Raman-Nath diffraction

Consequently, we can understand that sound waves change the refractive index of a medium according to Eq. (4.31). In a piezoelectric medium sound waves can induce a new electric field. This phenomenon is very complex because the induced electric field relates to a change in the refractive index of the medium. In general, the acousto-optic effects are classified into two phenomena depending on the frequency of the sound waves, the Raman-Nath diffraction and the Bragg diffraction (see Table 4.10). 

At lower ultrasonic frequencies (0.5-10 MHz), Raman-Nath diffraction of laser light by plane acoustic waves was used to measure the decay of acoustic energy inside an aerogel specimen [57], This method relies on the density variations produced by the sound wave that create a phase pattern inside the specimen. The intensity of the first order of the diffracted light beams is proportional to the sound intensity at the intercept of light and sound beam. In a log plot of sound intensity versus distance from the transducer, the slope is a measure of the attenuation. 

Hence, for Raman-Nath diffraction several discrete peaks are observed in the emerging optical beam. The intensity of these orders are given by (Hammer, 1982)... 

Further quantitation can be experimentally determined through the relation of these quantities to the diffraction efficiency q of a Raman-Nath orientational grating [20,48] ... 

For quantitative comparison of the grating strengths in the different liquid crystal composites, the first-order diffraction efficiency measurements of the Raman-Nath gratings are more amenable to analysis than the beam coupling ratio. Several concentrations for each of the dopants were utilized and Fig. 9 illustrates the highest diffraction efficiency values versus applied voltage for the samples with the optimal concentration of each dopant. A wavevector value of q = 1 x 103 cm-1 was again utilized. The first clearly noticeable fact is... 

Whether bulk or surface acoustic waves are used, two fundamentally different types of optical modulations are possible. The type of modulation is dictated by the interaction length L of the optical beam with the acoustic wave, where L is approximately the width of the acoustic wave front (or acoustic beam spot size). In the Raman-Nath type modulator the optical beam transverses the acoustic beam, and the interaction length of the optical path (i.e., the width of the acoustic wave) is so short that the optical waves only undergo a phase grating diffraction, producing many interference peaks in the far field. 

When the cell is thin (Fig. 3.9) and the acoustic wave is weak, the optical beam direction change is very small on transmission through the ceU. For Raman-Nath type diffraction, the interaction length must be so short that multiple diffractions do not take place. This condition occurs when... 

The Raman-Nath output is usually taken to be the zeroth-order mode. The modulation index equals the fraction of the light diffracted out of the zeroth-order and is expressed as... 

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