Les phonon-polaritons de surface

Étudions maintenant les conditions d’existence des phonon-polaritons de surface. Pour cela, nous considérons le cas d’un cristal polaire diatomique tel que le SiC. Nous avons déjà vu que la permittivité diélectrique d’un tel matériau peut être modélisée par un modèle d’oscillateur

ε(ω) = ε∞ · 1 +ω 2 L− ω2T ω_T2 _{− ω}2 ¸ (E.34) De même que pour l’étude des plasmon-polaritons, nous considérons ici un cristal sans perte afin de pouvoir obtenir une relation de dispersion en fonction de ω et K réels. Nous noterons ωsup la valeur de la fréquence pour laquelle Re(ε) = −1. Nous avons alors

ωsup=

s

ε∞ω2_L+ ω_T2

ε∞+ 1

Fig._{E.4 –Relation de dispersion pour les phonon-polaritons de volume dans un cristal dipolaire de carbure}

de silicium (ωL=18.253 1013rad.s−1, ωT=14.937 1013rad.s−1, ωsup=17.851 1013rad.s−1).

Cette fréquence limite, en dessous de laquelle des ondes de surface sont susceptibles d’exister, correspond à l’asymptote horizontale de la relation de dispersion lorsque K→ ∞ comme on peut le voir sur la figure E.4. Il est à noter que, comme pour les métaux, seule la branche en dessous de la ligne de lumière correspond à la relation de dispersion des phonon-polaritons de surface.

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