Application Note Waveplates Retarders

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Transcript of Application Note Waveplates Retarders

Page 1: Application Note Waveplates Retarders

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Waveplates�/�RetardersApplication�Note

Page 2: Application Note Waveplates Retarders

You�need�to�control�the�state�of�polarization�of�your�light�beam?�You�need�to�change�the�direction�of�polarization�of�your� beam?� Or� you� need� to� change� from� linear�polarization�to�circular�polarization�or�vice�versa?�Or�you�need�to�create�any�other�specific�state�of�polarization?

If�you�have�to�perform�any�‒�or�any�combination�‒�of�these�tasks,� then� you�will� have� to� use� (apart� from� polarizers)�retardation�plates;�sometimes�retardation�plates�are�just�called� wave� plates� or� retarders.� The� purpose� of� a�retardation�plate�is�to�introduce�a�specific�phase�difference�or�retardation�between�the�two�orthogonal�components�of� the� electromagnetic� light� field.� When� the� plate�introduces�a�retardation�of�90°�or�π/2,�then�the�plate� is�called�a� ,�for�a�retardation�of�180°�or�π�it�quarter�wave�plateis�called�a� .�Normally,�a�retardation�plate�half�wave�platewill�introduce�a�particular�retardation�only�for�one�specific�wavelength�(the�design�wavelength)�and�for�one�specific�orientation�of� the�plate�with� respect� to� the�direction�of�light�propagation,�which�in�almost�all�cases�is�the�direction�of�normal�incidence;�also�the�temperature�has�an�influence�on�the�actual�retardation.Retardation�plates�are�available�in�various�materials,�and�they�come�in�three�basic�types:

� �1.� Multiple�order�plates:They� create� a� large� phase� difference,� several� times� the�wavelength�plus�a�fraction�of�the�wavelength,�but�only�the�fraction�is�effective�because�multiples�of�2π�cancel�out.�2.� Quasi�zero�order�plates:�They�consist�of�a�pair�of�almost� identical�multiple�order�plates�with�crystal�axes�oriented�orthogonally,�such�that�only�the�difference�in�phase�retardation�is�effective.�3.� True�zero�order�plates:�They� are� extremely� thin,� such� that� they� create� a� phase�difference�which�is�truly�only�a�fraction�of�a�wavelength.Before�selecting�the�material,�the�appropriate�type�should�be�determined.�If�your�light�beam

�1.� is�directionally�stable,�2.� is�well�collimated,�3.� has�narrow�spectral�bandwidth,�4.� travels�in�a�thermally�stable�environment,�5.� has�low�intensity,�both�spatially�and�temporally,

then�the�type�does�not�really�matter,�and�you�should�make�your� selection�mainly� based� on� price� and� other� optical�properties� which� are� important� for� all� kinds� of� optical�components�(apart�from�other�considerations�such�as�lead�time,� reliability� etc.� which� you� apply� in� all� purchasing�decisions).

If� any� of� the� above� conditions� is� not� fulfilled,� then� the�decision� about� the� appropriate� type� will� be� more�demanding.� In� the� following�analysis,� the� impact�of� the�above�conditions�on�the�performance�of�the�three�types�of�wave�plates�is�examined.�Retardation�precision�is�shown�for� the� following� examples� which� are� paradigmatic� for�commercially�available�retardation�plates:

�1.� Multiple� order� plate:� single� Quartz� plate,� approx.� 1��mm�thickness,�2.� Quasi� zero� order� plate:� compound� Quartz� plate�(cemented,�optically�contacted,�or�air�spaced),�approx.�2��mm�total�material�thickness�(excluding�air�space),�3.� True� zero� order� plate:� Mica� or� Polymer,� bare� or�cemented�between�glass�flats,�thickness�corresponding�to�true�zero�order�condition.

Wavelength�of�light�is�in�the�green�range�(around�500�nm),�and�all�retardation�plates�are�considered�to�have�a�good�antireflective�coating.Let�us�first�consider�the�influence�of�direction�of�light�on�phase� retardation.�When� the�plate� is� rotated�around�an�axis� parallel� to� the� crystal� optical� axis,� then� the� phase�retardation�increases�approximately�with�the�square�of�the�angle�of�rotation,�whereas�for�rotation�around�a�perpen-dicular�axis� it�decreases.�The�absolute�values�of� increase�and�decrease�for�identical�rotation�angles�are�not�exactly�the� same,� but� almost� indistinguishable� for� all� practical�cases.�(Please�note�that�“increase”�and�“decrease”�do�not�have�an�absolute�meaning�here�but� relate� to� the�phase�retardation� at� zero� rotation:� If� this� phase� retardation� is�negative,� then� “increase”� means� that� it� becomes� even�more�negative.)

How�to�select�the�right�retardation�plate�for�your�particular�application

Page 3: Application Note Waveplates Retarders

The� following� three� diagrams� show� the� deviation� from�design�retardation�for�the�three�basic�types�of�retardation�plates,�both�as� �(left�scale,�red�line)�and�absolute�deviationas�a� � (right�scale,�blue�percentage�of�design�retardationline).�The�results�are�independent�of�the�particular�design�of�the�retardation�plate,� i.e.� it�does�not�matter� if� the�plate� is� a�quarter�wave�or�a�half�wave�plate�or�any�other�retardation�value:�the�deviation�is�always�the�same.�Please�note�that�the�scale�for�absolute�deviation�for�true�zero�order�plates�differs� (is� decreased� by� a� factor� of� 100)� from� the�corresponding�scale�for�the�other�two�types�so�that�the�deviation�becomes�visible.�

What�can�be�learned�from�these�diagrams?�

•�Retardation�plates�which�are�not�true�zero�order�plates�have� a� strong� dependence� of� retardation� on� angle� of�incidence.�•� Quasi� zero� order� plates� even� produce� twice� the� error�produced�by�multiple�order�plates.�Actually,�at�10°�angle�of�incidence� a� quarter� wave� plate� almost� becomes� a� half�wave�plate�and�vice�versa.�•�The�dependence�of�retardation�on�angle�of�incidence�is�almost�invisible�for�true�zero�order�plates�and�practically�negligible�for�most�real�life�applications.�

This�means�that�true�zero�order�plates�should�be�used�whenever�the�relative�orientation�of�the�light�beam�with�respect�to�the�retardation�plate�is�not�fully�controlled.�

But� this� is� not� just� a�matter�of�mechanical� instability�or�similar� effects,� but� also� a� matter� of� beam� collimation.�When� the� beam� is� not� perfectly� collimated,� then� it�contains�a�variety�of� ray�directions�‒�within� the�cone�of�beam� divergence.� All� these� ray� directions� will� have�different�angles�of�incidence�on�the�wave�plate,�resulting�in�different�phase�retardation�for�different�ray�directions.�Therefore�an�initially�completely�polarized�divergent�light�beam�will�become�partially�depolarized�on�transmission�through�a�retardation�plate.�Evidently,�the�depolarization�is�not�uniform�over�the�angular�field,�but�varies�with�the�individual�direction�of�each�light�ray.�As�mentioned�above,�retardation� is� decreased� for� rays� which� form� an� angle�≠90°�with�respect�to�the�crystal�optical�axis,�whereas�it�is�increased�for�rays�which�are�tilted�in�the�orthogonal�plane,�with� the� interesting� side� effect� that� retardation� is� not�changed�for�beams�which�are�tilted�by�the�same�angle�in�both�planes.�All�this�results�in�an�intensity�pattern�similar�to�the�pattern�shown�here�when�a�divergent,�initially�linearly�polarized�light�beam�is�transmitted�through�a�multiple�or�quasi�zero�order�half�wave�plate�and�then�through�a�linear�polarizer� (the� density� of� dark� and� bright� fringes� will�depend� on� birefringence,� plate� thickness,� and� beam�divergence).�

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Page 4: Application Note Waveplates Retarders

The� following� situation� may� serve� for� a� numerical�example:� A� linearly� polarized� beam� of� light� with� a�divergence� angle� of� 10°� is� transmitted� through� a� quasi�zero� order� half� wave� plate� oriented� at� 45°� (such� that� a�collimated�beam's�polarization�direction�would�be�rotated�by� 90°);� when� analyzed� with� a� crossed� polarizer,�approximately� 27%� of� the� incident� light� will� be�transmitted� instead�of�0%,�and� for�a�multiple�order�half�wave� plate,� which� is� not� quite� as� sensitive� to� angular�deviation,�it�is�still�9%.�In�other�words:�The�beam�becomes�heavily� depolarized� (50%� would� mean� "completely�depolarized").� This� is� particularly� annoying� when� the�application� is�an� imaging�application,�because� then� the�fringes�shown�above�will�become�visible.�In�contrast,�if�a�true� zero� order� plate� is� used,� the� depolarization� is�essentially�zero�(numerically:�0.0015%;�this�is�better�than�most�polarizers�can�achieve).�

Now�let's�consider�the�spectral�behavior�of�the�different�types� of� retardation� plates.� If� the� wavelength� of� light�changes,�then�the�retardation�of�the�wave�plate�will�also�change�for�2�reasons:�

1.�The�thickness�of�the�plate�when�measured�in�millimeters�remains�constant,�when�measured�in�units�of�wavelength,�it�evidently�changes�with�wavelength,�and�the�thickness�in�terms� of� wavelength� is� the� factor� that� determines� the�retardation.�

2.� As� usual,� the� difference� between� n � and� n � (the� two�o e

indices�of�refraction�which�determine�the�birefringence�of�the� material)� will� depend� on� wavelength,� so� that� the�retardation�will�change�even�if�the�mechanical�thickness�of�the�plate�is�adjusted�to�the�wavelength.�

nd stIn�general,�the�2 �effect�is�negligible�compared�to�the�1 .�ndNeglecting�the�2 �effect,�we�get�the�results�shown�in�the�

diagrams�on�the�right�for�our�3�types�of�retardation�plates:�By�design,�they�are�quarter�wave�plates�at�500�nm,�see�red�lines� and� left� scale� "Absolute� Retardation".� The� actual�retardation�of�multiple�order�plates�varies�drastically�with�wavelength�‒�as�expected:� It� is�exactly� the� result�of� the�multiplicity�of�the�retardation�order.�In�contrast,�quasi�and�true�zero�order�plates�behave�similar�and�show�only�very�moderate�wavelength�dependence�(~1/80�of�the�multiple�order� plate).� The� blue� lines� in� the� diagrams� show� the�deviation� from� design� retardation� in� percent.� The�percentage� scale� for� the�multiple�order� is�different� (is�increased�by�a�factor�of�40)�from�the�scales�in�the�other�two� diagrams,� otherwise� the� blue� line� would� be�essentially� horizontal� in� the� latter.� You� see� that� the�deviation� from� the�design� retardation� (one�quarter�of� a�wave)�reaches�and�exceeds�100%�within�a�few�nanometers�from�the�design�wavelength�for�multiple�order�plates,�or�in�

other�words:�Multiple�order�plates�change�their�character�over� very� small� wavelength� ranges,� even� become� half�wave�plates�(at�100%)�or�worse.�We�have� seen� above� that� directional� sensitivity� directly�translates� to� loss� of� polarization� for� divergent� beams.�Likewise,� wavelength� dependence� translates� to� loss� of�polarization�for�non-monochromatic�beams.�And�again,�zero�order�plates� turn�out� to�be�the�better�choice,�but�with�respect�to�wavelength�dependence�there�is�no�real�difference�between�true�and�quasi�zero�order�plates.�

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Page 5: Application Note Waveplates Retarders

The�retardation�of�any�given�wave�plate�also�depends�on�temperature�for�two�reasons:�

•��The�plate�thickness�varies�with�temperature.�

•� The� indices� of� refraction,� and� consequently� the� bire-fringence,�depend�on�temperature.�

These�effects�vary�with�material,�but�for�Quartz�and�Mica�the� temperature� dependence� is� similar.� For� any� given�material�the�following�statement�is�correct:�Quasi�and�true�zero�order�plates�exhibit�much�less�tem-perature�dependence�than�multiple�order�plates�made�of�the�same�material.�As�an�example�for�quarter�wave�plates�made� of� Quartz:� The� multiple� order� plate� will� be�approximately�80�times�more�sensitive�than�the�quasi�zero�order�plate.�From� the� discussions� above,� the� following� becomes�evident:�•� Whenever� the� wavelength� is� likely� to� change� or�whenever�the�spectral�bandwidth�is�not�extremely�limited,�a�multiple�order�plate�is�not�a�good�choice.�

•� Whenever� the� beam� direction� is� likely� to� change� or�whenever�the�beam�is�divergent�or�convergent,�neither�a�multiple�order�plate�nor�a�quasi�zero�order�plate�is�a�good�choice.�

•��A�true�zero�order�plate�is�a�good�technical�choice�under�all�conditions�that�make�the�other�types�unsuitable.�

Traditionally,� zero� order� plates� were� first�made� of�Mica�because�Mica�is�well�available�as�a�natural�mineral�and�was�

th(in�the�19 �century)�much�more�easily�handled�than�other�optical�crystal�materials.�In�particular,�by�simply�cleaving�Mica�sheets�along�a�natural�cleavage�plane,�one�was�able�to� obtain� wave� plates� with� good� quality� without� any�additional� optical� manufacturing� procedure.� Over� the�years,� optical� technology� proceeded,� and� it� became�commercially�feasible�to�produce�plates�from�more�or�less�

ndany�optical�crystal�material.�Furthermore,�in�the�2 �half�of�the�last�century�Polymers�were�developed�that�could�be�used� for� phase� retardation.� In� parallel,� Mica� somehow�

ndbecame� the� material� of� 2 � choice� only.� But� some�companies�in�the�world,�for�example�S�&�R�Optic�GmbH�of�Germany,� continued� to� improve� their� Mica� production�technology� further� and� further,� such� that� Mica� is� once�again�an�excellent�choice�for�zero�order�wave�plates.�In� the� following� table,� the�main� combinations� of� tech-nology�and�optical�material�are�compared�from�a�practical�perspective�as�far�as�they�differ�significantly.�Bare�Polymer�retarders�are�not�included�in�this�table�because�‒�due�to�their� extremely� small� thickness�‒� they�are�highly� fragile�and�not�suitable�for�the�vast�majority�of�applications:�

Material

Quartz

Quartz

Quartz

Quartz

Mica

Mica

Polymer

Type

Multiple�order

Quasi�zero�order

Quasi�zero�order

Quasi�zero�order

True�zero�order

True�zero�order

True�zero�order

Mounting�

Bare� Cemented

Optically�contacted

Air�spaced

Cemented

Bare� Cemented

Useable�wavelength�range�(nm)� 193�‒�2000

�400�‒�2000

�193�‒�2000

�193�‒�2000

�400�‒�1550

�350�‒�1550

�400�-�1550

�Practical�max.�diameter

�50�mm

�50�mm

�50�mm

�50�mm

�200�mm

�200�mm

�200�mm

�Typical�absorption��@�500�nm

negligible�

slight�

negligible�

negligible�

few�percent�

few�percent�

<�1%�

Damage�threshold,�pulsed�@�1064�nm,� 10-20�ns

�10�J/cm2� 0.5�J/cm2� 10�J/cm2� 10�J/cm2� 0.5�J/cm2� 10�J/cm2� 4�J/cm2�

Damage�threshold,�cw�@�VIS� -�NIR 10�MW/cm 2� 1.5�kW/cm2� 1�MW/cm 2� 1�MW/cm 2� 0.5�kW/cm2� 0.5�kW/cm2� 0.5�kW/cm2�

Homogeneity�of�retardation�over�aperture�(typ.�25�mm)

�λ/500

�λ/300

�λ/500

�λ/500

�λ/300

�λ/300

�λ/100

Precision�of�retardation � λ/300 � λ/200 � λ/300 � λ/300� λ/200� λ/200� λ/100�Temperature�dependence�of�retardation�per�o �C 0.3�% � negligible � negligible � negligible� negligible� negligible� 0.04�%�

Price�@�low�quantity � L L L LL J K LL Price�@�medium�quantity � J K K L JJ J K Price�@�high�quantity � J K K K JJ JJ J

Page 6: Application Note Waveplates Retarders

The�table�clearly�demonstrates�the�advantages�as�well�as�the� disadvantages� of� the� various� types� of� retardation�plates.�A�clear�advantage�of�Quartz�is�the�usability�in�the�UV�and� the� very� high� damage� threshold,� especially� the�continuous�wave� damage� threshold�which� results� from�the� very� low� absorption�of�Quartz.�Otherwise,�Quartz� is�usually�not�the�material�of�first�choice,�particularly�due�to�the� pricing� which� can� be� prohibitive� unless� a� multiple�order�plate�can�really�be�used�in�the�application.�

The� absorption,� and� the� associated� lower� cw� damage�threshold,� of� Polymer� and�Mica� are� essentially� the� only�disadvantages� of� these� materials� in� relation� to� Quartz.�Therefore,�usage�of�these�materials�is�generally�advisable�unless�the�particular�application�clearly�calls�for�one�of�the�positive� features� of� Quartz.� And� unless� the� lower�absorption� in� Polymers� justifies� a� considerably� higher�price,�true�zero�order�plates�made�of�Mica�are�the�best�choice� for� a� vast� majority� of� applications,� especially�when� price� is� a� consideration.� For� Mica,� "low� price"�generally�even�coincides�with� "good�availability":�Well�established�producers�of�Mica�retarders,�such�as�S�&�R�Optic�GmbH,�usually�have�a�great�variety�of�bare�Mica�sheets�in�single� nanometer� gradation� available� on� stock,� so� that�retardation� plates� for� almost� any� wavelength� in� the�useable�range�can�be�made�by�just�assembling�an�already�existing�Mica�sheet.�

In�conclusion:�

•��True�zero�order�plates�are�the�best�choice�under�technical�considerations.�

•� Quasi� zero� order� plates� behave� well� regarding�wavelength� and� temperature� effects,� but� behave� even�worse� than� multiple� order� plates� otherwise� under�variations�of�beam�direction.�

•� Multiple� order� plates� are� only� useful� when� all� optical�parameters�are�well�controlled.�

•� Cemented� Polymer� retarders� are� a� good� choice�technically,�but�are�usually�very�expensive.�

•��Mica�retarders�are�generally�the�preferred�choice�from�a� technical� point� of� view,� and� typically� they� are�more�easily�available�and�come�at�a�lower�price.�

Phone:��+49��641-�9�60�76�18Fax:�� +49��641-�9�60�79�43Email:� [email protected]:�� www.sr-optic.com

Dr.�Wolfgang�Schneider

Ludwig-Rinn-Str.�14�35452�HeuchelheimGermany