Gain optimization and data modeling of S-band of Tm-doped fiber amplifier based on genetic algorithm

At present, fiber amplifiers are indispensable in the field of communication, Erbium-doped fiber amplifiers (EDFA) are currently more mature fiber amplifiers, but because of electronic bottlenecks, they have approached saturation in recent years. Thus, the study and application of fiber amplifiers doped with other rare earth elements has become a new goal at present. At the same time, expanding the available bandwidth of the fiber amplifier to a higher or lower direction has also become a major task. This article discusses the gain of thulium-doped fiber amplifiers at 1400 nm – 1450 nm (S-band) and uses the genetic algorithm to optimize the fiber length and doping concentration to find the optimal solution, this article also analyzes the change in gain at different fiber lengths and doping concentrations. The results show that the fiber length is 56.2705 meters, and the doping concentration is 59.9502 ×1024 per square meter, at which the gain reaches the peak is 65.19. The results show that the thulium-doped fiber amplifier (TDFA) in this band has good amplification characteristics, and it can be meticulously studied based on this method in the future to obtain more accurate results. It can also be solved using other algorithms, such as Quantum Genetic Algorithms.


Introduction
In recent years, with the development of the communication field, optical fiber communication has become a hot technology in this field.When light travels along a single-mode fiber, it is distorted due to dispersion and polarization, to avoid distortion, the optical fiber amplifier (OFA) is used to amplify the signal, and the greater the gain, the farther the transmission distance is [1].The propagation of optical signals is also inseparable from the demand for fiber amplifiers.Optical Fiber amplifiers doped with rare earth elements play an extraordinary role in signal amplification [1].In the past few years, Erbiumdoped fiber amplifiers (EDFA) have been put into operation and production, and its optimized 1530 nm -1560 nm band (C-band) is also put into normal use in people's daily lives.A recent study has shown that thulium-doped fiber amplifiers (TDFA) exceed the available bandwidth of erbium-doped fiber amplifiers (EDFA) [2].This suggests that the thulium-doped fiber amplifier (TDFA) can fill the bandwidth gap, the band of optical fiber amplification is carried out to a lower band, and the pump power required is lower, which can effectively realize the amplification of the signal, this has also led to more attention for thulium-doped fiber amplifier (TDFA) at present.Some studies have also shown the excellent performance of thulium-doped fiber amplifier (TDFA) in wavelength division multiplexing

The model of the thulium-doped fiber amplifier
In this paper, a 793 nm pumped thulium-doped fiber amplifier is modeled [6].Figure1 shows our model.The signal light is input into WDM together with the pump light, then output as a composite light, amplified by thulium-doped fiber and finally demultiplexing, then output magnified light (the Demux is not given in this model).The role of isolation is to prevent the light from being reflected in front and returning to the fiber behind, to prevent instability in the amplification process.This article will focus on the thulium-doped fiber and discuss its parameters.

Figure 1.
The model of a 793 nm pumped thulium-doped fiber amplifier [6].Normally speaking, The energy level system of the thulium ion should be a four-level system in this band, but due to the high activity of the second and third energy levels, and  3 4 's ions are excited to the upper  3 4 level by the excited absorption [3,7].As Figure2(a) shows, The Tm-doped fiber amplifier in 1400 nm -1450 nm (S-band) is a three-level amplifier characteristic, this model is based on the energy level system in ZBLAN, which is the currently popular material in the field, because of the high-power conversion efficiency (48%) [8].So, the Rate equation and Power propagation equation are about the three-level system with different parameters.Figure 2 shows the different parameters between the normal three-level system and the system investigated in this article [4].The article revises the Rate equation as: And the Power propagation equation is as: () The equation shows that the power and the doping concentration are mainly connected with the second and the third level, this distinction can simplify the computation of the Tm-doped fiber amplifier in this band.About the equation,  is the absorption cross-section or the emission crosssection.is the Overlap factor that describes the rate that ions leap to another level, it is associated with fiber radius and light mode field radius, and the light mode field radius is related to the normalized frequency, and the normalized frequency is related to the refractive index of the core and cladding. is a non-radiated transition rate. is the rate of stimulated radiation.especially, the   is the rate of stimulated radiation of pump light.The  is the loss factor of the fiber optic material and the is full width at half maximum.h is the Planck constant, and c is the speed at which light travels in a vacuum.Table 1 shows the rest parameters and the formula of the equation.The   is the square of the core.

The result of the optimization
This article uses MATLAB to model the Tm-doped fiber amplifier's gain and analyze the data with the change of fiber length and doping concentration.The pump power is set to 200 mw because the gain with the change of pump power is not apparent, As Figure 3(c) shows, it is clear with the change of pump power, the image of the gain does not change much, but observe the image of gain as the fiber length and pump power change, the image of gain is obvious, so it can be referred that the effect of the change of pump power minimal effect the gain.Conversely, the change of fiber length and doping concentration has a greater effect on gain, so change the fiber length and doping concentration to discuss the change in gain.As shown in Figure 4, The author keeps one of the parameters and investigates the effect of the change of another parameter.Through the figure, it is found that in this band, the change in fiber length and doping concentration can well increase the fiber amplifier's gain.Especially, the change in doping concentration is more effective than the change in fiber length.The relationship between gain and fiber length or doping concentration is approximately linearly related.Obviously, at a wavelength of 1420 nm, the increase in gain creates a turn, the slope of the curve before and after is not the same, it is clear that the slope of the wavelength after 1420 nm is greater than the slope of the one of the wavelengths before 1420 nm, this can be seen in all the diagrams.The maximum gain can reach 20-25dB, this also shows that the thulium-doped fiber amplifier in this band has a good amplification effect.Keep the pump power at 200 mw, then analyze at which fiber length and doping concentration maximize the gain.To realize it, this article uses the genetic algorithm to solve this problem.The genetic algorithm is derived from the theory of biological reproduction and development [9].In the process of biological evolution, individuals are through heredity and mutation to eliminate inferior individuals and retain excellent individuals to adapt to the external environment [9].The genetic algorithm is formed by referring to the above phenomena and combining computer-related knowledge [9].This algorithm sets the possible solutions to the problem as a combination, one of the chromosomes in the organism, and the elements corresponding to these individual problems are genes [9].All monomers form the entire population of organisms, and each monomer is calculated according to the prescribed equation [9].First, initialize a portion of the chromosomes (the genetic data for these chromosomes are prescribed arbitrarily), the optimal solution is to select from these.monosomy chromosomes, record their matching degree values for all operations and rely on the obtained matching degree values to take biological evolution operations on all monomers [9].Individuals with insufficient matching values are eliminated, individuals with high matching values are selected, and selected individuals are treated as new populations [9].In this way, the optimal solution is finally solved after repeated iterations [9].The access of the genetic algorithm is shown in Figure 5.

Result and discussion
In this method, Table .2shows the parameters the article used in this model.The absorption and emission cross-section were fit by Figure 6 [7].It can tell by the image, both absorption and emission crosssections are relatively small, the emission cross-section reaches its maximum at 1450 nm, and the absorption cross-section is maximized at 1420 nm, the parameters used in this article are around the center wavelength of 1450 nm.The emission section is near the peak, The absorption cross-section, on the other hand, is not a peak.This article is based on these parameters, taking fiber length and doping concentration as variables, and optimization was carried out in the range of 1-60.As shown in Figure 7, the ASE (Amplified Spontaneous Emission) power increases with the increase of wavelength, and the rate of increase is first faster and then slow.Finally, as the length of the fiber increases, the power changes very little.And in the first short section, the power is zero.The second picture is about pump power, the pump power varies with wavelength, which is kept very low and increases rapidly when it is close to the optimized solution.The third picture is about the signal, The power of the signal light changes with the wavelength, it is first smaller, then gradually increases, and finally reaches a plateau stage.And in the first short section, the power is zero.The fourth picture is about gain, it increases gradually, It is clear that the gain has reached near the peak when the fiber length is relatively small, and later the change in fiber length has less effect on the gain, peaking when the fiber length is optimal.
Through the genetic algorithm, the Pump light wavelength is set to 793 nm [10].when the fiber length is 56.2705 meters and the doping concentration of 59.9502× 10 24 per square meter, the Tm-doped fiber amplifier reaches the highest gain 65.19.This allows Tm-doped fiber amplifiers in this band to achieve efficient amplification, the other algorithms can be used in this band to find the optimal solution in the future to realize the amplification of the signal.Although the algorithm can intuitively obtain the exact solution, the parameters used in this study are only related to the center wavelength, and it did not cover the whole band.And also, the wavelength used in this article is 1450 nm, but the center wavelength is 1470 nm, so it is also an approximate parameter.The pump power is also set to a smaller value, this can avoid the effects of Brillouin scattering [11].There are two types of pumping methods used in other research, one is singlewavelength pumping, and the other is the dual-wavelength pump, the dual-wavelength pump improves the conversion efficiency of pump power very well [12].The treatment of the range of independent variables is also sketchy, the range can be more detailed.The data used in this article are approximate values, and many parameters are also hypothetical values, future studies can conduct experiments to measure the more accurate values of each value so that the optimization results are more accurate.The pump light used in this article is 793 nm, some research shows that the ASE around this wavelength will have a negative effect on signal amplification [7].And This article provides an optimized genetic algorithm, Quantum Genetic Algorithm is to add the relevant content of quantum computing into Genetic Algorithms, and it simplifies some operations of the Genetic Algorithm.For example, quantum superposition properties are used to determine initial populations, quantum revolving doors can be used as an alternative to evolutionary processes, and the direction of evolution is controlled by changing the direction of quantum rotation in such a way.There is not much difference between the quantum genetic algorithm and the genetic algorithm in process, but the steps of the genetic algorithm are simplified by using quantum computing.The Quantum genetic algorithm is relatively new in the application of fiber amplifiers and optical fiber communication, and it is hoped that it can be applied in this field in the future.In the future, it can be discussed based on some of the above theories that are not used in this article and combined with intelligent optimization algorithms and get more precise results.

Conclusion
With the result of simulation and genetic algorithm in MATLAB, we found that at the fiber length of 56.2705 meters and the doping concentration of 59.9502 × 10 24 per square meter, the Tm-doped fiber amplifier reaches the highest gain 65.19.The change of gain with fiber length and doping concentration approximates the linear relationship, but changing the doping concentration affects the gain more.The results of genetic algorithms are not absolute, they can be calculated using other algorithms.Also, the genetic algorithm's value range is cursory, it can be more subdivided to find the best value.And the parameters only connect with the center wavelength, the absorption and emission cross-section is not with the change of wavelength, it is only the numeric value about the wavelength close to the center wavelength.The research shows that the Tm-doped fiber amplifier is available to be used in 1400 nm -1450 nm (S-band) and offers a possibility to extend the available band to the lower band.Later research can also use the optimization algorithm to find the optimal solution, and the advantages of each algorithm can be used to optimize an algorithm centrally, to achieve a more accurate value.

Figure 2 .
Figure 2. The models of Tm-doped fiber amplifiers' levels in the S-band.(a) This model shows the level system used by this article.(b) This model shows the normal three-level system [4].

Figure 3 .Figure 4 .
Figure 3.The change of gain with the different fiber length(a), doping concentration(b) and pump power (c).

Figure 5 .
Figure 5.The access of genetic algorithm.

Figure 6 .
Figure 6.The absorption (b) and emission (a) cross-section of Tm-doped fiber amplifiers in 1400 nm-1450 nm.

Table 1 .
The formula of the Rate equation and the Power propagation equation.

Table 2 .
The parameters that the article used in this model.