Abstract

A new method of measuring the complete optical field distribution (optical field mapping) is proposed and is applied to the measurement of Gaussian beam distribution at its beam waist. This method utilizes an interference technique and uses two single-mode optical fibers as flexible paths. The interference pattern caused by the output beams from the reference fiber and pickup fiber directly gives the relative phase distribution at the input end. For the intensity and phase distribution measurements the experimental ambiguity is as small as 0.1 μm and 1/10 of the wavelength, respectively. Stability of the interference fringe against the distortion of the fiber is also examined experimentally.

© 1978 Optical Society of America

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References

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  1. C. C. Timmermann, Appl. Opt. 15, 2432 (1976).
    [CrossRef] [PubMed]
  2. Y. Kohanzadeh, Appl. Opt. 15, 793 (1976);D. L. Bisbee, Appl. Opt. 15, 796 (1976).
    [CrossRef] [PubMed]
  3. Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
    [CrossRef]
  4. Y. Suzaki, A. Tachibana, Appl. Opt. 16, 1481 (1977).
    [CrossRef] [PubMed]
  5. S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949), Chap. 15.
  6. V. Vali, R. W. Shorthill, Appl. Opt. 15, 1099 (1976).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), Chap. 6.
  8. A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.
  9. D. L. Bisbee, Bell Syst. Tech. J. 50, 3159 (1971).
  10. D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).
  11. M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).
  12. Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

1977

1976

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).

Y. Kohanzadeh, Appl. Opt. 15, 793 (1976);D. L. Bisbee, Appl. Opt. 15, 796 (1976).
[CrossRef] [PubMed]

V. Vali, R. W. Shorthill, Appl. Opt. 15, 1099 (1976).
[CrossRef] [PubMed]

C. C. Timmermann, Appl. Opt. 15, 2432 (1976).
[CrossRef] [PubMed]

1973

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

1971

D. L. Bisbee, Bell Syst. Tech. J. 50, 3159 (1971).

Bisbee, D. L.

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

D. L. Bisbee, Bell Syst. Tech. J. 50, 3159 (1971).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), Chap. 6.

Chinnock, E. L.

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

Gloge, D.

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

Iiyama, M.

M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).

Kamiya, T.

M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

Kohanzadeh, Y.

Naruse, Y.

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

Shorthill, R. W.

Silver, S.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949), Chap. 15.

Smith, P. W.

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

Suzaki, Y.

Tachibana, A.

Timmermann, C. C.

Vali, V.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), Chap. 6.

Yamamoto, Y.

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

Yanai, H.

M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.

Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo

M. Iiyama, T. Kamiya, H. Yanai, Ann. Rep. Eng. Res. Inst. Fac. Eng. Univ. Tokyo 35, 129 (1976).

Appl. Opt.

Bell Syst. Tech. J.

D. L. Bisbee, Bell Syst. Tech. J. 50, 3159 (1971).

D. Gloge, P. W. Smith, D. L. Bisbee, E. L. Chinnock, Bell Syst. Tech. J. 52, 1579 (1973).

Proc. IEEE

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Proc. IEEE 64, 1013 (1976).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), Chap. 6.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.

Y. Yamamoto, Y. Naruse, T. Kamiya, H. Yanai, Conference Proceedings, Second European Conference on Optical Fiber Communication, Paris (27–30 September 1976), IX-6, p. 299.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, New York, 1949), Chap. 15.

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Figures (10)

Fig. 1
Fig. 1

Principle of optical field mapping. Two single-mode fibers form flexible optical paths. One has a tapered shape and is used as a pickup probe; the other is coupled with a Gaussian beam at the beam waist and transfers a reference beam. The interference pattern caused by the radiated two beams is used to determine the phase distribution.

Fig. 2
Fig. 2

Schematic representation of the experimental setup. A high-power objective lens focuses the output beam of the He–Ne laser. The optical field near the Gaussian beam waist is measured by the tapered fiber. The interference pattern is detected by a silicon vidicon tube and converted into an electrical signal.

Fig. 3
Fig. 3

A TV screen display of the interference pattern. The concentric fringe pattern is caused by the reflection at the window of the vidicon tube. The insertion shows the same interference pattern directly recorded on a photographic film.

Fig. 4
Fig. 4

Variation of the fringe visibility as a function of the intensity ratio between the two output beams. ID and IR are the light intensities radiated from the detecting fiber and from the reference fiber, respectively.

Fig. 5
Fig. 5

Phase shift Δδ as a function of the axial displacement Δz of the pickup fiber whose axis coincides with that of the optical beam to be measured. The phase shift is obtained from the fringe displacement normalized with the fringe spacing.

Fig. 6
Fig. 6

Phase shift Δδ as a function of the inclination angle ψ of the input quasi-plane wave. Displacement Δy′ of the pickup fiber is in the lateral direction and is a constant value of 10 μm for each ψ.

Fig. 7
Fig. 7

Phase distribution near the beam waist: (a) phase shift Δδ as a function of the lateral displacement Δy of the tapered fiber. The scanning is done at Δz = 50 μm where the radius of curvature of the wavefront Rz) has nearly its minimum value of 90 μm. The radius of curvature Rz) increases for both directions of Δz from Δz = 50 μm. There exist two values of Δz, where Rz) are the same. An example is shown for Rz) = 141 μm [(b), (c)]. The scale of (c) is different from those of (a) and (b).

Fig. 8
Fig. 8

Intensity distribution near the beam waist as a function of the lateral displacement Δy with axial displacement Δz from the beam waist as a parameter.

Fig. 9
Fig. 9

Variation of the spot size w′z) as a function of the lateral displacement Δz from the beam waist. True values of spot size wz) are obtained from a deconvolution procedure using a minimum square error method.

Fig. 10
Fig. 10

Rotation of the polarization axis caused by the applied distortion to the fiber: (a) rotation angle θp as a function of the bending radius R; (b) rotation angle θp as a function of the twisting angle θt. Both measurements are done for different values of fiber length at the distortion ranging from 5 cm to 20 cm.

Equations (13)

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s = ( l λ 0 ) / D n ,
Δ δ = 2 π λ 0 [ ( S 1 Q S 2 Q ) ( S 1 Q S 2 Q ) ] .
Δ u [ ( l λ 0 ) / D n ] = Δ δ 2 π .
E ( r , z ) = E 0 w 0 w ( z ) × exp { i [ k z η ( z ) ] r 2 [ 1 w 2 ( z ) + i k 2 R ( z ) ] } ,
w 2 ( z ) = w 0 2 [ 1 + [ z 2 / ( z 0 2 ) ] ] ,
R ( z ) = z { 1 + [ ( z 0 2 ) / z 2 ] } ,
η ( z ) = tan 1 [ z / ( z 0 ) ] ,
z 0 = ( π w 0 2 n ) / λ 0 .
R ( Δ y , Δ z ) 2 = ( Δ y ) 2 + [ R ( Δ y , Δ z ) Δ δ λ 0 2 π ] 2 ,
Δ δ = 2 π λ 0 1 2 R ( Δ z ) ( Δ y ) 2 ,
Δ δ = [ ( 2 π ) / λ 0 ] ( tan ψ ) ( 1 + tan 2 ψ ) 1 / 2 Δ y .
f 0 ( ρ , z ) exp { [ ( ρ 2 ) / ( a 2 ) ] } ,
E ( r , z ) exp [ r 2 w ( z ) 2 + a 2 ] ,

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