formal lab report_brillouin

8/13/2019 Formal Lab Report_brillouin

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Determination of velocity of sound in Carbon Tetra-Chloride and

Methyl Acetate by Brillouin Scattering

Rohan Ramdoyal1 996414759

1University of Toronto

In this experiment, the velocity of sound in Carbon Tetra-Chloride (CCl 4 ) and Methyl Acetate (MeOAc) as determined by investi!atin! "rillouin #catterin! of a $%%nm of a continuous ave laser li!ht usin! a &abry-'erot interferometer The experimentally measured values

obtained ere found to be in a!reement ith data found in literature

Keywords —Brillouin Scattering, Fabry-erot !nterferometer, Sto"es scattering

!#!$T%&D'CT!&$

Brillouin scattering is the inelastic scattering of light that

arises due to collective time-dependent density changes in a

medium such as sound aves! "hen sound aves ith

velocity Cs and fre#uency $s), ave vector qi travel in li#uid%

regions of different densities are set up as a result of the

rarefactions and compressions hich modulate the refractiveinde& of the medium! "hen incident light ith ave vector

( i, avelength ) and fre#uency i and speed ' interacts ith

such a li#uid of refractive inde& n% the light gets scattered

(ecause the li#uid acts li)e a diffraction grating! *iven that the

grating moves at the same velocity as the sound aves $Cs+%

the scattered light o(served ill have fre#uencies that are

,oppler shifted (y a fre#uency e#ual to the sound ave

fre#uency $s+! The interaction picture is given in igure 1!

Figure 1: Interaction picture of Incident light with the liquid

sample#

The sound velocity Cs is related to this ,oppler shift (y

Cs . C i / 0ns sin$θ/2) (1)

ince the velocity of sound in li#uids is of the order of 1

)m/s% the corresponding ,oppler shift is of the order of 1*23

hich is small compared to the incident lights fre#uency! The

detection of such relatively small fre#uencies is made possi(le

(y the a(ry-erot interferometer $+! The consists of 0

mirror plates that are highly reflective separated (y a distance

d and lo transmission coefficient that allo light to gothrough! "hen light of avelength ) satisfying the folloing

relation stri)es a mirror% constructive interference of the

transmitted light ta)es place

0nod . m ) *0+

"here(y m is an integer and no is the refractive inde& of the

medium (eteen the plates% hich in our case is air! "hen the

distance d is ramped such that it covers multiples of ) %identical pea) patterns corresponding to the fre#uencies of the

transmitted light are displayed! n this e&periment% there ill

(e a central pea)% called the Rayleigh pea) hich correspondsto the elastically scattered light% and 0 pea)s that arise due to

Brillouin scattering! Because of the ,oppler shift% one pea)

ill (e measured ith higher fre#uency than the Rayleigh

pea) $to)es pea)+ and the other ith loer fre#uency $8nti-

to)es pea)+! The distance (eteen to identical pea)s

represents the ree pectral Range $R+ hich is given (y

#uation :

R . *c+ d $:+

!!# AA%AT'S A$D %&CD'%

The optical setup is shon in igure 0! t consists of a6::nm continuous ave 2e;e laser% a sample cham(er to

contain the li#uids (eing investigated% the % to lenses for

focusing the scattered light and a pinhole that feeds the

scattered light into a hotomultiplier tu(e $<+ hich is used

to detect the very lo intensities of the scattered light (y

amplification! n this e&periment% the angle = is set constant at

9>>! *iven the dependence on the angle (eteen the incident

light ave vector $(i+ and the sound ave vector qi % care as

ta)en to ensure that the interaction occurred in a hori3ontal

plane and not inclined! This as done (y ensuring the (ac)



reflection of the laser from the and sample cham(er ere

incident (ac) into the laser itself! The s operation is prone

to fluctuations in vi(rations and temperature in the

environment ?0@! 2ence the hole apparatus is cooled for at

least an hour using a heat sin) (efore the e&periment is

performed! The alignment of the as done (y first using a

mirror ith the hotomultiplier pinhole closed! The laser as

turned on and the mirror spacing as changed using the

)no(s until circular fringes appeared on the pinhole! Thesefringes ere focused onto the pinhole using lens A0! The ramp

function of the as then activated until concentric circular

fringes appeared to (e converging onto the pinhole! Using A1

and A0% these fringes ere made to coincide e&actly onto the

pinhole center! 8t that point% the is said to (e aligned and

ith the (ac) reflections chec)ed as mentioned previously% the

e&periment using the li#uid samples could (e performed ith

the configuration in igure 1 respected% al(eit ith =.9>o!

Figure 2 Optical Setup of experiment ( reprinted ith

permission from "rillouin #catterin! an riel ./%0/1 )

The output of the < is connected to a chart recorder hich

displays the patterns of the pea)s o(tained! The e&periment

as run ith the <e8c sample first and then immediately

folloed (y the ''l4! This as done such that the results for

the 0 samples could (e compared assuming identical am(ient

conditions given the s high sensitivity to am(ient

conditions! The e&periment as performed in the dar) hile

the pinhole as opened (ecause of the very high sensitivity ofthe < to e&ternal (ac)ground light!

!!!# &BS%AT!&$S

The charts o(tained for <e8c and ''l4 are reproduced in

igures 4 and 5 respectively! The R for the samples as

recorded from the chart and the distance d (eteen the plates measured using a vernier caliper as d. $:!>>C/- >!>5+

mm! The R as measured on the chart as a function of its

scale and from #uation $:+% its value in angular fre#uency

units as determined! The ,oppler shift $s+ as then

trivially computed as a fraction of the R from the chart!

Using #uation $1+% the speed of sound as computed for each

sample and is summari3ed in Ta(le 1!

Figure Chart recorded for the MeOAc sample displayin!

the 2aylei!h pea3 and the oppler shifted #to3es and Anti-

to3es pea3s

Figure ! Chart recorded for the CCl 4 sample displayin! the

2aylei!h pea3 and the oppler shifted #to3es and Anti-#to3es

pea3s

Table . 2esults of 5xperiment Sample "elocity measured

(m#s$

"elocity from

literature

(m#s$



%ethyl &cetate

111' #) * 112*

+ar,on

-etra)+hloride .2/ #) 2* .*

!# D!SC'SS!&$

The results seen in Ta(le 1 sho that the measured values are

in agreement ith the values o(tained from literature ?:@ and

hence the e&periments successfully determined the speed of

sound in the samples (y Brillouin scattering! The main source

of uncertainty in the computations as in the determination of

the distance d! 2ad the value of d (een made larger% the

fractional error in its measurement ould have (een smaller

leading to more accurate results! The full idth half ma&ima$"2<+ of the pea)s ere measured and ere found to (e

a(out 6!DE of the R hich as deemed precise enough for

the e&periment! The Rayleigh pea) had the same "2< as

the Brillouin pea)s! 8ttenuation of the sound aves is

reflected only in the idening of the Brillouin ?4@ pea)s% and

not in the Rayleigh pea)% hich can (e #uantified (y the

attenuation coefficient% F, given (y #uation 4

F . "2< / Cs $4+

2oever since the 2"< for all pea)s are the same% e

conclude that the (roadening of the pea)s measured occurs as

a result of the poor finesse of the ! mprovement to this

e&periment for e&perimental determination of α ould re#uire

the "2< associated ith the finesse of the to (e smaller

than the (roadening resulting from the sound ave

attenuation! n comparison ith literature ?5@% the value of

"2< of the Rayleigh pea) ould have to (e less than 1!DEof the R for this analysis to (e possi(le! urthermore% it can

(e seen that from igure 5% the Brillouin pea) cannot (e

resolved (y the to produce a clean sharp pea)! This can (e

improved (y using a multi-pass to increase the 'ontrastratio such that the pea) can (e easily distinguished and

displayed!

# C&$C/'S!&$

ince the e&perimental values of the velocity of sound in

samples <ethyl 8cetate and 'ar(on Tetra-'hloride ere

found e&perimentally to agree ith the values given inliterature% the e&periment conducted as found to (e accurate

and precise! mprovements to the e&periment to determine

acoustic constants and to improve the pea)s resolution ere

also discussed for future or)!

!# % F%$CS

?1@ Brillouin cattering 2! van ,riel 0>1:?0@ Burleigh G Tech memo on a(ry erot nterferometry

?:@ ptical and acoustic properties of li#uids B!H! ,essai - 1970

?4@ 2ypersonic 8(sorption of li#uids ,etermined from pontaneous and

timulated Brillouin scattering 8!lau(reau% "! nglish% "!Iaiser 1969

formal lab report_brillouin

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