Equalization system of low differential mode delay few-mode fibers based on the neural network MIMO algorithm

Hao Guo; Fengping Yan; Fengping Yan; Wsenhua Ren; Wsenhua Ren; Zhenyu Gu; Ting Li; Xiangdong Wang; Dandan Yang; Haoyu Tan; Huan Chang

doi:10.1364/OE.515357

1. Introduction

With the emergence of new technologies, such as mobile internet, big data, and cloud computing, the transmission capacity of the traditional single-mode fiber is approaching its theoretical limit as was defined by Shannon [1]. Therefore, how to meet the increasing demand of data capacity has become a core problem of optical fiber communication research [2,3]. Currently, optical fiber can be multiplexed in several dimensions, including wavelength, polarization, and space. Among them, the mode division multiplexing (MDM) under space division multiplexing (SDM) is a key technology that is expected to be used for the next-generation of high-capacity optical fiber communication [4–6]. However, during the transmission process of few mode fiber (FMF), attenuation, dispersion, nonlinearity, and mode crosstalk deteriorate the signal quality of high rates and long-haul communication transmission, and the different propagation speeds of the different modes result in time delays between modes. The differential mode delay (DMD) is related to the complexity of the equalization algorithm at the receiving end [7–11]. Therefore, the study of the fiber DMD optimization and equalization algorithm becomes extremely important.

At present, research on MDM systems using FMF have many achievements in fiber design and the demultiplexing equalization algorithm based on the multiple input multiple output (MIMO) technique [12–15]. Concerning fiber design, the linear polarization (LP) mode based on FMF can be divided into weakly coupled FMF and low differential delay FMF according to its degree of isolation [16–18]. The weakly coupled FMF has a large refractive index difference between modes and high channel isolation, as well as a large DMD between modes. The complexity of the MIMO equalization algorithm at the receiver end is extremely high for long-distance transmission, and reliability is difficult to guarantee, so it is usually used for short and medium-distance transmission up to 300 km. For strongly coupled FMF, the DMD value can be kept small by precisely designing the refractive index profile of the core, making it suitable for longer distance scenarios where cost sensitivity is low. The design idea for differential delay FMF is to compensate for DMD by using small DMD FMF or by using fibers with positive and negative DMD [19]. The value of DMD affects the number of taps in the filter. A low DMD can reduce the cache requirement for multiplexed signal delay in MIMO-DSP [20]. However, for low DMD fiber, a 2N × 2N (2 represents two polarization states while N denotes the number of the spatial modes) MIMO technique is required to detect all modes simultaneously. A low DMD FMF also imposes high requirements on the equalization algorithm at the receiver end, and the current optical equalization algorithms mainly include least mean squares (LMS), recursive least squares (RLS), and blind equalization algorithms [21–26]. This latter is widely used in optical communication because of its ability to equalize the transmission channels using only the information of the received sequence without the help of the training sequences. It is challenging for the equalization algorithm for full MIMO to completely decouple the crosstalk between various modes in low DMD FMF. As a result, new solutions are required to further optimize the fiber parameter and to design equalization algorithms to get higher convergence accuracy.

For this purpose, we report the design of a trench-assisted gradient refractive index fiber in this paper. The fiber structure is optimized for low DMD by means of a global search with a genetic algorithm (GA), which is faster and easier to obtain a fiber structure that meets the desired DMD than the conventional multiparameter scanning. A least mean squares-feedforward neural network constant modulus algorithm (LMS-FNNCMA) is designed to achieve mode de-crosstalk based on the non-linear fitting capability of neural networks. A 60-channel (LP01, LP11, LP21, LP02 and their degradation modes × 5 wavelength) polarization division multiplexing-wavelength division multiplexing-mode division multiplexing (PDM-WDM-MDM) transmission system is built by simulation, and the designed MIMO equalization algorithm is verified by simulation for 1200 km at 1.2 Tbps.

2. Design of the low DMD FMF

As shown in Fig. 1, the low DMD FMF typically use a gradient refractive index distribution. The gradient refractive index FMF has stronger binding for higher order modes, while the bending loss of the FMF is reduced by introducing a trench-assisted structure [27–30]. The corresponding refractive index distribution of the designed fiber is as follows:

(1)$$n(r) = \left\{ \begin{array}{ll}{n_1}{[1 - 2\Delta {n_1} \cdot {(r/{a_1})^\alpha }]^{1/2}}, &0\mu \textrm{m } \le r \le {a_1}\\ {n_3}, &{a_1} \le r \le {a_2}\\ {n_2}, &{a_2} \le r \le {a_3}\\ {n_3}, &{a_3} \le r \le 62.5\mu \textrm{m} \end{array} \right. ,$$

where n₁ is the refractive index at the center and a₁ is the core radius. The corresponding refractive index is considered to be that of germanium-doped silica with a doping concentration of 3.1%. n₂ is the refractive index at the trench, using the fluorine-doped silica with a doping concentration of 1%. n₃ is the refractive index of pure silica and the refractive index difference between the core center and the cladding is defined as $\Delta {n_1} = (n_1^2 - n_3^2)/2n_1^2$. The relative refractive index difference between the trench-assisted structure and the cladding is defined as $\Delta {n_2} = (n_2^2 - n_3^2)/2n_2^2$. Δn₂ is limited by processing technology to less than 0.5%; w₁ = a₂ - a₁ is defined as the distance between the trench and the core, and w₂ = a₃ – a₂ is the width of the trench defined in the following. α is the refractive index modulation index. When α = 1, the refractive index of the core varies linearly with position, and when α = ∞, the refractive index of the fiber has a stepwise distribution.

Fig. 1. (a) Schematic of cross section and (b) refractive index profile of the gradient refractive index fiber with the trench-assisted structure.

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Considering the following analysis of fiber dispersion and DMD, the wavelength dependence of the refractive index of the fiber is usually calculated using the third-order Sellmeier equation [31,32]. The coefficients based on the Sellmeier equation for the materials considered in this paper are shown in Table 1 at a room temperature of 20 °C. In Table 1, A_i represents the Sellmeier amplitude and λ_i represents the wavelength. However, due to the gradient distribution of the refractive index of the fiber within the a₁ radius, it is not possible to calculate it directly using the Sellmeier equation. Therefore, it is solved using the following equation:

(2)$$n(\lambda ) = \left\{ {\begin{array}{ll} {\sqrt {n_b^2(\lambda )+ \frac{{{n^2}({\lambda_0}) - n_b^2({\lambda_0})}}{{n_{d + }^2({\lambda_0}) - n_b^2({\lambda_0})}} \cdot ({n_{d + }^2(\lambda )- n_b^2(\lambda )} )} ,} &{n > {n_b}}\\ {\sqrt {n_b^2(\lambda )- \frac{{n_b^2({\lambda_0}) - {n^2}({\lambda_0})}}{{n_b^2({\lambda_0}) - n_{d - }^2({\lambda_0})}} \cdot ({n_b^2(\lambda )- n_{d - }^2(\lambda )} ),} } &{n < {n_b}} \end{array}} \right.$$

where n_b is for the subject material, which is pure silica in this paper. n_d₊ is for the positively doped material, which is germanium-doped silica with a doping concentration of 3.1%. n_d- is the negatively doped material, which means fluorine doped silica with a doping concentration of 1%.

Table 1. Sellmeier resonance wavelength and Sellmeier amplitude for different doping cases

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Traditionally, the design of low DMD optical fibers is achieved through manual parameter settings and multi parameter scanning. Due to the large number of fiber parameters, traditional methods are not only time-consuming but also difficult to find low DMD fiber structure that meet the requirements. We introduce genetic algorithm to randomly generate multiple fiber structures and calculate their fitness. During the selection process, according to the roulette wheel method, individuals with higher fitness have a higher proportion and are more likely to be retained in each selection. To generate new individuals in the next iteration process, we change the individuals through crossover and mutation. After sufficient iterations, the individual's fitness will become higher and higher. Genetic algorithms (GAs), which originated from computer simulation studies of biological systems, are robust in multi-parameter optimization and can find the globally optimal solution to an optimization problem [33–35]. Figure 2 shows the structure for finding the minimum DMD of a fiber using the GA. This method has universality and can find fiber structures that meet our requirements in a shorter time compared to multiparameter scanning methods. This study aims to ensure six-mode (LP01, LP11, LP21, LP02 and their degradation modes) transmission, we set the normalized frequency to 7.2. The population size is set to 50 by binary coding of the α, Δn₁, Δn₂, a₁, w₁, and w₂ fiber structure parameters. The population continues to evolve into a group with high fitness. A co-simulation using Comsol and Matlab software is used to calculate the DMD, with the GA fitness function defined as F = 1/max|DMD|. The populations are selected using the roulette wheel method with crossover and mutation probabilities of 0.95 and 0.05, respectively. By setting a target DMD of less than 20 ps/km, the algorithm iterates to obtain the required fiber structure parameters.

Fig. 2. Flowchart of the intelligent design methodology for low DMD FMF.

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Figure 3(a) shows the iterative diagram of the optimized fiber structure by GA. By setting the threshold value as 20 ps/km, it is observed that the fiber with a DMD of 19.6 ps/km can be achieved after the eighth iteration. The corresponding target fiber structure parameters are α = 1.99, Δn₁ = 0.53%, Δn₂ = -0.42%, a₁ = 12.3 µm, w₁ = 1.6 µm, and w₂ = 3.4 µm.

Fig. 3. (a) The iterative diagram for the optimized fiber structure using the GA and (b) DMD of the optimized trench-assisted graded-index fiber as a function of wavelength.

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Table 2 lists the optical properties at 1550 nm obtained for the optimized gradient refractive index fiber with the trench- assisted structure. The bending loss is obtained by the conformal mapping method at a bending radius of 10 mm and an elastic-optical correction factor of 1.28 [36]. Due to the presence of the trench structure, it can be found that the bending loss of the fiber obtained is less and the mode field area is greater than 100 µm² for all modes, which ensures a smaller mode nonlinear action. The chromatic dispersion of the designed fiber is kept between 20 and 22 ps/nm/km and the chromatic dispersion is handled by a dispersion compensation algorithm at the receiving end. Figure 3(b) shows the variation of DMD with wavelength of the designed fiber with 7.3 and 7.6 throughout the C-band, which ensures the desired mode transmission. Also, the DMD value of this fiber tends to be flat and less than 30 ps/km in the whole C-band, which has good stability characteristics.

Table 2. Optical properties of optimized gradient refractive index fiber with the trench-assisted structure

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However, the fabrication of gradient refractive index FMF is very challenging for the processing technique. The effect of actual fabrication on the DMD of the designed fiber is considered. Figure 4 shows the variation of DMD values for parameters α, Δn₁, Δn₂, a₁, w₁, and w₂ at 1%, 3%, and 5% difference from the optimum values. The change of parameter α has a large effect on the DMD of the fiber; the rest of the parameters have a smaller effect on the DMD. However, under a design tolerance of 1%, the values of overall DMD are less than 80 ps/km, which reflects good manufacturing tolerance and proves the feasibility of the designed optical fiber.

Fig. 4. The change in DMD value for 1%, 3%, and 5% change in the parameters of the gradient refractive index fiber with the trench-assisted structure.

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3. Design of the MIMO equalization algorithm

The current mainstream equalization algorithms include mainly LMS and CMA, among others. LMS is simple to implement and has fast convergence speed, but the accuracy is poor, and CMA has high convergence accuracy but slow convergence speed and easily falls into the local optimal solution. At the same time, both LMS and CMA algorithms cannot fit nonlinear data. By analyzing the characteristics of various algorithms and overcoming the shortcomings of the existing algorithms, we improve the ability to process data by introducing neural network, and design the least mean squares-feedforward neural network constant modulus algorithm (LMS-FNNCMA) to obtain higher convergence accuracy and greater convergence speed.

Figure 5 shows a schematic framework diagram of the designed LMS-FNNCMA algorithm for MIMO equalization, which is composed of four parts: transversal filter, adaptive LMS algorithm, neural network, and blind equalization algorithm. The algorithm is divided into a training part for the training input signal u(n) and a testing part for the working input signal x(n). The algorithm first goes through the training part of the training input signal u(n) for data training; after that it passes through the test part of the working input signal x(n) for data transmission. The training portion of the training input signal u(n) consists of a transversal filter and a weight vector adjustment by the adaptive LMS algorithm. The training input signal u(n) is filtered by a transversal filter whose coefficients are controlled by the adaptive LMS algorithm. The data training part is completed after performing sufficient iterations. The test part of the work input signal x(n) consists of a neural network, a blind equalization algorithm, and a signal decision. The work input signal y(n) obtained from the training part is secondarily filtered by the neural network w(n), the weight coefficients of the neural network are controlled by the blind equalization algorithm, and after sufficient iterations, the output is obtained by the signal decision.

Fig. 5. Schematic framework diagram of the designed LMS-FNNCMA for MIMO equalization.

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The detailed algorithmic processing flow is as follows. The algorithm first turns on the A₁ and A₂ switches and passes the training input signal u(n) through the transversal filter, and then the weight coefficients are adjusted by the LMS algorithm to continuously approximate the known desired response d(n). After completing the learning process, the value of the transversal filter reaches the optimal design. One then fixes its weighting coefficients, open the B₁ and B₂ switches to filter the work input signal x(n), and after that, based on the cost function method, through the neural network w(n) coefficients adjusted by the blind equalization algorithm constantly coefficients, selects the appropriate nonlinear activation function, and carries out the secondary filtering operation on the work input signal y(n) filtered by the LMS algorithm, and finally get the judgment output through the signal decision.

The error signal e(n) of the adaptive LMS algorithm is determined by the difference between the known desired response d(n) and the estimated response $\hat{d}(n )$ obtained through the transversal filter. The desired response is continuously approximated by a minimum mean square error (MSE) criterion.

Figure 6 shows the neural network equalization architecture. Where INPUT is the signal input, N_C is the number of channels, N_T is the number of taps, W1 and W2 are filters, O_U is the hidden layer of input, and O_V is the hidden layer of output. The neural network consists of input, hidden and output layers. For a channel with N modes, the INPUT consists of N_T of data, and it is filtered by the W1 filter. The filters consist of N² groups, and the number of filters in each group corresponds to the number of input layers. After filtering, it enters the hidden layer to form N² data points O_U. In the next step, it forms O_I by passing the function f (·); then it is filtered again by W2 filter to get O_V. Finally, the output layer output EOUT is obtained by executing the function f (·). The state equation of the neural network is expressed as follows:

(3)$$J(n) = \frac{1}{2}{[{{{|{\tilde{x}(n)} |}^2} - {R_2}} ]^2},{R_2} = \frac{{E[|x(n){|^4}]}}{{E[|x(n){|^2}]}}$$

(4)$$O\_{U^k}(n )= \sum\limits_{j = 0}^{N\_C - 1} \cdot \sum\limits_{i = 0}^{N\_T - 1} {W1_{ji}^k(n )INPU{T_j}({n - i} )}$$

(5)$$O\_{I^k}(n )= f[{O\_{U^k}(n )} ]$$

(6)$$O\_{V^m}(n )= \sum\limits_{k = N\_C \times m}^{N\_C \times m + N\_C - 1} {W{2^k}(n )} O\_{I^k}(n )$$

(7)$$EOU{T^m}(n )= f[{O\_{V^m}(n )} ]$$

where k (an integer value between 0 and N² - 1) denotes the (k + 1)^th value of INPUT after the filter. As for the variable i (an integer value between 0 and N_T - 1), it denotes the number of taps whereas the variable j (j = 0, 1, ⋯, N - 1) denotes the number of channels. N is the total number of channels. W1 generated the connection weights of the input and the hidden layers whereas W2 represents the connection weights of the hidden and the output layers. After that, the following weight iteration formula is obtained according to the theory of the CMA algorithm:

(8)$$W{2^k}({n + 1} )= W{2^k}(n )- {\mu _1}\frac{{{p^k}(n )}}{{|{EOU{T^m}(n )} |}}O\_{I^k}^ \ast (n )$$

(9)$${p^k}(n )= ({|{EOU{T^m}(n )} |- {R_2}} ){q^k}(n )$$

(10)$$\begin{aligned} {q^k}(n ) &= f[{{\rm Re} \{{O\_{V^k}(n )} \}} ]f^{\prime}[{{\rm Re} \{{O\_{V^k}(n )} \}} ]\\ &+ jf[{{\mathop{\rm Im}\nolimits} \{{O\_{V^k}(n )} \}} ]f^{\prime}[{{\mathop{\rm Im}\nolimits} \{{O\_{V^k}(n )} \}} ]\end{aligned}$$

(11)$$W1_{ji}^k({n + 1} )= W1_{ji}^k(n )- {\mu _2}\frac{{{h^k}(n )}}{{|{EOU{T^m}(n )} |}}INPUT_j^ \ast ({n - i} )$$

(12)$$\begin{aligned} {h^k}(n ) &= 2({{{|{EOU{T^k}(n )} |}^2} - {R_2}} )f^{\prime}[{{\rm Re} \{{O\_{U^k}(n )} \}} ]{\rm Re} \{{{q^k}(n )W{2^k}^ \ast (n )} \}\\ &+ j2({{{|{EOU{T^k}(n )} |}^2} - {R_2}} )f^{\prime}[{{\mathop{\rm Im}\nolimits} \{{O\_{U^k}(n )} \}} ]{\mathop{\rm Im}\nolimits} \{{{q^k}(n )W{2^k}^ \ast (n )} \}\end{aligned}$$

where ${\mu _1} = {\mu _2} = \alpha |{EOU{T^m}(n )} |$ is the iteration step size, and $\alpha$ is a constant. The range of value of k in Eqs. (8) to (12) is $N\_C \times m \le k \le N\_C \times m + N\_C - 1$. In order to achieve both a faster and a more accurate convergence, we use the following activation function:

(13)$$f(x )= x + E[{{{({{R_2} - |{\tilde{x}(n)} |} )}^2}} ]\sin \pi x$$

Fig. 6. The architecture diagram of the neural network MIMO equalization.

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Traditionally, linear equalization in the optical MIMO case would use MMSE, zero-forcing or other such linear processing techniques that would simultaneously handle both dispersion and cross-talk. The CMA, LMS, and modified constant modulus algorithm (MCMA) algorithms have been studied in optical communication systems [37,38]. Using neural network is to improve the transmission performance in the presence of fiber nonlinearity. The iterative comparison of the designed LMS-FNNCMA algorithm with the CMA and LMS algorithms is shown in Fig. 7. The inset shows the training part, where training through 30000 data lengths brought the MSE down to a small range, while the coefficients of the filter are continuously adjusted. By comparing CMA, LMS, and LMS-FNNCMA, it can be found that the CMA algorithm and LMS algorithm have poor equalization effect, whereas the LMS-FNNCMA algorithm can reduce the MSE value effectively and has good convergence.

Fig. 7. The iterative diagram of the designed LMS-FNNCMA with the existing LMS and CMA.

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4. Optical fiber transmission system

We built a simulated optical communication system using the designed fiber and algorithm. The simulation model of the FMF based PDM-WDM-MDM system is shown in Fig. 8. The construction of the optical communication system is based on the VPI, and the system is shot noise limited. The system uses 4-quadrature amplitude modulation (4-QAM) modulation format for 12 modes (2 polarizations × 6 spatial modes (including LP modes degeneracies)) of the multiplexed system. At the transmitter side, the laser generates five signal lights with a center wavelength of 1550 nm and a wavelength spacing of 50 GHz. The light generated by the laser is modulated by a transmitter for PDM optical signal. In the transmitter the light is divided into two paths by a polarizing beam splitter (PBS) whose polarization states are orthogonal to each other. Two 10 Gbps signals are sent through the IQ driver loaded into the IQ modulator to obtain a 20 Gbps 4-QAM signal. After being modulated by the IQ modulator, the two signal paths are combined into a 40 Gbps PDM-4QAM signal through a polarization beam combiner (PBC), after which PDM-4QAM signals at five wavelengths are input to wavelength division multiplexer to form a 200 Gbps PDM-WDM-4QAM signal, which is then combined by the mode division multiplexer to form a 1.2 Tbps PDM-WDM-MDM-4QAM signal. At the transport link, the signal light is amplified by a few-mode erbium doped fiber amplifier (FM-EDFA), and the link is transmitted using the designed low DMD FMF, with the signal light being looped through the Loop.

Fig. 8. The PDM-WDM-MDM transmission simulation system diagram and DSP flowchart.

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After a multi-turn cyclic transmission, the signal light is sent to the mode demultiplexer and then photoelectrically converted through a polarization diversity coherent receiver (PD-CRX) with subsequent DSP processing. The specific parameters of the system are shown in Table 3. The obtained digital signal is first orthogonally normalized by IQ imbalance correction and normalization, after which the frequency offsets of the clock at the transmitter side and the sampling clock at the receiver side, as well as the phase jitter of the sampling clock, are removed by clock phase recovery. The frequency dispersion compensation algorithm is used to compensate for the dispersion characteristics of the designed low DMD FMF. After data synchronization, the designed LMS-FNNCMA algorithm is utilized for equalization to obtain the iterative diagram of the algorithm as shown in Fig. 9. The obtained MSE values of each mode are in a very low range, all less than 0.2, and good mode equalization effect is achieved. The optical signal to noise ratio (OSNR) of the signal is adjusted by introducing Gaussian white noise in the transmission link, and the OSNR is plotted as a function of bit error ratio (BER) as shown in the inset. The BERs of each mode at 20 dB are all less than 1 × 10⁻³ and the constellation diagrams have a very high degree of differentiation, which is able to satisfy high-speed long-distance transmission.

Fig. 9. The iterative diagram of the designed LMS-FNNCMA.

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Table 3. Main parameters of optical communication system

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5. Conclusion

In this work, we have designed a low DMD FMF along with a new equalization algorithm. We used a trench-assisted structural design and optimized the fiber using a GA to achieve a maximum DMD value of 19.6 ps/km. To achieve faster convergence and higher convergence accuracy, we also designed the LMS-FNNCMA algorithm based on LMS, CMA algorithm, and MIMO neural network.

In addition, the PDM-WDM-MDM transmission system is constructed considering the effect of the equalization algorithm in the MDM transmission system. After system equalization using LMS-FNNCMA, the MSE of each mode is in the very low range, and the constellation diagrams of each mode can be well distinguished, which fully supports the reliability of the transmission system. It is found that under the simulation conditions of 1.2 Tbps rate and 1200 km transmission distance, the BER of each mode at 20 dB optical SNR is less than 1 × 10⁻³, sufficient to ensure the high-speed and long-distance transmission requirements.

Funding

National Key Research and Development Program of China (2021YFB2800900); Program of the National Natural Science Foundation of China (62335001); National Natural Science Foundation of China (62075008).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Material	A₁	A₂	A₃	λ₁/µm	λ₂/µm	λ₃/µm
SiO₂	0.6961663	0.4079426	0.897479	0.0684043	0.1162414	9.896161
SiO₂ + 3.1% GeO₂	0.7028554	0.4146307	0.897454	0.0727723	0.11430853	9.8961609
SiO₂ + 1%F	0.69325	0.3972	0.86008	0.0672398	0.11714009	9.7760984

		LP₀₁	LP₁₁	LP₂₁	LP₀₂
n_eff	(×1)	1.4497	1.4477	1.4456	1.4456
A_eff	(µm²)	127	255	283	338
DMD vs. LP₀₁	(ps/km)	/	5.1	9.6	19.6
Dispersion	(ps/nm/km)	20.8	21.0	21.2	21.1
Bend Loss ₁₀ mm_radius	(dB/turn)	≪1	≪1	<1	1.2

Parameter name	Parameter value
Number of modes	6
Number of wavelengths	5
Wavelength spacing	50 GHz
Capacity	1.2 Tbps
Fiber length	80 km
Distance	1200 km
Modulation format	4-QAM
Laser linewidth	10 kHz
polarization mode dispersion	0.05 ps/km^1/2

Material	A₁	A₂	A₃	λ₁/µm	λ₂/µm	λ₃/µm
SiO₂	0.6961663	0.4079426	0.897479	0.0684043	0.1162414	9.896161
SiO₂ + 3.1% GeO₂	0.7028554	0.4146307	0.897454	0.0727723	0.11430853	9.8961609
SiO₂ + 1%F	0.69325	0.3972	0.86008	0.0672398	0.11714009	9.7760984

		LP₀₁	LP₁₁	LP₂₁	LP₀₂
n_eff	(×1)	1.4497	1.4477	1.4456	1.4456
A_eff	(µm²)	127	255	283	338
DMD vs. LP₀₁	(ps/km)	/	5.1	9.6	19.6
Dispersion	(ps/nm/km)	20.8	21.0	21.2	21.1
Bend Loss ₁₀ mm_radius	(dB/turn)	≪1	≪1	<1	1.2

Equalization system of low differential mode delay few-mode fibers based on the neural network MIMO algorithm

Abstract

1. Introduction

2. Design of the low DMD FMF

3. Design of the MIMO equalization algorithm

4. Optical fiber transmission system

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (3)

Equations (13)

Optics Express