Study of Bending Losses in Optical Fibers usingCOMSOL
Ashitosh Velamuri
Center for Lasers and PhotonicsIndian Institute of Technology Kanpur
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 1 / 19
Overview
1 Optical Fibers and Advantages
2 Bent Optical Fiber and AnalysisGeometric EffectStress Effect
3 Geometrically Exact Beam Theory (GEBT)
4 COMSOL Simulations
5 Simulation Results and Optimization
6 Bend Insensitive Fiber
7 Conclusions
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 2 / 19
Optical Fibers and Advantages
Material: Silica glass
Dimensions: In microns
Advantages:
Small size, easily installedLow power lossHigh transmission rate oververy long distances
Circulatory system thatnourishes our informationsystem
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 3 / 19
Overview
1 Optical Fibers and Advantages
2 Bent Optical Fiber and AnalysisGeometric EffectStress Effect
3 Geometrically Exact Beam Theory (GEBT)
4 COMSOL Simulations
5 Simulation Results and Optimization
6 Bend Insensitive Fiber
7 Conclusions
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 4 / 19
Bent Optical Fiber
FTTH: Fiber to the home networks
Bent at the tight corners of the walls
Bending of fibers cause severe powerloss
Bending range: 3− 10 mm bend radius
Two possible sources to modifyrefractive index are considered
Geometric effectStress effect
0Picture Reference: (a) https://www.rp-photonics.com/fibers.html(b) https://www.fiberoptics4sale.com/blogs/archive-posts/95053062-fiber-optic-cable-installation-overview
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 5 / 19
Geometric Effect: Conformal Mapping
Equivalent straight waveguideapproximation
Bent wave guide in Z-plane is mappedto straight wave guide in W-plane
Modified Index @ point A ↓, @ point B↑Refractive index of equivalentwaveguide is obtained using conformalmapping1
nG ≈ n(
1 +x
R
)1Schermer, Ross T., and James H. Cole, Improved bend loss formula verified for
optical fiber by simulation and experiment, IEEE JQE 43.10 (2007)Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 6 / 19
Stress Effect
Compression @ point (i),Elongation @ point (ii)
Modified Index @ point (i) ↑, @point (ii) ↓Stress effect counters geometriceffect
Conventional approach:Elasto-optic factor in conformalmapping Reff = 1.28− 1.31R1 2
nG+S = n
(1 +
x
Reff
)1Schermer, Ross T., and James H. Cole, Improved bend loss formula verified for
optical fiber by simulation and experiment, IEEE JQE 43.10 (2007).2Renner, Hagen, Bending losses of coated single-mode fibers: a simple approach,
JLT, 10.5 (1992).Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 7 / 19
Overview
1 Optical Fibers and Advantages
2 Bent Optical Fiber and AnalysisGeometric EffectStress Effect
3 Geometrically Exact Beam Theory (GEBT)
4 COMSOL Simulations
5 Simulation Results and Optimization
6 Bend Insensitive Fiber
7 Conclusions
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 8 / 19
Geometrically Exact Beam Theory (GEBT)
Captures bending of the fiber and calculates strain tensorcorresponding to the bend radius3
Strain tensors are employed in to stress-optic law to obtain modifiedrefractive index
nS (x , y) = n(x , y)[1− n2
2
(P11
GEBT︷ ︸︸ ︷ε
x1 + P12(ε
x2 + ε
x3 ))]
P11 = 0.113 and P12 = 0.252 are stress optic coefficientsε1, ε2, ε3 are the principle strains obtained from GEBT
Modified refractive index = GEBT + Stress-Optic law + Conformalmapping
nG+S = nS
(1 +
x
R
)3Simo, Juan C, A finite strain beam formulation. The three-dimensional dynamic
problem. Part I, Computer methods in applied mechanics and engineering 49.1 (1985)Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 9 / 19
Overview
1 Optical Fibers and Advantages
2 Bent Optical Fiber and AnalysisGeometric EffectStress Effect
3 Geometrically Exact Beam Theory (GEBT)
4 COMSOL Simulations
5 Simulation Results and Optimization
6 Bend Insensitive Fiber
7 Conclusions
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 10 / 19
Geometry and Material Properties
Geometry: 2D cross section ofoptical fiber (G652)
Core radius a = 3.05µm
Cladding radius b = 62.5µm
PML thickness = 7λ
Refractive index profile4
n(r) = nmax
√1− 2∆
(1− r
a
)2∆ =
n2max−n2
clad2n2
max
nmax =1.456, nclad = 1.444Radial Parameter (um)
-30 -20 -10 0 10 20 30
Refr
acti
ve I
nd
ex
1.435
1.44
1.445
1.45
1.455
1.46
Straight Fiber
G+S Effect
Reff=1.28R
4Watekar, Pramod R., Seongmin Ju, and Won-Taek Han, Design and development ofa trenched optical fiber with ultra-low bending loss, Op Exp 17.12 (2009)
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 11 / 19
Simulation Parameters
Module: Wave Optics
Physics: Electromagnetic wave,frequency domain (ewfd)
Solve the wave equation
∇×∇× ~E − k20 εr~E = 0
Mesh: Free triangular mesh withfine element size
Study: Mode Analysis, solve forthe effective index of the modes
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 12 / 19
Simulation Results
Bend Diameter (mm)
6 8 10 12 14 16 18 20
Ben
d L
oss
(d
B/t
urn
)
10-1
100
101
102
103
Simulation
Ref. [5]
Straight Fiber neff ≈ 1.4475Bent Fiber neff ≈ 1.4464− i1.3275e − 5
Loss[dB/turn] =20
ln(10)
2π
λ× Im{neff} × 2πR
Simulation results are compared with formula given in5
5Marcuse, Dietrich, Curvature loss formula for optical fibers, JOSA 66.3 (1976):216-220Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 13 / 19
Perfectly Matched Layer
Perfectly matched layer (PML)
Absorbs unwanted reflectionsfrom cladding boundary
What is the thickness we needto apply?
PML thickness varied from1λ− 7λ (λ is the operatingwavelength)
Thickness optimized to 7λPML Thickness × λ (µm)
1 2 3 4 5 6 7
Imagin
ary P
art
of
Eff
ecti
ve I
nd
ex ×
10
-5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Bend Diameter = 9.5 mm
Bend Diameter = 11.5 mm
Bend Diameter = 15.5 mm
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 14 / 19
Mesh Element Size
COMSOL solves this problemusing full-vectorial finite elementmethod (FEM) mode solver
Mesh element size along withthe type of mesh applied has itsinfluence on the end results
Fine element size was applied inthe simulations as the variationin bend loss is minimal in theregion of interest
Mesh Element Size
Extr
em
ely
Coarse
Extr
a C
oarse
Coarse
r
Coarse
No
rm
al
Fin
e
Fin
er
Extr
a F
ine
Extr
em
ely
Fin
e
Ben
d L
oss
(d
B/t
urn
)
2
2.2
Bend Diameter = 13.5 mm
Bend Diameter = 9.5 mm
Ben
d L
oss
(d
B/t
urn
)
13
14
15
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 15 / 19
Overview
1 Optical Fibers and Advantages
2 Bent Optical Fiber and AnalysisGeometric EffectStress Effect
3 Geometrically Exact Beam Theory (GEBT)
4 COMSOL Simulations
5 Simulation Results and Optimization
6 Bend Insensitive Fiber
7 Conclusions
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 16 / 19
Bend Insensitive Fiber
Designed to reduce bend lossinduced in a fiber by adding lowindex trench in cladding
Trench Parameters:
Trench depth∆ntrench = nclad - ntrench
Distance of trench from core bTrench width c
Optimization following standardITU-T recommendations4
∆ntrench = 0.002b/a = 2.12c/a = 2.84
Radial Parameter (um)
-30 -20 -10 0 10 20 30
Refr
acti
ve I
nd
ex
1.435
1.44
1.445
1.45
1.455
1.46
Straight Fiber
G+S Effect
GEBT + Conformal mapping +COMSOL Simulations to BIF
4Watekar, Pramod R., Seongmin Ju, and Won-Taek Han, Design and development ofa trenched optical fiber with ultra-low bending loss, Op Exp 17.12 (2009)
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 17 / 19
BIF: Simulation Results
Addition of trench has reducedthe bend loss induced in thefiber
Bend radius: 5 mm @ 1550 nmwavelength
Experiments4 = 0.014± 0.0023dB/turn
Simulations = 0.012 dB/turn
Bend Diameter (mm)
6 8 10 12 14 16 18 20
Ben
d L
oss
(d
B/t
urn
)10
-10
10-8
10-6
10-4
10-2
100
102
Simulation - Standard Fiber
Simulation-BIF
4Watekar, Pramod R., Seongmin Ju, and Won-Taek Han, Design and development ofa trenched optical fiber with ultra-low bending loss, Op Exp 17.12 (2009)
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 18 / 19
Conclusions
Proposed a new method to estimate bend losses in optical fiber witharbitrary index profiles.
Applied GEBT and conformal mapping to obtain modified refractiveindex.
Wave optics module, ewfd physics, mode analysis study and freetriangular mesh of COMSOL are used in solving the wave equation
PML thickness and mesh element size are optimized to minimize anyvariations in simulation results
Simulation results for standard G652 fiber along with bend insensitivefiber are presented.
Analytical approach and semi analytical formulas derived1 2 5 areapplicable for simple refractive index profiles
Ashitosh V ([email protected]) Study of Bend Loss using COMSOL 19 / 19
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