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Published byKatharine Whitfield Modified over 2 years ago

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

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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: tt

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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’)

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Total reflected field: factor combine

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

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

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Use:

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

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Double Beam Multiple Beam Add 50% reflective surfaces! Wavelength (nm) t = 500 nm, n = 1.515, = 0 0 0.2 0.4 0.6 0.8 1 1.2 400450500550600650700 R t = 500 nm, n = 1.515, = 0 R

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

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

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destructive: constructive: /20 off constructive:

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/20 off destructive destructive R

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Double Beam Multiple Beam Changing phase, not time

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R t = 500 nm, n = 1.515, = 600 nm 0 4590 ii Multiple beam interference also causes sharp peaks with angle of incidence:

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t = 500 nm, n = 1.515, = 0 T

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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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