Trinary mappings: a tool for the determination of potential spectral paths for optical monitoring of optical interference filters

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Trinary mappings: a tool for the determination of potential spectral paths for optical monitoring of optical

interference filters

Mael Vignaux, Fabien Lemarchand, Thomas Begou, Catherine Grezes-Besset, Julien Lumeau

To cite this version:

Mael Vignaux, Fabien Lemarchand, Thomas Begou, Catherine Grezes-Besset, Julien Lumeau. Trinary mappings: a tool for the determination of potential spectral paths for optical monitoring of optical interference filters. Applied optics, Optical Society of America, 2018, 57 (24), �10.1364/AO.57.007012�.

�hal-01870540�

Trinary mappings: a tool for the determination of potential spectral paths for optical monitoring of optical interference filters

M AEL V IGNAUX , ¹ F ABIEN L EMARCHAND , ¹ T HOMAS B EGOU , ¹ C ATHERINE G REZES - B ESSET , ² J ULIEN L UMEAU ^1,*

1

Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France

2

CILAS, Etablissement de Marseille, Pole ALPHA Sud - Saint Mitre, 13400 Aubagne, France

*Corresponding author: julien.lumeau@fresnel.fr

Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX

An alternative new technique for the determination of efficient optical monitoring strategy of optical interference filters is presented. This technique relies on the analysis of optical monitoring signals for different optical monitoring wavelengths and the comparison of these signals with some pre-defined criteria in order to generate potential spectral path compatible with a dedicated trigger point monitoring technique. Trinary mappings are then generated in order to determine possible optical monitoring strategies. This technique is finally implemented on various filter designs and experimentally validated.

OCIS codes: (310.0310) Thin films; (310.4165) Multilayer design; (310.1620) Interference coatings.

http://dx.doi.org/10.1364/AO.99.099999

1. Introduction

Optical interference filters offer a very broad range of optical functions for the control of the spectral properties of light. With the last 15-year improvement of both the design techniques and the manufacturing systems, it is now very common to fabricate very complex filters with very large number of layers and totally aperiodic structures [1]. In order to secure low errors on the thickness of each of the layers of the stack, it is best to combine stable deposition systems as provided by sputtering technique and in-situ optical monitoring [2,3]. By combining different algorithms based on optical criteria such as turning point monitoring (determination of the moment the derivative of the optical monitoring signals cancels) or trigger point monitoring (determination of pre-defined optical monitoring signal levels) it is possible to accurately stop the deposition of each of the layers [4]. More advanced versions of trigger point monitoring can be used, they are known Percentage Of Extremum Monitoring (POEM) [4]

or optical monitoring by swing [5] and consist in taking into account the amplitudes of the previous extrema of the optical monitoring signal to correct for the trigger point monitoring value. However, while such techniques can accurately determine the moment a deposition has to be stopped, the accuracy highly depends on the selected optical monitoring wavelength. The choice of the optimal optical monitoring wavelength is therefore a critical step that will directly affect the final performances of the filter. Indeed, with some classical [4,6] or very complex filters [7], the error can quickly diverge and result in large

discrepancies if the optical monitoring wavelengths are not properly selected.

While it is obvious that this critical problem has drawn large interest in the optical thin-film community, there have been quite a small amount of works published. Indeed, it is obvious that there have been a wide range of progresses in the domain. This is clearly illustrated by the increased complexity and the lower discrepancy of the fabricated filters [8]. However, most of the efforts have been carried out by industrials resulting in a limited spreading of the results and limited scientific work on the topic. We are aware of only a few academic studies on the topic. Several papers have been published by R. Willey, but mostly on some very specific filters and without generalization of the methods to filters with arbitrary structures [4,8-10]. A. Zoeller has also widely contributed to the domain, in particular in the improvement of optical monitoring systems [11] or virtual deposition process [10-12]. Finally, the main general investigations have been carried out by A. Tikhonravov and M. Trubetskov. For example, in ref.

[13] they provide a full investigation on how to find the best possible monitoring wavelengths in the case of a full Level Cut monitoring. For a given multilayer stack, they provide a monitoring spreadsheet that contains the sequence of monitoring wavelengths and their corresponding termination level. For the creation of such a spreadsheet they propose to follow different steps in order to perform a constrained optimization with several limited criteria:

• The number of different monitoring wavelengths is limited up to 5.

Hence, depending on the spectral region attainable with a given

monitoring system and the maximum allowed number of optical

m cre m ex is ex de se bu va sh im re th us we alg str Th so

fun for a s wi m th alt m de co th th low im for filt on ba we Tr th a p th In str str

2.

on wa im ne er th of

onitoring wavele eated.

• The amplitude inimum V

min

has xtrema are not ac too thin), they co xtrema are finally

• The initial and efined. It reflects eparating the last ut also between t alue of the signal f

• The distance Δ hould also be de mportant value an The strategy ela sulting from an e calculation alg sed as a merit fu

eighing factors f gorithm then all rategy (and sprea his is this type oftware such as O

However, one ca nction, and it is h r the parameters single path that ith optical mon onitoring.

In order to prop e efficient optic ternative approa onitoring wavele eviation of the ref onsists in running e reflected phase e optimal optical west phase er mplemented on b r the determinati ters. However, th n virtual depositio To overcome th ased method and eight parameter rubetskov et al., w e determination predetermined l is list is slightly m

addition, it does rategy but to help rategy, if not the b

. Description

The principle of n the generation avelengths within mplemented. Then eed to be taken in rrors with trigger ese different crit f success and use

engths an optim e (A) of the signa s to be defined b chieved during lay onsider a virtual y located in order d final signal Swi s the ratio betwe turning point fro the amplitude an from the first extr Δ from the Trigg efined. For some nd should not be t aborated by the c optimization pro gorithm. Indeed,

unction needs to for each of these ows one to find adsheet) for the d

of strategy whic ptilayer [15].

an see that this t hard to precisely s as it is case depe

might include so itoring and wou pose an alternativ al monitoring st ach based on t ength that allows flected phase at a g virtual depositi e at a single wav l monitoring wav rror at this w bandpass filters a ion of all-optical m his technique ten

on process simula ese limitations in d clear the tricky q rs values in ca we propose in thi of possible optic list of parameter modified and com s not intend to p p users to determ best.

of the metho

f the algorithm th n of the optical

n a spectral regio n, we analyze wh nto account in ord r point monitoring teria in order to d e them to generat

mal monitoring sp al between its max by the user. In th yer deposition (f

increase of its th to calculate the fi ing (S

in

and S

fin

) v een the amplitud om the trigger poi nd the distance se

rema (S

ini

).

ger Point to the n e monitoring de too small.

computer can the oblem, with stro a monitoring fun o be minimized.

e criteria that ar in a matter of m desired stack wit ch is implement technique uses w determine the m endent. Also, the t ome layers that a uld require time ve method for th

trategy, we rece the determinati s minimizing the a single waveleng ion process [10-1 velength for each velength is the on wavelength. This

and was shown t monitoring strate ds to be time-con ation of depositio n term of calculat question of the de ase of the meth is paper an altern

al monitoring str rs as proposed b mpleted with add

provide a single mine an efficient

od

hat we have deve monitoring sign on where optical hat are the critic der to minimize t g strategy [4,5]. F define regions wi te optimal paths

preadsheet can aximum V

max

and

he case that sign for example, a lay hickness until bo final amplitude.

value are also us de and the distan int of the layer (S eparating the init next Turning Poi evices this is qu en be considered ong boundaries f nction F

m

which This function us re predefined. Th

minutes a possib thin set boundari

ted in commerc weights in the me most efficient valu technique provid are not compatib e or quartz-bas he determination ently proposed

on of the optic e root mean squa

gth. This techniq 12] and calculati h of the runs. The ne that provides t

s technique w to be very efficie egies of this type nsuming as it reli on runs.

tion time for phas etermination of t hod proposed native approach f rategies. It relies by Trubetskov, b ditional paramete optical monitori optical monitori

eloped is first bas nal for each of t monitoring can cal parameters th the layers thickne Finally, we combi

ith high probabil for the creation

be nal its yer oth ser nce

fin

) tial int ite as h is for ses his ble es.

cial erit ues des sed ble

of an cal que are ng en, the was e of ent ies se- the by for on but ers.

ing ng

sed the be hat ess ine ity of

optical some fa thickne

Let u defining or not.

A. Crite The next ex parame monitor calculat extremu signal.

monitor criterion will be previou minimu intensit approac almost extrema to estab without intensit after e minimiz parame illustrat Using

monitoring stra factors that will ss of each layers.

• the distanc layer to lay

• the final de be triggere

• the spectra as compa transmittan

• the dynami

• the transm

• the numbe us analyze each g whether trigge

erion 1: Distance distance a trigge xtremum of the eter that strongly

ring. Indeed, trig tion of a ratio of d um as well as the Therefore, one ring is defined clo n will occur in a

more sensitive us layer thickne um when trigger ty modulation an ches an extremu

constant over b a is between 5 an blish a first crite t any virtual de ity must be at a each extremum zing phase erro eters will affect th ted this criterion g this criterion it

• trigger poi where the is more tha

• forbidden closest extr

ategies based on limit the optica Below is a non-e ce to extrema of yer,

erivative of the sig ed,

al resolution of t ared to the s

nce signal, ic on every single mittance value at t

er of extrema in th h of these criter er point monitori

e of the trigger p er point is locate

transmitted inte y influences the a gger point monit distances betwee e distance betwe can easily unde ose to an extrem

region with low to noise and th ess errors. Actua r point is equid nd severely incre um. It can also be

broad spectral r nd 95% of the lay erion that will s eposition process minimal distan m. This criterion ors but it is no he precision of th

in Figure 1, in cas is possible to gen int monitoring - distance to the c an 2%

regions (in grey remum of the sign

phase calculatio al monitoring acc exhaustive list:

f the signal that c gnal when depos the optical monit pectral fluctuat e layer, trigger point, he signal of a laye

ria and define ng can be implem

point to extrem ed from the prev ensity modulatio accuracy of the la toring is highly r en the trigger poin een the last two e

erstand, that if mum, in this case, w modulation of t hat can be mor ally, layer thickn distant to the ex

eases as soon as e shown that thic ranges when th yer. This observa secure low phas s runs, i.e. the t nce of 5 and 95%

is a necessary ot a sufficient o he layer optical m

se of a single Nb

2

nerate two differe -compatible regi closest extremum y) where the di nal is less than 2%

on. There are curacy of the can vary from sition needs to toring system tions of the

er. some criteria mented safely

ma

vious and the on is a critical ayer thickness relying on the nt and the last extrema of the trigger point the triggering the signal that re affected by ness error is xtrema of the s trigger point ckness error is he distance to ation allows us se error even trigger point

% before and condition for one as other monitoring. We

O

5

layer.

ent regions:

ions (in blue) m of the signal istance to the

%

Fig cri B.

eff str ap cri an ap lay as it mu wi th wi cri sig dif a m qu am tri

of mu th loc wi wa as wa sy ca de

gure 1. Illustrati iterion.

Criterion 2: Sig Another param ficiency of a tr rategy is the final pplied. This crit iterion as the sign nd next extremum pplied, i.e. regions

yer, is the worst it will induce ve is clear that the uch larger than ill be achieved, ickness (this ana ith the signal pr iterion also takes gnal and therefo

fferences in trans multilayer struct uarter-wave diel mplitude can va iggering point sta To define a crite f the optical moni ultiplicative and e derivative of th cal derivative re indow must be avelength will no sociated with th avelength is large ystem (forbidden ase of a single N

erivative must be Using this criteri

• trigge where deriva is larg

• forbid ampli when noise

on of the distan

nal derivative a meter to take in

igger point mo l derivative of the terion is somew nal slope will dep m. Indeed, region s where zero der condition for trig ry large errors. C distance betwee the noise level a

resulting in ver alysis neglects an rocessing if slop s into account the ore provides ad smittance can be ture. For exampl lectric mirror w ary very fast fro ays far from an ex erion on the deriv itoring signal. It c additive noise. By he signal, one can ecalculated over

larger than the ot be adapted for he optical monit er than the one a regions). We illu Nb

2

O

5

layer. Th larger than ±0.00 ion it is possible t er point monitor e the recalculate ative of the signa ger than the noise dden regions (i itude based from n deposition stop standard level of

nce of the trigger

t trigger point nto account wh

nitoring-based o e signal when tri what depending pend on the dista ns where TPM te rivative is reache gger point monit Conversely, if the en two measured and high precisio ry small error ny delay that wo pe is very large)

e amplitude of the dditional constra e very large durin e, it is the case w within the reflec

om one layer to xtremum.

vative, we first co can be defined us y comparing this n define the follo a standard quar noise deviation.

trigger point mon toring of this lay associated with a ustrated this crite he criterion than

005.

to generate two d ring -compatible ed amplitude bas al when depositio e standard level o in grey) where m the local deriv p is triggered is f the signal.

r point to extrem

hen analyzing t optical monitori iggering criterion on the previo nce to the previo echnique would ed at the end of t oring to be appli slope is very larg d intensities will

on triggering poi on the final lay ould be associat . However, such e modulation of t aints. Actually, t ng the deposition when monitoring ctance lobe whe o another even onsidered the noi sing two values: t s level of noise wi owing criterion: t rtz thickness err In other words nitoring if the err yer at this speci a quartz monitori erion in Figure 2, n we used is th different regions:

e regions (in blu sed from the loc on stop is trigger of the signal.

e the recalculat vative of the sign s smaller than t

ma

the ng n is ous ous be the ied ge, be int yer ted h a the the n of g a ere if ise the ith the ror , a ror ific ing in hat

ue) red cal

ted nal the

Figure 2 C. Crite monito system The optimal interfer transmi To illust of the t Perot fil transmi resoluti can see local tr resoluti optical known

Figure 3 resoluti

From the opti of the fi optical m criterion the opt calculat discrete

with the num percent monitor Using

In the 2 nm an D. Crite depend The

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T rans m ission

2. Illustration of th erion 3: Spectra oring system

spectral resoluti is another impo l optical monitor rence effects in t ittance of a filter trate this effect, w transmittance, in

lter centered at 6 ittance curve w ion, but with a fin

that for such a fil ransmittance of ion is not prope monitoring sign effect [16] and is

3. Illustration of ions from 1 to 4 n m this first result ical monitoring sy ilter, these wavel monitoring wave n that allows est tical monitoring ted for each mo e quantity E

R

with

, R being the full w mber of points.

t, of the spectra ring wavelength g this criterion it

• allowed reg

• forbidden r e examples prese nd a step size of 0 erion 4: Dynami fourth criterion ding on the moni

0 1 2 3 4 5 6 7 8 9 1

585 590

the signal derivati al resolution of ion of the mono ortant paramete ring strategy is b thin film filters,

can present broa we plotted in Figu n the 450-850 nm 600 nm (blue cur when measured,

nite spectral reso lter, the spectral r f the bandpass.

erly taken into nal can be affecte s critical in this stu

f a Fabry Perot f nm.

t, it is obvious th ystem is finite an lengths need to b elengths. To accou timating the effec system on the onitoring wavele h unit %T and de

, ∑

width spectral re This quantity q ral resolution of

and for each laye is possible to gen gions where E

R

<

regions where E

R

ented in this pape 0.1 nm

c on every singl n is related to

itoring waveleng

595 600

Waveleng

ive at trigger poin the monochrom ochromatic optica er to take into a being defined. Ac the spectral evo ad and sharp spe

ure 3 the spectra m spectral region rve). We then plo

not with an inf olution of 1, 2, 3 a resolution can hi . Therefore, if

account, the acc ed. This effect is udy.

filter measured w hat if the spectral nd not compatible be removed from unt for this effect ct of the spectral measured trans ngth and ea efined as:

/

,

/

esolution in nano quantifies the lo f the spectrome er.

nerate two differe

< 1%,

R

> 1%.

er, we supposed

e layer the signal dyna gth, the signal dy

605 6

gth (nm)

The 1 nm 2 nm 3 nm 4 nm

nt criterion.

matic optical al monitoring account when ctually, due to olution of the ectral features.

al dependence n, of a Fabry- otted the same

finite spectral and 4 nm. One ghly affect the this spectral curacy of the s a very well-

with different l resolution of e with the one m the potential t, we defined a l resolution of smittance. We ach layer a

(1) ometer and N, ocal effect, in eter for each ent regions:

a value of R of

amic. Indeed, ynamic can be

610 615

eoretical

m FWHM

m FWHM

m FWHM

m FWHM

very limited. This is for example the case for the matching layer that are placed between two Fabry-Perot cavities in order to make then coherent. For these layers, when depositing a matching layer with a refractive index close to the one of the substrate, as the admittance of the stack is equal to the one of a bare substrate, the signal dynamic is close to zero at the central wavelength of the filter. In order to disregard the wavelengths that would exhibit such low signal dynamics, we defined a new criterion: transmittance change between the lowest and the highest measured transmittance of a layer must be larger than 5%. Using this criterion it is possible to generate two different regions:

• allowed regions where transmittance change is larger than 5%,

• forbidden regions where transmittance change is smaller than 5%.

E. Criterion 5: Transmittance value at the trigger point

The fifth criterion is related to the transmittance level at trigger point. In order to secure as high as possible signal to noise ratio, one wants to avoid to have low transmission at trigger point. We therefore defined a criterion: transmittance must be larger than 10%. Using this criterion it is possible to generate two different regions:

• allowed regions where transmittance larger than 10%,

• forbidden regions where transmittance is smaller than 10%.

F. Criterion 6: Number of extrema during the deposition of a single layer

The number of extrema that are crossed during the deposition of every single layers is also an important factor to take into account [17,18]. Indeed, even if it is not mandatory to cross some extrema for every single layer of a multilayer stack if the same wavelength is used throughout the whole deposition process, it is generally very beneficial as trigger point monitoring by swing (or POEM) algorithm recalculates trigger points based on the errors of amplitude of the measured signal at each extremum. In this case, partial phase compensation is performed. But such a criterion becomes of high interest as soon as multi-wavelengths optical monitoring is applied. When optical monitoring wavelength is changed, the error compensation as performed by trigger point monitoring by swing (or POEM) becomes not as easy to implement as signal modulation can vary a lot from one monitoring wavelength to another. If the signal of the first layer to be monitored with a new wavelength does not crosses an extremum, POEM will act as a simple trigger point monitoring technique and intensity errors associated with the errors on the previous layers will not be compensated. However, if the signal of the first layer to be monitored with a new wavelength crosses one extremum, and better two extrema, trigger point monitoring by swing (or POEM) procedure will allow an efficient compensation of the errors on previous layers by recalculating a new trigger point using the values of these extrema.

Auto-compensation mechanism on the phase at the new monitored wavelength will be possible, and this correction will be effective for the following layers that will be monitored at the same wavelength.

In conclusion, it is particularly useful to change optical monitoring wavelength, every time it is possible, if one or two extrema are crossed in the monitoring of the first layer after this change. Using this criterion it is possible to generate two different regions:

• trigger point monitoring-optimized regions where the optical monitoring signal crosses two extrema,

• regular regions where the optical monitoring signal crosses zero or a single extremum.

Using this criterion, it is then straightforward to define regions where the change of optical monitoring wavelength would benefit from trigger point monitoring using swing (or POEM) error compensation.

G. Description of the approach

For each of these criteria, we have generated independent regions that are trigger point monitoring-compatible and other that are not.

However, it is obvious that each of these criteria are important for trigger point monitoring such as it is important to take in account all of then simultaneously. To do so, we calculated a score where:

• Score of zero corresponds the case at least one of the five first criteria is not met. In this case optimal trigger point monitoring conditions are not combined for this layer and the associated monitoring wavelength should not be considered. These regions will be represented by grey rectangles.

• Score of one corresponds the case all five first criteria are met simultaneously. In this case optimal trigger point monitoring conditions are all combined for this layer and the associated monitoring wavelength can be considered.

These regions will be represented by blue rectangles.

• Score of two corresponds the case all five first criteria are met simultaneously and the sixth criterion is also met. In this case optimal trigger point monitoring conditions are all combined for this layer and the associated monitoring wavelength can be considered. In addition, these regions are optimal regions for a change of the monitoring wavelength and will be represented by green rectangles.

Using these six criteria, it is then possible to generate trinary mappings for every new design that will provide an interesting visual input for the determination of an efficient optical monitoring strategy.

3. Illustration of the approach on various examples

A. The quarter-wave mirror

As a first example, we analyzed the trinary mapping technique on an 11-layer mirror centered at 600 nm composed with quarterwave layers at 600 nm with refractive indices of 2.35 and 1.46 deposited on a glass substrate with refractive index of 1.52 and with formula:

Glass │ (HL)

⁵

H │ Air. (

2)

This example is particularly interesting to start with as classical

Turning Point Monitoring at the central wavelength of a mirror is

generally limited to low reflecting mirrors and finding an efficient

trigger point monitoring wavelength is mandatory to produce high

performance dielectric quarter wave mirrors. While this problem is

not new, we provide here a comprehensive description on how to

achieve an efficient optical monitoring strategy that will result in the

lowest deviation from theory. In Figure 4, we plotted the evolution of

trinary mapping of the mirror versus monitoring wavelength

(horizontal axis) and layer number (vertical axis). These graphs read

from bottom to top, i.e. from first to last layer of the stack and one looks

for vertical paths that are all blue or green. One can see that as

expected, 600 nm is not a wavelength that can be used for trigger point

monitoring of a quarter-wave layer-based structure. Then, it appears

that there are two windows that are trigger point monitoring-

compatible that appear as blue or green continuous vertical lines. A

first region on the short-wavelength edge of the mirror between 475

and 525 nm and a second region on the long-wavelength edge of the

mirror between 710 and 765 nm. With this technique, we have been

able to eliminate 70% of the spectral regions that are not trigger point

m re m m

Fig 80 m de se tec th wa co low ge an wa

B.

wi ind

de m 49 m be filt wa pa inv po wo filt 60 m th co co ed

onitoring-compa gions on or clos irrors and are onitoring a quart

gure 4 Trinary m 00] nm spectral

onitoring-compa To select an a eposition process elect the one that chnique that wa e root means sq avelength for eac ompatible spectra west phase root m

By combining th enerate, in an effic n 11-layer mirro avelength of 502 Narrow bandpa

Another importa ith formula M10 dices as the one o Glass │ (H Using the phas emonstrated that

onitoring the 14 97 nm and then onitoring, when ecomes less effic ter [7]. However avelength is very arameters for ea vestigated if trin ossible spectral r

ould be calculate ter was generate 00 nm is not a w

onitoring of a qu at there are four ompatible for the ontinuous vertica dge of the mirror

atible. The rema se to the edges o

in accordance ter wave dielectri

mapping of an 1 region. Yellow atible regions.

appropriate stra s for different wa results in the low s recently presen quare deviation ch wavelength w al regions and se mean square dev he trinary and p cient way, an effi or consisting in

nm.

ass Fabry-Perot ant filter example 2H M10 centere of the mirror with HL)

⁵

2H (LH)

⁵

│ Ai

se root mean t an efficient opti 4 first layers us switching to a n trigger point cient, in order to

r, determining th y time consuming ach possible mon nary mappings ca ranges where p ed. Trinary mapp ed (Figure 5). On wavelength that uarter-wave layer narrow window e first 14 layers al lines. Two firs r between 475 a

aining regions co of the main refle with the well-k ic mirror.

11-layer mirror s w rectangles sh ategy, one can

avelengths within west discrepancy nted [7] that con of the reflected within the trigger lect the waveleng viation.

phase method, it icient optical mon n monitoring al

e is a narrowband ed at 600 nm with h formula:

ir.

square deviatio ical monitoring s sing a trigger po turning point m monitoring pha o guaranty perfec he optimal trigge

g as it requires cal nitoring wavelen an be used to re phase root mean ping of the consi ne can see again t can be used f rs-based structur ws that are trigger and that appear st regions on the

and 500 nm and

orresponds to t ection lobes of t known results f

stack in the [450 how trigger poi either run virtu n these ranges an y, or implement t nsists in calculati d phase at a sing

r point monitorin gth resulting in t

is then possible nitoring strategy ll the layers at

d Fabry-Perot filt h similar refracti

3 n at 600 nm, w strategy consists oint monitoring

monitoring optic ase compensati ct centering of t r point monitori lculating this pha ngth. We therefo estrict the range n square deviati idered Fabry-Per n that, as expecte for P trigger poi re. Then, it appea r point monitorin r as blue or gre e short-waveleng between 505 an

the the for

0 – int ual nd the ing ng- gle the to y of a

ter ive ( ) we in

at cal on the ase ng ore of on rot ed, int ars ng- een gth nd

512 nm mirror Similarl to elim monitor

Figure 800] nm regions

We t root me calculat regions regions the 14

^th

Figure deviatio compat first 14 One perfectl deviatio mappin can be wavelen square combin efficient layers o layers a

0 20 40 60 80 100 120 140 160

φ

RMSD

(°)

m and two additio between 720 a ly to the mirror, u minate 80% of t

ring-compatible.

5 Trinary mapp m. Yellow rectang s.

then overlapped ean square devia ted in ref [6] (Fi s that are not trig s the regions tha

h

first layers.

6 Comparison o on (ϕ

RMSD

) map tible spectral reg

Fabry-Perot laye can see that th ly coincide with t on is minimum.

ngs cannot provid used as a meth ngths that are s

deviation, sever ning these two m

t way, an efficien of a M10 2H M1 at a wavelength o

0 0 0 0 0 0 0 0 0

450 500

onal regions on th and 740 nm and using the trinary the wavelengths

ping of the first gles show trigger

these regions w ation (ϕ

RMSD

) of t igure 6). The gr gger point monito at are trigger poi

of the final laye pping and the gions as selected

ers.

he regions selec the regions wher In other words, de an efficient op hod to limit the scanned for the

rely reducing th methods, it is the nt optical monito 10 Fabry-Perot f of 497 nm.

550 600 6

Monitoring Wa

he long-waveleng d between 762 y mappings, we h s that are not

14 Fabry-Perot r point monitorin with the evolution the 14

^th

layer of rey regions corre

oring-compatible int monitoring-c

er phase root m e trigger point

by the trinary m cted by the trin re the phase root we see that whi ptical monitoring e range of optica

calculation of th e number of ca en possible to ge oring strategy of filter, i.e. the mon

650 700 75

avelength (nm)

gth edge of the and 782 nm.

have been able trigger point

layers [450 – ng-compatible n of the phase the mirror as espond to the e and the blue ompatible for

means square monitoring- mapping of the

nary mapping t mean square ile the trinary strategy, they al monitoring he root mean alculations. By enerate, in an f the 14

^th

first nitoring of all

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

50 800

re it d sq th an of sim eff co C.

wa stu

th at m 59 m on ro th filt be pr an ha m

Fig [5

th wa sta m 40 lin int

th Ho

One can also se gions associated did not select a re quare deviation ap

is zone is associa nd close to the spa f the trinary map mple and pretty f ficient all-optical omponent.

Non-conventio In ref [19], a m ave layers and udied. The stack f

Glass │ (0.5H (0.5H 1.5L)

³

3 3.632H (1.5L Using phase roo ere is a better op 600 nm [6]. Th onitoring the 37 96 nm and then

onitoring at 606 nce more to deter oot mean square is paper, we im ter (Figure 7). On e used for trigger roblem, R. Willey nd 42. We see on ave applied for

onitoring-compa

gure 7 Trinary 70 – 630] nm. Op

Then, if one loo ere is no compl avelength that al ack. However, 5 onitoring the lar 0 (blue or green ne). In this case, t terest but in a sin One can see tha e one that was owever, while th

ee that while the with the lowest egion in the 625-6 ppears also prett ated with the low

acer. From a prac pping and phase fast technique for l monitoring tec

nal three cavity multi-cavity Fabry centered at 600 formula is given b H 1.5L)

³

3.632H (1

3.632H (1.5L 0.5H L 0.5H)

³

1.19989L ot mean square d ptical monitoring his efficient optic 7 first layers us monitoring the 6 nm. The determ rmine for each w

deviation which plemented the t ne can see that 6 r point monitorin proposed to qua the trinary mapp each criterion, t atible and should

mapping of a n ptimal path is high oks at the overa

ete blue/green v llows using trigg 596 nm appears rgest number of l continuous verti rinary mapping d ngle optimal optic

at trinary mappin obtained from p he trinary mappi

e trinary mappin phase root mean 650 nm where th ty small. The reas w intensity modu ctical point of view e root mean squ r determining, if chnique for any

y bandpass filter y-Perot filter bas 0 nm proposed below:

1.5L 0.5H)

³

1.345L H)

³

1.345L (0.5H 1 0.96265H 0.9052 deviation, it was g strategy than m cal monitoring st sing a trigger po 5 last layers usi mination of this wavelength and ea

h is once more t trinary mapping 600 nm is not a w ng of all the layers artz monitor layer ping that based on

these layers are effectively be qua

non-conventional hlighted with yel ll trinary mappin vertical path, i.e.

ger point monito s as the wavele layer with a sing ical lines highligh did not result in a cal monitoring wa ng provides sim phase root mean ing showed that

ng could select t n square deviatio he phase root me

on for not selecti lation, especially w, the combinati uare deviation is not the optimal, y thin film optic

r

ed on non-quart by R. Willey w L

1.5L)

³

22L │ Air. 4 demonstrated th monitoring the sta trategy consists oint monitoring

ing a trigger poi strategy requir ach layer the pha time consuming.

technique for th wavelength that c

s. To overcome th rs 14, 27, 28, 40, 4 n the limits that w e not trigger poi

artz monitored.

Fabry-Perot filt low lines.

ng, it appears th there is no sing oring for the who ength that allow gle wavelength 1

hted with a yello a spectral region avelength: 596 nm ilar information n square deviatio t 596 nm is trigg the on, ean y in ing on s a an cal

ter was ( ) hat ack in at int red ase In his can his we 41 int

ter

hat ole gle ws to ow n of m.

as on.

ger

point m deviatio layers a minimiz wavelen as it cor an optic the trigg For t mappin monitor trinary phase r restrict D. Anti The l broadba with for

0 Antir nature.

to achie layer m wavelen transmi compat monitor mappin from 46 monitor is on lay We plot phase r that the associat higher p incomp combin efficient

Figure coating.

region.

monitoring-comp on showed that p and a change of m zing manufactu ngth at layer 38 a rresponds to a gr cal monitoring si ger point.

the monitoring o ng that there a

ring-compatible:

mapping include root mean square the number of po reflection coatin last standard thin and antireflection rmula:

Glass | 0.1703 0.2485L 1.1641H 0

reflection coating We restricted th eve perfect AR co must be equal to t ngth between 55 ittance of the l tible and the trigg ring or quartz m ng of the AR coat 60 to 500 nm tha ring based on the yers 2 and 6 tha tted in Figure 9 root mean squar ere is a good cor ted with a trigger phase errors the patible layers, the ning these two t t optical monitor

8 Trinary mapp . Yellow rectangl

atible until layer phase error incr monitoring wavel uring errors. T also appears as o green region, i.e. c ignal that crosses of the last 5 laye are two wavelen

603 and 606 nm es the waveleng e deviation and i ossible optical m ng

n film optical com n (AR) coating co 3H 0.4459L 2.05

0.9651L | Air.

g is hard to mon his analysis to the

oatings, the admit the one of the inc 50 and 650 nm. In

last layer is no gering method is monitoring. We p ting. One can se at is compatible w e criteria that we at are not trigger an overlap betw re deviation of th rrelation betwee r point monitorin larger the numb e higher the phas techniques, one ring procedure.

ping of the 7 fir gle shows trigger

r 39, phase root reases too much length at layer 38 This change of optimal in the trin

corresponding to s two extrema be rs, one can see o ngths that are m. One can see th gth that was dete

is therefore an ef onitoring strateg

mponent that wa overing the 550-6 544H 1.5162L 0.

nitor due to its e first 7 layers. Ind

ttance of the stac cident medium, i.

n other words, m ot trigger point s then limited to plotted in Figure e that there is a with single wave e have defined. M r point monitorin ween the trinary he last layer. One en these two crit ng-incompatible ber of trigger poin se error. We clear can quickly co

rst layers on an r point monitorin

mean square for the last 2 8 would allow f monitoring nary mapping o regions with efore reaching on the trinary trigger point hat once more, ermined from fficient way to gies.

as studied is a 650 nm region .2354H (

5) low reflective deed, in order ck after the 8

^th

.e. air for each monitoring the t monitoring-

turning point 8 the trinary a single region elength optical Main limitation ng-compatible.

mapping and e can also see teria. Regions layer result in nt monitoring- rly see that by nverge to an

antireflection

ng-compatible

Figure 9 Comparison of the final layer phase root mean square deviation (ϕRMSD) at 7th layer and the trigger point monitoring- compatible spectral regions as defined by trinary mappings.

However, we see that these two techniques did not permit to determine one single strategy but more a spectral range to select a monitoring wavelength. One can show that almost whatever the wavelength used in this range, good theory/experiment will be achieved. However, by running virtual deposition process for all the wavelength in this range, the strategy consisting in monitoring layers [1-8] at 488 nm can be shown to result in the lowest phase root mean square deviation and the spectral performances the closest to the theoretical one.

4. Experimental validations

We experimentally validated the determined strategies by depositing the thin film components using a Plasma Assisted Reactive Magnetron Sputtering (PARMS, Bühler HELIOS machine) combined with a Bühler OMS 5000 optical monitoring system. Each of the studied components were fabricated, except for the Fabry-Perot filter as the OMS 5000 did not allow easily switching from trigger point monitoring to turning point monitoring. For each of the components, the strategy was slightly adapted in order to account for refractive index dispersion of the HELIOS machine (Nb

2

O

5

and SiO

2

), but the determined wavelength did not deviate by more than a few nanometers compared to the one determined in section 3 without dispersion as the considered refractive indices are close to the one of the HELIOS machine. Finally, all samples were characterized using a Perkin Elmer Lambda 1050 spectrophotometer. We plotted in Figure 10 an overlay between theoretical and experimental performances.

Figure 10 Comparison the theoretical and experimental transmission/reflection in case of a) a mirror, b) a multicavity bandpass filter and c) an antireflection coating .

Regarding the mirror, one can see that trigger point monitoring- monitored mirror shows almost no measurable deviation from the theoretical profile, confirming that selecting a wavelength on the short- wavelength side of the main reflection lobe is an efficient strategy.

Regarding the multi-cavity bandpass filter, one can see a good theoretical/experimental agreement both close to the bandpass and over a broader spectral range. The central wavelength is shifted by

~0.5 nm and the main discrepancies in broadband domain are associated with the limited resolution of the spectrophotometer (here 1 nm) to maximize the signal-to-noise ratio. This result confirms that while Willey proposed to optically monitor most of the filter at 600 nm (except for some layers that need to be quartz-crystal monitored), a slight adjustment by a few nanometers of the monitoring wavelength allows accurate all-optical monitoring of this kind of filter.

Finally, one can see that we have been able to fabricate an antireflection coating with residual reflection within the [550-650] nm spectral range not exceeding 0.02%, confirming that the all-optical strategy is valid and efficient. Over a broad spectral range, the two curves match very well proving that we are very close to theoretical performances. In the low reflection zone, one can see that the discrepancy is lower than one order of magnitude. It can be due to limited sensitivity and precision of the spectrophotometer or very small errors that should not exceed 0.2 nm for each layer. In conclusion, this experimental demonstration shows that the proposed strategy is also compatible with all-optical monitoring of this type of optical function.

0 5 10 15 20

450 465 480 495 510 525 540 555 570 585 600 615 630 645 660 675 690 705 720 735 750 765 780 795

φ

RMSD

(°)

Wavelength (nm)

0 10 20 30 40 50 60 70 80 90 100

350 450 550 650 750 850 950 1050 1150

T ransm ittance (% )

Wavelength (nm)

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90 100

500 550 600 650 700

T ransm ittance (% )

Wavelength (nm)

Theoretical Experimental

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

500 550 600 650 700

T ransm ittance (% )

Wavelength (nm)

Theoretical

Experimental

5. Conclusions

We have developed a new approach for the determination of efficient all-optical monitoring strategy for the manufacturing of thin film optical components. It is based on the generation of a trinary mappings that allow defining a range of possible wavelengths that are trigger point monitoring-compatible. These mappings that do not rely on virtual deposition process, but on an analysis of the optical monitoring signals obtained for all monitoring wavelengths, using some criteria and applying some limits to determine whether a wavelength can be used for the optical monitoring of its thickness or not. This method does not provide the best optical monitoring strategy, but a range of possible one. This technique can then be combined with a technique based on phase root mean square deviation analysis at a single representative wavelength (ϕ

RMSD

). The wavelength that allows minimizing ϕ

^RMSD

is then selected an optimal optical monitoring wavelength. By combining these two techniques, it is then possible to find an efficient optical monitoring strategy. This approach was illustrated on different examples including mirror, bandpass filters and antireflection coatings. For each of them we determined a single all optical monitoring strategy that was validated using virtual depositions process. It is finally worth noting that all these results were experimentally validated by implementing these strategies on plasma Assisted Reactive Magnetron Sputtering machines.

Acknowledgment. This work was performed within the LabTOP (Laboratoire commun de Traitement OPtique des surfaces), a research cooperation agreement between Institut Fresnel (Aix-Marseille Univ, CNRS, Centrale Marseille) and CILAS Company.

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