Dec. 5, 2006 Lori Moore 1
Single Mode Fiber CouplingSensitivities and Tolerancing
Dec. 5, 2006 Lori Moore 2
Overview
• Basic Definitions• Misalignments
– Lateral– Angular– Longitudinal– Mode mismatch
• Example Tolerancing Problem– Coupling between two single mode fibers in air
• Figure of Merit – Coupling Efficiency
– Why• Starting point for more complex systems
• Non-linear tolerancing problem
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Single Mode Fiber Definitions
Variables used• ωo = mode field radius (1/e2)
• n0 = index outside of fiber
• λ = wavelength
λ (um) ω0 (um)
1.55 5.251.3 4.65
1.06 3.10.86 2.50.63 1.85
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Loss Due to Lateral Misalignment
2
01
x
eLoss
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Loss Due to Lateral Misalignmentλ = 1.3 μm ω0 = 4.65 μm
0 2 4 6 8 100%
20%
40%
60%
80%
100%Lo
ss (
%)
Lateral Misalignment (um)
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Loss Due to Angular Misalignment
2sin1 oon
eLoss
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Loss Due to Angular Misalignmentλ = 1.3 μm ω0 = 4.65 μm
0 2 4 6 8 100%
20%
40%
60%
80%
100%Lo
ss (
%)
Angular Misalignment (degrees)
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Loss Due to Longitudinal Misalignment
zn
Z
002
1
11
2 Z
Loss
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Loss Due to Longitudinal Misalignment λ = 1.3 μm ω0 = 4.65 μm n0 = 1
0 100 200 300 400 5000%
20%
40%
60%
80%
100%Lo
ss (
%)
Longitudinal Misalignment (um)
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Loss Due to Mode Mismatch
2
1
2
2
1
41
Loss
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Loss Due to Mode Mismatchλ = 1.3 μm ω0 = 4.65 μm n0 = 1
1 2 3 4 50%
20%
40%
60%
80%
100%Lo
ss (
%)
Mode Mismatch (1/
2)
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Example Tolerancing Problem
• Goal– Loss < 0.46 dB (10%)
• Other constrains– Fiber to Fiber coupling– Wavelength = 1.3 μm– Mode field radius = 4.65 μm (1/e2)– Gap material is air (n = 1)
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Perturbation AnalysisCan’t Assume Linearity
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One Possible Solution
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Closing Remarks and References
• Other issues to consider– Dirt on fiber– Burning the fiber with too much power– Humidity– Wavelength
• References– OFR catalogue
• http://www.ofr.com/misc/OFR_2001_Fiber.pdf– Further Reading
• For gaussian beam propagation – Lasers, A. E. Siegman (1986) especially Chapter 17 and 20
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Conversion from Decibels to Transmission Percent
LdB L%
0 0%1 21%2 37%3 50%4 60%5 68%6 75%7 80%8 84%9 87%10 90%
%10010%100 10%
dBL
L
%100
%100log10 %LLdB
L% LdB
0% 0.010% 0.520% 1.030% 1.540% 2.250% 3.060% 4.070% 5.280% 7.090% 10.0
Calculating Loss in dB (LdB) Calculating Loss in % (L%)
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