07 Optical Fibers and Dispersion

07 Optical Fibers and Dispersion - Circular Step Index...

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Unformatted text preview: Circular Step Index Waveguides Optical Fibers Core n 1 Cladding n 2 n 1 > n 2 The solution to this problem is best done in cylindrical coordinates The z component of E does not couple to the other components as the wave propagates, while the r and components are strongly coupled. We can write an equation for the z component of the electric field 2 2 2 = + E n k E o Solutions 1 ( , , ) ( ) ( ) ( ) ( ) and ( ) . . z j z j E r z R r Z z Z z e Ae c c = = = + The general solution for E z is of the form where Inside the core of the waveguide where is a Bessel function of the first kind of order and Outside the core where is a Bessel function of the second kind of order and ( ) ( ) R r J r = 2 2 2 2 o k n =- ( ) ( ) R r K r = 2 2 2 2 o k n =- ( ) J r ( ) K r Solutions 2 2 for large ( r) ( ) cos( ) 2 4 for large ( r) ( ) . 2 For the solutions to oscillatory we require r o core o clad J r r r e K r r k n k n - -- = Solutions 3 Then for r < a...
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07 Optical Fibers and Dispersion - Circular Step Index...

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