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

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16 Chapter 2 Theory curve shown in Fig. 2.5 can be calculated with Eq. (2.35). For the dielectric functions ε (1) = εAg = −17 + i1.51 [36] and ε ′(0) = εBK7 = 1.514 2 is used. As evident from p re fle c tiv ity R 1 .0 0 .8 0 .6 0 .4 0 .2 0 .0 0 2 0 4 0 6 0 8 0 θ λ ε ε Figure 2.5: Simulation of the angular dependence of the reflectivity for a 50 nm thick silver film. At θ ≈ 43 ◦ a clear resonance of the surface plasmons can be seen. Fig. 2.5, at a light incident angle of θ = 43 ◦ a clear dip in the reflectivity can be seen. At this angle the dispersion relations of the light and of the surface plasmons at the silver-air interface match (see Fig. 2.2). The strong decrease of the reflected light intensity can be explained with Eq. (2.35) and Fig. 2.4. The light reflected into medium 0 is minimal when all light paths reflected into medium 0 interfere destructively, e.g. 2α = π = 2k (i) z d. As mentioned in Sect. 2.2.1 at angles greater than the angle of total internal reflection θc an evanescent wave propagates throughout the silver film. At the silver-air the light is then scattered back into the silver film. The back scattered light is out of phase with the incoming light and thus interferes destructively at the metal-prism interface, so that the reflectivity decreases. Until now the surface of the metal was treated as smooth, so that no light can be emitted into the air or vacuum. But real surfaces have a finite roughnesses which will have an effect on the reflectivity. Thus they will be discussed in the next chapter before continuing with the reflectivity of multilayer systems in Sect. 2.3.3.
Section 2.3 Reflectivity of surface plasmons 17 2.3.2 Surface plasmons at rough surfaces For smooth surfaces, surface plasmons, excited at the metal-air interface, cannot radiate light into air or vacuum as it is depicted in Fig. 2.2(b). There it is shown that surface plasmons at an air-metal interface have a greater wave vector than light and thus are "nonradiative" surface plasmons. This changes when the surface has afinite roughnesses. To understand why surface plasmons can radiate light into air when the surface is rough, it has to be mentioned that surface plasmons can also be excited by a grating coupler [37, 9, 22]. Then to the wave vector kx a ∆kx is added which depends on the grating constant. The sum of both can then fulfil the dispersion relation. kx + ∆kx = ω c sin θ ± ∆kx = kSPP (2.36) With a grating coupler not only surface plasmons can be excited, but also the inverse can take place, surface plasmons propagating along a grating can transform into light. Of course, rough surfaces are not periodic like a grating but rather show a statistical distribution. Nevertheless, due to surface roughness light is radiated from the metal surface into air by surface plasmons [38, 39]. In a simple picture this can be explained by scattering of surface plasmons at roughnesses. Due to the scattering the wave vector of the surface plasmons changes so that it matches the light wave vector and surface plasmons can transform into light. In a more mathematical consideration a Fourier transformation of the statistical distribution yields not only one ∆kx like for a grating coupler but a continuum of ∆kx. With this Fourier transformation a correlation function f(∆kx) is introduced which is then solved for the ∆kx by perturbation calculations [40, 9, 22]. The effects of surface roughnesses on the reflectivity R p are a broadening of the resonance dip as well as a shift of θSPP to larger angles [41]. Further effects on R p will be regarded when the measurements are dicsussed. 2.3.3 Reflectivity at a multilayer system As shown in Sect. 2.3.1 the reflectivity for a single layer can easily be derived by summing up all light paths in the layer. To calculate the reflectivity of a system consisting of n layers, Fig. 2.4 has to be extended as shown in Fig. 2.6. Now, the reflectivity at an interface i is given not only by the reflection coefficient of the ith
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 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 32 and 33: 28 2.5.1 Interaction of an external
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
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66 4.4 Summary Chapter 4 Experiment
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68 Chapter 4 Experimental study of
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70 Chapter 5 Surface plasmons in ma
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72 U A -B , -1 5 m T (θ) [V ] 0 .0
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76 Δ θ 0 2 0 1 5 1 0 5 0
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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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Surface magneto-plasmons in magnetic multilayers - Walther ...

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