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Encoding and decoding by the states of
vector modes for vortex beams propagating in
air-core fiber
XIAOHUI WANG1,2,* AND YINGXIONG SONG1
1Key Laboratory of Specialty Optics and Optical Access Networks, Shanghai Institute for Advanced
Communication and Data Science, Shanghai University, 99 Shangda Road, Shanghai, DC 200444,
China
2Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, 1 Meicheng road,
Huaian, DC 223303, China
*allenwxh@163.com
Abstract: In order to enhance the channel capacity and spectrum efficiency, the technology
of space division multiplexing (SDM) has become research hotspot in optical
communications. In this paper, a new encoding/decoding concept is proposed by the states of
vector modes (polarized direction, rotational direction of phase and topological charge) for
vortex beam propagating. To support encoded vector modes propagating in fiber, an OAM
fiber with air-core structure is designed for encoding/decoding. Meanwhile, a new mode
recognition method of judging states of the received vector modes is presented by the
technology of digital image processing and digital signal processing (DSP). To verify the
feasibility of encoding/decoding, an experimental platform to verify that encoded 16-QAM
signal (0010_1100_1110_1010) is established. The vector modes of OAM beams can be
propagated in OAM fiber with the length of 80 cm, and the received signal can be decoded to
16-QAM by image processing successfully. In addition, we also evaluate and analyze the
influence factor (OAM fiber length and bit rate) on the transmitting performance in terms of
BER, crosstalk and constellation figures.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
OCIS codes: (050.4865) Optical vortices; (060.4510) Optical communications; (100.2000) Digital image processing.
References and links
1. L. Zhu, J. Liu, Q. Mo, C. Du, and J. Wang, “Encoding/decoding using superpositions of spatial modes for image
transfer in km-scale few-mode fiber,” Opt. Express 24(15), 16934–16944 (2016).
2. C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Design, fabrication and validation of an
OAM fiber supporting 36 states,” Opt. Express 22(21), 26117–26127 (2014).
3. I. B. Djordjevic, “Heterogeneous Transparent Optical Networking Based on Coded OAM Modulation,” IEEE
Photonics J. 3(3), 531–537 (2011).
4. I. B. Djordjevic, L. Tao, X. Lei, and W. Ting, “On the Multidimensional Signal Constellation Design for Few-
Mode-Fiber-Based High-Speed Optical Transmission,” IEEE Photonics J. 4(5), 1325–1332 (2012).
5. J. Du and J. Wang, “High-dimensional structured light coding/decoding for free-space optical communications
free of obstructions,” Opt. Lett. 40(21), 4827–4830 (2015).
6. B. Guan, C. Qin, R. P. Scott, N. K. Fontaine, T. Su, R. Proietti, and S. J. B. Yoo, “Polarization Diversified
Integrated Circuits for Orbital Angular Momentum Multiplexing,” IEEE Photonics Technol. Lett. 27(10), 1056–
1059 (2015).
7. Q. Kang, P. Gregg, Y. Jung, E. L. Lim, S. U. Alam, S. Ramachandran, and D. J. Richardson, “Amplification of
12 OAM Modes in an air-core erbium doped fiber,” Opt. Express 23(22), 28341–28348 (2015).
8. S. Li, Q. Mo, X. Hu, C. Du, and J. Wang, “Controllable all-fiber orbital angular momentum mode converter,”
Opt. Lett. 40(18), 4376–4379 (2015).
9. S. Li and J. Wang, “Performance evaluation of analog signal transmission in an orbital angular momentum
multiplexing system,” Opt. Lett. 40(5), 760–763 (2015).
10. C. Lin, I. B. Djordjevic, and M. Cvijetic, “Quantum Few-Mode Fiber Communications Based on the Orbital
Angular Momentum,” IEEE Photonics Technol. Lett. 25(1), 3–6 (2013).
11. J. Liu, S. Li, J. Du, C. Klitis, C. Du, Q. Mo, M. Sorel, S. Yu, X. Cai, and J. Wang, “Performance evaluation of
analog signal transmission in an integrated optical vortex emitter to 3.6-km few-mode fiber system,” Opt. Lett.
41(9), 1969–1972 (2016).
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29342
#307672
Journal © 2017
https://doi.org/10.1364/OE.25.029342
Received 22 Sep 2017; revised 3 Nov 2017; accepted 6 Nov 2017; published 9 Nov 2017
12. J. Liu and J. Wang, “Polarization-insensitive PAM-4-carrying free-space orbital angular momentum (OAM)
communications,” Opt. Express 24(4), 4258–4269 (2016).
13. J. Liu, L. Zhu, A. Wang, S. Li, S. Chen, C. Du, Q. Mo, and J. Wang, “All-fiber pre- and post-data exchange in
km-scale fiber-based twisted lights multiplexing,” Opt. Lett. 41(16), 3896–3899 (2016).
14. A. Wang, L. Zhu, S. Chen, C. Du, Q. Mo, and J. Wang, “Characterization of LDPC-coded orbital angular
momentum modes transmission and multiplexing over a 50-km fiber,” Opt. Express 24(11), 11716–11726
(2016).
15. A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum
multiplexing and time-division multiplexing passive optical network,” Opt. Express 23(23), 29457–29466
(2015).
16. A. J. Willner, Y. Ren, G. Xie, Z. Zhao, Y. Cao, L. Li, N. Ahmed, Z. Wang, Y. Yan, P. Liao, C. Liu, M.
Mirhosseini, R. W. Boyd, M. Tur, and A. E. Willner, “Experimental demonstration of 20 Gbit/s data encoding
and 2 ns channel hopping using orbital angular momentum modes,” Opt. Lett. 40(24), 5810–5813 (2015).
17. X. Zeng, Y. Li, Q. Mo, W. Li, Y. Tian, Z. Liu, and J. Wu, “Experimental Investigation of LP11 Mode to OAM
Conversion in Few Mode-Polarization Maintaining Fiber and the Usage for All Fiber OAM Generator,” IEEE
Photonics J. 8(4), 1–7 (2016).
18. H. Zhang, W. Zhang, L. Xi, X. Tang, X. Zhang, and X. Zhang, “A New Type Circular Photonic Crystal Fiber for
Orbital Angular Momentum Mode Transmission,” IEEE Photonics Technol. Lett. 28(13), 1426–1429 (2016).
19. J. Zhou, J. Zong, and D. Liu, “The Higher Order Statistics of OAM Modal Amplitudes Under Atmosphere
Turbulence,” IEEE Photonics Technol. Lett. 28(23), 2653–2656 (2016).
1. Introduction
Recently, vortex beams with the characteristic of orbital angular momentum (OAM) have
been concerned as research focus for the potential ability of enhancing the channel capacity.
It is generally known that multiplexing techniques have been widely used to increase the
channel capacity in optical and wireless communications, which mainly contain Wavelength
Division Multiplexing (WDM), Time Division Multiplexing (TDM), Polarization Division
Multiplexing (PDM), Frequency Division Multiplexing (FDM), etc. The vortex beams
possess the helical phase wave-front in the form of exp( )il
θ
, where l is the topological
charge with the units of (simplify the Planck’s constant),
θ
is the azimuth [1–5]. The phase
of vortex beams possesses the phase singular, and the intensity distribution shows the shape
of doughnut. The phases of beams with different l are mutually orthogonal to each other, and
the value of l is unlimited in theory [6-7]. Therefore, it can provide the new domain for
multiplexing, which is also called Space Division Multiplexing (SDM). The technology of
SDM is potential to enhance the channel capacity and spectral efficiency [8].
Moreover, vortex beams are also potential to be used to encode and decode with OAM
states, LP modes and the abundant states of vector modes, when it propagates in the OAM
fiber. The first two have been reported by Zhu’s group and Du’s group [1,5]. Zhu’s group
showed that the images were transmitted by encoding/decoding with superposition of spatial
modes (LP01, LP11a, LP11b and LP11a + i × LP11b) in km-scale few-mode fiber [1]. Du’s
group demonstrated that the information could be encoded and decoded with different
l(1l=± ,3±, …, 15±) in high-dimensional for representing hexadecimal data in a free-space
optical communication [5]. However, the last one has never been reported. With the
development of OAM fiber (ring-core, hollow fiber, etc.), the performance of OAM
propagation has been significantly improved, and more vector modes can be supported by
OAM fiber with less modal couple and energy leakage [8–10].
In this paper, the new methods of encoding and decoding are demonstrated by the states of
OAM combined with vector modes for transmitting information, which have never been
reported. When the OAM beams propagate in an OAM fiber, the combined vector modes of
HE and EH are excited in the OAM fiber, which are different from the scalar modes of LP.
Compared to Zhu’s report and Du’s report, the same functions can be realized only by using 2
OAM states and 8 OAM states combined with vector modes. Therefore, it is of great
significant to reduce cost and improve the performance on encoding/decoding efficiency by
the new methods. In addition, as another important innovation, an OAM fiber with the
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29343
structure of air-core is designed and fabricated, which can support up to 26 vector modes for
encoding/decoding.
2. The proposed scenario of encoding/decoding based on vector modes
According to the optics theory, angular momentum of photon is comprised of spin angular
momentum (SAM) and orbital angular momentum (OAM) [11-12]. The two kinds of angular
momentum are different. The SAM represents the rotational direction of the polarization state
of vortex beams, which includes left-hand or right-hand circular polarization [13-14]. The
OAM contains the rotational direction (clockwise or counterclockwise) of helical phase and
topological charge. The value of l and the sign of l in exp( )il
θ
denote the topological
charge and rotational direction of OAM phase (field), respectively [15]. When the vortex
beams propagate in the fiber, the OAM modes have to be converted to common eigenmodes
(vector modes) for propagating in OAM fiber. OAM modes can be defined as ,lm
OAM ±
±,
where m denotes the number of concentric rings in the intensity profile of OAM mode, l is
the topological charge [16–19]. The symbol of ± in the superscript and subscript of ,lm
OAM ±
±
depicts the direction of OAM circular polarization state and the rotational direction of OAM
field (phase), respectively.
In fiber, the vector mode mainly contains TE, TM, HE and EH mode, of which HE and
EH mode can be called the basis mode or eigenmodes for OAM modes [16-17]. The OAM
modes can be expressed in one of the two vector modes (EH or HE) by linear combination, as
shown in Eq. (1) and Eq. (2) [2]. It is not difficult to find that the direction of circular
polarization is consistent with the rotational direction of phase, when the OAM mode is
comprised of HE mode in Eq. (1). Otherwise, if the OAM mode is comprised of EH mode,
the direction of circular polarization is contrary to the rotational direction of phase in Eq. (2).
,1, 1,
even odd
lm l m l m
OAM HE jHE
±
±+ +
=± (1)
,1, 1,
even odd
lm l m l m
OAM EH jEH
±− −
=±
(2)
In order to further illustrate the linear combination of vector modes in Eq. (1) and Eq. (2),
the classification chart has been plotted in Fig. 1. Figures 1(a)-1(d) demonstrate the
relationship of circular polarization and rotary phase, which are consistent with the
consequence of Eq. (1) and Eq. (2) by different linear combination based on vector modes,
respectively.
The abundant states of the polarization, topological charge and the rotational direction of
phase are all potential physical quantity to be used to encode or decode information for
optical fiber communication system. According to the above discussion about polarization,
topological charge and phase, each OAM with different topological charge can be described
as four different states, i.e., right-hand circular polarization, left-hand circular polarization,
counterclockwise phase, and clockwise phase for a certain l(0,1l≠). If =0l, the vector
modes can be only described in the form of vector HE mode, 0, 1, 1,
even odd
mm m
OAM HE jHE
±=+,
which has only two circular polarization states. It doesn’t belong to the domain of OAM
modes, but belong to fundamental vector modes of
1,m
H
E. If =1
l, the vector modes can be
described with two combined vector modes in the form of +
1, 2, 2,
+
even odd
mmm
OAM HE jHE= and
1, 2, 2,
even odd
mm m
OAM HE jHE
−
−=− with the same direction of polarization and phase. Furthermore,
if 2
l≥, there are four different combining methods of l
OAM ±
± by vector modes. For
example, if =3
l, the OAM modes can be depicted as
+
3, 4, 4,
+
even odd
mmm
OAM HE jHE=,3, 2, 2,
+
even odd
mmm
OAM EH jEH
−=,3, 4, 4,
-
even odd
mmm
OAM HE jHE
−
−=, and
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29344
+
3, 2, 2,
-
even odd
mmm
OAM EH jEH
−= by the linear combination of vector modes based on Eq. (1) and
Eq. (2).
Fig. 1. The rotational direction of polarization and phase based on different vector modes. (a)
HE mode for left-hand circular polarization and counterclockwise phase, (b) EH mode for left-
hand circular polarization and clockwise phase, (c) HE mode for right-hand circular
polarization and clockwise phase, (d) EH mode for right-hand circular polarization and
counterclockwise phase.
The above described characteristics of OAM are potential to be used to encode/decode for
information, thus we propose a new encoding/decoding scheme by topological charge, the
direction of circular polarization, and the direction of rotary phase. The concept of
encoding/decoding information by the linear combined vector modes is shown in Fig. 2. The
whole process of encoding and decoding can be divided into five steps, i.e., encoding-convert,
map-modulation, propagation, demodulation (de-mapping), and decoding-convert.
Firstly, the transmitted data is converted to binary sequence with the length of 4 or 6 bit as
a group for expressing data of 0-15 or 0-64. The binary sequences are located in the 3rd-6th
bit and 1st-6th bit, respectively. After that, the converted original sequences are encoded with
the rules in the left of Fig. 2.
Secondly, the encoded sequences are mapped to the OAM mode in the form of ,
L
m
OAM ±
±
based on the combination of vector modes. It should be noted that the valve of m is set as a
fixed value of 1 in this paper for simplicity. According to the mapped ,
L
m
OAM ±
±beams, the
relevant direction of polarization states, rotational direction of phase, and topological charge
are modulated and generated by the spatial light modulator (SLM) and polarizer. The SLM
loaded complex phase pattern is used to generate the rotational direction of phase and
topological charge for OAM beams. The polarizer can control the polarized directions of
OAM, which include left-hand and right-hand circular polarization.
Thirdly, the modulated OAM beams are coupled into the OAM fiber by objective lens and
beam expander. The incident free-space OAM beams are propagated in the OAM fiber with
special construction by exciting the vector modes for keeping the states of circular
polarization. The relationships between converted free-space OAM beams and vector mode
beams are consistent with the rules, which have been shown in Fig. 2 and discussed by the
above.
Fourthly, the received OAM beams in the form of linear combination of vector modes is
shined into free-space in the terminal of OAM fiber, and demodulated by the technology of
image processing and digital signal processing (DSP) based on the received images by
camera.
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Finally, the demodulated beams are converted into electrical signal by the technology of
image processing. Meanwhile, the data is de-mapped into original consequence and evaluated
for the transmitting quality by offline processing.
Fig. 2. The concept of encoding and decoding for hexadecimal data by the direction of
polarization, rotational direction of phase and topological number based on the vector states of
OAM mode.
3. The design of OAM fiber
In order to support the plenty of OAM modes, the excellent performance on the effective
index separation between the vector modes is of great significance for encoding/decoding
information based on states of vector modes, i.e., the direction of polarization states, the
rotational direction of phase, and topological charge. In addition, the other parameter of
crosstalk (mode couple) between the modes needs to be considered for improving the quality
of propagation of encoded information in the OAM fiber. It has been popularly recognized
that a high contrast in refractive indices is beneficial to obtain good modes separation, which
can reduce the modes coupling and prevent vector modes degenerating into LP modes. In this
paper, we use the linear combination of vector modes (EH, HE) to represent the OAM modes
in the fiber. The effective index separation between EH and HE in a group must be greater
than 4
10− for preventing the vector modes coupling, which is consistent with the rules of
polarization maintaining fiber. The contrast of refractive index is determined by the fiber
structure, manufacturing material, and the manufacturing procedure. Since the refractive
indices of air or special fiber core approximately equal to 1, and the refractive indices of
doped silicon dioxide with other chemical elements in annular region of ring-core or air-core
fiber can reach more than 1.45, the ring-core fiber and air-core fiber may possess the higher
contrast of refractive index.
In this paper, the OAM fiber with a step-index profile is designed to support plenty of
vector modes which can be used to encode/decode by the states of vector modes. The
constraint conditions of maximum and minimum refractive indices are designed for
supporting sufficient vectors modes which possess large enough of effective index separation
among the groups of vector modes. After that, we design the physical size of fiber profile
which includes the radius of each circular region (layer). The procedure of design OAM fiber
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29346
can be combined with gradually adding layers and checking the performance of the effective
index separation. According to the consequence of checking, we modified the design
synchronously. The designed final profile of OAM fiber with an annular shape is shown in
Fig. 3. Due to the imperfections of the fabrication procedure, we have to adopt a compromise
approach to solve the question of balance between the supported maximum number of vector
modes and the separation of effective refractive indices in the designing procedure.
According to the above assumption of the parameter, 1m=, the doped area is designed to be
very thin for supporting the intensity profile of single ring shape. Meanwhile, it can also
suppress the crosstalk among the vector modes belonged to different groups and it is benefit
to the development of SDM. Moreover, it also guarantees the large enough of separation of
vector modes over the whole wavelengths of C-band. The designed profiles of physical
structure and refractive indices of OAM fiber are shown in Figs. 3(a) and 3(b), respectively.
The whole profile of physical structure of OAM fiber can be divide into four layers. The
refractive indices of layers from the innermost layer to the outermost layer are around 1.481,
1.487, 1.451 and 1.455, respectively. The OAM fiber is fabricated by the technology of
modified chemical vapor deposition (MCVD) and pull with doping different chemical
elements for adjusting the refractive indices in each layer, such as SiO2, P2O5, GeO2, and F
in different layers. We use finite element analysis in the COMSOL software to compute the
effective refractive index of fiber eigenmodes as well as the electric field and phase
distribution of OAM modes. We also use instruments to evaluate and measure the refractive
indices. With the help of the software of COMSOL and the equipment of refracted near filed
analyzer (NR-9200HR), it demonstrates that the measured refractive index is consistent with
simulated value on the whole, and the difference between the two refractive indices main be
caused by the fabrication process in Fig. 3(b).
Fig. 3. The profiles of refractive indices and physical structure of OAM fiber, (a) the profile of
physical structure, (b) the profile of refractive indices.
According to the profile of physical structure of OAM fiber, the effective indices and
group indices for all supported vector modes are calculated. As shown in Fig. 4, it is obvious
that the supported vector modes contains TE0,1, HE1,1, HE2,1, HE3,1, TM0,1, EH1,1, HE4,1, EH2,1,
HE5,1, EH3,1, HE6,1, EH4,1, HE7,1, EH5,1, HE8,1, EH6,1, HE9,1, and EH7,1 in Fig. 4(a). However,
some vector modes can’t be combined to OAM modes, such as TE0,1, HE1,1 and TM0,1.The
vector mode of HE2,1 only can be combined to two OAM modes, which
contains +
1,1
OAM and 1,1
OAM −
−. In order to coexist in fiber, the minimum separation of
refractive index needs to be more than -4
10 for avoiding the mode couple and crosstalk.
Figure 4(a) shows the good performance on the separation of effective indices, and the
minimum separation is around 4
1.09 10−
× between TE0,1 and HE1,1 in 1550nm. The modes of
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29347
HE9,1 and EH7,1 are not considered, because they only support the low wavelength. The each
of OAM modes combined by the EH and HE with the topological from 2 to 7 contains 4
combination ways. The OAM modes with the topological charge 1 only can be combined by
2 ways with EH modes or HE modes. So all vector modes except for TE0,1, HE1,1, TM0,1,
HE9,1 and EH7,1 can be combined to 26 different OAM modes with the topological charge
from 1 to 7.
Figure 4(b) depicts the calculated group indices based on the prior Neff, which also shows
that the OAM modes group with larger topological charge possess larger group delay and
usually transmit more slowly than those with lower larger topological. In addition, it also
demonstrates that the same topological charge of OAM modes beams combined by HE modes
with the same direction of polarization and the rotational phase propagate more slowly than
those combined by EH modes with the opposite direction of polarization and the rotational
phase.
Fig. 4. The effective indices and group index of vector modes for the design of OAM fiber, (a)
effective indices of vector modes, (b) group index of the vector modes.
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29348
4. Experimental setup and discussion
The method of encoding/decoding by the states of vector modes (i.e., polarized direction,
rotational direction of phase and topological charge) has been discussed in section 2, which
can provide additional dimension for encoding/decoding. Therefore, it can be used to enhance
the efficiency of encoding/decoding with the limited optical devices. The OAM fiber with the
structure of air-core has also been designed for supporting sufficient vector modes in section
3. The effective index separation, effective indices, and group index of the vector modes have
been calculated and measured by software and instruments for the design OAM fiber, which
can support at least 26 vector modes for encoding/decoding. Next, an experimental platform
is established for verifying that the information can be encoded/decoded by the states of
vector modes in transmitting terminal; the vector modes can be propagated in the designed
OAM fiber with relative optical components by exciting the vector modes; according to the
captured images, the received vector modes can be detected and analyzed by two cameras and
the modules of offline processing in the receiving terminal. To verify the feasibility of the
scheme of the whole system, the encoded 16-QAM signal (0010_1100_1110_1010) in the
form of combining vector modes were propagated through OAM fiber with the length of 80
cm by exciting the vector modes. Meanwhile, the received signals were decoded and
translated to 16-QAM by image processing in the receiving terminal. Figure 5 demonstrates
the whole process of the experimental scheme, which can be divided into 5 parts, which
contains the source of beams, encoding information, SLM, propagation, and decoding
information.
Fig. 5. The experimental scheme for encoding/decoding with the vector modes by OAM fiber.
PC: polarization controller, EDFA: erbium-doped fiber amplifier, BPF: bandpass filter, OC:
optical coupler, Col: collimator, Pol: polarization, HWP: half-wave plate, SLM: spatial light
modulator, PBS: polarizing beam splitter, BS: beam splitter, BE: beam expander, SMF: single
mode fiber.
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29349
Firstly, the generated Gaussian beam by laser is amplified and filtered to guarantee the
enough intensity and purity by EDFA and BPF in single mode fiber (SMF). After that, the
beam is split into 3 lines for different purpose, one is used to illuminate the SLM for
generating the OAM beams and the other two lines are used as the referred beams to interfere
the received the OAM beams for analyzing the phase, polarization and topological charge.
The top branch beam shines into free-space by the collimator (Col) and be expanded to match
the size of OAM fiber for enhancing the efficiency of couple. Following, the polarization of
beams are adjusted into linearity by Col. and half wave plate (HWP), and the beams are
irradiated on the SLM for generating OAM beams.
Secondly, the generated PRBS is modulated to the signal of 16-QAM, then the signal is
converted to sequence group with a certain length of 4 bits for hexadecimal encoding.
Following, the sequence group is mapped into the encoding sequence from 3rd bit to 6th bit
based on the above of encoding rules in Fig. 2. It’s worth noting that the 1st and 2nd are not
necessary to be used, because the sequence group’s length only is 4 bits for 16-QAM, which
can be used as expanded bits to represent 32 or 64-QAM, respectively. The mapped
sequences are divided into two lines to control SLM and circular polarizer. The 3rd and 4th
bit in the mapped sequence are combined as the control signal to select the topological
charge, and the 5th bit is used as control signal to select the rotational phase direction of
OAM beams for SLM. Furthermore, the 6th bit in the mapped sequence is used as the control
signals to control the polarized direction for circular polarizer. The 1st and 2nd bit are
reserved for future use.
Thirdly, the SLM is used to generate alternant OAM beams based on the referred the
control signal for selecting the topological charge and the rotational direction of phase. In this
paper, we design 4 kinds of fork grating holograms for SLM to generate OAM beams. The
topological charges contain 2, 4, 6 and 8 based on the 3rd-4th bit in the mapped sequence.
The value of the 5th bit in the mapped sequence is used to represent the rotational phase (i.e.,
clockwise and counterclockwise). Thus, the topological charge can be depicted as 2±, 4±,
6± and 8±. The sign of “+” and “-” represent the counterclockwise and clockwise direction
of phase, respectively.
Fourthly, the OAM beams in free-space are illuminated into the circular polarizer and
focusing lens (FL) for configuring circularly polarized direction, which contains left-hand or
right-hand based on the control signal of polarized direction that located in the 6th bit in the
mapped sequence. Following, the OAM beams are coupled into the OAM fiber, then the
related vector modes are excited based on the incident OAM beams. The relationships of
OAM modes and combined vector modes have been discussed in section 2. It is worth noting
that the propagating length of beams modulated by the SLM in free-space and OAM fiber
with the air-core structure is around 20 cm and 80 cm.
Finally, the beams with the OAM modes are shined into free-space again from the OAM
fiber by the collimator and QWP for better directivity and polarization. Next, the OAM beams
are split into 2 parts based on the different circular polarized direction by the polarizing beam
splitter (PBS), which also can be called left-hand polarized OAM beams and right-hand
polarized OAM beams from left to right in Fig. 5, respectively. After that, the two branch
beams with different polarized direction are combined with the relevant referred Gaussian
beams by a beam splitter (BS), then we can observe the interference figures. Therefore, we
can decode the information (direction of circular polarization, topological charge, and
rotational direction of phase) based on the observed interference figures by the technology of
image processing and DSP.
The above has been discussed about the whole procedure of experiment in detail on
source of beams, information encoding, SLM, propagation, and encoding/decoding
information. Further, Pseudo Random Binary Sequences (PRBS) are employed to verify the
performance of whole system. According to the original polynomial ( 76
1xx++) of PRBS7,
the generated PRBS (0010, 1100, 1110, 1010, ……) with the initial values of 1111 can be
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29350
depicted as 2, C, E, A, ……, in the form of hexadecimal. According to the relationship of
map in Fig. 2, the sequence of 2, C, E and A can be described as 2,1
OAM −
+,8,1
OAM −
−,
8,1
OAM +
−,6,1
OAM −
+by the combining vector modes.
According to received images from the camera 1# and 2#, we can observe the interference
fringes of the received OAM modes in Fig. 6. To analyze the polarized direction, rotational
direction of phase and topological charge, we carefully distinguish the origin of received
images from camera 1# or 2#, then we design reference lines (L1, L2) and reference circle (C)
for analyzing the intensity distribution in the form of equipotent pulse sequences.
Figure 6(a1) depicts the consequence of L1_pulse = L2_pulse, which demonstrates that
there is no rotational phase distribution in Fig. 6 (a3). Figure 6(a2) describes the expression of
C_pulse = 0, which means that there are no interference fringes distributed on the circle C in
Fig. 6(a3). Therefore, the received Fig. 6(a3) doesn’t belong to the OAM beams, which may
be induced by the referred beams. Figure 6(a5) depicts that the expression of C_pulse = 2,
which means that there are 2 interference fringes distributed on the circle C in Fig. 6(a4).
Figure 6(a6) demonstrates that the consequence of L1_pulse < L2_pulse means that there’s
counterclockwise rotational phase in Fig. 6(b4). Furthermore, the image of Fig. 6(b4) is
captured by camera 2#, which indicates the image belongs to the right-hand circular
polarization. So we can determine that Fig. 6(a4) represents the OAM beams with topological
charge 2l=, counterclockwise rotational phase and right-hand circular polarization, which
also can be expressed as 2,1
OAM −
+ (0010).
Fig. 6. The interference image and analyzed the image of received OAM beams by camera and
offline processing. (a3)-(d3): the received images by camera 1#; (a4)-(d4): the received images
by camera 2#; (a1)-(d1): the intensity distribution in the form of pulse by L1 and L2 for (a3)-
(d3), (a2)-(d2): the intensity distribution in the form of pulse by circle C for (a3)-(d3); (a5)-
(d5): the intensity distribution in the form of pulse by circle C for (a4)-(d4); (a6)-(d6): the
intensity distribution in the form of pulse by L1 and L2 for (a4)-(d4).
Figure 6(b1) depicts the consequence of L1_pulse = L2_pulse, which demonstrates that
there is no rotational phase distribution in Fig. 6 (b3). Figure 6(b2) describes the expression
of C_pulse = 0, which means that there are no interference fringes distributed on the circle C
in Fig. 6(b3). Hence, the received Fig. 6(b3) doesn’t belong to the domain of OAM beams,
which may be induced by the referred beams. Figure 6(a5) depicts that the expression of
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29351
C_pulse = 8, which means that there are 8 interference fringes distributed on the circle C in
Fig. 6(b4). Figure 6(b6) demonstrates that the consequence of L1_pulse > L2_pulse means
that there’s clockwise rotational phase in Fig. 6(b4). Furthermore, the image of Fig. 6(b4) is
captured by camera 2#, which indicates the image belongs to the right-hand circular
polarization. So we can determine that Fig. 6(b4) represents the OAM beams with topological
charge 8l=, clockwise rotational phase and right-hand circular polarization. It also can be
expressed as 8,1
OAM −
− (1100).
Figure 6(c2) depicts that the expression of C_pulse = 8, which means that there are 8
interference fringes distributed on the circle C in Fig. 6(c3). Figure 6(c1) demonstrates that
the consequence of L1_pulse > L2_pulse means that there’s clockwise rotational phase in Fig.
6(c3). Furthermore, the image of Fig. 6(c3) is captured by camera 1#, which indicates the
image belongs to the left-hand circular polarization. Therefore, we can determine that Fig.
6(c3) represents the OAM beams with topological charge 8
l=, clockwise rotational phase,
and left-hand circular polarization, which also can be expressed as 8,1
OAM +
−(1110). Figure
6(c6) depicts the consequence of L1_pulse = L2_pulse, which demonstrates that there is no
rotational phase distribution in Fig. 6(c4). Figure 6(c5) describes the expression of C_pulse =
0, which means that there’s no interference fringes distributed on the circle C in Fig. 6(c4).
So, the received Fig. 6(c4) doesn’t belong to the OAM beams, which also may be induced by
the referred beams.
Figure 6(d1) depicts the consequence of L1_pulse = L2_pulse, which demonstrates that
there is no rotational phase distribution in Fig. 6(d3). Figure 6(d2) describes the expression of
C_pulse = 0, which means that there’s no interference fringes distributed on the circle C in
Fig. 6(d3). So, the received Fig. 6(d3) doesn’t belong to the OAM beams, which may be
induced by the referred beams. Figure 6(d5) depicts that the expression of C_pulse = 6, which
means that there are 6 interference fringes distributed on the circle C in Fig. 6(d4). Figure
6(d6) demonstrates that the consequence of L1_pulse < L2_pulse means that there’s
counterclockwise rotational phase in Fig. 6(b4). Furthermore, the image of Fig. 6(b4) is
captured by camera 2#, which indicates the image belongs to the right-hand circular
polarization. So we can determine that Fig. 6(d4) represents the OAM beams with topological
charge 6l=, counterclockwise rotational phase, and right-hand circular polarization, which
also can be expressed as 6,1
OAM −
+(1010). Next, we translate the decoded 2,1
OAM −
+,8,1
OAM −
−,
8,1
OAM +
−and 6,1
OAM −
+to 0010, 1100, 1110 and 1010 by de-mapping, which are consistent with
the transmitted PRBS. Other received images by camera 1# and 2# also can be analyzed
based on the above criterion for decoding the information.
According to the received images by camera 1# and 2#, the criterion for recognizing the
OAM states have been described in the previous paragraph. The encoded sequence, 0010,
1100, 1110 and 1010, can be decoded into 2,1
OAM −
+,8,1
OAM −
−, 8,1
OAM +
−, and 6,1
OAM −
+ that are
combined the vector modes. To evaluate the propagation performance of information encoded
by the states of vector modes, the 16-QAM signal is selected as the testing signal, which is
filled with PRBS. Bit Error Rate (BER) and constellation diagrams are used to exhibit the
assessment results. The length of OAM fiber is a key factor for the vector modes propagation
in the communication system. Figure 7(a) demonstrates the measured performance of BER
for vector modes by propagating through different length OAM fiber. It also depicts that the
performance of BER declines with the increase of OAM fiber length. Compared with F_L =
0.8m, the performance of BER degenerates about 1.8 dB, 3.2dB and 5.2 dB based on the
threshold value of FEC (3.8e-3) for F_L = 1.0m, F_L = 1.2m and F_L = 1.4m, respectively.
As shown in Figs. 7(b)-7(e), the constellation diagrams demonstrate that the convergent
validity becomes more inattentive by increasing the length of fiber from 0.8m to 1.0m, 1.2m
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29352
and 1.4m at the same SNR = 17.5dB. The primary causes mainly contain the mode
degradation, mode couple, crosstalk and imperfect fabricating procedure of OAM fiber.
Furthermore, we also need to take into account another important factor of bit rate of 16-
QAM, which also can lead to significant influence on the performance in terms of BER when
the vector modes propagate along the certain length of OAM. In order to get better
performance, the OAM fiber with the length of 0.8m are also selected for evaluating the
influence of bit rate using BER and constellation diagrams at SNR = 17.5dB. Figure 8(a)
indicates that the performance of BER deteriorates gradually with the increase of bit rate from
80 bps to 200 bps, which demonstrates that BER is sensitive to the transmitting rate. As
shown in Figs. 8(b)-8(e), the constellation diagrams also reveal that the convergent validity
becomes more inattentive with the increase of transmitting rate. The primary causes may be
induced by the limited of switching rates of common SLM with the best rates of 100Hz,
which can’t support the faster transmitting rates. In addition, the limited switch rate of
polarizer is another important factor to decline the performance on BER and constellation
diagrams.
Fig. 7. The measured performance of BER and constellation for encoding/decoding against
SNR for the different length of OAM fiber. (a) BER, (b) F_L = 0.8 m, (b) F_L = 1.0 m, (c)
F_L = 1.2 m, (d) F_L = 1.4 m.
In addition, the crosstalk between vector modes plays a very important role in SDM. The
weaker crosstalk can effectively reduce the BER and enhance the quality of constellation. The
length of OAM fiber is the key factor to evaluate the crosstalk. In order to simplify the
measuring procedure, the single signal of 2,1
OAM −
+(encoded sequence 0010) is emitted and
coupled into OAM fiber for exciting the correlative combination of vector modes. Figure 9
demonstrates that crosstalk is induced by the leakage of intensity of 2,1
OAM −
+ along the same
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29353
circular polarization direction. With the increase of the length of OAM fiber (0.6 m −1.4 m),
the crosstalk becomes worse and worse. The intensity of the received OAM modes declines to
~0.5, when it propagates through the OAM fiber with the length of 1.4 m.
So far, the SLMs combined with high speed optical switch have been used to realize 20
Gbps encoding/decoding in free-space [16]. By using the same technic in future, higher speed
encoding/decoding with high efficiency and better performance on BER, constellation, and
crosstalk can be achieved, which is combined to 16 OAM states by 4 vector modes for OAM
beams.
Fig. 8. The measured performance of BER and constellation for encoding/decoding against
SNR for the different length of OAM fiber. (a) BER, (b) b_r = 80 bps, (b) b_r = 120 bps, (c)
b_r = 160 bps, (d) F_L = 200 bps.
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29354
Fig. 9. The measured OAM intensity against received OAM mode for the different length of
OAM fiber.
5. Conclusion
In this paper, a new encoding/decoding method by states of vector modes (i.e., polarization
direction, rotational direction of phase and topological charge) for OAM beams is proposed.
Furthermore, we also design a kind of OAM fiber with the air-core structure for supporting
enough vector modes (i.e., TE0,1, HE1,1, HE2,1, HE3,1, TM0,1, EH1,1, HE4,1, EH2,1, HE5,1, EH3,1,
HE6,1, EH4,1, HE7,1, EH5,1, HE8,1, EH6,1, HE9,1 and EH7,1). In order to identify the OAM modes,
the special decoding approach to judge received states of the vector modes is proposed with
the help of the technology of image processing. In order to verify the feasibility of
encoding/decoding, we set up an experimental platform to demonstrate that encoded 16-QAM
signal (i.e., 2,1
OAM −
+,8,1
OAM −
−, 8,1
OAM +
−and 6,1
OAM −
+) can be propagated through OAM fiber
with the length of 80 cm. Finally, the received signal can be decoded to 16-QAM by the
technology of image processing and DSP. In addition, we evaluated the influence factor
(OAM fiber length and bit rate) on the transmitting performance in terms of BER, crosstalk
and constellation figures. The primary causes of deteriorating the performance can be
concluded to the limited switching rates of SLMs, polarizer and imperfect fabricating
procedure. In addition, we also propose the improved methods by using the SLMs with high
switching rates, polarizer with high switching rate and high performance OAM fiber.
Funding
National Natural Science Foundation of China (Project No. 61420106011, 61601279,
61601277); Shanghai Science and Technology Development Funds (Project No.
17010500400, 15530500600, 16511104100,16YF1403900).
Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 29355
