Field guide to polarization by Edward Collett

By Edward Collett

The polarization of sunshine is among the so much awesome phenomena in nature and has resulted in various discoveries and purposes. the character and mathematical formula of unpolarized mild and in part polarized gentle weren't without problems drawing close till the Fifties, while questions about polarized mild and the mathematical instruments to house it all started to be addressed in earnest. consequently, there's a first-class realizing of polarized mild today.

The fundamental goal of this consultant is to supply an advent to the advancements in polarized gentle that experience taken position over the last half-century, and current the main salient themes of the subject material resembling Mueller matrices, Stokes polarization parameters, and Jones matrices

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Along the optic axis v ″ 2 = v o 2 , and perpendicular to the optic axis v ″ 2 = v e 2 . The maximum phase shift occurs when the propagation is perpendicular to the optic axis. The phase shift φ of the wave propagating through a wave plate is then φ= 2π (no − ne )d, λ where no and ne are the refractive indices of the ordinary and extraordinary axes, respectively, and d is the path length. org/terms The Observable Polarization Sphere 41 Multiple and Zero-Order Wave Plates For a QWP and a HWP, the optical thickness ( no − ne )d can be expressed as (no − ne )d = ( 4m + 1 ) λ λ = mλ + = mλ + k1λ, 4 4 (no − ne )d = ( 2m + 1 ) λ λ = mλ + = mλ + k2 λ, 2 2 where m = 0 , 1 , 2 ⋅ ⋅ ⋅ , and k 1 = 1 / 4 and k 2 = 1 / 2 , respectively.

The Stokes vector SR is SR ⎛ cos2 α − + cos2 α + ⎞ ⎛ S0 R ⎞ 2 ⎜ ⎟ ⎜ ⎟ S1 R ⎟ 1 ⎛ tan α − ⎞ ⎜ cos2 α − − cos2 α + ⎟ ⎜ . = = ⎟ ⎜ S2 R ⎟ 2 ⎝⎜ sin α + ⎠⎟ ⎜ 0 ⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ 0 ⎝ S3 R ⎠ ⎝ ⎠ The DOP P of the reflected light is P= S1 R S0 R = cos2 α − − cos2 α + . cos2 α − + cos2 α + In general, P is less than 1. If, however, cos α + = 0 then P = 1 ( = 100%) and i + r = π / 2 . This is the Brewster’s angle condition and SR then reduces to ⎛ S0 R ⎞ ⎛1 ⎞ ⎜ ⎟ ⎜ ⎟ S1R ⎟ 1 1 2 SR = ⎜ = cos 2iB ⎜ ⎟ . ⎜ S2 R ⎟ 2 ⎜0⎟ ⎜⎜ ⎟⎟ ⎜ ⎟ ⎝0⎠ ⎝ S3 R ⎠ Thus, at the Brewster’s angle, iB, the reflected light is LHP and the LVP component vanishes.

A crystal is generally characterized by three orthogonal axes, the x-, y-, and z-axis. Along these axes the propagation velocities of a wave are called the principal velocities vx, vy, and vz , and are expressed by vx = c / ε x , vy = c / ε y , vz = c / ε z , where εx, εy, and εz are the principal dielectric constants and c is the speed of light. The velocity of propagation v of a wave in a crystal is governed by Fresnel’s equation of wave normals sx, sy, and sz: 2 sy sx 2 sz 2 + + = 0. v2 − vx 2 v2 − vy 2 v2 − vz 2 There are two solutions for v and are found to correspond to a spherical wave and an ellipsoidal wave.

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