4.2 Interferometers Flashcards
uses of itnerferometers
When more resolution needed than even very large spectrometer
- measuring Y of single mode lasers
- laser linewidth
Basic principle of interferometers
-Incident lightwave with intensity I0 is divided into partial beams with amplitudes Ak,
-which pass digerent optical path lengths sk = nxk (where m is the refractive index)
- before they are again superimposed at the exit of the interferometer.
-Partial beams come from the same source, they are coherent
- Total amplitude of the transmitted wave is the superposition of all partial waves, and depends on the amplitudes Ak and on the phases phik = phi0 + 2pisk/Y of the partial waves
Partial beams in an interf come from the same source adn they coherent so long as ….
as long as the maximum path diverence does not exceed the coherence length.
WHy in interfometer sensitively dep on the wavelength Y
the transmitted wave is the superpos of all partial waves ad dep on their amplitudes and phases (phik(Y))
Maxima.minima in interfogram obtained when
All partial waves interefere constrcutively
OPDiff = dsik = si-sk =mY (full wavlenegths apart)
minima when mY/2 (half wavelength apart -> total destrc intef)
FSR of interometer
dY = Ym - Ym+1 = deltas/m - deltas/(m+1)
but note that form one terferometric measurement you can only determine Y module m.dY because all Y are equibalent wrt transmission in interf Y = Y0 +mdY
what can use use with interf
Need to masure within 1 FSR of interf first using maybea spectrometer
interformeter CANNOT unqieuly det a wavlength on its own
Michaelson Intef
Y dependent filter for accurate Y measurement
usual 2 mirors BS assume no losses at mirror
ohse difference between two waves phi = factor due to path diff + additional phase delta phi due to reflections (constnat)
since R and T are for intensities the resultant waves moduled (A not I) both by sqrt(RT), typical 5050 BS => T = R = 1/2
enforce that A1^2 + A2^2 = A0^2
What does the detector measure in a michaelson I
The time avged intensity
I = 1/2 nc ep0 AA*
where A is the resultant E wave of summed two beams towgether
I = 1/2I0 (1+cos(theta))
when you sub in teh E = sqrt(RT) A0 exp{i(wt+phi0} (1+esxp(iphi))
where the exp (iphi ) contrib is the shifted wave (addiational phase …)
Howdoes interfereogram output look
Intensity vs time
peaks and troughs
peaks at separations of mY -> 2mPi
troughs at sep of mY/2 -> (2m+1) pi -> half wavelgnths (total destr)
What is used to move th edelay stage
not a micrometer since that is not nm secnsitive
use piezo electric crystals to adjust OPL and cycle through many many cycles of peaks and troughs in intensity to get a good grip on Y (statistically)
Def coherence length
The max path difference delta s that still gives interference finrges in the plane B is limited by the coherence length of the incident radiation
spectral lamps the coherence length is a few cm , usingsingle mode stabilized laser this is several km.
what if you go past coherence length
IRL never get infinite coherence length since that requires perfect Y, if you only see a constnat I you are past the conherence length and no interference pattern is visible
Use of MI
LIGO
side arms of 1km where OPL can be increases to 100km by using highly relfective mirros and ultra stable laser with very very long coherence length
Spectral resolving power of MicInt calc
Y/dY = ds/Y
determine by saying the the number of maxima at Y1 -> N1 and numebr of maxima at Y2 -> N2 must differ by at least 1 to resolve them N2 >= N1+1
note then that you mean Y1 = Y2 +dY rearr to get resolution
Spectral resolving power of MicInt in words
the spectral resolving power ( how closely can you distinguish wavlengths)Y/dY of the MicInt = the amximum path difference delta s/Y measyred in units of wavelength
hwo does wavlenth relate to number of maxima achineved in the michaelson interf
Shorter wavlength means more cycles can fit in which means more maxima
longer Y -> smaller N (#peaks)
in multiple beam interferometer what does F or R determine
and phi
F (not the finesse) determines the peak height (F(R))
phi determines the periodicity of the peaks
in IT and IR expressions
Sagnac rundown
1) BS splits incoming beam into a trans and refl beam as usaul
2) two beams circulate in xyplane in OPP directions while the whole interferometer roates around z axis
3) OPL diff for two beams
phase shaift between partial waves -> interference
this change can also be attrib to dopler effect
How can you make sagnac more effective
Have optical fibreas circulate N times round cavity such that the effective area become NxA and that increases teh sensitivty significantly
it is already very sensitve to even small angular velocities Omega since that changes path length
what is triangle phi usualy here in interferometers
Phase shift between two partial waves that interfere
