Analysis of Fiber Connection Loss
Associated with Mechanical Tolerances
Alan Kost
College of Optical Sciences
University of Arizona
Tucson, AZ
Katherine Liu & Charles Qian
All Optronics, Tucson, AZ
All
Optronics
Outline

Background
–
–

Worst-Case Loss
–
–

Polyimide fiber and mechanical splices
Fiber and capillary specifications
Contributions to loss
Results for coated and uncoated fiber
Statistical Analysis of Loss
All
Optronics
All Optronics Fiber-Optic Splice
RuggedConnectTM
For Permanent In-Field Repair
Spliced Fiber / Cable Reconstruction
All
Optronics
Fusion Splicing
Fiber Optics Handbook for Engineers and Scientists, Frederick C. Allard, Ed.
All
Optronics
Avionic Fiber and Splices
An analysis of loss is essential for estimating link budgets.
Polyimide Fiber
Advantages

Polyimide coating offers protection in harsh environments

Fiber has a wide temperature operating range (-60 to 200 ºC)
Emitting
Fiber
Input
Capillary
Receiving
Fiber
Output
Advantages

Bulky, expensive equipment is not required

There is no spark hazard, as in fusion splicing
All
Optronics
Fiber & Capillary Specifications
OFS Polyimide-Coated, Multi-Mode, Graded Index Fiber
Dcore
a2 + b2
=2
2
Dclad
A2 + B 2
=2
2
Capillary
Tmax
Coating
Clad
B
T
Coating Concentricity ≡ min
Tmax
2a − 2b
Core Non-circularity =
Dcore
Cladding Non-circularity =
All
Optronics
2 A − 2B
Dclad
A
a
Core
b
Tmin
Dcoat Dcap
Fiber & Capillary Specifications
OFS Polyimide-Coated, Multi-Mode, Graded Index Fiber
Capillary
Parameter
Specifications
Core diameter
Cladding diameter
Coating diameter
Coating
concentricity
Core non-circularity
Clad non-circularity
Core/clad offset
Numerical aperture
Capillary diameter
(coated fiber)
Capillary diameter
(uncoated fiber)
100 ± 3 µm
140 ± 2 µm
171.5 ± 1 µm
80%
2%
2%
2 µm
0.29 ± 0.015
173.5 µm + 1/ - 0 µm
Tmax
Coating
Clad
B
A
a
Core
b
144.4 µm + 1/ - 0 µm
Tmin
All
Optronics
Dcoat Dcap
Loss from Fiber Core Offset
The worst-case offset occurs when displacements for and
emitting and receiving fibers are in opposite directions.
Coating
Clad
Core
Emitting Fiber
All
Optronics
Capillary
y
Receiving Fiber
Fiber Core Offset Components
Coated Fiber
Uncoated Fiber
Capillary
Capillary
Coating
Clad
∆1
∆2
Clad
∆3
Core
∆3
Core
∆1 = Capillary/Coating Offset (coated fiber)
∆1 = Capillary/Cladding Offset (uncoated fiber)
∆2 = Coating/Cladding Offset
∆3 = Cladding/Coating Offset
All
Optronics
∆1
Other Sources of Splice Loss
Core Diameter Mismatch
Core Ellipticity
emitting
core
receiving y
core
emitting
core
receiving
core
Numerical Aperture Mismatch
Emitting
Fiber
All
Optronics
θe
θr
Receiving
Fiber
“Textbook” Loss Expressions
 8d 
Core Offset Loss [dB] = −10log 
 3π a 
 D rec  2 

Core Diameter Mismatch Loss [dB] = −10log  core
emit 
 Dcore  
 NArec ( 0 )  2 
NA Mismatch Loss [dB] = −10log 
 
emit

NA
0
( )  


4
 b 
Ellipticity Loss [dB] = −10log  tan −1   
 a 
π
All
Optronics
Modified Loss Expressions
 8d 
Core Offset Loss [dB] = −10log 
 3π a 
Stays the same
For other contributions to splice loss, linear loss
is reduced by a factor of 1/2
 1   D rec  2  

Core Diameter Mismatch Loss [dB] =
−10log 1 − 1 −  core
emit 
 2   Dcore   


2
rec




NA ( 0 )  
1
NA Mismatch Loss [dB] =
−10log 1 − 1 − 
  
emit

 2   NA ( 0 )   



 1 4
 b  
Ellipticity Loss [dB] =
−10log 1 − 1 − tan −1    
 a  
 2 π
All
Optronics
The Factor of 1/2
NAe(0) = NAr(0)
receiving
core has
larger NA
NAe(0) > NAr(0)
Receiving
Core
transmitted
power
unchanged
emitting
core has
larger NA
additional
loss
Emitting
Core
=
NA ( r ) NA ( 0 ) 1 −
All
Optronics
r2
( Dcore 2 )
2
Worst-Case Loss
Loss
Coated Fiber
Core Offset = 11.8
µm
Uncoated Fiber
Core Offset = 12.8
µm
Offset
1.0 dB
1.1 dB
Core Diameter Mismatch
0.3 dB
0.3 dB
Numerical Aperture Mismatch
0.4 dB
Core Non-Circularity
< 0.1 dB
Total
All
Optronics
1.7 dB
1.8 dB
A Monte Carlo Analysis of Loss
Statistical Assumptions

Quantities have normal or chi square distributions.

0.27 % of fibers have values larger than the manufacturer’s
tolerance.
The probability is 0.27% that a normally distributed
quantity will have a value greater than the “3 sigma
value”.

All positions and orientations for a fiber in a capillary are
equally likely.
All
Optronics
Numerical Calculations
Grid Size = 100 x 100
Grid Spacing = 1 µm
Receiving
Core
 ∑ Pr ( i,j ) 


Loss[dB] = -10log  i,j

P
i,j
(
)
∑
e


 i,j

Pe ( i,j ) , NA r ( i,j ) ≥ NA e ( i,j )

2
Pr ( i,j ) = 
 NA e ( i,j ) 
 , NA r ( i,j ) < NA e ( i,j )
Pe ( i,j ) 
NA
i,j
r( ) 


All
Optronics
Emitting
Core
Distribution of Core Offsets
Of 10000 offsets, none were as large as the worst-case.
Mean = 1.8 µm
(Worst Case = 11.8 µm)
800
Mean = 2.4 µm
(Worst Case = 12.8 µm)
600
600
Count
Count
Uncoated Fiber
Coated Fiber
1000
400
400
200
200
0
0
All
Optronics
1
2
3
4
Offset (µm)
5
6
0
0
1
2
3
4
Offset (µm)
5
6
7
Loss Statistics
The worst-case loss is roughly 3 times the “1%” value.
Coated Fiber
Uncoated Fiber
2000
Mean = 0.18 dB
(Worst Case = 1.7 dB)
Mean = 0.22 dB
(Worst Case =
1.7 dB)
1200
1000
1%
500
0.61 dB
0
0
All
Optronics
0.2
0.4
0.6
Loss (dB)
0.8
Count
Count
1500
800
1%
400
0
0.66 dB
0
0.2
0.4
0.6
Loss (dB)
0.8
Summary

A geometrical argument gives the rule of thumb:
Divide loss (other than that due to core offset) by
2 for offset fiber cores

A statistical analysis gives the rule of thumb:
Divide the worst-case loss by 3 for the
1% value.
All
Optronics