LI Tian-qi, MAO Xiao-jie, LEI Jian, BI Guo-jiang, JIANG Dong-sheng

(Science and Technology on Solid-State Laser Laboratory,North ChinaResearch Institute of Electro-Optics,Beijing 100015,China)

Abstract: The high or low coupling efficiency and the good or bad coupling facula directly affect the amplification effect of the Rod-type photonic crystal fiber. Therefore, it is necessary to research the coupling effect of seed light and choose a suitable laser as a seed source. In this paper, the coupling efficiency of Rod-type photonic crystal fibers in a solid-state laser and a fiber laser was theoretically analyzed. The changing regulation of the coupling efficiency and the effect of the alignment error on the coupling efficiency were calculated with two different lasers. A suitable lens or group of lenses were selected and an experiment was conducted to couple the solid-state laser beam and the fiber laser beam to the Rod-type photonic crystal fiber. Compared with the coupling effect of the two kinds of lasers, the maximum coupling efficiency of the solid laser is only 62.4%, while the coupling efficiency of the fiber laser is more than 80%. In the case of fiber laser coupling, the coupling efficiency at different power injection and the coupling facula were analyzed. The experimental results will guide the amplification experiment of the Rod-type photonic crystal fiber.

Key words: rod-type photonic crystal fiber;solid-state laser;fiber laser;coupling efficiency

1 Introduction

引 言

Rod-type photonic crystal fibers(ROD-PCF), hereinafter referred to as ROD Fiber for their large area, single mode and high gain, are very suitable for ultrashort pulse amplification[1-2]. At present, countries abroad have successfully developed crystal core picosecond pulse laser systems that can have a maximum average output power of up to 2 kW[3]. However, domestic research on optical fibers is rare, where most current research in this field occurs at the Shanghai Institute of Optics and Mechanics, CAS[1,4]. Optical fibers are also a form of photonic crystal fiber, which have a wide range of industrial applications. They might be used in medical fields, scientific research,etc.[5-8].

光子晶體光纖棒(Rod-type photonic crystal fiber，ROD-PCF)下文簡稱光纖棒(ROD Fiber)因其具有模場面積大、無截止單模、高增益的特點(diǎn)，十分適合于超短脈沖放大[1-2]。目前國外研制成功的光纖棒皮秒脈沖激光系統(tǒng)最大平均輸出功率可以高達(dá)2 kW[3]。但是國內(nèi)對光纖棒的研究報(bào)道較少見，目前在該領(lǐng)域研究較多的是中科院上海光機(jī)所[1,4]。光纖棒也是一種光子晶體光纖，其在工業(yè)、醫(yī)療、科研等方面有著廣泛的應(yīng)用[5-8]。

A key issue in the experimentation of ROD Fiber ultrashort pulse amplification systems is the method used to efficiently couple seed light into the core of a ROD Fiber. Coupling effect of seed light with ROD Fiber is important as effective coupling can cause seed light to be amplified more powerfully and the ROD Fiber can consequently receive light of higher quality.

在進(jìn)行光纖棒超短脈沖放大系統(tǒng)的實(shí)驗(yàn)中一個(gè)十分關(guān)鍵問題就是如何高效地將種子光耦合進(jìn)入光纖棒的纖芯。種子光與光纖棒之間的耦合效果十分重要，良好的耦合可以使種子光功率在光纖棒中得到充分的放大，并且可以得到高光束質(zhì)量的信號光。

Since the used fiber is a photonic crystal fiber and has a large mode field area, it has a large diameter and a regular air hole microstructure[9-10]. If the fiber is welded, its air holes collapse. For this reason, the ROD Fiber is usually fitted with end caps at either end and free-space lens is used to couple the seed light with the pump light[11]. Lens coupling is very demanding on the position and focal length of lenses. It requires complex calculations, simulation and practice to obtain a suitable lens focal length[12]. Lens coupling systems have difficulty performing adjustments. They require adjustments in multiple dimensions for a single lens and require adjustment of multiple lenses for best results[13].

由于光纖棒是大模場面積的光子晶體光纖，因此其直徑較大，而且具有規(guī)則的空氣孔微結(jié)構(gòu)[9-10]，如果對其進(jìn)行光纖熔接會(huì)造成空氣孔的塌陷，因此光纖棒通常都是在端面接有端帽，并使用自由空間透鏡對種子光和泵浦光進(jìn)行耦合[11]。透鏡耦合對透鏡的位置、焦距等要求非?？量?，需要經(jīng)過較為復(fù)雜的計(jì)算、仿真與實(shí)踐才能獲得合適的透鏡焦距[12]。透鏡耦合系統(tǒng)在調(diào)整的時(shí)候具有不小的難度，需要對單個(gè)透鏡的多個(gè)維度進(jìn)行調(diào)整，以及對多個(gè)透鏡進(jìn)行配合調(diào)整才能達(dá)到最好的效果[13]。

The beam generated by the seed source can be approximated as a Gaussian beam. The basic principle of Gaussian beams in regards to fiber coupling is pattern matching the Gaussian beam mode field with the fiber mode field[14-15]. In the following experiment, photonic crystal fiber is coupled to a solid laser with a larger facula using single lens coupling and the relationship between coupling efficiency, lens position and focal length are calculated. A fiber laser with a smaller facula is then coupled to the photonic crystal fiber with expanding bean coupling and the relationship between coupling efficiency and beam expansion ratio are calculated. A solid-state laser with an output beam waist diameter of 800 μm and a fiber laser with output beam waist diameter of 25 μm(both with a beam quality ofM2≤1.2) were used as seed lasers with a wavelength ofλ=1 030 nm. Experiments were performed by coupling then with a rod-shaped photonic crystal fiber that has a core diameter ofD=85 μm(mode field diameter ofDMF=65 μm).

種子源產(chǎn)生的光束可以近似為高斯光束，高斯光束到光纖耦合的基本原理就是高斯光束模場與光纖模場的模式匹配[14-15]。本文模擬計(jì)算了光斑較大的固體激光器在單透鏡耦合情況下，耦合效率與透鏡位置和焦距的關(guān)系，以及光斑較小的光纖激光器在擴(kuò)束透鏡組耦合情況下，耦合效率與擴(kuò)束倍率的關(guān)系。利用λ=1 030 nm輸出束腰直徑分別為800 μm和25 μm的固體激光器與光纖激光器作為種子源(光束質(zhì)量均為M2≤1.2)，對芯徑D=85 μm(模場直徑為DMF=65 μm)的棒狀光子晶體光纖進(jìn)行了耦合實(shí)驗(yàn)。

2 Analysis of Solid-state Laser Single Lens Coupling

固體激光器單透鏡耦合分析

The schematic diagram of the single lens coupling system is shown in Fig.1.

單透鏡耦合系統(tǒng)的原理圖如圖1所示。

Fig.1 Diagram of the single-lens coupling system 圖1 單透鏡耦合原理圖

The beam is theoretically an ideal fundamental Gaussian distribution, where the lens in the optical system is an ideal lens,M2=1.Lis the distance between the incident beam waist and the end of the fiber,l1is the distance between the incident beam waist and the lens,lis the distance between the lens and the end of the ROD Fiber,ω0is the radius of the incident beam waist, andωis the radius of the spot on the end face of the ROD Fiber. Using what is already known, the following can be obtained that:

理論推導(dǎo)中的光束為理想基模高斯光束即M2=1，光學(xué)系統(tǒng)中的透鏡為理想透鏡。L是入射光束束腰與光纖端面之間的距離，l1為入射光束束腰與透鏡的距離，l為透鏡與光纖棒端面之間的距離，ω0為入射光束腰半徑，ω為光纖棒端面上的光斑半徑。由已知可以得到：

L=l1+l, (1)

Let the lens focal length beF, allowing the propagation matrix of the system to become:

設(shè)透鏡焦距為F，則該系統(tǒng)的傳播矩陣為：

(2)

Using the known incident beams, confocal parameters become:

由已知入射光束的共焦參數(shù)為：

(3)

Then theqparameter at the waist of the incident beam is:

則入射光束束腰處的q參數(shù)為：

qin=jf, (4)

Theqparameter on the lens plane after transformation by the system is:

通過該系統(tǒng)變換后透鏡平面上的q參數(shù)為：

(5)

Then the distance between the output beam waist and the focusing mirror is:

則輸出光束束腰與聚焦鏡的距離為：

l2=-Re(qout) , (6)

The confocal parameters of the output beam are:

輸出光束的共焦參數(shù)為：

f1=Im(qout) (7)

The radius of the waist of the output beam is:

輸出光束的束腰半徑為：

(8)

Theqparameter of the output beam on the fiber end face is:

輸出光束在光纖端面上的q參數(shù)為：

q=jf1+(l-l2) , (9)

The spot radius of the output beam on the face of the fiber′s end is:

輸出光束在光纖端面上的光斑半徑為：

(10)

For the fundamentally Gaussian beam that is transformed by the system, the mode field distribution on the fiber end face can be expressed as[16]：

對于經(jīng)過系統(tǒng)變換后的基模高斯光束，其在光纖端面上的模場分布可以表示為[16]：

WhereU0is the mode field amplitude of the Gaussian beam, and the wave numberkis:

其中，U0為高斯光束的模場振幅，波數(shù)k為：

k=2π/λ, (12)

For the ROD Fiber, the end mode field distribution can be approximated as a Gaussian distribution[17-18]:

對于光纖棒，其端面模場分布為可以近似為高斯分布[17-18]：

WhereUR0andDMFare the mode field amplitude and mode field diameter of the ROD Fiber, respectively.

其中，UR0與DMF分別為光纖棒的模場振幅和模場直徑。

The ideal coupling efficiency is given by[18]:

則理想的耦合效率為[18]：

(14)

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%[17]. 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 lightλis 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.

結(jié)合式(1)～(14)分別計(jì)算出當(dāng)透鏡焦距、入射光束束腰與光纖端面的距離一定時(shí)，耦合效率隨透鏡位置的變化關(guān)系以及當(dāng)透鏡與光纖端面的距離、入射光束束腰與光纖端面的距離一定時(shí)，耦合效率隨透鏡焦距的變化關(guān)系。對于光纖端面而言，當(dāng)光束入射并且通過光纖傳導(dǎo)輸出時(shí)，在光纖的前后兩個(gè)端面會(huì)存在菲涅爾反射損耗。一般來說單獨(dú)一個(gè)端面的菲涅爾反射損耗約為3.5%～4%，光纖的前后兩個(gè)端面的總的菲涅爾反射損耗約為8%左右[17]。當(dāng)忽略高斯光束與光纖耦合的失準(zhǔn)損耗時(shí)，前兩種情況下的耦合效率如圖2與圖3所示。模擬計(jì)算所用的參數(shù)為：入射光波長λ=1 030 nm，DMF=65 μm,ω0=0.4 mm，L=885 mm，第一種情況所用F=103.26 mm，第二種情況所用l=120 mm。

Fig.2 Relationship between coupling efficiency and lens position 圖2 耦合效率與透鏡位置的關(guān)系

Fig.3 Relationship between coupling efficiency and focal length of the lens 圖3 耦合效率與透鏡焦距的關(guān)系

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%.

從圖2可以看出，當(dāng)入射光束束腰與光纖端面的距離以及透鏡的焦距一定時(shí)，耦合效率隨著透鏡與光纖端面的距離增大而先增大后減小。從圖3可以看出，當(dāng)入射光束束腰與光纖端面的距離以及透鏡與光纖端面距離一定時(shí)，耦合效率隨著透鏡焦距增大而先增大后減小。兩種情況下最大耦合效率均可達(dá)到80%以上。

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.

從圖2中可以看到，當(dāng)透鏡焦距為103.26 mm，且與端面的距離在90～150 mm之間時(shí)耦合效率會(huì)急劇地變化。從圖3中可以看到，當(dāng)透鏡固定在距離端面120 mm處時(shí)，透鏡的焦距在80～140 mm之間時(shí)耦合效率會(huì)急劇地變化。

3 Analysis of Fiber Laser Beam Expander Lens Group Coupling

光纖激光器擴(kuò)束透鏡組耦合分析

The schematic diagram of the beam expander lens group coupling system is shown in Fig.4.

擴(kuò)束透鏡組耦合系統(tǒng)的原理圖如圖4所示。

Fig.4 Diagram of the beam expanding lens group coupling system 圖4 擴(kuò)束透鏡組耦合原理圖

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 isn,n∈(0,∞), the beam waist mode after beam expansion is:

由于光纖調(diào)整較為簡單，因此很容易通過移動(dòng)尾纖或者擴(kuò)束透鏡組位置，使得擴(kuò)束后的束腰在光纖端面處，而且只要擴(kuò)束透鏡組倍率一定，無論怎么移動(dòng)擴(kuò)束透鏡組，擴(kuò)束后的束腰大小都是不變的。擴(kuò)束倍率為n,n∈(0,∞)，則擴(kuò)束后的束腰模場為：

(15)

The mode field distribution of the ROD Fiber end face is given in equation (13). The ideal coupling efficiency is given by:

而光纖棒端面模場分布在式(13)已經(jīng)給出。則理想的耦合效率為：

(16)

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.

實(shí)驗(yàn)中的透鏡組位置與光纖尾纖位置可以靈活變化，因此可以很容易找到擴(kuò)束后的束腰，并讓束腰所在平面恰好與光纖端面所在平面重合。所以擴(kuò)束鏡的倍率將成為影響耦合效率的主要因素。下面將對擴(kuò)束倍率與耦合效率的關(guān)系進(jìn)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 usednvaries between 0xand 70x, and the plane where the beam is located coincides with the end face of the fiber after the beam is expanded.

結(jié)合式(13)、(15)、(16)分別計(jì)算出擴(kuò)束倍率與耦合效率的關(guān)系，并考慮光纖兩個(gè)端面8%左右的菲涅爾損耗。當(dāng)忽略高斯光束與光纖耦合的失準(zhǔn)損耗時(shí)，擴(kuò)束倍率與耦合效率如圖5所示。模擬計(jì)算所用的參數(shù)為：λ=1 030 nm，DMF=65 μm，ω0=0.02 mm，所使用的n在0x～70x之間變化，擴(kuò)束后束腰所在的平面與光纖端面重合。

Fig.5 Relationship between the coupling efficiency and magnification of the beam expander 圖5 耦合效率與擴(kuò)束倍率的關(guān)系

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.

從圖5可以看到，耦合效率隨著擴(kuò)束倍率的增加先迅速增大隨后緩慢減小，這是因?yàn)樵谶@種情況下有兩種損耗起主導(dǎo)作用，這兩種損耗分別為衍射損耗與數(shù)值孔徑失配損耗。在耦合效率達(dá)到最大值前，隨著擴(kuò)束倍率的增加，數(shù)值孔徑失配損耗迅速減小，衍射損耗緩慢增大，因此，耦合效率在此范圍內(nèi)迅速增加；在耦合效率達(dá)到最大值后，數(shù)值孔徑失配損耗已經(jīng)小到可以忽略不計(jì)，而衍射損耗依舊緩慢增加，因此，耦合效率在此范圍內(nèi)緩慢下降。

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.

最大值點(diǎn)是擴(kuò)束后的束腰模場與光纖棒的模場完全匹配的那一點(diǎn)，通常不易得到這樣合適的透鏡組，因此，在實(shí)驗(yàn)中可以此曲線作為指導(dǎo)，選擇盡量合適的耦合透鏡組，以提高耦合效率。

4 Influence of misalignment loss on coupling efficiency

失準(zhǔn)損耗對耦合效率的影響

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.

在自由空間高斯光束與光纖耦合的過程中存在3類失準(zhǔn)損耗，它們分別是：縱向失準(zhǔn)損耗、橫向失準(zhǔn)損耗、角度失準(zhǔn)損耗。下面將對這3類損耗對耦合效率的影響做出簡要分析。

The schematic diagram of longitudinal misalignment loss is shown in Fig.6.

縱向失準(zhǔn)損耗示意圖如圖6所示。

Fig.6 Diagram of longitudinal misalignment loss 圖6 縱向失準(zhǔn)損耗示意圖

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]:

正如圖6所示，在實(shí)際調(diào)整的過程中，光束束腰在縱向上不能完全與光纖端面重合，這樣引入的損耗稱為縱向失準(zhǔn)損耗。耦合效率與縱向失準(zhǔn)損耗的關(guān)系式為[17,19]：

(17)

WhereU1is the distribution of the incident beam waist mode field,U2is the position mode field distribution from the incident beam waists,S1is the plane of the beam waist, andS2is the plane from the position of the incident beam waists

式中，U1為入射光束束腰模場分布，U2為距離入射光束束腰為s位置的模場分布，S1為光束束腰的平面，S2為距離入射光束束腰為s的位置所在的平面。

Assuming thatω0=32.5 μm,DMF=65 μm, andλ=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.

假設(shè)ω0=32.5 μm，DMF=65 μm，λ=1 030 nm，根據(jù)式(17)可以得到歸一化耦合效率與縱向偏移量的關(guān)系如圖7所示。

Fig.7 Influence of longitudinal error on coupling efficiency 圖7 縱向誤差對耦合效率的影響

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%.

由圖7可知，耦合效率對縱向誤差極其敏感，當(dāng)縱向偏移量由0 mm逐漸增大到5 mm的過程中歸一化耦合效率降低了50%以上，當(dāng)縱向偏移量超過13 mm歸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.

橫向失準(zhǔn)損耗示意圖如圖8所示。

Fig.8 Diagram of lateral misalignment loss 圖8 橫向失準(zhǔn)損耗示意圖

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]:

正如圖8所示，在實(shí)際調(diào)整的過程中，光束在橫向上不能完全與光纖端面重合，這樣引入的損耗稱為橫向失準(zhǔn)損耗。耦合效率與橫向失準(zhǔn)損耗的關(guān)系式為[17,19]：

(18)

WhereDMF/2 is the mode field radius of the ROD Fiber, andω0is the incident beam waist radius. Assume that:

式中，DMF/2為光纖棒模場半徑，ω0為入射光束束腰半徑。設(shè)：

αc=arccos(d/DMF) , (19)

Then, when 0<α<αc,

則有當(dāng)0<α<αc時(shí)，

rb=DMF/2 (20)

Whenαc<α<π,

當(dāng)αc<α<π時(shí)，

rb=dcosα+[(DMF/2)2-d2sin2α]1/2, (21)

Assume thatω0=32.5 μm,DMF=65 μm, andλ=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:

假設(shè)ω0=32.5 μm，DMF=65 μm，λ=1 030 nm，根據(jù)式(18)～(21)可以得到歸一化耦合效率與橫向偏移量的關(guān)系如圖9所示。

Fig.9 Influence of transverse error on coupling efficiency 圖9 橫向誤差對耦合效率的影響

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%.

由圖9可知，耦合效率對角度誤差極其敏感，當(dāng)橫向偏移量由0 μm逐漸增大到30 μm的過程中，歸一化耦合效率降低了約50%，當(dāng)橫向偏移量超過50 μm時(shí)歸一化耦合效率降到了10%以下。

The angular misalignment loss diagram is shown in Fig.10.

角度失準(zhǔn)損耗示意圖如圖10所示。

Fig.10 Diagram of transverse misalignment loss 圖10 角度失準(zhǔn)損耗示意圖

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]:

正如圖10所示，在實(shí)際調(diào)整的過程中，光束無法于光纖平行入射，這樣引入的損耗稱為角度失準(zhǔn)損耗。耦合效率與角度失準(zhǔn)損耗的關(guān)系式為[19-20]：

(22)

Wheren2is the refractive index of the inner cladding of the rod-shaped photonic crystal fiber.

式中，n2為棒狀光子晶體光纖內(nèi)包層折射率。

Assuming the inner cladding refractive indexn2=1.4, the incident beam waist radiusω0=32.5 μm, andλ=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.

假設(shè)內(nèi)包層折射率n2=1.4，入射光束束腰半徑ω0=32.5 μm，λ=1 030 nm，根據(jù)式(22)可以得到歸一化耦合效率與角度偏移量的關(guān)系如圖11所示。

Fig.11 Influence of transverse error on coupling efficiency 圖11 角度誤差對耦合效率的影響

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.

由圖11可知，耦合效率對角度誤差及其敏感，當(dāng)角度偏移量由0 mrad逐漸增大到6 mrad的過程中歸一化耦合效率降低了約50%，當(dāng)角度偏移量超過15 mrad，歸一化耦合效率基本為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.

根據(jù)上文對3種失準(zhǔn)情況的分析可知，耦合效率對各種失準(zhǔn)誤差非常敏感，其中縱向失準(zhǔn)誤差和角度失準(zhǔn)誤差的量級分別為毫米級和毫弧度級，而橫向失準(zhǔn)誤差的量級在微米級。在實(shí)際調(diào)整中為了盡量減少失準(zhǔn)誤差對耦合效率的影響，應(yīng)選用精度和可靠性較高的調(diào)整架，并且操作時(shí)應(yīng)認(rèn)真細(xì)致。

5 ROD Fiber Coupling Experiment Analysis

光纖棒耦合實(shí)驗(yàn)分析

The basic parameters required by the laser experiments used in the experiment are shown in Tab.1 and Tab.2.

實(shí)驗(yàn)所用兩種激光器實(shí)驗(yàn)所需基本參數(shù)如表1與表2所示。

Tab.1 Basic parameters of the solid-state laser

Tab.2 Basic parameters of fiber laser

The photonic crystal ROD Fiber used is aeroGAIN-ROD-PM85, produced by NKT. The core diameter isD=85 μm, the mode field diameterDMF=65 μm, and the core numerical apertureNA=0.015. In order to avoid high Fresnel reflection loss, both ends of the fiber are plated with antireflection film.

所用光子晶體光纖棒為NKT公司生產(chǎn)的aeroGAIN-ROD-PM85，纖芯直徑為D=85 μm、模場直徑DMF=65 μm、纖芯數(shù)值孔徑NA=0.015，為了避免較高的菲涅爾反射損耗，光纖兩端面均鍍有增透膜。

The coupling experimental optical path of a solid-state laser is shown in Fig.12.

固體激光器的耦合實(shí)驗(yàn)光路如圖12所示。

Fig.12 Diagram of solid-state laser coupling 圖12 固體激光器耦合實(shí)驗(yàn)光路圖

The lenses used are total reflection mirrors whereF=103.26 mm andM1-M4are 45°. In order to prevent back light interference or damage to the laser, an isolator is added to the experiment′s optical path.

所使用的透鏡F=103.26 mm，M1-M4為45°全反射鏡，為了防止回光干擾或損傷激光器，實(shí)驗(yàn)光路中加入了隔離器。

The coupling experimental optical path of the fiber laser is shown in Fig.13.

光纖激光器的耦合實(shí)驗(yàn)光路如圖13所示。

Fig.13 Diagram of fiber laser coupling 圖13 光纖激光器耦合實(shí)驗(yàn)光路圖

Among the used lenses,F1=30 mm andF2=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 whereM1-M4is 45° . In order to prevent back light interference or damage to the laser, an isolator is also added to the experiment′s optical path.

所使用的兩個(gè)透鏡分別為F1=30 mm、F2=77 mm，兩個(gè)透鏡的作用分別為準(zhǔn)直和聚焦，這兩個(gè)透鏡可以看作是一個(gè)將光纖尾纖輸出束腰擴(kuò)束一定倍率的透鏡組，M1-M4為45°全反射鏡，為了防止回光干擾或損傷激光器，實(shí)驗(yàn)光路中同樣加入了隔離器。

The coupling efficiencies of the two lasers at low power and medium power were tested as shown in tables 3 and 4.

實(shí)驗(yàn)中分別測試了兩種激光器在低功率和中等功率時(shí)的耦合效率，如表3和表4所示。

Tab.3 Comparison of coupling efficiency under low power conditions

Tab.4 Comparison of coupling efficiency under medium power conditions

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.

由于光纖激光器的穩(wěn)定輸出功率最低只能設(shè)定為1 000 mW，因此，低功率測試時(shí)的注入功率與固體相差較多。

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.

通過對比固體激光器與光纖激光器的數(shù)據(jù)可以得知，在低功率下，固體激光器的耦合效率只有42.2%，而光纖激光器的耦合效率可達(dá)60.0%；在中等功率下，注入功率同樣為4 W，固體激光器的耦合效率只有62.4%，而光纖激光器的耦合效率已經(jīng)達(dá)到了80.5%。無論是低功率情況下還是中等功率情況下，光纖激光器的耦合效率均比固體激光器高。分析其原因可能是，光纖激光器的光束質(zhì)量高于固體激光器，耦合后的光斑能量更加集中，因此，光纖激光器的耦合效率要高于固體激光器。

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.

通過對比相同激光器在不同輸出功率下的數(shù)據(jù)可知，固體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為4 W，耦合效率為62.4%，比低功率下有所增長；同樣的現(xiàn)象也發(fā)生在光纖激光器的耦合實(shí)驗(yàn)中，光纖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，耦合效率增長到了為80.5%。也就是說在低功率下耦合效率較低，而在中等功率下耦合效率有所增長。分析其原因可能是，纖芯對1 030 nm的激光有所吸收。在低功率下，由于注入功率較小，所以纖芯吸收所占比例較大，CCR(包層纖芯功率比)較低，因此耦合效率較低；在中等功率情況下，由于注入功率較大，纖芯吸收所占比例小，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.

為了驗(yàn)證光纖激光器耦合后的光斑能量是否比固體激光器的集中，以及耦合后的光斑形狀是否更好，實(shí)驗(yàn)中利用CCD對耦合后的光斑進(jìn)行了觀察，觀察結(jié)果如圖14所示。

Fig.14 Solid-state laser(left) and fiber laser(right) coupling facula 圖14 固體激光器(左)與光纖激光器(右)耦合后光斑對比圖

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.

通過兩幅光斑圖的對比可以看出，固體激光器的耦合光斑周圍有明顯的逸散在包層中的雜散光，而光纖激光器的耦合光斑周圍逸散到包層中的雜散光十分暗淡。從光斑的形狀來看光纖激光器的耦合光斑比固體激光器的耦合光斑圓。

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.

為了驗(yàn)證功率逐漸增加的過程中耦合效率是否會(huì)逐漸增大，實(shí)驗(yàn)中測定了光纖激光器耦合情況下，注入功率由1 W逐漸增加到6 W時(shí)耦合效率的變化情況。

Tab.5 Transmission power and couplingefficiency vary with injection power

Fig.15 Relationship between the coupling efficiency and injected power 圖15 耦合效率隨注入功率的變化情況

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.

從表5和圖15可以看出，其它情況一定時(shí)，耦合效率的確是隨著注入功率的增加而逐漸增大。而且在實(shí)驗(yàn)中，還觀察了光纖激光器耦合情況下，注入功率由1 W逐漸增加到6 W時(shí)耦合后光斑的變化情況。

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.

從圖16可以看出，隨著注入功率的增加，耦合后的光斑能量有逐漸集中的趨勢，原因可能是，隨著功率的增加纖芯對功率的吸收比例逐漸減小，而且光纖激光器本身的光束質(zhì)量在逐漸增加，使得經(jīng)過耦合系統(tǒng)的光束模場與光纖棒本身的模場更加匹配，致使耦合后的能量向纖芯集中。

Fig.16 Changing law of coupling facula when injection power growing from 1 W to 6 W 圖16 注入功率1 W到6 W的情況下耦合光斑的變化規(guī)律

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:

根據(jù)實(shí)驗(yàn)情況來看，雖然光纖激光器的耦合效果比固體激光器好很多，但是，仍與模擬計(jì)算所得的理想耦合效率有所差距，造成這種差距的主要原因可能有以下幾點(diǎn)：

First, the beam quality of the fiber laser isM2～1.1 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，光纖激光器的光束質(zhì)量是M2～1.1，不是仿真中所用的理想狀態(tài)下的基模高斯光束，非理想的光束質(zhì)量將帶來一定的耦合效率損失。

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，光纖激光器輸出的光束在光路中經(jīng)過3個(gè)反射鏡、一個(gè)隔離器和兩個(gè)透鏡，這些光學(xué)器件的表面可能存在缺陷，缺陷造成光束的畸變，這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，耦合透鏡調(diào)整的精度不夠高造成了各種對準(zhǔn)誤差的出現(xiàn)，由于光纖對各種對準(zhǔn)誤差十分敏感，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[21], and this absorption is unavoidable in the measurement process. Once again, this would also reduce coupling efficiency.

第四，由于棒狀光子晶體光纖為增益光纖，光纖中摻雜有Yb3+離子，而光纖中的Yb3+離子對1 030 nm的波段有一定的吸收作用[21]，這種吸收在測定過程中是無法避免的，因此會(huì)造成耦合效率的下降。

6 Conclusion

結(jié) 論

The quality of a laser′s beam has a large influence on coupling efficiency. A fiber laser with high beam quality and a solid laser with poor beam quality can have a difference in coupling efficiency of nearly 20% under the same circumstances. When the power injected into the fiber laser is gradually increased, the coupling efficiency also gradually increases. This is because, as the injection power increases, the portion of power that is absorbed by the core decreases. Also, as the quality of the injected beam increases, the CCR increases as well. During experimentation, the maximum coupling efficiency obtained by using the fiber laser was slightly lower than simulated coupling efficiency obtained through calculation. Regardless, results were marginally close to the expected target. The coupling experiment has guiding significance for subsequent ROD Fiber amplification experiments. Higher coupling efficiency can allow more seed light to enter a ROD Fiber core which can effectively suppress ASE(spontaneous radiation amplification) and increase its gain. A good coupling facula can also improve quality in the amplified laser beams.

光束質(zhì)量的好壞對耦合效率的影響十分大，光束質(zhì)量較好的光纖激光器和光束質(zhì)量較差的固體激光器在相同注入功率下，其對光纖棒的耦合效率可以相差近20%。當(dāng)注入光纖的功率逐漸增加時(shí)，耦合效率也會(huì)逐漸增大，這是由于隨著注入功率的增加，纖芯吸收的功率所占比例越來越低，注入光束的光束質(zhì)量逐漸變好，使得CCR逐漸增大。在耦合實(shí)驗(yàn)中，使用光纖激光器所得到的最大耦合效率雖然略低于仿真所得到的耦合效率，但是已經(jīng)十分接近，達(dá)到了所預(yù)期的目標(biāo)。整個(gè)耦合實(shí)驗(yàn)對后續(xù)光纖棒放大實(shí)驗(yàn)具有指導(dǎo)意義，較高的耦合效率可以使更多的種子光進(jìn)入光纖棒纖芯，從而可以有效的抑制ASE(自發(fā)輻射放大)，使得光纖棒獲得更高的增益，而良好的耦合光斑也可以有效改善放大后的光束質(zhì)量。