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Surface magneto-plasmons in magnetic multilayers - Walther ...

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Chapter 2<br />

Theory<br />

In this chapter a short overview of the theoretical basics of surface <strong>plasmons</strong> is given,<br />

where the focus is on the aspects necessary to understand and <strong>in</strong>terpret the experi-<br />

mental results. At first, the nature of surface <strong>plasmons</strong> is discussed, lead<strong>in</strong>g to the<br />

dispersion relation for surface <strong>plasmons</strong>. Next, the reflectivity of s<strong>in</strong>gle and multi<br />

layer systems is derived and simulations are presented and discussed. F<strong>in</strong>ally, the<br />

<strong>in</strong>teractions of surface <strong>plasmons</strong> with an external <strong>magnetic</strong> field is considered.<br />

2.1 <strong>Surface</strong> Plasmon Polaritons<br />

Collective longitud<strong>in</strong>al oscillations of quasi-free electrons <strong>in</strong> a metal or semiconductor<br />

are called <strong>plasmons</strong>. When these oscillations propagate along the <strong>in</strong>terface of a metal<br />

and a dielectric medium (or vacuum), they are called surface <strong>plasmons</strong>. For surface<br />

<strong>plasmons</strong> the component of the electro<strong>magnetic</strong> wave perpendicular to the <strong>in</strong>terface<br />

decays exponentially, what can be described by an evanescent wave. Thus, the sur-<br />

face <strong>plasmons</strong> are localised near the <strong>in</strong>terface, giv<strong>in</strong>g rise to an enhancement of the<br />

electro<strong>magnetic</strong> field [9, 22]. The enhancement can be expla<strong>in</strong>ed and calculated by<br />

regard<strong>in</strong>g energy conservation [23].<br />

2.2 Dispersion relation<br />

Plasmons <strong>in</strong> general can be described by a plane wave.<br />

A(r, t) = A0e i(kr − ωt) . (2.1)<br />

Here, k = (kx, ky, kz) is the wave vector, r = (rx, ry, rz) the position vector, ω the<br />

5

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