chapter 5

chapter 5 - THE FIBER FORUM Fiber Optic PRESENTED BY Click...

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Click to edit Master subtitle style 5/13/10 THE FIBER FORUM Fiber Optic JOSEPH C. PALAIS PRESENTED BY
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5/13/10 Joseph C. Palais 5.1 22 Chapter 5 OPTIC FIBER WAVEGUIDES
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5/13/10 Joseph C. Palais 5.1 33 Section 5.1 Step-Index Fiber Step Index Fiber (SI Fiber) n1 n2 Cladding index n2 Core index n1 n1 > n2 For total reflection we require p > c sin 1 2 n n c = θ n1 n2
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5/13/10 Joseph C. Palais 5.1 44 Section 5.1 Step-Index Fiber 1 2 1 n n n - = As for the slab waveguide, we have the fractional refractive index change Typically is on the order of 0.01 for fibers.
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5/13/10 Joseph C. Palais 5.1 55 STEP-INDEX FIBER Both core and cladding must be very low loss. Evanescent waves travel in the cladding. If the cladding is thick (~ 20 m or more), very little light reaches the outer edge of the cladding. Common SI Waveguides 1.) Glass core Glass cladding 2.) Glass core Plastic cladding 3.) Plastic core Plastic cladding
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5/13/10 Joseph C. Palais 5.1 66 All Glass Lowest loss. Used for longest distances (up to about 100 km) Glass/Plastic Moderate loss. Moderate distances (up to about 100 m) All Plastic High loss. Short distances (up to about 10 m) STEP-INDEX FIBER
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5/13/10 Joseph C. Palais 5.1 77 STEP-INDEX FIBER Fiber n 1 n 2 NA α o All-glass 1.48 1.46 0.24 13.9 ° Plastic-Clad Silica 1.46 1.4 0.41 24.2 ° All-plastic 1.49 1.39 0.53 32 ° Typical fiber properties:
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5/13/10 Joseph C. Palais 5.1 88 STEP-INDEX FIBER Example: Compute NA and o for an all-glass fiber having NA = 0.24. From the slab waveguide analysis 2 2 2 1 sin n n n NA o o - = = α 24 . 0 sin = o If no= 1 (air), we have that
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5/13/10 Joseph C. Palais 5.1 99 STEP-INDEX FIBER ° = 28 2 o α 2 o Acceptance Cone Lost Light ° = 14 o cone. acceptance the of angle half the is o
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5/13/10 Joseph C. Palais 5.1 1010 STEP-INDEX FIBER Cladding modes may also be trapped in the fiber by total reflection at the outer boundary of the cladding. The cladding modes are lossy and do not travel far. n2 n1 Total Reflection
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Click to edit Master subtitle style 5/13/10 THE FIBER FORUM JOSEPH C. PALAIS PRESENTED BY
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5/13/10 Joseph C. Palais 5.2 1212 Section 5.2 Graded-Index Fiber Cladding Core z 2a n1 n2 a 0 Ray Paths Index
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5/13/10 Joseph C. Palais 5.2 1313 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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5/13/10 Joseph C. Palais 5.2 1414 GRADED-INDEX FIBER Solve for Á [ ] 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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5/13/10 Joseph C. Palais 5.2 1515 GRADED-INDEX FIBER 1 2 1 n n n - = Usually n1 û n2. 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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5/13/10 Joseph C. Palais 5.2 1616 GRADED-INDEX FIBER Analysis of Curving Ray Paths a a 0 0 r r Snell’s Law n(r) 1 2 c 1 2 1 2 sin sin θ n n = n2 n1 2 2 1 1 sin sin n n =
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5/13/10 Joseph C. Palais 5.2 1717 GRADED-INDEX FIBER Since n2 < n1, then sin θ 2 > sin θ 1 and 2 > ª 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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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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chapter 5 - THE FIBER FORUM Fiber Optic PRESENTED BY Click...

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