考试时间4上课时和教室

1、考试时间：2011.1.4上课时间和教室chapter 7. lasers light amplification by stimulated emission of radiation (acronym)the historyv1916, einstein predicted the stimulated emission.v1954, townes and co-workers developed a microwave amplifier by stimulated emission of radiation(maser) using ammonia, nh3.v1958, schawl

2、ow and townes showed that the maser principle could be extended into the visible region .v1960, maiman built the first laser using ruby as the active medium. vfrom then on, laser development was nothing short of miraculous, giving optics new impetus and wide publicity.7.1 stimulated emission of radi

3、ation 1. boltzmann distribution the transitions that occur between different energy statesv absorption: the upward transition from a lower energy state to a higher state, e1 e2v emission: the downward transition, e2 e1, v population n : the number of atoms, per unit volume, that exist in a given sta

4、te. given by boltzmanns equationteen/e : energy lever of the system : boltzmanns constantt : absolute temperature. 7.1 stimulated emission of radiation vboltzmanns ratio or relative population : the ratio of the populations in the two states, n2 / n1.orvplot the energy in the higher state relative t

5、o that in the lower state, versus the population in these states(e versus n), the result is an exponential curve known as a boltzmann distribution.v when the boltzmann distribution is normal, it means that the system is in thermal equilibrium, having more atoms in the lower state than in the higher

6、state. teteeenn/1212teeenn/)(12127.1 stimulated emission of radiation 2. einsteins prediction vassume first: an ensemble of atoms is in thermal equilibrium and not subject to an external radiation field. at higher temperatures, a certain number of atoms is in the excited state; on return to the lowe

7、r state, these atoms will emit radiation, in the form of quanta h . - spontaneous emission rate of the transition: the number of atoms in the higher state that make the transition to the lower state, per second. lifetime of the transition: the reciprocal of the rate of transition. rate of the sponta

8、neous transition:a21: constant of proportionality n2 : number of atoms (per unit volume) in the higher state21221anp7.1 stimulated emission of radiation vassume next: the system is subject to some external radiation field. one of two processes may occur, depending on: the direction (the phase) of th

9、e field with respect to the phase of the oscillator.7.1 stimulated emission of radiation the two phases coincide:a quantum of the field may cause the emission of another quantum. - stimulated emission.its rate is b21 : constant of proportionality u(): energy density (j m-3), function of frequency .t

10、he two phase is opposite : the impulse transferred counteracts the oscillation, energy is consumed, and the system is raised to a higher state - absorption. its rate is b12 : constant of proportionality. ubnp21221 ubnp121127.1 stimulated emission of radiation transitions between energy states 7.1 st

11、imulated emission of radiation einsteins coefficients: a21, b21, b12einsteins relations b21 = b123321218chba(1) the coefficients for both stimulated emission and absorption are numerically equal(2) the ratio of the coefficients of spontaneous versus stimulated emission is proportional to the third p

12、ower of the frequency of the transition radiationexplains why it is so difficult to achieve laser emission in the x-ray range, where is rather high7.1 stimulated emission of radiation 3. population inversion v thermal equilibrium system absorption and spontaneous emission take place side by side n2

13、n1 on return to the ground state, the system will probably lase. incandescent vs. laser light light from bulbs are due to spontaneous emission1. many wavelengths2. multidirectional3. incoherent1. monochromatic2. directional3. coherentcoherencecoherent: if the phase of a light wave is well defined at

14、 all times (oscillates in a simple pattern with time and varies in a smooth wave in space at any instant).example: a laser produces highly coherent light. in a laser, all of the atoms radiate in phase.incoherent: the phase of a light wave varies randomly from point to point, or from moment to moment

15、.example: an incandescent or fluorescent light bulb produces incoherent light. all of the atoms in the phosphor of the bulb radiate with random phase. stimulated vs spontaneous emissionstimulated emission requires the presence of a photon. an “incoming” photon stimulates a molecule in an excited sta

16、te to decay to the ground state by emitting a photon. the stimulated photons travel in the same direction as the incoming photon.spontaneous emission does not require the presence of a photon. instead a molecule in the excited state can relax to the ground state by spontaneously emitting a photon. s

17、pontaneously emitted photons are emitted in all directions.two-level system(ex. ammonia maser)en, nnem, nmen, nnem, nmeven with very a intense pump source, the best one can achieve with a two-level system is excited state population = ground state populationthree-level system in equilibrium normal b

18、oltzmann distribution absorptive rather than emissive excited population inversion7.2 practical realization 1. general constructionvpumping: an energy source to supply the energy needed for raising the system to the excited state. vactive medium: in which, reaches population inversion and lases when

19、 excited. may be a solid, liquid, or gas thousands of materials that have been found to lasevcavity:optionallaser amplifiers: no cavitylaser oscillators: medium enclosed in a cavity provides feedback and additional amplification cavity formed by two mirrors: one full reflectance, the other partially

20、 transparent7.2 practical realization energy source medium full reflectance mirrors partially transparent mirrors radiationbasic components of a laser oscillatorcommon components of all lasers1. active medium the active medium may be solid crystals such as ruby or nd:yag, liquid dyes, gases like co2

21、 or helium/neon, or semiconductors such as gaas. active mediums contain atoms whose electrons may be excited to a metastable energy level by an energy source. 2. excitation mechanism excitation mechanisms pump energy into the active medium by one or more of three basic methods; optical, electrical o

22、r chemical. 3. high reflectance mirror a mirror which reflects essentially 100% of the laser light. 4. partially transmissive mirror a mirror which reflects less than 100% of the laser light and transmits the remainder. 2. excitation voptical pumping: ruby laser a light source another laser.velectro

23、n excitation: argon laser , helium-neon laserv direct conversion of electric energy into radiation: light-emitting diodes(leds), semiconductor lasers vthermal excitation : co2 laser.vchemical pumping: chemical laserh2 + f2 2hf 7.2 practical realization 7.2 practical realization 3. cavity configurati

24、ons vplane-parallel cavity: very efficient ( good filling), difficult alignment(low stability) vconfocal cavity: poor filling, easier to alignvconcentric cavity (spherical cavity) : poor filling, easier to alignvhemispherical cavity: poor filling, much easy to alignvlong-radius cavity: good compromi

25、se between the plane-parallel and the confocal variety, type of cavity used most often in todays commercial lasers. 7.2 practical realization cavity configurationsl:distance between mirrorsr:radius of curvature7.2 practical realization 4. mode structure assume: the cavity is limited by two plane-par

26、allel mirrors. vthe wavelength possible of the standing-wave pattern inside the cavity is:l : length of the cavityq : number of half-wavelengths, or axial modesv the resonance condition for axial modes: n: index of medium contained in a laser cavitylq2 nl2cq 7.2 practical realization vdifferent freq

27、uencies are closely, and evenly, spaced, lie within the width of a single emission line. v the output of the laser consists of a number of lines separated by c/2s two consecutive modes (which differ by q = 1), are separated by a frequency difference ,s2c mode-lockingactive mode-locking7.2 practical

28、realization v tem: transverse electromagnetic, modesv few in number, easy to see.v aim the laser at a distant screen, spread the beam out by a negative lens.: bright patches, separated from one another by intervals called nodal lines. within each patch, the phase of the light is the same, but betwee

29、n patches the phase is reversed. 7.2 practical realization lowest possible axial mode: laser oscillates in one frequencyhighest possible temporal coherencetem modestem00 : lowest possible transverse mode no phase reversal across the beam, the beam is uniphase highest possible spatial coherence, can

30、be focused to the smallest spot size and reach the highest power density.5. gain gain of a laser depends on several factors. foremost among them is the separation of the energy levels that provide laser transition. the two levels are father apart, the gain is higher because then the laser transition

31、 contains a larger fraction of the energy compared to the energy in the pump transition7.2 practical realization gain is the opposite of absorption-definition : initial power in the cavity : power of exit lightabsorptivity positive: for thermal equilibrium where n2 n1, laser emission could be consid

32、ered negative absorption gain coefficient : the negative of the absorption coefficient“xe0 xe007.2 practical realization as the wave is reflected back and forth between the mirrors, it will lose some of its energy, mainly because of the limited reflectivity of one of mirrors. if the two mirrors have

33、 reflectivities r1 and r2, -each round trip210rr err21: loss per round trip -for the system xe)(0 : system will lase, threshold condition necessary to sustain laser emission. 7.2 practical realization 7.3 types of lasers 1. solid-state lasersruby laser ruby is synthetic aluminum oxide, al2o3, with 0

34、.03 to 0.05% of chromium oxide, cr2o3, added to it. the cr3+ ions are the active ingredient; the aluminum and oxygen atoms are inert. the ruby crystal is made into a cylindrical rod, several centimeters long and several millimeters in diameter, with the ends polished flat to act as cavity mirrors. p

35、umping is by light from a xenon flash tube.7.3 types of lasers e3: fairly wide and has a short lifetime; the excited cr3+ ions rapidly relax and drop to the next lower state, e2. this transition is nonradiative.e2: metastable and has a lifetime longer than that of e3, and the cr3+ ions remain that m

36、uch longer in e2 before they drop to the ground state, e1.the e2 e1 transition is radiative; it produces the spontaneous, incoherent red fluorescence typical of ruby, with a peak near 694 nm. as the pumping energy is increased above a critical threshold, population inversion occurs in e2 with respec

37、t to e1 and the system lases, with a sharp peak at 694.3 nm.three-level energy diagram typical of ruby lasing action diagramenergy introductionground stateexcited statemetastable statespontaneous energy emissionstimulated emission of radiationefficient pumpingslow relaxationmetastable statefastslowp

38、opulation inversionfast relaxationrequirements for laser actionneodymium: yag laser the active ingredient is trivalent neodymium, nd3+, added to an yttrium aluminum garnet, yag, y3al5o12. it has four energy levels. the laser transition begins at the metastable state and ends at an additional level s

39、omewhat above the ground state.7.3 types of lasers 7.3 types of lasers 2. gas lasers gas lasers consist of a gas filled tube placed in the laser cavity. a voltage (the external pump source) is applied to the tube to excite the atoms in the gas to a population inversion. the light emitted from this t

40、ype of laser is normally continuous wave (cw).helium-neon laser typically, it consists of a tube about 30 cm long and 2 mm in diameter, with two electrodes on the side and fused silica windows at both ends. the tube contains a mixture of 5 parts helium and 1 part neon, kept at a pressure of 133 pa.

41、7.3 types of lasers argon laseri t g e n e r a t e s a s t r o n g turquoise-blue line at 488 nm and a green line at 514.5 nm, in either pulsed or c. w. operation. helium-cadmium it emits a brilliant blue at 441.6 nm.7.3 types of lasers carbon dioxide laserv high power: the first co2 lasers had a co

42、ntinuous output of a few milliwatts. today we have powers of some 200 kw, more than enough to cut through steel plates several centimeters thick in a matter of seconds. v high efficient: the efficiency in converting electrical energy into radiation is better (more than 10%) than that of any other la

43、ser.(tea co2 laser)v relatively simple in construction and operation are. vtunable in a small range emission is at 10.6 m.7.3 types of lasers excimer lasers contain rare-gas halides such as xecl, krf, or others. these molecules are unstable in the ground state but bound in the excited state. vexceed

44、ingly powerful, with outputs as high as several gw. vemit in the ultraviolet.7.3 types of lasers 3. semiconductor lasers led: light-emitting diode emit almost anywhere in the spectrum, from the uv to the ir an efficiency much higher than with optical pumping (around 40% versus 3%). small ,less than

45、1 mm in diameter main application : waveguides integrated optics7.3 types of lasers 4. tunable lasers dye lasers: first tunable lasers parametric oscillator: more compact less expensive easier to operate tuning range much wider color center lasers: tuned over wide bands in the uv, the visible, and t

46、he ir. free-electron laser: high powers of the order of megawattsvery efficient tuned through a wide range of wavelengths.tunable lasers are most welcome to spectroscopistsargon fluoride (excimer-uv)krypton chloride (excimer-uv)krypton fluoride (excimer-uv)xenon chloride (excimer-uv)xenon fluoride (

47、excimer-uv)helium cadmium (uv)nitrogen (uv)helium cadmium (violet)krypton (blue)argon (blue)copper vapor (green)argon (green)krypton (green)frequency doubled nd yag (green)helium neon (green)krypton (yellow)copper vapor (yellow)0.1930.2220.2480.3080.3510.3250.3370.4410.4760.4880.5100.5140.5280.5320.

48、5430.5680.570helium neon (yellow)helium neon (orange)gold vapor (red)helium neon (red)krypton (red)rohodamine 6g dye (tunable)ruby (cralo3) (red)gallium arsenide (diode-nir)nd:yag (nir)helium neon (nir)erbium (nir)helium neon (nir)hydrogen fluoride (nir)carbon dioxide (fir)carbon dioxide (fir)0.5940

49、.6100.6270.6330.6470.570-0.6500.6940.8401.0641.15 1.5043.392.709.6 10.6 key: uv = ultraviolet (0.200-0.400 m) vis = visible (0.400-0.700 m) nir = near infrared (0.700-1.400 m) wavelengths of most common laserswavelength ( m)laser type laser outputcontinuous output (cw)pulsed output (p) watt (w) - un

50、it of power or radiant flux (1 watt = 1 joule per second).joule (j) - a unit of energy energy (q) the capacity for doing work. energy content is commonly used to characterize the output from pulsed lasers and is generally expressed in joules (j).irradiance (e) - power per unit area, expressed in wat

51、ts per square centimeter.energy (watts)timeenergy (joules)time7.4 applications compared to radiation from other sources, laser radiation stands out in several ways:v highly coherent, both spatially and temporallyv generated in the form of very short pulses, at high powers 7.4 applications1. beam sha

52、pe laser operating in the tem00 modethe energy has a gaussian distribution at a given distance r from the axis, the irradiance i falls off exponentiallyparameter w: the distance from the axis at which i has dropped to 1/e2 of i0, the irradiance in the center2)/2(0)(wreiriw(z) :beams radius : wavelen

53、gth w0:radius at the waist.for a confocal cavity, this simplifies tol : distance between the mirrors.22001)(wzwzw20lw 7.4 applicationsfar field: farther away from the laser beams parameters can be considered linear functions of the distancefar-field half-angle divergence 0w7.4 applicationsplace a co

54、nverging lens in the path of the light: beam to contract to a focus“ another waist where the beams wavefronts are plane diameter radius of beam at the focus 2r:f: the lens a focal lengthradius of beam at the focus r7.4 applications042dfrdfr22. 1rayleighs criterion :d22. 17.4 applications2. power and

55、 power density a typical laser pulse contains about 10 j of energy. if this energy is delivered within a pulse only 0.5 ms long, the output power is 20 kw. q awitching: compressing the energy into a very short period of time. 7.4 applications3. nonlinear effects vlinear:the refractive index and the

56、absorptivity of a material are independent of the intensity of the light that passes through. vnonlinear: with very intense light, either the index or the absorptivity or both may become nonlinear functions of the intensity. change the refractive index, even of completely transparent material.heat a

57、nd thermal expansion, as they occur with absorbing materials, are not involved.7.4 applications plasma: a mixture of ions and free electrons rarely found in nature except in the atmosphere of the sun self-focusing: a beam of light contracts into thin, short lived, powerful threads of light that quic

58、kly shatter the material through which they pass. optical bistability arises in saturable systems phase conjugation(wavefront reversal): a molecular reflection of light. the reflected wavefronts are now distorted opposite to those in the incident beam, frequency doubling: generation of second harmon

59、ics. 7.4 applications4. industrial applications v cutting v drilling v welding v communications v optical radar v precision measurements laser technique in gis data acquisitiongis:globe information systemtasksacquire laser mapping equipment for gis spatial data acquisition: utility mapping (power po

60、les, water valve, gas pipe, water pipe, etc) construction (ask for higher accuracy) digital geology mapping (geologic features)laser mapping why it is neededlaser + gps = fast 3d spatial data acquisitionmapping the inaccessible areamore efficient and cost effectivetechnical basicsdistance measure + angle (h & v)