Abstract

We derive a far-field diffraction integral by (vector) electromagnetic theory; the result differs from the (scalar) Rayleigh–Sommerfeld or Kirchhoff result in that it depends on polarization. For unpolarized light, we derive a factor (1+cos2θ)1/2/2 that replaces the usual obliquity factor. Omitting this factor can cause an error of the same order as the measurement uncertainty in determining the mode-field diameter of a single-mode fiber from far-field data.

© 1993 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 33–46.
  2. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), pp. 17–40.
  3. W. Freude, A. Sharma, J. Lightwave Technol. LT-3, 628 (1985).
    [CrossRef]
  4. M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 387; J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 281.
  6. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  7. C. Pask, Electron. Lett. 20, 144 (1984), Eq. (5).
    [CrossRef]
  8. B. Walkerthe COST 217 Group, in Technical Digest—Symposium on Optical Fiber Measurements, 1990, G. W. Day, D. L. Franzen, eds., Natl. Inst. Stand. Technol. Spec. Publ. 792, 11 (1990).
  9. M. Garnder, in Skeptical Inquirer (Spring1993), p. 261; C. Murphy, in The Atlantic (February1992), p. 18.

1993

M. Garnder, in Skeptical Inquirer (Spring1993), p. 261; C. Murphy, in The Atlantic (February1992), p. 18.

1986

M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
[CrossRef]

1985

W. Freude, A. Sharma, J. Lightwave Technol. LT-3, 628 (1985).
[CrossRef]

1984

C. Pask, Electron. Lett. 20, 144 (1984), Eq. (5).
[CrossRef]

1971

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 387; J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 281.

Freude, W.

W. Freude, A. Sharma, J. Lightwave Technol. LT-3, 628 (1985).
[CrossRef]

Garnder, M.

M. Garnder, in Skeptical Inquirer (Spring1993), p. 261; C. Murphy, in The Atlantic (February1992), p. 18.

Gloge, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 33–46.

Kitayama, K.

M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
[CrossRef]

Ohashi, M.

M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
[CrossRef]

Pask, C.

C. Pask, Electron. Lett. 20, 144 (1984), Eq. (5).
[CrossRef]

Seikai, S.

M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
[CrossRef]

Sharma, A.

W. Freude, A. Sharma, J. Lightwave Technol. LT-3, 628 (1985).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), pp. 17–40.

Walker, B.

B. Walkerthe COST 217 Group, in Technical Digest—Symposium on Optical Fiber Measurements, 1990, G. W. Day, D. L. Franzen, eds., Natl. Inst. Stand. Technol. Spec. Publ. 792, 11 (1990).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 387; J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 281.

Appl. Opt.

Electron. Lett.

C. Pask, Electron. Lett. 20, 144 (1984), Eq. (5).
[CrossRef]

J. Lightwave Technol.

W. Freude, A. Sharma, J. Lightwave Technol. LT-3, 628 (1985).
[CrossRef]

M. Ohashi, K. Kitayama, S. Seikai, J. Lightwave Technol. LT-4, 109 (1986).
[CrossRef]

Skeptical Inquirer

M. Garnder, in Skeptical Inquirer (Spring1993), p. 261; C. Murphy, in The Atlantic (February1992), p. 18.

Other

B. Walkerthe COST 217 Group, in Technical Digest—Symposium on Optical Fiber Measurements, 1990, G. W. Day, D. L. Franzen, eds., Natl. Inst. Stand. Technol. Spec. Publ. 792, 11 (1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 387; J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 281.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 33–46.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), pp. 17–40.

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Figures (1)

Fig. 1
Fig. 1

Radius vector between a fiber at the origin of coordinates and a point in the far field.

Equations (4)

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U ( θ ) cos θ 0 u ( R ) J 0 ( k R sin θ ) R d R ,
u ( R ) 0 π / 2 [ U ( θ ) / cos θ ] J 0 ( k R sin θ ) sin ( 2 θ ) d θ .
E ( θ , ϕ ) = E x ( θ ) ( 1 + tan 2 θ cos 2 ϕ ) 1 / 2 .
e t ( R ) 0 π / 2 [ E m ( θ ) / ( 1 + cos 2 θ ) 1 / 2 ] × J 0 ( k R sin θ ) sin ( 2 θ ) d θ ,

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