In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which concisely represents the refractive indices and associated polarizations of light, as functions of the orientation of the wavefront, in a doubly-refractive crystal (provided that the crystal does not exhibit optical rotation). When this ellipsoid is cut through its center by a plane parallel to the wavefront, the resulting intersection (called a central section or diametral section) is an ellipse whose major and minor semiaxes have lengths equal to the two refractive indices for that orientation of the wavefront, and have the directions of the respective polarizations as expressed by the electric displacement vector D. The principal semiax
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| - مؤشر إهليجي (ar)
- Indexellipsoid (de)
- Index ellipsoid (en)
- Ellissoide degli indici di rifrazione (it)
- Indicatrix (nl)
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| - المؤشر الإهليجي هو عبارة عن شكل رياضي يستخدم لوصف إنكسار الضوء في البلورات التي يحدث فيها انكسار مزدوج للضوء. حيث لا يتبع انكسار الأشعة قانون الانكسار إلا في حالات استثنائية في البلورات، طبقا لبنيتها. (ar)
- Das Indexellipsoid, auch Fletcher-Ellipsoid nach Lazarus Fletcher, ist eine Indikatrix zur Beschreibung der Lichtbrechung (genauer: der Brechungsindizes, Einzahl: -index, daher der Name) in einem doppelbrechenden Kristall. Zusammen mit dem Fresnel-Ellipsoid (nach Augustin Jean Fresnel) ermöglicht dieses Ellipsoid eine anschauliche Beschreibung der Ausbreitung von Licht in Materie. (de)
- Een indicatrix of index-ellipsoïde is een ellipsoïde die de oriëntatie en relatieve grootte van de brekingsindices in een kristal aangeeft. In kristallen is de brekingsindex niet in alle richtingen gelijk, omdat kristalstructuren niet in alle richtingen licht op dezelfde manier doorlaten. In drie dimensies kan de brekingsindex van een kristal daarom beschreven worden met drie principiële waardes, die samen een ellipsoïde definiëren. (nl)
- In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which concisely represents the refractive indices and associated polarizations of light, as functions of the orientation of the wavefront, in a doubly-refractive crystal (provided that the crystal does not exhibit optical rotation). When this ellipsoid is cut through its center by a plane parallel to the wavefront, the resulting intersection (called a central section or diametral section) is an ellipse whose major and minor semiaxes have lengths equal to the two refractive indices for that orientation of the wavefront, and have the directions of the respective polarizations as expressed by the electric displacement vector D. The principal semiax (en)
- L'ellissoide degli indici di rifrazione è uno strumento matematico per descrivere in maniera completa come varia l'indice di rifrazione di un materiale anisotropo a seconda della direzione di propagazione di un'onda elettromagnetica al suo interno. Si può dimostrare che in ogni materiale è sempre possibile definire 3 assi ottici, in base ai quali si scrive l'ellissoide degli indici in forma canonica Nei materiali birifrangenti, due degli assi sono identici tra loro (ovvero, c'è simmetria cilindrica), per cui l'ellissoide degli indici è scrivibile come (it)
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| - المؤشر الإهليجي هو عبارة عن شكل رياضي يستخدم لوصف إنكسار الضوء في البلورات التي يحدث فيها انكسار مزدوج للضوء. حيث لا يتبع انكسار الأشعة قانون الانكسار إلا في حالات استثنائية في البلورات، طبقا لبنيتها. (ar)
- Das Indexellipsoid, auch Fletcher-Ellipsoid nach Lazarus Fletcher, ist eine Indikatrix zur Beschreibung der Lichtbrechung (genauer: der Brechungsindizes, Einzahl: -index, daher der Name) in einem doppelbrechenden Kristall. Zusammen mit dem Fresnel-Ellipsoid (nach Augustin Jean Fresnel) ermöglicht dieses Ellipsoid eine anschauliche Beschreibung der Ausbreitung von Licht in Materie. (de)
- In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which concisely represents the refractive indices and associated polarizations of light, as functions of the orientation of the wavefront, in a doubly-refractive crystal (provided that the crystal does not exhibit optical rotation). When this ellipsoid is cut through its center by a plane parallel to the wavefront, the resulting intersection (called a central section or diametral section) is an ellipse whose major and minor semiaxes have lengths equal to the two refractive indices for that orientation of the wavefront, and have the directions of the respective polarizations as expressed by the electric displacement vector D. The principal semiaxes of the index ellipsoid are called the principal refractive indices. It follows from the sectioning procedure that each principal semiaxis of the ellipsoid is generally not the refractive index for propagation in the direction of that semiaxis, but rather the refractive index for wavefronts tangential to that direction, with the D vector parallel to that direction, propagating perpendicular to that direction. Thus the direction of propagation (normal to the wavefront) to which each principal refractive index applies is in the plane perpendicular to the associated principal semiaxis. (en)
- L'ellissoide degli indici di rifrazione è uno strumento matematico per descrivere in maniera completa come varia l'indice di rifrazione di un materiale anisotropo a seconda della direzione di propagazione di un'onda elettromagnetica al suo interno. Si può dimostrare che in ogni materiale è sempre possibile definire 3 assi ottici, in base ai quali si scrive l'ellissoide degli indici in forma canonica Nei materiali birifrangenti, due degli assi sono identici tra loro (ovvero, c'è simmetria cilindrica), per cui l'ellissoide degli indici è scrivibile come dove è detto indice di rifrazione ordinario e è detto indice di rifrazione straordinario e il suo asse è detto asse ottico (nel nostro caso, l'asse z).Un'onda elettromagnetica che si propaghi con il suo vettore d'onda parallelo all'asse ottico vede l'indice di rifrazione ordinario per ogni polarizzazione del campo elettrico, mentre potrà vedere un indice di rifrazione variabile tra ed se il suo vettore d'onda non è parallelo all'asse ottico.In alcuni casi, può capitare di aver disponibile l'equazione non canonica dell'ellisse degli indici, ovvero un'equazione del tipo In questo caso, grazie al teorema spettrale, ci si può ricondurre alla forma canonica tramite un cambiamento di base. La maniera più semplice per compiere questa operazione è la seguente:1) Scrivere l'equazione non canonica in forma matriciale, ovvero in una espressione del tipo :; 2) Detta , gli autovalori di M sono gli indici di rifrazione nel sistema canonico, mentre i suoi autovettori sono gli assi del sistema canonico espressi nel sistema in cui si sta lavorando (it)
- Een indicatrix of index-ellipsoïde is een ellipsoïde die de oriëntatie en relatieve grootte van de brekingsindices in een kristal aangeeft. In kristallen is de brekingsindex niet in alle richtingen gelijk, omdat kristalstructuren niet in alle richtingen licht op dezelfde manier doorlaten. In drie dimensies kan de brekingsindex van een kristal daarom beschreven worden met drie principiële waardes, die samen een ellipsoïde definiëren. (nl)
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