cilindrical_normalized_handout_final

cilindrical_normalized_handout_final - 2 = J ' Ka ( 29 KJ...

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Today Normalized parameters (review) Circular waveguides (p.73-83)
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a = n s 2 - n c 2 ( 29 / n e ff 2 - n s 2 ( 29 a = as sym e try b = n eff 2 - n s 2 ( 29 / n f 2 - n c 2 ( 29 n eff / K 0 V m = hK o n f 2 - n s 2
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a = n s 2 - n c 2 ( 29 / n e ff 2 - n s 2 ( 29 a = ass ym e try b = n eff 2 - n s 2 ( 29 / n f 2 - n c 2 ( 29 n eff / K 0 V m = hK o n f 2 - n s 2
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Effective Index method Why does this waveguide work?  There is nothing that  confines it to the y direction.    
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Example P. Cheven, Optics express (2007)
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Circular Waveguides
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Circular waveguides 2 E -με 2 E t 2 = 0
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Wave equation in cylindrical  coordinates 2 E -με 2 E t 2 = 0 1 r r r E z r + 1 r 2 2 E z ∂φ 2 + 2 E z z 2 + K 0 2 μ 2 E z = 0
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z = e - j β z φ= Ae j νφ + c .c . r 2 2 R r + r R r + r 2 K 0 2 n 2 2 - ν 2 r 2 R = 0
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Optics: The light fantasticMartin Hegner Nature 419, 125-127(12 September 2002)
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For large arguments:
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β 2 ν 2 a 2 1 γ 2 + 1 K 2
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Unformatted text preview: 2 = J ' Ka ( 29 KJ Ka ( 29 + K ' a ( 29 K a ( 29 × K 2 n core 2 J ' Ka ( 29 KJ Ka ( 29 + K 2 n clad 2 K ' a ( 29 K a ( 29 β 2 ν 2 a 2 1 γ 2 + 1 K 2 2 = J ' Ka ( 29 KJ Ka ( 29 + K ' a ( 29 K a ( 29 × K 2 n core 2 J ' Ka ( 29 KJ Ka ( 29 + K 2 n clad 2 K ' a ( 29 K a ( 29 J 1 Ka ( 29 KJ Ka ( 29-K 1 γ a ( 29 K a ( 29 =...
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This note was uploaded on 08/10/2010 for the course ECE 4370 at Cornell.

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cilindrical_normalized_handout_final - 2 = J ' Ka ( 29 KJ...

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