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Applied Optics

Applied Optics


  • Vol. 37, Iss. 3 — Jan. 20, 1998
  • pp: 473–478

Effects of phase shifts on four-beam interference patterns

Andres Fernandez and Don W. Phillion  »View Author Affiliations

Applied Optics, Vol. 37, Issue 3, pp. 473-478 (1998)

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An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by π from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.

© 1998 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(110.3960) Imaging systems : Microlithography
(260.3160) Physical optics : Interference
(350.7420) Other areas of optics : Waves

Original Manuscript: March 10, 1997
Revised Manuscript: June 20, 1997
Published: January 20, 1998

Andres Fernandez and Don W. Phillion, "Effects of phase shifts on four-beam interference patterns," Appl. Opt. 37, 473-478 (1998)

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