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White n t Wavelength (nm) R t = 400 nm, n = 1.515,  = 0.

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Presentation on theme: "White n t Wavelength (nm) R t = 400 nm, n = 1.515,  = 0."— Presentation transcript:

1 white n t Wavelength (nm) R t = 400 nm, n = 1.515,  = 0

2 E o Reflection coefficient: Transmission coefficient: for internal: rE o t E o t r ’ E o tt’r’E o tt’r’ 3 E o tt’r’ 5 E o tt’r’ 7 E o for internal: n d Multiple Beam Interference Amplitude of each reflection: tt

3 Modify amplitude and phase for each reflected ray: For N >= 2 Phase lag between reflections: (difference between the first and the rest will be covered by reflection amplitudes r and r’)

4 Total reflected field: factor combine

5 Which converges to:for |x|<1 This makes a geometric series: By the way: Stoke’s Relations

6 …but when using complex notation for fields: …which means… …where * means the complex conjugate ( j -> - j )

7 Use:

8 Double Beam Multiple Beam R t = 500 nm, n = 1.515,  = 0 Wavelength (nm) t = 500 nm, n = 1.515,  = 0 R

9 Double Beam Multiple Beam Add 50% reflective surfaces! Wavelength (nm) t = 500 nm, n = 1.515,  = R t = 500 nm, n = 1.515,  = 0 R

10 Phasors: Describe amplitude and phase with vector length and direction. A B A+B constructive destructive A B A+B

11 A B A+B Phasors: Describe amplitude and phase with vector length and direction. in between

12 destructive: constructive: /20 off constructive:

13 /20 off destructive destructive R

14 Double Beam Multiple Beam Changing phase, not time

15 R t = 500 nm, n = 1.515, = 600 nm ii Multiple beam interference also causes sharp peaks with angle of incidence:

16

17 t = 500 nm, n = 1.515,  = 0 T

18 Multiple beams interfere constructively and destructively with a much sharper phase dependence than double beam interference since the multiple interfering components dephase at different rates.


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