Correspondence rule and reciprocity theorem in the ultrasonic light-diffraction phenomenon

概要

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Based on theoretical and computational analysis, a striking symmetry property of the ultrasonic light diffraction spectrum with respect to the angle of incidence is obtained. This is to be stated as the following correspondence rule:(a)The intensity of the Braggside qth-order spectrum under (q+s)th-order Bragg incidence is the same with the intensity of the Bragg-side qth-order spectrum under (q-s)th-order Bragg incidence (q, s=1, 2, 3, . . . ;q>s). (b)In case q=s, the correspondence rule becomes as follows: The Bragg-side qth-order spectrum under 2qth-order Bragg incidence is of the same intensity with the +-qth-order spectra under normal incidence. (c)If q-s < 0, the rule becomes as: The Bragg-side qth-order spectrum under (s+q)th-order Bragg incidence is of the same intensity with the anti-Bragg side qth-order spectrum under (s-q)th-order Bragg incidence. This rule holds true irrespective of the values of the parameters pertaining to this phenomenon. The correspondence rule is equivalent to the following reciprocity theorem: The intensity of the ultrasonic light diffraction spectrum remains the same when the light is incident in the reversed direction of the diffraction spectrum and the spectrum produced in the inverted direction of the initial incident light is observed.
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