CA1286520C - Photodetector arrangement for measuring the state of polarization of light - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
An apparatus and method for the measurement of at least one parameter of the state of polarization of a light beam is described. The apparatus includes only a photodetector and no other optical elements. The detector surface is partially specularly reflecting and intercepts the light beam at an oblique angle of incidence. The absorbed fraction of incident radiation produces a corresponding electrical output signal that is detected and from which the at least of parameter of the state of polarization can be determined. The detector may also be rotated to modulate the electrical output signal to determine the elliptic polarization of light except for handedness. A two detector ellipsometer is disclosed wherein light reflected from one detector is absorbed by the second detector and the entire system is rotated.

Description

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T~ S~ATE OF POLARIZATION OF LIGEIT

1, ~ield o~ th~ I~Y~n~ion ~he prs~en~ lnvention relate~ generally to a relatively simple photopolarimeter and method ~or mea~urin~
the s~te o~ pol~rization o~ a light beam, and mor~
parkicularly per~ains to A unlq~e and simple photopolHrimetor and me~hod ~or measu~in~ A~ l~a~ one paramet~r de~ining the ~t~te o~ polarization o~ a light beam whiçh doe8 not r2~uir~
~ny of th~ u5u~ prio~ ar~ pol~r~2i~g elements such a8 w~ve xetarders ~nd pol~riz~r~.

Many photopolarimeters have been ~oposed and built to measurs the stata o~ polarization of light. See, fo~
exaMple, R,M.~. AZZ~ and ~.L. ~of~ean, VoI. 112 o~ Proc. So~ ~hoto-Opt. I~rum. Eng. ~SP~
~elltngham ~A, 1977).. Generally, the polarimeter~ employ e , sequence o~ polarizing optical e~ement~ such a~ wave : re~arder~ ana linear polari~er3 followed ~y a photodeteotor.
Polar~zation 8an8i~ivlty 0~ pho~odetector~ is con6idered ~n annoyance and a po~ible ~ourc2 o~ er~or ~o be eliminated.
or ar~ ellip~omete~ al80 ~mploy a 8equen~e o~
pol~rizing op~ic~l elements ~ollowed by a photodetector to m~a~ure the pol~rization &tate ~ incident light. U.S.
PAten~ 4,053,Z32 ~i9c109~8 a rotRtin~ ellipqome~er wher~in ~he ligh~ beam ls passed throu~h a polarize~ before being re~ te~ ~o~ ~ ~ampl~ ~Ur~aCe. ~he xefl~ct~d baam 1 ;~

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passed through an encode~, a compPnsator, and an analyzex 1 be~ore bQln~ inc~dent on a photodetector.
SUMMARY o~ THE INVE~TION
._ . . .
In ac~ord~nce wi~h the teachings herein, the pxese~t i~ven~ion is directed ~o a photopola~imeter ~nd method ~hich introduceg a new polarimetric concept, ~hat of combining~ or integrating, the polariza~ion analysls and photodetec~i~n f~nction~ in the same components. The ~pparatus of the pres~nt inYention include6 at least one polar~zation sensitLve photodetector having ~ p~rti~lly speculfl~ly reflecting ~urfa¢e on which ~he light beam is incid~nt, The pola~ization ~ensitiv~ photodetector yroduce~
an electx~l ou~put ~ign~l havin~ a magnitude proportional to the r~diation Absorbed by the photodetector.
A photopolarimeter which is related to the present polarmetric concept is disclosed in Applicant'~
copending Canadian Patent application Serial No. 511,800 filed June 18, 1986.
In that application, ~ light beam is inc~ent on a first photodete~tor h~ving ~ partially specularly xe~ecting ~n ~urfaGe at an oblique angle ~ith ~ first plane Or incidence, and ~s partially r&~lected there~rom. rhe firfit photodetector produoes a f~rst electrical output si~nal havin~ a m~gPitude proportional to the radlatlon absorbed thereby. The li~h~ bqam 18 then $ub~e~uently re1ec~ed and absarb~d by second and third photodetector6 also having partially specu~arly refleotlng ~urfaces which are positioned such tha~ ~he light beam iB incident thereon at ~n a~liq~e angle ~t different plane~ o incidence, that are different ~rom the ~irst plane of in~idenc~. The ~econd ~nd tkird 3 photcdetecto~ also produ~e output signals proportional to ~h~ radis~ion ab~orbed ~hereby. ~he fourth ~low detector i8 to~ally ~b~orbin~ an~ p~o~u~8 a ~ourth electrical ou~put slgnal proportlonAl t~ the r~dia~ion ab~orbed.

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~ n another embo~,imellt di9c:10sed in ~he pre~3nt inventio~ ~ an ellip50met~r i9 provided which in~lude~ a photodetector havin~ a partially ~pecularly refl~cting surface on whi~h the light beam is ir.cident at an obll~ue : :
angl~ and which produ~es an electrical outpu~ signal proportional to the radiation absorbed~ ~leans is provide~
coupled to the photodetector ~or rotating the photod~tector around ~n axi3 defined by ~he ~c~dent light beam to modulate the elec~rical outpu~ signal. An auxillary photodetector that int~r¢ep~s the ligh~ beam r~flected ~rom th~ specularly reflecting photodete~tor may be provided to ~ene~ate a timing pulse ~or angular encoding of the modulsted output signal&.
A urther embodiment includes two photodetect~r~
wherein the ir~t detector has a partially specularly re~lecting dete~or s~rPaoe ~nd the secon~ detector absorb~
at least a portion o~ the light refle~ed from kh~ fir~t photodet~tor, ~n yet another embodiment, the ~ir~t and ~econd photodetec~ors ar~ rot~ted ~ ~ unit t~ pr~en~
second plane of ~ncidenoe for ea~h photodeteot~. The ele~trical sighals p~oduoed by the photodetectors at e~ch of the planes o~ i~cidence are proce~ed to determine the ~lliptic stat~ of polarization.
B~ef-Descri~tion ~_~b~ a~
~IGURE 1 i~ a ~chemati~ diagr~m of an exemplary embodiment of a photopolarimeter utill2i~g ~ polarization ~ensiti~e photodetector of th~ present invention.
~ IGU~E 2 is A schemati~ dia~ram o an exemplary embodiment u~ilizin~ ~wo polariza~io~-sensitive photodetector8.
~IG~S 3 is an exempl~ry ~mbodiment of a rot:ating elllp~omete~ eons~ructed ~ccord~n~ to the pre~ent invention.
URE 4 is a diagram illu~tr~ting the ellipse of p~laxlz~t~on tAken f~om Fi~ure 3.

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FI~U~E 5 is a graph lllu3tr~ting ~he modula~ion depth of the dstected s~gnal ~or incident linearly polariæed li~ht versus the photon energy at dif rerent angles ~
ihcidence.
FIGUR~ 6 is a bloc~ diagram illu$tratin~ th~ -connec~ion o~ a pol~rization ~en~iti~e photodetec~or to a 5ignal proce~sing arrangement.

As shown in ~igure 1, a photopolarimeter may be Cons~ruc~ed ~rom a'single polarization sensitiv~
photodetector 10 ha~ing a spe¢ularly ref.lecting BU~aCe D.
A ligh~ b~am S iq incident upon the ~ur~ac~ D ~t ~n o~liqu~
angle ~ to the normal N of the dbtector 10. A portion S1 o the lig~t~ is reflected from ~he ~urfa~e D whlle ~he compon~nt ~ the incident radiation that i~ not refle~ted ~y the detector 10 i~ ~b~orbed thereby. A proportional ~ignal i is generated a a xesUlt of ~hi absorpt~on and is de~e~ted. ~y ~ntegx~tin~ the polarization-analyRis Rnd ~e~ection ~unctions, we aGhieve a simple and novel polarim~ter ~rom 20 whlch at leas~ one parameter of the polarization of ligh~ ~an : be de~rmined.
~ igu~e 2 shows ~nother em~odiment inc~uding two polarizat~n sen~i~iVe photodetector~ 12 and lq ~aoh havin~
par~ially ~p~cularly reflecting ~urfac~ nd D~. Ide~lly, the ~ete~or ~urfa~es Dl a~d ~2 are pa~allel and ~hey al~o ~-mctlon ~5 a palr of cro~s~d thin ~ilm ref~ec~ion polarizers; however, th~ not e~ontial.
All of th~ incident radl~tion is ~apture~ ~y the ~wo deteotors 12, 14 and eac:h detector ~en~rate~ an output elect~ical ~ignal, 11 And 1~, propo~tional to th~ ~ra~ion o~
radiation lt ~bsorbs. For simplici~y w~ ~sumed the ~110win~ ideal ~power) re~l~ot~nce~ o the de~e~tor ~iuraces ~r incid~n~ p- and 9- polarlz~d ligh~:

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_g_ }~p l ~ Rs l a 82 - 12) P,~u~tions ~1) and ~2) indicate ~hat the sur~ace of Pl a~t~ a8 8n ~de~l reflectior, polarizer and that the sul face of Dz $B
antire~lection-coated ~o~ the s-polarized 1~ ght re~lected by In general, we denote by Ip and 13 the compon~nt fluxes tpowers) o~ inciden~ llght that ar~ polaxized p~rallel (p) and perpendicular ~s) to the common plane o inçld~nce for ~he two r~flec~ions at ~1 and r~2 ~1 ~nd T2 ~ h~3 ~luxes a~sorbed by Dl and t)2 which produce output elec~rical ~ignals il 21nd iz, re~pectiv~ly" Linear photodetection i8 a~umQd so ~ha~
~5 i 2 k 2 2 ' where kl and k2 ~re sensi~tity cons~an~s characteri~tic of nd D2 ~ re~pectively, and inc}ude ~ny postdetection a~pliica~ion ~actors.
When the ideal condition~ of ~:~s . ( 1 ) and t 2 ) ar satisfied, Il ~- Ip and I2 = ~s~ Furthermore, if k,l ~ k2 (i~e. ~ the de~ector sen~itivitie~ ~xe equal o:c ec~ualized), ~he degree of linear polaxization o~ inciden~ light, w~ich i8 de~ine~ by P ~ (Ip ~ Ip ~ I~;), 14) iq ob~ained from the outpUt signal~ of the photodet~ctors by . .
30p= ~ iz) / (il ~ i2)-~ ~ , . . .
.. ~ ~ , . . .

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1 Equation (5) indicates that, with such an a~rangement, we hav~ perhap$ xealized the simplest possible instrument for measuring the deg~ee of linear polarization of light.
Por Si photodetectors, null reflec~ances, Rpl ~ 0 and Rs2 ~ can be readily ~chieved by si~gle-layer coatin~
at a given wavelength. For ex~ple, at A = fi32. anm ~o~ th~
often-used ~e-Ne laser~, ~pl ~10 S At the pseudo-~rewster angle~ ~ = 75.44~, of ~are Si wl~h ~omplex refractive index 3.~5-jO.0~. In this CA e R~l = 0.76 and the second of E~s.
0 ~1) i8 not Qatisfied. To ma~e Rs~ ~ o a~ ~he same ~gle (p~rallel detecto~ ~ur~ces), the Si sur~ce of D2 i~ :
coated with a tran~parent layer ~ re.rac~ive lndex 1~37 ~.g., M~2) a~d of ~uax~er-wa~e optical thickness ~ .2nm actuAl thickness). A p~3~ective layer of hal~ave optical ~hlckness of the ~ame (or o~ different, e.g., Sio2) di~lectric can be applied to Dl, withou~ affecting the condi~lon ~p~ = 0. Multila~er ¢oa-ings ~re rPquired to satisfy all o4 ~ ~1) and t2). a~ least approximataly, ~er the u~eful $pe~t~1 bandwidth o~ the pho~odetector~.
It is not essential th~t ~he two detector surface~
be p~rallel or that they shou~d ~unction as a pair of Grossed . polarizers, desirable ~s thesa conditions m~y be. However we wil~ continue to assume a ~ommon plane of in~idence r-or ligh~
refl~ctions at the su~faces o~ the two detectorc Dl and ~2~
In terms of ~pl~ R~l and Rp2, R~2, the p And s rbflectances of Dl and D~, re~pecti~ely, ~he detected signals are given by Rpl) Ip ~ ~1 - Rf~l~ I

2 2 p2) ~p1 Ip I ~1 R82) R;1 Is~ (6) 3 It~ Eq~ ), Xp and I E~ Are the compc)ne~t .~lux~ ~f incldent light that are p ~nd ~ polarized, Bnd k;L ~nd k2 ~e the '' '' , . ~ .

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photodete~tion ~en~itivity constant~ o~ Dl and ~, 1 r~spe~tivel~, as has ~l~eady been indicated~ Equa~ionS (6) can be writt~n in ma~rix ~orm:

~ Pl ) L ~ L J l J
wher~

~1~ = k~ pl) ~ al2 ~ k~ Rs~
a 1 ~ ~Rp~ p2)~ a~2 ~ k2Rsl ~ s2 Put mor~ concisely, Eq. ~7) reads ~ ~ q I, wher~ 1 i2~t is the si~nal vec~or, ~ = (Ip I5)t is the flux ~e~tor (w~ere t in~icates the ~ran~pose), and a =
~ ) i6 the 2x~ ins~rum~n~ matrix charac~eri~ic o~ the ~wo a~ photodetectors. ~rom q. ~9), I a~l i (10 which lndi¢ates that the input ~lux vector I ls obtained by premultiplying the outp~t signal v~ctor 1 wi~h the inverse ~f the instrumen~ matrix a ~ na~biguou~ determina~ion of I from Eq. (10) reguirefi that a 1 ~xi~ts, i.e., a mu~t be nonsingular. I~
turn, ~ i8 nonsin~ular when i~8 determ~nant i5 not zero, l.e.
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det a ~ 0, ~11) ~rotn } q5 . ( 8 1 we get , d~t a ~ a11 a22 - a1~ a21 - k 1 k ~ [ RS ~ RP ~ R5 2 ) P 1 ( 1-RP ~ ~ ] . (12) It is instruc'cive to COnSider SOme e:Pe~ia1 ~aS~5 a~
10 ~XamP1eS~ I.Ft US aSSUme ident~ deteCkOr5 and d~OP the SUbSCriPtS ~ ar~d 2 frOm E~ 2) I ~e Obt~in det a ~ ~2 ~RB ~ ~P) t1 ~ P~S) l1 - RP) (13) 15 Apar~ from the tri~tially ob~ious r~quirement that k~0, Eq.
ti3) shows that the c~nly essen~ial condi~ion for D. to be nonsingul~r is tha~
.
Rp ~ Rs i~ 14 ~

A particularl~r simple ~orm of the deJcerminant is obtained if we further a~sume inciden~e at 45 on un~oated detec~or sur~ace~t in this ca~e Rp ~ R~2, and Eq, (13) redu~3 ~co det a ~ k2 Rs (1 + Rs) ~ s) 3. ~15~

~or Si wi~h the xefr~ctive index 3.85-jO.02 at A ~ 6~2.8nm, '8 ' 0-47 a~ 45~ incidence~ and det a ~ O.lk2, from E~. ~lS),, Cos~ider also the e~se o~ parallel Si detec~or 30 ~urfaces that ~r~ coa~ed such that P~pl ~ O, Pc!3l = 0~76~ ~s2 ~
O at th~ ~ame angle o~ inaidence ~ ~ 75.44 Rnd A~ 632.8nm. Here aii ~ ~5qg~ lmplify to :: .

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. ' 1 all ~ kl, al2 = 0.~4kl, ~16) a21 ' a22 0~761;2t and det ~ ~ 0.76 ~lk~. (17) Ae a final example, ~onsid~r ~hb ar~ang~ment obtained ~en th~ ~econd dete~tor sur4ace is set to intercep normally ~and totally absorb, ~ging an ant:~reflection co~ing) the liqht beam reflected from the f~rst ~e~actor. In this case all and ~12 ~ Eqs. (8~ remain unahanged but a21 and a2z becom~

a21 k2 Rp " ~2~ = k2~sl The ~ete~inant o a reduces ~o d~t a ~ klk~ (Rsl RPl)' ~lg~ . .

which is nonzero provided that ~lk2 ~ 0 ~nd Rsl ~ Rpl.
For Si d~tectors at A = 632.8nm, in~iden~e at 75.44~ on ~he irst surface, whi~h ~s ~ncoa~d or ~o~ted ~ith a t~an~parent prot~c~ive dielectri~ ~yer of half-wave optical thickness, kes Rpl = ~ ~sl ~ 0~76 t and det a ~ 0.7fiklk . ~he - second sur~ac~ can be antireflection-co~ted at normal inc~denc~ usin~ a Si3~ ilm o~ reractive index 1.9622 and of 80.4nm thiekness, onc~ the input ~lux ~ ur I is ob~ained from Eq.
~)~ tha degre~ of linear pol~rization o~ the incident light P can be d~ermined f~om E~. ~q), , .
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~36S;~i~3 Figure 3 shows a unique el~ipsom~er that use~ only l a photodete~t~r 16 and dispenseg of all other optical elements. The detgctor surface ~o is partially specularly r~fle~ting and is set kO intercep~ the inco~ing li~ht ~eam So ~t An oblique angle o~ in~iden~ ~O. Only a ~raction of the inciden~ radi~tio~ is abso~bed ~;nich depends on the in~ident polarization and the azimuthal orien~ation or the plane of insiden¢e ~POI)I The detector ~s s~nchrono~51y rotated around ~he li~ht be~m as an axis~ ~he surface normal No preceyseS in ~ ~onical ~ashion and the POI ~ecomes ~
0 revolving plane th~ou~h and aroun~ ~he ir.~id~nt beam. The output electri~l sign~l id of the L~hc~cdetector, ~hich is propor~ivnal to the frac~ion of radiation it absorbs, i~
modulated by ~he rota~ion. It is this modula~ion ~ha~
determineg the input state o~ polari~ation~
~igure 3 is a ~chem~tic di~gram o~ this simple rotating-deteotor ellipsometer (ROD~. The detector Do is mounted~ in a tilted orientation, on the sh~f~ o~ ~
$mall synchronous motor M that ~t~tes a~ ~n angul~r speed o. The light be~m So, whose ~ta~e of polarization is tO be ~ measured, strike~ ~he çpecularly reflee~ing detector surrace ~o at sn an~le of obli~ue incidence ~o. The absor~ed r~di~tion genera~es ~he outp~t electrical signal id. P ~nd s deno~e ~he orthogonal linear polarization dire~ions par~llel p and perpendicul~r s to the plane of incidence ~the plane o~ the page ~n Fig. 3), . A ~ixed reference plane, with respect to Which the Az~muth of the major ~is of the polarization ellip3e is determin~d~ i8 established by a s~ll aperture 18 and an auxil~ary de~¢tor Da that is placed to ir.tercep~ the 3 ~coni~ally) r~t~t~ng ~lected ~eam~ ~h~ outpu~ sign~ o.
Da provid~ a re~rence t:Lmln~ pulse that permit~ the . 35 - . ~ . .
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~ ~ ~ 6~2 l determination of the azimu~h of th~ polarization ellipse ~ro~
the p~se angle of the Ac co~pon~nt of i~. It iB al~o possibl~ to u8e an array o~ photodetectors, po$iti~ed behind a uni~orml~ angularly ~paced array of holes or slit~ ~o~nd the Circ~Mferen~e of a circle traced b~ the reflec~ed light be~m, as an angular encoding s~heme or the digi~al sampling 0~ the detecked signal id.
With referenc~ to Fig. 4 le~ a and jb, where ~ ~nd b are real and j = ~ , be the phasor component-~ of the ~lectric ~ec~o~ o~ ineident ~otally pola~ized light alon~ ~he major ~nd ~ino.r a~ o the polaxizctlo~ ellipse. ~he orthogon~l directions p a~a s ~parallel and perpendicular to the plan~ o~ incidence) ~ot~te uith the rotation of the de~c~ox at the angular speed ~o, and B is the instan~:aneous azimuth h~tw~n t.h~ major 2Y.i~ ~ f th~ ellip6e and ~he rot2ting p ~xis. The p and g phasor ~omponents of ~he elec.-ic ~.~e~tor are obtained by simple projection as Ep - a cos ~ ~ jb sin ~, (21) s = a sin ~ + jb cos ~.

~part f rom a multiplicative cons~ant, the corroqponding p-and s- polarized ~omponent fluxe~ of incident light are ~p ~ Ep ~ p - ~ Io ll ~ cos2~ cos2~), (21) ~ -I - E E = ~ cos2~ cos2~), where : Io ~ Ip ~ s ~Z2a) ~ a~ + b2 cos2~ ~ (A~ - b2)/~a2 ~ b2)~ ~22b~

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, i -, . - . , --~ 2--E_ tan~l ~b/a~ he ellipticit~ angle ~hich falls in th~
~an~e -45~45; ~.he limiting ~value~ of ~- -45~ ~nd ~= ~4S
rQpresent l~t- and right-handed circ~larly polarized light, respec~ively ~ The light f lux Absorbed by ~he photode~ecto~
5 is given by Id a (l-Rp) Ip t ~l-RS) Is~ ~23) where Rp and R e~re the ~power) reflectanc~ o_ h~ det~ctor 10 surface ~or inciderit p- and 8- polarized li~ht. W~ ascum~
lirlear ph~tv~etec~tion, ~v th~t the outpu~ electri~ iqnal o~ the d~tectox i~
id ~ k ~d~ ~2~) .

~:h~re th~ sensitivity con~t2nt k i~ ir dependent or It3 but may vary :it)~. ~.avelens~h. Substitutior. of E~s. ~l) and ~22a~
into ~q. ~23), and using tne result into Eq. 12~), yield the simpLi~iad e;:pression id 5 io 11 ~ m cos2~ 25 where .:
io ~ k Io (1 ~u) ~ ~26) P~ Rp + Rs) ~ (~7) m = mI, c09 2E ~ (28) m~ R~; - Rp) / t2 - R5 - Rp) . ~ ~g) 3~ Ru or Et~o ~27) i5 ~he de~ector suxfa~e re~lec:tan~e fox incid~n~ unpolarized or circularly polarized light. :~n Ecl~ :
~25) m repxesents t}~e modulAtion d~pth o:~ the detecte~ ~ignal ~ratlo o:e amplitudes o~ ~he ac and dc compon~nt~ o~ th~ :

.

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~ S2 ~
1 signal) that resu~ts ~rom rota~ion o~ the dete~tor. Equation ~8) lndicAtes that when ~- 0, m - mL; i.e. mL i~ the ~odula~io~ depth obtained when the incident lig~t is linearly polariæed.
Equation ~2~) tells us that ~L i5 also ~ p~op~r~y o~ th~ detector su~ace at a given angle o~ inciden~e and wavelength, In ~i~. 5 m~, computed ~rom Eq. (29), is plotted A~ a unction o~ photon energy between 1~5 2nd 6 e~ ~or an Uncoated Si su~face using known optical constant~, at three angles o~ incidence ~ = 451 60 and 75. At a giv~n ~ ~L
ch~nges within a narrow r~nge7 e.~. et ~ ~ 6~, 0.355 ~mL
0.519. Purthermore, mL incr~ases as ~ in~rease~ and approac~les 1 a~ ~ ~g0~ (broken cur~e).
mL can be determined by ~alibr~tion, or.ce ant ~or all, ~or a gi~en detector ~ a gi~n angle o incidence ~y ; recording the modulation depth o~ tne detected signal a~
~unction of waveleng~h with a (broad-band, ~ery-low-extinction-~atio) linear pola~izer placed in th~ path o~ th~
light be~m.
When incident light of unknown polarization shines on the ~otatin~ p~.otodetector, the resulting measurea modulation depth m determines the ellipticity ~ngle ~y cosZ~ - m/mL~ t30 ~rom Eq. (28), where m~ i now considered Xnown. ~he siqn of : i5 indetermiAate and RODE is handedness ~lind, si~ilar to known rotating-analyzer ~llip~ometers.
; ~he instanta~eous azimuth ~ that appe~ri in E~.
~ t20), ~21) and (2S) can ~2 wr~t~en as ; 30 ~ ~0~ ~31) :

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~ ~6 5~(~
1 where ~0 is the desired m~jor-axis azimuth of the polari2~tion ellipse rn~asured ~rom ~he fixed re~renee plane Ithe reference direc~i~n r in ~ig. 4). 5ub~titution of ~.
(31) lnto Eq. ~S) glvas id i~ m co~ ~2~ot + 2e~)]. .~32) Equa~ion 132) shows that t~e azimuth angl~ ~0 i~ deter~ined ~y the phase angle ~f the ac ~omponen~ of the dete~ed signal id ~hose frequency-is dcu~le the rotational frequency of the da~ecto~, ~he timing pulse fro~ th~ auxiliary det~ct4r ~a in FLg, 3 de~ines the time ~ - 0, or the besinning o a perlod ~of dur~tion ~/~) o~ th~ periodic signal i~ o~ Eq.
(32), The advantayes ~f RODE are summzrized below.
(1) RC~DE iS the simplest possible ~llipsometer b~c~use it has the least r.umber o, optica~ co~.ponents, onl~
one - the pho~odetector it~elf, ~or polari~a~ion measu_ement.
(2) Ro~ is sui~ed for speetroccopic ellip ometry 2~ beoa~se its spectral r?nge i~ limited only b~ a~ail~bl~
pho~odete~tors, and not by ar.y other pc.lari~i~g optical el~ments. .
(3) ~imin~ pulses, ~s~ntial fox ~bsolute a2i~uth measurement and analo~-~o~di~it~l conver~io.. ~f the detected ~ignal, are ~eadily available b~ interceptin~ the rotating reflect~d ~eam ~y ~n ~rray of auxiliary detectors arranged 2round ~ ci~cle.
~ 4~ A simple c~llbr~tion procedure permi~s the direct determin~tion of ellipticity an~le Irom the modulation d~pth of ~h~ det~ed signal.
t5) The sensitivity o~ the ellipbometer can b~ ~
conv~nient-ly ~on~roll~d by ad~u~t~ n~ the angle o~ incidenc~
~0 . .

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3L;~ ~65i2~
I:)ielectric~laye~ Coatirlgs can al o be applied to the d9~ec~r 3urface to alter its ref lectance ~haracteri!3ticsi and a~hieve optlm~l performance ove~ Certain spec~ral ~nges.
Alte~natively, to measure the ellipse (state) of po1Ari zation of in~ident totally pola~ized light, ex~ept ~or handedne5s, the t~h~o-~etector system of ~igure 2 is ~otated as one unit around the irciden~ ~eam b~ a pre pet;:ified angle ~
and the measuremer~t of P i~ ~epeated. TQ main~ain a ~omItlon plasle C~f inci~ent:e fc:~ the ~wo refl~ctior~s independen~ of the 10 rotation of the detector as6am~1y, ~n:i xetain mechaniC~l simplicity, the detector s~lrfAcf~s should be parallel Th~ input stat~ of polariz ~ion i~; repr~sen~ed cor~cisely ~y the o~mplex polarizatios~ nurr~er X ~ I;s / Ep - tan~ exp t~ 33) where l:p and E~ are the phaso~ ~mpor.ents of the electri¢
ec~or o~ light parallel and perpenQi~ular ~o the plane of inciden~, respe~tively, in the referen~e orier~ta~ion ~ = O.
20 The deg~ee of linear polarization ~ iB relate~ to X by P ~ XX ) / ~1 + XX ), ~34 henee p ~ ~o~

if Eq. (33) is use~. Ro~ation o~ ~he dete~tor ~berhb.Ly rotate6 the plane of incidence ~y the an~le ~. A con~reni~n~
O choice of ~ ~ 4S ~crans~orms .

-~ ~3652~`D
X ~o X' wher~

X' ~ ~X 1) / ~x ~ 3~) From Egs- t33), ~34) and t35), the deqree o~ polari2~tior. P' in ~e new ~ ~ 45 orientation i~ ~iven ~

P~ = sin2YJ cos ~ ~ 137) According to Eqs, ~35) and (3~), measurements of P an~ P' determine thQ polarization p~rameters ~ and ~ ~i~ply, directly, ~nd compl~tely. ~etice, ho~ever, that it is ~os~ :
th~t is determined. Con~eouently the si~n o~ ~, hen~e the handednes~ o~ the incidenk pol~rization, remains amblguous.
The ~itua~ion is identical to that encountered in the ~5 ro~a~ing-analyzer ellip~ometer.
A ealibrated scal~ for ~he deteotor rotati~n is no~
necessary~ ~r.ly pinncd rotation~l pOgitibn~ at ~ ~ O
(ref~rence), ~ = 45, an~ ~ c 900 ~re needed. Mech~ni~l rotation can b~ altogeth~r avoided if a half-wave reta~der :~ :
(HWRI is inserted in the incident beam to achie~b ~n e~uivalent rotation O r the plane of incidence. The half-wave retar~ation can be electro-opticall~ or piezo-optic~lly induced 50 that an ellip~o~eter ~ith no moving p~rts iæ
obtained, ~t should be noted th~t the degree o~ linear polarization P of incident totally,or partially polariz~d ; li~ht is of its o~in important in ~everal appli~ations, such ac ir. atmospheric optic~ and in line~r-dic~roi~m measurem~hts, and it can be measure~ ~a ~ by the two~detec~or ellipsometer (IDE) in th~ ~ = O orientation.
3 ~he inst~ument matrix a can be calculated from t~e known ah~r~at~ristic~ o~ the two det~tors u~in~ ~q~

~.
:;

l Howe~er, ~ more practical approach is to detexmne a by ~alibration~ a is a function of wavelength and must be measured over the u5eful sp~ctral bandwidth of ~he detectors.
A light source-monoc~rom~tor ~o~bination produces collimated monochromatic light be~m which is linea~
polarized by pa~s1ng i~ through a good (~rystal1 po.l~ri~er.
The d~tector assembly i~ set in ~he ~ = O referen~e orientatiOn ~nd the polarizer is ro~ted ur.~il the transmi~ted electric vectox i5 parallel ~p) and t~ the plane ~ incidence. The input 1~x ve~to~ becomes I = ~I~ o)t, The output signals of ~he two photode~ctors, denote~ by ilpC and i2pC, are r~corded AS ~un~ti~ng of ~avelen~th A.
~t ~ given ~ pC ~s ~he maximum outp~t signal of uncoa~ed, ox very-t~in-~ilm-coated, detector that i~ ob~ained when the polarizer is rotationally adjusted ~o its prop~r ~zimuth~]
~ 'ith ~he polariæer fixed, the detector as~e~bly is r~tated ~Q itQ ~ ~ ~0 position. The input light is now s pol~xized, with flux vector I = (0 I~ nd thq induc~d 2~ g s ilSC and i~se of the ~wo photodetectors are again recorded. ~ThP flux of light leaving the polarizer Ic i~ the same in the ~ - 0 ~nd ~ ~ 90 c~libration ~teps if a stable sour~e is used, but Ic may vary wi~h ~.) Th~ ~our calibration signals i~pc, i2pC, 1lS~ and i2~ ~r~ su'ficient to determine the instrument matrix a throu~h Eq. ~7)~ the re~ul~ iB

l ~ilpC(~ 5c(~) a ~ , ~ 3~) IC(~) l/2pC~ 2sc(~)1 -~ ~ .
.

-1~
~ 5~ ~
wher~ th~ argu~ent A ha~ been ~dded ~o emph~ize ~he wavelen~th dependence of ~he various quantitie5. IC~Al need not be measure~ ar.d r.o absolute pho~ometry i5 required. To determine P reouires onl~ that a ~e cetermined up to a Cons~ant ~cal~r multiplier. Thereiore, the ltIC~) term in Eq, (38) can be ignor~d.
Cali~ration of a given TD~ neea only ~e c~r~ied out on~e, ~n~ ~h~ instrument matri~ s~ored or all subsequen~ polarization measure~ents. ~he T~E can be interfaced wi~ an on-line microcomputer which acGept 1~ input the digitized (sample~) ou~put siqn~ls of the two photodete~tors and produ~e~ ~he d~sired polariza~ion parameters of the inciden~ light A5 output.
This type o~ instrument i9 p~rticularly u~eful or 201a~ tion-~tate measurements in th~ ~acuum ultra~iolet, 1J ~:here cor.ver.tior,a'. tr5.nsm'ssion optics are not usable. In thi~ spect-al range he pho~ons are energetic enough to eje~ c~rons from the ~i-ror sur.aces, and these e}ec~ron ; currents can he ampli-ied b~ suitable dynode st~uctures.
Pigure 6 is a bloek dia~ra~ of an eY~emplary signal processing arrangement in which the ou~put signals o~ one or r.ore ohotod~tector~ D are initi~lly ampliried at 20, and are ther. eonverted to diqit~l equivalent values by ~r,alog to digit~l convert~rs 22 which a~e directed ag inputq to a processor 24, preferably a microprocessor, which per~orms the ~5 necessary c~l~ulations. In an alternative embodiment, the processor ~ ~,ay be equipped to handle th~ AID conversions.
A~ sho~n in ~igure 6, ~ny of the instruments o~
~igu~eg 1, 2 or 3 c~n be readily inter~aced to an on~line microcomputer ~4 which recei~es as its input the digitized 3 output electricAl ~i~nals, ~he microeomputer determines the ~he s~t~ of polz~ri~at~on o ~he li~ht beam. In u~e t~i~]l the ' ' :. , . .
.
.. . .
. - , . .
.
.

5~
1 ellipsometers described abova, the microcompute~ 24 may ha~e t~e calibration data stored in memory to de~er~ine ~he state of polarization, The result can be displaye~ on a suita~le output de~io~ 26.
~hile several embodi~.ents and ~ariations of th~
p-esent invention ~or a photodete~tor a~angement or measuring the sta~e o~ polarization of li~h~ are described in detail herein, it should be apparent that the disclosure and teachings of the present invention will sugg~$t many alternatiye designs to those skill~d in th~ art~

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.

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.,' ~ ' ,'. ' . ' ' "' " '' ' ' ' ' .' ~ ' ' ' ~ . ~ ' . '

Claims (42)

1. An apparatus for the measurement of at least one parameter of the state of polarization of a light beam comprising: at least one polarization sensitive photodetector having a partially specularly reflecting surface on which the light beam is incident, said polarization sensitive photodetector producing an electrical output signal having a magnitude proportional to the radiation absorbed by the photodetector from which at least one parameter of the state of polarization may be determined.

2. The apparatus of Claim 1 wherein the photodetector is positioned to intercept the light beam at an oblique angle of incidence.

3. The apparatus of Claim 1 further including means for determining at least one parameter of the state of polarization or the light beam from said electrical output signal.

4. The apparatus of Claim 1 further including means for rotating said at least one photodetector around an axis defined by the incident light beam.

5. The apparatus of claim 1 wherein there are two of said polarization sensitive photodetectors such that;
(a) a first of said photodetectors partially reflects the light beam incident thereon and produces a first electrical output signal having a magnitude proportional to the radiation absorbed by the first photodetector; and (b) a second of said photodetector being positioned so that the light beam partially reflected from the first photodetector is incident on said second photodetector and produces a second electrical output signal having a magnitude proportional to the radiation absorbed by the second photodetector.

6. The apparatus of Claim 3 wherein said means for determining the at least one parameter of the state of polarization includes a microcomputer.

7. An ellipsometer for measuring the state of polarization of a light beam comprising:
(a) a photodetector having a partially specularly reflecting surface on which the light beam is incident at an oblique angle with a plane of incidence and is partially reflected therefrom, said photodetector producing an electrical output signal having a magnitude proportional to the radiation absorbed by the photodetector; and (b) means coupled to said photodetector for rotating said photodetector around an axis defined by the incident light beam to modulate the electrical output signal.

8. The ellipsometer of Claim 7 wherein said rotating means includes a synchronous or stepping motor.

9. The ellipsometer of Claim 7 further including means coupled to said modulated electrical output signal for determining the state of polarization of a light beam.

10. The ellipsometer of Claim 7 wherein said rotating means rotates the photodetector such that said photodetector precesses about an axis normal to said specularly reflecting surface whereby said light partially reflected therefrom is a conically rotating reflecting light beam.

11. The ellipsometer of Claim 7 further including means for determining the azimuth angle of the plane of incidence of the light beam.

12. The ellipsometer of Claim 11 wherein said means for determining the azimuth angle includes an auxiliary photodetector the intercepts the light beam reflected from said specularly reflecting photodetector, said auxiliary photodetector producing an auxiliary electrical output signal in the form of a timing pulse.

13. The ellipsometer of Claim 12 further including a plurality of said auxiliary photodetectors positioned around said specularly reflecting photodetector to intercept the rotating reflected light beam at a plurality of angles to provide an angular encoding scheme for converting said modulated electrical output signals to corresponding digital signals.

14, The ellipsometer of Claim 13 further including means coupled to receive said corresponding digital signals for calculating the elliptic polarization of a light beam.

15. The ellipsometer of Claim 13 wherein said calculating mean is a microcomputer having calibration data obtained with a linearly polarized light beam stored therein.

16. The ellipsometer of Claim 12 including means coupled to said modulated electrical output signal and said auxiliary output signal for determining the input state of polarization of a light beam with respect to a reference plane of incidence of the light beam.

17. The ellipsometer of Claim 16 wherein said means for determining the input state of polarization includes a microcomputer having calibration data stored therein.

18. An apparatus for the measurement of at least one parameter of the state of polarization of a light beam comprising:
(a) a first photodetector having a partially specularly reflecting detecting surface on which the light beam is incident at an oblique angle and is partially reflected therefrom, said first photodetector producing a first electrical output signal having a magnitude proportional to the radiation absorbed by the photodetector; and (b) a second photodetector having a detecting surface on which the light beam partially reflected from the first photodetector is incident, said second photodetector producing a second electrical output signal having a magnitude proportional to the radiation absorbed by the second photodetector.

19. The apparatus of Claim 18 wherein the light beam incident on the first photodetector and the partially reflected light beam incident on the second photodetector are incident at a common plane of incidence.

20. The apparatus of Claim 15 wherein the detecting surface of said second detector is a partially specularly reflecting surface.

21. The apparatus of Claim 20 wherein the partially reflected light beam is incident on said second photodetector at an oblique angle.

22. The apparatus of Claim 19 wherein the detecting surface of said second detector is a substantially totally light absorptive surface.

23. The apparatus of Claim 22 wherein the partially reflected light beam is incident on said second photodetector normal to the detecting surface of said second photodetector.

24, The apparatus of Claim 20 or 22 wherein the detecting surface of said first and second photodetectors are parallel to each other.

25. The apparatus of Claims 20 or 22 including means coupled to said first and second output signals for measuring the degree of linear polarization of the light beam.

26. The apparatus of Claim 24 including means for rotating the first and second photodetector as an integral unit by a predetermined angle with respect to the light beam incident on the first photodetector, said first photodetector producing a third electrical output signal at the rotated position and the second photodetector producing a fourth electrical output signal at the rotated position.

27, The apparatus of Claim 26 including means coupled to receive said first, second, third and fourth electrical output signals for determining the state of polarization of the light beam.

28. An ellipsometer for measuring the state of polarization of a light beam, comprising:
(a) a first photodetector having a partially specularly reflecting detecting surface on which the light beam is incident at an oblique angle with a first plane of incidence and is partially reflected therefrom, said first photodetector producing a first electrical output signal having a magnitude proportional to the radiation absorbed the first photodetector;
(b) a second photodetector having a detecting surface on which the light beam partially reflected from the first photodetector is incident at a plane of incidence, substantially coincident with the first plane of incidence, said second photodetector producing a second electrical output signal having a magnitude proportional to the radiation absorbed by the second photodetector;
(c) means for rotating the plane of incidence of the light beam incident on the first photodetector to a second plane of incidence different from the first plane of incidence, said first photodetector producing a third electrical output signal at the second plane of incidence and the second photodetector producing a fourth electrical output signal at the second plane of incidence.

29. The ellipsometer of Claim 26 wherein the detecting surface of said first and second photodetectors are parallel to each other.

30. The ellipsometer of Claim 29 including means coupled to said first, second, third and fourth electrical output signals for measuring the polarization parameters ?
and cos .DELTA..

31. The ellipsometer of Claim 30 including means for storing calibration data to thereby determine the state of polarization of the light beam.

32. The apparatus of Claim 28 wherein the detecting surface of said second detector is a partially specularly reflecting surface.

33. The apparatus of Claim 28 wherein the partially reflected light beam is incident on said second photodetector at an oblique angle.

34. The apparatus of Claim 28 wherein the detecting surface of said second detector is a substantially totally light absorptive surface.

35. The ellipsometer of Claim 28 wherein said rotating means is provided by a half-wave retarder inserted within the light beam incident on the first photodetector.

36. The ellipsometer of Claim 35 wherein said half-wave retarder is an electro-optical retarder.

37. The ellipsometer of Claim 35 wherein said half-wave retarder is a piezo-optical retarder.

38. The ellipsometer of Claim 28 wherein said rotating means includes a stepping motor.

39. A method for measuring at least one parameter of the state of polarization of a light beam, comprising:
(a) directing the light beam on to a photodetector having a partially specularly reflecting surface on which the light beam is incident, (b) producing with said photodetector an electrical output signal having a magnitude proportional to the radiation absorbed by the photodetector, (c) detecting said electrical output signal, and (d) determining the at least one parameter of the state of polarization from said electrical output signal.

40. The method of Claim 38 further including the step of rotating the photodetector around an axis defined by the incident light beam.

41. A method for measuring the elliptic polarization of a light beam comprising:
(a) directing the light beam onto a first photodetector having a first partially specularly reflecting surface on which the light beam is incident at an oblique angle, and producing an electrical output signal having a magnitude proportional to the radiation absorbed thereby;
(b) rotating said first photodetector around an axis defined by the incident light beam; and (c) directing the light beam reflected from said first photodetector on to a second photodetector producing a second electrical output signal having a magnitude proportional to the radiation absorbed thereby.

42. A method for measuring the elliptic state of polarization of the light beam comprising:
(a) directing the light beam onto a first photodetector having a partially specularly reflecting detecting surface on which the light beam is incident at an oblique angle with a first plane of incidence and is partially reflected therefrom, and producing with said first photodetector a first electrical output signal having a magnitude proportional to the radiation absorbed thereby;

(b) directing the light beam partially reflected from the first photodetector on to a second photodetector at a plane of incidence substantially coincident with the first plane of incidence, and producing with said second photodetector a second electrical output signal having a magnitude proportional to the radiation absorbed thereby; and (c) rotating the plane of incidence of the light beam incident on the first photodetector to a second plane of incidence different from the first plane of incidence, and producing with said first photodetector a third electrical output signal and producing with said second photodetector a fourth electrical output signal having a magnitude proportional to the radiation absorbed thereby.