Abstract

Diffraction of a one-dimensional Gaussian beam by a slit is theoretically investigated. In the visible and microwave regions a new property of the diffracted energy is presented. Analytical expressions for the transmission coefficient and the diffracted energy at normal direction are obtained in simple practical form for experimentalists. These expressions suggest a simple method for measuring Gaussian beams of 1.5-μm diameter or larger.

© 1991 Optical Society of America

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References

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  1. O. Mata-Mendez, Phys. Rev. B 37, 8182 (1988).
    [Crossref]
  2. R. M. Herman, J. Pardo, T. A. Wiggins, Appl. Opt. 24, 1346 (1985).
    [Crossref] [PubMed]
  3. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, Appl. Opt. 10, 2775 (1971).
    [Crossref] [PubMed]
  4. D. K. Cohen, B. Little, F. S. Luecke, Appl. Opt. 23, 637 (1984).
    [Crossref] [PubMed]
  5. R. Csomor, Appl. Opt. 24, 2295 (1985).
    [Crossref] [PubMed]
  6. M. A. Karim, A. A. S. Awwal, A. M. Nasiruddin, A. Basit, D. S. Vedak, C. C. Smith, G. D. Miller, Opt. Lett. 12, 93 (1987).
    [Crossref] [PubMed]
  7. C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
    [Crossref]
  8. D. Maystre, O. Mata-Mendez, A. Roger, Opt. Acta 30, 1707 (1983).
    [Crossref]
  9. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 504.
  10. N. S. Kapany, J. J. Burke, K. Frame, Appl. Opt. 4, 1229 (1965).
    [Crossref]
  11. O. Mata-Mendez, M. Cadilhac, R. Petit, J. Opt. Soc. Am. 73, 328 (1983).
    [Crossref]
  12. O. Mata-Mendez, P. Halevi, Phys. Rev. B 36, 1007 (1987).
    [Crossref]
  13. P. Philippe, S. Valette, O. Mata-Mendez, D. Maystre, Appl. Opt. 24, 1006 (1985).
    [Crossref] [PubMed]

1988 (1)

O. Mata-Mendez, Phys. Rev. B 37, 8182 (1988).
[Crossref]

1987 (2)

1985 (3)

1984 (1)

1983 (2)

D. Maystre, O. Mata-Mendez, A. Roger, Opt. Acta 30, 1707 (1983).
[Crossref]

O. Mata-Mendez, M. Cadilhac, R. Petit, J. Opt. Soc. Am. 73, 328 (1983).
[Crossref]

1971 (1)

1965 (1)

1954 (1)

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
[Crossref]

Arnaud, J. A.

Awwal, A. A. S.

Basit, A.

Bouwkamp, C. J.

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
[Crossref]

Burke, J. J.

Cadilhac, M.

Cohen, D. K.

Csomor, R.

de la Claviere, B.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 504.

Frame, K.

Franke, E. A.

Franke, J. M.

Halevi, P.

O. Mata-Mendez, P. Halevi, Phys. Rev. B 36, 1007 (1987).
[Crossref]

Herman, R. M.

Hubbard, W. M.

Kapany, N. S.

Karim, M. A.

Little, B.

Luecke, F. S.

Mandeville, G. D.

Mata-Mendez, O.

O. Mata-Mendez, Phys. Rev. B 37, 8182 (1988).
[Crossref]

O. Mata-Mendez, P. Halevi, Phys. Rev. B 36, 1007 (1987).
[Crossref]

P. Philippe, S. Valette, O. Mata-Mendez, D. Maystre, Appl. Opt. 24, 1006 (1985).
[Crossref] [PubMed]

O. Mata-Mendez, M. Cadilhac, R. Petit, J. Opt. Soc. Am. 73, 328 (1983).
[Crossref]

D. Maystre, O. Mata-Mendez, A. Roger, Opt. Acta 30, 1707 (1983).
[Crossref]

Maystre, D.

Miller, G. D.

Nasiruddin, A. M.

Pardo, J.

Petit, R.

Philippe, P.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 504.

Roger, A.

D. Maystre, O. Mata-Mendez, A. Roger, Opt. Acta 30, 1707 (1983).
[Crossref]

Smith, C. C.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 504.

Valette, S.

Vedak, D. S.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 504.

Wiggins, T. A.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the model. The slit (of width l) is parallel to the z axis, i.e., perpendicular to the plane of the figure. The position of the incident Gaussian beam is fixed by the parameter b.

Fig. 2
Fig. 2

Maximum transmitted power (Pmax) normalized to I0 as a function of L/l in the scalar region.

Fig. 3
Fig. 3

ai and ai′ coefficients of τ(b) as a function of λ/l for TE (solid curves) and TM (dashed curves) cases. The results of the scalar region are included (0.001 ≤ λ/l ≤ 0.1).

Fig. 4
Fig. 4

Same as in Fig. 3 but for ℰ(b) coefficients.

Equations (16)

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I ( x , b ) = I p exp [ - 4 ( x - b ) 2 / L 2 ] ,
E ( x , y ) = i 2 y - l / 2 l / 2 u ( x ) H 0 1 ( k r ) d x ,
I ( θ ) = k 2 sin 2 θ u ^ ( k cos θ ) 2 ,
u ^ ( α ) = 1 ( 2 π ) 1 / 2 - l / 2 l / 2 u ( x ) exp ( - i α x ) d x .
0.001 λ / l 0.1.
erf ( x ) = 1 ( 2 π ) 1 / 2 - x exp ( - t 2 / 2 ) d t
E ( b ) = I p k 2 L 2 4 I 0 { erf [ 2 L ( l 2 - b ) ] - erf [ - 2 L ( l 2 + b ) ] } 2 ,
τ ( b ) = 1 0.89 L + 0.106 exp [ - 4 b 2 ( 1.011 L + 0.0315 ) 2 ] ,
E ( b ) = 1 λ ( 0.89 L + 0.106 ) exp [ - 4 b 2 1.011 L - 0.0234 ) 2 ] ,
P max = 1 0.89 L / l + 0.106 ,
0.3 λ / l 8.
τ ( b ) = 1 a 1 L + a 2 exp [ - 4 b 2 ( 1.011 L + 0.015 ) 2 ] ,
E ( b ) = 1 λ ( a 3 L + a 4 ) exp [ - 4 b 2 ( 1.013 L - 0.021 ) 2 ] ,
τ ( b ) = 1 a 1 L + a 2 exp [ - 4 b 2 ( 0.9991 L + 0.1035 ) 2 ] ,
E ( b ) = 1 ( a 3 L + a 4 ) exp [ - 4 b 2 ( 0.988 L + 0.104 ) 2 ] ,
P max = 1 q 1 L / l + q 2 ,

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