Diffraction of Light by Ultrasound: Finite Analytical Expressions for the Spectra up to Order 3

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Abstract:

In connection with the diffraction of light by an ultrasonic wave at normal incidence, a 3rd order approximation method is proposed in order to solve the system of differential equations of Raman and Nath. Analytical expressions for the amplitudes and the intensities of order 0, ± 1, ± 2, and ± 3 are established and a graphical comparison with the 2nd order approximation method is presented. Simultaneously the limits of validity of both approximation methods are discussed, leading to the conclusion that the solution derived in the paper may replace previous numerical methods for a large range of the experimental parameters.

Zusammenfassung

Im Zusammenhang mit der Beugung von Licht an einer Ultraschallwelle bei senkrechtem Einfall wird eine Näherungsmethode 3. Ordnung vorgeschlagen zur Lösung des Systems von Differentialgleichungen von Raman und Nath. Es werden analytische Ausdrücke für die Amplituden und die Intensitäten der Ordnungen 0, ± 1, ± 2 aufgestellt und ein graphischer Vergleich mit der Näherung 2. Ordnung vorgenommen. Gleichzeitig werden Gültigkeitsgrenzen beider Näherungsmethoden diskutiert mit dem Ergebnis, daß die in dieser Arbeit abgeleitete Lösung frühere numerische Methoden für einen großen Bereich experimenteller Parameter ersetzen kann.

Sommaire

A propos du problème de la diffraction de la lumière par une onde ultrasonore sous incidence normale, on propose une méthode d'approximation du troisième ordre afin de résoudre le système d'équations de Raman et Nath. On établit des expressions analytiques pour les amplitudes et les intensités des spectres diffractés d'ordres 0, ± 1, ± 2 et ± 3 ainsi qu'un graphique de comparaison avec les résultats de l'approximation du second ordre. En même temps on discute des limites de validité de ces deux approximations et on en conclut que la solution présentée ici mérite de remplacer, pour une gamme étendue de valeurs des paramètres expérimentaux, les méthodes numériques utilisées antérieurement.

Document Type: Research Article

Publication date: March 1, 1985

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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