜌, 𝜑) = 𝐽𝑙 (𝑘𝑟 𝜌) exp(
−𝜌2 𝜔20
) exp(𝑖𝑙𝜑)
(1)
where 𝐽𝑙 is an 𝑙th order Bessel function of first kind, l is also the topological charge, 𝜔0 corresponds to the waist radius of the Gaussian beam that confines the BG beam, and 𝑘𝑟 is the radial wave vector. After BG beams passing through a Fourier lens (FL), optical fields can be written as ( ) ∞ 2𝜋 𝑘 𝑖𝑘 𝐸(𝑟, 𝜃) = 𝐸(𝜌, 𝜑)𝜌𝑑𝜌𝑑𝜑 exp − 𝑟𝜌 cos(𝜃 − 𝜑) (2) 2𝜋𝑓 𝑖 ∫0 ∫0 𝑓
Fig. 1. (a) The setup of perfect optical vortices’ generation. TL, tunable laser; Col, collimator; Pol, polarizer; HWP, half-wave plate; SLM, spatial light modulator. (b) Holograms of BG beams and perfect optical vortices by them.
When 𝜔=2f /k𝜔0 is an extremely small value, exp(2𝑟0 r/𝜔2 ) can be regarded as an approximation of Dirac 𝛿-function. Then, Eq. (6) will be highly according with the ideal model of POVs proposed by [10]. We performed numerical simulations of POVs based on the mathematical model provided by Eq. (6). For the POV, diameter is the only parameter of its physical size, so we can adjust it by setting the value of radial wave vector 𝑘𝑟 directly. In this paper, the 𝑘𝑟 value of all POVs are set as 6.3. Fig. 1(a) shows the setup of POVs generating, we firstly generate a BG beam with a controllable kr, and then convert it into a POV beam by using a FL, the CCD is placed at the focus of the FL. The results of numerical simulations and experiments are given in Fig. 1(b). It can be seen that the diameter of the POV beam does not change with the topology charge.
and this expression can be simplified as 𝐸(𝑟, 𝜃) = 𝑖𝑙−1
−𝑟2 + 𝑟20 𝜔0 2𝑟 𝑟 )𝐼𝑙 ( 0 ) exp(𝑖𝑙𝜃) exp( 𝜔 𝜔2 𝜔2
(3)
where 𝜔=2f /𝑘𝑤0 is the width of the annular ring, k =2𝜋/𝜆 is the wave vector and 𝐼𝑙 is the 𝑙th order modified Bessel function of first kind. The parameter 𝑟0, the ring radius of the perfect vortex beam, can be expressed as 𝑟0 =
𝑘𝑟 𝑓 𝜆𝑓 = √ 𝑘 𝑑 2 + 𝜆2
(4)
with 𝑘𝑟 the radial wave vector, d the axicon period and 𝜆 the wavelength. In practice, 𝑑 2 ≫ 𝜆2 , Eq. (4) can be rewritten as
3. Free space optical link based on POVs multiplexing
𝜆𝑓 (5) 𝑑 It illustrates that, the radius of a POV is determined by the wavelength, focal length of the lens, and the axicon period, and it is independent of its topological charge. Notice that, Eq. (3) shows the Fourier plane locating at the focus point of the lens. Thus, 𝑟 = 𝑟0 and 𝐼𝑙 (2𝑟0 r/𝜔2 ) can be approximated to exp(2𝑟0 r/𝜔2 ) [9]. Eq. (3) can be further simplified as 𝑟0 =
𝐸(𝑟, 𝜃) = 𝐴 exp(𝑖𝑙𝜃) exp(
2𝑟20 𝜔2
)
The 2-channel OAM (de)multiplexed free space optical link using POV beams is illustrated in Fig. 2, and the total optical length of our experimental setup is 160 cm. The collimator (Col.) converts the optical signal transmitted from a polarization maintaining fiber (PMF) to a Gaussian beam 4.6 mm in diameter. Then the Gaussian beam filtered linearly by a polarizer (Pol.) irradiates the SLM loading a phase hologram based on Bessel function to generate a BG beam. And Fourier lens is used to transform BG beams to POV beams. It should be noted that the focal points of FL-1 and FL-2 must coincide and the microscope objectives
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Fig. 2. A 2-channel OAM (de)multiplexed free space optical link using POV beams: PMF, polarization maintaining fiber; Col, collimator; Pol, polarizer; SLM, spatial light modulator; BS, beam splitter; FL, Fourier lens; MO, microscope objectives; SMF, single mode fiber. Table 1 Parameters of OFDM system.
should (MO) be placed at this common focal point. The MO and the lens behind collimate the coaxial superposition of two POV beams to transmit a certain distance. The principle and the optical setup of the demultiplexing part are same with the correspondence based on LG vortex beams. In this part of the optical link, the coaxially superimposed beams are indifferently divided into two duplications by a beam splitter (BS), and they are sent to the SLM loading the opposite topological hologram with spiral phase pattern for demodulation. The demodulated Gaussian spots are coupled into the single mode fibers (SMF) and sent to the subsequent part for further photoelectric conversion and digital signal processing. We supervise the transmission of POV beams from ‘‘MO’’ to ‘‘SLM3’’/ ‘‘SLM4’’ (the distance is 104 cm) in the link with the help of an IR CCD. Take the multiplexing of topological charge number 𝑙 = 2 and 𝑙 = 5 for example, their profiles, before propagation and after propagation, are shown in Fig. 3(a) and (b) respectively. Although the waists of POVs with different topological charge numbers have a certain width after propagated a distance in space, they still maintain a consistent relative size. The greatly different from the hybrid optical lattice formed by the LG vortex beams, their coaxial superposition is still a ring but with equally spaced breakpoints caused by phase jump. The number of breakpoints is determined by ||𝑙1 − 𝑙2 ||. This brings a biggest benefit to the receiver: there is no need to choose optical elements with different parameters for different topological charge numbers. The two figures in Fig. 3(c) are taken at the positions behind SLM-3 and SLM-4 respectively. The coaxially superimposed beams are demodulated by the spiral phase pattern holograms with opposite topological charges 𝑙 = −2 and 𝑙 = −5, and generate the corresponding Gaussian spots. The above results show that information can be correctly modulated, transmitted and demodulated in this POVs multiplexing based FSO link.
Parameters
Value
OFDM modulation format Number of effective subcarriers IFFT/FFT CP length Sampling rate of AWG Data rate Optical detector bandwidth Sampling rate of Oscilloscope
16-QAM 28 64 8 2 GS/s 3.05 Gb/s 1 GHz 2 GS/s
In the experiment, we test two groups of topological charges. One group is smaller (𝑙 = 2 and 𝑙 = 5), and the other is larger (𝑙 = 17 and 𝑙 = 20). The relevant parameters of OFDM-16QAM signals for our communication experiments are listed in Table 1. The constellation diagram of the received signal can intuitively reflect the performance difference that POVs and LG vortex beams bring to the communication system. We randomly select 4 subcarriers (3, 11, 20, 26) and display their constellations in Fig. 5, (a) and (b) are the case of multiplexing with small topological charges numbers and large topological charges numbers respectively, when the received power is −15 dBm. Different colors (blue and red) are used to distinguish the results of different signal carriers (POVs or LG vortex beams) transmitted in the FSO. When comparing the two corresponding constellation diagrams, it is not difficult to find that the profiles of the scatter distribution of the received signal under the same subcarrier are similar, but the constellation diagrams are cleaner when POVs are used as carriers. Fig. 6 shows the mean BER measurements of all subcarriers as a function of received optical power. Notice that we use logarithmic coordinates here. For smaller topology charge numbers, when the received power is greater than the FEC threshold, the advantage of the POV for the LG vortex beam is not very obvious, and the BER of the two are basically in the same order of magnitude. However, when the received power is reduced to −17 dBm, the signals transmitted by POV can still be correctly received by the system through FEC; at the same time, the BER of the LG vortex beam signal has far exceeded the FEC threshold. All above are illustrated in Fig. 6(a). While, Fig. 6(b) shows that, when the topological charges number are larger, the BER of multiplexing of POVs are generally an order of magnitude lower than LG vortex beams at any of the same received power. The comparison of graphs (a) and (b) shows that, with the increasing of LG vortex beams’ topological charge numbers, the BER of the system will deteriorate rapidly. However, the system is less sensitive to the change of the topological charge numbers when POVs are multiplexed. It can be asserted that the performance of FSO employing POVs multiplexing is better than the correspondence of LG vortex beams multiplexed FSO.
4. Experiments and results In this chapter, we test the performance of our FSO link and compare it with the traditional FSO link based on LG vortex beams multiplexing. Due to the difference in power loss of each channel between the two caused by the incompletely identical link structure, in this paper, we only compare the performance of them at the same received power. (The power loss range of each channel in LG-OV based link is 9.20–9.31 mW, and this range in POV based link is 10.36–10.43 mW). The setup of the entire experimental communication system is shown in Fig. 4. In the signal transmission section, OFDM-16QAM signals are sent to laser for electrooptical modulation by an arbitrary waveform generator (AWG). And then, data-carrying beams are transmitted to our FOS link by the polarization maintaining fibers (PMF). In FSO link, signals in two different channels will be transmitted coaxially in the form of POVs. In the signal receiving unit, the detectors obtain the spatially demodulated signals passing by single mode fibers (SMF), and an oscilloscope (OSC) is used to collect the information for digital signal processing (DSP). 547
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Fig. 3. POVs in propagation in the FSO link: (a) before propagation, and (b) after propagation; (c) the demodulated Gaussian spots.
Fig. 4. Experimental communication system with FSO link based on POVs (de)multiplexing.
5. Conclusions
bring a better performance to the system than the corresponding link based on LG vortex beams multiplexing; the system can always obtain a lower BER when the received power are the same. At the same time, the using of POVs as carriers greatly reduces the systems’ sensitivity to the change of OAM topological charge number, the increasing of topological charge number will not bring a rapid deterioration to the system performance. Also benefiting from the constant diameter of POVs, the system does not need to select optics with specific parameters for optical vortices with different topological charge numbers during transmission and reception; therefore, the versatility of the optical devices of different channels in the system has been significantly improved. Compared with the LG vortex beams, the characteristics of POVs can extend the range
In this paper, we have demonstrated a 2-channel OAM multiplexed free space optical communication link using POV beams. In our link, perfect vortex beams are generated by a SLM loaded with phase holograms based on Bessel function with the assistance of a FL, transmitted coaxially over than 1m with the assistance of a microscope objective and normal lens, and finally are indifferently divided into two duplications for demodulation. 16QAM-OFDM signals are used to test the performance of our link. It is also compared with the traditional FSO based on LG vortex beams multiplexing in the same experimental environment. The results show that, the FSO link employing POVs multiplexing can 548
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Fig. 5. Constellation diagram of subcarrier 3, 11, 20, 26, with a −15 dBm received power, (a) 𝑙 = 2 & 𝑙 = 5 (de)multiplexing and (b) 𝑙 = 17 & 𝑙 = 20 (de)multiplexing.
Fig. 6. BER measurements for demodulation of 16QAM-OFDM signals.
of multiplexing of the topological charge to a certain extent. We believe, the FSO link based on POVs multiplexing has great potential in the freespace optical communication field.
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