direction of linear elliptical circular linear polarisation unpolarised vector components, Haidinger s brush

Transcription

1 Plarisatin f The f is scarcel discernable with ur ees Plarisatin describes the behaviur f the electric field assciated with tpes f are linear, elliptical, circular, unplarised Remember that in istrpic materials, Plane f electric is a transverse field Directin f travel wave Linear The directin f the electric field at a pint stas cnstant in time its directin is the directin f linear its cmpnents alng the and aes must alwas sta in step Directin f travel Linearl plarised mathematicall, the 2 cmpnents f at pint alng the wave can be written, t csk t, t csk t A nte n cmpnents f, the electric field, has a directin and a sie it is a vectr, like a displacement ver electric field f magnitude has cmpnents, and cs the sies f the cmpnents depend n the angle between and the ais sin Plarid transmits the cmpnent f alng its ais (see later) alng + alng is equivalent t Haidinger s brush Sme peple can detect the directin f linear f linear directin A ver faint figure is visible in linearl plarised a few degrees acrss in the centre f ur field f view if u rtate a piece f plarid in frnt f ur ee, this figure rtates with the plarid The figure is called Haidinger s brush Relatinship between irradiance f and electric field Light meters measure irradiance, cameras and ur ees respnd t irradiance The irradiance,, is prprtinal the average square f the electric field: 2 Plarisatin phenmena are abut the directin and amplitude f the electric field wave, Plarid sheet Plarid prduces linear f b transmitting the electric vectr alng the ais f the plarid and absrbing the perpendicular electric vectr Directin f absrptin Plarid Plarid sheet Directin f transmissin Plarid placed in frnt f plarised transmits the mst when its ais is rtated t the directin f and least when Plarised 1

2 % f Light can be partiall plarised Measure the maimum intensit ma and the minimum intensit min Calculate the % in the directin f maimum intensit ample: % Named directin Measuring min if ma = 2 min, then % = 100/3 = 33% ma ma min min Measuring ma 100 Circular With circular, the and amplitudes are bth equal (call them ) but there is a phase difference f /2 between them Circular cmes in tw flavurs right circular, in which rtates clckwise lking back dwn alng the directin f prpagatin Circularl plarised csk t sink t left-hand circular circular can t be distinguished thrugh a sheet f plarid Lking back twards the surce Cmbinatin f ppsite circular s f u cmbine right-handed and left-handed circular in equal amunts, u get linear Right circular + Left circular linear cs k t cs k t sink t sink t k t 2 cs The angle (i.e. the directin f the linear ) depends n the phase difference between ne cmpnent (e.g. cmpnent) f the tw hands relevant t interpreting ther phenmena = Applicatin f circular Circular plarisers are used t enhance the cntrast f LD displas Backgrund is circularl plarised befre it reaches the reflecting frnt f the displa The handedness f the is changed b the reflectin and it fails t get back thrugh the plariser The direct frm the displa des pass thrugh the plariser Backgrund incident Displa nl seen Circular plariser ncident circularl plarised Reflected with ppsite circular Displa llipticall plarised With elliptical, the amplitudes f and cmpnents are generall nt equal and neither are phases between the cmpnents anthing special csk t csk t llipticall plarised lliptical is the mst general case = 0 is the special case f linearl plarised = ±/2 and = gives circularl plarised Lking back twards the surce Unplarised Unplarised cnsists f where the directin f varies at randm between successive measurements at ne pint an directin is equall likel Unplarised can be cnsidered as a cmbinatin f equal amunts f linear in tw directins at right angles, where the tw cmpnents are incherent Unplarised values in successive instants 2

3 Prducing linear Wire grid plariser Plarid sheet Transmissin thrugh a wire grid the distance between wires < /4 Transmissin directin mdern plarid sheet wrks in a similar wa Scattering f sun b the atmsphere bees and ther insects use plarised t navigate Reflecting reflectins can be reduced b lking thugh plarid sunglasses riented t cut ut the strngest Transmissin thrugh birefringent materials used in the petrlgical micrscpe analsis f strain in transparent materials Malus law Plarised, amplitude A = cs 2 nd plarid, analser 1 st plarid, plariser Linearl plarised, amplitude, intensit Malus law gives the irradiance transmitted b an analsing plariser, A, set at angle t the directin f plarised f irradiance The irradiance f the transmitted varies as cs 2 this is just what u d epect frm ur earlier sectin n the relatinship between irradiance and amplitude A 0 cs e.g. a plariser is set at 30 t the directin f plarised, hw much is transmitted b the plariser? fractin transmitted = 0.75 A cs Unplarised 2 Rtating the directin f Optical activit Plarised beam Sample Several sheets f plarid in successin will rtate the directin f f 3 plarisers rtated b 20 t each ther Sme mlecules, such as sugar slutins and quart, can d the same nl mre efficientl. This abilit is called ptical activit, r smetimes rtar Opticall active materials rtate the directin f as the prpagates thrugh detr-rtatr; lev-rtatr measured b specific rtatin, in mm -1 fr slids Cause is that left and right circularl plarised have different refractive indices n R and n L. linearl plarised travels thrugh as tw circularl plarised ras, at sl different speeds as their phase difference varies, s the directin f linear alters Chiral mlecules Optical activit is caused b mlecules that have a helical twist, called chiral mlecules All chiral amin acids are l- rtatr wh? Natural sugars like detrse are d-rtatr (Sme ptical activit can be caused b twisted mlecular arrangements) Detrse red ellw - C blue H bnds Liquid crstal displas An LCD piel uses crssed plarisers t prduce the dark state and an electricall induced change f t prduce the bright state The ppular twisted nematic LCD: LCD Liquid crstal (~10m) Cnducting laer Glass Crssed plariser Linear plariser Glass Thin cnducting laer Mirrr 3

4 Mlecular rientatins with an LCD The alignment f mlecules is induced b a surfactant t prduce a highl pticall active cell A small vltage is sufficient t re-align the mlecules N vltage Natural state with built-in 90 twist. +ve ve Applied vltage Mlecules awa frm surface re-align Plarisatin b scattering Vibrating electrns emit asmmetricall mst is emitted t their vibratin directin n is emitted alng their vibratin directin Unplarised incident lectric field mst strngl seen lectrn vibratin Light scattered thrugh 90 is strngl plarised The blue sk is plarised, particularl at 90 frm the sun use is made f this b insects, particularl bees, fr navigating The Brewster angle tan B n incident Parallel Refractive inde n Perpendicular transmitted reflected The Brewster angle, B, is the angle f incidence at which the reflected is 100% plarised, t the plane f incidence The reflected and transmitted ras are at 90 ample: fr n = 1.5, B = 56.3 B Plarisatin b reflectin Fractin f reflected at different angles f incidence depends n its linear pl n Fractin reflected versus angle f incidence fr n= i Strng transmitted beam plarised in plane f diagram Weak Brewster angle reflectin, plarised t plane f diagram Pile f plates Brewster angle ncident Observatin in nature Pile f plates plariser The plarising micrscpe Birefringence The plarising micrscpe incrprates a plariser the sample is illuminated b linearl plarised An analser allws the f the image t be investigated the analser is ften set at 90 t the plariser the gelgists versin is the petrlgical micrscpe bserver analser eepiece bjective specimen plariser cndenser surce Birefringence is a new range f phenmena pened up b the anistrp f materials t the prpagatin f These materials usuall transmit as tw ras, even when ne is incident CaCO 3 (calcite, celand spar) is the archetpical slid CaCO 3 viewed up heagnal ais 4

5 Ordinar & etrardinar ras Principal plane O Tp view f rhmb O. Side view f rhmb in principal plane indicates plarised t principal plane indicates plarised t principal plane lcates image f dt belw surface The rdinar ra bes Snell s law The etrardinar ra deviates in a plane cntaining the ptic ais directin f the crstal such a plane is called a principal plane Bth ras are linearl plarised at right angles t each ther Christiaan Hugens: eureka! Hugens' packing drawings Waves in a uniaial crstal Prpagating rdinar waves Calcite ptic ais 3-fld ais Ordinar ras are prpagated b an epanding spherical wave the electric vectr is ptic ais refractive inde n = c/v trardinar ra is prpagated b an epanding ellipsidal wave the electric vectr is princ. plane smallest refractive inde n e =c/v b Sectin ptic ais a Ordinar waves prpagate as u wuld epect frm Hugens principle The refractive inde n fr calcite is n e fr calcite is Crstal surface Spherical wavelets f rdinar waves calcite is an eample f a negative uniaial crstal, because n e < n Prpagating rdinar wavefrnts in crstal Prpagatin f etrardinar waves Prpagating etrardinar wavefrnts in crstal Birefringence is related t crstal class Cubic istrpic Remember that etrardinar wavelets prpagate as ellipsidal wavefrnts Crstal surface ellipsidal wavelets f etrardinar waves The aes f the ellipsids are inclined t the surface The cmmn tangent cuts the ellipsids ff t the side The directin f the prpagating ra is therefre nt perpendicular t the surface inside an anistrpic crstal, the etrardinar is generall nt a purel transverse wave Biaial crstals have 2 etrardinar ras; the are cmplicated (Trignal) Tetragnal, Heagnal, Rhmbhedral uniaial Orthrhmbic, Mnclinic, Triclinic - biaial 5

6 Light incident ptic ais Bth ras travel tgether, prducing n special effects Light incident ptic ais The 2 s travel at speeds c/n and c/n e, acquiring a phase difference Plate thickness Optic ais dge-n view f plate Plate thickness Optic ais int plane indicates plarised plane f diagram indicates plarised plane f diagram dge-n view f plate Light incident when the ptic ais is t the plate n interesting effects Light incident when the ptic ais is t the plate Plarisatin change during prpagatin Minerals and the micrscpe The phase change between the 2 ras is (n -n e )2/ vac f the 2 ras start ff with equal amplitude, then the diagram shws hw the changes with, the distance travelled the sequence happens ever 3 m in calcite 100 m is mre tpical f minerals Phase difference Analser Sample Plariser picture Appearance f Mn rck in the plarising micrscpe curtes : micr.magnet.fsu.edu strpic material appears black; birefringent material appears with clurs the mst intense clurs are when the ptic ais is at 45 etinctin ccurs when the ptic ais is r t the plariser additinal cluring is prvided b plechrism, selective dependent absrptin f sme clurs Demnstratin eample The first picture shws several sheets f mica f different thicknesses seen in rdinar Strain in transparent materials Clurs are caused b strain induced birefringence als b variatins f thickness fr a 1 mm thick material, 360 phase shift is caused when (n n e ) The secnd picture, the same sheets between crssed plarids 6

7 Retarders Thickness d Fast ais Slw ais A retarder is a unifrm plate f birefringent material whse ptic ais lies in the plane f the plate. Retarders can be used t make circularl plarised analse ellipticall plarised interpret clurs in the plarising micrscpe Slw ais is ptic ais fr calcite fast ais is slw ais Phase retardatin, in radians k dn n vac slw fast Retardance A full-wave plate retards the slw wave relative t the fast wave b 2 radians A quarter-wave plate retards b /2 in terms f phase, the retardance is chrmatic the retardance ma be measured in wavelength e.g. a retardance f 250 nm, which is d(n slw -n fast ) Wh bther? e.g. in the plarising micrscpe, sliding in a retarding plate between sample and analser enables a micrscpist t decide hw birefringent the sample is, helping identificatin f the sample Making circularl plarised Circular is made b shining linearl plarised at 45 nt a quarterwave retarder An in Linear plarising sheet A circular plariser Plarising ais Quarter-wave plate ais at 45 t the plarid ais Circular ut The utput lks like: t cs k t sin k the + sign ccurs if the slw ais is directin, giving right circularl plarised utput -ve sign fr slw ais t ais, giving left circularl plarised 7