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M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959).

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H. Fröhlich, Theory of Dielectrics (Oxford University Press, New York, 1949), pp. 149–155.

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This is true for suitable linear combinations of the functions (2).

K. L. Kliewer and R. Fuchs, Phys. Rev. 150, 573 (1966).

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954), Ch. II, Sec. 10; Ch. VII, Sec. 47.

We are using gaussian units, whereas Stratton uses mks units. Equation (4) is written for a nonmagnetic material (µ=1). The time dependence e^{-iωt} is understood.

"Electric" and "magnetic" modes are often also called "TM" and "TE" modes, respectively.

In LiF the longitudinal optical frequency, 27defined as the frequency for which ε=1, is Ω_{L}=ωL/ωT = 2.197 in dimensionless units, while the transverse optical frequency is Ω_{T}=1.

The sphere must in practice remain larger than the lattice parameter.

K. L. Kliewer and R. Fuchs, Phys. Rev. 144, 495 (1966). The surface modes for a slab, shown in Fig. 2 of this reference, approach the frequency determined by ε= - 1 as *k*_{x} →∞, *k*_{x} being the component of the wave vector parallel to the slab. In this limit the fields become localized at the surfaces. The condition ε= - 1 also determines the frequency of the surface modes in a semi-infinite medium. Therefore, if the fields fall off fast enough inside the medium, the frequency of the surface modes does not depend on whether the solid is in the form of a sphere, a slab, or a semi-infinite medium.

Our expression for the cross sections can be obtained from those given in Sec. 9.26 of Ref. 4 by dividing by π*a*^{2} and making the replacements *a*_{n}^{r} → -1/A_{l} and *b*_{n}^{r} → -1/B_{l}. Equations (26), (29), and (31) in Sec. 9.26 have the wrong sign, since they give a negative extinction cross section *Q*_{T}.

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J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley & Sons, Inc., New York, 1952), Sec. VIII.

There is one exception to the statement that the surface modes do not give rise to visible structure at low frequencies: the unmarked plateau in the extinction cross section *Q*_{T} between the 1*LM*_{1} and 2*LM*_{1} peaks can be attributed to the 1*S* surface mode.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

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