Differential Mode Group Delay Research Articles

Nonlinear compensation for few-mode fiber MDM-WDM systems using probabilistic neural network

In this paper, we propose for the first time to apply probabilistic neural network (PNN) to fiber nonlinear compensation (NLC) in a high-speed coherent optical communication system that combines few-mode fiber (FMF) mode division multiplexing (MDM) with wavelength division multiplexing (WDM). By training on a small number of symbols, the PNN equalizer can compute the statistical distribution of the signal nonlinearity, make decisions on test symbols, and thereby compensate for the nonlinear impairments of the signals. To verify the effectiveness of the proposed scheme, we construct a MDM-WDM simulation system with 28 GBaud polarization division multiplexing (PDM) 16-quadrature amplitude modulation(QAM) and 64 GBaud PDM-64QAM, 6 spatial mode signals are transmitted over 11 wavelength channels with link lengths of 1500 km and 400 km, respectively. The results show that the PNN equalizer can make nonlinear judgments on received signals and effectively compensate the signal impairments caused by Kerr nonlinearity and device nonlinearity in a large launch power range after undergoing carrier phase recovery (CPR). Meanwhile, this scheme exhibits strong robustness against residual linear mode coupling (LMC), differential mode group delay (DMGD), and amplified spontaneous emission (ASE) noise. Finally, by the computational complexity comparison, it is proved that the complexity of the probabilistic neural network nonlinear compensation (PNN NLC) scheme is lower than that of digital back propagation (DBP) with comparable performance, which is on the order O(N).

A cost-effective joint multi-parameter optical performance monitoring scheme for high baud rate mode division multiplexing system

Inter-symbol interference (ISI), mode coupling (MC) and other impairments present in high baud rate mode division multiplexing (MDM) systems significantly degrade the reliability and accuracy of optical signal transmission. Therefore, performing joint multi-parameter optical performance monitoring (OPM) is crucial to ensure the efficient operation of the system. We propose a scheme that combines asynchronous single channel sampling (ASCS) images with a multi-task residual neural network (MT-ResNet) to enable cost-effective joint OPM at intermediate nodes in a 100 GBaud MDM system. The scheme requires only one photodetector to receive the signal. Based on the distinct characteristics exhibited by ASCS images for different parameters in the MDM system, the MT-ResNet is improved to capture correlations among parameters and learn residual information between inputs and outputs. This enables high-precision and rapid simultaneous implementation of modulation format identification (MFI), MC estimation, optical signal-to-noise ratio (OSNR) estimation, and chromatic dispersion identification (CDI) in the intermediate nodes of a 100 GBaud MDM system. The effectiveness of the proposed scheme is verified using a 100 GBaud QPSK/8QAM/16QAM/32QAM/64QAM MDM simulation transmission system with five spatial modes (LP01/LP11a/LP11b/LP21a/LP21b). The results show that under the influence of different linewidth (LW) of laser and differential mode group delay (DMGD), a 100 % identification success rate can be achieved for five commonly used MFs and eight different cumulative CD values in high baud rate MDM systems, across a wide range of OSNR. Additionally, the mean absolute error (MAE) of OSNR estimation corresponding to the five MFs is 0.22 dB, 0.26 dB, 0.30 dB, 0.32 dB, and 0.36 dB, respectively. The MAE of the eight different MC intensities fluctuate between 0.015 and 0.030. These results fully demonstrate the superior performance of the proposed scheme. Furthermore, the scheme exhibits favorable tolerance to large LWs and fiber nonlinear effects. Moreover, the complexity of the scheme is accurately analyzed through floating-point operations (FLOPs) and parameters (Params), which are much less than existing typical schemes, with specific values of 14.8849 M and 1.3798 M.

Measurement of differential mode group delay in few-mode fibers based on Fresnel reflection peaks.

Mode-division multiplexing communication based on few-mode fibers (FMFs) is the most competitive scheme to address the bandwidth exhaustion in single-mode fibers. The differential mode group delay (DMGD) among different modes in FMFs is an important aspect in characterizing FMFs, and the convenient, fast, and accurate measurement of DMGD in different modes of FMFs is a crucial task. This paper presents a single-ended measurement method for DMGD in FMFs based on Fresnel reflection peaks. Experimental measurements were conducted to determine the DMGD of a 3.689km six-mode fiber and a 9.7km three-mode fiber, and the results were compared with the traditional time-of-flight method. The findings demonstrate that our proposed method based on Fresnel reflection peaks exhibits good accuracy in measuring the DMGD of FMFs. Moreover, this method enables single-ended measurement and offers simplicity and practicality.

A tunable microwave photonic filter based on hole-assisted graded-index few mode fiber with uniform differential modal group delay

A tunable delay-line microwave photonic filter (MPF) based on hole-assisted graded index few mode fiber (HGI-FMF) is proposed. The HGI-FMF is designed with low mode crosstalk, low nonlinear effect and multiple modal groups. In particular, the designed HGI-FMF shows uniform differential modal group delay (MGD) to form finite impulse response (FIR) MPF. The uniform differential MGD is tunable with wavelength, which results in tunable MPF response. The free spectrum range (FSR) of MPF is continuously tunable from 11.73 GHz down to 10.84 GHz with 120 m designed HGI-FMF as the optical source is tuned from 1530 nm up to 1630 nm. The main sidelobe suppression ratio (MSSR) of the 4-taps filter is larger than 9.93 dB, and the 3 dB bandwidth is around 2.62 GHz.

Heterogeneously Integrated Multicore Fibers for Smart Oilfield Applications

In the context of Industry 4.0, the smart oilfield is introduced, which relies on large-scale information exchange among various parts, and there is an urgent need for special fiber links for both increased data transmission capacity and high-sensitivity distributed sensing. Multicore fibers can be expected to play a critical role, in the parts of cores that are responsible for data transmission, while others are used for sensing. In this paper, we propose a heterogeneously integrated seven-core fiber for interconnection and awareness applications in smart oilfields, which could not only support digital and analog signal transmission but could also measure temperature and vibration. The core for digital signal transmission has a low differential mode group delay of 10 ps/km over the C-band, and the crosstalk between adjacent cores is lower than −55 dB/km at the pitch of 50 μm. A 25-Gbaud transmission over 50 km is simulated. Each core for analog signal transmission has a large effective area of 172 μm2 to suppress the nonlinear effect due to the watt-scale input power. The proposed heterogeneously multicore fiber exhibits great potential to be applied in smart oilfields, meeting the demand for efficient and cost-effective oil production.

Characterization of differential modal group delay in few-mode fiber using a digital re-sampling technique.

We characterize the differential modal group delay (DMGD) arising in few-mode fibers (FMFs) based on the digital re-sampling technique, which is commonly used in current digital signal processing flow at the receiver-side. When the DMGD of a 291-m two-mode fiber is characterized over the C-band by using a 500-Mb/s non-return-to-zero (NRZ) signal and 1-GSa/s real-time oscilloscope, the experimental results are consistent with the DMGD obtained from the traditional time-of-flight (TOF) method. However, the wide-bandwidth instruments of the traditional TOF method can be replaced by cheap ones with a bandwidth of only a few hundred MHz, but the same temporal precision is achieved. Moreover, our proposed DMGD characterization method is not limited by the number of guided modes arising in the FMF, together with the capability to obtain both the DMGD value and its sign between two arbitrary guided modes.

Design and Analysis of Z-Trench-Assisted 9-LP-Mode Fiber With Low Differential Modal Group Delay and High Spatial Density

Design and Analysis of Z-Trench-Assisted 9-LP-Mode Fiber With Low Differential Modal Group Delay and High Spatial Density

Compact cyclic fiber three-mode converter based on mechanical fiber grating.

In this Letter, a compact cyclic mode converter (CMC) based on a mechanical fiber grating is proposed and fabricated to eliminate differential mode group delay and mode-dependent loss in the mode division multiplexing (MDM) transmission system. The proposed CMC can realize cyclical interchange of any input mode among the LP01/LP11a/LP11b modes, which requires only one mechanical grating. The mode conversion is evaluated by observing the mode field patterns of the fiber output. The experimental results prove that the introduction of CMC does not significantly degrade the transmission performance of the photonic lanterns back-to-back system. The insertion loss and the average cross talk of the whole system are lower than 5 dB and -11.3 dB, respectively. The proposed CMC provides a new method for reducing link damage in the MDM transmission system.

Impulse Response Characterization of a Commercial Multimode Fiber Using Superconducting Nanowire Single-Photon Detectors

Time-of-flight measurements are key to study distributed mode coupling and differential mode group delay (DMDG) in multimode fibers (MMFs). However, current approaches using regular photodetectors with limited sensitivity preclude the detection of weak modal interactions in such fibers masking interesting physical effects. Here we demonstrate the use of high-sensitivity superconducting nanowire single-photon detectors (SNSPDs) to measure the mode transfer matrix of a commercial graded-index multimode fiber. Two high performance 45-mode multi-plane light conversion (MPLC) devices served as the mode multiplexer/demultiplexer. Distributed mode coupling and DMDG among different mode groups are accurately quantified from the impulse response measurement. We also observed cladding modes of the MMF as a pedestal of the pulse in the measurement. This work paves way for applications such as quantum communications using many spatial modes of the fiber.

Measurement of differential mode group delay in few-mode fiber with correlation optical time-domain reflectometer.

A measurement system of differential mode group delay (DMGD) in few-mode fiber with correlation optical time-domain reflection was proposed. A photonic lantern used in the system can be utilized for mode separation and selection and can generate six LP modes: LP01,LP11a,LP11b,LP21a,LP21b, and LP02. The signal reflected by the end of the fiber is correlated with the data sequence sent, which realizes the single-ended measurement of 5 km few-mode fiber DMGD. This method is not destructive for detecting fiber transmission systems and is simple and easy to implement. It can be used for detecting fiber transmission characteristics in the mode-division multiplexing communication system.

Modified S2 schemes for estimating differential mode group delay in polarization-maintaining few-mode fiber

In the mode-division-multiplexed (MDM) system, the few-mode fiber (FMF) replaces the single-mode fiber (SMF) as the transmission medium, to increase the per-fiber transmission capacity. The polarization-maintaining few-mode fiber (PM-FMF) can greatly enhance the optical communication system, since it can both preserve the polarization state and allow the transmission of multiple modes. To obtain the differential mode group delay (DMGD) value of the PM-FMF, which determines the computational complexity of the equalization algorithm at the receiver, the characterization of the fiber is essential. The conventional S2 method, which can estimate the DMGD of the FMF, cannot be directly applied to the PM-FMF, because it is impossible to determine which of the LP01x and the LP01y mode is the dominant mode. In this work, two new approaches are developed, for the first time to our knowledge, to measure the DMGD in the PM-FMF. The former method is to measure the DMGD in both polarization directions, and LP01x and LP01y are selected as dominant modes, respectively. The latter approach is to realize a simultaneous DMGD measurement of all LP modes, and only LP01y is selected as the dominant mode. It is demonstrated in the experiments that a good agreement has been achieved between the measurement results from both schemes.

Novel Eight-Core Double-Trench Fiber Displaying Low Loss and Supporting Five Linearly Polarized Modes

A novel eight-core double-trench fiber that supports five linearly polarized modes is proposed. The characteristics of the designed fiber are analyzed systematically using the finite element method. A step-pure silicon core and a ring refractive index trench are employed to effectively reduce loss. Furthermore, an internal trench is used to reduce dispersion and the differential mode group delay. The nonlinear coefficient and crosstalk are also reduced effectively by adjusting the fiber geometric parameters and material refractive index. The designed eight-core fiber has potential applications in high-capacity and high-quality fiber communication by mode division multiplexing.

Analysis and optimization of few-mode fibers with low differential mode group delay by variational method

Mode-division multiplexing (MDM) technology based on few-mode fibers (FMFs) is the current research hotspot of optical fiber communication system because of its ability to increase the transmission capacity several times. When the number of multiplexed modes is large, the crosstalk between modes can be removed by multiple input multiple output digital signal processing algorithm at the receiving end. The larger the differential mode group delay (DMGD, <inline-formula><tex-math id="Z-20220504070336-1">\begin{document}$ \tau_{\rm DMGD} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070336-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070336-1.png"/></alternatives></inline-formula>), the more complex the algorithm is. Therefore, in order to reduce the complexity of the receiver, it is necessary to use FMFs with low DMGD. The variational method is proposed to analyze any FMFs with higher refractive index of core than that of cladding. The analytical formula of the fundamental mode size, the normalized propagation constant for each of all guided modes, and DMGD relative to the fundamental mode are derived. Moreover, their relationship with the normalized frequency and other fiber manufacturing parameters are given. On this basis, the graded-index FMFs are studied, and the fiber parameters are optimized. The optimization parameters are the difference between the maximum core refractive index and cladding refractive index <i>n</i><sub>1</sub> – <i>n</i><sub>2</sub> = 0.01, the core radius <i>a </i>= 14 μm, and the paramenter of refractive index distribution <i>α </i>= 1.975. In the optimized FMF, 6 LP modes can be guided and |<inline-formula><tex-math id="Z-20220504070445-1">\begin{document}$ \tau_{\rm DMGD} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070445-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070445-1.png"/></alternatives></inline-formula>| is less than 15 ps/km within the C band and L band. In the end, the effects of the fiber manufacturing errors on DMGD are discussed.

Design and Analysis of Trench Assisted Grade-Index Fiber with Flattened Differential Mode Group Delay by Finite Element Method

Design and Analysis of Trench Assisted Grade-Index Fiber with Flattened Differential Mode Group Delay by Finite Element Method

Applicability of Optical Time Domain Reflectometer for Measuring Differential Modal Group Delay in Few-Mode Fibers

Applicability of Optical Time Domain Reflectometer for Measuring Differential Modal Group Delay in Few-Mode Fibers

Superposition-assisted 125-μm cladding multi-core fibers with ultra-low inter-core crosstalk and high relative core multiplicity factor

We propose a novel superposition-assisted structure (SAS), composed of trench and air holes, in few-mode multi-core fibers (FM-MCFs) to effectively suppress the inter-core crosstalk (XT). The proposed SAS can minimize the inter-core XT to −70.58 dB/100 km in the 7-core fibers, which is 60 dB/100 km lower than the typical trench-assisted structure and 29 dB/100 km lower than the typical hole-assisted structure, respectively. In addition, the SAS does not introduce extra fiber loss and dispersion. In this paper, the key properties of SAS MCFs are numerically simulated using the finite element method (FEM). The large effective area (Aeff) over 90 μm2 enables the suppression of nonlinear effects. The values of dispersion coefficient and differential mode group delay (DMGD) are in the range of 24–42 [ps/(nm·km)] and 5–23 ps/m over C + L band, respectively, which are favorable for fiber communication systems. Such SAS 7-core 5-LP-mode fibers can be further optimized to obtain the cladding diameter of 125 μm, where five propagation modes achieve inter-core XT target below −50 dB/100 km with the bending radius less than 500 mm. Besides, the optimized relative core multiplicity factor (RCMF) can be up to 97.55. The proposed SAS provides a promising solution for the design of FM-MCFs with ultra-low inter-core XT and high capacity for space division multiplexing (SDM).

Simple and precise characterization of differential modal group delay arising in few-mode fiber.

In this Letter, we propose a simple and high-precision differential modal group delay (DMGD) characterization method for few-mode fibers (FMF) by using the frequency-modulated continuous wave. Since the detected signals are located at the low-frequency range, our DMGD characterization method waives the use of expensive equipment, such as vector network or optical spectrum analyzers. Due to the high linearity of the used Mach-Zehnder modulator, our DMGD measurement is free from the complex auxiliary interferometer, leading to an improvement of characterization precision. Meanwhile, we propose a novel spectrum recovery algorithm to overcome the shortcoming that the traditional fast Fourier transform (FFT) method is incapable to deal with spectrum features arising in a periodic signal. Therefore, the characterization precision is no longer limited by the FFT length. When a commercial 23299.8 m two-mode fiber is used in the experiment, the DMGD measurement of LP11 mode relative to LP01 mode has a high precision of ±0.007ps/m over the C-band. Our proposed method shows the potential for characterizing the wavelength-dependent DMGD of FMF with more than two LP modes.

Mode switching using optically induced long-period gratings: a theoretical analysis.

We show that optically induced long-period grating (OLPG) is a particular case of inter-modal Bragg-scattering four-wave mixing (BS-FWM). To carry out such analysis, a vector model for the inter-modal BS-FWM was proposed and further tailored to investigate the energy transfer induced by OLPGs. Both processes, BS-FWM and OLPGs, have been proposed for in-line all-optical mode switching in transmission systems with space-division multiplexing (SDM). In this scope, we demonstrate that the bandwidth of OLPGs is larger than the BS-FWM. Furthermore, we show that OLPG-based mode switching can take place in two windows, if both pump beams are launched near the zero value of the differential mode-group delay, and the central wavelength and the bandwidth of such windows can be tuned by properly adjusting the wavelength and the optical power of the pump beams.

Design and optimization of a microwave photonic filter exploiting differential mode group delay of a multi-mode fiber

A reconfigurable and application-specific tunable microwave photonic filter having finite impulse response is proposed. The filter exploits the differential mode group delays of linearly polarized modes in a multi-mode fiber to achieve single and multiple high-frequency passband response. The filter taps are realized using a single continuous wave laser source and differential delays among modes that are propagated through a single spool of graded index multi-mode fiber. Depending upon the application requirement, different values of free spectral range of the microwave photonic filter are obtained by employing fiber spools of different lengths. The reconfigurability of the microwave photonic filter is achieved by varying the number of linearly polarized modes. It has been shown that the passband ripple can be reduced by employing higher order spatial modes and unequal power ratio among different modes. The proposed filter enables application-specific free spectra range tunability and reconfigurability along with added advantages of easy implementation and passband optimization.

An improved LMS algorithm for mode demultiplexing in frequency domain

In order to solve the problem that the traditional frequency domain least mean square (FD-LMS) algorithm will lose efficacy with the increase of differential mode group delay (DMGD) when the algorithm is used for demultiplexing of the 6×6 mode division multiplexing (MDM) system, an improved FD-LMS demultiplexing algorithm is proposed. By improving the error signal calculation method, the convergence performance of the output signal of the equalization filter is improved, and the steady-state error of the algorithm is reduced. Besides, the equalization performance of the traditional FD-LMS algorithm is compared with the improved FD-LMS algorithm. Simulation results show that the improved FD-LMS algorithm has great advantage over the traditional FD-LMS algorithm in demultiplexing performance on the premise that the computation complexity does not significantly increase. The optical signal to noise ratio (OSNR) penalty of the improved FD-LMS algorithm is 2.6 dB lower than that of traditional FD-LMS algorithm at a transmission distance of 80 km with DMGD is 50 ps/km.