wk6b - Todays summary Polarization Energy / Poyntings...

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Unformatted text preview: Todays summary Polarization Energy / Poyntings vector Reflection and refraction at a dielectric interface: wave approach to derive Snells law reflection and transmission coefficients total internal reflection (TIR) revisited IT 2.71/2.710 Optics 0/13/04 wk6-b-1 Polarization IT 2.71/2.710 Optics 0/13/04 wk6-b-2 Propagation and polarization x y k wave-vector z E electric field vector const. efront planar wav = r k ) to parallel not have could one crystals, e.g. media, c anisotropi in : (reminder generally, More i.e. etc.) glass, amorphous space, free (e.g. media isotropic In D E D k E k E k = = IT 2.71/2.710 Optics 0/13/04 wk6-b-3 Linear polarization (frozen time) z y x t =0 E ( z =0, t =0) E ( z = , t =0) p h a s e = c o n s t a n t o n t h e p l a n e E ( z = /2, t =0) =0 =2 IT 2.71/2.710 Optics 0/13/04 wk6-b-4 Linear polarization (fixed space) t y x z =0 E ( z =0, t =0) E ( z =0, t =2 / ) p h a s e = c o n s t a n t o n t h e p l a n e E ( z =0, t = / ) =0 =2 IT 2.71/2.710 Optics 0/13/04 wk6-b-5 Circular polarization (frozen time) z y x t =0 E ( z =0, t =0) E ( z = /2, t =0) p h a s e = c o n s t a n t o n t h e p l a n e E ( z = , t =0) =0 =2 IT 2.71/2.710 Optics 0/13/04 wk6-b-6 Circular polarization: linear components + E x E y z z IT 2.71/2.710 Optics 0/13/04 wk6-b-7 IT 2.71/2.710 Optics 0/13/04 wk6-b-8 Circular polarization (fixed space) z y x E ( z =0, t =0) E ( z =0, t = / ) E ( z =0, t = /2 ) E ( z =0, t =3 /2 ) rotation direction /4 plate z Linear Linear polarization polarization Circular Circular polarization polarization birefringent /4 plate IT 2.71/2.710 Optics 0/13/04 wk6-b-9 /2 plate z Linear Linear polarization polarization Linear (90 Linear (90 o-rotated) rotated) polarization polarization birefringent /2 plate IT 2.71/2.710 Optics 0/13/04 wk6-b-10 Think about that birefringent /4 plate L i n e a r L i n e a r p o l a r i z a t i o n p o l a r i z a t i o n z mirror I n c o m i n g I n c o m i n g ? ? ? ? ? ? ? ? O u t g o i n g O u t g o i n g IT 2.71/2.710 Optics 0/13/04 wk6-b-11 Relationship between E and B ( ) E k B k x E B E r k = = = 1 and e where i t i E t t i E B k Vectors k , E , B form a right-handed triad. Note: free space or isotropic media only IT 2.71/2.710 Optics 0/13/04 wk6-b-12 Energy IT 2.71/2.710 Optics 0/13/04 wk6-b-13 The Poynting vector B E B E S = = 2 1 c E B S so in free space k S || S has units of W/m 2 so it represents energy flux (energy per unit time & unit area) IT 2.71/2.710 Optics 0/13/04 wk6-b-14 Poynting vector and phasors (I) 2 2 1 E S E E B E k B B E S c c k c = = = = = For example, sinusoidal field propagating along z ( ) ( ) t kz E c t kz E = = 2 2 cos cos S x E Recall: for visible light, ~10 14-10 15 Hz IT 2.71/2.710 Optics 0/13/04 wk6-b-15 Poynting vector and phasors (II)...
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wk6b - Todays summary Polarization Energy / Poyntings...

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