Optical Fibers a cylindrical dielectric waveguide multimode - - PowerPoint PPT Presentation

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Optical Fibers a cylindrical dielectric waveguide multimode - - PowerPoint PPT Presentation

Mar 04, 2024 414 likes β€’525 views

Optical Fibers a cylindrical dielectric waveguide multimode step-index singlemode step-index GRIN Modes in Optical Fibers Cartesian coordinates 2 , + 2 , + 2 2 2 2 ,

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SLIDE 1

Optical Fibers

step-index multimode step-index singlemode GRIN

a cylindrical dielectric waveguide

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SLIDE 2

Modes in Optical Fibers

πœ–2𝐹 𝑦, 𝑧 πœ–π‘¦2 + πœ–2𝐹 𝑦, 𝑧 πœ–π‘§2 + π‘œ2πœ•2 𝑑2 βˆ’ 𝛾2 𝐹 𝑦, 𝑧 = 0 πœ–2𝐹 𝑠, 𝜚 πœ–π‘ 2 + 1 𝑠 πœ–πΉ 𝑠, 𝜚 πœ–π‘  + 1 𝑠2 πœ–2𝐹 𝑠, 𝜚 πœ–πœš2 + π‘œ2πœ•2 𝑑2 βˆ’ 𝛾2 𝐹 𝑠, 𝜚 = 0

Cartesian coordinates Cylindrical coordinates 𝑭 𝑦, 𝑧, 𝑨, 𝑒 = 𝐹 𝑦, 𝑧 π‘“π‘˜ πœ• 𝑒 βˆ’ 𝛾 𝑨 𝑭 𝑠, 𝜚, 𝑨, 𝑒 = 𝐹 𝑠, 𝜚 π‘“π‘˜ πœ• 𝑒 βˆ’ 𝛾 𝑨

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SLIDE 3

Solutions

𝑒2𝑣 𝑒𝑠2 + 1 𝑠 𝑒𝑣 𝑒𝑠 + π‘œ2πœ•2 𝑑2 βˆ’ 𝛾2 βˆ’ π‘š2 𝑠2 𝑣 = 0 𝐹 𝑠, 𝜚 = 𝑣 𝑠 𝑓 π‘˜ π‘š 𝜚 𝑓 π‘™π‘ˆ

2 ≑ π‘œπ‘‘π‘2πœ•2

𝑑2 βˆ’ 𝛾2 𝛿2 ≑ 𝛾2 βˆ’ π‘œπ‘‘π‘š2πœ•2 𝑑2 Boundary conditions for

𝐹𝑨, 𝐼𝑨, 𝐹𝜚, 𝐼𝜚

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SLIDE 4

Graphical Representation

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SLIDE 5

Power Confinement

Right above the cut-off, very little power is inside the core. As the core diameter increases, the power of the mode becomes confined inside the core. Fraction of the power propagating inside the core against the V-number.

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SLIDE 6

Optical Attenuation

1 𝑒𝐢 = βˆ’10 π‘šπ‘π‘• π‘ˆ

0.16 dB = (3.6 %)

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SLIDE 7

Dispersion

  • modal dispersion
  • material dispersion
  • waveguide dispersion
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SLIDE 8

Number of Guided Modes in an Optical Fiber

𝑁 = 4 𝜌2 π‘Š2 π‘Š = 2𝜌 𝑏 πœ‡ π‘œπ‘‘π‘2 βˆ’ π‘œπ‘‘π‘š2 = 2𝜌 𝑏 πœ‡ 𝑂𝐡

V-number

𝑂𝐡 = π‘œ0 sin πœ„0 = π‘œπ‘‘π‘2 βˆ’ π‘œπ‘‘π‘š2

Numerical Aperture

π‘Š < 2.405

single-mode operation

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SLIDE 9

End Coupler

π”½π‘—π‘œ 𝑦, 𝑧 = 𝑏𝛽

𝛽

𝑭𝛽 𝑦, 𝑧

πœƒπ›½ = π”½π‘—π‘œ . 𝑭𝛽

βˆ—π‘’π΅ 2

π”½π‘—π‘œ

2 𝑒𝐡 𝑭𝛽 2 𝑒𝐡

π”½π‘—π‘œ

𝑭𝛽

input field decomposed into modes of the guide Overlap Integral: fraction

  • f coupled power into each mode