CN111999795A - High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method - Google Patents

High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method Download PDF

Info

Publication number
CN111999795A
CN111999795A CN202010731406.2A CN202010731406A CN111999795A CN 111999795 A CN111999795 A CN 111999795A CN 202010731406 A CN202010731406 A CN 202010731406A CN 111999795 A CN111999795 A CN 111999795A
Authority
CN
China
Prior art keywords
optical fiber
mode
fiber
power
gain
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010731406.2A
Other languages
Chinese (zh)
Other versions
CN111999795B (en
Inventor
陈诗静
杨雨
武春风
李强
姜永亮
吕亮
刘厚康
胡金萌
宋祥
雷敏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan Optical Valley Aerospace Sanjiang Laser Industry Technology Research Institute Co Ltd
Original Assignee
Wuhan Optical Valley Aerospace Sanjiang Laser Industry Technology Research Institute Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Wuhan Optical Valley Aerospace Sanjiang Laser Industry Technology Research Institute Co Ltd filed Critical Wuhan Optical Valley Aerospace Sanjiang Laser Industry Technology Research Institute Co Ltd
Priority to CN202010731406.2A priority Critical patent/CN111999795B/en
Publication of CN111999795A publication Critical patent/CN111999795A/en
Application granted granted Critical
Publication of CN111999795B publication Critical patent/CN111999795B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/02—Optical fibres with cladding with or without a coating
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/02—Optical fibres with cladding with or without a coating
    • G02B6/036—Optical fibres with cladding with or without a coating core or cladding comprising multiple layers
    • G02B6/03616—Optical fibres characterised both by the number of different refractive index layers around the central core segment, i.e. around the innermost high index core layer, and their relative refractive index difference
    • G02B6/03622—Optical fibres characterised both by the number of different refractive index layers around the central core segment, i.e. around the innermost high index core layer, and their relative refractive index difference having 2 layers only
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
    • H01S3/05—Construction or shape of optical resonators; Accommodation of active medium therein; Shape of active medium
    • H01S3/06—Construction or shape of active medium
    • H01S3/063—Waveguide lasers, i.e. whereby the dimensions of the waveguide are of the order of the light wavelength
    • H01S3/067—Fibre lasers
    • H01S3/06708—Constructional details of the fibre, e.g. compositions, cross-section, shape or tapering
    • H01S3/06716—Fibre compositions or doping with active elements
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
    • H01S3/05—Construction or shape of optical resonators; Accommodation of active medium therein; Shape of active medium
    • H01S3/06—Construction or shape of active medium
    • H01S3/063—Waveguide lasers, i.e. whereby the dimensions of the waveguide are of the order of the light wavelength
    • H01S3/067—Fibre lasers
    • H01S3/06708—Constructional details of the fibre, e.g. compositions, cross-section, shape or tapering
    • H01S3/06729—Peculiar transverse fibre profile
    • H01S3/06733—Fibre having more than one cladding

Abstract

The invention discloses a high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect, wherein the optical fiber is a double-clad fiber and sequentially comprises a fiber core and an inner cladding from inside to outside, or other rare earth ions are doped in the fiber core to serve as a gain medium, the inner cladding is a quartz cladding, and the diameter of the fiber core is 15-100 mu m; the numerical aperture NA of the fiber core is 0.01-0.1; the cross section of the inner cladding is regular octagon; the diameter of the inner cladding is 300-; the absorption coefficient @915nm of the cladding pump is 0.2-1.0 dB/m; the optical fiber is bent and coiled, and the bending radius is between 2.5 and 80 cm. According to the invention, parameters influencing the threshold values of the nonlinear effect and the mode instability effect in the optical fiber are brought into a theoretical model for calculation, and the optical fiber parameters and the bending radius which can meet the requirements of a high-power optical fiber laser and inhibit the gains of the nonlinear effect and the mode instability effect are selected in combination with the existing process level and experimental conditions, so that the threshold values of the mode instability and the nonlinear effect are changed simultaneously, and the maximum output power of the optical fiber is improved.

Description

High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method
Technical Field
The invention belongs to the technical field of fiber laser, and particularly relates to a high-power gain fiber capable of simultaneously inhibiting mode instability and nonlinear effect and a design method thereof.
Background
High power lasers have no alternative role in many fields such as industrial manufacturing, remote detection, communication transmission, military equipment and the like. The high-power fiber laser combines the advantages of optical fibers and high-power lasers, has the advantages of small volume, high power, good beam quality and the like, and realizes single-fiber 2 kW-level near-diffraction limit output at present.
The gain medium in the optical fiber laser utilizes the optical fiber doped with rare earth ions to realize laser gain output, and the most widely applied is the Nd (neodymium) doped quartz optical fiber at present, which has the advantages of mature process and stable performance. With the continuous development of optical fiber materials, -doped optical fibers attract people's attention due to lower quantum loss and higher doping concentration, and through years of research, the -doped optical fibers have been successfully developed, so that the output power of the optical fiber laser is greatly improved, and the application range of laser is expanded.
As fiber lasers continue to evolve to higher powers, nonlinear effects and mode instability effects become two more and more important factors that limit the increase in laser output power. In order to reduce the nonlinear effect in the optical fiber, the core diameter of the optical fiber needs to be increased, but the effect of suppressing mode instability of the optical fiber is poor due to the increase of the core diameter of the optical fiber; conversely, reducing the fiber core may suppress mode instability effects but may enhance nonlinear effects. Therefore, by combining the power requirement of the development of the high-power fiber laser, a new design research is carried out on the gain fiber under the existing fiber laser overall industrial design framework, and a foundation is laid for the further development of the high-power fiber laser.
The research of the factors limiting the improvement of the laser output power by utilizing the optical fiber theory simulation has a certain theoretical basis. In 2018, Zervas et al published a document "Power scaling limits in high Power fiber amplifiers products to transverse mode instability," thermal length, and fiber mechanical reliability "(proc. spie 10512), and calculated the model of the highest output Power of the optical fiber under the condition of considering the limiting factors such as the nonlinear effect, the mode instability effect, etc., but the calculated mode instability effect threshold in the model is too coarse, the accuracy is too low, and the influence of the numerical aperture change on the mode instability threshold cannot be reflected. In 2015, a detailed model is established in doctor's graduation paper by the university of defense science and technology of ceramic ru mao to analyze the influence of optical fiber parameters on the mode instability threshold. However, the influence caused by bending loss is not considered, and the nonlinear effect is not connected to calculate the highest power value of the output of the optical fiber.
Disclosure of Invention
In order to solve the problems, the invention mainly refers to a theoretical model and a formula of the high-power gain optical fiber designed in the two documents, combines experimental data, provides a method for designing the high-power gain optical fiber for simultaneously inhibiting mode instability and nonlinear effect, and designs the high-power gain optical fiber for simultaneously inhibiting the mode instability and the nonlinear effect. The numerical aperture NA of the fiber core, the diameter of the inner cladding, the absorption coefficient of the cladding pump and the coiling bending radius of the optical fiber are optimized, the purpose of balancing the stimulated Brillouin effect and the mode instability effect during high-power laser output in the optical fiber is achieved, and the highest output power of the optical fiber is improved.
The high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect is a double-clad optical fiber and sequentially comprises a fiber core and an inner cladding from inside to outside, wherein or other rare earth ions are doped in the fiber core to serve as a gain medium, the inner cladding is a quartz cladding,
the diameter of the fiber core is 15-100 mu m;
the numerical aperture NA of the fiber core is 0.01-0.1;
the cross section of the inner cladding is in a regular octagon shape or a quincunx shape, a D shape, a hexagonal shape or other non-circular shapes;
the diameter of the inner cladding is 300-;
the position of the cladding pumping absorption coefficient @915nm is 0.2-1.0 dB/m;
the optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm.
Furthermore, the diameter of the fiber core is 35-80 μm.
Furthermore, the numerical aperture NA of the fiber core is 0.03-0.07.
Further, the diameter of the inner cladding layer is 500-1000 μm.
Further, the cladding pumped absorption coefficient @915nm is 0.4-0.8 dB/m.
Further, the optical fiber is bent and coiled, and the bending radius is between 17.5 and 65 cm.
The invention relates to a design method of a high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect, which comprises the following steps:
s1, establishing a nonlinear effect threshold calculation model of the gain optical fiber and different mode laser gain calculation models of signal light in the optical fiber;
s2, setting a plurality of variation ranges of optical fiber parameters according to experimental experience, wherein the variation ranges comprise numerical aperture NA, fiber core diameter, cladding diameter, absorption coefficient and optical fiber length;
s3, bringing the optical fiber parameters into a nonlinear effect calculation model, calculating the range of the nonlinear effect threshold at the moment, and selecting the optical fiber parameter group meeting the high power requirement;
s4, substituting the fiber parameter group into a mode gain calculation model in the fiber, calculating the signal light output power and the high-order mode ratio of the fiber parameter group under the changed bending radius, selecting the corresponding bending radius range in the proper bending loss range, and when the mode instability effect does not occur, taking the highest output signal light power in the bending radius range as the theoretical highest output power of the fiber, namely the mode instability effect threshold of the parameter fiber;
and S5, comparing the mode instability effect threshold calculated in the step S4 with the nonlinear effect threshold calculated in the step S3, and taking the smaller value as the design value of the highest output power of the optical fiber to ensure that the mode instability effect threshold and the nonlinear effect threshold of the optical fiber are not less than the highest output power of the optical fiber.
Specifically, in step S3, the nonlinear effect threshold calculation formula is specifically as follows:
Figure BDA0002603282260000031
Figure BDA0002603282260000032
wherein, V is normalized working frequency, U is normalized transverse phase parameter, W is normalized transverse attenuation parameter, and the calculation formula is V2＝W2+U2,V＝kRNA，
Figure BDA0002603282260000041
k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m is 0; j. the design is a square0(U)、
Figure BDA0002603282260000042
The representative variables are U,
Figure BDA0002603282260000043
First class 0 Bessel function, Km-1(W)，Km+1(W) represents a second class of m-1, m +1 order Bessel functions with the variable W.
gB(Δ v) is the SBS gain coefficient, typically taken at 5 x 10 in silica fiber-11；
G is the laser gain of the fiber;
r is the core radius of the optical fiber;
l is the fiber length;
a is an experimental fitting coefficient which is experimentally measured for multiple sets of nonlinear effect thresholds
Figure BDA0002603282260000044
Substituting the formula (1) to calculate a plurality of groups of A (n) values, and taking an average value to obtain the value; from the above equation, it can be seen that changing the core radius R and the length L of the optical fiber can significantly change the threshold of the nonlinear effect.
Specifically, in step S4, there are two modes, namely, a fundamental mode and a high-order mode, in the optical fiber, and the gain amplification conditions of different modes are different, and the calculation formulas of the fundamental mode and the high-order mode power in the output-end signal light are specifically as follows:
Figure BDA0002603282260000045
Figure BDA0002603282260000046
Figure BDA0002603282260000047
Figure BDA0002603282260000048
wherein the content of the first and second substances,
P1(0) is the incident signal optical power;
2is a high-order mode overlapping factor, and is calculated when m is 1 according to the formula (2);
g (z) is the gain coefficient when the laser propagates along the axial direction of the fiber by a distance z;
Figure BDA0002603282260000051
is the absorption and emission cross section of the corresponding signal light, nuThe upper energy level particle number proportion is determined by the pump light power;
NYbthe rare earth ion doping concentration of the optical fiber is in direct proportion, G is total pump absorption which is generally a constant value and is in inverse proportion to the length L of the optical fiber;
χ is the mode coupling coefficient, which is related to the cladding radius;
P1(L)、P2when z is equal to L, that is, the power of the fundamental mode and the high-order mode in the signal light at the output end;
xi is the signal light power P when the high order mode accounts for the total signal light ratio and xi is 0.051(L) as the mode instability threshold at this time,
therefore, the mode instability threshold is related to the core size, the cladding size, the fiber length, and the numerical aperture parameters, and besides, the mode instability threshold can be significantly increased due to different optical losses of different mode signals in the optical fiber caused by bending of the optical fiber. The loss coefficient calculation formula of different modes generated by fiber bending (coil) is as follows:
Figure BDA0002603282260000052
β is the propagation constant;
Km-1(W)，Km+1(W) represents a second class of m-1, m +1 order bessel functions with variables W, the base mode m being 0, the higher order mode m being 1; j. the design is a square0(U)、
Figure BDA0002603282260000053
The representative variables are U,
Figure BDA0002603282260000054
To (1) aClass 0 Bessel function, K0(U)、
Figure BDA0002603282260000055
The representative variables are U,
Figure BDA0002603282260000056
Second class 0 order bessel functions;
when m is 0, emWhen m is 1, em＝2；
RcoilIs the bend radius of the optical fiber;
therefore, when the optical fiber parameters are fixed and the wavelength of the signal light is not changed, the bending loss coefficient alpha iscoilFrom the bending radius RcoilDetermining that the bending loss can be changed by changing the bending radius, so that the power ratio of each mode in the signal light power is influenced; the power relations of the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the optical fiber is bent are as follows:
Figure BDA0002603282260000061
P01(L)、P′01(L)、P11(L)、P′11(L) are respectively the LP01 fundamental mode and LP11 high-order mode powers before and after bending,
Figure BDA0002603282260000062
bending-induced bending loss coefficients of LP01 fundamental mode and LP11 higher-order modes
Figure BDA0002603282260000063
When the high-order mode power accounts for 0.05 of the total power of the signal light, the mode instability effect is considered to occur, so that the proportion of the high-order mode in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold value is improved.
Specifically, in step S4, the fiber parameter set meeting the high power requirement in step S3 is substituted into the mode gain model in the optical fiber, and the mode instability threshold under the fiber parameter set is calculated, specifically, the calculation steps are as follows:
s41, establishing a transmission amplification model of a fundamental mode and a high-order mode of signal light in the gain fiber, and assuming that the initial signal light power is P1(0) Fundamental mode fraction (1-n), higher order mode fraction n, incident pump light power Pp, fiber core radius R, cladding radius R1, fiber length L, cladding absorption coefficient α dB/m, bend radius RcoilCalculating the power P of the high-order mode in the length direction of the optical fiber in a steady state2(z), power P of fundamental mode1(z) distribution;
s42, substituting the above parameters into formulas (2), (3), (4), (5), (6), (7) and (8), judging whether the higher-order mode ratio xi is more than 0.05, if not, the mode instability effect does not occur, at this time, the higher-order mode ratio xi is not more than 0.05
Figure BDA0002603282260000064
If greater than 0.05, a mode instability effect has occurred.
S43, according to S42, adjusting power of input signal light and pump light, when xi is close to 0.05, outputting signal light P1(L) threshold for the effect of mode instability
Figure BDA0002603282260000071
According to the high-power gain optical fiber design method capable of simultaneously inhibiting the mode instability and the nonlinear effect, parameters influencing the nonlinear effect and the mode instability effect threshold value in the optical fiber are brought into a theoretical model for calculation, the existing process level and experimental conditions are combined, the optical fiber parameters and the bending radius which can meet the requirements of a high-power optical fiber laser and inhibit the gains of the nonlinear effect and the mode instability effect are selected, the mode instability and the nonlinear effect threshold value are changed simultaneously, the minimum value of the two is increased as much as possible, and therefore the maximum output power of the optical fiber is improved.
On the basis of not changing other devices of the existing fiber laser, only the parameters of the fiber are changed: the radius of a fiber core, the radius of a cladding, the length, the numerical aperture and the bending radius of the optical fiber are optimized, and the effect of simultaneously inhibiting the nonlinear effect and the mode unstable effect is achieved; meanwhile, the method has the advantages of low resource and time consumption, high process maturity, low implementation difficulty, capability of quickly, obviously, low cost and high reliability improving the output power of the optical fiber and meeting the development requirement of the current high-power optical fiber laser.
Drawings
FIG. 1 depicts the core and inner cladding of a fiber cross-section;
FIG. 2 depicts fiber bend coiling for laser output;
FIG. 3 depicts a graph of the dependence of the mode instability threshold of a laser on the bend radius;
FIG. 4 depicts a two-dimensional plot of the dependence of the mode instability threshold of a laser on the fiber core size, length; expressing the variation of the calculated threshold value of the nonlinear effect (SBS in the embodiment) along with the radius of the fiber core and the length of the optical fiber, the threshold values are respectively 1000w, 3000w and 5000w, and because the cladding size (set to 400um) and the numerical aperture NA (set to 0.06) of the optical fiber, the SBS threshold value increases along with the increase of the radius of the fiber core, and the threshold values below the contour lines are all higher than the threshold values of the contour lines.
FIG. 5 depicts a two-dimensional plot of the dependence of the nonlinear effect threshold of the laser on the fiber core size, length; the size of a cladding of the optical fiber (set to be 400um), the numerical aperture NA (set to be 0.06), the bending loss (set to be 10dB/m) at a certain time, and the calculated value of a mode instability effect (MI) threshold value are in a change relation with the radius of a fiber core and the length of the optical fiber, wherein the threshold values are respectively 2000w, 3000w and 5000w, and since the MI threshold value is reduced along with the increase of the radius of the fiber core, the threshold value above the contour line is higher than the threshold value of the contour line; it can be seen from the figure that when the core radius is 15um and the length of the fiber is 10m, the SBS threshold of the fiber is 3kW and the MI threshold is about 2.6kW, and the theoretical maximum optical power of the fiber is limited by the MI effect and is 2.6 kW.
In the figure 10-core, 20-inner cladding, 30-bend radius.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are further described below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
With the first introduction, many documents currently perform threshold estimation for limiting the power boosting effect in the optical fiber, but these estimation formulas are obtained by a large number of estimation and omission, such as mode instability threshold
Figure BDA0002603282260000081
Estimating a formula:
Figure BDA0002603282260000082
U01、U11normalized transverse phase parameters, thermal conductivity κ, for LP01, LP11, respectively0＝1.38W/m-K，
Figure BDA0002603282260000083
Is the temperature coefficient of variation of the refractive index of the optical fiber, neffIs the effective refractive index, alpha, of the optical fibersBackground transmission loss, qDIs the quantum loss, gsIs the small signal gain factor. According to this formula, the MI (mode instability) threshold decreases with a decrease in NA, which is quite contrary to theoretical analysis, experimental results, and therefore this formula is not suitable for guiding experiments.
Although the MI (mode instability) theoretical model in the present invention has been proposed in other documents, the previous documents only study the effect of the MI (mode instability) threshold in theory for parameters such as the core radius, cladding, length, numerical aperture, etc. of the optical fiber. The invention combines the mode instability threshold calculation model and the nonlinear effect threshold calculation model for the first time, provides an optical fiber design scheme for theoretically inhibiting the nonlinear effect (SBS) and the mode instability effect at the same time, realizes high power output, and performs experimental verification to prove that the theoretical design value is reliable and has a guiding function for experiments.
The high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect is a double-clad optical fiber and sequentially comprises a fiber core and an inner cladding from inside to outside, wherein or other rare earth ions are doped in the fiber core to serve as a gain medium, the inner cladding is a quartz cladding,
the diameter of the fiber core is 15-100 mu m; in the examples, the values 22 μm, 24 μm, 25 μm,28 μm and 30 μm were calculated and shown in Table 1.
The numerical aperture NA of the fiber core is 0.01-0.1; in the examples, the values 0.045, 0.055 and 0.05 were calculated as shown in table 1.
The cross section of the inner cladding is regular octagon or other non-circular, specifically in other embodiments, the inner cladding is respectively quincunx, D-shaped, hexagonal and other non-circular; in the embodiment shown a regular octagon.
The diameter of the inner cladding is 300-; in the examples, values of 450 μm and 500 μm were calculated and shown in Table 1.
The position of the cladding pumping absorption coefficient @915nm is 0.2-1.0 dB/m; in the examples, values of 0.4dB/m, 0.42dB/m, 0.45dB/m,0.48dB/m, and 0.6dB/m were calculated, as shown in Table 1.
The optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm. In the examples, the values 10cm, 11cm, 13cm,14.5cm, 17.5cm and 19cm were calculated and shown in Table 1.
Preferably, the core diameter is 35-80 μm.
Preferably, the numerical aperture NA of the fiber core is 0.03-0.07.
Preferably, the diameter of the inner cladding is 500-.
Preferably, the cladding pumped absorption coefficient @915nm is 0.4-0.8 dB/m.
Preferably, the optical fiber is bent and coiled, and the bending radius is 17.5-65 cm.
The invention relates to a design method of a high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect, which comprises the following steps:
s1, establishing a nonlinear effect threshold calculation model of the gain optical fiber and different mode laser gain calculation models of signal light in the optical fiber;
s2, setting a plurality of variation ranges of optical fiber parameters according to experimental experience, wherein the variation ranges comprise numerical aperture NA, fiber core diameter, cladding diameter, absorption coefficient and optical fiber length;
s3, bringing the optical fiber parameters into a nonlinear effect calculation model, calculating the range of the nonlinear effect threshold at the moment, and selecting the optical fiber parameter group meeting the high power requirement;
specifically, in step S3, the nonlinear effect threshold calculation formula is specifically as follows:
Figure BDA0002603282260000101
Figure BDA0002603282260000102
wherein, V is normalized working frequency, U is normalized transverse phase parameter, W is normalized transverse attenuation parameter, and the calculation formula is V2＝W2+U2,V＝kRNA，
Figure BDA0002603282260000103
k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m is 0; j. the design is a square0(U)、
Figure BDA0002603282260000104
The representative variables are U,
Figure BDA0002603282260000105
First class 0 Bessel function, Km-1(W)，Km+1(W) represents a second class of m-1, m +1 order Bessel functions with the variable W.
gB(Δ v) is the SBS gain coefficient, typically taken at 5 x 10 in silica fiber-11；
G is the laser gain of the fiber;
r is the core radius of the optical fiber;
l is the fiber length;
a is an experimental fitting coefficient which is experimentally measured for multiple sets of nonlinear effect thresholds
Figure BDA0002603282260000111
Substituting the formula (1) to calculate a plurality of groups of A (n) values, and taking an average value to obtain the value; from the above equation, it can be seen that changing the core size R and the length L of the optical fiber can significantly change the threshold of the nonlinear effect.
S4, substituting the fiber parameter group into a mode gain calculation model in the fiber, calculating the signal light output power and the high-order mode ratio of the fiber parameter group under the changed bending radius, selecting the corresponding bending radius range in the proper bending loss range, and when the mode instability effect does not occur, taking the highest output signal light power in the bending radius range as the theoretical highest output power of the fiber, namely the mode instability effect threshold of the parameter fiber;
in step S4, the fiber parameter set meeting the high power requirement in step S3 is substituted into the mode gain model in the fiber, and the mode instability threshold under the fiber parameter set is calculated, specifically the calculation steps are as follows:
s41, establishing a transmission amplification model of a fundamental mode and a high-order mode of signal light in the gain fiber, and assuming that the initial signal light power is P1(0) 99.9% of fundamental mode, 0.1% of high-order mode, incident pump light power Pp, fiber core radius R, cladding radius R1, fiber length L, cladding absorption coefficient alpha dB/m, and bending radius RcoilCalculating the power P of the high-order mode in the length direction of the optical fiber in a steady state2(z), power P of fundamental mode1(z) distribution;
s42, substituting the above parameters into formulas (2), (3), (4), (5), (6), (7) and (8), judging whether the higher-order mode ratio xi is more than 0.05, if not, the mode instability effect does not occur, at this time, the higher-order mode ratio xi is not more than 0.05
Figure BDA0002603282260000112
If greater than 0.05, a mode instability effect has occurred.
S43, according to S42, adjusting the power of the input signal light, when xi is close to 0.05, the output signal light P is output at this time1(L) threshold for the effect of mode instability
Figure BDA0002603282260000113
Specifically, in step S4, there are two modes, namely, a fundamental mode and a high-order mode, in the optical fiber, and the gain amplification conditions of different modes are different, and the calculation formulas of the fundamental mode and the high-order mode power in the output-end signal light are specifically as follows:
Figure BDA0002603282260000121
Figure BDA0002603282260000122
Figure BDA0002603282260000123
Figure BDA0002603282260000124
wherein the content of the first and second substances,
P1(0) is the incident signal optical power;
2the high-order mode overlap factor is obtained by calculation when m is 1 in formula (2);
g (z) is the gain coefficient when the laser propagates along the axial direction of the fiber by a distance z;
Figure BDA0002603282260000125
is the absorption and emission cross section of the corresponding signal light, nuThe upper energy level particle number proportion is determined by the pump light power;
NYbthe rare earth ion doping concentration of the optical fiber is in direct proportion, G is total pump absorption which is generally a constant value and is in inverse proportion to the length L of the optical fiber;
χ is the mode coupling coefficient, which is related to the cladding radius;
P1(L)、P2when z is equal to L, that is, the power of the fundamental mode and the high-order mode in the signal light at the output end;
xi is the signal light power P when the high order mode accounts for the total signal light ratio and xi is 0.051(L) as the mode instability threshold at this time,
therefore, the mode instability threshold is related to the core size, the cladding size, the fiber length, and the numerical aperture parameters, and besides, the mode instability threshold can be significantly increased due to different optical losses of different mode signals in the optical fiber caused by bending of the optical fiber. The loss coefficient calculation formula of different modes generated by fiber bending (coil) is as follows:
Figure BDA0002603282260000131
wherein the content of the first and second substances,
β is the propagation constant;
m is the maximum logarithm of the field component of the mode along the circumferential direction of the optical fiber, wherein the basic mode m is 0, and the high-order mode m is 1;
when m is 0, emWhen m is 1, em＝2；
RcoilIs the bend radius of the optical fiber;
therefore, when the optical fiber parameters are fixed and the wavelength of the signal light is not changed, the bending loss coefficient alpha iscoilFrom the bending radius RcoilDetermining that the bending loss can be changed by changing the bending radius, so that the power ratio of each mode in the signal light power is influenced; the power relations of the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the optical fiber is bent are as follows:
Figure BDA0002603282260000132
P01(L)、P′01(L)、P11(L)、P′11(L) are respectively the LP01 fundamental mode and LP11 high-order mode powers before and after bending,
Figure BDA0002603282260000133
bending-induced bending loss coefficients of LP01 fundamental mode and LP11 higher-order modes
Figure BDA0002603282260000134
When the high-order mode power accounts for 0.05 of the total power of the signal light, the mode instability effect is considered to occur, so that the proportion of the high-order mode in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold value is improved.
S5, selecting a bending radius range corresponding to a proper bending loss according to the mode instability effect threshold value under the bending radius change calculated in the step S4, selecting the maximum value of the bending radius range, and selecting the corresponding bending radius value as a design bending radius; and comparing the maximum output power with the nonlinear effect threshold calculated in the step S3, and taking the smaller value as the design value of the maximum output power of the optical fiber to ensure that the mode instability effect threshold and the nonlinear effect threshold of the optical fiber are not less than the maximum output power of the optical fiber.
The several sets of calculated data in this example are shown in table 1, where table 1 gives the fiber parameters, the optimum bend radius at that time and the corresponding theoretical maximum output power.
TABLE 1
Figure BDA0002603282260000141
The experimental results are as follows: the optical fiber adopting the design has the advantages that the fiber core size is 30 mu m, the cladding diameter is 500 mu m, the absorption coefficient is 0.6dB/m, the length is 7m, the optical fiber is bent and coiled, the bending radius is 19cm and is selected as the designed bending radius, the highest 2700W power output is obtained under the condition that the mode instability effect and the nonlinear effect do not occur, and the theoretical calculated value is 2600W.

Claims (10)

1. A high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect is characterized in that the optical fiber is a double-clad fiber and sequentially comprises a fiber core and an inner cladding from inside to outside, or other rare earth ions are doped in the fiber core to serve as a gain medium, and the inner cladding is a quartz cladding
The diameter of the fiber core is 15-100 mu m;
the numerical aperture NA of the fiber core is 0.01-0.1;
the cross section of the inner cladding is in a regular octagon shape or a quincunx shape, a D shape, a hexagonal shape or other non-circular shapes;
the diameter of the inner cladding is 300-;
the position of the cladding pumping absorption coefficient @915nm is 0.2-1.0 dB/m;
the optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm.
2. The high power gain fiber of claim 1, wherein the core diameter is 35-80 μm.
3. The high power gain optical fiber according to claim 2, wherein the core numerical aperture NA is 0.03-0.07.
4. The high power gain optical fiber according to claim 3, wherein the diameter of the inner cladding is 500-1000 μm.
5. The high power gain fiber of claim 4, wherein said cladding pumped absorption coefficient @915nm is in the range of 0.4-0.8 dB/m.
6. The high power gain fiber of claim 5, wherein said fiber is bend coiled with a bend radius between 17.5cm and 65 cm.
7. The method of designing a high power gain optical fiber according to claims 1-6, comprising the steps of:
s1, establishing a nonlinear effect threshold calculation model of the gain optical fiber and different mode laser gain calculation models of signal light in the optical fiber;
s2, setting a plurality of variation ranges of optical fiber parameters according to experimental experience, wherein the variation ranges comprise numerical aperture NA, fiber core diameter, cladding diameter, absorption coefficient and optical fiber length;
s3, bringing the optical fiber parameters into a nonlinear effect calculation model, calculating the range of the nonlinear effect threshold at the moment, and selecting the optical fiber parameter group meeting the high power requirement;
s4, substituting the fiber parameter group into a mode gain calculation model in the fiber, calculating the signal light output power and the high-order mode ratio of the fiber parameter group under the changed bending radius, selecting the corresponding bending radius range in the proper bending loss range, and when the mode instability effect does not occur, taking the highest output signal light power in the bending radius range as the theoretical highest output power of the fiber, namely the mode instability effect threshold of the parameter fiber;
and S5, comparing the mode instability effect threshold calculated in the step S4 with the nonlinear effect threshold calculated in the step S3, and taking the smaller value as the design value of the highest output power of the optical fiber to ensure that the mode instability effect threshold and the nonlinear effect threshold of the optical fiber are not less than the highest output power of the optical fiber.
8. The method for designing a high power gain optical fiber according to claim 7, wherein in the step S3, the nonlinear effect threshold calculation formula is specifically as follows:
Figure FDA0002603282250000021
Figure FDA0002603282250000022
wherein, V is normalized working frequency, U is normalized transverse phase parameter, W is normalized transverse attenuation parameter, and the calculation formula is V2＝W2+U2,V＝kRNA，
Figure FDA0002603282250000023
k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m is 0; j. the design is a square0(U)、
Figure FDA0002603282250000024
The representative variables are U,
Figure FDA0002603282250000025
First class 0 Bessel function, Km-1(W)，Km+1(W) represents a second class of m-1, m +1 order Bessel functions with the variable W.
gB(Δ v) is the SBS gain coefficient, typically taken at 5 x 10 in silica fiber-11；
G is the laser gain of the fiber;
r is the core radius of the optical fiber;
l is the fiber length;
a is an experimental fitting coefficient which is experimentally measured for multiple sets of nonlinear effect thresholds
Figure FDA0002603282250000031
Substituting the formula (1) to calculate a plurality of groups of A (n) values, and taking an average value to obtain the value; from the above equation, it can be seen that changing the core radius R and the length L of the optical fiber can significantly change the threshold of the nonlinear effect.
9. The method for designing a high power gain optical fiber according to claim 8, wherein in step S4, the optical fiber has two modes of a fundamental mode and a high-order mode, the gain amplification conditions of different modes are different, and the calculation formulas of the powers of the fundamental mode and the high-order mode in the signal light at the output end are as follows:
Figure FDA0002603282250000032
Figure FDA0002603282250000033
Figure FDA0002603282250000034
Figure FDA0002603282250000035
wherein the content of the first and second substances,
P1(0) is the incident signal optical power;
2is a high-order mode overlapping factor, and is calculated when m is 1 according to the formula (2);
g (z) is the gain coefficient when the laser propagates along the axial direction of the fiber by a distance z;
Figure FDA0002603282250000036
is the absorption and emission cross section of the corresponding signal light, nuThe upper energy level particle number proportion is determined by the pump light power;
NYbthe rare earth ion doping concentration of the optical fiber is in direct proportion, G is total pump absorption which is generally a constant value and is in inverse proportion to the length L of the optical fiber;
χ is the mode coupling coefficient, which is related to the cladding radius;
P1(L)、P2when z is equal to L, that is, the power of the fundamental mode and the high-order mode in the signal light at the output end;
xi is the signal light power P when the high order mode accounts for the total signal light ratio and xi is 0.051(L) as the mode instability threshold at this time,
therefore, the mode instability threshold is related to the core size, the cladding size, the fiber length, and the numerical aperture parameters, and besides, the mode instability threshold can be significantly increased due to different optical losses of different mode signals in the optical fiber caused by bending of the optical fiber. The loss coefficient calculation formula of different modes generated by fiber bending (coil) is as follows:
Figure FDA0002603282250000041
β is the propagation constant;
Km-1(W)，Km+1(W) represents a second class of m-1, m +1 order bessel functions with variables W, the base mode m being 0, the higher order mode m being 1; j. the design is a square0(U)、
Figure FDA0002603282250000042
The representative variables are U,
Figure FDA0002603282250000043
First class 0 Bessel function, K0(U)、
Figure FDA0002603282250000044
The representative variables are U,
Figure FDA0002603282250000045
Second class 0 order bessel functions;
when m is 0, emWhen m is 1, em＝2；
RcoilIs the bend radius of the optical fiber;
therefore, when the optical fiber parameters are fixed and the wavelength of the signal light is not changed, the bending loss coefficient alpha iscoilFrom the bending radius RcoilDetermining that the bending loss can be changed by changing the bending radius, so that the power ratio of each mode in the signal light power is influenced; the power relations of the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the optical fiber is bent are as follows:
Figure FDA0002603282250000046
P01(L)、P′01(L)、P11(L)、P′11(L) are respectively the LP01 fundamental mode and LP11 high-order mode powers before and after bending,
Figure FDA0002603282250000051
respectively, LP01 fundamental mode caused by bendingAnd LP11 higher order mode bending loss coefficient
Figure FDA0002603282250000052
When the high-order mode power accounts for 0.05 of the total power of the signal light, the mode instability effect is considered to occur, so that the proportion of the high-order mode in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold value is improved.
10. The method for designing high power gain optical fiber according to claim 9, wherein in step S4, the fiber parameter set meeting the high power requirement in step S3 is substituted into the mode gain model in the optical fiber, and the mode instability threshold under the fiber parameter set is calculated by the following steps:
s41, establishing a transmission amplification model of a fundamental mode and a high-order mode of signal light in the gain fiber, and assuming that the initial signal light power is P1(0) Fundamental mode fraction (1-n), higher order mode fraction n, incident pump light power Pp, fiber core radius R, cladding radius R1, fiber length L, cladding absorption coefficient α dB/m, bend radius RcoilCalculating the power P of the high-order mode in the length direction of the optical fiber in a steady state2(z), power P of fundamental mode1(z) distribution;
s42, substituting the above parameters into formulas (2), (3), (4), (5), (6), (7) and (8), judging whether the higher-order mode ratio xi is more than 0.05, if not, the mode instability effect does not occur, at this time, the higher-order mode ratio xi is not more than 0.05
Figure FDA0002603282250000053
If greater than 0.05, a mode instability effect has occurred.
S43, according to S42, adjusting power of input signal light and pump light, when xi is close to 0.05, outputting signal light P1(L) threshold for the effect of mode instability
Figure FDA0002603282250000054
CN202010731406.2A 2020-07-27 2020-07-27 High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method Active CN111999795B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010731406.2A CN111999795B (en) 2020-07-27 2020-07-27 High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010731406.2A CN111999795B (en) 2020-07-27 2020-07-27 High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method

Publications (2)

Publication Number Publication Date
CN111999795A true CN111999795A (en) 2020-11-27
CN111999795B CN111999795B (en) 2023-08-04

Family

ID=73467777

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010731406.2A Active CN111999795B (en) 2020-07-27 2020-07-27 High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method

Country Status (1)

Country Link
CN (1) CN111999795B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113093328A (en) * 2021-03-15 2021-07-09 武汉光谷航天三江激光产业技术研究院有限公司 Gain optical fiber with axial fiber core numerical aperture change, sleeve and preparation method thereof
CN113252087A (en) * 2021-05-21 2021-08-13 苏州清恒智能科技有限公司 Annular loop single-mode optical fiber sensor based on Renner correction model and annular optical fiber loop design method thereof
CN114942490A (en) * 2022-04-01 2022-08-26 中国科学院软件研究所 Multi-cladding step optical fiber design method based on characteristic matrix
CN116539279A (en) * 2023-03-13 2023-08-04 中国工程物理研究院激光聚变研究中心 Measuring system and measuring method for absorption coefficient of cladding pumping light

Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1564032A (en) * 2004-03-17 2005-01-12 天津大学 Double cladding optical fiber having external cladding as pump light guide, and its coating mould
CN1877926A (en) * 2006-06-29 2006-12-13 西北大学 High-power blue-light fiber laser
CN101485054A (en) * 2006-07-05 2009-07-15 索雷克核研究中心 Optical apparatus comprising a pump-light-guiding fiber
CN101657943A (en) * 2007-08-28 2010-02-24 株式会社藤仓 Rare-earth doped core multi-clad fiber, fiber amplifier, and fiber laser
CN101738682A (en) * 2010-01-18 2010-06-16 烽火通信科技股份有限公司 Large-mode active optical fiber and manufacture method thereof
CN104865634A (en) * 2015-06-11 2015-08-26 长飞光纤光缆股份有限公司 Yb-doped fiber and manufacturing method thereof
US20150260910A1 (en) * 2012-08-29 2015-09-17 Ofs Fitel, Llc Gain-producing fibers with increased cladding absorption while maintaining single-mode operation
CN105244741A (en) * 2015-11-05 2016-01-13 长飞光纤光缆股份有限公司 Large-mode-field ytterbium-doped optical fiber
US20180109064A1 (en) * 2016-10-13 2018-04-19 Nlight, Inc. Tandem pumped fiber amplifier
CN108152883A (en) * 2018-01-09 2018-06-12 北京交通大学 Negative double clad tapered active optical fiber
CN109031516A (en) * 2018-07-11 2018-12-18 烽火通信科技股份有限公司 A kind of large mode field Double Cladding Ytterbium Doped Fiber
CN109861066A (en) * 2019-01-31 2019-06-07 华南理工大学 A kind of 1.6 μm of powerful single-frequency lasers of high light beam quality
CN110190496A (en) * 2019-06-27 2019-08-30 深圳市创鑫激光股份有限公司 A kind of triple clad Active Optical Fiber, light amplification structure and optical fiber laser
US20190288474A1 (en) * 2016-07-20 2019-09-19 University Of Rochester Lma fibers for suppression of thermal mode instability
US20190302354A1 (en) * 2018-03-30 2019-10-03 Nlight, Inc. Single mode lma (large mode area) fiber

Patent Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1564032A (en) * 2004-03-17 2005-01-12 天津大学 Double cladding optical fiber having external cladding as pump light guide, and its coating mould
CN1877926A (en) * 2006-06-29 2006-12-13 西北大学 High-power blue-light fiber laser
CN101485054A (en) * 2006-07-05 2009-07-15 索雷克核研究中心 Optical apparatus comprising a pump-light-guiding fiber
CN101657943A (en) * 2007-08-28 2010-02-24 株式会社藤仓 Rare-earth doped core multi-clad fiber, fiber amplifier, and fiber laser
CN101738682A (en) * 2010-01-18 2010-06-16 烽火通信科技股份有限公司 Large-mode active optical fiber and manufacture method thereof
US20150260910A1 (en) * 2012-08-29 2015-09-17 Ofs Fitel, Llc Gain-producing fibers with increased cladding absorption while maintaining single-mode operation
CN104865634A (en) * 2015-06-11 2015-08-26 长飞光纤光缆股份有限公司 Yb-doped fiber and manufacturing method thereof
CN105244741A (en) * 2015-11-05 2016-01-13 长飞光纤光缆股份有限公司 Large-mode-field ytterbium-doped optical fiber
US20190288474A1 (en) * 2016-07-20 2019-09-19 University Of Rochester Lma fibers for suppression of thermal mode instability
US20180109064A1 (en) * 2016-10-13 2018-04-19 Nlight, Inc. Tandem pumped fiber amplifier
CN108152883A (en) * 2018-01-09 2018-06-12 北京交通大学 Negative double clad tapered active optical fiber
US20190302354A1 (en) * 2018-03-30 2019-10-03 Nlight, Inc. Single mode lma (large mode area) fiber
CN109031516A (en) * 2018-07-11 2018-12-18 烽火通信科技股份有限公司 A kind of large mode field Double Cladding Ytterbium Doped Fiber
CN109861066A (en) * 2019-01-31 2019-06-07 华南理工大学 A kind of 1.6 μm of powerful single-frequency lasers of high light beam quality
CN110190496A (en) * 2019-06-27 2019-08-30 深圳市创鑫激光股份有限公司 A kind of triple clad Active Optical Fiber, light amplification structure and optical fiber laser

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
王小林，等: "掺镱全光纤激光振荡器横向模式不稳定与", 《中国激光》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113093328A (en) * 2021-03-15 2021-07-09 武汉光谷航天三江激光产业技术研究院有限公司 Gain optical fiber with axial fiber core numerical aperture change, sleeve and preparation method thereof
CN113252087A (en) * 2021-05-21 2021-08-13 苏州清恒智能科技有限公司 Annular loop single-mode optical fiber sensor based on Renner correction model and annular optical fiber loop design method thereof
CN114942490A (en) * 2022-04-01 2022-08-26 中国科学院软件研究所 Multi-cladding step optical fiber design method based on characteristic matrix
CN114942490B (en) * 2022-04-01 2023-03-24 中国科学院软件研究所 Multi-cladding step optical fiber design method based on characteristic matrix
CN116539279A (en) * 2023-03-13 2023-08-04 中国工程物理研究院激光聚变研究中心 Measuring system and measuring method for absorption coefficient of cladding pumping light
CN116539279B (en) * 2023-03-13 2023-10-20 中国工程物理研究院激光聚变研究中心 Measuring system and measuring method for absorption coefficient of cladding pumping light

Also Published As

Publication number Publication date
CN111999795B (en) 2023-08-04

Similar Documents

Publication Publication Date Title
CN111999795B (en) High-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect and design method
US8797642B2 (en) Large mode area optical fiber
US6909538B2 (en) Fiber amplifiers with depressed cladding and their uses in Er-doped fiber amplifiers for the S-band
US8428409B2 (en) Filter fiber for use in Raman lasing applications and techniques for manufacturing same
EP2608328B1 (en) Apparatus and method for mode control in a semi-guiding amplifier medium
US20150077837A1 (en) Gain-Equalized Few-Mode Fiber Amplifier
JPH04212131A (en) Erbium-doped fiber amplifier
Saitoh et al. Limitation on effective area of bent large-mode-area leakage channel fibers
US9667024B2 (en) Suppression of stimulated Brillouin scattering in higher-order-mode optical fiber amplifiers
Aljaff et al. Design optimization for efficient erbium-doped fiber amplifiers
Hotoleanu et al. High-order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant
CN102147551B (en) Multimode optical fibre amplifier and multimode optical fibre amplifying system
Zhang et al. An optimization of Raman effects in tandem-pumped Yb-doped kilowatt fiber amplifiers
Mondal et al. Designing high performance Er+ 3-doped fiber amplifier in triangular-lattice photonic crystal fiber host towards higher gain, low splice loss
Shen et al. A segmented heterostructure cladding fiber designed for extreme large mode area
Tian et al. Numerical modeling and optimization of cladding-pumped tapered fiber Raman amplifiers
Lebreton et al. Design optimization of 12 Core Er3+/Yb3+ co-doped amplifier and its experimental validation
Emami et al. S-band gain and noise figure improvements in thulium-doped fiber amplifier by using macro-bending approach
Nemova et al. High-power long-period-grating-assisted erbium-doped fiber amplifier
Song et al. Design for non-uniformly doped Erbium-doped waveguide amplifiers in the propagation direction
Zhou et al. Design of a Hybrid Multimode Fiber Amplifier with Optimized Mode Dependent Gain and Wavelength Dependent Gain
Desbiens et al. Novel 30/400 ytterbium-doped LMA polarization-maintaining fiber with very efficient higher-order modes filtering capabilities
CN115327695A (en) Double-cladding tapered gradient-refractive-index gain optical fiber
Vazeerpour et al. The impact of higher order modes on transverse mode instability in bent optical fiber amplifiers
He et al. Wavelength selective bending sensitive multi-ring fiber for suppressing stimulated Raman scattering

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant