Abstract

The problem of restoring the misaligned output from a grating hologram under READ beam deviations has been investigated recently using a variety of resonant triad models [1-3]. Initially, it was proposed that selective angular and/or wavelength tuning of the READ beam would restore the output beam direction [1]. Subsequently, upon closer examination, it was found that the problem is amenable to different geometrical interpretations depending on whether the grating is untilted or tilted, and whether the READ beam deviation (Δλ or Δθ) is positive or negative [2]. The latter problem has generally been analyzed by assuming a single-deviation model (i.e., with the READ beam having either an angular or a wavelength deviation and not both). It may be shown that the deviation in the desired reconstructed beam direction may be graphically determined from appropriate resonant triads superposed on wavenumber (or β) circles. For the case of an untilted grating with a READ angular mismatch, for instance, an appropriate wavelength tuning will restore the reconstructed beam direction. The amount of tuning necessary will depend on the sign of the angular mismatch (i.e., whether it is greater or less than the Bragg angle). One such scenario is shown in Fig. 1.

© 1996 Optical Society of America