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05_03_16

# 05_03_16 - 95 Projection amplitudes for linear and circular...

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[email protected] 95 Projection amplitudes for linear and circular polarization 03/16/2005 The field of any plane light wave with frequency Q can be decomposed in linear polarization and in circular polarization: Example: Corresponding projection amplitudes Example of circular polarization: Corresponding complex projection amplitudes ] ) Re[( ) ( t z k i y y x x e A e A e E ϖ - + = & & & , ] } Re[{ ) ( t z k i y L x R e B e B e E ϖ - + = & & & T T y e & x e & x e & y e & ] ) sin cos Re[( ] Re[ ) ( ) ( t z k i y x t z k i x e e e e e ϖ ϖ ϑ ϑ - - + = & & & ϑ ϑ ϑ ϑ cos | , sin | sin | , cos | = < - = < = < = < y y y x x y x x x e E & & ] ) Re[( ] Re[ ) ( 2 1 2 1 ) ( t z k i y x t z k i R e e i e e e ϖ ϖ - - - = & & & 2 2 , y x y x e i e L e i e R e e & & + - = = 2 1 2 1 2 1 2 1 | , | | , | i L y L x i R y R x = < = < - = < = <

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[email protected] 96 Properties of projection amplitudes 03/16/2005 Probability to be in a given state: After the analyzer: After the combiner: Since this has to hold for arbitrary states Y and for any complete sets of states like R and L : 1 | | | 2 = Ψ Ψ < * | | Ψ Φ =< Φ Ψ < 1 | | | | | 1 | | | | 1 | | | | | | * * 2 2 = Ψ Ψ =< Ψ < Ψ < + Ψ < Ψ < = Ψ < Ψ < + Ψ < Ψ < =
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05_03_16 - 95 Projection amplitudes for linear and circular...

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