National Institute of Standards and Technology
Symposium on Optical Fiber Measurements
September 24-26, 2002
Mode-Field Diameter and “Spot Size”
Measurements of Lensed and Tapered
Specialty Fibers
Jeffrey L. Guttman
Photon Inc.
6860 Santa Teresa Blvd.
San Jose, CA 95119
ABSTRACT
The Mode-Field Diameter (MFD) and “spot size” of an assortment
of lensed and tapered specialty fibers were determined from farfield and near-field measurements. In the far field, measurements
were made using a 3D-scanning goniometric radiometer that
provides a complete hemispherical profile. Indirect measures of the
near field derived from these data are reported, including the
Petermann II MFD, the 1/e2 spot size using the far-field Gaussian
approximation, and a measure obtained from 2D Fourier transform
inversion of the far field using phase retrieval techniques. In the
near field, direct profile measurements were made using an IR
Vidicon camera and magnifying objective lenses, with the spot size
reported as the 1/e2 diameter of the imaged profile.
PRESENTATION OUTLINE
„
Characterize Lensed and Tapered Fibers at Focus
•Direct
Near Field Techniques & Issues
•Indirect
Measures from Far Field & Benefits
„
Near Field Data
„
Far Field Data
„
Analysis and Results
„
Summary
Tapered Fiber
Main and Scattered Beams
Scattered Beam
Fiber
Fiber Mode
10μm
1/e2
Focus
Main Beam
(High NA)
Direct Near Field Source
Measurement Techniques/Issues
„
Camera/Magnifying Objective
•
•
•
•
„
Scanning Pinhole/Knife-Edge
•
„
Diffraction Limited for “μm-subμm” Structures
NA, MTF, and λ Dependence of Optics
Positioning at Focus
Dynamic Range
Positioning at Focus
Near Field Scanning Optical Microscopy (NSOM)
•
•
•
Speed of Measurement
Positioning at Focus
Expensive
Indirect Near Field Characterization
from Far Field Measurement
„
„
Far-Field Scanning
Ease of Measurement
•
•
•
„
„
„
No Optics Limitations
No Access Constraints
Minimal Positioning Required
Large Dynamic Range
Calculate Near Field Quantities
from Measured Far Field
Provides “sub-µm” Resolution
Characterization of Lensed and
Tapered Fiber
„
Direct Near Field
•
„
1/e2 Diameter
Indirect Far Field
•
•
•
Gaussian Approximation: d=4λ/πθ
1/e2 Diameter
Petermann II MFD
2D Fourier Transform with Phase Retrieval
1/e2 Diameter
Near-Field Profiles
Fiber #6
100X
40X
Far-Field Profiles
a.) Fiber #1
b.) Fiber #2
c.) Fiber #3
d.) Fiber #4
e.) Fiber #5
f.) Fiber #6
MFD
Far Field
Petermann II Integral*
∞
λ 2 ∫ I (θ ) sin θ cosθdθ
MFD =
π ∫ I (θ ) sin θ cosθdθ
−∞
∞
−∞
*TIA/EIA FOTP-191
3
Mode-Field Diameter
vs
Petermann II Integral Angle
12
11
10
M FD (m icrons )
9
#1 Major
#1 Minor
#2 Major
#2 Minor
#3 Major
#3 Minor
#4 Major
#4 Minor
#5 Major
#5 Minor
#6 Major
#6 Minor
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
Peterm ann II Integral Angle (degrees)
70
80
90
Lensed and Tapered Fibers
MFD vs Integral Angle
Fiber
Integral Limit
1
2
Mode-Field Diameter (μm)
3
4
Major and Minor Axes
5
6
40
45
50
55
60
10.406 10.375 5.069 5.118 4.141 4.154 3.851 3.742 3.478 3.506 2.668 1.920
Average
10.380 10.344 5.045 5.097 4.106 4.117 3.832 3.724 3.428 3.463 2.402 1.887
10.395 10.361 5.054 5.104 4.113 4.128 3.842 3.734 3.442 3.476 2.593 1.902
10.382 10.345 5.043 5.095 4.100 4.110 3.832 3.725 3.420 3.457 2.391 1.887
10.367 10.328 5.034 5.087 4.091 4.100 3.823 3.715 3.405 3.443 2.221 1.873
10.352 10.311 5.026 5.081 4.084 4.094 3.814 3.705 3.395 3.434 2.139 1.851
Difference from Average MFD
40
45
50
55
60
0.2%
0.3%
0.5% 0.4% 0.9% 0.9% 0.5% 0.5% 1.5% 1.2% 11.1% 1.8%
0.1%
0.2%
0.2% 0.1% 0.2% 0.3% 0.3% 0.3% 0.4% 0.4%
0.0%
0.0%
0.0% 0.0% -0.1% -0.2% 0.0% 0.0% -0.2% -0.2% -0.5% 0.0%
7.9%
0.8%
-0.1% -0.2% -0.2% -0.2% -0.4% -0.4% -0.2% -0.2% -0.7% -0.6% -7.6% -0.7%
-0.3% -0.3% -0.4% -0.3% -0.5% -0.6% -0.5% -0.5% -1.0% -0.8% -11.0% -1.9%
1/e2 Near Field Diameter from 2D
Fourier Transform of Far Field
Phase Retrieval Technique:
“Error-Reduction” Algorithm*
•Fourier transform estimate
G ( u) = G ( u) exp[i φ ( u)] = F [ g ( x )]
k
k
k
k
•Substitute measured modulus G ′ ( u) = F ( u) exp[i φ ( u)]
k
k
•Inverse Fourier transform
g′ ( x ) = g′ ( x ) exp[i θ ′ ( x )] = F [G ′ ( u)]
•Apply support constraints
g ( x ) = f ( x ) exp[i θ ( x )] = f ( x ) exp[i θ ′ ( x )]
−1
k
k +1
k
k
k +1
*J. R. Fienup, “Phase retrieval algorithms: a comparison,”
Applied Optics Vol. 21, No. 15, pp. 2758-2769, Aug. 1982.
k
k
Far Field/Near Field Measurements of
1/e2 Spot Size
1/e2 Diameter (μm)
Fiber
1
Method of Analysis
2
1/e FF Gaussian
11.77×11.77
2
1/e NF Profile 100X
10.29×9.71
2
1/e NF Profile 40X
9.24×9.03
2D FF Fourier Transform
9.94×9.93
2
3
4
5
6
4.23×4.25
3.50×3.36
4.03×3.79
3.71×3.30
3.62×2.07
3.58×2.34
3.55×2.77
2.96×1.94
Major Axis × Minor Axis
6.20×6.16
4.67×4.67
4.85×4.73
5.04×5.03
5.07×5.11
4.37×4.29
4.24 ×4.15
4.02×4.07
3.64×3.51
4.23×4.09
3.79×3.55
3.60×3.55
Gaussian Approximation:
Is it Appropriate?
G a u s s ia n A p p r o x im a t io n
10000000
SMF 28
S M F 2 8 G a u s s ia n
LTF #5
L T F # 5 G a u s s ia n
Am p litud e (Ar b itr ar y Un its )
1000000
100000
10000
1000
100
10
1
-90
-70
-50
-30
-10
10
A n g le ( d e g r e e s )
30
50
70
90
Petermann II MFD Issues
„
Errors1,2
•
„
Elliptical Fiber3
•
„
1 M.
Obliquity Factor and Aperture Field
Radial Symmetry for Hankel Transform
Field Within Fiber vs Field at Focus
Young, “Mode-field Diameter of single-mode optical fiber by farfield scanning”, Applied Optics, Vol. 37, No. 24, August 1998
2 R. C. Wittmann and M. Young, “Are the Formulas for Mode-Field
Diameter Correct?”, NIST SOFM 1998
3 M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode
Optical Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8.
August 1989
Is MFD Appropriate for Focused
Beam Diameter in Free Space?
„
Fraunhofer Diffraction:
k (ξ + η )
z >>
2
2
jkz
j
k
( x2 + y2 )
2z
e e
U ( x, y) =
jλ z
„
„
1
2
∞ ∞
2
max
⎡
⎣
∫ ∫ U (ξ ,η ) exp⎢ − j
−∞ −∞
2π
⎤
( xξ + yη )⎥ dξdη
λz
⎦
2D Fourier Transform Pair1
Similar Expression for Laser Beam
Propagation in Free Space2
J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, San Francisco, CA, 1968, p.46
A. E. Siegman, Lasers
MFD
Near Field
Petermann I Integral*
1/ 2
⎫
⎧∞ 2
3
E
(
r
)
r
dr
∫
⎪⎪
⎪⎪ 0
MFD = 2 2 ⎨ ∞
⎬
⎪ ∫ E 2 ( r ) rdr ⎪
⎪⎩ 0
⎪⎭
*M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode Optical
Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8. August 1989
ISO/DIS 13694 Laser Standard
Second Moment Beam Diameter
For Radially Symmetric Beams*
1/ 2
⎫
⎧ 2
3
⎪⎪ 0∫ E ( r ) r dr ⎪⎪
D = 2 2⎨ ∞
⎬
⎪ ∫ E 2 ( r ) rdr ⎪
⎪⎩ 0
⎪⎭
∞
4σ
*
ISO/DIS Standard 13694, “Test methods for laser beam power (energy) density
distribution”, International Organization for Standardization, September 1998.
Lensed and Tapered Fiber Characterization
CONCLUSION
Small Spot/High NA Pose Measurement Challenges
„ Far Field Measurements are Easier to Perform and Less
Prone to Error than Near Field Measurements
„ Near Field Characterization from Far Field:
„
•Measurement
Must Extend to Large Angles….≥ 60°
•Gaussian Approximation is Questionable
•MFD Appears to be “OK” in Free Space
•“θ” is Important and Should Be Specified
•2D Fourier Transform Methods Warrant Further Investigation
•Different Metrics Yield Different Results
„
What is the Correct Answer?……...Standardization!
Near-Field Profiles
Far-Field Profiles
a.) Fiber #1
b.) Fiber #2
c.) Fiber #3
d.) Fiber #4
e.) Fiber #5
f.) Fiber #6
Far Field Measurement of Mode-Field
Diameter of Optical Fiber
TIA/EIA FOTP-191 Direct Far-Field Method
“Reference Method”
Petermann II Integral:
θ
MFD = (λ / π )
2 ∫ I (θ ) sin(θ ) cos(θ )dθ
θ
−θ
∫θ I (θ ) sin
−
3
(θ ) cos(θ )dθ
MFD
Far Field
Petermann II Integral:
θ
MFD = (λ / π )
2 ∫ I (θ ) sin(θ ) cos(θ )dθ
θ
−θ
∫θ I (θ ) sin
−
3
(θ ) cos(θ )dθ
MFD
MFD vs. Petermann II Integral Angle
12
11
10
#1 Major
#1 Minor
#2 Major
#2 Minor
#3 Major
#3 Minor
#4 Major
#4 Minor
#5 Major
#5 Minor
#6 Major
#6 Minor
MFD (microns)
9
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
Peterm ann II Integral Angle (degrees)
70
80
90
Far Field/Near Field Measurements of
1/e2 Spot Size
1/e2 Diameter (μm)
Fiber
Method of Analysis
2
1/e FF Gaussian
2
1/e NF Profile 100X
2
1/e NF Profile 40X
2D FF Fourier Transform
1
2
3
4
5
6
4.23×4.25
3.50×3.36
4.03×3.79
3.71×3.30
3.62×2.07
3.58×2.34
3.55×2.77
2.96×1.94
Major Axis × Minor Axis
11.77×11.77
10.29×9.71
9.24×9.03
9.94×9.93
6.20×6.16
4.67×4.67
4.85×4.73
5.04×5.03
5.07×5.11
4.37×4.29
4.24 ×4.15
4.02×4.07
3.64×3.51
4.23×4.09
3.79×3.55
3.60×3.55
Indirect Near Field Characterization
from Far Field Measurement
„
MFD
•
„
Gaussian Approximation
•
•
„
Petermann II Integral
Diffraction Limited 1/e2 “Spot” Size
Calculated from Far-Field Divergence
d=4λ/πθ
Calculated Near Field
•
•
2D Fourier Transform with Phase Retrieval
1/e2 width
Characterization of Lensed and
Tapered Fiber
„
„
„
Direct Near Field
Indirect Far Field
Is MFD Appropriate?
•
•
Field Within Fiber vs Field at Focus
MFD Errors
„
•
1
Obliquity Factor and Aperture Field1
Elliptical Fiber
Matt Young and Wittman reference