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%)