The Production of Polarization

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Adele Caldwell
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1 Physics 36: Waves Lecue 13 3/31/211 The Poducion of Polaizaion Today we will alk abou he poducion of polaized ligh. We aleady inoduced he concep of he polaizaion of ligh, a ansvese EM wave. To biefly eview (see Lecue 3): A. Linea o Plane Polaizaion The ±-diecion of E (o B ) says consan in ime. Popagaion diecion E B Popagaion diecion E B E B ½ peiod, T, lae B E Le Geneally, E E e = ( kz" ) E E xi ˆ = + E i y ˆj Re ( E) = E cos( kz " ) iˆ + E cos( kz " ) ˆj = ( E iˆ + E ˆj ) cos( kz " ) x y x y No ime dependence Page 1 of 9

2 Physics 36: Waves Lecue 13 3/31/211 y E ( kz " ) E y cos ( ) E x cos kz " Linea Polaizaion Schemaic: x B. Unpolaized The diecion of E vaies andomly wih ime. C. Cicula Polaizaion The E - (and B -) field oae wih ime. We wie he elecic field as Page 2 of 9

3 Physics 36: Waves Lecue 13 3/31/211 E i( kz ) i( kz ) ( iˆ " " + ij ˆ) E e = ( xˆ + iy) E e = ˆ Fom Eule s equaion fo complex vaiable e i = cos + isin We will subsiue in fo he exponenial on he igh-hand side o ge E = = = i( kz" ) ( xˆ + iyˆ ) E e ( xˆ iyˆ = + ) E( cos( kz " ) + isin( kz " ) E ( ( kz ) xˆ i ( kz ) xˆ i ( kz ) yˆ ( kz ) yˆ cos " + sin " + cos " " sin " ) E ( cos( kz " ) xˆ " sin( kz " ) yˆ + i( sin( kz " ) xˆ + cos( kz " ) yˆ ) Hence, Re ( E) = E cos( kz " ) xˆ " E sin( kz " )yˆ We see he x- and y-componens ae 9º ou of phase and he magniude, E, is independen of ime. To see wha is happening in his complex siuaion, le us fix z = and vay ime. j E a a lae ime sin (" ) = " sin( ) k i E a = E y sas wih zeo value and evolves inceasing o be >. Looking ino an on-coming wave, E oaes aniclockwise. This is lefhanded cicula polaizaion. Cicula Polaizaion Schemaic: Page 3 of 9

4 Physics 36: Waves Lecue 13 3/31/211 E-field vaiaion ove ime (and space) y x kz- = 9 kz- = Poducion of Polaized Ligh How do we poduce polaized ligh? Any ineacion of ligh wih mae whose opical popeies ae asymmeic along diecions ansvese o he popagaion veco => polaized ligh. We will conside he following pocesses ha poduce polaized ligh: 1. Dichoism (o, selecive absopion) 2. Reflecion 3. Scaeing 4. Bifingence (o, double efacion) 1.Dichoism A dichoic polaizes by selecively absobing ligh wih E field along a unique diecion chaaceisic of he dichoic maeial. Simples such device: Wie gid polaize Page 4 of 9

5 Physics 36: Waves Lecue 13 3/31/211 As shown above, his consiss of simply paallel conducing wies whee gid spacing << λ (can do his fo micowaves). Le us suppose we have unpolaized ligh inciden on his gid. The E field can be esolved ino 2 ohogonal coodinaes in he x and y diecions. Le us say ha he y-axis is chosen o be along he wies. Then, E y : Dives conducion elecons along wies. Gives ise o a cuen. Enegy ansfeed fom field o wie (wie heas up) Acceleaing elecons adiae like dipoles Dipoles do no adiae along dipole axis They adiae in fowad and backwad diecion I uns ou ha he fowad diecion is emied a 18 ou of phase fom inciden adiaion Resuls in cancellaion of fowaded ansmied componen along y-diecion The backwad componen is he efleced ay E x canno similaly dive elecons ino oscillaion since i is pependicula o he wies in gid Ne esul: Lile ansmission of y-componen. x-componen ansmied unaleed. You ge polaized ligh ou wih diecion pependicula o wie gid. Fo opical wavelenghs Simila idea bu conducion pahs analogous o wies in gid mus be much close. Page 5 of 9

Physics 36: Waves Lecue 13 3/31/211 Mos common polaize: Polaoid H-shee invened by Edwin Land. This is a clea shee of polyvinyl alcohol heaed and seched along one diecion.

Tansmission axis is pependicula o diecion of seching.

6 Physics 36: Waves Lecue 13 3/31/211 Mos common polaize: Polaoid H-shee invened by Edwin Land. This is a clea shee of polyvinyl alcohol heaed and seched along one diecion. Hydocabon molecules align along diecion of seching. Maeial hen dipped in iodine soluion povides conducion elecons molecula chains fomed (analogous o wies in gid). Tansmission axis is pependicula o diecion of seching. If linealy polaized ligh is inciden on he polaize and he angle beween he E field and he ansmission axis of he polaize is θ, hen we have: This is called Maus Law. E I ansmied ansmied = E cos = I cos 2 2.Reflecion This is he pinciple behind Polaoid sunglasses. I is one of he mos common foms of polaized ligh. Conside he case whee a linealy polaized wave is inciden on an ineface whee E is pependicula o he plane of incidence as shown below: The E field dives he bound elecons in he medium, in his case pependicula o he plane of incidence (pependicula o he page). hey adiae. Some of his adiaion is adiaed along he efleced beam diecion = efleced beam. E, E ae also pependicula o he plane of incidence as shown in he Figue. Page 6 of 9

7 Physics 36: Waves Lecue 13 3/31/211 θ E i θ i E n i n θ E i Now conside he case whee E is paallel o plane of incidence as shown below. E field in ansmied medium is pependicula o diecion of popagaion and also paallel o he inciden plane. This is he diecion ha he oscillaos ae diven (noe: diecion of beam can be calculaed via Snell s law). Noice ha in his case, he efleced ay diecion makes a small angle θ w. o dipole axis of efaced ay lile adiaion is emied fom a dipole o dipole axis. If θ= + = 9. In his case, efleced ay would vanish eniely. (Why? Because efleced ay diecion is fully paallel o dipole axis no adiaion). E i θ i θ E θ n i n θ E i The paicula angle of incidence whee his occus is called Bewse s angle θ P i = = p when + = 9 So, using Snell s Law: n sin = n sin i P Bu, = 9 ", so we have: n sin = n cos P i P P n an P = Bewse s Law n i P Page 7 of 9

Physics 36: Waves Lecue 13 3/31/211 When n i =1 (ai) and n =1.5 (glass) θ P 56 So, a his angle of incidence, only he componen of E pependicula o he plane of incidence is efleced.

8 Physics 36: Waves Lecue 13 3/31/211 When n i =1 (ai) and n =1.5 (glass) θ P 56 So, a his angle of incidence, only he componen of E pependicula o he plane of incidence is efleced. No eflecion of componen of E paallel o he plane of incidence. 3.Scaeing Scaeing of ligh off ai molecules poduces linealy polaized ligh in a plane pependicula o inciden ligh. Why? Can hink of scaees (molecules in amosphee) ad dipole adiaos: Remembe, dipole adiao emi max. adiaion pependicula o dipole axis (no adiaion along axis of oscillaion). Theefoe, 9 away fom beam of incidence diecion, scaeed ligh will be linealy polaized. Vibaions fom paicles adiae o obseves only when vibaion is pependicula o obseve s line of sigh, so ligh will be polaized along diecion of vibaion. 4.Bifingence Thee ae maeials displaying asymmeic behavio whee he speed of he wave in one diecion is diffeen han in he pependicula diecion wo diffeen values of index of efacion, n wo efaced beams. These maeials ae said o be bifingen. Le s say you shine ligh hough a plae of bifingen maeial. Le s say E is paallel o opic axis ligh will avel wih some velociy. Page 8 of 9

Physics 36: Waves Lecue 13 3/31/211 Le s say E is pependicula o opic axis ligh will avel wih some diffeen velociy. Le s say E is a 45 o opic axis. Can beak up ino equal ampliude x and y componens.

9 Physics 36: Waves Lecue 13 3/31/211 Le s say E is pependicula o opic axis ligh will avel wih some diffeen velociy. Le s say E is a 45 o opic axis. Can beak up ino equal ampliude x and y componens. Since E and E avel a diffeen speeds, if hey sa ou in phase, hey x y will no coninue o be in phase as hey avel hough he maeial. Resul: polaizaion changes as wave passes hough plae. If hickness of plae is chosen such ha hee is a 9 phase shif beween E x and E y when hey emege ge ciculaly polaized ligh ou. This is called a quae wave plae because i poduces a λ/4 phase shif. This is illusaed below: If he hickness of he plae is d, he hickness of a quae wave plae would be given by: n1d " n2d = 4 Page 9 of 9

Lecture 22 Electromagnetic Waves

Lecture 22 Electromagnetic Waves Lecue Elecomagneic Waves Pogam: 1. Enegy caied by he wave (Poyning veco).. Maxwell s equaions and Bounday condiions a inefaces. 3. Maeials boundaies: eflecion and efacion. Snell s Law. Quesions you should