Multi-step-index fiber with a large number of weakly coupled OAM mode groups for IM/DD systems in data centers: design, fabrication, and characterization.

Mode division multiplexing (MDM) technique based on weakly coupled few-mode fibers (FMF) is promising to enhance the capacity of short-reach transmission. We design and fabricate a multi-step-index FMF (MSIF), which supports weakly coupled first-order radial orbital angular momentum mode group (OAMl,1 MG) for MDM transmission. We use three layers of core to regulate the minimum effective refractive index difference (min|Δneff|) between OAMl,1 MG and the adjacent MGs. In experiments, we demonstrate that the fabricated MSIF can support up to OAM6,1 with the interferometric method, and the loss measured by an optical time-domain reflectometer (OTDR) can achieve <0.5 dB/km for the OAMl,1 with an order from |l| = 0 to |l| = 6. The inter-mode-group cross talk (XT) is tested by the power measurement, and the system-level XT after 20 km fiber transmission in the worst case is about -11.1 dB.

Extending orbital angular momentum multiplexing to radially high orders for massive mode channels in fiber transmission.

Orbital angular momentum (OAM) beams with different angular indices l have the potential to greatly increase communication capacity. However, the finite aperture of optical systems limits the value of the angular index. In order to fully use the orthogonal mode channels supported in the fiber for high-capacity communications, we propose extending the radial indices p of OAM modes as an additional multiplexing dimension. In this paper, we introduce spatially discrete multiple phase planes to multiplex the angular and radial OAM modes simultaneously. Due to the orthogonal property of the central symmetric OAM modes, a two-dimensional (2D) input Gaussian beams array can be converted to coaxial OAM modes through Cartesian to log-polar coordinate transformation by inverse design. For a proof-of-concept demonstration, a 10-mode multiplexer for high-order radial OAM modes was designed using five phase planes. The fabricated multiplexer generated high-quality multiplexed OAM modes with a loss of less than 5.4 dB. The multiplexed OAM modes were coupled into a specially designed ring-core fiber by mode-field matching, achieving stable mode transmission in 2 km fiber. The approach provides a scalable technology to increase the number of transmission channels and could lead to the practical applications of OAM multiplexing in communication.

OAM mode generation in helically twisted hollow-core antiresonant fiber.

We investigate the orbital angular momentum (OAM) mode-generating process of a long-period onefold chiral fiber grating (L-1-CFG) based on a helically twisted hollow-core antiresonant fiber (HC-ARF). Taking the right-handed L-1-CFG for an example, we theoretically and experimentally prove that the first-order OAM+1 mode can be generated by only inputting a Gaussian beam. We fabricated three right-handed L-1-CFG samples based on the helically twisted HC-ARF with twist rates (α) of -0.42, -0.50, and -0.60 rad/mm, where the twisted HC-ARF with α of -0.42 rad/mm can achieve high OAM+1 mode purity of 94%. Subsequently, we present simulated and experimental transmission spectra at the C-band, and sufficient modulation depths were obtained at wavelengths of 1550 nm and 1561.5 nm in the experiment.

112 orbital angular momentum modes amplification based on a 7RC-EDF with low differential mode gain.

We demonstrate 112 orbital angular momentum (OAM) modes amplification based on a designed and fabricated 7-ring-core erbium-doped fiber (7RC-EDF). The differential mode gain (DMG) of all the intra-core OAM modes in 7RC-EDF is effectively reduced. The DMG of intra-core modes can be suppressed by the high overlap between the signal modes and pump fundamental mode resulting from the designed structures of the ring core assisted by a trench. The differential gain of the inter-core can be controlled by the power of the core-pump configuration as well. With an experimentally optimized scheme of the pump power of each core, a record low-DMG of 2.8 dB among the 112 OAM modes (16-OAM-mode per core in the 7-core) is achieved at a wavelength of 1550 nm. The obtained favorable performance of the 112 OAM modes based on 7RC-EDF indicates it may promote a long-haul high-density OAM modes multiplexed transmission.

Multi-channel higher-order OAM generation and switching based on a mode selective interferometer.

A multi-channel orbital angular momentum (OAM) mode generation and switching scheme is proposed and demonstrated based on an in-fiber mode selective interferometer (MSI), which is formed in a four-mode fiber. The MSI consists of two strong modulated long-period fiber gratings (LPFGs), which realizes the mode selected coupling between a target mode pair. With the optimized structural parameters, the MSI can couple a launched LP01 (or OAM0) into a desired higher-order azimuthal mode (HAM, LPl1 or OAM±l, l≥1) at multiple wavelength channels and generate the HAM with high-purity. To verify this concept, we fabricate two LPFGs in a four-mode fiber with designed distance and hence realize a MSI which can generate the second-order HAM (OAM2 or LP21) at 17 wavelength channels. The mode conversion efficiency is more than 90% at 17 wavelengths and the corresponding mode purity is no less than 97%, respectively. In addition, we also demonstrate that the selected mode pair (OAM0 and OAM2) can be switched at multiple channels by changing the state of the MSI. This MSI can also be used as a wavelength band-rejection filter on different spatial modes and find potential applications in optical communications and sensing.

Amplification of 20 orbital angular momentum modes based on a ring-core Yb-doped fiber.

An orbital angular momentum (OAM) fiber amplifier supporting 20 OAM modes based on a ring-core Yb-doped fiber (RC-YDF) is proposed and demonstrated. The RC-YDF we designed and fabricated has two successive Yb-doped annular layers in the ring-core and can support the amplification of OAM (|l|=1, 2, 3, 4, 5) modes at the wavelength of 1064 nm. With a core pump configuration, we characterize the amplification performance of the RC-YDF based amplifier by simulation and experiments. The amplification of each supported OAM mode is proved by the achieved gain of more than 8 dB and a low differential modal gain less than 1dB with an input signal power of about 5dBm. This is the first experimental demonstration, as far as we know, of the amplification of the OAM mode from 1- to 5-order in aYb-doped fiber.

Third-order orbital angular momentum pulse generation from a passively Q-switched fiber laser.

We propose and demonstrate an all-fiber passively Q-switched laser generating a third-order orbital angular momentum (OAM) pulse by introducing a few-mode long-period fiber grating (LPFG) into the laser cavity. The LPFG with asymmetric cross structure and strong refractive index modulation overcomes the coupling issue between the fundamental and the third-azimuthal-order (LP31 or OAM3) modes and realizes their direct conversion. A homemade graphene-based saturable absorber is used to realize Q-switched operation. The laser operates at a center wavelength of 1548.2nm, with a 3 dB spectral bandwidth of 0.4nm, and the OAM+3 and OAM-3 beams can achieve the purity of 90.0% and 90.2%, respectively. This all-fiber Q-switched laser has simple and compact structure and high purity of OAM±3 beams, which has potential applications in the fields of optical tweezers and material processing.

Spin-orbit coupling suppressed high-capacity dual-step-index ring-core OAM fiber.

We design and fabricate a dual-step-index ring-core fiber (RCF) for orbital angular momentum (OAM) mode transmission. It has been proven that the proposed novel, to the best of our knowledge, dual-step-index ring-core structure can suppress the spin-orbit coupling and cut off the radial higher-order modes when the mode number becomes very large. In experiments, we demonstrate that the fabricated fiber can support OAM8,1 with the interferometric method, where four higher-order mode groups are weakly-coupled. We also measure the loss of each mode according to the cut-back method and the loss can achieve <0.3 dB/km for the OAM modes with an order from |l| = 1 to |l| = 5. The exploration of this novel optical fiber structure may provide ideas and knowledge for the improvement of the optical fiber communication capacity.

Design, fabrication, and characterization of a low-index center and trench-assisted 7-ring-core 5-mode-group fiber for dense space-division multiplexing.

An optimized design of 7-ring-core 5-mode-group fiber for mode-group-based dense space-division multiplexing (DSDM) is proposed. It is found that decreasing the refractive index of the center and trench of each ring core can increase the available ring-core thickness and meanwhile suppress the radial higher-order modes. Based on the simulation, a fiber, with a thicker ring core and a relatively low refractive index contrast at the ring-core boundaries, is found of higher mode purity and lower macro-bending-caused mode coupling. In the experiment, the seven cores of the fabricated fiber have low transmission losses around -0.25 dB/km with only a few fluctuations. The three higher-order mode groups (MG2,1, MG3,1, and MG4,1) are verified to be in a weak-coupling state (crosstalk of which are less than -12 dB) over a transmission length of 23 km.

Third- and fourth-order orbital angular momentum multiplexed amplification with ultra-low differential mode gain.

In this Letter, a ring-core erbium-doped fiber (RC-EDF), with a two-layer erbium-doped structure, supporting up to the fourth-order orbital angular momentum (OAM) mode was designed and fabricated for the OAM mode multiplexed amplification. Using the RC-EDF, the amplification of the third- and fourth-order OAM modes with an ultra-low differential mode gain (DMG) has been demonstrated by observing both the modal intensity and phase distribution and measuring the modal gain under the fundamental mode core pumping. The measured average gain of four modes' (OAM±3,1 and OAM±4,1) multiplexed amplification is >19dB, covering the C band, and the DMG is <1dB. Additionally, the gains of two conjugate OAM modes are almost the same under different pump power, regardless of whether they are amplified simultaneously or separately.

Sorting OAM modes with metasurfaces based on raytracing improved optical coordinate transformation.

Optical coordinate transformation (OCT) has attracted widespread attention in the field of orbital angular momentum (OAM) (de)multiplexing or manipulation, but the performance of OCT would suffer from its distortion. In this paper, we quantitatively analyze the distortion of OCT from the perspective of ray optics and explain its rationality to work under non-normal incident light. For the special case of log-polar coordinate transformation (LPCT), we use a raytracing assisted optimization scheme to improve its distortion, which is related to a Zernike polynomial based phase compensation. After raytracing optimization, the root mean square error (RMSE) of the focused rays is reduced to 1/5 of the original value and the physical optic simulation also shows great improvement. In the experiment, we use three phase masks which are realized by metasurfaces, the measured results show well consistency with the simulation. Results in this paper have great potential to improve the performance of OCT related applications.

Multiple orbital angular momentum mode switching at multi-wavelength in few-mode fibers.

Mode division multiplexing has attracted great attention because it can potentially overcome the limitation of single-mode fiber traffic capacity. However, it has been challenging to realize multiple modes controlling and switching due to the intrinsic overlap of the modes in the transmission waveguide. As a solution, we propose a cascaded phase-shifted long-period fiber grating (PS-LPFG) based multiple mode switching scheme. Using the PS-LPFGs, the multiple guided orbital angular momentum (OAM) modes selective controlling and switching at multi-wavelength can be achieved in few-mode fibers by regulating the grating resonance condition. In principle, a N × N mode switch matrix can be realized by cascading CN2 gratings, where each grating acts as a mode switch element to achieve a couple selected OAM mode switching and meanwhile the other modes are under nonblocking status. As a proof of the concept, a 2 × 2 mode switching between two OAM modes at different wavelengths based on one PS-LPFG element is demonstrated in our experiments. The switching efficiency of the two modes at two wavelengths 1537nm and 1558nm are ∼98.4% and ∼98.7%, respectively. The proposed multiple OAM mode switch has potential applications in the future hybrid multi-dimensional multiplexing optical fiber communication systems.

All-fiber third-order orbital angular momentum mode generation employing an asymmetric long-period fiber grating.

The third-order orbital angular momentum (OAM±3) guided mode generation is demonstrated for the first time, to the best of our knowledge, by employing an asymmetric long-period fiber grating (AS-LPFG). The proposed AS-LPFG is modeled by coupled local-mode theory, which is extended to the coupling of core modes and is fabricated by multicycle scanning ablation with increasing power in a six-mode fiber. The experiments demonstrate that one fabricated AS-LPFG can convert the LP01 mode to the third-azimuthal-order (3AO, LP31 or OAM±3) guided mode with efficiency of ∼99.8%. The model and the method presented, in principle, can be used to generate any other high-order modes.

Ring-core fiber with negative curvature structure supporting orbital angular momentum modes.

Compared to glass walls with a positive curvature, those with a negative curvature have been proven to have stronger confinement of light. Therefore, we change the multi-layered air holes in a photonic crystal fiber into several negative curvature tubes. As a result, the confinement medium is shifted from a low-index cladding material into a special structure. The theoretical analysis shows that each vector eigenmode has a corresponding threshold value for the outer tube thickness. It means that we can confine the target modes and filter the unnecessary modes by shifting the outer tube thickness. After substantial investigation on this fiber, we obtain the appropriate values for each structural parameter and then fabricate this negative curvature ring-core fiber under the guidance of the simulation results. Firstly, we draw the central cane under vacuum condition, then stack the cane and six capillaries to form the preform, and finally draw the ring-core fiber by using vacuumization method. The fiber test experiment indicates that the fiber length should be at least 15 m∼20 m to form the donut facula, and the tested losses of OAM+1,1, OAM+2,1, OAM+3,1, and OAM+4,1 are 0.30 dB/m, 0.36 dB/m, 0.37 dB/m, and 0.42 dB/m, respectively.

Transmitter and receiver DSP for 112 Gbit/s PAM-4 amplifier-less transmissions using 25G-class EML and APD.

The transmission performance of 112 Gbit/s PAM-4 signal with commercial 25 G-class EML and APD is experimentally studied by using advanced digital signal processing (DSP) algorithms, i.e. pre-equalization (Pre-EQ), error-table based pre-correction (ETC), least-mean square (LMS) based equalization, direct detection faster than Nyquist (DD-FTN) algorithm. Among them, Pre-EQ and ETC are implemented at the transmitter, and ETC is a symbol-pattern-dependent pre-compensation algorithm based on the look-up-table approach. In order to obtain these pre-compensated parameters readily, a joint equalization and error table generation (JEEG) module is proposed. Employing the combination of ETC, LMS, and DD-FTN, a single line 112 Gbit/s PAM-4 40 km amplifier-less transmission with a record receiver sensitivity of -16.6 dBm (at 7% HD-FEC threshold) is experimentally demonstrated. In addition, the computational complexities of different DSP schemes are analyzed and discussed in detail. The receiver computational complexity can be effectively reduced by employing appropriate ETC and Pre-EQ in the transmitter.

Torsion sensor based on inter-core mode coupling in seven-core fiber.

We proposed a novel torsion sensor based on inter-core mode coupling in seven-core fiber (SCF). The torsion sensor is fabricated by tapering a commercially available SCF spliced with two single mode fibers. Waist diameter and length of the taper structure were experimentally optimized to achieve good transmission spectrum. Based on this structure, the torsion measurement was conducted, and the experimental results demonstrated that the transmission spectrum shows a red shift with the fiber twist. The torsion sensitivity increases with the twisting angle, which can achieve as high as 1.00 nm/°. The direction of wavelength shift was observed to be opposite when twisting the tapered SCF in clockwise and counter-clockwise direction, demonstrating its capability to discriminate the rotation orientation. Moreover, all the measurements were repeated in attempts to confirm its stable performance as well as high accuracy. Mode coupling dynamics and theory of optical anisotropy in twisted fiber are adopted to discuss the sensitivity performance, which agrees well with experimental results. The novel torsion sensor could provide a promising candidate for the applications requiring accurate rotation.

Design and optimization of 32-core rod/trench assisted square-lattice structured single-mode multi-core fiber.

We propose and design a kind of heterogeneous rod-assisted and trench-assisted multi-core fiber (Hetero-RA-TA-MCF) with 32 cores arranged in square-lattice structure (SLS), and then we introduce the design method for Hetero-RA-TA-MCF. Simulation results show that the Hetero-RA-TA-32-Core-Fiber achieves average effective area (Aeff) of about 74 µm2, low crosstalk (XT) of about -31 dB/100km, threshold value of bending radius (Rpk) of 7.0 cm, relative core multiplicity factor (RCMF) of 8.74, and cable cutoff wavelength (λcc) of less than 1.53 µm.

Heterogeneous trench-assisted few-mode multi-core fiber with graded-index profile and square-lattice layout for low differential mode delay.

We propose a kind of heterogeneous trench-assisted graded-index few-mode multi-core fiber with square-lattice layout. For each core in the fiber, effective area (A(eff)) of LP(01) mode and LP(11) mode can achieve about 110 µm(2) and 220 µm(2). Absolute value of differential mode delay (|DMD|) is smaller than 100 ps/km over C + L bands, which can decrease the complexity of digital signal processing at the receiver end. Considering the upper limit of cladding diameter (D(cl)) and cable cutoff wavelength of LP(21) mode in the cores located at the inner layer, we set core pitch (Λ) as 43 µm. In this case, D(cl) is about 220.4 µm, inter-core crosstalk (XT) is lower than -40 dB/500 km and the relative core multiplicity factor (RCMF) reaches 15.93.

Simple analytical expression for crosstalk estimation in homogeneous trench-assisted multi-core fibers.

An analytical expression for the mode coupling coefficient in homogeneous trench-assisted multi-core fibers is derived, which has a simple relationship with the one in normal step-index structures. The amount of inter-core crosstalk reduction (in dB) with trench-assisted structures compared to the one with normal step-index structures can then be written by a simple expression. Comparison with numerical simulations confirms that the obtained analytical expression has very good accuracy for crosstalk estimation. The crosstalk properties in trench-assisted multi-core fibers, such as crosstalk dependence on core pitch and wavelength-dependent crosstalk, can be obtained by this simple analytical expression.

Heterogeneous trench-assisted few-mode multi-core fiber with low differential mode delay.

We propose a kind of heterogeneous multi-core fiber (Hetero-MCF) with trench-assisted multi-step index few-mode core (TA-MSI-FMC) deployed inside. After analyzing the impact of each parameter on differential mode delay (DMD), we design a couple of TA-MSI-FMCs with A(eff) of 110 µm2 for LP01 mode. DMD of each TA-MSI-FMC is smaller than |170| ps/km over C + L band and the total DMD can approach almost 0 ps/km over C + L band if we adopt DMD managed transmission line technique by using only one kind of Hetero-TA-FM-MCF. For such Hetero-TA-FM-MCF, crosstalk is about -30 dB/100km at wavelength of 1550 nm as bending radius becomes larger than 15 cm, core number can reach 12, a relative core multiplicity factor (RCMF) is 15.7, and the RCMF can even reach 26.1 if we treat LP11 mode as two special modes thanks to the multiple-input-multiple-output technology.