Abstract

It is known that near grating anomalies of the resonance type a beam may undergo a lateral shift of the order of the beam width, and a pulse may be delayed by a time of the order of the pulse duration. These numerical investigations are extended to Rayleigh anomalies that occur when, upon variation of the wavelength or the angle of incidence, an additional propagating diffraction order emerges. It is shown that delays and displacements are 1 order of magnitude smaller than in the resonance case. However, with increasing beam width (or pulse duration), the lateral displacement (or the temporal delay) can become large.

© 2000 Optical Society of America

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References

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1999 (1)

F. Schreier, M. Schmitz, O. Bryngdahl, “Superluminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

1998 (3)

1992 (1)

R. Magnusson, S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

1990 (1)

1986 (1)

1984 (1)

1978 (1)

1973 (1)

1966 (1)

1965 (1)

Bagby, J.

Bryngdahl, O.

Burckhardt, C. B.

Garea, M. T.

Güther, R.

R. Güther, B. H. Kleemann, “Shift and shape of grating reflected beams,” J. Mod. Opt. 45, 1375–1393 (1998).
[CrossRef]

Hessel, A.

Kaspar, F. G.

Kleemann, B. H.

R. Güther, B. H. Kleemann, “Shift and shape of grating reflected beams,” J. Mod. Opt. 45, 1375–1393 (1998).
[CrossRef]

Knop, K.

Magnusson, R.

Moharam, M.

Oliner, A. A.

Schmitz, M.

Schreier, F.

Simon, J. M.

Simon, M. C.

Wang, S.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. Magnusson, S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

J. Mod. Opt. (1)

R. Güther, B. H. Kleemann, “Shift and shape of grating reflected beams,” J. Mod. Opt. 45, 1375–1393 (1998).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

F. Schreier, M. Schmitz, O. Bryngdahl, “Superluminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

Opt. Lett. (2)

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Figures (9)

Fig. 1
Fig. 1

Maximum diffraction efficiency ηmax of the +1st diffraction order in transmission as a function of the index modulation and maximum lateral displacement Δx of the 0th transmitted diffraction order as a function of Δ∊.

Fig. 2
Fig. 2

Diffraction efficiencies of the propagating orders as a function of the wavelength near the Rayleigh wavelength.

Fig. 3
Fig. 3

Temporal delay of a pulse incident on the index-modulated grating at Θinc=23°, calculated from the phase of the diffraction coefficients: (a) -1st, (b) 0th, (c) +1st diffraction order.

Fig. 4
Fig. 4

Delays of the propagating orders of a pulse of 500 ps (FWHM) near the Rayleigh wavelength.

Fig. 5
Fig. 5

Maximum delay as a function of the pulse duration (FWHM).

Fig. 6
Fig. 6

Lateral displacement of the maximum of intensity, calculated from the phase of the diffraction coefficient: (a) -1st, (b) 0th, (c) +1st diffraction order.

Fig. 7
Fig. 7

Lateral displacement of a beam with a beam width (FWHM) of 133 µm as a function of the mean angle of incidence near ΘR.

Fig. 8
Fig. 8

Comparison of the displacement curves of the 0th transmitted order for an infinite beam width [calculated from the phase of the diffraction coefficients according to Eq. (2)] (solid curve) and beams having widths of 2081 µm (dashed curve), 533 µm (dotted curve), and 133 µm (dotted–dashed curve).

Fig. 9
Fig. 9

Maximum displacement of diffraction orders as a function of the beam width (FWHM).

Equations (2)

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Δt=-λ22πc arg(T)λ.
Δx=- arg(T)Θincλ2π cos Θinc,

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