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

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28 2.5.1 Interaction of an external magnetic field with light in condensed matter Chapter 2 Theory Until now the dielectric function ε(ω) was treated as a scalar. This is only true for isotropic media with no applied magnetic field, as then the dielectric tensor ˆε is symmetric. The off-diagonal elements are zero and the diagonal elements are identical [48, 49]. In a magnetised material (M = 0), ˆε becomes asymmetric with none- vanishing off-diagonal elements. For a material with cubic symmetry ˆε is given to first order in mi by [50] ⎛ 1 ⎜ ˆε = ε ⎝ iQmz −iQmz 1 ⎞ iQmy ⎟ −iQmx⎠ , (2.50) −iQmy iQmx 1 with the projections mi = Mi/ |M|, of the components of the magnetisation M along the x−, y−, and z−directions. ε is the dielectric constant for vanishing magnetisation, and Q is the so-called Voigt constant [18] or gyroelectric constant [51]. . The latter is given by [52, 53] Q = i εxy , (2.51) and is a material constant which describes the magneto-optical rotation of the light polarisation and is proportional to the induced magnetisation of the medium [54]. Using the dielectric tensor, Eq. (2.50), the optical behaviour of a magnetic material can be described. This is exploited in magneto-optical experiments, i.e. Kerr- or Faraday measurements [55, 56]. As only the so-called transversal geometry is of interest in experiments related to surface plasmons, here it is only stated that there εxx are also a polar and longitudinal geometry, see Fig. 2.14. In the transversal geometry (Fig. 2.14(c)) the Fresnel coefficients become [58, 59, 57] r ss t = n1 cos θ1 − n2 cos θ2 n1 cos θ1 + n2 cos θ2 (2.52) r pp t = n2 cos θ1 − n1 cos θ2 n2 cos θ1 + n1 cos θ2 + i 2n1n2Q cos θ1 sin θ2 (n2 cos θ1 + n1 cos θ2) 2 (2.53) r sp t = r ps t = 0. (2.54)
Section 2.5 Magnetic field dependence of surface plasmons 29 (a) (b) (c) M polar longitudinal transversal M Figure 2.14: Illustration of the Kerr effect geometries with respect to the plane of incidence. (a) In the polar Kerr effect the magnetization is oriented perpendicular to the sample surface. (b) The magnetization is parallel to the the sample surface and parallel to the plane of incidence in the longitudinal Kerr effect. (c) In the transversal geometry the magnetization is within the film plane, but perpendicular to the plane of incidence[57]. These equations show that in the transversal geometry there is no polarisation rotation like in the polar and longitudinal configuration [59, 57]. The magnetisation (Q) only influences the amplitudes of the light waves. Furthermore, magnetisation or magnetic field effects will only be seen in the p-polarised component, because it is the only component that depends on Q. In this component the magnetic field of the light wave is parallel (antiparallel) to M. 2.5.2 Change of the dispersion relation of surface plasmons Like the Kerr and Faraday effect show, electromagnetic waves interact with the magnetisation in a magnetic material. Since surface plasmons are also electromagnetic waves there should also be an interaction with the magnetisation or an applied magnetic field. The interaction of surface plasmons with an external magnetic field was first reported by Chiu and Quinn [17] and will here be shortly reviewed. When a magnetic field is applied kx is no longer symmetrical, regarding positive and negative propagation directions. Thus, the lower branch of the dispersion relation shown in Fig. 2.2(b) splits up into two branches, each for every propagation direction (Fig. 2.15). To calculate the splitting of the dispersion relation ωB(kx) under an applied magnetic field parallel to the sample surface, the Maxwell equations with the dielectric tensor have to be solved. Since Chiu and Quinn use a different notation for their dielectric tensor, its components for the transversal geometry will be shown. M
Page 1: TECHNISCHE UNIVERSITÄT MÜNCHEN WA
Page 4 and 5: II Contents 4.2 Reflectivity of mul
Page 6 and 7: 2 Chapter 1 Introduction via a grat
Page 8 and 9: 4 Chapter 1 Introduction
Page 10 and 11: 6 angular frequency, t the time, an
Page 12 and 13: 8 Chapter 2 Theory Here, µ (1) =
Page 14 and 15: 10 electron density. Chapter 2 Theo
Page 16 and 17: 12 Chapter 2 Theory [8]. In this co
Page 18 and 19: 14 2.3.1 Reflectivity of a single l
Page 20 and 21: 16 Chapter 2 Theory curve shown in
Page 22 and 23: 18 t 10 t 10 t 10 r 01 E 0 r 10 e i
Page 24 and 25: 20 Chapter 2 Theory Hereby, i = 1,
Page 26 and 27: 22 2.4 Simulation of the reflectivi
Page 28 and 29: 24 dopt = |ε ′(1) | − 1 4π |
Page 30 and 31: 26 p R 1 .0 0 .8 0 .6 0 .4 0 .2 0 .
Page 34 and 35: 30 ω |k x | Chapter 2 Theory Figur
Page 36 and 37: 32 Chapter 2 Theory enhancement wil
Page 38 and 39: 34 LASER lter beam splitter polaris
Page 40 and 41: 36 (a) εsubstrate εCo ε prism ε
Page 42 and 43: 38 Chapter 3 Excitation of surface
Page 46 and 47: 42 p h o to -d e te c to r s ig n a
Page 48 and 49: 44 9 0 8 5 8 0 7 5 7 0 6 5 6
Page 50 and 51: 46 5 V 0 V U out Chapter 3 Excitati
Page 54 and 55: 50 U A-B (θ) [V] 0.00 -0.05 -0.10
Page 56 and 57: 52 U A -B (θ) [V ] U A (θ) [V ] U
Page 58 and 59: 54 will be discussed. 4.1.1.2 Deter
Page 60 and 61: 56 p R 1 .0 0 .8 0 .6 0 .4 0 .2 0 .
Page 62 and 63: 58 p R 0 .8 0 .4 0 .0 0 .8 0 .4
Page 64 and 65: 60 Chapter 4 Experimental study of
Page 70 and 71: 66 4.4 Summary Chapter 4 Experiment
Page 74 and 75: 70 Chapter 5 Surface plasmons in ma
Page 76 and 77: 72 U A -B , -1 5 m T (θ) [V ] 0 .0
Page 78 and 79: 74 Chapter 5 Surface plasmons in ma
Page 80 and 81: 76 Δ θ 0 2 0 1 5 1 0 5 0
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78 Chapter 5 Surface plasmons in ma
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80 ΔU θ = c o n s t (θ) [m V ]
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84 p x 1 0 -4 p /δθ 1 /R δR 0 .5
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86 δU /U (H ) x 1 0 -3 2 .5 2 .0 1
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90 s M /M 1 .5 1 .0 0 .5 0 .0 -0 .5
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94 Chapter 6 Conclusions and Outloo
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100 Chapter 6 Conclusions and Outlo
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102 (*Thickness of the layers in An
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104 /Extract[Ms[lambda, theta], {1,
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106 40 mm 10 mm 130 mm Figure B.2:
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108 and d sin 45 = h/2 sin(90 + θ)
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110 Appendix C Prism correction
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112 Appendix D Code for SPP simulat
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114 (*MO Reflectivity*) Appendix D
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116 Bibliography [12] J. Weeber, E.
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118 Bibliography [40] A. A. Maradud
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120 Bibliography [67] F. E. Luborsk
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122 Bibliography [93] T. Sidiropoul
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Robert Müller, Helmut Thies and hi
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