Chapter 5 . Polarization

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TABLE 2 Transmittances and Degree of <strong>Polarization</strong> for a Single Plate and Multiple Plates at the Brewster Angle θ B , where tan θ B n and θ 0 θ 1 90 † One plate (two surfaces) —————— ( T p ) sample ———————— ( T s ) sample ( T p ) sample ( T s ) sample m plates (2 m surfaces) P T p T s T p T s 1 T s / T p 1 T s / T p Single transmitted beams , no multiple reflections , no absorption Multiple reflections within plate , no interference ef fects , no absorption Multiple reflections within plate , no interference ef fects , small absorption Multiple reflections within plate , interference within plate , no absorption 1 2 n 4 n 2 1 1 e d 1 2 n 2 n 4 1 Œ 2 n 4 n 2 1 1 n 2 1 4 n 2 1 1 2 n 4 n 2 1 1 1 2 n 2 m n 4 1 m ‡ 1 [2 n / ( n 2 1)] 4 m ‡ 1 [2 n / ( n 2 1)] 4 m ‡ , Œ 1 [2 n 2 / ( n 4 1)] m ‡ , Œ 1 [2 n 2 / ( n 4 1)] m 1 § m § , 1 1 m ( n 2 1) 2 / 2 n 2 m [2 n / ( n 2 1)] 2 2 n 4 m [2 n / e d n 2 e m d ( n 2 1)] 4 m ‡ ‡ 1 1 1 [( n 2 1) / ( n 2 1)] 4 e 2 d m e 2 d 1 n 2 1 4 n 2 e m [2 n / 2 d ( n 2 1)] 4 m 1 1 1 [( n 2 1) / ( n 2 1)] 4 e 2 d m m 1 1 1 ( n 4 1) 2 4 n 4 sin 2 ‡ max 1 min 2 n 2 2 m n 4 1 e d 1 ( n 4 1) 2 4 n 4 sin 2 R p 0 R s n 2 1 2 n 2 1 Single surface T p 1 R p 1 T s 1 R s 2 n 2 n 2 1 P 1 [2 n / ( n 2 1)] 2 1 [2 n / ( n 2 1)] 2 † Where 4 π k ( n 2 1) 1/2 / n , 2 π n 2 d / ( n 2 1) 1/2 , n refractive index , k extinction coef ficient , d plate thickness , wavelength . ‡ No multiple reflections between plates . § Multiple reflections between plates . Formula of Provostaye and Desains , Ref . 23 . Œ Also holds for coherent multiple reflections averaged over one period of sin 2 .
POLARIZATION 5 .19 (a) (b) FIGURE 6 ( a ) Transmittance and ( b ) extinction ratio of four plane-parallel plates of refractive index n as a function of angle of incidence , for angles near the Brewster angle . Assumptions are multiple reflections but no interference within each plate and no reflections between plates . assumption is not valid for most real transmission polarizers (see Chap . 3 , ‘‘Polarizers , ’’ in Vol . II of this Handbook , specifically Brewster Angle Transmission Polarizers) . For most parallel-plate polarizers it is reasonable to assume incoherent multiple reflections within each plate and no reflections between plates . Figure 6 shows the principal transmittance ( p component) and extinction ratio for several four-plate polarizers having the refractive indexes indicated . † The extinction ratio improves considerably with increasing refractive index . It is also improved by using the plates at an angle of incidence slightly above the Brewster angle . This procedure , which is most helpful for high refractive index plates , reduces the transmission per plate so that a trade-of f is required between losses resulting from absorption or scattering when many plates are used and the † The extinction ratio of a pile of m plates (no multiple reflections between plates) is simply the product of the extinction ratios of the individual plates .
Page 1 and 2: CHAPTER 5 POLARIZATION † Jean M .
Page 3 and 4: POLARIZATION 5 .3 where 2 laplaci
Page 5 and 6: POLARIZATION 5 .5 FIGURE 1 Coordina
Page 7 and 8: POLARIZATION 5 .7 For nonabsorbing
Page 9 and 10: POLARIZATION 5 .9 calculate the ref
Page 11 and 12: POLARIZATION 5 .11 so that s 180
Page 13 and 14: POLARIZATION 5 .13 and p in terms
Page 15 and 16: POLARIZATION 5 .15 (a) (b) FIGURE 5
Page 17: TABLE 1 Transmittances and Degree o
Page 21 and 22: POLARIZATION 5 .21 be 1 . 10 m and
Page 23 and 24: POLARIZATION 5 .23 FIGURE 9 Light i
Page 25 and 26: POLARIZATION 5 .25 ratio of the min
Page 27 and 28: POLARIZATION 5 .27 preference is fo
Page 29 and 30: POLARIZATION 5 .29 6 . J . A . Bern

Chapter 5 . Polarization

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