Ch5Sec2 - THE FIBER FORUM Fiber Optic Communications...

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THE FIBER FORUM Fiber Optic Communications JOSEPH C. PALAIS PRESENTED BY
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Joseph C. Palais 5.2 2 Section 5.2 Graded-Index Fiber Cladding Core z 2a n 1 n 2 a 0 Ray Paths Index
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Joseph C. Palais 5.2 3 Section 5.2 Graded-Index Fiber In the core In the cladding a r a r n r n - = , 2 1 ) ( 1 α a r n n r n = - = , 2 1 ) ( 2 1 α is a design parameter. It is usually close to α = 2.
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Joseph C. Palais 5.2 4 GRADED-INDEX FIBER Solve for [ ] 2 1 2 2 2 2 2 1 2 1 2 1 n n n n = - = - 2 1 2 2 2 1 2 1 2 2 2 1 2 n n n n n - = - =
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Joseph C. Palais 5.2 5 GRADED-INDEX FIBER 1 2 1 n n n - = Usually n 1 2245 n 2 . Then This is just the fractional refractive index change (as we have seen before for step-index and dielectric slab waveguides). 2 1 1 2 1 2 1 2 1 2 1 2 2 ) ( 2 ) )( ( n n n n n n n n n - = + - 2245
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Joseph C. Palais 5.2 6 GRADED-INDEX FIBER Analysis of Curving Ray Paths a a 0 0 r r Snell’s Law n(r) θ 1 θ 2 θ c 1 2 1 2 sin sin θ n n = n 2 n 1 2 2 1 1 sin sin n n =
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Joseph C. Palais 5.2 7 GRADED-INDEX FIBER Since n 2 < n 1 , then sin θ 2 > sin θ 1 and θ 2 > θ 1 , Result: Rays are bent away from the normal. Thus the rays are continually bent as they progress towards the cladding. At some point, the incident angle is greater than the critical angle and total reflection occurs.
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Joseph C. Palais
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This note was uploaded on 05/11/2010 for the course EEE EEE-448 taught by Professor Palais during the Fall '09 term at ASU.

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Ch5Sec2 - THE FIBER FORUM Fiber Optic Communications...

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