CH8: coherence theory Flashcards
Temporal coherence
fields offset in time
E(r,t) E(t,t-tau)
Mich int is sensitive ot spectral content of wave
Spatial coherence
fields at difference spatial locations
E(r,t) E(r+delta r,t)
HOw do we detect coherence effects
Interference
Temportal, michaelson interefeormeter
Spatial - yongs two slit interferometer
If high degree of coherence then we see
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
What dspecial about PW and coherence
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
What makes a light source temporally incoherent
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
Fluence
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
Does the mich int depend on phase
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
D.o.coherence functoion
gamma(Tau)
describes the oscillations in intensity at the detector as the mirror arm is moved
What happens for large Tau in temporal coherence
If not coherent (not monochormatic light)
then the oscillations die of as the diff freq get out of sync
some interfere dest, others constructively
Is narrow band light more coherent than boradband
Yes because there is less opportunity for freq to get out of sunc
for larger Tau the osciallations will still die off
Define coherence time
The amount of delay needed to cause gamma(tau) to quit oscillating (amplitude approach 0)
arb. vanishsing pt givin in tau_c formula
Define fringe visibility
depends only on freq of light not whether these freq are organised into a long or very short pulse
How can we determine pulse length by looking at intereference pattern on mich. in
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
Diff between youhng and michealson
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
If mich is sensitive to ___ then young is sensitive to __________
mich: spectral content of the light
young: spatial extent of the light source illuminating the two slits
How did oyoung use to measure star width
wide angular width of stars -» poor finge visibilitit -> very wide spatial extent
Partial spatial coherence
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
The more extended the source the mroe___
Wahsed out the fringe pattern.
less contrast in fringe patten
When are the approximations valid for youngs
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»_space; the slit width
Tau in temporal is what in spatial
h
slit separation
What is the stochastic assumption
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
Where is the stochastic assumption valoid/not
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
simplyfying arpporximation reuslt of tay series
d1(y) - d2(y) approx = hy/D
In the degree of coherence function fro spatial we have
gamma(h)
depeneding on I(y’) wjocj jas imots pf omtemsotu [er ;emgtj pf tje spirce
in the defree of coh. func spatial what does the exp(-ikhy/D) define
The locations ofthe periodic fringes on the screen
depth of such fringes are dep on the rest pf the docoh. function
wehn h increases what happens to gamma(h)
amplitude of Gamma(h) diminises until the intensity becomes uniform
larger slit separation -> poorer spatial coherence
When do we get very good spatial coherence
|When gamma(h)|=1
the two slits have very small spearation h
What is hc
Analogous with Tc
it is the slit spearation h that will cause th finge patterns to totally wash our (here bcome totally uniform)
