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Diffraction of Light by Ultrasound at Oblique Incidence: An Exact 4-Order Solution

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Abstract:

The light diffraction by a progressive ultrasonic wave at oblique incidence is treated starting from the system of differential equations of Raman and Nath. Finite analytical expressions for the amplitudes and intensities of order 0, ± 1 and −2 at Bragg incidence and in the vicinity of the Bragg angle are established by means of the N th order approximation method. The formulae are a considerable improvement of the solution obtained by Phariseau by means of successive approximations, and are valid for ϱ ≧ 1. A graphical comparison with the Phariseau expressions is included, illustrating at the same time some symmetry properties exhibited by the calculated intensities.

Zusammenfassung

Ausgehend von dem Differentialgleichungssystem von Raman und Nath wird die Lichtbeugung an einer fortschreitenden Ultraschallwelle bei schrägem Einfall behandelt. Für die Amplituden und Intensitäten der Ordnung 0, ± 1 und ± 2 bei Bragg-Einfall und in der Nähe des Bragg-Winkels werden geschlossene analytische Ausdriicke mit Hilfe der Näherung N-ter Ordnung aufgestellt. Die Formeln stellen einen betrachtlichen Fortschritt gegenüber der von Phariseau mittels sukzessiver Approximation erhaltenen Lösung dar und gelten für ϱ ≧ 1. Es wird ein graphischer Vergleich mit den Phariseauschen Ausdrücken vorgenommen, der gleichzeitig einige Symmetrieeigenschaften der berechneten Intensitäten veranschaulicht.

Sommaire

On traite le problème de la diffraction d'une onde lumineuse par une onde ultrasonore progressive sous incidence oblique à partir du système d'équations différentielles de Raman et Nath. La méthode d'approximation jusqu'à l'ordre N a servi a établir des expressions analytiques en termes finis pour les amplitudés et intensites d'ordres 0, +1, −1 et − 2, a l'incidence de Bragg ou au voisinage de l'angle de Bragg. Les formules obtenues présentent d'importants avantages par rapport à la solution que Phariseau avait obtenue au moyen d'approximations finies. Elles sont valables pour ϱ ≧ l . Une comparaison graphique avec les résultats de Phariseau montre en même temps certaines propriétés de symétrie des intensités calculées selon les formules proposées.

Document Type: Research Article

Publication date: 1986-01-01

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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