Note: Descriptions are shown in the official language in which they were submitted.
CA 02465168 2004-04-23
F
~9E~L~ ~~ ~i"ii~ Ll~i~~~i~i~~
s ~'he pr~~~r~t i~~~~r~ti~r~ r~l~t~a ~c~ the r~~ki~~g of I~~r~gg gr~tir~gs
~r~d rr3ore
p~rti~a~6'~rfy ~~r~~err~~ r~~th~~a to ~~r~p~r~~~t~ for defeats f~~ar~d nr~
e~rr~r~tly
~~nuf~~t~r~d ~r~gg gr~ti~g~.
~A~C~~~~N~ ~5F ~ H~ f~'~~~l~l~
~a ~r~gg gr~tir~g t~~hr~c~logy h~~3 b~~r~ ~ ~~b~~~t ~t i~lt~r~~i~~~ r~~~~r~h
fir the i~st
deoede, espec;ieliy for its ~ppii~ti~~~ i~ the tel~~~r~~t~~i~.ti~r~
ir~dta~try. ~Ltlh~~agh
the optiee! per~~ar~er~ee of r~gg greti~~g~ is high er~d eictre~~ely
~ttr~~ti~e for ~~~y
~ppli~eticsr~~, ~er~e prmbfer~ stiii persist ~~eh ~~ they tee!! k~e~r~ rippies
ire the
grc~~sp defy ~pectr~r~, e~peei~lly eb~er~ed ire grotirrgs for di~persi~~
~s eerrape~~tie~..
'~arie~ ~ppre~ehe~ h~~e be~~r~ ~a~ed to f~~~~he9 i~~pr~~e ~:h~~ ~pti~~f
pr~per~rie~ of
~regg gr~ti~g~, rid ire p~rti~~~L~r ~ir~ii.~e the gre~ap ~eley r ipples
~C3~~~. regg
grati~g~ ire ~~~a~lLy rr~~de by ph~~teir~deir~g ire ~~~~ eptic~f fiber, or
other
2~ phete~er~~iti'Je r~edi~rr~y ~ diffr~etier~~ p~t~err~g or~d~~ed by ~ctir~ie
r~di~ti~r~
pre~eeted thre~gh ~ phi;>e ~~~~~k. r~ i~p~r~~r~t ~e~.~reft e~f dE,fects is~
the re~~altir~g
gr~tir~g is the rr~~~k itself ~~l~~i~h ~~~~Lly e~~teir~~ ph~~e errors doe to
it~~ e~~
c~~r~~f~ot~rir~g process. ~;ffort~3 h~~e therefore been rr~eide to i~apro~e
the c,~aiity of
phase r~osks, e~~d therefore r~.;d~~oe the ~aefe~ts i~°~ the res~ltir~g
regg grti~cas. For
2s exerr;p!le, ~° f et ei ~~af..~~~~ c~'o~~~ r~~~;~o re~~~tic~,~ ~~~~ n
efleofie~i~~ ~f~ore~~e i~
~ uir~ec~ fi~~r r~~ ~r~~~~~a~;= ~ s~~~ti~~e-cwe~~~~~ira~ i ~ C~~~e ~s~~it6~ ~~
efeo~ror~-~e~~~oq l~~E ~hotc~r:. ~reoh~c~f. i-ett., ~~l. ~~, pip. ~3~~-~~~
~a?On~))
discloses a step-ohirped phase ~~esk rr3ode by o~~errv~s°itir~g ~~
petter~ of the sore
place ors ~ s~bstrete s~e~er~~9 ties, sing ereleota~or~--b~~orr~ ire a
ooE~tir~~ao~s
~a ~~o~e~~ter~t epprc~~oh. the sr;~e ~~afihors he~fe also s~~;geared mother
str~te~gy for
f~briCeti~g a step-ohirped pr~~~se r~~sk ~sir~g ~ tester scs~~~type laser-
be~r~~~ rn~ritir~g
CA 02465168 2004-04-23
2
system (T. ~Lor~nukai, T. Inui, 1:. I~urihara, arid ~. Pujin eoto, 'eGro~rp-
~elay Ripple
~'edcrctaorr in step-~birpeei ~:~ber ~~agg c~ra~ting~ by (~s~°~~g ~ase~
~ea~n V~lritten
~~'ep-~trirped Pbase iUiasks,'F IEEE Photon. Technol. Left.,, veal. 14, pp.
1554-1556
(2002)). It is notable that, L~ they modify the rasH;s tl~e~mselves, bofl~
these
s ~ethcds ~nrill only correct for mask-related; systematic defects in the
res~ultir~
gratings.
instead of trying to r~ir~irni~e or eli~~ir~ate pl ease errors is phase masks,
arrot~rer
apprr~ach is f:c~ minimize fl7eir effect cn the ~~suh'~i~rg grating, by a
~:roper
to characterization of the origirr of systematic defects in the gratings
produced by a
given system, and an appeopriate feed-back on the fobs i~catior~ process. such
a
technique is for example shov~n in published U.. patent application no.
2003105g16~. (~TEPI-~A~~~' et ~1.;~ aria A.~. ur~ya~~, and ~.1'. ~tepar~e~v,
°'Correction of systematic errors in the ~abricatiorr of .fiber l3ragg
gratings,y' apt.
~s ~ett., vol. 2~°, pp. 1090-11~~ :22002;x. ~TEI~-IAN~~ et al.
di:;closes a ~~efh~od for
compensating for phase errors in a ~ragg grating by first making a test
grating,
a~~d then measuring its spear al characteristics. These characteristics are
u;~ed to
reconstruct the actual design of the grating, preferably using a Layer Peeling
i~lethe~d. A cc~rnpensafed de,~ign i~ obtained b~ co~r~~p~~rirag the
recor~st~~ucted
2c design to the theoretical structure, fe~i example by direct subtraction of
deviations
therebet~reen, and the cor np~~nsated desig~~ is ~'inally u~seod to rake
subsequent
gratings using the same optical system. ~f course, only systematic defects
inherent to the particular o~~fical ~yster~t used t~ rake the gratings will be
compensated f~r by thss rneth~~d.
Another alter native is to ;apply a pouf-~:reatrr~ent to the photoinduced
grating. Post-
correctir~n of ~3r egg gratings vas alrwady proposed for ~ther purposes, such
as
tuning the dispersion oir other optical characteristic; of the grating ( see
for
example I<. ~. dill et ar. °"Clrpee~ in-fibre Bragg grating
e~ispersiorr compensators:
Linear isatior~ c~~ eiisporsie~~~ cbarac~rristic ano" ~e~rr~or~stratio~~ of
dispersion
compensation in ~t3g krra, ~O~bitfs optical fibre tinfe,~~ Electron. Lett.,
voi. 30, pp.
CA 02465168 2004-04-23
r i 5~-1 ~~~ ~19g~~9 rid . ~. Vii!( ev ai. °y~~ti~~~ri i.ra-
~i~~~r° r~~c~ a~~ti~~~s t~~~°
~~rnp~rrs~tic~~ c~f ~ptic~f-~i~o dis~~~°si~a~," ~?pt. ir.ett., ~~~i. 1
g, pp. 1 ~ 14°-131 ~
i;1 g9~.~~.. ~°llh~re ~ppiied t~ ti ,~ ~c~t°r~~,tio~ ~f
d~f~ct<~, this ~ppr~~ch h~~C~ the
'~dv~r~t~ge ef ~li~~ri~ti~g i~cat~:systerr~ti~ rgd r~~~~-systernatice ~rrc~r~.
F~~ferrirag to
s p~cbli~h~d .~. patent ~ppii~~tic~~ ~. ~6g~11~~1~.~ (F:~~~F~i~J~i~ et ~i.~
~r~d
~c~rr~~t~~y et ai, ~y~c~~a~ti~~ ~~~ ~f~irp~~ ~ib~~ ~~Wir~~ r~~~~~,~~ t~el~~
~ip~?~ ~~n~lt~
th~c~crgf~ ~~' ~~st ~~~~~ss~ls~~,~7 ~y~~h. g. F~~~t deadline papers,
~~~'2rJ~3, F'~~~,
~:h~r~ is ~h~v~r~ ~~~F~ ~ t~~ie~~~~. °n he rgg gr~ti~~g is
ph~t~ir~d~~~d in ~
ph~tr~~~~siti~~ r~~di~rr~, grid ~t~~v b~~r~ is i~r~~h~d i~~ fihis
i~~di~rr°~ dts~-i~~~g, er at
~o i:he er~d ef the ~n9ritir~g pr~~~~~s to eptiraaiiy ~~~r~~t~ris~: the
g~r~tir~g. ~'h~ cc~fi~ct~d
data is seed tc~ ~~i~~lat~ pest-~~rr~~ti~~~ tc~ the g~°tir~, ~a~i~g ~
s°:e~rrF=ctien
a~lgoriti~rs~ based ~~ ~ sirr~pl~ ~~~6~ti~r~ tc~ the i~°w~rs~
prc~i:~s~r~~ r~~itir~g the r~~~sur~d
~~~F2 ~~. ~~eieragth to the d.~~sired ch~r~ge ire ~r~gg
~~~°~~reiE:r~gth vs. pc~~iti~~r~. ire
this appreacb, er~iy the levy freg~era~y part cue the ~~t~ m ~:err~perr~~ted
fc~r, p~rhie
~5 ~~eer?~ that the teehr~ig~e ~ar~iy ec~rre~t~ fer i~;rg~ def~~t~ in the r~gg
grating, that
is ~bc~~t 1 rr~rr~ er higher. ~e~~~r~i itertic~r~s ~<~ra b~~ made to eptii~e
the benefit ef
$;his te~hnig~e; after the c;erre~aier~ is ~~ppii~d9 the epti~al pr~perti~~ ef
the grating
are a~~in:rrieascared; arid ~.~ea~ ~.rsrr~;~t3c~r~ c~ic~ia'~ed, Li'~i~
prc~~e~s being r~p~~ated
anti! ~ satisfying ~,~~pre~sien ~f the ~'~-~ ripples is aehiE~~~red:
2d
ire spite c~f ail the abc~rre-rr~er~ti~:~ned u~eriC, there is still a reed
irer defe~t~-~s~rr~:~tic~ri
te~hniq~es h~v~i~ig ir~preved ~~~tieai perterr~~ar~~ev. ire p~~r~i~~i~~~-,
fibers is a r~e~~d fc~r
a techr~iq~se that takes inns ~en~iderr~tinn arr~r er ail ef the typE.~ ef
defe~t~ fe~.'nd in
i3ragg gratir5gs arid apprc~~priate~ly ~er~pQn~ate~ tier eferr~.
~~i3~i~~'~~ ~ ~~.9f~~/~F~t~~ ~~~ '~i°%~ iP~o/~i t~
fiat ebse~t c~f the present iover~tir~ is to pre~~ide a DwethE~d fer ipre~ing
the
r~pti~ai ~hara~te~isties ef ~ragg gratings by adding a pest-e~rreeti~n step in
the
f~bricatier~ pr~a~edt~re.
~o
CA 02465168 2004-04-23
mother object of the invention is vo apply such a po~;t-coorrection ~~hicP~
can
successfuPPy correct both systematic and non-systematic error's.
Pn accordance pith the first object of the invention, there is provided a
method for
s improving optical propetl:ies cf a ~ragg grating P~aaviny a spatiaP
refractive index
profiPe along a propagation axis. The rrrethod includes tlr~e folPr~v~ing
steps:
a) ~P~aracterising defects of the spatial refractive index profile of the
~ragg
grating. This characterising includes tPT~e sub-steps of:
to i. I~Peasuring optic~r! properties of the gratinca;
ii. P~ecorrstructing the spatial refracti~°e index profile of the
grating
based on t~~ese rrreasured opticaP properti~.~s; and
iii. ~ornparing the reconstructed spatial refr~activE; index profiPe ~~ith a
target spatiaP refractive index profile;
ys b~ ~~alculating an avE~rage index correction to the sl:~atial refractive
index profile
as a function of the defects characterised in sfep a); and
c~ applying this average index correction to the ~r~rgg ~grr~ting.
~referabPy, the defects characterised in step a) are period defects,
apodi~ation
2o defects or both. APthough a°~erage index defects can .aPso exist,
they are virtuaPly
undistinguishable from per iod for phase) defects and carr be ignored.
~ second object of the irr~fention is to provide a pre-correction step in the
fabrication procedure of the ~raggrating, the correction serving as a
feedb~acPs to
2~ the fabrication process for a series of =ether gratings in cases where onPy
systerrratic errors are to be coimpensated fo~~.
Pn accordance vrith this second aspect of the invention, there is therefore
also
provided a method for r~al<in~; an ire proved ~ragg grating u~~ing an opticaP
system
generating systematic defects, v~fhich incPudes the steps of:
CA 02465168 2004-04-23
a~ r~air~g ai leapt s~r~~ fi~~~t l3ragg grating t~~ar~g tho a~ac~~-
r~~ratiorrec! optical
~y~t~r~y ~rl~ich i~ sot up tc~ prc~d~~o a target ~pati;~~ r~:fractivo ir~de~
profile;
b~ ~haracteri~ir~g period ~~efectarid apodi~ation defeci:~ of paid test ;Bragg
grating to re~pecti~e!°~ obtain a period defer;t~ f~r7ctior~ ~p(~~ and
an
s ap~sdi~ation defects f~r~~,tior~ c'~;,(:~~~;
c) ~alc~slatir~g are average irsdex: cc~:~-ecticrro to ~:he ta; gev ~patia!
refracti~o index
profile a~ a fr.~r~ctio,~ cf tz~e period arid apcdi~atioo g defe~vt~
f~r~ctior~~9
dy ~alc~alating a ccsrrecte~~ ~patia! refrac~ti~e index profile c~~ing the
average
index cc~rrectior~; arid
i~ e; l~iaicir~the irr~prc~~ed k~ragg grtir~g ~~ir~g the opisicr~! ~y~ter~,
yet up to
produce the corrected spatial refractive index prcwige.,
lr~ either case, tree correction cG~r~ adva~ltagec~u~ly bc~ aplied to
~ophi~ticated
gratir3gs such a~ rnuiti-chai~r~ei gratir~g~ r~r° lo~v-di~per~ic~~~
~l~I~~IVI ~ragg gratings, a~
is gel! a~ ~iple ~ir~gle-ch~~r~r~ey apc~di~ed grafi:ir~g. l=or r~~ulti-
cllar~nel grating, ~r3ly
the defects affecting all t!~~e cl~~~r~r~el~ rr~ay be cur rested for.
further features arid ad~ar~tage~ of ~~he present i~ ~e~er~tic:~~~ ~eill lae
hatter understood
~apor~ reading of preferred er~bc~dir~er~ts therer~f 5.~ith rwfereace to the
apps=r~ded
2~ drawir~g~.
~l~l~~ ~~hll~~!~°J~ ll~ ~l~ilhl
Fl~~. r~ arid ~~ (PRi~E~ ~.1~~) are graphics! repres~~r~atatioE~~ ~f the
apodi~atior~
arid period pr~files, ~-especti~~ely, obfiair~ed f~vrr~ a Layf.~~ l~eelir~g
rect~n~truc~:i~n in
2s corrrpari~or~ with the theoretical p~°ofiie~ (dotted lirie~~.
~E~. 2 (hF~l~l~T~ i~ a graphics! ~°epreeratati%cr~ c~f tam cerwral
rerlectios~ lo~~atic~r~
a~ a furbctior~ c~f the ~nraa~eler~gth for the grating and for jingle-
freg~sency parasitic
refleotic~r~s.
3~
CA 02465168 2004-04-23
i=IG. ~.~ (~Rl~3l~ ,F~~'I°) ~rsd ~~ ~sr~ gr~pl~ic~!
r~pr~:~~r~i:~tiicr~s c~f Group ~eiay
Ripples as ~ fs.ancti~~ of ~~~~~i~rsgt! ~ fcr ~ disp~rsi~~r9 cc~~~p~r~s~tic~r~
gr~tis~g ha~irsg
E~ dispersions of -~~t~ ps/c~rrs, r~sp~cti~~ly h~f~~r~ as vd ~ft~r the
application oaf ~ post-
correction according to ~ preferred er~c~dis~e~t of the pE~es~rr~t
ir7~enticr~.
FIGS. ~~A to 4!~ (~~ZIC~R e~~°) g°especti~ely shc~~ the;
refle~ticr~ spectr~rr~ (d~),
'~'_rar~sra~issicr~ spectr~srr~ (d~)g grc~sp daisy (ps) nil ~~f~ as ~
f~r~cti~~r~ of
~~r~~reler~gth of ~ 4-cl~~r~~mi dispersions ccs~perss~~ion c~r~tir~g r~s~de
~sir~g ~ norz-
a~c~rrected target perir~d profile.
9~s. ~~. to ~(~lC~f~ ~~'J respecfii~el~ shc~th~a reflection spectr~r~s (d),
i:rarisr~issior~ spectr~srr" (dE~~, gro~.sp daisy (ps) ~n~! ~L~F~~ f~snction
of
~~~~eleslgth of ~ ~-ch~nr~ei diaper lion cos~pens~tic>r~ c~r~r~ing made ~sFng
~
corrected targef period profile according to another preferred es~dodirraent
~~f the
~s invention.
l~I~. ~ is schern~tic represes~at~tio~s c~v ~r~ o,ptica! syst~~s'x-s for
applying an average
index core°ec'~ion t~ a ~ragg gratirsg accordi~~g ~:c~ a pr~~ferirec~
err~bodirr~ent ~~f the
in~entior~.
z~
!=i~. '~ (!~l~l,~l~T) is a side ~ieof an optics! syster~r to write test
gratings and
i~spro~ed gratings according to a preferred es~s~odirr~ent. ~~f the
in~entiori.
1~~~~~l~~I~N ~F FR~F~E~FCC~ ~~l~~i~t~~~7F ~-~!F ii~l/~Ti~i~
~s °~he present ir~~er~tion pro~ids~s methods for ir~°spro~rir~g
tl~e ~aptica! properties of
i3ragg gratir3gs ire generals ~,~ calculating arsd appfyar~g sns a~eoage index
corm=ctic~n
mhich c~crnper~sates for defect ins tl~e ~;ratis~gs. ~'o ~ett~~~°
~rsd~:rstand the principles
of the in~er~ticar~, it is rele~ar°,t to def ire arid rs
~atl~e~~~~atica!!y desori~e hat is
s.~r~derstood by °'defects" in the grating.
CA 02465168 2004-04-23
°7
~y dafir~itic~, a ~ragg gr'atir~g ccrisist~-~ ws a rr~c~d~~iatic~r~ cf tl~a
index ~f rafracticar~
aic~g a propagation axis cf a v~a~egs~id~. i~~ t~ics~Jcrr~rr~.ar~icati~ns
applications the
~.~ave~side is ~as~aliy a ler~gti~9 c~f t~ptic~l fiber, bit it is
~.~~dc~r~~tc~cd that the piresent
ir~~e~tir~r~ r~~y be ernb~died g~ a. plar=ar ~,~aa~eg~ide cr~ ar~y cJth~r
fcrr~s et ~~pticai
rr~edl~r~r~ ire ~~hich a light b~~ar~rnay be g~id;~d. ~~ hrcug~~~c~t the
descripti~n bei~,
the prc~pagati~r~ antis is der~c~te~ as the ~ axis bit it v~~iii ire readily
~r~derstc~c~d that it
iv si~piy a c~ar~~enier~t label.
~ ~ragg grating can be rr~~deiled generally as:
~Q
~o(z~' - ~~~ro~z~ -E C~~ro(z~.s~a~(~o(z.)~9 (~)
~rhere ~e~o(,~) is the average effective index of the rtredi:a~~, ~r~o(z) is
the index
r~~ds~iati~r~ (or "apcd~zatacnlS profile) and ~o(z) aepr~oser~~ts the
absci~ate phase
t ~ pr~file of the grating. the proriie ~~~o(~) is ~~aiified of "~~~~erage
index°y e~err~ if it is a
spatially dependent f~r~ctior~7 as it contaiE°~s n~shs;~t-peris~d
rr~~dt~iatir~n; it is
c~nsidered tee vary sioiy iortg ~, the ter~~ "average" ~'eir~g ~~nderst~od to
b~= ~n a
spatial scale ~f vhe grating fringes.
2~ ~iterrati~ely, ~g~atiar~ (~ ) carp be written as:
2~
b2o~~~ - ~~fio~~~ + ~~'a~o~~'S9~'~ --.~_~~~Q~;w~~ s (~)
d~crv
where ,~a" rep~°eser~ts the average period and ~~o(z) i~ ti~~e phase
s~f the Grating
2s which describes the ~ariaticr~s of the period anriti-r espec~~ to it~~
average ~al~e pa". It
is ass~ed that- ~~o(z) is a si~~uviy var~~ing f~ ~nctior~, or ii other words,
that o(z) in
eq~aatic~r~ (1 ~ is apprc~xir~ateiy t~ iir~e- f,ar~ctis~r~ ~~t' .~. ~itl~o~gh
the represerrtatior~ of
a grating by ~ct~atic~r~ (~) is ~~idefy fc~~.snd ire the literat~r~:, i:he
representati~n by
~g~atican ('i ) ~iil be preferred in this doe~~ent, as the use c~f the
absc~l~te phase
CA 02465168 2004-04-23
~o(z~ is ra~~r~ c~r~~er~ier~t tc~ descr ibe the prin~9ipl~~ of th~~ present
ir~~renti~r~.
Vibe iocai period ~n(z3 of t3~~~ ratirsg is d~rir~~:d ~ ~~ td~e distance aiong
the
propagation axis of 'i:he gr~tir~~~ ~~~r v~i~~ ~ phase difi;~r~~r~c:~~ ~~
e~i~t~. ora ~th~r
s words, the local period ~c~(~~ is defined ~~:
_ ~~ a .
it v~ili be noted That ire ~-g~~fi~r~~ ~~ ~ to ~~~, aJ iii ~
til~°~~gb~~t the p~°eser~t
m description, the indices ~ are ~ of related to ~~r~~ point of origin, but
refer to perfect
csr ideas q~~ntities, that is, v~~~~t ~:bese g~s~r~tities v~o~id be if the
grating had no
defects.
~r~ irr~perfect grating that cor ~t~~ir~s defects cry be r~nodo~iied ~;~:
Is
~~z° __ w~Lll ~z% '~ ~;~3(z) ~ si~(~(z,ds 3
~~lE?r~ ~e1/ ~~) ~cYjO~z~ ~ ~YLefl ~z~'
_-- ~ l~ ~z~ ° (i '~ ~~l ~Zl~ 3
20 q){z, -. ~ ~z) + tSr~~z~ ,
and ~~raere ~~t~.~), ~n~~~ ~r~d ~~~ ire f~nctic~ris representing the iocai
~~er~ge
index defects, ~podis~tio~~ ~:~r r~od~l~tiorr ir~de~~ dE~~3rcts and phase
d~:fects,
respecti~rei~e l-o ir~pro~e the opticai properties of an irp~:rfE~ct grating,
ore rr~~st
2s therefore rninirni~e or negate tire effec~: of these tree t~~rrs ~sn the
refr~cti~e index
profile of the gr~tir~g.
~ o change the opfica3 properties e~f ~ k~r~gc; r~tir~~g, or~~: nla;y sits per
effect ~ post-
correctiorr, that is an ~dditior~~ii prr~cessirrg ~~f ~~~ ~ireed~ ~t,~riiaen
grating, or ~ pre-
CA 02465168 2004-04-23
correction, which involves mss.ing the eas,~red properties of a test grating
to
modify the writing set up to irriprove subseqc~ent gratings ohtained
therewit(~. In the
case cf a pc~st~correction, the grating phase profile can riot be: rriodified,
that is, the
physical locations where clear aid dark fr inges are alo~rg ~th~o grating axis
can riot
be changed. It is therefore not possible to a..hange ~,~~. ~'h~ apodisation
profile,
that is 8~~1~ could be modified by s~aperirnposir~g a correction grating to
the
alrear~y written grating but t(~i;~ approac:,h is difficult to successfully
achieve. ~niy
the direct modificatior3 of the average index ~~e~(z} is easy to realise. It
is therefore
advantageous to calculate an aveE-age index correctio ~ taking into account
the
~o three types of defects of the grating, gi~~ing tl~~e fines raiti~g profile:
3Z(Z3 - 3Zej~iZ~ ~- ~p?~Z~W3Il~l~~Z~l 'F ~;Ze~Yrch~ ~ ~~'
~ he correction tc~ be calc;uiated is therefore an a~~erac(e index function
exert tC~~~.
~s t4s expressed by IEc~uation ~~.j, three kinds of defects have to be
considered to
cor~pietely ~~ode( a ~ragg g~.ating: ttve average ir~deJ~, phase, and
apodisatiori
~~efects. It will be shown beiew that aaa average index ~~orrec~tic~n function
can be
calculated for each of them. It is assumed that an appropriate total
correction
t~uncfic~rt d~~r; r~(~~ is obtained by sur~rr=ing the corrections calculated
for each kind
20 ~~f defect:
L~Yteff_tc~z~ - ~Yl~~_Cn~~: '~- ~7Z~~~_~P~~~ -I- ~i1~1% _~a~~~ j'.
~Yl~~~_o~~set ~
t?tfhC~~'~ l~~l'Pay~ cn~~~, ~l7atf cp~a~~ ~i~s~~ L~r~lcff ca~~~ a~~~ the
Corr&~,tlon fu r3CtiCris as so6~iated
2s with the average index, phase and apodisation defects respectively, and
where
~ner~ OrrS~t is a ur~iforr~ index ~;har~ge offset that .~enders the correction
Eur~ction
~net~ tc~Z~ strictly 'positive for ail pr~sltloP~s, while Dr'te,~ cn(,~"~,
!~~'~ert Cp(z~ and ~~~t~ aa(~)
could be negative at some points. It will be understood that for post-
correction of
the gr sting tl~e total c~rrectio n function has to be positive in Grder to be
physically
~o applicable, due to the nature of tl~e photosensitivit~° that causes
an increase of the
CA 02465168 2004-04-23
r~fr~cti~~ ir~d~~. I~a tl~~ case cf ~ ~r~~ccrr~cticr~., vhe tc~tl
~~crrectic~r~ fur~ctic~~ cc~~ald
~ r~eg~ati~r~ ~r~d the cffs~t fi~rr:~ cc~ald I~~ r~rr~itted.
~rr~~l~r~ ~f t~~~r~~ ~~~d~~~~c
s ~r~~:ir~~ t~~t ccr~t~ir~s ~r~gy ~~rc~~ ir:d~~ defects ct~ ~~ rr~cd~lied s:
~'t~Z) :'~"~r0~z)-f-G';211'~Z),'-/fir?Q~Z,i~Sl&I~a~~~Z~)~
The ~~~r~~~ ir~d~ac cc~rr~:cticr~= f~~r~ctic~ ~~~~ ~"(,z) is sip ~~~Iy tile
c~~ t~~t r~~lls the
is Icc~i ~~er~e ir~de~ deflects ~~~~~~):
~~ex~_~»~z) - -~'~~,f~(z).
~~rre~~ii~~f ~~~ ~~~~ e~~~~fs
~, e~r~tir~~ that ccnt~ins ~ar~iy ~i'~~se defects can ~e ~~d~~iled use
~~z) ~~~Jfo~Z)+~°$~o~z)~~F~r(~o~z)+~i~~z))~ ~ °~)
rn~l~ere eS~) is the ~I~ese d~:fects ~'~r~cticr~. ~ I~e rel~tier~ship hetv~ee~
thc~ Icc~l
2~ ~ericd ~~~) grad the ~~sc~i~ate ~~~~se, ~s expressed by ~ci~ticr~ ~3)y
deccrr~es in this
~rtic~s8~r case:
(~, ~-
P~z) - ~~c~dz ~l~o~z)+~~~z)~~
2~ ~~e fic tl ~e ~ah~se defecta ~~), the ~ericd rcfile is dii=~er~ar~t frc~r~
the ideal ~rcfile
~o~Z) dy ~ cert~i~ ~~~ntity ~~~~;
- ~po ~Z) + ~~~Z) .
CA 02465168 2004-04-23
Psssurnir~g that the spafi:ial vp~riatic~r~ of ~~~) is srnail co~r~pared to
the ;spatial
variation of ~(z), the combination of Equations (3), (13) and (14.) yields a
period
defects function ~p(a) given bar:
z~
~'r~(z) _ _ pro ~z) . ~ (8r/~~z)) ~ (1 ~')
2~z dz
~huss there is equivalence betv~eer~ phase errors car ~d pE~riod errors,
~vY~ich is
explicitly expressed by Equation (1~).
m there is also equivalence between period and average index er tore. indeed,
the
local optical period length, tl~~at is, the pr o~~uct of the local values of
period and
average index, is the param~aer that affec:.r the opticfal properties. Two
different
gratings for which, at each point, the product of the period by the average
index is
the earns, will vir~uaily h~~ve the earns optical characteE°istics. As
an exanlpl~:, from
is the spectral characteristics, a Layer Peeling algorithm can not distinguish
between
period and ave~page index fiuutuati~f~s. losing such a recon;~truction
aigorithr~, all
the fluctuations are attributed to the period and the average index is
assur~ned to
be uniforra~ along the grating.
2c Accordingly, a grating that contains period errors ~(z~ behaves as a
grating that
contains average index error s ~~~~~,(~) if, at each poinfi:,, their optical
period lengths
are the same, that is:
.~aCZ)'(~e~o~~)t~i~t~.~'_n~Z)~ -- ~a~Z)-1-~P~z)~°~~~of~~)~ (1~i)
2~
in other words, .index errors ~n~~ n(z) arid period ,errors ~;o(z) are
equivalent if they
satisfy:
pr~~(/' B
~~t''~-.h ~~l
V ~a~,'~ ° (1 d')
CA 02465168 2004-04-23
I~
therefore, an average index c~orroc~tiorr function ~i7e~ C~(z) nulls the
period errors
~p(z) (or phase errors ~S~(z)) if it satisfi~a:
L'~YI~lT _ ~P ~Z) - -19D~~~!' _ n ~z) - - ~'/.f~e iz) . ~~J~z) - yge~,.o (L) ~
~o ~Z) ~
~~0 ~ ~) ~J2 (Rz
('~ ~)
~, period correction fur~c~tion ~,~~,~ ~~(z;~, thaf is, a'~r a~e:aage ude~
correction as a
function of the period or phase defects earl ~~her°efore be calculated
using equation
(1 ~) above.
IO
~~rrecfi~r~ c~f fbe a~~ctiizaf~o~ d~fecfs
the correction of apodisatior~ defects using :an a~erag~: index; correction
function is
less sfraightfor~ard than the other twv~~ kids of ~lefoct;~ and preferably
in~oltues an
analysis of the apodizatic;n defect f~.~nction in the ieTequEyr~cy domain.
is
~ grating that contains only apodisatic~r~ def~:cts can b~: ~~odelled as:
~t(z~ - nefJO(z) + ~~~(z).(T+~i~(Z))°~in(~o~G3~~ ~1~)
2~ where rS"(z) is the ap~cdization defects function. l.~sing a frequency dor-
nain
analysis, ~"(zj can be v~rittep ,as the s~r~~ of perioic error components:
~,t ~ ~~ - ~ ~~i ~W ) Gt~S(C~'~ -I- fl,s ~~~ SdII~CLZ)) C~~,' .,
0
2~ where ~~(~) ar~d'~S(~) are ~~aurier coefficients.
~ornbining ~quavions (1 g) arid ~~~3) yields to:
CA 02465168 2004-04-23
~a(z) - ~e~~.o (z) ~- l~~o (z) ~ sin(~c lz)) ~- I~tab (z) -+~ I9,~r,. ~(z) ~
(~ ~ )
~uherc:
tlnn(z) _ ~~o(zi'~~(a).s;c1(~o(z)+~) - ~~o(z)~A~,(~).c~s(q'~o(z)+~)~ ~~x,
0 2 2
(~2)
~no (z) - .~~ (ex ) r~no ( z ) ~ A,S. (a )
0
~23~
to In Equafiio~~ (2'I~~ the fir:~fi fi~~~~ torrrss c~~ fih~: righfi side
~°~~~rasent the idoa! grating,
while ~r~b(~~ and ar~~{z~ contain inforrr~ation about the defects (through the
Fourier
coefficients ~C(~~ and AS(~~) and hehaVe as parasitic gra,tings9 respectively,
at the
blue arid red sides of the speetrurs~ ~iith respdct to the idea! reflecfiicr~
of the
grating.
IS
Exarrrples of such parasitic reflections are represented in Fly. ~ (PRIE~FZ
~RT~ in
the case of c~ lineariy chirped grating. In Fig. 4, 'clue pcsiiior~ z~
corresponds to the
grating front while z2 corresponds fio the grafir~g hacl~ arid accordingly the
grating
provides a negative dispersion. ~s illustrafied, the light of wa~relength ~,~
corning
2Q frorr3 the grating ie~put is p<~~tly reflecfied at paint ~ f by i:he blue
side parasitic
grating while the main reflection acc~ars at z~ near the hack of the grating.
Such a
parasitic reflection affects ~tl~~~ PerFc~rrr~ances of the gr,~fiing. The
fight of wa~oeler~gth
X22 is r effected at location z~ and by fibs red side parasitic grating at z~.
Since a
large part of the lighfi has already been reflected at d~, s~sl~ecially if the
grating is
2s strongly reflective, the parasitic reflection at ~2 I~as less effect when
compared to
what occurs at wavelength ~,~. ~°hcs; fibs '~ror~fi parasitic
reflections in this case afi
the blue side, is worse fihan 'the bacl~ parasitic reflection at fibs red
side.
Oppositely, the parasitic reflection at the red side is worse than the
parasitic
CA 02465168 2004-04-23
reflection at the blue side ar~3~~:n the grating pro~~idos a po;~i~tive
dispor~iong that is,
~nrhen z~ corresponds rather to the grating front and z' go the hack.
The blue parasitic reflectio ~ can he rtiulled by a prop~;~~ phase correction
function
s a~a(z). it vviii he noted that ~~~(~;~ is a working par~~r~~aer
corresponding to a
h~potheticai correction to the ideal phase function ~o(~~, arid has no
relation to the
phase error function ~~.?~ which is based on a~ct~ai rn~eas~rtar~ents of the
grating.
With such a correction, Equation ~1 g) k~ecomes:
~tz> - ne~ro (z) + ~a~Q (z) . (1 + ~'n (z)) ~ ~in(9~~ f.~) + ~S~SG (z)) ~ (~~)
~ssunii~g that r~~a(z) ~~ ~, Eciuation ~24~ reduces toe
~(z) - ~~~~~o (z) + Ltr~o (z) si~(gjo (')) + dtzo (z)c~f~ (z) si~i(~o (z)) +
~ra~ (z)~~'~ (z) Cos(~o (z)) .
~s (~~)
t~s gas the case for the def~uct f~anctior~ b~,~~z~, given ~~ equation (2n),
the phase
correction function eS~a(z) can be es;pressed as ~e~urier spectra, that is:
2~ ~~a (z) - ~~>~ (rx) c~sc',rxz) + ~,,. (ce) sin(e~ )) cire~ . X26)
0
Combining Equations (~g~, ~~?~) and ~~6~g one obtains:
~(z) - nyo (z) + C~~~o (z ) . sin(~o tz)) + dt~a>> (z) + 119,~~F. (z) ~ (~~~
~Ttbh~r~
CA 02465168 2004-04-23
1~
X820 (z) ° A~ (~,''~ . 53.I1 Z ~- tXZ) - ~~1'%0 ~Z) ° f,~~. ('~)
° Ct)S(~0(Z~'t GYZ
(~o( )
~rrb (z~ - ~ ~r~o (z) ~ 13 (a) ,,~ girl (z) ~ ~ . (~) ~ ~'c~ ,
0 -~ ~ C ° ~i~S(~0 (2) -'- ~) + 0 ~ s_'-' ° g11.'t(Y'0 (Z) + ~~
r~r~o(z)°A~(~) , ~n~'z)~A,S.~~~ ~
~stti(~o(z)-~) '~" ~ _~.~os(~o(Z~-~~~
L~n,.(z) - ~ ~~o(z).13 (tx) ~J2o(z)~13.~~~ ~"~.
(~~)
s
oho hloe p~r~sitic rofl~;ctior~ c~~a thorefore he eiir~i~atod ~~ oddir~g ~
ph~so
correct'sor~ function ~~a(z) such th~tD for ai! v~l~~s of cc
t=.r~~'~ s (~1.~
J,s t Q,') - - sly (CX.)
~1s developed ire the previoaas section (~~:~atio~s (1~) and (1~~)), ~ phase
correction
functi~n 8~ba(z) is ec~~sivaier~t to an average index correction ft~nctior~
~~aff ca(~)
given h~:
~s
~r~«.rr_e«(z% - -~c<Iro(z). ~o(z) , ~ (~'~d:(z)~- ~3~)
2~c caz
~Itern~ti~rel, ~~~~~ v~~z) c~r~ he exp~ ossed ~s ~ fus~otion of a period
correction
vur~ction ~pa~~)
2Q
p ~~fIO (z)
~~'~3C'~~_CfX (z) ~ ~~~Cd ('Z ~ .-
~o(z)
v~here ~a(z) i~ defined ~~:
CA 02465168 2004-04-23
2Te dz
Finally, combining Equations ~~~), (3~;, (~~) and (32), C~r~~rr Ca(z) can be
expressed
as a function of the Fou~~isr coefficients of ~"(z), 'shat is ~C(cx) and
f~s(~) ~rrhi~ch are
s defined b~ Equation (~0), so tl~aat or~c ~abtair~s:
tl~a,. z _ ~''~o~~)'~'o~z) ~ A. c~ cos
~tf_~~f ~ ) ~~ ~ ~ C ) (~=) + ~.,. ~~x) sz~~(az)~ ~x d~ . (~fi)
0
Equation (35) therefore gives are aver'age index c~rrection compensating for
the
m bias parasitic reflection, defcending on t~~e apodizatior~ c~afacts function
b'"(z),
through the Fourier coefficie~~ts ~C(a) arid ~S(rx).
!n cases vrhere the red paraa>itic reflection vends to be compensated for, it
can be
seen '~ror~t equation (fig) goat the signs on the Fourier coefficients given
by
is equations (fig) and (31) need to be reversed to properi~ nail the term
~r~,(z). This
simpi~r has the effect of changing the sign of tire apodizai:ion correction
junction
~r~~~ ~a(z), ~rhich therefc>re b~:cornes:
d~~.tr _.~~ (z~ - _ ~ef~~o ~ ~~ ~o z~ 1(~' ~~~ ~~s~c~z.~ ~- A, ~~~ sin~~xz)~ ~
da . (~6)
2f7
host-correctA~n of fihe defects
used on the principles above; a first ernbodirnent of the present invention
therefore provides a post-correction meti~cod for improving optical properties
of a
~ragg grating using oni~ an ~ve=age index correction.
2s
The first step a) of this ~~~~thod invoiVes characterising the phase defects,
the
apodization defects or both in the spatial refs active index profile of the
~ragg
CA 02465168 2004-04-23
1 ~7
grating. since this particular ~~rnbodin7enfi refers to a correction post-
writing, it is
understood that the grating ilea already been photoindo~cc~d in an appropriate
photosensitive medium, acrd can therefore be characterised spectrally.
Clptical
properties of fibs grating are obtained, using routine ,measuring techniques.
For
examp6e, any spectrum of ahe reflection, transmission, group delay either in
reflection or transmission rna~r be obtained, frorr~ either extrE,~-nity of
the grating or
both. Preferably, at least one reflectivity spectrum and one grotap delay
sp~ctrurr~
in reflection are r~easared. ~'I-;e spatial refractive index profile of the
grating is then
reconstructed, based on fibs measured optical properties. this is preferably
~a achieved fihroc~gh the case of ;~ recons~t~-uctic~n algorithrr~ each as the
Layer Feeling
Method (see F~. Feced, A~. l~. ~er~~as, and lul. ~. rvluriel, '"An efficient
inverse
scafte.ring alc~r~rithrr~ for tine ~esi~~~ c~f non~rnifc~r~r fiber ~ragg
gratings," IEEE J.
C~uantt~rn Electron., vol. ~~, ~,~p. 11 gb-111 ~ (1'u9g), aced ~. ~kaar, L.
bang, and 1'.
Erdogan, ''C)n ~~he sg~ntbesi~ cat' finer ~ra~~ ~ratirrgs b~° ia~yer
peeling," IEEE J.
~s t~~antum Electron., veil. #°, pp. ~6~ -- 173 (2gg~~)). fJther
characterization
technie~ues based on direct easurernent of the apodisation and phase profiles
can be used as ~rvel! (see P. ,~:. ~r ug, l~. ~tolte, and ~. ~I~-ich,
"~~'Iea~urernent ~f
incieac r~oo"ulati~n aJ~n~ an ~rpticai fiber ~3rag~~ grati~Yeg,°' Copt.
~.ett., vol. ~0, pp.
1767-179 (1985); IVI. ~sl~nc~, J. Cranr7ing, and L. l~oladias~, "~Vovei
characterization
2o technique ~itia ~.~ ~~rn sa~~ai acccarac~ c~f fr.~nc~.e p~~r~o~ ir~~ ~ragg
grafin~s," ~pt.
Express, vol. 1 1, pp. X38-~~~' (~Og~).
Referring to Fl~s. 1f~ and 1 fit, are ~:xample of such a g~ atinel
characterization using
this technique is shown ire vhe case of a dispersion cora~pensation grating.
~s Apodisation (FIC3. 1/~) and p;rriod (FICA. 1 ~) profiles obfiained from a
Layer Peeling
reconstructican of the refractive index; profile are illustrated in comparison
v~ith the
theoretical profiles (dotted lines -- a srr~afl offset has been added to the
curve of
FICA. 1 P to better see the differences between the sz~perposed profiles). It
can be
seen that bofih profiles are very close to the theoretical curves. fi~lso
shov~rn in
FIC~s. 'lob and 1 ~ are the respective profiles' reconstr~actions frorra the
data taken
frora~ both grating ends. i~ezsimilar results are obtained which is an
indication that
CA 02465168 2004-04-23
the reconstructed profiles pr~perly describe the grating., In such a case, the
profile
From either ends rrsa~ be used to ch~ractes~ize t~se defects. In the
alternative, a
properly weighted corrsbir~atiors of the A~rofiles fror~i both4 end: cos.~id
be computed
as the final reconstructed profile.
s
'fhe fluctuations of the recons~:rocted apodization profile from the
theoretic~si curve
correspond to the apodizatior, defects function ~"(z), and the differences in
the
theoretical and reconstructed pericsd pE ofifes give the period defects
function 8p(z).
The ~:rror function on the average. index ~~~~) is riot ci~saracterisect with
this
ro Technique arid is assumed ~to be zero. This assumption cornea from the
virtual
redt~t~dancy~ that exists between the phrase and average index errors as
e~plair~ed
above.
once the defects have been properly characterised, and the defects functions
~s ~"(z) or ~p(~) or both are obtained, ~ second step b)~ of calculating an
a~aerage
index correction s ,~~~~ t~(z) to the spatial refractive index profile of the
grating is
performed. The average index; correction depends on at least one of the two
kinds
of defects &,~(z) and S~(z), as obtained in step a), through ;appropriate
correction
functions ~<~~,~ ~p(z) and ~~vt~ ca(z). iro cases where Loth types of defects
are
considered, the average irsd~~x correction erae~ ~~(~) is a ,urn of ~n~f~
~,~(e~) and
~~~e~ ~a(z). n offset tears ~~e~f 0~s8t =s added when necessary to the average
index
correction ~rre~ t~(z) to render it positive for all values of z.
Preferably, based on the pr inciples explained sbove~, ,hen needed the period
2~ correction (sanction ~~E~ ~~~~) is given by euatioir~ (~9~), repeated h~:re
fos
convenience:
~'~rr0 ~Z) ~- ~ ( )
~a (Z)
CA 02465168 2004-04-23
I9
where z is the propagation axis of the grating, n~if~=(z) i > the targefi
average
effective index and ~o(z) is tl~e target lc~ca! period.
s again, as previously explained, v~~ren the apodizatlon correction
frrrnctior~ ~nL~ ~a(z)
is needed, a frequency domain analysis of the apodization defects function is
preferably performed. ~r~ apodizaticn correction f~ncti~;~n ~n~~ Ca(z) is
calc~rl~~ted to
compensate for a front parasitic reflection ird the frequency domain, which
rr~ay be
on the blue or red side of ~~h~u idea! rwflection from thm grai:ing depending
on the
to sign of thre grating dispersion. l~he result of this analysis is an
apodizatiorr
correction function taking the forr-n cf eg~ration {3~) or (~6)~
~~.~~v (a:) ~ ~o (z) °°
t~~a~~~ _ca ~z) - ~ ,~~ (fd~. (~) cos~c~) + _A,4. r~rx) sin(az)) ~ ~~~x ,
a
v~here z is t!°e propagation axis of the gratlr-rg, rr,~,~ro(z.) is the
Target average
effective index, ~o(z) is the target lc~cai p~.riod and ~S(~) and .~~(cc) are
Forrrier
coefficients of said freqoenc~y domain analysis. The positive sign applies in
the
case of a negative grating dispe9sior~, and the r:egati~be sigG~r for a
positive grating
2o dispersion.
The lasf step of the rnethoc! according to the present embodirr~ent consisf of
c)
applying the average index ~~;orrection to the gracing. 'the ao~erage index
correction
is photoindr_aced in the photosensitive rnec~iurr~ o~rer tine ~ragg grating,
preferably
2s by exposing the grating to a spatia!!y variable dose of ~!!~ light along
its
propagation axis.
Referring to Fl~. 6, an exag~~ple of an optics! system, s 0 tc~ perForrr~ this
operation
is shown. The optical system: ~ 0 incit~des a light source 1 ~ generating
actinic
radiation, preferably in the forrrt of a tJ~ light bearr~ ~~.. ~'he light
bearr~ impinges
CA 02465168 2004-04-23
z~
transversally ors the ~ragg gr~~ting 1g, photcainduced in an optics! fiber 18,
and is
scanned along its propagatic~r~ axis. Ire the ill~ostrated el~~bodi~~nent,
this is achieved
by appropriate re-directing end shaping optical corponents r~o~anted on a
translation stage 2~, but of course ar~y appropriate scanning assembly could
be
used. Ts~ create the proper i~°~J profile as dictated by tt~e
calcaulated average index
correction, the intensity of the h~l~' light beam 1~. is ~raried during the
scanning
prefer ably ;sing a variable c~ptic;al attenuator fig. any aiterr~ative
methods to vary
the strength of the photoir~dc:~ced larofile ray also be used, sdch as varying
the
scanning speed of the beam 1~, roving the fiber 18 it~steac~ of, or in
combination
m with, the scanr~~ng cf the ~~gh~ oearre, e~cc.
It is also understood that the optics: system of Fl~. 6 is illustrated by way
of
example and that any other set-up affo~ri~~g to photcinc~uc~e a variable
average
index profile could alternatively be used. For ex;~rnpie, the average index
is correction could be applied u:~ir~g the same optical systerr~ used t~
retake the >3ragg
grating in the girst place. l~re~~erably, sucl°~ a system ir'cludea a
phase mash; in the
path of fhe light bear, diffracting the beam to generate the interference
fringes of
the grating (see for example ~.~. patent r~e~. 5,:7,588 (I-~1L~ et a!)). the
applicatior: of tire correction hoer~ever does riot req~,iire ar~y phase
rnask, as no
zo fringes have to be written in the photosensitive rr~edie~rt~ but rather
only an average
index change. Insfead of rerovir~cg the phase rraasN;, it can remain ire piece
f~r
convenience best the fringes it produces can be washed out by vibrating the
phase
mask (see CVl.,I. Cole et al, "~~o~rir~c~ fibrelphase ~°~a~k-scanning
beam fec~r~ir~ere f~r
enbafrce~ f9exibitif~r ire ,o.rc~ca~rr~ir~~ fibre ~ratir~~s v~ifh crrriforf~
,chase rrr~ask," Electron.
zs ~ ett., pp.1~.88-14g~ (1gg~)), or by using a curvature in the wavefront of
the lJ~/
beam (as for example expiai~~ed ire ~.. patent r~o 6,bC~ 1,88 (I~~II~CF
lJ~L9l~ et al)).
Pre-c~rrecfio~ ~f the c~ef~cta
In accordance with another aspect of the present invention, the post-
correction
.~o described in the previo~ss s~~ctior~ carp be replaced by a pre-correction
when the
grating defects are found to ,~e systematic from gratirog to grating. !r~ this
case, one
CA 02465168 2004-04-23
2~
or many tort gratings are rr~a~do arsd serve to charac~~~ris~~ the defects ar
dd allo~ns
calculating a correction. °~herr, the fabrication proceduo~e its
adapted accordling to
the calculated correction.
In accordance with a preferred er~abodir~errt for such a pre-correction, there
is
provided a method for rr~akir~e~q an improved ~ragg grating usPing an optical
system
generating systematic defects, v~hicll includes the follo~~~ir~g steps of:
a) r~al<ing at least one test l~ragg grating using this optical system. l~he
~Q system is set up i:o pr~odr.rce a targef spatial refractive index profile
s~rch as
the idea: profile giver yy equation ~~)e
b) Characterising period defects and apodizatiorE defects of the test l3ragg
grating, to respectively obtain E a period defects function ~~~z) and an
~s apodization defects frir~rctior~ cSn~z). the reconstruction techniqr_re
explained
above may be used, but t.l~e present invention is not limited to ;such a
technique. It is ur~deastood thai although data f~ror~ a single grating rnay
be
sufficient to properly characterise the systerrratic defects generated by the
optics! systerra it can also be advantageous to rsrse severe! gratings and
2~ compare their results to obtain this information.
c) Calculating an average inde~c correction to the target spatial refractive
index
profile; as a furrctior~~ of the period and apodization defects fur~ctlons.
Preferably, the calculations developed above resulting in equations (37)
2s and ~3~) are used.
d) Calculating a corrected spatial refractive index profile using said average
index correction; arid
s~ e) il~aking the ira~pr~oved Pragg grating using the optical system set u~
to
produce the corrected spatial ref ractive index p~ofiie.
CA 02465168 2004-04-23
22
The fabrication pro~ed~re carp include the average index c~ocwrection
ftanction given
by Egoatio~ (g) directly as thc: g~°atir~g is ~~ri~aer~, a~oidi~g the
need of an additions!
post-correction step. ~lternati~;eely, for an easier fabrication, the
correction can also
be applied ors the period pr ofiie of the grating to be ~r3tten using the
eqoi~alet~ce
between average index and ;period expressed by ~g~atior~ ~1 ~). Then, the
target
period profile ~~~~) can be ~~eplaced by a corrected period profile ~C(~)
given ioyo
.f~c'iZ.y.~ -' ~~o~~J ~' ~l?rciz~ s
t0
~ ~z~
~Jl9he~'~ ~r~'~~ ~~) -- ~ 6 a ~ . ~~r~il'_« (z) ~ '~Q''~~
gz~yo ~'~
F2eferring to i='I~. ~, there is shov~fr~ are exemplary optical system to
write the test
gratings and unproved gra~:ings according to a preferred embodiment of the
is inver~tior~. ~n example of arz appropriate r-~ethod to ~~°rite
complex period profiles
using each a system is disclosed in ~1.~. patent no. ~,~J~,~~3 ~~~IIVC~iAi.Ji~
et al).
The optics! system 11 g fi~~st includes a phase ~r~ask 1 1 ~ l7rovided
proximate the
photosensitive medium '! 1~ along the propagation axis 1'l2. ~ light source
l1Fs,
2o preferably a t~~ laser source, is also provided and generates a light beam
120
which is directed to pro)ect ~~:hrough a portioro of the l;~ha:~e mask 116.
Thi>~ in turn
generates a licdht beam on~ith a modulated intensity profile ~nrhich impinges
on the
photosensitive medium 11~ to locally record therein a portion of the optical
grating
having a charavteristic period.
iVieans for rr~ovir~g the light beam 12g along the propagation axis 11~ of the
photoserDSitive ~nediurre 1 1~., to successively record portio~~s of the
optics! grating
therealorig, are further prcwidec~. !n the illustrated ernb~cdiment, these
moving
means incltade a 46° mirror 1~~ disposed to redirect the light beam
1~from the
CA 02465168 2004-04-23
light source 11~ towards the phase ~rask 116, this rryirror being mounted on a
translation stage 124..
~irrailarly, means for moving the phase mask 11fi ire a direction parallel to
the
s moving of the light bearr~ 12g and cor~c~rrently f~hereto are provided.
~refvrably,
this is embodied by a second translation stage 126 0°~ which the phase
mask 116
is r~oc~ntea. The relative r~c~~rer~nents of the phase mask 1'l6 and the light
beam
12g are ad~casted to locally tore the characteristic period of each portion of
the
optics! grating.
m
Appropriate optics! compor~erats fo~°rr~irig are optics! a:~ser~b~ly
126 may f;~rther be
provided to give fhe !igllt beam 120 a wavefror~t ctrr~~at~re along the
direction of
the wavegcaiding axis. The wavefront radius of cc~rvatc~re, in the plane of
the phase
mask, is selected to gers~ra!!~~ optimize the efficiency of the recording of
the optics!
~s grating.
The application of the post-=;orrectian was done by s~sperimposir~g a tJ~-
indrced
spatially-dependent average index correction using a scar~nir~g technique.
~/arying
zs the power of the ~~ beam during the scanning process allowed inducing a non-
uniforrr~ index charge. This process carp b~e calibrated such that, for a
giver scan
speed, a given CJ~ p~wer causes a kn~wn index change.
As can be seen from a co°nparison of FlC;s. ~A arid ~~9 the application
of the
correction visibly imprr~ved ~che optics! properties of tire grating. The
amplitude of
CA 02465168 2004-04-23
the G~~ vas reduced fror~n ~~v ps tc 'l~ ps peak-to-peak which corresponds to
sore than a factor of 2 ire irnprovec~.ent.
pre-correction was also successfully tested of ~ ~~ ~~-channel dispersion
s compensation grating, faavir~c~ a dispersion of about ..-'I ~~JC~ ps~nr~.
'IWhre~: non-
corrected gratings were wriiten from ~ hich systerr~a~t'cc ~~1~ was observed.
~fhe
measured properties of one of them are shown in Fl. ~ (t~F~ll~l~ ~i~~). ~~hen
a
correction period profile was ~:aiculated from these gratings and applied to
another
grating frorr~ which the characteri~atirn, shorn~n in FICA. ~ was obtained.
significant
Io irr~preavemer~ts to the optical characteristics have been obtained,
noteworthy on the
~~(~i ~ ps peak-to-peG~k co:°npared to 4g ps) and the ~ effectivity
flatness (~.2g d~
corr~pared to C~.~2 d~).
~f course, numerous modifications could be applied to the embodiments
~s described above without departing from the scope of the present invention
as
defined in the appended clain7s.
