Chapter 2 Laser

Home , Laser construction

9/11/2015

Chapter 2

Laser

Light Amplification by Stimulated Emission of Radiation

1 9/11/2015

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 filament)

2 9/11/2015

Blackbody Radiation • The color changes with temperature – At high temperatures emission color is whitish, at lower temperatures color is more reddish, and finally disappear – Radiation is still present, but “invisible” – Can be detected as heat • Heaters; Night Vision Goggles

Electromagnetic Spectrum

visible light

1000 100 10 1 0.1 0.01

0.7 to 0.4 m

 (m)

3 9/11/2015

Electromagnetic Spectrum

visible light ultraviolet

1000 100 10 1 0.1 0.01

 (m)

Electromagnetic Spectrum

visible infrared light ultraviolet

1000 100 10 1 0.1 0.01

 (m)

4 9/11/2015

Electromagnetic Spectrum

visible infrared light ultraviolet

1000 100 10 1 0.1 0.01

THz Far IR Mid IR Near IR  (m)

Electromagnetic Spectrum

visible microwaves infrared light ultraviolet x-rays

1000 100 10 1 0.1 0.01

 (m)

5 9/11/2015

Electromagnetic Spectrum

visible microwaves infrared light ultraviolet x-rays

1000 100 10 1 0.1 0.01

Low High Energy Energy  (m)

Kirchoff’s Question (1859) Radiant Energy and Matter in Equilibrium What is the thermal radiation of a bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature T?

6 9/11/2015

Observation

• All object at finite temperatures radiate electromagnetic waves (emit radiation) • Objects emit a spectrum of radiation depending on their temperature and composition • From classical point of view, thermal radiation originates from accelerated charged particles in the atoms near surface of 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 of the nature of the object – Blackbodies radiate, but do not reflect and so are black

Blackbody Radiation is EM radiation emitted by blackbodies

7 9/11/2015

Blackbody Radiation • There are no absolutely blackbodies in nature – this is idealization • But some objects closely mimic blackbodies: – Carbon black or Soot (reflection is <<1%) • The closest objects to the ideal blackbody is a cavity with small hole (and the universe shortly after the big bang)

– Entering radiation has little chance of escaping, and mostly absorbed by the walls. Thus the hole does not reflect incident radiation and behaves like an ideal absorber, and “looks black”

Kirchoff's Law of Thermal Radiation (1859)

• Absorptivity αλ is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength.

• The emissivity of the wall ελ is defined as the ratio of emitted energy to the amount that would be radiated if the wall were a perfect black body at that wavelength. • At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity

αλ = ελ • If this equality were not obeyed, an object could never reach thermal equilibrium. It would either be heating up or cooling down.

• For a blackbody ελ = 1 • Therefore, to keep your frank warm or your ice cream cold at a baseball game, wrap it in aluminum foil

8 9/11/2015

Blackbody Radiation Spectra

Blackbody Radiation Laws • Emission is continuous

9 9/11/2015

Blackbody Radiation Laws Stefan-Boltzmann Law

• The total emitted energy increases with temperature, and

represents, the total intensity (Itotal) – the energy per unit time per unit area or power per unit area – of the blackbody emission at given temperature, T.

4 Itotal  T

– σ = 5.670×10-8 W/m2-K4

• To get the emission power, multiply Intensity Itotal by area A

Blackbody Radiation Laws • The maximum shifts to shorter wavelengths with increasing temperature – the color of heated body changes from red to orange to yellow-white with increasing temperature

10 9/11/2015

Blackbody Radiation Laws Wien’s Displacement Law

• The wavelength of maximum intensity per unit wavelength is defined by the

max  T  b – b = 2.898×10-3 m/K is a constant • For, T ~ 6000 K,

2.898103    483 nm max 6000

Nobel 1911

Blackbody Radiation Spectra

11 9/11/2015

How to understand Blackbody radiation from fundamental physical principle?

The Birth of Quantum Mechanics

Classic Physics View

• Radiation is caused by EM wave radiation

• Consider a cavity at temperature T whose walls are considered as perfect reflectors

• The cavity supports many modes of oscillation of the EM field caused by accelerated charges in the cavity walls, resulting in the emission of EM waves at all wavelength

• They are considered to be a series of standing EM wave set up within the cavity

12 9/11/2015

Classic Physics View

• Radiation is caused by EM wave radiation • Average energy of a harmonic oscillator is

• Intensity of EM radiation emitted by classical harmonic oscillators at wavelength λ per unit wavelength: 2 I(,T)  E c 3 • Or per unit frequency ν: 2 2 I( ,T)  E c3

Classic Physics View

• In classical physics, the energy of an oscillator is continuous, so the average is calculated as: E    kBT  EP(E)dE  EP0e dE 0 0 E    E  kBT   P(E)dE kBT   P0e dE 0 0

E  kBT is the Boltzmann distribution P(E)  P0e

E  kBT

13 9/11/2015

Classic Physics View

• This gives the Rayleigh-Jeans Law

2 E 2 k T 2 2 2 2 I(,T)   B , I( ,T)  E  k T c  3 c  3 c3 c2 B

Agrees well with experiment long wavelength (low frequency) region

Classic Physics View

• Predicts infinite intensity at very short wavelengths (higher frequencies) – “Ultraviolet Catastrophe”

• Predicts diverging total emission by black bodies

No “fixes” could be found using classical physics

14 9/11/2015

Planck’s Hypothesis Max Planck postulated that A system undergoing simple harmonic motion with frequency ν can only have energies E  n  nh

where n = 1, 2, 3,… and h is Planck’s constant h = 6.63×10-34 J-s 1918 Nobel

Planck’s Theory E  nh E  (n 1)h  nh  h E is a quantum of energy

For  = 3kHz E  h E  6.631034 J  s 3000s1  21030 J

15 9/11/2015

Planck’s Theory • 2 2 As before: I (  , T )  E c3 • Now energy levels are discrete, En  nh  n   h

n  kBT P0e • So P( En )  n   k T B n P0e    k T n0 E P e B  n 0 n0  E  n   • Sum to obtain average energy:   k T k T P e B e B 1  0 n0

2 2  2 2 h Thus I (  , T )   c3  c3 h e kBT 1 e kBT 1

Blackbody Radiation Formula

2 2 h I( )  c2  h  exp  1 kBT 

c is the speed of light, kB is Boltzmann’s constant, h is Planck’s constant, and T is the temperature

16 9/11/2015

Blackbody Radiation from the Sun Plank’s curve Stefan-Boltzmann Law I  T4 λ BB max 4 IBB = T

Stefan-Boltzmann constant  =5.67×10-8 J/m2K4 More generally: I = T4  is the emissivity

Wien's Displacement Law -3 peak T = 2.898×10 m K

At T = 5778 K: -7 peak = 5.015×10 m = 5,015 A

• Cosmic microwave background (CMBR) as perfect black body radiation 1965, cosmic microwave background was first detected by Penzias and Wilson

Nobel Prize 1976

17 9/11/2015

The Nobel Prize in Physics 2006 • "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation"

John C. George F. Mather Smoot

Part II

Stimulated Emission

How is light generated from an atomic point of view?

18 9/11/2015

Mechanisms of Light Emission

For atomic systems in thermal equilibrium with their surrounding, the emission of light is the result of:  Absorption

E = hv

Mechanisms of Light Emission

For atomic systems in thermal equilibrium with their surrounding, the emission of light is the result of:  Absorption  And subsequently, spontaneous emission of energy

E2 Phase and propagation direction of created photon is random.

19 9/11/2015

Mechanisms of Light Emission For atomic systems in thermal equilibrium with their surrounding, the emission of light is the result of:  Absorption  And subsequently, spontaneous emission of energy  Stimulated emission

E Created photon 2 has the same phase, frequency, polarization, and propagation direction as the E 1 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 of incident light whose energy is the same as the energy-level difference involved in the jump. The electron thus emits a photon of the same wavelength as the incident photon. The incident and emitted photons travel away from the atom in phase. • This process is called stimulated emission.

20 9/11/2015

Population of Energy Levels

How many atoms are in the ground states? And how many are in the excited states?

E1 E2 Excited electron

Unexcited electron

Population of Energy Levels

Maxwell-Boltzmann distribution

Excited electron

21 9/11/2015