Abstract

Previous analytical results for Bragg scattering of a Gaussian beam by a periodic medium are extended to angles close to a Bragg angle. The effects of deviations from the exact Bragg condition are illustrated by numerical examples.

© 1976 Optical Society of America

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References

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  1. Ruey-Shi Chu and Theodor Tamir: “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976).
    [CrossRef]
  2. T. Tamir, editor, Integrated Optics (Springer-Verlag, New York, 1975), Sec. 4.6.2, p. 175.
  3. R. S. Chu and T. Tamir, “Erratum to ‘Bragg diffraction of Gaussian beams by periodically modulated media,’” J. Opt. Soc. Am. 66, 1141A (1976).

1976 (2)

Ruey-Shi Chu and Theodor Tamir: “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976).
[CrossRef]

R. S. Chu and T. Tamir, “Erratum to ‘Bragg diffraction of Gaussian beams by periodically modulated media,’” J. Opt. Soc. Am. 66, 1141A (1976).

Chu, R. S.

R. S. Chu and T. Tamir, “Erratum to ‘Bragg diffraction of Gaussian beams by periodically modulated media,’” J. Opt. Soc. Am. 66, 1141A (1976).

Chu, Ruey-Shi

Tamir, T.

R. S. Chu and T. Tamir, “Erratum to ‘Bragg diffraction of Gaussian beams by periodically modulated media,’” J. Opt. Soc. Am. 66, 1141A (1976).

Tamir, Theodor

J. Opt. Soc. Am. (2)

Ruey-Shi Chu and Theodor Tamir: “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976).
[CrossRef]

R. S. Chu and T. Tamir, “Erratum to ‘Bragg diffraction of Gaussian beams by periodically modulated media,’” J. Opt. Soc. Am. 66, 1141A (1976).

Other (1)

T. Tamir, editor, Integrated Optics (Springer-Verlag, New York, 1975), Sec. 4.6.2, p. 175.

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Figures (2)

FIG. 1
FIG. 1

Field intensity of the refracted beam at x = D1/2 for incidence at exactly the Bragg angle (solid curve) and away from that angle (dashed curve).

FIG. 2
FIG. 2

Field intensity of the Bragg-scattered beam at x = D1/2 for incidence at exactly the Bragg angle (solid curve) and away from that angle (dashed curve).

Equations (8)

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( k 0 d / π ) sin θ 0 = 1 + s 0 ,
s 0 = ( 2 d / λ ) ( sin θ 0 - sin θ B ) ,
F ˜ ( z ) = exp [ - ( z / 2 w 0 ) 2 ] exp [ i π z s 0 / d ] .
E ˜ 0 ( x , z ; t ) = - V ¯ 0 exp [ i ( ξ ˆ 0 x + ( 1 + s 0 ) π z / d - ω 0 t ) ] × - x tan θ ¯ B x tan θ ¯ B q 4 f ( z - z ) ( x tan θ ¯ B + z x tan θ ¯ B - z ) 1 / 2 × J 1 ( π q 2 d ( x 2 tan 2 θ ¯ B - z 2 ) 1 / 2 ) d z ,
E ˜ - 1 ( x , z ; t ) = - i V ¯ 0 exp [ i ( ξ ˆ 0 x - ( 1 - s 0 ) π z / d - ω - 1 t ) ] × - x tan θ ¯ B x tan θ ¯ B q 4 f ( z - z ) J 0 ( π q 2 d ( x 2 tan 2 θ ¯ B - z 2 ) 1 / 2 ) d z ,
f ( z ) = - exp [ - ( z - z 2 w 0 ) 2 ] exp ( - i π s 0 d z ) sin ( 2 π q z / d ) ( π z / d ) d z .
( 1 + s 0 ) π z / d = r k 0 z sin θ ¯ 0 and ξ ˆ 0 x ξ ¯ 0 x = r k 0 x cos θ ¯ 0 ,
E ˜ 0 ( x , z ; t ) = V ¯ 0 exp [ i r k 0 ( x cos θ ¯ 0 + z sin θ ¯ 0 ) - i ω 0 t ] × { exp [ - ( z - x tan θ ¯ 0 2 w 0 ) 2 ] - - x tan θ ¯ B x tan θ ¯ 0 q 4 f ( z - z ) ( x tan θ ¯ B + z x tan θ ¯ B - z ) 1 / 2 × J 1 ( π q 2 d ( x 2 tan 2 θ ¯ B - z 2 ) 1 / 2 ) d z } .