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Ch3Sec5

# Ch3Sec5 - THE FIBER FORUM Fiber Optic Communications JOSEPH...

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Unformatted text preview: THE FIBER FORUM Fiber Optic Communications JOSEPH C. PALAIS PRESENTED BY Joseph C. Palais 3.5 2 Section 3.5 REFLECTION AT A PLANE BOUNDARY Consider normal incidence of light at a boundary. This is referred to as Fresnel Reflection . n 1 n 2 Incident Wave Transmitted Wave Reflected Wave Reflection Coefficient: field electric incident field electric reflected = ρ Boundary Joseph C. Palais 3.5 3 Reflection at a Plane Boundary We will prove this starting on the next page. 2 1 2 1 n n n n +- = ρ The result is: Reflection Coefficient Joseph C. Palais 3.5 4 Reflection at a Plane Boundary Proof: x n 1 n 2 H i H r E i E r z E t H t x (1) 1 1 1 ε μ η = 2 2 2 ε μ η = (2) Intrinsic impedances: Joseph C. Palais 3.5 5 Reflection at a Plane Boundary Assume non-magnetic materials, then the permeability and permittivity are: 2 2 1 1 2 2 1 1 2 1 n k k n k k n n r = = = = = = = ε ε ε ε ε ε μ μ μ (3) Joseph C. Palais 3.5 6 Reflection at a Plane Boundary z jk r r z jk r r z jk i i z jk i i e E H e E E e E H e E E 1 1 1 1 1 1 1 1 1 1 η η = = = =-- Incident Wave Reflected Wave (4) (5) Joseph C. Palais 3.5 7 Reflection at a Plane Boundary 2 2 2 2 2 1 1 2 jk z jk z t t t t i r t i r t E E E e H e E E E or E E E η-- = = + = + = Transmitted Wave Apply the boundary conditions: E and H are continuous at the boundary. Thus at z = 0, (6) (7) Joseph C. PalaisJoseph C....
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Ch3Sec5 - THE FIBER FORUM Fiber Optic Communications JOSEPH...

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