Twisted light carrying orbital angular momentum (OAM) is a special kind of structured light that has a helical phase front, a phase singularity, and a doughnut intensity profile. Beyond widespread developments in manipulation, microscopy, metrology, astronomy, nonlinear and quantum optics, OAM-carrying twisted light has seen emerging application of optical communications in free space and specially designed fibers. Instead of specialty fibers, here we show the direct use of a conventional graded-index multi-mode fiber (MMF) for OAM communications. By exploiting fiber-compatible mode exciting and filtering elements, we excite the first four OAM mode groups in an MMF. We demonstrate 2.6-km MMF transmission using four data-carrying OAM mode groups (OAM0,1, OAM+1,1/OAM-1,1, OAM+2,1, OAM+3,1). Moreover, we demonstrate two data-carrying OAM mode groups multiplexing transmission over the 2.6-km MMF with low-level crosstalk free of multiple-input multiple-output digital signal processing (MIMO-DSP). The demonstrations may open up new perspectives to fiber-based OAM communication/non-communication applications using already existing conventional fibers.
© 2017 Optical Society of America
In 1992, Allen recognized that twisted light beams comprising a helical phase term , carry an orbital angular momentum (OAM) of per photon (: topological charge,: azimuthal angle,: reduced Plank’s constant) . Since then OAM beam has facilitated a variety of applications ranging from optical manipulation to quantum optics [2–13] and very recently in optical communications [14–22]. OAM is a natural property of a variety of helically phased beams, covering a wide range of electromagnetic waves [1,23,24], electron beams , and neutron beams . Different from spin angular momentum (SAM) linked to circular polarization, which has only two possible values of , OAM associated with spatial distribution, in principle, can take theoretically unlimited values of . Such distinct property facilitates OAM-carrying twisted light modulation (or encoding/decoding) and multiplexing, which is analogous to multi-level complex amplitude modulation and wavelength-division multiplexing (WDM) in optical fiber communications for increased capacity . OAM multiplexing might provide an alternative approach to the well-established space-division multiplexing (SDM) using linearly polarized (LP) modes in fiber . SDM is widely employed in applications such as short reach optical interconnects and enterprise data centers [29–32]. In 2004, Gibson proposed the free-space information transfer by OAM encoding/decoding . In 2012, free-space data transmission employing OAM multiplexing was demonstrated . In 2013, OAM multiplexing transmission in a specially designed vortex fiber was demonstrated without using multiple-input multiple-output digital signal processing (MIMO-DSP) . In 2015, OAM multiplexing transmission with large crosstalk in a few-mode fiber (FMF) was demonstrated assisted by MIMO-DSP . It is always believed that specialty fibers are necessary to enable OAM multiplexing transmission with negligible crosstalk free of MIMO-DSP. However, the most widely deployed or commercially available fiber is single-mode fiber (SMF) and multi-mode fiber (MMF). Conventional MMFs are widespread for short-reach optical interconnect applications because of their relaxed connector tolerances and efficient coupling to low-cost laser sources like vertical-cavity surface-emitting lasers (VCSELs) [34–36]. Many present and future optical communication links for enterprise and data center applications are based on MMFs. Recently, some works on SDM with LP modes in MMFs have been reported [37–40], showing impressive performance. Fundamentally, the standard SMF does not support OAM modes. In this scenario, a laudable goal would be to exploit conventional MMF for data-carrying OAM multiplexing transmission [41,42]. The challenges would be the excitation and multiplexing transmission of OAM modes in MMF with low-level crosstalk.
2. Concept and principle
The concept and principle of OAM mode groups excitation and multiplexing transmission in a conventional MMF are illustrated in Fig. 1. Two OAM modes with different OAM values are multiplexed and coupled into a conventional MMF for transmission. Considering the fact that conventional MMF supports hundreds of OAM modes, direct coupling from free space to MMF can easily mess up the desired OAM modes. A homemade mode exciting element, i.e. a short section of large-core fiber fusion spliced to the MMF, is employed for easy excitation of multiplexed OAM mode groups with low-level crosstalk in the MMF. After the OAM modes multiplexing transmission, a homemade mode filtering element, i.e. the MMF fusion spliced to another short section of large-core fiber, is employed to couple out multiplexed OAM mode groups with low-level crosstalk followed by OAM modes demultiplexing. The mode exciting and filtering elements and OAM mode groups multiplexing benefit twisted light multiplexing communications with low-level crosstalk free of MIMO-DSP.
The conventional MMF employed in the experiment is a 2.6-km OM3 MMF, which has a 50-µm core diameter and a measured graded-index profile, as depicted in Fig. 2(a). According to the measured refractive index profiles of the conventional MMF and the large-core fiber used for making mode exciting/filtering elements, we use the full-vector finite element method to calculate the electric fields and phase distributions of all supported OAM modes. The OM3 MMF supports 10 OAM mode groups in total at 1550 nm. Each mode group is formed by a set of degenerate OAM modes, which have nearly the same effective refractive index , as shown in Fig. 2(b). Here OAM modes are denoted by , where is the topological charge of OAM and is the number of concentric rings in the intensity profile. The OAM mode group number n fulfills the equation . The total number of spatial modes counting the degenerate ones is 110 ( is two-fold degenerate when while four-fold degenerate when ). Remarkably, the effective refractive index separations () among 10 OAM mode groups are all above , indicating relatively low-level crosstalk between different mode groups. Hence, OAM mode groups multiplexing transmission is preferable for mitigating the crosstalk.
The short section of large-core fiber (~0.2 m), which is used for making mode exciting and filtering elements, has a measured hybrid step-index and inverse-parabolic graded-index profile and a low refractive index trench outside the core, as depicted in Fig. 2(c). The core size is larger than the standard SMF but smaller than MMF. Only the first four OAM mode groups are supported by the short section of large-core fiber, as shown in Fig. 2(d).
Remarkably, the conventional MMF and the large-core fiber are mismatched in terms of effective refractive index and core size. The beam sizes of supported OAM modes are also mismatched. The mode coupling of the mode exciting and filtering elements can be analyzed by the overlap integral of different OAM modes guided in the large-core fiber and MMF spliced to each other. Based on the overlap integral, for a perfect splicing between the large-core fiber and MMF, mode coupling to unwanted OAM modes is negligible in spite of existing fiber mismatch. However, the fiber mismatch could introduce extra insertion loss.
Accordingly, the mode exciting and filtering elements help to excite and select desired OAM modes in the conventional MMF and suppress unwanted high-order OAM modes.
3. Experimental configuration
The experimental configuration of OAM mode groups excitation and multiplexing transmission in a conventional MMF is illustrated in Fig. 3. Two 20-Gbit/s quadrature phase-shift keying (QPSK) signals at 1550 nm from the transmitters are sent to spatial light modulators (SLM1, SLM2), which are loaded with complex phase patterns to generate desired QPSK-carrying OAM modes. The collimator (Col.) and polarizer (Pol.) are used for light collimation and polarization alignment with the SLM. After the combination by a beam splitter (BS) and passing through a two-lens (L1 and L2 with a focal length f = 200 mm) 4-f system, the multiplexed OAM beams are focused by a 10X objective lens (OL1) with a focal length f = 20 mm and then coupled into the MMF via a mode exciting element. After the multiplexing transmission over a 2.6-km MMF, the OAM beams are coupled out via a mode filtering element and collimated by another 20X objective lens (OL2) with a focal length f = 10 mm. The mode exciting and filtering elements and in-line polarization controllers (PCs) on the short section of large-core fiber and MMF (not shown in Fig. 3) help to achieve better performance. In the experiment, we use two OAM modes (OAM-11 and OAM+21) in different mode groups for OAM mode groups multiplexing. In such case, the PCs have little impact on the crosstalk between them. The mode crosstalk is below −11 dB without adjusting the PCs. By properly adjusting the PCs, the crosstalk can be further reduced to be about −13 dB. All the experimental results for OAM mode groups multiplexing are measured without adjusting PCs. The output OAM beams pass through a lens pair (L3 with f = 200 mm, L4 with f = 100 mm) to reduce the beam size, and then sent to a third SLM (SLM3) for demultiplexing, the output of which with a bright spot at the beam center (Gaussian-like) is coupled into an SMF for coherent detection at the receiver. A half-wave plate (HWP) is used to adjust the polarization to be aligned with SLM3. A camera is used to measure the intensity profiles at the input and output of MMF by placing a flip mirror after L1 and SLM3, respectively (not shown in Fig. 3).
The implementation details of the transmitter and receiver in the experimental configuration are shown in Fig. 4. At the transmitter (Tx) side, two independent pseudo-random binary sequence (PRBS) of length 32768 are used for the in-phase (I) and quadrature (Q) components of a quadrature phase-shift keying (QPSK) signal. The QPSK signal is generated using an arbitrary waveform generator (Tektronix AWG 70002) operated at 10 Gbaud to drive an in-phase/quadrature (I/Q) modulator. A laser at a wavelength of 1550 nm with a 1-kHz linewidth is used as the optical source. The QPSK-carrying light from the I/Q modulator is pre-amplified by an erbium-doped fiber amplifier (EDFA). The pre-amplified QPSK signal is divided into two branches by an optical coupler (OC) and relatively delayed using a single-mode fiber (SMF) for decorrelation. The two branch QPSK signals serve as transmitter1 (Tx-1) and transmitter (Tx-2) in the experimental configuration. In each branch a polarization controller (PC) is used to optimize the polarization state of the light for OAM mode generation. At the receiver (Rx) side, the demultiplexed Gaussian-like beam is coupled into the SMF and amplified by an EDFA for coherent detection. A variable optical attenuator (VOA) followed by another EDFA is employed to adjust the received optical signal-to-noise ratio (OSNR). The received QPSK signal and a local oscillator (LO) laser with a linewidth of 1 kHz are mixed in the optical hybrid. Two PCs are used to adjust the polarization state of the received signal and LO laser for optimized coherent detection. After the optical hybrid, the received waveforms are sampled and stored using a real-time sampling oscilloscope (Keysight DSA-Z 204A) operating at 80 GS/s with a bandwidth of 20 GHz. The offline digital signal processing is then followed to recover the received signals as follows. The received signal is first re-sampled to two samples per symbol. After that, a 9-tap, T/2-spaced adaptive finite impulse response (FIR) filter, based on the constant modulus algorithm (CMA), is utilized for channel equalization. After equalization, the fast Fourier transform (FFT)-based frequency offset estimation and Viterbi-and-Viterbi (V&V) algorithm based phase estimation are employed for carrier synchronization and phase tracking. Finally, the recovered signal is de-mapped to the Rx bit sequence. The bit-error rate (BER) curves as a function of the received OSNR are measured by comparing the Rx bit sequence with the Tx bit sequence.
4. Experimental results
We first demonstrate the single OAM mode transmission over the 2.6-km MMF without using OAM mode groups multiplexing. We measure the transmission performance of OAM0,1, OAM+1,1, OAM-1,1, OAM+2,1 and OAM+3,1 separately. The measured intensity profiles at the input and output of MMF are shown in Figs. 5(a) and 5(b), respectively. One can see doughnut intensity profiles of OAM modes () with phase singularity at the beam center. In the interferograms measured by the interference between the OAM modes and a reference Gaussian beam, the number of twists indicates the magnitude of , with the sign implied by the twist direction. The back converted Gaussian-like beams, having bright spot at the beam center, are obtained by loading the SLM3 with corresponding phase patterns. The total coupling and transmission loss of OAM0,1, OAM+1,1, OAM-1,1, OAM+2,1 and OAM+3,1 from the input mode exciting element to output mode filtering element are measured to be about 3.7, 4.4, 5.6 and 7.3 dB, respectively. The total loss increases with the mode group number, which might be due to the non-perfect splicing and increased coupling loss of higher-order modes. We measure the bit-error rate (BER) performance as a function of the received optical signal-to-noise ratio (OSNR) for the first four mode groups, as shown in Fig. 6(a). The observed OSNR penalties at a BER of 2 × 10−3 (enhanced forward error correction (EFEC) threshold) for OAM0,1, OAM+1,1, OAM-1,1, OAM+2,1 and OAM+3,1 are less than 1.6, 2.0, 2.0, 2.7 and 2.8 dB, respectively.
We further demonstrate the OAM mode groups multiplexing transmission over the 2.6-km MMF without using MIMO-DSP. Two OAM modes (OAM-1,1 and OAM+2,1 from two mode groups) each carrying a 20-Gbit/s QPSK signal are considered for OAM mode groups multiplexing transmission. The measured intensity profiles for the multiplexing and demultiplexing of OAM-1,1 and OAM+2,1 modes are shown in Fig. 5(c). The measured BER performance for the OAM mode groups multiplexing transmission is shown in Fig. 6(b). For the OAM mode groups multiplexing transmission, the observed OSNR penalties at a BER of 2 × 10−3 for OAM-11 and OAM+21 with crosstalk are less than 4.2 and 5.5 dB, respectively, which are 2.2 and 2.8 dB higher than the OAM-1,1 only and OAM+2,1 only transmission without crosstalk. The insets in Fig. 6 show constellations of QPSK signals.
Remarkably, we also characterize in detail the mode crosstalk matrix. Note that the OAM-1,1 and OAM+2,1 from two mode groups used in the experiment have the same polarization. For simplicity we measure a 4x4 mode crosstalk for OAM+1,1, OAM-1,1, OAM+2,1 and OAM-2,1 modes having the same polarization, as shown in Fig. 7. One can also get similar mode crosstalk when considering the other orthogonal polarization. The measured results shown in Figs. 6 and 7 indicate relatively low-level crosstalk of OAM mode groups multiplexing (OAM-1,1 and OAM+2,1).
In summary, we propose and demonstrate the direct use of a conventional MMF for data-carrying OAM mode groups excitation and multiplexing transmission. The obtained results show favorable performance of OAM mode groups multiplexing transmission in a 2.6-km conventional MMF. The demonstrated OAM mode groups multiplexing transmission may find potential short-reach optical interconnect applications in data center for capacity scaling. The demonstrations may open a door to facilitate more extensive fiber-based OAM mode groups communication and even non-communication applications by direct use of a commercially available conventional MMF.
National Basic Research Programme of China (973 Program) (2014CB340004); National Natural Science Foundation of China (NSFC) (61761130082, 11574001, 11774116, 11274131, 61222502); Royal Society-Newton Advanced Fellowship; National Programme for Support of Top-notch Young Professionals; Yangtze River Excellent Young Scholars Programme; Programme for New Century Excellent Talents in University (NCET-11-0182).
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