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

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18 t 10 t 10 t 10 r 01 E 0 r 10 e iα 1 t 01 e iα 1 1 2 d 1 r 12 e iα 1 t 12 e iα 2 d 2 r 23 e iα 2 t n-1n e iα n n r nn+1 e iα n d n Chapter 2 Theory Figure 2.6: The sketch shows the light propagation through a system with n layers. E is again the amplitude of the electric field of the incident light wave. rij and tij are the reflection and transmission coefficients, respectively (Eq. (2.26)), and e iαi describes the damping and phase shift of light when propagating through media i. The transmission into media n + 1 is neglected since only the reflectivity is investigated. interface, but the transmission of the backscattered light at the interfaces j > i also contributes. To calculate the reflectivity for a multilayer system this becomes tedious. A very elegant, alternative method to derive the reflectivity of a multilayer system is the 2 × 2 matrix method which was introduced in 1980 by Pochi Yeh [42, 43], an extension of the 2 × 2 matrix method introduced by Abéles [44]. The 2 × 2 matrix method is quite similar to the method of calculating the tunneling of a wave through a barrier in quantum mechanics. Instead of considering the light path through the layers, the matrix method is based on the light waves which are reflected and transmitted at the interface. Fig. 2.7 illustrates the matrix method concept. The electric field of the light wave is written as E = E(z)e i(ωt−kxx) . (2.37) This equation is the same as Eq. (2.3) only that the z-component and the amplitude are combined as E(z). Now, E(z) can be split into a right-travelling and a left- travelling wave
Section 2.3 Reflectivity of surface plasmons 19 E(z) = Re −ik(i) z z ik + Le (i) z z ≡ A(z) + B(z). (2.38) R and L are constants in each layer. A(z) represents the amplitude of the right- travelling and B(z) the amplitude of the left-travelling wave. Further, as shown in 0 1 2 n 0 A 0 B 0 A ’ 1 B ’ 1 n 1 d A 1 B 1 Figure 2.7: Illustration of the matrix method after Yeh [43]. Ai represents the amplitude of a right-travelling wave and Bi of a left-travelling wave on the left side of the interface ij. And A ′ j and B′ j are the amplitudes of a right- and a left-travelling wave on the right side of the interface ij. ni is the complex refractive index of the medium i. Fig. 2.7, it is not only differentiated between right- and left-travelling waves but also between waves on the right (with prime) and left (without prim) side of a given interface. Regarding A (′) i by a matrix. Ai Bi and B(′) i = ˆ D −1 i ˆ Dj n 2 A ’ 2 B ’ 2 x as column vectors, the amplitudes are connected A ′ j B ′ j ≡ ˆ Dij where the ˆ Di are the so-called dynamical matrices given by Di = ⎧⎛ ⎝ ⎪⎨ ⎛ 1 1 √ ε (i) cos θi − √ ε (i) cos θi √ ε (i) − √ ε (i) ⎞ ⎞ z A ′ jB ′ j , (2.39) ⎠ for s-polarised light ⎝ ⎪⎩ cos θi cos θi ⎠ for p-polarised light . (2.40)
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 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
Page 70 and 71: 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
Page 106 and 107:
102 (*Thickness of the layers in An
Page 108 and 109:
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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