CN111999795B - 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 PDFInfo
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- 239000000835 fiber Substances 0.000 claims abstract description 95
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- 238000005253 cladding Methods 0.000 claims abstract description 51
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- 238000010521 absorption reaction Methods 0.000 claims abstract description 21
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims abstract description 10
- 238000005086 pumping Methods 0.000 claims abstract description 9
- -1 rare earth ions Chemical class 0.000 claims abstract description 8
- 229910052761 rare earth metal Inorganic materials 0.000 claims abstract description 8
- 239000010453 quartz Substances 0.000 claims abstract description 6
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- 238000003199 nucleic acid amplification method Methods 0.000 claims description 6
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- 239000002245 particle Substances 0.000 claims description 3
- NAWDYIZEMPQZHO-UHFFFAOYSA-N ytterbium Chemical compound [Yb] NAWDYIZEMPQZHO-UHFFFAOYSA-N 0.000 claims description 3
- 230000003287 optical effect Effects 0.000 claims 1
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- 239000000377 silicon dioxide Substances 0.000 description 2
- 229910052779 Neodymium Inorganic materials 0.000 description 1
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- QEFYFXOXNSNQGX-UHFFFAOYSA-N neodymium atom Chemical compound [Nd] QEFYFXOXNSNQGX-UHFFFAOYSA-N 0.000 description 1
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- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
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- G02B6/036—Optical fibres with cladding with or without a coating core or cladding comprising multiple layers
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- H—ELECTRICITY
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- 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
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- 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
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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-cladding, 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 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 300-1200 mu m; the absorption coefficient of cladding pumping at 915nm is 0.2-1.0dB/m; the optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm. According to the invention, parameters influencing nonlinear effects and mode instability effect thresholds in the optical fiber are brought into a theoretical model for calculation, and the optical fiber parameters and bending radius which can meet the requirements of high-power optical fiber lasers and inhibit gains of the nonlinear effects and the mode instability effects are selected in combination with the prior art level and experimental conditions, so that the mode instability and the nonlinear effect thresholds are changed simultaneously, and the maximum output power of the optical fiber is improved.
Description
Technical Field
The invention belongs to the technical field of fiber lasers, and particularly relates to a high-power gain fiber capable of simultaneously inhibiting mode instability and nonlinear effects and a design method thereof.
Background
High power lasers have irreplaceable roles in many areas of industrial manufacturing, remote detection, communication transmission, military equipment, and the like. The high-power fiber laser combines the advantages of the fiber and the high-power laser, has the advantages of small volume, high power, good beam quality and the like, and has realized single-fiber 2 kW-order near diffraction limit output at present.
The gain medium in the fiber laser realizes laser gain output by utilizing the fiber doped with rare earth ions, and the most widely used quartz fiber doped with Nd (neodymium) at present has the advantages of mature process and stable performance. With the continuous development of optical fiber materials, ytterbium-doped optical fibers attract attention due to lower quantum loss and higher doping concentration, and after years of research, the ytterbium-doped optical fibers have been developed successfully, so that the output power of an optical fiber laser is greatly improved, and the application range of laser is widened.
As fiber lasers continue to move toward higher power, nonlinear effects and mode-instable effects become two increasingly important factors limiting 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 increase of the core diameter of the optical fiber leads to poor effect of inhibiting the mode instability of the optical fiber; conversely, reducing the fiber core can suppress mode instability effects, but can enhance nonlinear effects. Therefore, in combination with the power requirement of the development of the high-power fiber laser, under the whole industrial design framework of the existing fiber laser, a new design research is carried out on the gain fiber, and a foundation is laid for the further development of the high-power fiber laser.
Factors limiting the increase of laser output power are studied by utilizing optical fiber theory simulation. In 2018, zervas et al publication "Power scaling limits in high power fiber amplifiers due to transverse mode instability, thermal lens, and fiber mechanical reliability" (proc. Spie 10512) calculated a model of the highest output power of an optical fiber under consideration of nonlinear effects, mode instability effects, and other limiting factors, but calculated a mode instability effect threshold in the model that was too rough, had too low accuracy, and could not reflect the effect of numerical aperture changes on the mode instability threshold. In 2015, national defense science and technology university Tao Rumao established a detailed model in doctor graduation paper to analyze the effect of fiber parameters on mode instability threshold. But does not take into account the effects of bending losses and does not relate to nonlinear effects to calculate the highest power value output by the fiber.
Disclosure of Invention
In order to solve the problems, the invention mainly refers to the theoretical model and the formula of the high-power gain optical fiber designed in the two documents, and provides a design method of the high-power gain optical fiber for simultaneously inhibiting the mode instability and the nonlinear effect by combining experimental data, and designs the high-power gain optical fiber for simultaneously inhibiting the mode instability and the nonlinear effect. The numerical aperture NA, the core diameter, the inner cladding diameter, the cladding pumping absorption coefficient and the coiling bending radius of the fiber are optimized, the purposes of balancing the stimulated Brillouin effect and the mode instability effect when high-power laser output in the fiber are achieved, and the highest output power of the fiber is improved.
The invention relates to a high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect, which is a double-clad layer, and sequentially comprises a fiber core and an inner clad layer from inside to outside, wherein ytterbium or other rare earth ions are doped in the fiber core as gain medium, the inner clad layer is a quartz clad layer,
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 quincuncial shape, a D shape and other non-circular shapes;
the diameter of the inner cladding is 300-1200 mu m;
the absorption coefficient of the cladding pumping is 0.2-1.0dB/m at 915 nm;
the optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm.
Further, the core diameter takes a value of 35-80 μm.
Further, the numerical aperture NA of the fiber core is 0.03-0.07.
Further, the diameter of the inner cladding is 500-1000 μm.
Further, the absorption coefficient of the cladding pumping is 0.4-0.8dB/m at 915 nm.
Further, the optical fiber is bent and coiled, and the bending radius is between 17.5cm 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 a gain optical fiber and different modes of laser gain calculation models of signal light in the optical fiber;
s2, setting the variation range of a plurality of optical fiber parameters according to experimental experience, wherein the variation range comprises 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 nonlinear effect threshold range at the moment, and selecting an optical fiber parameter set meeting the high power requirement;
s4, the optical fiber parameter set is brought into a mode gain calculation model of the optical fiber, the signal light output power of the optical fiber parameter set under the changed bending radius and the high-order mode duty ratio at the moment are calculated, a corresponding bending radius range in a proper bending loss range is selected, and when no mode instability effect occurs, the highest output signal light power in the bending radius range is used as the theoretical highest output power of the optical fiber, namely the mode instability effect threshold of the parameter optical fiber;
s5, comparing the mode unstable effect threshold calculated in the step S4 with the nonlinear effect threshold calculated in the step S3, and taking a smaller value as a design value of the highest output power of the optical fiber to ensure that the mode unstable effect threshold and the nonlinear effect threshold of the optical fiber are not smaller than the highest output power of the optical fiber.
Specifically, in the step S3, the nonlinear effect threshold calculation formula is specifically as follows:
wherein Γ is a signal light overlap factor, wherein V is a normalized working frequency, U is a normalized transverse phase parameter, W is a normalized transverse attenuation parameter, and a calculation formula is V 2 ＝W 2 +U 2 ,V＝kRNA，k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m=0, j 0 (U)、/>The representative variable is U, U->0 th order Bessel function of the first class, J m-1 (U)，J m+1 (U) represents the second class m-1, m+1 order Bessel function with variable U.
g B (Deltav) is the SBS gain factor, typically 5 x 10 in silica fiber -11 ；
G is the laser gain of the fiber;
r is the core radius of the fiber;
l is the length of the fiber;
a is an experimental fit coefficient, which is a measure of multiple sets of nonlinear effect thresholdsCarrying out calculation in the formula (1) to obtain a plurality of groups of A (n) values, and taking an average value to obtain; as can be seen from the above equation, changing the core radius R, length L of the fiber can significantly change the threshold of the nonlinear effect.
Specifically, in step S4, two modes of a fundamental mode and a high-order mode exist in the optical fiber, gain amplification conditions of different modes are different, and a calculation formula of the power of the fundamental mode and the high-order mode in the signal light at the output end is specifically as follows:
wherein,,
P 1 (0) Is the incident signal light power;
Γ 2 is a higher-order mode overlap factor, calculated by the formula (2) when m=1;
g (z) is a gain coefficient when the propagation distance of the laser along the axial direction of the optical fiber is z;is the absorption and emission section of the corresponding signal light, n u The upper energy level particle number proportion is determined by the pump light power;
N Yb is the proportion of the rare earth ion doping concentration of the optical fiber, GG is the total pumping absorption, which is generally a fixed value and inversely proportional to the length L of the optical fiber;
χ is the mode coupling coefficient, related to the cladding radius;
P 1 (L)、P 2 (L) is z=l, i.e. the power of the fundamental mode, higher order mode in the output signal light;
ζ is the total ratio of the higher order modes to the signal light, and the signal light power P when ζ=0.05 1 (L) as a mode instability threshold at this timeThe value of the sum of the values,
thus, the mode instability threshold is related to the core size, cladding size, fiber length, numerical aperture parameters, and besides, the mode instability threshold can be significantly raised by different signal light losses in different modes in the fiber due to fiber bending. The loss factor calculation formula for the different modes generated by the fiber bending (coil) is as follows:
beta is the propagation constant;
K m-1 (W)，K m+1 (W) represents a second class m-1, m+1 order bessel function of variable W, fundamental mode m=0, higher order mode m=1; j (J) 0 (U)、The representative variables are U, (-)>0 th order Bessel function, K of the first class 0 (U)、/>The representative variables are U, (-)>0 th order bezier function of the second class;
when m=0, e m When=1, m=1, e m ＝2；
R coil Is the bending radius of the optical fiber;
therefore, when the optical fiber parameter is fixed and the wavelength of the signal light is unchanged, the bending loss coefficient alpha coil From the radius of curvature R coil Determining, changing the bending radius can change bending loss, and further influence the power ratio of each mode in the signal light power; the power relation between the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the bending of the optical fiber is as follows:
P 01 (L)、P 0 ′ 1 (L)、P 11 (L)、P 1 ′ 1 (L) the LP01 fundamental mode and LP11 higher order mode powers before and after bending respectively,bending loss coefficients of the LP01 fundamental mode and the LP11 higher order modes, respectively, caused by bending +.>The mode instability effect is considered to occur when the higher order mode power occupies 0.05 of the total power of the signal light, so that the ratio of the higher order modes in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold is improved.
Specifically, in the step S4, the optical fiber parameter set meeting the high power requirement in the step S3 is brought into the mode gain model of the optical fiber, and the mode instability threshold value under the optical fiber parameter set is calculated, and the specific 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 P 1 (0) A fundamental mode duty ratio (1-n), a high-order mode duty ratio n, an incident pump light power Pp, a fiber core radius R, a cladding radius R1, a fiber length L, a cladding absorption coefficient alpha dB/m, a bending radius R coil Calculating the power P of a high-order mode in the length direction of the optical fiber in a stable state 2 (z), power of fundamental mode P 1 (z) distribution;
s42, the parameters are put into formulas (2) (3) (4) (5) (6) (7) (8), whether the higher-order mode duty ratio xi is larger than 0.05 is judged, if not, the mode instability effect does not occur,if it is greater than 0.05, a mode instability effect has occurred.
S43, according to the step S42, adjusting the power of the input signal light and the pump light, and when the xi is close to 0.05, inputting the xi at the momentOutput signal light P 1 (L) regarded as mode-instability effect threshold
The invention relates to a high-power gain optical fiber design method for simultaneously inhibiting mode instability and nonlinear effect, which is characterized in that parameters influencing nonlinear effect and mode instability effect threshold values in an optical fiber are brought into a theoretical model to be calculated, the requirements of a high-power optical fiber laser can be met by combining the prior art level and experimental conditions, and the parameters and bending radius of the optical fiber for simultaneously inhibiting the gain of the nonlinear effect and the mode instability effect are selected, so that the mode instability and the nonlinear effect threshold values are simultaneously changed, the minimum value in the mode instability and the nonlinear effect threshold values is increased as much as possible, and the maximum output power of the optical fiber is improved.
On the basis of not changing other devices of the existing fiber laser, only changing parameters of the fiber: optimizing the core radius, cladding radius, length, numerical aperture and bending radius of the optical fiber to achieve the effect of simultaneously inhibiting nonlinear effect and mode instability effect; meanwhile, the method has the advantages of less resource and time consumption, high process maturity and low realization difficulty, can rapidly, remarkably, low-cost and high-reliability improve the output power of the optical fiber, and meets the development needs of the current high-power optical fiber laser.
Drawings
FIG. 1 depicts a core and an inner cladding of a fiber cross-section;
FIG. 2 depicts a fiber optic sinuous coil performing laser output;
FIG. 3 depicts a graph of the mode instability threshold of a laser versus bend radius dependence;
FIG. 4 depicts a two-dimensional plot of the dependence of the mode instability threshold of the laser on fiber core size, length; the relation of the calculated value of the threshold of the nonlinear effect (SBS in the embodiment) is expressed along with the change of the radius of the fiber core and the length of the fiber, three contour lines of 1000w,3000w and 5000w are respectively shown in the figure, the threshold of the SBS is increased along with the increase of the radius of the fiber core due to the cladding size (set to 400 um) of the fiber and the numerical aperture NA (set to 0.06), and the threshold under the contour lines is higher than the threshold of the contour lines.
FIG. 5 depicts a two-dimensional plot of the dependence of the nonlinear effect threshold of a laser on fiber core size, length; expressing the cladding size (set to 400 um) of the optical fiber, the numerical aperture NA (set to 0.06), and the bending loss (set to 10 dB/m) at a certain time, the mode instability effect (MI) threshold calculated value is changed along with the radius of the fiber core and the length of the optical fiber, wherein three contour lines with thresholds of 2000w,3000w and 5000w are respectively shown in the figure, and the MI threshold value is reduced along with the increase of the radius of the fiber core, and 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 optical fiber is 10m, the SBS threshold of the optical fiber is 3kW, and the MI threshold is about 2.6kW, and the theoretical maximum light output of the optical fiber is limited by the MI effect and is 2.6kW.
10-core, 20-inner cladding, 30-bend radius in the figure.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description of the present invention will be further described with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely to aid in the understanding of the present invention and are not to be construed as limiting the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
In the first introduction, several documents currently make threshold estimation for the effect of limiting power rise in optical fibers, but these estimation formulas are obtained by extensive estimation, omitting, such as mode instability thresholdThe estimation formula:
U 01 、U 11 normalized transverse phase parameters, thermal conductance, of LP01, LP11, respectivelyRate k 0 ＝1.38W/m-K，Is the temperature change coefficient of the refractive index of the optical fiber, n eff Is the effective refractive index of the optical fiber, alpha s Background transmission loss, q D Is the quantum loss, g s Is a small signal gain factor. According to this formula, the MI (mode instability) threshold decreases as NA decreases, which is quite contrary to theoretical analysis, experimental results, and thus this formula is not suitable for guiding experiments.
Although the theoretical model of MI (mode instability) in the present invention has been proposed in other documents, the previous documents have studied the theoretical influence on the MI (mode instability) threshold solely for parameters such as core radius, cladding, length, numerical aperture 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 simultaneously inhibiting nonlinear effect (SBS) and mode instability effect theoretically and realizing high power output, and performs experimental verification, thereby proving that the theoretical design value is reliable and having guiding effect on experiments.
The invention relates to a high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect, which is a double-clad layer, and sequentially comprises a fiber core and an inner clad layer from inside to outside, wherein ytterbium or other rare earth ions are doped in the fiber core as gain medium, the inner clad layer is a quartz clad layer,
the diameter of the fiber core is 15-100 mu m; the values of 22 μm,24 μm,25 μm,28 μm,30 μm were calculated in the examples and are shown in Table 1.
The numerical aperture NA of the fiber core is 0.01-0.1; the values 0.045,0.055,0.05 in the examples are calculated as shown in Table 1.
The cross section of the inner cladding is regular octagon or other non-circular, and in other embodiments, the inner cladding is respectively quincuncial, D-shaped, hexagonal and other non-circular; in the embodiment of regular octagons.
The diameter of the inner cladding is 300-1200 mu m; the values of 450 μm and 500 μm were calculated in the examples and are shown in Table 1.
The absorption coefficient of the cladding pumping is 0.2-1.0dB/m at 915 nm; the values of 0.4dB/m,0.42dB/m,0.45dB/m,0.48dB/m and 0.6dB/m in the examples are 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. The values of 10cm,11cm,13cm,14.5cm,17.5cm and 19cm were calculated in the examples and are shown in Table 1.
Preferably, the core diameter has a value of 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 500-1000 μm.
Preferably, the absorption coefficient of the cladding pumping is 0.4-0.8dB/m at 915 nm.
Preferably, the optical fiber is bent around a bend radius of 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 a gain optical fiber and different modes of laser gain calculation models of signal light in the optical fiber;
s2, setting the variation range of a plurality of optical fiber parameters according to experimental experience, wherein the variation range comprises 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 nonlinear effect threshold range at the moment, and selecting an optical fiber parameter set meeting the high power requirement;
specifically, in the step S3, the nonlinear effect threshold calculation formula is specifically as follows:
wherein Γ is a signal light overlap factor, wherein V is a normalized working frequency, U is a normalized transverse phase parameter, W is a normalized transverse attenuation parameter, and a calculation formula is V 2 ＝W 2 +U 2 ,V＝kRNA，k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m=0, j 0 (U)、/>The representative variables are U, (-)>0 th order Bessel function of the first class, J m-1 (U)，J m+1 (U) represents the second class m-1, m+1 order Bessel function with variable U.
g B (Deltav) is the SBS gain factor, typically 5 x 10 in silica fiber -11 ；
G is the laser gain of the fiber;
r is the core radius of the fiber;
l is the length of the fiber;
a is an experimental fit coefficient, which is a measure of multiple sets of nonlinear effect thresholdsCarrying out calculation in the formula (1) to obtain a plurality of groups of A (n) values, and taking an average value to obtain; as can be seen from the above equation, changing the core size R, length L of the fiber can significantly change the threshold of the nonlinear effect.
S4, the optical fiber parameter set is brought into a mode gain calculation model of the optical fiber, the signal light output power of the optical fiber parameter set under the changed bending radius and the high-order mode duty ratio at the moment are calculated, a corresponding bending radius range in a proper bending loss range is selected, and when no mode instability effect occurs, the highest output signal light power in the bending radius range is used as the theoretical highest output power of the optical fiber, namely the mode instability effect threshold value of the parameter optical fiber;
in step S4, the optical fiber parameter set meeting the high power requirement in step S3 is brought into the mode gain model of the optical fiber, and the mode instability threshold under the optical fiber parameter set is calculated, and the specific 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 P 1 (0) The ratio of the fundamental mode is 99.9%, the ratio of the high-order mode is 0.1%, the incident pump light power Pp, the fiber core radius R, the cladding radius R1, the fiber length L, the cladding absorption coefficient alpha dB/m and the bending radius R coil Calculating the power P of a high-order mode in the length direction of the optical fiber in a stable state 2 (z), power of fundamental mode P 1 (z) distribution;
s42, the parameters are put into formulas (2) (3) (4) (5) (6) (7) (8), whether the higher-order mode duty ratio xi is larger than 0.05 is judged, if not, the mode instability effect does not occur, and at the momentIf it is greater than 0.05, a mode instability effect has occurred.
S43, according to the step S42, adjusting the power of the input signal light, when the xi is close to 0.05, outputting the signal light P at the moment 1 (L) regarded as mode-instability effect threshold
Specifically, in step S4, two modes of a fundamental mode and a high-order mode exist in the optical fiber, gain amplification conditions of different modes are different, and a calculation formula of the power of the fundamental mode and the high-order mode in the signal light at the output end is specifically as follows:
wherein,,
P 1 (0) Is the incident signal light power;
Γ 2 is a higher-order mode overlap factor, and is calculated by the formula (2) when m=1;
g (z) is a gain coefficient when the propagation distance of the laser along the axial direction of the optical fiber is z;is the absorption and emission section of the corresponding signal light, n u The upper energy level particle number proportion is determined by the pump light power;
N Yb is the proportion of the rare earth ion doping concentration of the optical fiber, GG is the total pumping absorption, which is generally a fixed value and inversely proportional to the length L of the optical fiber;
χ is the mode coupling coefficient, related to the cladding radius;
P 1 (L)、P 2 (L) is z=l, i.e. the power of the fundamental mode, higher order mode in the output signal light;
ζ is the total ratio of the higher order modes to the signal light, and the signal light power P when ζ=0.05 1 (L) as the mode instability threshold at this time,
thus, the mode instability threshold is related to the core size, cladding size, fiber length, numerical aperture parameters, and besides, the mode instability threshold can be significantly raised by different signal light losses in different modes in the fiber due to fiber bending. The loss factor calculation formula for the different modes generated by the fiber bending (coil) is as follows:
wherein,,
beta is the propagation constant;
m is the maximum logarithm of the field component of the mode in the circumferential direction of the fiber, the fundamental mode m=0, and the higher order mode m=1;
when m=0, e m When=1, m=1, e m ＝2；
R coil Is the bending radius of the optical fiber;
therefore, when the optical fiber parameter is fixed and the wavelength of the signal light is unchanged, the bending loss coefficient alpha coil From the radius of curvature R coil Determining, changing the bending radius can change bending loss, and further influence the power ratio of each mode in the signal light power; the power relation between the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the bending of the optical fiber is as follows:
P 01 (L)、P 0 ′ 1 (L)、P 11 (L)、P 1 ′ 1 (L) the LP01 fundamental mode and LP11 higher order mode powers before and after bending respectively,bending loss coefficients of the LP01 fundamental mode and the LP11 higher order modes, respectively, caused by bending +.>The mode instability effect is considered to occur when the higher order mode power occupies 0.05 of the total power of the signal light, so that the ratio of the higher order modes in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold is improved.
S5, selecting a bending radius range corresponding to the proper bending loss according to the mode instability effect threshold 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 the designed bending radius; and comparing the optical fiber with the nonlinear effect threshold calculated in the step S3, taking a smaller value as a design value of the highest output power of the optical fiber, and ensuring that the mode unstable effect threshold and the nonlinear effect threshold of the optical fiber are not smaller than the highest output power of the optical fiber.
Several sets of calculated data in this example are shown in table 1, table 1 giving the fiber parameters, the optimum bend radius at this time, and the corresponding theoretical maximum output power.
TABLE 1
Experimental results: with the optical fiber designed as above, the fiber core size is 30um, the cladding diameter is 500um, the absorption coefficient is 0.6dB/m, the optical fiber with the length of 7m is wound in a bending way, the bending radius is 19cm and is selected as the designed bending radius, and the highest 2700W power output is obtained under the condition that no mode instability effect and no nonlinear effect occur, and is close to the theoretical calculated value 2600W.
Claims (9)
1. A design method of high-power gain optical fiber capable of simultaneously inhibiting mode instability and nonlinear effect comprises a double-cladding layer, a fiber core and an inner cladding layer sequentially from inside to outside, ytterbium or other rare earth ions are doped in the fiber core as gain medium, the inner cladding layer is quartz cladding layer,
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 quincuncial shape, a D shape and other non-circular shapes;
the diameter of the inner cladding is 300-1200 mu m;
the absorption coefficient of the cladding pumping is 0.2-1.0dB/m at 915 nm;
the optical fiber is bent and coiled, and the bending radius is between 2.5 cm and 80 cm;
the method is characterized by comprising the following steps of:
s1, establishing a nonlinear effect threshold calculation model of a gain optical fiber and different modes of laser gain calculation models of signal light in the optical fiber;
s2, setting the variation range of a plurality of optical fiber parameters according to experimental experience, wherein the variation range comprises 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 nonlinear effect threshold range at the moment, and selecting an optical fiber parameter set meeting the high power requirement;
s4, the optical fiber parameter set is brought into a mode gain calculation model of the optical fiber, the signal light output power of the optical fiber parameter set under the changed bending radius and the high-order mode duty ratio at the moment are calculated, a corresponding bending radius range in a proper bending loss range is selected, and when no mode instability effect occurs, the highest output signal light power in the bending radius range is used as the theoretical highest output power of the optical fiber, namely the mode instability effect threshold of the parameter optical fiber;
s5, comparing the mode unstable effect threshold calculated in the step S4 with the nonlinear effect threshold calculated in the step S3, and taking a smaller value as a design value of the highest output power of the optical fiber to ensure that the mode unstable effect threshold and the nonlinear effect threshold of the optical fiber are not smaller than the highest output power of the optical fiber.
2. The method of designing a high power gain optical fiber according to claim 1, wherein said core diameter has a value of 35-80 μm.
3. The method of designing a high-power gain optical fiber according to claim 2, wherein the core numerical aperture NA takes a value of 0.03 to 0.07.
4. The method for designing a high-power gain optical fiber according to claim 3, wherein said inner cladding diameter has a value of 500 to 1000 μm.
5. The method of designing a high power gain optical fiber according to claim 4, wherein said cladding pumped absorption coefficient @915nm is 0.4-0.8dB/m.
6. The method of designing a high power gain optical fiber according to claim 5, wherein said optical fiber is bent around a bend radius of between 17.5cm and 65 cm.
7. The method for designing a high-power gain optical fiber according to claim 1, wherein in the step S3, the nonlinear effect threshold calculation formula is specifically as follows:
wherein Γ is a signal light overlap factor, wherein V is a normalized working frequency, U is a normalized transverse phase parameter, W is a normalized transverse attenuation parameter, and a calculation formula is V 2 ＝W 2 +U 2 ,V＝kRNA，k is the wavenumber, R is the core radius, NA is the numerical aperture of the fiber, where m=0; j (J) 0 (U)、/>The representative variables are U, (-)>0 th order Bessel function of the first class, J m-1 (U)、Jm(U)、J m+1 (U) represents a Bessel function of the first class m-1, m, m+1 with the variable U;
gB (Deltav) is SBS gain factor, 5 x 10 in quartz fiber -11 ；
G is the laser gain of the fiber;
r is the core radius of the fiber;
l is the length of the fiber;
a is an experimental fit coefficient, which is a measure of multiple sets of nonlinear effect thresholdsCarrying out calculation in the formula (1) to obtain a plurality of groups of A (n) values, and taking an average value to obtain; as can be seen from the above equation, changing the core radius R, length L of the fiber can significantly change the threshold of the nonlinear effect.
8. The method for designing a high-power gain optical fiber according to claim 7, wherein in the step S4, two modes of a fundamental mode and a high-order mode exist in the optical fiber, gain amplification conditions of different modes are different, and a calculation formula of the fundamental mode and the high-order mode in the signal light at the output end is specifically as follows:
wherein,,
P 1 (0) Is the incident signal light power;
Γ 2 is a higher-order mode overlap factor, calculated by the formula (2) when m=1;
g (z) is a gain coefficient when the propagation distance of the laser along the axial direction of the optical fiber is z;is the absorption and emission section of the corresponding signal light, n u The upper energy level particle number proportion is determined by the pump light power;
N Yb is that the doping concentration of rare earth ion of optical fiber is positiveThe ratio GG is the total pump absorption, which is a constant value inversely proportional to the fiber length L;
χ is the mode coupling coefficient, related to the cladding radius;
P 1 (L)、P 2 (L) is z=l, i.e. the power of the fundamental mode, higher order mode in the output signal light;
ζ is the total ratio of the higher order modes to the signal light, and the signal light power P when ζ=0.05 1 (L) as the mode instability threshold at this time,
therefore, the mode instability threshold is related to the fiber core size, the cladding size, the fiber length and the numerical aperture parameters, and besides, the mode instability threshold can be obviously improved due to the fact that the optical loss of different modes of signals in the optical fiber is different due to the bending of the optical fiber; the loss coefficient calculation formula for the different modes generated by the bending of the optical fiber is as follows:
beta is the propagation constant;
K m-1 (W)，K m+1 (W) represents a second class m-1, m+1 order bessel function of variable W, fundamental mode m=0, higher order mode m=1;
when m=0, e m When=1, m=1, e m ＝2；
R coil Is the bending radius of the optical fiber;
therefore, when the optical fiber parameter is fixed and the wavelength of the signal light is unchanged, the bending loss coefficient alpha coil From the radius of curvature R coil Determining, changing the bending radius can change bending loss, and further influence the power ratio of each mode in the signal light power; the power relation between the LP01 fundamental mode and the LP11 high-order mode transmitted before and after the bending of the optical fiber is as follows:
P 01 (L)、P′ 01 (L)、P 11 (L)、P′ 11 (L) the LP01 fundamental modes before and after bending, respectivelyAnd the LP11 high-order mode power,bending loss coefficients of the LP01 fundamental mode and the LP11 higher order modes, respectively, caused by bending, +.>The mode instability effect is considered to occur when the higher order mode power occupies 0.05 of the total power of the signal light, so that the ratio of the higher order modes in the signal light can be reduced by selecting the optimal bending radius, and the mode instability threshold is improved.
9. The method for designing a high-power gain optical fiber according to claim 8, wherein in the step S4, the optical fiber parameter set meeting the high-power requirement in the step S3 is brought into the mode gain model of the optical fiber, and the mode instability threshold under the optical fiber parameter set is calculated 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 P 1 (0) A fundamental mode duty ratio of 1-n, a higher-order mode duty ratio of n, an incident pump light power Pp, a fiber core radius R, a cladding radius R1, a fiber length L, a cladding absorption coefficient alpha dB/m, a bending radius R coil Calculating the power P of a high-order mode in the length direction of the optical fiber in a stable state 2 (z), power of fundamental mode P 1 (z) distribution;
s42, the parameters are put into formulas (2) (3) (4) (5) (6) (7) (8), whether the higher-order mode duty ratio xi is larger than 0.05 is judged, if not, the mode instability effect does not occur, and at the momentIf greater than 0.05, a mode instability effect has occurred;
s43, according to the step S42, adjusting the power of the input signal light and the pump light, and outputting the signal light P when the xi is close to 0.05 1 (L) regarded as mode-instability effect threshold
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