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本科生畢業(yè)設(shè)計（論文） 翻譯資料 中文題目：一個方法測量所有光線的焦點長度在 徑向和高的力量 Nd 的切線方向中極化的熱透鏡: YAG 激光 英文題目：A method measuring thermal lens focal length of all rays polarized in radial and tangential direction of high power Nd:YAG laser 學(xué)生姓名： 學(xué) 號： 班 級： 專 業(yè)：機械工程及自動化 指導(dǎo)教師： Optics Communications 241 (2004) 155–158 www.elsevier.com/locate/optcom A method measuring thermal lens focal length of all rays polarized in radial and tangential direction of high power Nd:YAG laser Qiang Li *, Zhimin Wang, Tiechuan Zuo College of Laser Engineering, Beijing University of Technology, Beijing 100022, PR China Received 23 December 2003; received in revised form 21 June 2004; accepted 29 June 2004 Abstract A novel method is applied to measure the focal length of thermal lens of a CW Nd:YAG laser. Using resonator critical stable point G1 ? G2=0, by measuring output power as pumping power increasing, the laser rod thermal lens focal length fr of all rays polarized in radial direction and the thermal lens focal length fhof all rays polarized in tangential direction can be calculated. The method can also be used to obtain the average e?ective thermal lens focal length f. The method requires no special equipment and is simple to implement. The measuring deviation of the method comparing with probe beam method is within the accuracy that is in the range of ±10%. It is less than the unstable-resonator method that is in the range of ±20%. ? 2004 Elsevier B.V. All rights reserved. PACS: 42.55.Rz; 42.60.Da; 42.60.Lh; 42.60.Pk 1. Introduction For high power laser operation, the focal length of thermal lens of laser crystal is a crucial parameter for optimizing the laser system. There are many techniques for measuring thermal lens focal length, such as using probe beam [1–4], interfero * Corresponding author. Tel.: +8601067396562; fax: +8601067392514. E-mail address: ncltlq@bjut.edu.cn (Q. Li). metric method [5–7], unstable-resonator method [8–10], and transverse beat frequency method [11,12]. However, all these methods are used to measure the average thermal lens focal length. For perfect compensating thermal lens e?ect, it is more useful to know the thermal lens focal length r of all rays polarized in radial direction and the thermal lens focal length fhof all rays polarized in tangential direction. In this paper, we present a novel method to measure thermal lens focal length of high power 0030-4018/$ -see front matter ? 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.06.061 Q. Li et al. / Optics Communications 241 (2004) 155–158 CW Nd:YAG laser. The methods can measure not only the average e?ective focal length of thermal lens f, but also the focal length fr and fhof the thermal lens. The idea is based on the dependence of the critical stable point on the equivalent G parameter of the stable resonator, which depends on the thermal lens. Our method requires no special equipment and is simple to implement. 2. Analysis of measure method According to the theory of resonators [1], a resonator is stable if 1 6 G1G2 6 +1, where G1 and 2 are the G parameters describing the design of the resonator. For a resonator with optical elements inside, the rod can be approximated to ?rst order by a thin spherical lens of focal length f, and its G parameters are given as follows: __ __ 1 L1L2 1 ? a11 ? L2 L1 t L2 ? f ; e1T 2 f ? R1 __ __ 1 L1L2 ; e2T 2 ? a21 ? Lf 1 ? R2 L1 t L2 ? f 1 where a1 and a2 are the apertures of the mirrors, 1 and R2 are the radius of curvature of the mirrors, L1 and L2 are the distances from the principal planes to the mirrors, respectively. The laser rod (of length l) can be approximated to a thin lens and two pieces of isotropic medium with refractive index n0 and length h. The parameter h is the distance from the principal planes of the lens to the end of the laser rod [13], i.e., h = l/2n0. In our experiments, ?at mirrors with identical apertures have been placed separately at equal distances from the Nd:YAG rod. Therefore, a1= a2, 1= R2, and L1= L2. Eqs. (1) and (2) were simpli?ed as 1 ? G2 ? 1 ? L tel=2Te1 e1=n0 TT : e3T f Hence, the resonator stability is dependent only on the focal length of intra-cavity lens and length of the resonator. The stability diagram of an optical resonator is shown in Fig. 1. Blank areas indicate regions of stable operation. The straight line (points A–C) corre- Fig. 1. Stability diagram of an optical resonator. Shaded areas indicate regions of unstable operation. Points A, B, C correspond to plane parallel, confocal, and concentric resonators, respectively. sponds to a symmetrical resonator with an internal lens of di?erent focal length. Since the thermal lens of the rod is a function of input power, the con?guration of the equivalent resonator changes from plane parallel to confocal and ?nally to concentric. Beyond this point the resonator becomes unstable. The point B (in Fig. 1), corresponds to G1 ? G2=0, it is a critical stable point of resonator stable region. From Eq. (3), we have e?ective focal length: f ? L tel=2Te1 e1=n0TT: e4T At the critical stable point B, the focal length of the thermal lens f is the half of the resonator length. For a resonator length, the increment of output power will have a distinct decrease at the critical stable point as input powers increase. Using this method, we measured the thermal lens focal length with di?erent resonator lengths. In fact, the critical stable point is not simply a point. It can be found that is actually a region for careful adjustment of input powers. It is well known that the thermal lens focal length can be expressed as [14]: __ AK 1dn 2fi ? dt t n0bCr;ht r0 ben0 ? 1T1 P inn02n0 n0l ; e5T where there are two focal lengths fr and fh, i.e., all rays polarized in radial direction and all rays polarized in tangential direction, respectively. And Q. Li et al. / Optics Communications 241 (2004) 155–158 normally, there is fr/fh= 1.2–1.5 for Nd:YAG crystal. So we can measure not only the average thermal lens focal length f of the rod but also the radial and tangential direction thermal lens focal lengths r and fh, simultaneously. 3. Experiment and discussion In our experiments, a B9mm · 155 mm AR coated Nd:YAG (science materials 0.8% Nd) laser rod was used in a di?use re?ecting cavity which was pumped by double Krypton ?ashlamps. The ?ashlamps were provided by a laser power supply rated up to 16 kW. The laser head was water cooled by a double cycle chiller, with constant experiments temperature of 20 C(1 C). A plane parallel resonator with an output coupling mirror of 20.5% was used in the experiments. Two apertures with a diameter of 9.5 mm were placed adjacent to the end of the laser rod, respectively. The output power was detected by an Ophir Model 5000W-SH power meter. The critical stable points of the resonator were determined by detected output power curve. The critical stable points were founded when the output power does not linear increase as input pumped powers increase. In these experiments, the resonator alignment was strictly ensured. Every experiment curve was the average of detected output power as input pumped power changing from 0 to 16 kW and from 16 to 0 kW. For symmetrical resonator with length in a certain extent, the experimental results were obtained by drawing the function curve of laser output power and pump input power. Fig. 2 shows the measurement results for relationship between the output laser power and the pump power with ?ve di?erent resonator lengths. In the curves, it can be found that the output laser power increased linearly as pumping power increased at ?rst, and then appeared a knee point followed by a plateau region, then increased linearly again, ?nally a decrease to zero. The changing process corresponds to the straight line in Fig. 1, in which pumping power increased and the focal length of the rod changed, as well as the con?guration of the equivalent resonator changed from A point to B point and ?nally to C point. Fig. 2. The measurement results for the output laser power vs. the pump power with a plane parallel resonator at resonator lengths of 584–1344 mm. We could survey the experiment curves. When the ?rst knee point appears, the resonator enters the critical stable points (near B point). So in our experiment curves, the output power decreased gently. According to (5), the e?ective focal length fhis relative to the pump power. At second knee, the resonator departs from the critical stable point, and the e?ective focal length is fr in relation to the pump power. Between the two knees, there is a plateau region and average the e?ective thermal lens focal length f is in the center of the region. Fig. 3. Measured thermal lens focal length of YAG crystal rod as a function of lamp input power. Each point represents the calculated e?ective focal length of YAG crystal for fr (), fh(), and average f (.), respectively. Q. Li et al. / Optics Communications 241 (2004) 155–158 Fig. 4. E?ective focal length of YAG crystal as a function of lamp input power. The average focal length of experimental values are obtained by resonator critical stable points (.) and values obtained with a He–Ne laser (). Using Eqs. (5) and (4), the e?ective thermal lens focal lengths fr, fh, and average f, can be calculated, respectively. The results are shown in Fig. 3. In order to check the accuracy of the method, the measurement results were compared with those of probe beam method [3] with He–Ne laser in the same condition (Fig. 4). The values of the average e?ective focal length obtained with our method were a little higher than the values obtained with probe beam method, especial as pumping power increase and the focal length of the thermal lens decrease. The deviation is within the accuracy of the method, which is in the range of ±10%. The limitation for the accuracy of the measurement is attributed to the experiment deviation. The distance deviation of the two mirrors placed separately from the Nd:YAG rod. However, it is less than the unstable-resonator method [8] of ±20%. 4. Conclusion We have presented a novel method to measure the average e?ective focal length of a ?ash-lamp-pumped CW Nd:YAG laser. Because critical stable points of stability resonator are used, the result is more precise than unstable-res-onator method, and the method is very simple. Especially for measuring the thermal lens focal length fr and fh, to our knowledge, this is the practical one so far. References [1] W. Koechner, Appl. Opt. 9 (11) (1970) 2548. [2] H.P. Kortz, R. I?ander, H. Weber, Appl. Opt. 20 (23) (1981) 4124. [3] P. Driedger, W. Krause, H. Weber, Opt. Commun. 57 (6) (1986) 403. [4] D. Sumida, D. Rockwell, M. Mangir, IEEE J. Quantum Electron. QE-24 (6) (1988) 985. [5] T. Omatsu, Y. Kato, M. Shimosegawa et al., Opt. Commun. 118 (4) (1995) 302. [6] S.C. Tidwell, J.F. Seamans, M.S. Bowers et al., IEEE J. Quantum Electron. 28 (4) (1992) 997. [7] C. Phstner, R. Weber, H.P. Weber, IEEE J. Quantum Electron. 30 (7) (1994) 1605. [8] D.G. Lancaster, J.M. Dawes, Opt. Laser Technol. 30 (2) (1998) 103. [9] L. Junhai, L. Jianren, L. Junhua et al., Chin. Phys. Lett. 16 (3) (1999) 181. [10] F. Song, C. Zhang, X. Ding et al., Appl. Phys. Lett. 81 (12) (2002) 2145. [11] B. Ozygus, J. Erhard, Appl. Phys. Lett. 67 (11) (1995) 1361. [12] B. Ozygus, Q. Zhang, Appl. Phys. Lett. 71 (18) (1997) 2590. [13] V. Magni, Appl. Opt. 25 (1) (1986) 107. [14] W. Koechner, Solid-state Laser Engineering (M), Springer, New York, Heidelberg, 1995. 一個方法測量所有光線的焦點長度在徑向和高的力量 Nd 的切線方向中極化的熱透鏡: YAG 激光 摘要 一個新穎的方法用于測量 CW Nd 的熱透鏡的焦點長度:YAG 激光。使用共嗚器 鑒定 穩(wěn)定的點，：G1*G2=0, 藉由測量輸出使～有力量當(dāng)抽泵力量增加, 所有光線的焦點長度 fr 全部極化在光線的方向和熱透鏡中焦點的長度 fhof 光線的激光竿熱透鏡在切線的方向中極化可能是有計劃的方法也能用來獲得平均的 焦點的長度 f 的有效熱透鏡。這個方法不需要特別的儀器而且是簡單實現(xiàn)，與探查光線方法相比較這個方法測定偏離是在 ± 10% 的范圍中的準確性里面，改方法在 ± 20% 的范圍中的比不穩(wěn)定- 共嗚器的方法更少。版權(quán)所有。 介紹 對于高能激光操作，激光水晶的熱透鏡的焦點長度是決定性的參數(shù)對于最佳化的激光系統(tǒng)。為測量熱透鏡焦點的長度有許多技術(shù), 比如用做使用探查光線 [1-4],干涉測量法[5-7]。 正文 不穩(wěn)定- 共嗚器方法 [8-10], 而且橫斷物打頻率方法 [11,12]。然而，所有的這些方法都用來測量平均的熱透鏡焦點的長度。為完美的修正熱透鏡的熱效應(yīng)， 更有用的是知道全部被極化在光線的方向和熱的透鏡中焦點的長度 fhof 光線的所有光線的焦點長度 r 在切線的方向中極化的熱透鏡。在這個論文中，我們將呈現(xiàn)一個新奇的方法來測量熱透鏡焦點長度對于高能激光- 見到序文 ? 光學(xué)溝通，方法不光只能測量平均的，f 的有效焦點長度 , 也可以測量 fr 焦點的長度和 fhof ther- mal 的透鏡。這個觀點是以在穩(wěn)定的共嗚器的相等的 G 參數(shù) 上的為基礎(chǔ),依賴熱透鏡。我們的方法不需要特別的儀器而且是簡單實現(xiàn)。 尺寸方法的分析，依照共嗚器的理論 [1], 穩(wěn)定共鳴器如果 16 G1G26+1, 那么 G1 和 2 是描述共嗚器的設(shè)計 G 參數(shù) 描述共鳴器的設(shè)計，為和光學(xué)的原理 的內(nèi)部一個共嗚器，竿能被接近到。一個焦點長度 f 的瘦球透鏡的 rst 次序, 而且它的 G 叁數(shù)依下列各項有: 1 L1L2 1 ? a11 ? L2 L1 t L2 ? f ; e1T 2 f ? R1 __ __ 1 L1L2 ; e2T 2 ? a21 ? Lf 1 ? R2 L1 t L2 ? f 1 在 a1 和 a2 是鏡子的孔地方,1 而且 R2 是村落的屈曲半徑-分別地 rors, L1 和 L2 是從主要的飛機到鏡子的距離。激光竿 (長度 l) 能被接近到和折射的索引 n0 和長度 h 的瘦透鏡和等方性媒體的二塊，parame- ter 的 h 是來自透鏡的主要飛機的距離為目的激光竿 [13],也就是,h=l/2 n0。 在我們的實驗方面, 在和同一的孔鏡子在相等的 dis 分開的已經(jīng)被放置-來自 Nd 的 tances:YAG 竿。因此,a1=a2 ， 1= R2 和 L1=L2。因此，共嗚器安定是依賴的只有在洞內(nèi)透鏡和共嗚器的長度焦點長度上。光學(xué)的共嗚器的安定圖表在圖 1 中被顯示。 直線 ( 點一-C) corre-圖 1. 一個光學(xué)的共嗚器的安定圖表。陰暗的區(qū)域指出不穩(wěn)定操作的區(qū)域。指出 A ， B,C corre- spond 將平行刨平,共焦的, 和同中心的共嗚器,分別地。對和一個 di 的內(nèi)在透鏡的一個對稱的共嗚器的 sponds，焦點的長度 erent。因為竿的熱透鏡是一個輸入力量的功能，gu- 相等的共嗚器的定額改變從飛機平行到共焦的和，對同心的，超過這點共嗚器變成不穩(wěn)定。點 B(在圖 1 中), 符合 G1? G2=0,它是共嗚器馬房區(qū)域的緊要關(guān)頭穩(wěn)定點，從Eq,我們有 e? 焦點的長度 ective: f? L tel=2Te1 e1=n0TT: e4T在緊要關(guān)頭的穩(wěn)定點 B ，熱的透鏡 f 的焦點長度是一半的共嗚器長度對于共嗚器長度，輸出力量的增量將會在緊要關(guān)頭的穩(wěn)定點有一個清楚的減少如輸入權(quán)力增加。美國- ing 這一個方法,我們用 di 測量熱的透鏡 fo- cal 的長度。erent 共嗚器長度。 事實上，緊要關(guān)頭的穩(wěn)定點不只是點。資訊科技能被發(fā)現(xiàn)那實際上是輸入權(quán)力的小心調(diào)整的一個區(qū)域。資訊科技是廣為人知的熱透鏡焦點的長度可能是新聞媒體當(dāng)做 [14] e5T 哪里有二焦點的長度 fr 和 fh,也就是,所有的光線在光線的方向和所有的光線 po 中極化-切線的方向 larized,分別地。正常地,為 Nd 有 fr/fh=1.2-1.5: YAG -tal。因此我們能測量不只有平均的 ther- mal 的透鏡竿的焦點長度 f 但是也光線的和切線的方向上升溫暖氣流透鏡焦點的長度 r 和 fh,同時地。ashlamps 是由激光力量提供供應(yīng)定格的達到 16個千瓦。 激光頭是被一個兩倍的周期冷卻冷鐵的水,藉由 20個 C(1個 C) 的持續(xù)前任 periments 溫度和一面 20.5% 的輸出聯(lián)結(jié)鏡子的一個飛機平行共嗚器被用于實驗。 二 aper-和一個 9.5 毫米的直徑 tures 被放置 adja- 分為目的激光竿,分別地。輸出力量被一個 Ophir 模型 5000 W- SH 的力量公尺發(fā)現(xiàn)了。共嗚器的緊要關(guān)頭穩(wěn)定點被 de- tected 輸出力量曲線決定了。緊要關(guān)頭的穩(wěn)定點被發(fā)現(xiàn)當(dāng)輸出力量如輸入的線增加不抽了權(quán)力嗎在-折痕。在這些實驗方面，共嗚器排列-ment 嚴格地被確定。每個實驗曲線是如被抽從 0 到 16個千瓦和 16 到 0個千瓦變更的力量輸入的發(fā)現(xiàn)輸出力量的平均。對于對稱的 resona-和特定的范圍長度山,experimen- tal 的結(jié)果被藉由畫條線獲得激光輸出力量和泵的功能曲線輸入力量。為在輸出激光力量和泵之間的關(guān)系圖 2 表演測量結(jié)果使～有力量由于，在曲線中，它能被發(fā)現(xiàn)，當(dāng)抽泵力量增加，外面者放線地被增加的激光力量的在rst, 然后出現(xiàn)了被一個高地區(qū)域跟隨的膝點, 然后再一次線地增加。nally 一個減少對準零位。 變更程序符合圖 1 的直線, 在哪一抽泵力量增加和被改變的竿焦點長度 相等的共嗚器 chan 的 guration- 從點到 B 的 ged 指出和對 C 點的 nally。 測量在 584-1344 毫米的共嗚器長度為和一個飛機平行共嗚器的輸出激光力量和泵力量比較產(chǎn)生。我們可以審視實驗曲線。 何時那rst 膝點出現(xiàn), 共嗚器進入緊要關(guān)頭的馬房點。 ( 在 B 的附近點)，如此在我們的前任 periment 中曲線,輸出力量減少了一般布告-tly。依照與泵力量相關(guān)的焦點長度 fhis 的 ective。在第二個膝，共嗚器從緊要關(guān)頭的穩(wěn)定點 , 和 e 結(jié)束。 焦點的長度 fr ， fh 和平均 f 的 ective 上升溫暖氣流透鏡,可能是 calculat-ed,分別地，結(jié)果在圖 3 中被顯示。 為了要檢查方法的準確性，測量結(jié)果被與探查光線方法的相較 [3] 由于他- 相同的情況 (圖 4) 的舊姓激光. 平均的 e 的值，與我們的方法一起獲得的焦點長度稍微比價值更高的 ective 以探查光線方法獲得, 特別的當(dāng)抽泵使～有力量增加和熱的透鏡減少的焦點長度。偏離是在方法的準確性里面,是在 ± 10% 的范圍中。為測量的準確性的限制被歸因于實驗偏離。二面鏡子的 dis- tance 偏離放置了分開-來自 Nd 的 ly:YAG 竿。然而，它比不穩(wěn)定- 共嗚器的方法更少 [± 20% 的 8]. 結(jié)論 我們已經(jīng)將一個新奇的方法呈現(xiàn)給 meas- ure 平均的 e焦點長度的 ective 一灰-燈抽的 CW Nd:YAG 激光。因為安定共嗚器的緊要關(guān)頭穩(wěn)定點被用,結(jié)果比不穩(wěn)定精確- 再 onator 方法,而且方法非常簡單。尤其為測量熱的透鏡焦點的長度 fr 和 fh ，到我們的知識，這到現(xiàn)在為止是一個實際的。