激光原理第四章-3

1、三 輸出功率與能量In section 4.1 we derived an expression for the threshold population inversion at which the laser gain becomes equal to the losses. We would expect that as the pumping intensity is increased beyond the point at which N2-N1=Nt the laser will break into oscillation and emit power. In this sec

2、tion we obtain the expression relating the laser power output to the pumping intensity. We also treat the problem of optimum coupling-that is, of the mirror transmission that results in the maximum power output.激光器穩(wěn)態(tài)工作的建立連續(xù)或長脈沖激光器的輸出功率(output power)短脈沖激光器的輸出能量(output energy)In chapter 3 we found tha

3、t an atomic medium with an inverted population (N2N1) is capable of amplifying an electromagnetic wave if the latters frequency falls within the transition lineshape. Consider next the case in which the laser medium is placed inside an optical resonator. As the electromagnetic wave bounces back and

4、forth between the two reflectors it passed trough the laser medium and is amplified. If the amplification exceeds the losses caused by imperfect reflection in the mirrors and scattering in the laser medium, the energy stored in the resonator will increase with time. This causes the amplification con

5、stant to decrease as a result of gain saturation.The oscillation level will keep increasing until the saturated gain per pass just equals the losses. At this point the net gain per pass is unity and no further increase in the radiation intensity is possible-that is, steady state oscillation obtains.

6、（一）激光器穩(wěn)態(tài)工作的建立如果腔內(nèi)某一振蕩模式的頻率為q，開始時，由于, 腔內(nèi)光強Iq逐漸增加，同時由于飽和效應(yīng)，g(q,Iq) 將隨Iq的增加而減少，但只要g(q,Iq) 仍比gt大，這一過程就將繼續(xù)下去，即Iq 繼續(xù)增加， g(q,Iq) 不斷減小，直到 ,增益和損耗達到平衡， Iq不再增加。這時，激光器建立了穩(wěn)定工作狀態(tài)。當g0()gt時，dNl/dt0，腔內(nèi)光強不斷增加。無限增加?當外界激發(fā)作用增強時，小信號增益系數(shù)g0()增大，此時Iq必須增大到一個更大的值才能使g(q,Iq) 降低到gt并建立起穩(wěn)定工作狀態(tài)，因此激光器的輸出功率增加。穩(wěn)態(tài)工作時的大信號增益系數(shù)總是等于gt 。結(jié)論：

7、在一定的激發(fā)速率下，即當g0()一定時，激光器的輸出功率保持恒定；當外界激發(fā)增強時，輸出功率隨之上升，但在一個新的水平上保持恒定。（二）連續(xù)或長脈沖激光器的輸出功率1、均勻加寬單模激光器?腔內(nèi)平均光強Iq 在駐波型激光器中，腔內(nèi)存在著沿腔軸方向傳播的光I+和反方向傳播的光I-，二者同時參與飽和作用如果T1，穩(wěn)態(tài)工作時增益系數(shù)也很小，近似認為I+=I-，腔內(nèi)平均光強Iq=2 I+。穩(wěn)態(tài)情況下，求得腔內(nèi)平均光強為?輸出功率設(shè)激光束的有效截面面積為A，則激光器的輸出功率為1）在T1時， ，a為往返指數(shù)凈損耗因子，通常a1。上式改寫為2）光泵激光器 Pp及Ppt分別為工作物質(zhì)吸收的泵浦功率及閾值吸收泵

8、浦功率，S為工作物質(zhì)橫截面面積s稱為斜率效率結(jié)論：一旦激光器確定了，斜率效率就確定了；輸出功率隨泵浦功率線性增加。上式對于放電激勵的氣體激光器例外耦合系數(shù)：0=T0/2The total loss encountered by the oscillating laser mode can conveniently be attributed to two different sources: (a) the inevitable residual loss due to absorption and scattering in the laser material and in the mir

9、rors, as well as diffraction losses in the finite diameter reflectors; (b) the (useful) loss due to coupling of output power through the partially transmissive reflector. It is obvious that loss (a) should be made as small as possible since it raise the oscillation threshold without contributing to

10、the output power.The problem of the coupling loss (b), however, is more subtle. At zero coupling (that is, both mirrors have zero transmission) the threshold will be at its minimum value and the power emitted by the atoms will be maximum. But since none of this power is available as output, this is

11、not a useful state of affairs. If on the other hand, we keep increasing the coupling loss, the increasing threshold pumping will at some point exceed the actual pumping level. When this happens, oscillation will cease and the power output will again be zero. Between these two extremes there exists a

12、n optimum value of coupling (that is, mirror transmission) at which the power output is a maximum.3）最佳透射率及功率輸出功率和反射鏡的透射率T有關(guān)。當T增大時，一方面提高了透射光的比例，有利于提高輸出功率，同時又使閾值增加，從而導(dǎo)致腔內(nèi)光強的下降。在透射率T1時，令dP/dT=0，求出最佳透過率Tm最佳輸出功率Maximizing P with respect to T by setting yields as the condition for the mirror transmission

13、that yields the maximum power output.（1）q0 （多普勒非均勻加寬）I+和I-兩束光在增益曲線上分別燒兩個孔，對每一個孔起飽和作用的分別是I+或I-，而不是二者的和。振蕩模的增益系數(shù)為2、非均勻加寬單模激光器的輸出功率激光器穩(wěn)態(tài)工作時（2）q=0I+和I-兩束光同時在增益曲線上中心頻率處燒一個孔，燒孔深度取決于腔內(nèi)平均光強I0。穩(wěn)定工作時振蕩模的增益系數(shù)為求得腔內(nèi)平均光強為輸出功率蘭姆凹陷：在單模輸出功率P和單模頻率q的關(guān)系曲線中，在q=0處，曲線有一凹陷，稱作蘭姆凹陷。由于兩個燒孔在 時開始重疊，所以蘭姆凹陷的寬度大致等于燒孔的寬度，即蘭姆凹陷形成的機制

14、：當q=0時，兩個燒孔完全重合，此時只有z=0附近的原子對激光有貢獻。雖然它對應(yīng)著最大的小信號增益，但由于對激光作貢獻的反轉(zhuǎn)集居數(shù)減少了，即燒孔面積減少了，所以輸出功率下降到某一極小值，Pq關(guān)系曲線在0處出現(xiàn)蘭姆凹陷凹陷的深度和激發(fā)參量gml/成正比，當gml/小時蘭姆凹陷變淺，當gml/很小時，蘭姆凹陷消失。激光管的氣壓增高時，碰撞線寬增加，蘭姆凹陷變寬、變淺。當氣壓高到一定程度，譜線加寬以均勻加寬為主時，蘭姆凹陷消失If the oscillation frequency is equal to0, only a single “hole” exists in the velocity d

15、istribution function of the inverted atoms. This “hole” is centered on Z=0. We may, thus, expect the power output of a laser oscillating at =0 to be less than that of a laser in which is tuned slightly to one side or the other of0 (this tune can be achieved by moving one of the laser mirrors). This power dip first predicted by Lamb is indeed observed in gas lasers. The phenomenon is referred to as the “Lamb dip” and is used in frequency stabilization schemes of gas lasers.3、多模激光器的輸出功率在非均勻加寬激光器中，每個模式各自消耗表觀中心頻率與其頻率相應(yīng)的激活粒子。如果模間隔足夠大，各個模式相互獨立，分別計算每個縱模的輸出功率，總的輸出功率是各模輸