CH8: coherence theory

Question 1

Temporal coherence

Answer 1

fields offset in time
E(r,t) E(t,t-tau)

Mich int is sensitive ot spectral content of wave

Question 2

Spatial coherence

Answer 2

fields at difference spatial locations

E(r,t) E(r+delta r,t)

Question 3

HOw do we detect coherence effects

Answer 3

Interference
Temportal, michaelson interefeormeter
Spatial - yongs two slit interferometer

Question 4

If high degree of coherence then we see

Answer 4

HIGH COHERENCE

• The light consistently interferes either constructively or destructively at the detection point,
• Time avg intensity signal shows the interference
• ocilllates wihtou diminisihing as time delay or spatial something is introduced/adjusted

LOW COHERENCE
-NO INTERFERENCE SEEN

Question 5

What dspecial about PW and coherence

Answer 5

MONOCHROMATIC PW is temporatlly coherence (i.e. in miachealson int.)

-any change of tau not affect intereference pattern at detector,
-PW must have 1 frequence, 1 wavelngth 1 k,
a continous band of freqyuencies we get a degree of incoherenceincoherence

Question 6

What makes a light source temporally incoherent

Answer 6

when it has a continous band of frequencies (i.e. not a monochromatic anymore)
we get fast fringe cisibibility diminishes as a delay is introduced in the michealson int

Question 7

Fluence

Answer 7

Sig(tau)
time integrated intensity
units” energy per area
integral of Itot(t,tau) (over dt from -inf,inf)

sort of like total energy, not useful for CW sourses of light

Question 8

Does the mich int depend on phase

Answer 8

no
The signal out of the int does not dep on E(w)
it depends only on the amount of light associated wiht each frequency thorgh I(w)

since the degree of coherence function only has I(w) in

Question 9

D.o.coherence functoion

Answer 9

gamma(Tau)

describes the oscillations in intensity at the detector as the mirror arm is moved

Question 10

What happens for large Tau in temporal coherence

Answer 10

If not coherent (not monochormatic light)
then the oscillations die of as the diff freq get out of sync
some interfere dest, others constructively

Question 11

Is narrow band light more coherent than boradband

Answer 11

Yes because there is less opportunity for freq to get out of sunc
for larger Tau the osciallations will still die off

Question 12

Define coherence time

Answer 12

The amount of delay needed to cause gamma(tau) to quit oscillating (amplitude approach 0)
arb. vanishsing pt givin in tau_c formula

Question 13

Define fringe visibility

Answer 13

depends only on freq of light not whether these freq are organised into a long or very short pulse

Question 14

How can we determine pulse length by looking at intereference pattern on mich. in

Answer 14

We look at the detectorl signal - focus on getting coherence time since

If long pulse -> T_c is long
since T_c = sqrt (2pi) T
where T is a measure of the length of a gaussian pulse

Question 15

Diff between youhng and michealson

Answer 15

two beams of light travel different paths and then interfere

Mich: one path delay wrt ot he other so that temporal effects studied
Young: two laterally separate points of the same wave are compared as they are sent through two slits

Question 16

If mich is sensitive to ___ then young is sensitive to __________

Answer 16

mich: spectral content of the light
young: spatial extent of the light source illuminating the two slits

Question 17

How did oyoung use to measure star width

Answer 17

wide angular width of stars -» poor finge visibilitit -> very wide spatial extent

Question 18

Partial spatial coherence

Answer 18

Collection of point sources distrib over a finite lateral extent, only slighlty diminished finged pattern that is washed out.

We assume the poiunt sources vary only in the y dimension

Question 19

The more extended the source the mroe___

Answer 19

Wahsed out the fringe pattern.

less contrast in fringe patten

Question 20

When are the approximations valid for youngs

Answer 20

We taylor expanded d1(y) and d2(y) and these are validwhen
D»y, D»h
i.e. only true in the middle of the finger pattern, only true when the distance between the screena dn the slit&raquo_space; the slit width

Question 21

Tau in temporal is what in spatial

Answer 21

h

slit separation

Question 22

What is the stochastic assumption

Answer 22

Used in derivation of Itot(h) in young’s two slit exp

Assume that the phase of the emission (phi(yj)) varies in time independently at every point on the source

Question 23

Where is the stochastic assumption valoid/not

Answer 23

Valid in stars, glowing filaments spontaneous emission from excited gas or plasma, not coherent sources (coherent in the tyoic sense not really spatial or temporally here)
Not valid: lasers which are coherent sources

Question 24

simplyfying arpporximation reuslt of tay series

Answer 24

d1(y) - d2(y) approx = hy/D

Question 25

In the degree of coherence function fro spatial we have

Answer 25

gamma(h)

depeneding on I(y’) wjocj jas imots pf omtemsotu [er ;emgtj pf tje spirce

Question 26

in the defree of coh. func spatial what does the exp(-ikhy/D) define

Answer 26

The locations ofthe periodic fringes on the screen

depth of such fringes are dep on the rest pf the docoh. function

Question 27

wehn h increases what happens to gamma(h)

Answer 27

amplitude of Gamma(h) diminises until the intensity becomes uniform

larger slit separation -> poorer spatial coherence

Question 28

When do we get very good spatial coherence

Answer 28

|When gamma(h)|=1

the two slits have very small spearation h

Question 29

What is hc

Answer 29

Analogous with Tc

it is the slit spearation h that will cause th finge patterns to totally wash our (here bcome totally uniform)