超音波による光の回折 : 逐次回折による計算法

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First the relations amongst various theoretical parameters-θ, D, v and ξ(eqs. (4)〜(7))-concerning the phenomenon of the diffraction of light by ultrasound are discussed and presented in Fig. 1, together with their relations with experimental parameters-acoustic frequency and output-for water under certain experimental conditon. Then the present state of the correspondence between theory and experiments is discussed and summarized in Fig. 2. Under certain conditions (eq. (13)), a simple approximation, the phase-lattice approximation, is valid both for normal incidence of light and for oblique incidence, and this makes the starting point of the present calculation. We subdivide the parallel beam of sound in thin layers or subbeams of equal thickness each, and consider the light diffraction by ultrasound as a multiple or successive diffraction process by these sub-beams, assuming phase-lattice approximation for each step diffraction taking place by these sub-beams with various angles of incidence. Generally speaking, the s-th order spectrum emergent from the j-th sub-beam of sound consists of many components as shown in Fig. 4. Especially, the light incident in the j-th sub-beam in the direction of the zero-order spectrum and diffracted as the s-th order by crossing this layer -the (0, s) component-has the amplitude and phase pressented in eq. (14) according to the phase-lattice theory for unit incident light-0-order-in the j-th layer and with the phase referred to point B in Fig. 3 and 4. The other component-the (p, s)-component-, produced from the light incident in the direction of the p-th order spectrum on the j-th layer and diffracted as the m-th order (m=s-p) by this layer has the phase difference (16) with respect to the (0, s)-compont, while the phase-lattice parameter for determining the amplitude becomes (22). In calculating the phase-difference (16), the effective shift of the phase-lattice with respect to the sound wave (Fig. 3) in case of the oblique incidence is taken into account. The phase-difference has the symmetry property (17) for the changes of signs of p and s. The rule for constructing the (j+1)th layer complex amplitudes of the diffraction spectra from the j-th layer complex amplitudes becomes (21), and this results in the working formulas (25) and (26) when resolved into real and imaginary parts by (24) by taking account of the symmetry property (23). The result of the computation revealed that a normalization process as indicated in (28) becomes necessary in practice. With decreasing step-width of computation, however, the normalization constant approaches unity as indicated in Table 1. The results of the computation for various of θ ranging from 0. 1 to 6 are shown in Fig. 5〜15 together with the comparison with the exact results by the extended Brillouin theory (Nomoto, to be published). While the agreement has not been satisfactory for the range of small θ(≦0. 5), except for θ=0. 1, rather good agreements have been obtained for the range θ=1〜6. The discrepancy for smaller range of θ is due to the somewhat too rough step-width of D(=0. 05) employed in computation for this range. As the requirement for making the step of D sufficiently small (D=0. 01〜0. 02) becomes more easy to be fulfilled for larger values of θ, the present method is estimated to be a good method of approximation for obtaining the intensity distribution of the ultrasonic lightdiffraction spectrum, not only for the range θ=1〜6, but also for the range θ>6, where exact results are not available as yet except for θ=10. The present paper lays emphasis on the evaluation of the method, and the results for range θ=7〜100 are to be published elsewhere.
社団法人日本音響学会の論文
1970-09-10

超音波による光の回折 : 逐次回折による計算法

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