考前复习参考

1、Chapter 1light wavesphotonsmodes & statescoherencetemporal coherencespatial coherencecoherence areacoherence volumetemporal coherence lengthtransverse coherence lengththermal radiationPlancks Lawabsorptioninduced emission spontaneous emission. transition probabilitythe Einstein coefficientbasic elem

2、ents of a laserpopulation inversionthreshold conditionThe number of modes1. In the visible part of the spectrum (l = 500 nm; n = 6 x 1014 s-1), the number of modes per unit volume within the Doppler width of a spectral line (Dn=109 s-1) is .2. In the microwave region (l = 1 cm; n = 3 x 1010 s-1), th

3、e number of modes per unit volume within the typical Doppler width Dn=105 s-1 is .3. In the X-ray region (l = 1 nm; n = 3 x 1017 s-1), the number of modes per unit volume within the typical Doppler width Dn=1011 s-1 of an X-ray transition is .Light Sourcesa) Examples of real radiation sources with s

4、pectral energy distributions close to the Planck distribution are the sun, the bright tungsten wire of a light bulb, flash lamps, and high-pressure discharge lamps.b) Spectral lamps which emit discrete spectra are examples of nonthermal radiation sources. In these gas-discharge lamps, the light-emit

5、ting atoms or molecules may be in thermal equilibrium with respect to their translational energy, which means that their velocity distribution is Maxwellian. However, the population of the different excited atomic levels may not necessarily follow a Boltzmann distribution and there is generally also

6、 no thermal equilibrium between the atoms and the radiation field. The radiation may nevertheless be isotropic.c) Lasers are examples of nonthermal and anisotropic radiation sources. The radiation field is concentrated in a few modes, and most of the radiation energy is emitted into a small solid an

7、gle. This means that the laser represents an extreme anisotropic radiation source.Induced Emission a) In the thermal radiation field of a 100 w light bulb, 10 cm away from the tungsten wire, the number of photons per mode at l = 500 nm is about 10-8. If a molecular probe is placed in this field, the

8、 induced emission is therefore completely negligible.b) In the center spot of a high-current mercury discharge lamp with very high pressure the number of photons per mode is about 10-2 at the center frequency of the strongest emission line at l = 253.6 mm. This shows that even in this very bright li

9、ght source the induced emission only plays a minor role.c) Inside the cavity of a He-Ne laser (output power 1 mw with mirror transmittance T = 1%) which oscillates in a single mode, the number of photons in this mode is about 107. In this example the spontaneous emission into this mode is completely

10、 negligible. Note, however, that the total spontaneous emission power at l = 632.8 nm, which is emitted into all directions, is much larger than the induced emission. This spontaneous emission is more or less uniformly distributed among all modes. Assuming a volume of 1 cm3 for the gas discharge, th

11、e number of modes within the Doppler width of the neon transition is about 108, which means that the total spontaneous rate is about 10 times the induced rate.Temporal Coherence What is the temporal coherence length Lc of (1) a mercury vapor lamp emitting in the green portion of the spectrum at a wa

12、velength of 546.1nm with an emission bandwidth of Dn = 6 x 108 Hz, and(2) a helium-neon laser operating at a wavelength of 632.8nm with an emission width of Dn = 106 Hz?Spatial CoherenceA laser-produced plasma consisting of a 100 mm diameter ball radiates very strongly at a wavelength of 10 nm. At a

13、 distance of 0.5 m from source, what is the spatial coherence resulting from light emitted from opposite sides of the plasma? JE=hc/l=hneVE(J)/1.602110-19nml=c/ncm-11/l(cm)=n/c(cm/s)Hzn=c/l1.00mm?1.00GHz?cm-1表示单位长度（厘米）中的波数。e = 1.602110-19 C，即1eV = 1.602110-19 J，h = 6.625610-34 J.s。思考题：1.1* 设一光子的波长l

14、= 510-1mm，单色性Dl/l=10-7，试求光子位置的不确定量Dx。若光子的波长变为510-4mm（x射线）和510-8mm (g射线), 则相应的Dx又是多少？1.2* 假定工作物质的折射率h=1.73,试问n为多大时，A21/B21=1JS/m3，这是什么光范围？1.3* 如果工作物质的某一跃迁波长为100nm的远紫外光，自发跃迁几率A10等于106S-1，试问：1 该跃迁的受激辐射爱因斯坦系数B10是多少？2 为使受激跃迁几率比自发跃迁几率大三倍，腔内的单色能量密度应为多少？1.4* 如果受激辐射爱因斯坦系数B10=1019m3s-3w-1，试计算在 1=6mm (红外光)； 2=

15、600nm (可见光)； =60nm(远紫外光)； =0.60nm(X射线时)，自发辐射跃迁几率A10和自发辐射寿命。又如果光强I=10W/mm2，试求受激跃迁几率W10。1.5* 有一支输出波长为6328A，线宽为103Hz,输出功率为1mW的氦氖激光器，发散角为1mrad。问：每秒发出的光子数目是多少？ 如果输出光束的直径是1毫米，那么对于一个黑体来说，要求它从相等的面积上以及整个相同的频率间隔内，发射出与激光器发射相同数目的光子，所需温度应多高？Answer to the Questions of Chapter 11. Dl/l = l/Lc = 6 1010 5 1019 s1 (l

16、 = 10mm );2. Dn21/Dt = P/hn = Pl/hc = 2.5 1018 s1 (l = 500nm); 5 1023 s1 (n = 3000MHz).3. (a) n2/n1 = e4.8x104 1; (b) n2/n1 = e48 0; (c) T = hn/k ln(n2/n1 ) = hc/k l ln(n2/n1 ) = 6.26 103 k4. 三能级系统，在理想情况下有N/2的粒子产生激光(l=694.3nm) Emax = hn N/2 = (p/8) d2l n hc/l = 16.9 JP = Emax /t = 1.69 109 W = 1.69

17、GW6. (a) t 4 = 1/(A41+ A42 + A43) = (1/9 ) 107 s； (b)稳态时各能级上的粒子数保持不变，忽略受激辐射以及E3和 E2能级的自发辐射对其他能级布居数的影响, 则有： n3 n2n3/t 3 = n4 A43 n3/n4 = A43t 3= 0.5n2/t 2 = n4 A42 n2/n4 = A42t 2= 0.06n2/t 2 = n4 A42 n1/n4 = A41t 1= 158. (1) I/I0 = e-az= 1/e = 36.8%(2) I/I0 = egz= 2, g = (ln2)/z = 0.693m-1ExampleNd3+

18、 ions are doped into YAG at a 1% atomic concentration, which corresponds to a density of Nd atoms of 1.38 x 1026 per cubic meter in the laser rod. If all of these atoms were instantly pumped to the upper laser level and then began to radiate, what would be the radiated energy per cubic meter and the

19、 average power per cubic meter radiated from this material at the emission wavelength of 1.06 mm? If the power radiated from one cubic centimeter could be concentrated into a spot 1mm in diameter, what would be the intensity (power/m2)?Each photon radiated at 1.06 mm would have an energy of E = hn =

20、 hc/l = 1.87 x 10-19 J = 1.17 ev.Thus, the total energy radiated per cubic meter would be ER = ( 1.38 x 1026 photons/m3 )( 1.87 x 10-19 J/photon ) = 2.58 x 107 J/m3PR, the total average power radiated per cubic meter, would thus equal the energy radiated per cubic meter multiplied by the transition

21、rate of the level. If the level has radiative lifetime of 230 ms and we assume that the dominant decay occurs at 1.06 mm (which is only approximate, since there are other low-lying levels to which the upper laser level can decay), then according to A21 = 1/ts, we have A21 = 1 /(2.3 x 10-4 s) = 4.35

22、x 10-4 s-1PR = ( 2.58 x 107 J/m3 ) (4.35 x 10-4 s-1 ) = 1.12 x 1011 W/m3This is a very high power, but we must remember that it lasts only for an average of 230 ms. The amount of power radiated from one cubic centimeter would thus be (1.12 x 1011 W/m3 ) (1 m3/106 cm3 ) (1 cm3 ) = 1.12 x 105 W.If thi

23、s power is collected and focused on a 1-mm (diameter) spot, or on an area of p (5 x 10-4)2 m2 = 7.85 x 10-7 m2, then the intensity would be I = (1.12 x 105 W) (7.85 x 10-7 m2) = 1.43 x 1011 W/m2.an extremely high intensity. This indicated the kind of intensity that would be obtained in a laser beam

24、from a crystal of this size if all of the radiated energy could be concentrated in a single direction. Chapter 4widths and profiles of spectral linesFWHM (full width at half maximum of line)natural line widthcollision broadeningDoppler widthNonradiative decayDephasing collisionAmorphous crystal broa

25、deningIsotopes shiftshomogeneous line broadeninginhomogeneous line broadeningLorentzian line profileGaussian line profile.Example 1 a) The natural linewidth of the sodium D1 line at l = 589.1 nm (n0 = 5 x 1014 s-1) which corresponds to a transition from 3P3/2 level ( t = 16 ns ) to the 3S1/2 ground

26、state is 10 MHz (Dnn = 109 / (16 x 2p) = 107 s-1). b) The natural linewidth of a molecular transition between two vibrational levels of the electronic ground state with a wavelength in the infrared region is very small because of the long spontaneous lifetimes. For a typical life time of t = 3 ms th

27、e natural linewidth becomes Dnn = 160 Hz.c) Even in the visible or ultraviolet range, atomic or molecular electronic transitions with very small transition probabilities exist. In a dipole approximation these are “forbidden” transitions. One example is the 2S 1S transition for the hydrogen atom. The

28、 upper level 2S cannot decay by electric dipole transition but a two-photon transition to the 1S ground state is possible. The natural life time t is about 1S and the natural linewidth of such a two-photon line is therefore Dnn = 0.15 s-1 !Example 2a) Vacuum ultraviolet: For the Lymann a line (2P 1S

29、 transition in the H atom) in a discharge with temperature T = 1000 K, M = 1, l = 121.6nm, n0 = 2.47 x 1015 s-1 DnD = 5.6 x 109 s-1 = 5.6 GHz, DlD = 2.8x 10-2 nm.b) Visible spectral region: For the sodium D line (3P 3S transition of the Na atom) in a sodium-vapor cell at T = 500 K, l = 589.1 nm, n0

30、= 5.1 x 1014 s-1 DnD = 1.7GHz, DlD = 10-3nm.c) Infrared region: For a vibrational transition between two rovibronic levels (quantum numbers J, V) (Ji, Vi) (Jk, Vk) of the CO2 molecule in a CO2 cell at room temperature (T = 300 K), l = 10 mm, n0 = 3 x 1013 s-1, M = 44 DnD = 5.6 x 107 s-1 = 56 MHz, DlD = 1.9 x 10-2 nm.Chapter 2optical resonator/cavitypassive resonatoractive resonatorplane-parallel (Fabry-Perot) resonatorconcentric (or spherical) resonatorconfocal resonator/cavityhemiconfocal resonator/cavityhemispherical resonator/cavitylongitudinal modestra