Spectral dependence of the magnetic modulation of surface plasmon polaritons in noble/ferromagnetic/noble metal films

The magnetic field is an interesting candidate for the development of active plasmonic devices as it is able to modify the surface plasmon polariton (SPP) wave vector. Both real and imaginary parts of the SPP wave vector are affected. Here, we have experimentally determined the contribution of both modulations in the spectral range ${\lambda }_0=500$–1000 nm for magnetoplasmonic systems consisting of noble/ferromagnetic/noble multilayered metal films. We have seen that the real part usually exceeds the imaginary one, but in the longer wavelength range the contribution of the imaginary part cannot be neglected. We have analyzed the spectral dependency of the modulation, and we conclude that it is dominated by the evolution of the SPP properties with wavelength and not the magneto-optical parameter. A figure of merit including modulation and propagation distance is also studied for the three ferromagnetic metals, Fe, Co, and Ni.

Figure 1

(a) Left side: Sketch of the magnetoplasmonic interferometer with definition of the system geometry and structural parameters. Right side: Image from the slit back side, showing the transmitted intensity interference pattern resulting from the interference between the light directly transmitted through the slit and the surface plasmon polariton excited at the groove and decoupled at the slit after having traveled the groove-slit distance. (b) Optical (top panel) and magnetoplasmonic (bottom panel) interferograms for an interferometer with the following particular geometry: slit-groove angle $\theta =5^{\circ }$, minimum slit-groove distance $d\left(0\right)$ = 20 $\mu$m, AuCoAu trilayer of $h$ = 25 nm. The measurements correspond to ${\lambda }_0$ = 633 nm. The right side inset shows a zoomed portion of both interferometers to depict in more detail the phase shift, $\phi$.

Figure 2

Wavelength dependence of $\Delta k_{sp}^r$ (top graph) and $\Delta k_{sp}^i$ (bottom graph) obtained for magnetoplasmonic trilayers with three different positions of the Co layer, $h$ = 15, 25, and 35 nm. The filled symbols correspond to experimental values and the dashed lines to values obtained numerically. The inset shows the calculated ratio $\Delta k_{sp}^i/\Delta k_{sp}^r$, which corresponds to $\tan \phi$.

Figure 3

(a) Wavelength dependence of the magneto-optical parameter Q for our Co layers, as obtained from ellipsometric and polar Kerr characterization. (b) Evolution of the plasmonic term from the analytical expression of $\Delta k_{sp}$ for the AuCoAu trilayers. Both the long-wavelength approximation (real part in black dash-dot line and imaginary part in dashed red line) and complete expressions (real part in black solid line and imaginary part in dotted red line) are plotted. (c) Spectral dependence of the intensity of the SPP magnetic field at the middle of the Co layer in a AuCoAu trilayer with $h$ = 15 nm. The SPP magnetic field intensity is normalized in such a way that the intensity integrated along the $z$ axis is 1 for each wavelength. (d) Evolution with wavelength of the separation of the SPP wave vector from the light line (left axis; real part in black solid line and imaginary part in red dotted line) compared with the evolution of $\Delta k_{sp}$ (right axis; real part in black dash-dot line and imaginary part in dashed red line) for a AuCoAu trilayer (in particular, the case for $h$ = 15 nm is plotted).

Figure 4

(a) Wavelength dependence of the magneto-optical parameter $Q$ for the three ferromagnetic metals Fe (dotted green line), Co (solid black line), and Ni (blue dashed line), calculated from typical optical and magneto-optical constants for the bulk materials referred to in the literature: ${\epsilon }_{xx}^{\mathrm{Fe}}$ (Ref. 37), ${\epsilon }_{yz}^{\mathrm{Fe}}$ (Ref. 38), ${\epsilon }_{xx}^{\mathrm{Co}}$ (Ref. 37), ${\epsilon }_{yz}^{\mathrm{Co}}$ (Ref. 38), ${\epsilon }_{xx}^{\mathrm{Ni}}$ (Ref. 39), and ${\epsilon }_{yz}^{\mathrm{Ni}}$ (Ref. 40). (b) Right axis: Dependence on wavelength of the real part (black dash-dot line) and the imaginary part (red dashed line) of calculated $\Delta k_{sp}$ for trilayers of Au/FerromagneticMetal/Au with $h$ = 15 nm and $t_{\mathrm{Ferro}}$ = 6 nm, where Fe (top panel), Co (middle panel), and Ni (bottom panel) are the ferromagnetic metal. Left axis: Comparison of the calculated $\Delta k_{sp}$ with the separation of the SPP wave vector from the light line (real part in black solid line and imaginary part in red dotted line). The Q parameter used in the calculations is the one shown in part (a) of the figure.

Figure 5

Spectral evolution of the figure of merit $\sqrt{{\left(\Delta k_{sp}^r\right)}^2+{\left(\Delta k_{sp}^i\right)}^2}\times L_{sp}$ for the same Au/FerromagneticMetal/Au trilayers as in Fig. 4, with the ferromagnetic metal being Fe (dotted green line), Co (solid black line), and Ni (blue dashed line).