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

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20 Chapter 2 Theory Hereby, i = 1, 2, 3 and θi is the angle of incidence with respect to the normal for each layer i. 2 The matrix ˆ Dij is the so-called transmission matrix. It links the amplitudes of the waves to the right and to the left of the interface and thus describes the transmission of the light wave through the interface: ˆDij = 1 tij 1 rij rij 1 , (2.41) where rij and tij are the reflection and transmission curves for p- or s-polarised waves Eq. (2.26) or Eq. (2.27), respectively. The amplitudes inside one medium A (′) i and B(′) i are linked by the so-called propagation matrix ˆ Pi: A ′ i B ′ i = ˆ Pi Ai Bi ≡ e iαi 0 0 e −iαi Ai Bi , (2.42) with the damping term αi = k (i) z di in medium i of thickness di. The propagation matrix describes the damped propagation of the light wave through medium i. With the transmission matrix ˆ Dij (Eq. (2.41)) and the propagation matrix ˆ Pi (Eq. (2.42)) the incident light waves A1, B1 and the transmitted light waves A ′ 3,B ′ 3 in Fig. 2.7 can be connected: A1 B1 = ˆ D12 ˆ P2 ˆ D23 A ′ 3 B ′ 3 (2.43) In the matrix formalism, a light wave propagation through a thin film thus is described by the multiplication of transmission and propagation matrices. This can easily be extended to multilayer systems. Each interface ij is described by a transmissions matrix ˆ Dij and every layer i by a propagation matrix ˆ Pi. For a multilayer system as studied in Fig. 2.8, the incident and transmitted wave amplitudes are linked by where A0 B0 = ˆ D01 N i=1,j=i+1 ˆPi ˆ Dij A ′ N B ′ N , (2.44) 2 The dynamical matrix for s-waves is not needed to describe the reflectivity of surface plasmons but it shown for the sake of completeness
Section 2.3 Reflectivity of surface plasmons 21 0 1 2 . . . N-1 N N+1 n 0 A 0 B 0 A ’ 1 B ’ 1 n 1 d 1 A 1 B 1 A ’ 2 B ’ 2 n 2 d 2 . . . . . . . . . . . . n N-1 d N-1 A N-1 B N-1 A ’ N B ’ N n N d N A N B N n N+1 A ’ N+1 B ’ N+1 Figure 2.8: Here a sketch of a multilayer system with n layers is shown. 0 and N +1 are not regarded as layers since they are assumed to be semi-infinite half spaces which cover the multilayer system. Ai represents the amplitude of a right-travelling wave and Bi the amplitude of a left-travelling wave, both on the left side of the interface. A ′ i and B′ i are the amplitudes of right- and left-travelling waves on the right side of the interface. And ni is the complex refractive index of the medium i. ˆM = M11 M12 M21 M22 = ˆ D01 N i=1,j=i+1 ˆPi ˆ Dij x z (2.45) is the so-called transfer matrix ˆ M. The reflection coefficient of a multilayer system can then be written as the ratio of the reflected wave amplitude (B0) and the incident amplitude (A0): r = B0 With Eq. (2.44) and Eq. (2.45) this yields the reflectivity of a multilayer system. A0 R = |r| 2 = M21 M11 B ′ =0 2 (2.46) (2.47)
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 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
Page 70 and 71: 66 4.4 Summary Chapter 4 Experiment
Page 74 and 75:
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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