![Page 1: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/1.jpg)
Dec. 5, 2006 Lori Moore 1
Single Mode Fiber CouplingSensitivities and Tolerancing
![Page 2: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/2.jpg)
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
![Page 3: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/3.jpg)
Dec. 5, 2006 Lori Moore 3
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
![Page 4: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/4.jpg)
Dec. 5, 2006 Lori Moore 4
Loss Due to Lateral Misalignment
2
01
x
eLoss
![Page 5: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/5.jpg)
Dec. 5, 2006 Lori Moore 5
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)
![Page 6: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/6.jpg)
Dec. 5, 2006 Lori Moore 6
Loss Due to Angular Misalignment
2sin1 oon
eLoss
![Page 7: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/7.jpg)
Dec. 5, 2006 Lori Moore 7
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)
![Page 8: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/8.jpg)
Dec. 5, 2006 Lori Moore 8
Loss Due to Longitudinal Misalignment
zn
Z
002
1
11
2 Z
Loss
![Page 9: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/9.jpg)
Dec. 5, 2006 Lori Moore 9
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)
![Page 10: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/10.jpg)
Dec. 5, 2006 Lori Moore 10
Loss Due to Mode Mismatch
2
1
2
2
1
41
Loss
![Page 11: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/11.jpg)
Dec. 5, 2006 Lori Moore 11
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)
![Page 12: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/12.jpg)
Dec. 5, 2006 Lori Moore 12
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)
![Page 13: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/13.jpg)
Dec. 5, 2006 Lori Moore 13
Perturbation AnalysisCan’t Assume Linearity
![Page 14: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/14.jpg)
Dec. 5, 2006 Lori Moore 14
One Possible Solution
![Page 15: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/15.jpg)
Dec. 5, 2006 Lori Moore 15
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
![Page 16: Dec. 5, 2006Lori Moore1 Single Mode Fiber Coupling Sensitivities and Tolerancing](https://reader035.vdocument.in/reader035/viewer/2022081603/5697bf851a28abf838c877c4/html5/thumbnails/16.jpg)
Dec. 5, 2006 Lori Moore 16
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%)