Modern optics, Exams of Optics

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Modern optics

Chapter 13

Phys 322Lecture 36

Presentations

Name

Presentation topic

date

Abdallah, Daniel ultrafast optics

5-Dec

Brown, Timothy

adaptive optics

3-Dec

Chen, Qingyu

OCT

28-Nov

Foote, Evan

LCDs

30-Nov

Lazar, Dennis

lasers

28-Nov

Lee, Gen Joo

magn. Res. Spect.

3-Dec

Navarro, Tyler

optical computing

5-Dec

Ohlwine, Ross

x-ray imaging

5-Dec

Simiele, Eric

tomography

Sun, Yubo

metamaterials

3-Dec

Tempel, Nicholas holography

30-Nov

Tran, Tu

holography

30-Nov

Blackbody radiation

MotivationDefinition of a BlackbodyBlackbody Radation Laws

1- The Planck Law2- The Wien Displacement Law3- The Stefan-Boltzmann Law4- The Rayleigh-Jeans Law

Motivation The blackbody is important in thermal radiation theory and

practice.

The blackbody has universal characteristics.The ideal blackbody notion is important in studying thermal

radiation and electromagnetic radiation transfer in allwavelength bands.

The blackbody is used as a standard with which the absorption of

real bodies is compared.

Blackbody radiation

Blackbody radiation is emitted from a hot body. It's anything but black!The name comes from the assumption that the body absorbs at everyfrequency and hence would look black at low temperature.It results from a combination of spontaneous emission, stimulatedemission, and absorption occurring in a medium at a giventemperature.

It assumes thatthe box is filledwith moleculesthat, together,have transitionsat everywavelength.

Black-Body Radiation Laws The Rayleigh-Jeans Law 

It agrees with experimental

measurements for longwavelengths. 

It predicts an energy output that

diverges towards infinity aswavelengths grow smaller. 

The failure has become known

as the ultraviolet catastrophe.

4

2

)

,

(

 



ckT

T

I



Remindeer: Rayleigh-Jeans

, but Blackbody

Comparison between Classical and Quantum viewpoint

Cosmic black body backgroundradiation, T = 3K.

Color temperature

Blackbodies are so pervasive that alight spectrum is often characterizedin terms of its temperature even ifit’s not exactly a blackbody.

Gives the total energy being emitted at all wavelengths by the blackbody (whichis the area under the Planck Law curve). 

Explains the growth in the height of the curve as the temperature increases.Notice that this growth is very abrupt. 

Sigma = 5.67 * 10

J s

m

K

Known as the Stefan-Boltzmannconstant.

The Stefan-Boltzmann law

4

4

T

j

AT

P

 

Where P is the total radiant power atall wavelengths

Atomic and molecular vibrationscorrespond to excited energy levels inquantum mechanics.



Energy

Excited level Ground level



E = h



The atom is at least partially inan excited state.

The atom is vibratingat frequency,

Energy levels are everything in quantum mechanics.

Atoms and molecules can also absorbphotons, making a transition from a lowerlevel to a more excited one.

This is, ofcourse,absorption.

Energy

Excited level Ground level

Absorption lines in anotherwise continuouslight spectrum due to

a cold atomic gas infront of a hot source.

In what energy levels do molecules reside?Boltzmann population factors

N

i^

is the numberdensity ofmolecules instate

i

(i.e.,

the numberof moleculesper cm

T

is the temperature,and

k

B

is

Boltzmann’sconstant.

^



exp

i^

i^

B

N

E

k T

Energy

Population density

N

1

N

3

N

2

E

3

E

1

E

2

In 1916, Einstein showed that anotherprocess, stimulated emission, can occur.

Before

After

Spontaneousemission AbsorptionStimulatedemission

Einstein A and B coefficients^ In 1916, Einstein considered the various transition rates betweenmolecular states (say, 1 and 2) involving light of irradiance,

I

Spontaneous emission rate =

A N

2

Absorption rate =

B

12

N

1

I

Stimulated emission rate =

B

21

N

2

I

In equilibrium, the rate of upward transitions equals the rate ofdownward transitions:

Recalling the Maxwell-Boltzmann Distribution

( B

12

I

A + B

21

I

= N

2

/ N

1

exp[

E

/ k

B

T

]

B

12

N

1

I^

= A N

2

+ B

21

N

2

I

Solving for

N

N