The schematic diagram of the single lens coupling system is shown in Fig. 1.
The beam is theoretically an ideal fundamental Gaussian distribution, where the lens in the optical system is an ideal lens, M2=1. L is the distance between the incident beam waist and the end of the fiber, l1 is the distance between the incident beam waist and the lens, l is the distance between the lens and the end of the ROD Fiber, ω0 is the radius of the incident beam waist, and ω is the radius of the spot on the end face of the ROD Fiber. Using what is already known, the following can be obtained that:
理论推导中的光束为理想基模高斯光束即M2=1, 光学系统中的透镜为理想透镜。L是入射光束束腰与光纤端面之间的距离, l1为入射光束束腰与透镜的距离, l为透镜与光纤棒端面之间的距离, ω0为入射光束腰半径, ω为光纤棒端面上的光斑半径。由已知可以得到:
Let the lens focal length be F, allowing the propagation matrix of the system to become:
Using the known incident beams, confocal parameters become:
Then the q parameter at the waist of the incident beam is:
The q parameter on the lens plane after transformation by the system is:
Then the distance between the output beam waist and the focusing mirror is:
The confocal parameters of the output beam are:
The radius of the waist of the output beam is:
The q parameter of the output beam on the fiber end face is:
The spot radius of the output beam on the face of the fiber′s end is:
For the fundamentally Gaussian beam that is transformed by the system, the mode field distribution on the fiber end face can be expressed as:
Where U0 is the mode field amplitude of the Gaussian beam, and the wave number k is:
其中, U0为高斯光束的模场振幅, 波数k为:
Where UR0 and DMF are the mode field amplitude and mode field diameter of the ROD Fiber, respectively.
The ideal coupling efficiency is given by:
Where S is the plane of the optical end face and UROD-PCF* is the conjugate field of UROD-PCF.
其中, S为光端面所在平面, UROD-PCF*为UROD-PCF的共轭场。
Combining equations (1)-(14) yields the coupling efficiency as a function of the lens position when the focal length of the lens and the distance between the incident beam waist and the end face of the fiber are fixed. It also yields the relationship between the coupling efficiency and the focal length when the distance between the lens and the fiber′s end face as well as the distance between the incident beam waist and the fiber′s end face are held constant. For the fiber end face, when the beam is incident and conducts through the fiber, Fresnel reflection loss occurs at the front and rear ends of the fiber. Generally, the Fresnel reflection loss of a single end face is approximated to 3.5%~4%. The total Fresnel reflection loss of the front and rear end faces of the fiber is approximately 8%. When loss from misalignment of the Gaussian beam coupled to the fiber is ignored, coupling efficiency in the first two cases is shown in Fig. 2 and Fig. 3. The parameters used in the simulation calculation are:the wavelength of the incident light λ is 1 030 nm, DMF=65 μm, ω0=0.4 mm, L=885 mm. In the first case, F=103.26 mm and in the second case, l=120 mm.
结合式(1)~(14)分别计算出当透镜焦距、入射光束束腰与光纤端面的距离一定时, 耦合效率随透镜位置的变化关系以及当透镜与光纤端面的距离、入射光束束腰与光纤端面的距离一定时, 耦合效率随透镜焦距的变化关系。对于光纤端面而言, 当光束入射并且通过光纤传导输出时, 在光纤的前后两个端面会存在菲涅尔反射损耗。一般来说单独一个端面的菲涅尔反射损耗约为3.5%~4%, 光纤的前后两个端面的总的菲涅尔反射损耗约为8%左右。当忽略高斯光束与光纤耦合的失准损耗时, 前两种情况下的耦合效率如图 2与图 3所示。模拟计算所用的参数为:入射光波长λ=1 030 nm, DMF=65 μm, ω0=0.4 mm, L=885 mm, 第一种情况所用F=103.26 mm, 第二种情况所用l=120 mm。
It can be seen from Fig. 2 that when the distance between the incident beam waist and the end face of the fiber and the focal length of the lens are all constant, the coupling efficiency increases and then decreases as the distance between the lens and the end face of the fiber increases. It can be seen from Fig. 3 that when the distance between the incident beam waist and the end of the fiber, and the distance between the lens and the end face of the fiber are constant, the coupling efficiency increases and then decreases as the focal length of the lens increases. In both cases, the maximum coupling efficiency can surpass 80%.
As can be seen from Fig. 2, the coupling efficiency changes drastically when the focal length of the lens is 103.26 mm and the distance from the end face is between 90 mm and 150 mm. As can be seen from Fig. 3, when the lens is fixed at a distance of 120 mm from the end face of the fiber, the coupling efficiency changes drastically when the focal length of the lens is between 80 mm and 140 mm.
The schematic diagram of the beam expander lens group coupling system is shown in Fig. 4.
Since the fiber adjustment is relatively simple, it is easy to move the pigtail or the beam expander lens group position so that the beam waist is at the end face of the fiber after the beam expansion. And if the magnification of the beam expander lens group is constant, the size of the waist is also constant regardless of how the beam expander lens group is expanded. When the beam expansion ratio is n, n∈(0, ∞), the beam waist mode after beam expansion is:
由于光纤调整较为简单, 因此很容易通过移动尾纤或者扩束透镜组位置, 使得扩束后的束腰在光纤端面处, 而且只要扩束透镜组倍率一定, 无论怎么移动扩束透镜组, 扩束后的束腰大小都是不变的。扩束倍率为n, n∈(0, ∞), 则扩束后的束腰模场为:
The mode field distribution of the ROD Fiber end face is given in equation (13). The ideal coupling efficiency is given by:
The position of the lens group and the position of the fiber pigtail can be changed with some flexibility during the experiment so that the beam waist after the expansion can be found easily, and so that the plane of the beam waist coincides with the plane of the end face of the fiber. Therefore, the magnification of the beam expander will become the main factor affecting coupling efficiency. The relationship between the expansion ratio and the coupling efficiency is simulated below.
实验中的透镜组位置与光纤尾纤位置可以灵活变化, 因此可以很容易找到扩束后的束腰, 并让束腰所在平面恰好与光纤端面所在平面重合。所以扩束镜的倍率将成为影响耦合效率的主要因素。下面将对扩束倍率与耦合效率的关系进行仿真。
Combine the equations (13), (15), and (16) to calculate the relationship between the expansion ratio and the coupling efficiency, and consider the Fresnel loss around the two end faces of the fiber is 8%. When neglecting the loss due to misalignment of the Gaussian beam coupled to the fiber, the beam expansion ratio and coupling efficiency are shown in Fig. 5. The parameters used in the simulation calculation are:λ=1 030 nm, DMF=65 μm, ω0=0.02 mm, the used n varies between 0x and 70x, and the plane where the beam is located coincides with the end face of the fiber after the beam is expanded.
图 5 耦合效率与扩束倍率的关系
Figure 5. Relationship between the coupling efficiency and magnification of the beam expander
结合式(13)、(15)、(16)分别计算出扩束倍率与耦合效率的关系, 并考虑光纤两个端面8%左右的菲涅尔损耗。当忽略高斯光束与光纤耦合的失准损耗时, 扩束倍率与耦合效率如图 5所示。模拟计算所用的参数为:λ=1 030 nm, DMF=65 μm, ω0=0.02 mm, 所使用的n在0x~70x之间变化, 扩束后束腰所在的平面与光纤端面重合。
It can be seen from Fig. 5 that the coupling efficiency increases rapidly with an increase in the expansion ratio and then decreases slowly thereafter. In this case, this is because two kinds of losses dominate: Diffraction loss and Numerical aperture mismatch loss. Before the coupling reaches maximum efficiency, as the beam expansion ratio increases, the numerical aperture mismatch loss decreases rapidly as the diffraction loss increases slowly, causing the coupling efficiency to increase rapidly within this range. After the coupling reaches the maximum efficiency, the numerical aperture mismatch loss is negligibly small and the diffraction loss is still slowly increasing. This causes the coupling efficiency to slowly decrease within this range.
从图 5可以看到, 耦合效率随着扩束倍率的增加先迅速增大随后缓慢减小, 这是因为在这种情况下有两种损耗起主导作用, 这两种损耗分别为衍射损耗与数值孔径失配损耗。在耦合效率达到最大值前, 随着扩束倍率的增加, 数值孔径失配损耗迅速减小, 衍射损耗缓慢增大, 因此, 耦合效率在此范围内迅速增加; 在耦合效率达到最大值后, 数值孔径失配损耗已经小到可以忽略不计, 而衍射损耗依旧缓慢增加, 因此, 耦合效率在此范围内缓慢下降。
The maximum point is the point at which the beam waist mode field after beam expansion completely matches the mode field of the ROD Fiber. Usually, obtaining a suitable lens group such as this is difficult. Therefore, in the experiment, we can use this curve as a guide and select the proper coupling lens groups that can best improve coupling efficiency.
最大值点是扩束后的束腰模场与光纤棒的模场完全匹配的那一点, 通常不易得到这样合适的透镜组, 因此, 在实验中可以此曲线作为指导, 选择尽量合适的耦合透镜组, 以提高耦合效率。
Here are three types of misalignment loss in the process of coupling free-space Gaussian beams with fibers. They are longitudinal misalignment loss, lateral misalignment loss, and angular misalignment loss. A brief analysis of the effects of these three types of loss on coupling efficiency is given below.
The schematic diagram of longitudinal misalignment loss is shown in Fig. 6.
As shown in the above figure, during the adjustment process, the beam waist cannot completely coincide with the fiber end face in the longitudinal direction. This form of loss is called the longitudinal misalignment loss. The relationship between coupling efficiency and longitudinal misalignment loss is[17, 19]:
Where U1 is the distribution of the incident beam waist mode field, U2 is the position mode field distribution from the incident beam waist s, S1 is the plane of the beam waist, and S2 is the plane from the position of the incident beam waists
式中, U1为入射光束束腰模场分布, U2为距离入射光束束腰为s位置的模场分布, S1为光束束腰的平面, S2为距离入射光束束腰为s的位置所在的平面。
Assuming that ω0=32.5 μm, DMF=65 μm, and λ=1 030 nm in Formula (17), the relationship between the normalized coupling efficiency and the longitudinal offset can be obtained as shown in Fig. 7.
假设ω0=32.5 μm, DMF=65 μm, λ=1 030 nm, 根据式(17)可以得到归一化耦合效率与纵向偏移量的关系如图 7所示。
It can be seen from Fig. 7 that coupling efficiency is sensitive to the longitudinal error. When the longitudinal offset is gradually increased from 0 mm to 5 mm, the normalized coupling efficiency reduced by more than 50%. When the longitudinal offset exceeded 13 mm, the normalized coupling efficiency dropped below 10%.
由图 7可知, 耦合效率对纵向误差极其敏感, 当纵向偏移量由0 mm逐渐增大到5 mm的过程中归一化耦合效率降低了50%以上, 当纵向偏移量超过13 mm归一化耦合效率就降到了10%以下。
The schematic diagram of lateral misalignment loss is shown in Fig. 8.
As shown in the above figure, during the adjustment process, the beam cannot completely coincide with the end face of the fiber in the lateral direction. This form of loss is called the lateral misalignment loss. The relationship between coupling efficiency and lateral misalignment loss is[17, 19]:
Where DMF/2 is the mode field radius of the ROD Fiber, and ω0 is the incident beam waist radius. Assume that:
式中, DMF/2为光纤棒模场半径, ω0为入射光束束腰半径。设:
Then, when 0 < α < αc,
则有当0 < α < αc时,
When αc < α < π,
当αc < α < π时,
Assume that ω0=32.5 μm, DMF=65 μm, and λ=1 030 nm. According to the equations (18)-(21), the relationship between the normalized coupling efficiency and the lateral offset can be obtained as shown in Fig. 9:
假设ω0=32.5 μm, DMF=65 μm, λ=1 030 nm, 根据式(18)~(21)可以得到归一化耦合效率与横向偏移量的关系如图 9所示。
It can be seen from Fig. 9 that the coupling efficiency is sensitive to the transverse error. When the lateral offset is gradually increased from 0 μm to 30μm, the normalized coupling efficiency is reduced by about 50%. When the lateral offset exceeds 50 μm, the normalization coupling efficiency dropped below 10%.
由图 9可知, 耦合效率对角度误差极其敏感, 当横向偏移量由0 μm逐渐增大到30 μm的过程中, 归一化耦合效率降低了约50%, 当横向偏移量超过50 μm时归一化耦合效率降到了10%以下。
The angular misalignment loss diagram is shown in Fig. 10.
As shown in the above figure, during the adjustment process, the beam cannot be incident with the fiber in parallel. This form of loss is called the angular misalignment loss. The relationship between coupling efficiency and angular misalignment loss is[19-20]:
Where n2 is the refractive index of the inner cladding of the rod-shaped photonic crystal fiber.
Assuming the inner cladding refractive index n2=1.4, the incident beam waist radius ω0=32.5 μm, and λ=1 030 nm, according to the equation (22), the relationship between the normalized coupling efficiency and the angular offset can be obtained as shown in Fig. 11.
假设内包层折射率n2=1.4, 入射光束束腰半径ω0=32.5 μm, λ=1 030 nm, 根据式(22)可以得到归一化耦合效率与角度偏移量的关系如图 11所示。
It can be seen from Fig. 11 that the coupling efficiency is sensitive to the angular error. When the angular offset is gradually increased from 0 mrad to 6 mrad, the normalized coupling efficiency is reduced by about 50%. When the angular offset exceeds 15 mrad normalized coupling efficiency is roughly 0.
由图 11可知, 耦合效率对角度误差及其敏感, 当角度偏移量由0 mrad逐渐增大到6 mrad的过程中归一化耦合效率降低了约50%, 当角度偏移量超过15 mrad, 归一化耦合效率基本为0。
According to the above analysis of the three misalignment conditions, the coupling efficiency is very sensitive to various misalignment errors, wherein the magnitude of the longitudinal misalignment error and the angular misalignment error are a millimeter and a milliradian, respectively, and the tranverse misalignment error′s magnitude is on the order of microns. During adjustment, in order to minimize the influence of misalignment error on the coupling efficiency, an adjustment frame with high accuracy and reliability should be selected and the operator should be both careful and meticulous.
根据上文对3种失准情况的分析可知, 耦合效率对各种失准误差非常敏感, 其中纵向失准误差和角度失准误差的量级分别为毫米级和毫弧度级, 而横向失准误差的量级在微米级。在实际调整中为了尽量减少失准误差对耦合效率的影响, 应选用精度和可靠性较高的调整架, 并且操作时应认真细致。
表 1 固体激光器基本参数
Table 1. Basic parameters of the solid-state laser
Parameter Name Parameter Value Parameter Name Parameter Value Output Power 1~4.5 W Output Waist Diameter 800 μm M2 ~1.2 Wavelength 1 030 nm
表 2 光纤激光器基本参数
Table 2. Basic parameters of fiber laser
Parameter Name Parameter Value Parameter Name Parameter Value Output Power 1~6 W Output tail Fiber Core Diameter 25 μm M2 ~1.1 Wavelength 1 030 nm
The photonic crystal ROD Fiber used is aeroGAIN-ROD-PM85, produced by NKT. The core diameter is D=85 μm, the mode field diameter DMF=65 μm, and the core numerical aperture NA=0.015. In order to avoid high Fresnel reflection loss, both ends of the fiber are plated with antireflection film.
所用光子晶体光纤棒为NKT公司生产的aeroGAIN-ROD-PM85, 纤芯直径为D=85 μm、模场直径DMF=65 μm、纤芯数值孔径NA=0.015, 为了避免较高的菲涅尔反射损耗, 光纤两端面均镀有增透膜。
The coupling experimental optical path of a solid-state laser is shown in Fig. 12.
The lenses used are total reflection mirrors where F=103.26 mm and M1-M4 are 45°. In order to prevent back light interference or damage to the laser, an isolator is added to the experiment′s optical path.
所使用的透镜F=103.26 mm, M1-M4为45°全反射镜, 为了防止回光干扰或损伤激光器, 实验光路中加入了隔离器。
The coupling experimental optical path of the fiber laser is shown in Fig. 13.
Among the used lenses, F1=30 mm and F2=77 mm, and the both are respectively collimated and focused. These two lenses can be regarded as a lens group that expands the waist of the output beam of the fiber pigtail by a certain magnification. Also, a total reflection mirror is used where M1-M4 is 45°. In order to prevent back light interference or damage to the laser, an isolator is also added to the experiment′s optical path.
所使用的两个透镜分别为F1=30 mm、F2=77 mm, 两个透镜的作用分别为准直和聚焦, 这两个透镜可以看作是一个将光纤尾纤输出束腰扩束一定倍率的透镜组, M1-M4为45°全反射镜, 为了防止回光干扰或损伤激光器, 实验光路中同样加入了隔离器。
表 3 低功率情况下的耦合效率对比
Table 3. Comparison of coupling efficiency under low power conditions
Laser type Injected power/mW Transmitted power/mW Coupling efficiency/% Solid State 100.1 42.3 42.2 Optical Fiber 1 000 600 60.0
表 4 中等功率情况下的耦合效率对比
Table 4. Comparison of coupling efficiency under medium power conditions
Laser type Injected power/mW Transmitted power/mW Coupling efficiency/% Solid State 4.20 2.62 62.4 Optical Fiber 4.00 3.22 80.5
Since the stable output power of the fiber laser can only be set to 1 000 mW, the injected power in the low power test is significantly different from that of the solid state laser.
由于光纤激光器的稳定输出功率最低只能设定为1 000 mW, 因此, 低功率测试时的注入功率与固体相差较多。
By comparing the data of the solid-state laser to the fiber laser, it can be known that at low power, the coupling efficiency of the solid-state laser is only 42.4%, and that the coupling efficiency of the fiber laser is higher at 60.0%. When using medium power, the injection power is also 4 W. The coupling of the solid-state laser had an efficiency of only 62.4%, while that of the fiber laser exceeded 80%. Fiber lasers have higher coupling efficiencies than solid-state lasers in both low-power and medium-power conditions. The reason for this may be that the beam quality of the fiber laser is higher than that of the solid laser and that the coupled spot energy is more concentrated, which would theoretically cause the coupling efficiency of the fiber laser to be higher than that of the solid laser.
通过对比固体激光器与光纤激光器的数据可以得知, 在低功率下, 固体激光器的耦合效率只有42.2%, 而光纤激光器的耦合效率可达60.0%;在中等功率下, 注入功率同样为4 W, 固体激光器的耦合效率只有62.4%, 而光纤激光器的耦合效率已经达到了80.5%。无论是低功率情况下还是中等功率情况下, 光纤激光器的耦合效率均比固体激光器高。分析其原因可能是, 光纤激光器的光束质量高于固体激光器, 耦合后的光斑能量更加集中, 因此, 光纤激光器的耦合效率要高于固体激光器。
When comparing the data of the same laser at different output powers, the solid-state laser has a coupling efficiency of only 42.4% at low injection power, and a higher coupling efficiency of 62.4% at 4 W medium power. The same phenomenon occurs during the fiber laser coupling experiment. The fiber laser has a coupling efficiency of only 60.0% at low power, which increases to 80.5% at 4 W medium power. In other words, the coupling efficiency is low at low power, while the coupling efficiency is increased at medium power. The reason for this result may be that the core absorbs light at 1 030 nm. At low power, the light absorption in the core is significant due to lower injection power causing the CCR(cladding core power ratio) to be low. Therefore, in the case of medium power, since the injection power is large, the core absorption accounts for a small portion of the overall power, the CCR increases causing the coupling efficiency to also increase.
通过对比相同激光器在不同输出功率下的数据可知, 固体激光器在低功率下耦合效率只有42.4%, 在中等功率下注入功率为4 W, 耦合效率为62.4%, 比低功率下有所增长; 同样的现象也发生在光纤激光器的耦合实验中, 光纤激光器在低功率下耦合效率只有60.0%, 在中等功率下注入4 W, 耦合效率增长到了为80.5%。也就是说在低功率下耦合效率较低, 而在中等功率下耦合效率有所增长。分析其原因可能是, 纤芯对1 030 nm的激光有所吸收。在低功率下, 由于注入功率较小, 所以纤芯吸收所占比例较大, CCR(包层纤芯功率比)较低, 因此耦合效率较低; 在中等功率情况下, 由于注入功率较大, 纤芯吸收所占比例小, CCR增加, 因此耦合效率增加。
In order to verify whether the spot energy after fiber laser coupling is better than the concentration of the solid laser and the shape of the spot after coupling, the coupled spot is observed by CCD in the experiment. The observation result is shown in Fig. 14.
图 14 固体激光器(左)与光纤激光器(右)耦合后光斑对比图
Figure 14. Solid-state laser(left) and fiber laser(right) coupling facula
为了验证光纤激光器耦合后的光斑能量是否比固体激光器的集中, 以及耦合后的光斑形状是否更好, 实验中利用CCD对耦合后的光斑进行了观察, 观察结果如图 14所示。
It can be clearly seen when comparing the above two facula patterns that there is stray light that escapes in the cladding surrounding the coupling of the solid laser, and the stray light that escapes into the cladding around the coupling facula of the fiber laser is dim. From the shape of the spot, it is obvious that the coupling spot of the fiber laser is smaller than the coupling spot of the solid laser.
通过两幅光斑图的对比可以看出, 固体激光器的耦合光斑周围有明显的逸散在包层中的杂散光, 而光纤激光器的耦合光斑周围逸散到包层中的杂散光十分暗淡。从光斑的形状来看光纤激光器的耦合光斑比固体激光器的耦合光斑圆。
In order to verify that the coupling efficiency increases with an increase in power, the injected power is gradually increased from 1 W to 6 W to determine the coupling efficiency of the experiment.
为了验证功率逐渐增加的过程中耦合效率是否会逐渐增大, 实验中测定了光纤激光器耦合情况下, 注入功率由1 W逐渐增加到6 W时耦合效率的变化情况。
It can be seen from Tab. 5 and Fig. 15 that in all cases, the coupling efficiency increased gradually with increases in the injected power. Moreover, the changes in the fiber laser′s facula after coupling were also monitored as the injected power was gradually increased from 1 W to 6 W.
表 5 注入功率、透过功率与耦合效率
Table 5. Transmission power and coupling efficiency vary with injection power
Injected power/W Transmitted power/W Coupling efficiency/% 1 0.60 60.0 2 1.42 71.0 3 2.31 77.0 4 3.22 80.5 5 4.17 83.4 6 5.23 87.2
It can be seen from Fig. 16 that the coupled facula tends to gradually concentrate as the injection power increases. The reason for this may be that the core′s power absorption ratio gradually decreases as the power increases. Moreover, the beam quality of the fiber laser is also gradually increasing, meaning that the beam mode field passing through the coupled system matches more closely with the mode field of the ROD Fiber itself. This causes the coupled energy to be more concentrated to the core.
图 16 注入功率1 W到6 W的情况下耦合光斑的变化规律
Figure 16. Changing law of coupling facula when injection power growing from 1 W to 6 W
从图 16可以看出, 随着注入功率的增加, 耦合后的光斑能量有逐渐集中的趋势, 原因可能是, 随着功率的增加纤芯对功率的吸收比例逐渐减小, 而且光纤激光器本身的光束质量在逐渐增加, 使得经过耦合系统的光束模场与光纤棒本身的模场更加匹配, 致使耦合后的能量向纤芯集中。
According to the experimental results, although the coupling effect of the fiber laser is much better than that of the solid-state laser, there is still a gap between it and the ideal coupling efficiency demonstrated by calculations. The main reasons for this may be as follows:
根据实验情况来看, 虽然光纤激光器的耦合效果比固体激光器好很多, 但是, 仍与模拟计算所得的理想耦合效率有所差距, 造成这种差距的主要原因可能有以下几点:
First, the beam quality of the fiber laser is M2~1.1 and not a fundamental Gaussian beam in the ideal state used in the simulation. The non-ideal beam quality will create loss in coupling efficiency.
第一, 光纤激光器的光束质量是M2~1.1, 不是仿真中所用的理想状态下的基模高斯光束, 非理想的光束质量将带来一定的耦合效率损失。
Second, the beam′s output from the fiber laser passes through three mirrors, an isolator, and two lenses. The surface of these optical devices may have defects and those defects would cause distortion, which may also reduce coupling efficiency.
第二, 光纤激光器输出的光束在光路中经过3个反射镜、一个隔离器和两个透镜, 这些光学器件的表面可能存在缺陷, 缺陷造成光束的畸变, 这也可能使耦合效率降低。
Third, the accuracy of the coupling lens adjustment is not high enough to cause completely remove errors in alignment. Because the fiber is very sensitive to various alignment errors, the coupling efficiency would decrease.
第三, 耦合透镜调整的精度不够高造成了各种对准误差的出现, 由于光纤对各种对准误差十分敏感, 因此造成了耦合效率的降低。
Fourth, since the rod-shaped photonic crystal fiber is a gain fiber, the fiber is doped with Yb3+ ions, and the 1 030 nm wavelength of the Yb3+ ion pair in the fiber has an absorption effect, and this absorption is unavoidable in the measurement process. Once again, this would also reduce coupling efficiency.
第四, 由于棒状光子晶体光纤为增益光纤, 光纤中掺杂有Yb3+离子, 而光纤中的Yb3+离子对1 030 nm的波段有一定的吸收作用, 这种吸收在测定过程中是无法避免的, 因此会造成耦合效率的下降。