Chapter 2 Laser Light Amplification by Stimulated Emission of Radiation

Transcription

1 Chapter Laser Light Ampliication by Stimulated Emission o Radiation

2 Part I How does an object emit light or radiation? Blackbody Radiation Solids heated to very high temperatures emit visible light (glow) Incandescent Lamps (tungsten ilament)

3 Blackbody Radiation The color changes with temperature At high temperatures emission color is whitish, at lower temperatures color is more reddish, and inally disappear Radiation is still present, but invisible Can be detected as heat Heaters; Night Vision Goggles Electromagnetic Spectrum visible light to 0.4 m (m) 3

4 Electromagnetic Spectrum visible light ultraviolet (m) Electromagnetic Spectrum inrared visible light ultraviolet (m) 4

5 Electromagnetic Spectrum inrared visible light ultraviolet THz Far IR Mid IR Near IR (m) Electromagnetic Spectrum microwaves inrared visible light ultraviolet x-rays (m) 5

6 Electromagnetic Spectrum microwaves inrared visible light ultraviolet x-rays Low Energy (m) High Energy Kircho s Question (859) Radiant Energy and Matter in Equilibrium What is the thermal radiation o a bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature T? 6

7 Observation All object at inite temperatures radiate electromagnetic waves (emit radiation) Objects emit a spectrum o radiation depending on their temperature and composition From classical point o view, thermal radiation originates rom accelerated charged particles in the atoms near surace o the object Ideal System to Study Thermal Radiation: Blackbody A blackbody is an object that absorbs all radiation incident upon it Its emission is universal, i.e. independent o the nature o the object Blackbodies radiate, but do not relect and so are black Blackbody Radiation is EM radiation emitted by blackbodies 7

8 Blackbody Radiation There are no absolutely blackbodies in nature this is idealization But some objects closely mimic blackbodies: Carbon black or Soot (relection is <<%) The closest objects to the ideal blackbody is a cavity with small hole (and the universe shortly ater the big bang) Entering radiation has little chance o escaping, and mostly absorbed by the walls. Thus the hole does not relect incident radiation and behaves like an ideal absorber, and looks black Kircho's Law o Thermal Radiation (859) Absorptivity α λ is the ratio o the energy absorbed by the wall to the energy incident on the wall, or a particular wavelength. The emissivity o the wall ε λ is deined as the ratio o emitted energy to the amount that would be radiated i the wall were a perect black body at that wavelength. At thermal equilibrium, the emissivity o a body (or surace) equals its absorptivity α λ = ε λ I this equality were not obeyed, an object could never reach thermal equilibrium. It would either be heating up or cooling down. For a blackbody ε λ = Thereore, to keep your rank warm or your ice cream cold at a baseball game, wrap it in aluminum oil 8

9 Blackbody Radiation Spectra Blackbody Radiation Laws Emission is continuous 9

10 Blackbody Radiation Laws Stean-Boltzmann Law The total emitted energy increases with temperature, and represents, the total intensity (I total ) the energy per unit time per unit area or power per unit area o the blackbody emission at given temperature, T. 4 I total T σ = W/m -K 4 To get the emission power, multiply Intensity I total by area A Blackbody Radiation Laws The maximum shits to shorter wavelengths with increasing temperature the color o heated body changes rom red to orange to yellow-white with increasing temperature 0

11 Blackbody Radiation Laws Wien s Displacement Law The wavelength o maximum intensity per unit wavelength is deined by the max T b b = m/k is a constant For, T ~ 6000 K, max nm Nobel 9 Blackbody Radiation Spectra

12 How to understand Blackbody radiation rom undamental physical principle? The Birth o Quantum Mechanics Classic Physics View Radiation is caused by EM wave radiation Consider a cavity at temperature T whose walls are considered as perect relectors The cavity supports many modes o oscillation o the EM ield caused by accelerated charges in the cavity walls, resulting in the emission o EM waves at all wavelength They are considered to be a series o standing EM wave set up within the cavity

13 Classic Physics View Radiation is caused by EM wave radiation Average energy o a harmonic oscillator is <E> Intensity o EM radiation emitted by classical harmonic oscillators at wavelength λ per unit wavelength: I(, T ) E 3 c Or per unit requency ν: (, T) c I 3 E Classic Physics View In classical physics, the energy o an oscillator is continuous, so the average is calculated as: E 0 EP( E) de 0 P( E) de 0 0 E kbt 0 EP e E kbt 0 P e de de k T B P( E) 0 P e E k T B is the Boltzmann distribution E k B T 3

14 Classic Physics View This gives the Rayleigh-Jeans Law E I(, T) 3 c kbt, 3 c I(, T) 3 c E c k T B Agrees well with experiment long wavelength (low requency) region Classic Physics View Predicts ininite intensity at very short wavelengths (higher requencies) Ultraviolet Catastrophe Predicts diverging total emission by black bodies No ixes could be ound using classical physics 4

15 Planck s Hypothesis Max Planck postulated that A system undergoing simple harmonic motion with requency ν can only have energies E n nh 98 Nobel where n =,, 3, and h is Planck s constant h = J-s E Planck s Theory E nh E ( n ) h nh h E is a quantum o energy For = 3kHz E h J s 3000s 0 J 5

16 6 As beore: Now energy levels are discrete, So Sum to obtain average energy: Thus E c T I 3 ), ( T k n T k n n T k n n B B B e P e P e E E ), ( 3 3 T k h T k B B e h c e c T I nh n E n n T k n T k n n B B P e P e ) E ( P Planck s Theory h Blackbody Radiation Formula c is the speed o light, k B is Boltzmann s constant, h is Planck s constant, and T is the temperature exp ) ( T k h h c I B

17 Blackbody Radiation rom the Sun Plank s curve λ max Stean-Boltzmann Law I BB T 4 I BB = T 4 Stean-Boltzmann constant = J/m K 4 More generally: I = T 4 is the emissivity Wien's Displacement Law peak T = m K At T = 5778 K: peak = m = 5,05 A Cosmic microwave background (CMBR) as perect black body radiation 965, cosmic microwave background was irst detected by Penzias and Wilson Nobel Prize 976 7

18 The Nobel Prize in Physics 006 "or their discovery o the blackbody orm and anisotropy o the cosmic microwave background radiation" John C. Mather George F. Smoot Part II Stimulated Emission How is light generated rom an atomic point o view? 8

19 Mechanisms o Light Emission For atomic systems in thermal equilibrium with their surrounding, the emission o light is the result o: Absorption E E = hv E For atomic systems in thermal equilibrium with their surrounding, the emission o light is the result o: Absorption Mechanisms o Light Emission And subsequently, spontaneous emission o energy E Phase and propagation direction o created photon is random. E 9

20 For atomic systems in thermal equilibrium with their surrounding, the emission o light is the result o: Absorption Mechanisms o Light Emission And subsequently, spontaneous emission o energy Stimulated emission E E Created photon has the same phase, requency, polarization, and propagation direction as the input photon. Stimulated Emission It is pointed out by Einstein that: Atoms in an excited state can be stimulated to jump to a lower energy level when they are struck by a photon o incident light whose energy is the same as the energy-level dierence involved in the jump. The electron thus emits a photon o the same wavelength as the incident photon. The incident and emitted photons travel away rom the atom in phase. This process is called stimulated emission. 0

21 Population o Energy Levels How many atoms are in the ground states? And how many are in the excited states? E E E E Excited electron Unexcited electron Population o Energy Levels Maxwell-Boltzmann distribution E E E E Excited electron

22 Rate Equation o Absorption and Emission For absorbance, the # o E atoms decrease ater absorption absorption h E Rate Equation o Absorption and Emission For emission, the # o E atoms increase emission

23 Rate Equation o Absorption and Emission For stimulated, the # o E atoms increase ater absorption Stimulated emission Rate Equation o Absorption and Emission By considering all 3 processes, the change rate o # o E atoms becomes absorption emission Stimulated emission h E 3

24 Rate Equation o Absorption and Emission I the system is under equilibrium (blackbody), then Rate Equation o Absorption and Emission 4

25 Rate Equation o Absorption and Emission I needs to approach to ininite when T approaches ininite, which implies Rate Equation o Absorption and Emission Compared to Plank s ormula, For a visible light, v ~ 0 4 Hz, A/B ~ 0-6 5

26 Part III The Laser Population Inversion In order to obtain the coherent light rom stimulated emission: BN I BN I + AN << Thus: N N 6

27 Population Inversion In order to obtain the coherent light rom stimulated emission, two conditions must be satisied:. The atoms must be excited to the higher state. That is, an inverted population is needed, one in which more atoms are in the upper state than in the lower one, so that emission o photons will dominate over absorption. E Population Inversion In order to obtain the coherent light rom stimulated emission, two conditions must be satisied:. The higher state must be a metastable state a state in which the electrons remain longer than usual so that the transition to the lower state occurs by stimulated emission rather than spontaneously. Metastable state E 3 Photon o energy E E Metastable system E E E 3 E E Stimulated emission Incident photon Emitted photon 7

28 Four Key Elements o a LASER - Gain medium (Active medium) - Pumping source - Cavity (Resonator) - Output coupler pumping relaxation laser cavity (resonator) gain medium relaxation Laser light total relector pumping source output coupler Lasing Process Population Inversion Mirror Mirror E E i 8

29 Lasing Process Mirror Spontaneous emission Mirror E E i Mirror Lasing Process Stimulated emission Mirror E E i 9

30 Lasing Process Feed-back by the cavity Mirror Mirror E E i Lasing Process Mirror Stimulated emission Mirror E E i 30

31 Lasing Process Mirror Feed-back by the cavity Mirror E E i Lasing Process Ater several round trips/many pumps Mirror Mirror E E i Laser beam Photons with: - same energy : Monochromatic - same direction o propagation : Spatial coherence - all in synchrony: Temporal coherence 3

32 An Ampliication and Cascade Process During the entire process, the population must be kept inversed, i.e., the ampliication media should be pumped all the time, either pulsed or continuously. An Ampliication and Cascade Process 3

33 Laser Construction Ampliying Medium Laser Construction Atoms: helium-neon (HeNe) laser; heliumcadmium (HeCd) laser, copper vapor lasers (CVL) Molecules: carbon dioxide (CO) laser, ArF and KrF excimer lasers, N laser Liquids: organic dye molecules dilutely dissolved in various solvent solutions Dielectric solids: neodymium atoms doped in YAG or glass to make the crystalline Nd:YAG or Nd:glass lasers Semiconductor materials: gallium arsenide, indium phosphide crystals. 33

34 Homework Please ind out the principles o the ollowing lasers rom internet or books, and in your irst lab report, i.e., Lab # report, please add an Appendix section to describe the principle o one o the ollowing lasers, with at least two igures, the construction o the laser and energy lever diagram, you have to describe these igures and the laser operation principle: () Helium-neon (HeNe) laser () Ruby laser (3) Dye laser (4) Semiconductor laser Resonance Cavities and Longitudinal Modes Since the wavelengths involved with lasers spread over small ranges, and are also absolutely small, most cavities will achieve lengthwise resonance L = nλ/ c Plane parallel resonator Concentric resonator c Hemiocal resonator Hemispheric al resonator Conocal resonator Unstable resonator c: center o curvature, : ocal point 34

35 Resonance Cavities and Longitudinal Modes Fabry-Perot boundary conditions Multiple resonant requencies Resonance Cavities and Longitudinal Modes antinode node 35

36 Resonance Cavities and Longitudinal Modes Multi-mode laser Resonance Cavities and Transverse Modes TEM 00 TEM 0 TEM 0 TEM 0 TEM TEM Gauss-Hermite Moden TEM 03 TEM 3 36

37 Gaussian Beams Zero order mode is Gaussian Intensity proile: I I 0 e r / w Gaussian beam intensity Gaussian Beams I I 0 e r / w Beam waist: w 0 Conocal parameter (Rayleigh range): Z 0 w = w 0 + (z/z 0 ) z 0 = kw 0 37

38 Gaussian Beams Far rom waist Divergence angle w z kw 0 θ w z = 4 kw 0 = λ πnw w 0 Spread angle : / / nw 0 I w 0 z 0 w 0 z Gaussian proile z 0 Near ield (~ plane wave) Far ield (~ spherical wave) Power Distribution in Gaussian r w Intensity distribution: I I0e Experimentally to measure ull width at hal maximum (FWHM) diameter Relation is d FWHM = w ln ~.4 w Deine average intensity I avg = 4 P / (p d FWHM) Overestimates peak: I 0 = I avg /.4 / 38

39 Propagation o Gaussian Beam - ABCD law Propagation o Gaussian Beam - ABCD law Matrix method (Ray optics) a i Optical Elements a o y o Optical axis y i yo a o A C B yi D a i y o = Ay i + Bα i α o = Cy i + Dα i A C B D : ray-transer matrix 39

40 Ray Transer Matrices Free space propagation α o y i α i y o (paraxial ray approximation) y o = y i + dα i α o = α i yo d ao 0 yi ai Ray Transer Matrices Propagation through curved reracting surace n y i y o n h a i R a o s S n s + n s = n n R α o = n α n i + ( n ) y i n R y i = y o = h y o n n ao nr 0 y n i n ai 40

41 Ray Transer Matrices Ray Transer Matrices 4

42 ABCD Law or Gaussian Beam yo A a C o B yi D a i y o a Cy Da o Ay Ba i i i i R o yo a o Ayi Bai Cy Da i Ayi / ai B Cy / a D i ARi B CR D i i i ABCD Law or Gaussian Beam R o ( ray optics) q ( Gaussian optics) q optical system A B C D q ABCD law or Gaussian beam : q Aq B Cq D q z iz 0 nw0 z0 4

43 43 Focusing a Gaussian beam 0 w 0 w z z?? / z / / z z z z / z z / z D C B A ABCD Law or Gaussian Beam ) / ( / ) / ( ) / ( z q z z z z q z q w z w w ) ( ) / ( ) ( ) ( 0 w z z z 0 w 0 w - I a strong positive lens is used ; => 0 0 w w 0 ) ( / z w - I => z => d w w N N /, ) ( 0 0 : -number ; The smaller the # o the lens, the smaller the beam waist at the ocused spot. Note) To satisy this condition, the beam is expanded beore being ocused. ABCD Law or Gaussian Beam

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