Déformation photoinduite dans les films minces contenant des ...

Chapter 3. Microscopic mechanisms at the origin of the photo-induced deformation inazobenzene-containing thin films 71As shown in Figure 3.11, we define a new coordinate frame: the axis along the x direction,represented by the versor û ‖ = ˆx and the orthogonal axis û ⊥ = √E y ŷ + E z ẑ(Ey ) 2 + (E z ) 2where E y , E z are the amplitude of the respective field projections on the y- and z-axisat an arbitrary point (x, y, z).In this sense, for each z, we decompose the total field in two components along the newû ‖ and û ⊥ axes, respectively, and as a function of x and t only:⃗E g,tot (x, t) = ⃗ E ‖ (x, t) + ⃗ E ⊥ (x, t) (3.14)⃗E ‖ (x, t) = −E 0 gsinϕcosθ g[cosωt ′ − cos(ωt ′ − 2φ x ) ] û ‖ (3.15)= 2E 0 gsinϕcosθ g sin(ωt ′ − φ x )sin(φ x )û ‖pastel-00527388, version 1 - 19 Oct 2010where:⃗E ‖ (x, t) = E 0 ‖ (ϕ)sin(ωt′ − φ x )sin(φ x )û ‖ (3.16)√⃗E ⊥ (x, t) = Eg0 cos 2 (ϕ) + sin 2 (ϕ)sin 2 (θ g ) [ cosωt ′ + cos(ωt ′ − 2φ x ) ] û ⊥ (3.17)√= 2Eg0 cos 2 (ϕ) + sin 2 (ϕ)sin 2 (θ g )cos(ωt ′ − φ x )cos(φ x )û ⊥⃗E ⊥ (x, t) = E 0 ⊥ (ϕ)cos(ωt′ − φ x )cos(φ x )û ⊥ (3.18)E‖ 0 (ϕ) = 2E0 gsinϕcosθ g (3.19)√E⊥ 0 (ϕ) = 2E0 g cos 2 (ϕ) + sin 2 (ϕ)sin 2 (θ g ) (3.20)Equations 3.16 and 3.18 describe the temporal evolution and the spatial distribution(along the x-axis) of the E ⃗ ‖ (x, t) and E ⃗ ⊥ (x, t) field components. Since the two componentsare temporally in quadrature, for each x they give rise to an elliptical polarizationdescribed by:() 2 ()E ‖E 2⊥E‖ 0 (ϕ)sin(φ +x) E⊥ 0 (ϕ)cos(φ = 1 (3.21)x)