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Lecture4-228a

# Lecture4-228a - Lecture 4 Propagation in Optical Fibers ECE...

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ECE 228A Fall 2011 Daniel J. Blumenthal 4.1 Lecture 4 - Propagation in Optical Fibers

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ECE 228A Fall 2011 Daniel J. Blumenthal 4.2 Step Index Fibers a n 1 2 Fiber core Fiber cladding Defnition: Fractional re±ractive index di±±erence Δ = (n 1 - n 2 )/n 1 Typical value ±or silica (glass) fbers n 1 = 1.48, n 2 = 1.46 Δ = .0135 1%
ECE 228A Fall 2011 Daniel J. Blumenthal 4.3 Geometrical Optics Model Use of total internal refraction for optical ±eld guiding Light rays that enter the ±ber with an angle smaller than an acceptance angle θ 0 will be guided by total internal refection within the ±ber when: ! ! " # \$ \$ % & = 0 2 2 2 1 1 max , 0 0 sin n n n θ Unguided ray n 1 n 2 Fiber core Fiber cladding 1 Air n 0 = 1.0 θ 0 Unwanted unguided ray Guided ray

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ECE 228A Fall 2011 Daniel J. Blumenthal 4.4 Numerical Aperture Defnition: The light collecting capacity of the optical ±ber is measured by the Numerical Aperature (NA) NA = n 0 sin θ 0,max = n 1 2 n 2 2 n 1 Δ Example: if we couple light from air into a ±ber with Δ = .01 and n 1 = 1.5 , then the NA 0.2121 and 0,max 12˚ (For small ) The maximum acceptable “angular error” when launching an optical beam into a ±ber is consequently of the order of 0,max 12˚
ECE 228A Fall 2011 Daniel J. Blumenthal 4.5 Modes in Step Index Fibers Defnition: Modes are light intensity profles (patterns) that propagate down the fber maintaining their transversal feld shape • Multimode fbers can support many thousands o± modes. • Single mode fbers support one mode. Gaussian frst order mode intensity profle Gaussian secon order mode intensity profle E ( x , y , z , t ) = J ( x , y ) Cos ( ω 0 t − β ( 0 ) z ) In order to accurately study optical modes, the complete Maxwell equations are to be solved. Anyway, ±or multimode fbers, the ±ollowing intuitive explanation can be given: Each mode corresponds to a light beam traveling inside the fber core with di±±erent angles

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ECE 228A Fall 2011 Daniel J. Blumenthal 4.6 Normalized Frequency Parameter V ( ) Δ " # \$ % & ' = = 2 2 1 2 1 2 2 2 1 0 an n n a V λ π κ V is a design parameter that takes into account the fber parameters ( n 1 , n 2 and a ) and the ±ree space wavelength 0 .
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Lecture4-228a - Lecture 4 Propagation in Optical Fibers ECE...

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