Abstract

Continuing a previous analytical and numerical work, an experimental investigation of seven intrinsic properties of the optical coupling between axisymmetric Gaussian beams is presented. In this study, two single-mode fibers are used as the receiver and the emitter and a five-axis nanopositioning system is used to investigate optical coupling properties by moving one fiber relative to the other. Experiments demonstrate the existence of sufficiently accurate hyperbolic, parabolic, and linear trends for the optical coupling phenomenon, which can be useful for developing model-based alignment algorithms.

© 2005 Optical Society of America

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References

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  1. Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
    [CrossRef]
  2. Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
    [CrossRef]
  3. Y. St-Amant, D. Gariépy, D. Rancourt, “Intrinsic properties of the optical coupling between axisymmetric Gaussian beams,” Appl. Opt. 43, 5691–5704 (2004).
    [CrossRef] [PubMed]
  4. H. Kogelnik, Coupling and Conversion Coefficients for Optical Modes in Quasi-Optics, Microwave Research Institute Symposia Series, Vol. 14 (Polytechnic, New York, 1964), pp. 333–347.
  5. L. A. Wang, C. D. Su, “Tolerance analysis of aligning an astigmatic laser diode with a single-mode optical fiber,” J. Lightwave. Technol. 14, 2757–2762 (1996).
    [CrossRef]
  6. W. B. Joyce, B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. 23, 4187–4196 (1984).
    [CrossRef] [PubMed]
  7. S. Nemoto, T. Makimoto, “Analysis of splice loss in single-mode fibers using a Gaussian field approximation,” Opt. Quantum Electron. 11, 447–457 (1979).
    [CrossRef]
  8. J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995).

2004

2001

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
[CrossRef]

1996

L. A. Wang, C. D. Su, “Tolerance analysis of aligning an astigmatic laser diode with a single-mode optical fiber,” J. Lightwave. Technol. 14, 2757–2762 (1996).
[CrossRef]

1984

1979

S. Nemoto, T. Makimoto, “Analysis of splice loss in single-mode fibers using a Gaussian field approximation,” Opt. Quantum Electron. 11, 447–457 (1979).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995).

DeLoach, B. C.

Gariépy, D.

Joyce, W. B.

Kogelnik, H.

H. Kogelnik, Coupling and Conversion Coefficients for Optical Modes in Quasi-Optics, Microwave Research Institute Symposia Series, Vol. 14 (Polytechnic, New York, 1964), pp. 333–347.

Makimoto, T.

S. Nemoto, T. Makimoto, “Analysis of splice loss in single-mode fibers using a Gaussian field approximation,” Opt. Quantum Electron. 11, 447–457 (1979).
[CrossRef]

Mondal, S. K.

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Nemoto, S.

S. Nemoto, T. Makimoto, “Analysis of splice loss in single-mode fibers using a Gaussian field approximation,” Opt. Quantum Electron. 11, 447–457 (1979).
[CrossRef]

Rancourt, D.

Shi, F. G.

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
[CrossRef]

St-Amant, Y.

Su, C. D.

L. A. Wang, C. D. Su, “Tolerance analysis of aligning an astigmatic laser diode with a single-mode optical fiber,” J. Lightwave. Technol. 14, 2757–2762 (1996).
[CrossRef]

Tang, Z.

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
[CrossRef]

Wang, L. A.

L. A. Wang, C. D. Su, “Tolerance analysis of aligning an astigmatic laser diode with a single-mode optical fiber,” J. Lightwave. Technol. 14, 2757–2762 (1996).
[CrossRef]

Zhang, R.

Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
[CrossRef]

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Appl. Opt.

J. Lightwave. Technol.

L. A. Wang, C. D. Su, “Tolerance analysis of aligning an astigmatic laser diode with a single-mode optical fiber,” J. Lightwave. Technol. 14, 2757–2762 (1996).
[CrossRef]

Opt. Commun.

Z. Tang, R. Zhang, S. K. Mondal, F. G. Shi, “Optimization of fiber-optic coupling and alignment tolerance for coupling between a laser diode and a wedged single-mode fiber,” Opt. Commun. 199, 95–101 (2001).
[CrossRef]

Z. Tang, R. Zhang, F. G. Shi, “Effects of angular misalignments on fiber-optic alignment automation,” Opt. Commun. 196, 173–180 (2001).
[CrossRef]

Opt. Quantum Electron.

S. Nemoto, T. Makimoto, “Analysis of splice loss in single-mode fibers using a Gaussian field approximation,” Opt. Quantum Electron. 11, 447–457 (1979).
[CrossRef]

Other

J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995).

H. Kogelnik, Coupling and Conversion Coefficients for Optical Modes in Quasi-Optics, Microwave Research Institute Symposia Series, Vol. 14 (Polytechnic, New York, 1964), pp. 333–347.

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Figures (15)

Fig. 1
Fig. 1

(a) Three-dimensional, (b) side, and (c) top views of a two-fiber system.

Fig. 2
Fig. 2

Definition of a transverse misalignment line.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

Experimental investigation of property A: (a) Two-dimensional transverse scans for zd = 500 μm and βd = 0.035 rad. In (b), (c), and (d), coupled optical power (solid circles) is compared with the best parabola fit (solid curve) for the three one-dimensional transverse scans highlighted in (a).

Fig. 5
Fig. 5

Comparison of the theoretical transverse distribution of the fundamental propagation mode of a single-mode fiber (solid curve) with its Gaussian approximation (dashed curve).

Fig. 6
Fig. 6

Experimental investigation of property A: MAVR as a function of axial misalignment for 5, 10, and 20 dB threshold values.

Fig. 7
Fig. 7

Experimental investigation of property B: Comparison of the experimental coupled optical power (solid circles) with the best parabola fit (dashed curves) for angular misalignment scans performed at (a) zd = 3000 μm, θd = 0.01 rad and (b) zd = 1500 μm, θd = 0.04 rad.

Fig. 8
Fig. 8

Experimental investigation of property B: MAVR as a function of axial misalignment for transverse misalignment lines inclined by 0, 0.01, 0.02, and 0.04 rad.

Fig. 9
Fig. 9

Experimental investigation of property C: (a) Two-dimensional and (b) three-dimensional views of optical power measurement locations.

Fig. 10
Fig. 10

Experimental investigation of property C: (a) Comparison of experimental optimal transverse misalignment (solid circles) with the best straight line fits (dashed curves). In (b) the slope of the optimal transverse misalignment lines in (a) is presented as a function of the angular misalignment (solid circles) and compared with its best straight line fit (dashed curve).

Fig. 11
Fig. 11

Experimental investigation of property D: (a) Comparison of experimental optimal angular misalignment (solid circles and curves) with its theoretical value (dashed curves). In (b) the optimal angular misalignment is presented as a function of θd for axial misalignment equal to 3000 μm.

Fig. 12
Fig. 12

Experimental investigation of property E: Experimental width coefficient (x and y) of the coupled optical power transverse distribution (solid circles) for (a) βd = 0 and (b) βd = 0.08 rad. The best hyperbola fit (dashed curves) and the calculated asymptote (dotted curves) are also presented.

Fig. 13
Fig. 13

Experimental investigation of property E: (a) Asymptote slopes and (b) predicted zero axial misalignment locations as a function of the angular misalignment. Data for x (solid curves) and y (dashed curves) directions are compared.

Fig. 14
Fig. 14

Experimental investigation of property F: (a) Raw and (b) normalized experimental coupled optical power along optimal transverse misalignment lines.

Fig. 15
Fig. 15

Experimental investigation of property G: (a) Absolute rate of variation of experimental coupled optical power along optimal transverse misalignment lines. In (b) a zoomed view of (a) is presented.

Tables (2)

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Table 1 Experimental Investigation of Property C

Tables Icon

Table 2 Experimental Investigation of Property E

Equations (9)

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P = P x P y ,
P x = 4 σ G 2 + ( σ + 1 ) 2 exp { - p × [ ( σ + 1 ) F x 2 - 2 σ F x G sin β d + σ ( G 2 + σ + 1 ) sin 2 β d G 2 + ( σ + 1 ) 2 ] } ,
P y = 4 σ G 2 + ( σ + 1 ) 2 exp { - p × [ ( σ + 1 ) F y 2 + 2 σ F y G sin α d + σ ( G 2 + σ + 1 ) sin 2 α d G 2 + ( σ + 1 ) 2 ] } ,
σ = ( w 02 w 01 ) 2 ,             p = 2 ( π n w 01 λ ) 2 ,             F x = x d z R 1 , F y = y d z R 1 ,             G = z d z R 1 ,             z R 1 = π n w 01 2 λ .
P dB = 10 log ( P ) .
ϕ o p t d = - σ σ + 1 α d , θ o p t d = σ σ + 1 β d .
MAVR = 1 n i = 1 n P n = P n e ,
C L = L y - y 0 = 2 A ,
E = ( Δ z * Δ z - 1 ) d P d z ,

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