Effective medium approximation for hybrid plasmonic multilayers

Hybrid metallic multilayer structures consisting of functionally different materials represent the building blocks for linear and nonlinear plasmonic devices, which are often coupled to acoustic [1,2] and magnetic [3-6] ... [ view full abstract ]

Hybrid metallic multilayer structures consisting of functionally different materials represent the building blocks for linear and nonlinear plasmonic devices, which are often coupled to acoustic [1,2] and magnetic [3-6] phenomena. Despite of the nano-scale plasmonic confinement, optical fields inside metallic nanostructures overlap with several materials characterized by different optical properties, including anisotropy. Straightforward transfer-matrix calculations are often bulky, particularly for optically anisotropic materials [5], and a simple effective medium approximation (EMA) would be helpful. The complexity of the rigorous microscopic treatment becomes even more crucial in the nonlinear optics, where, for example, the generation of optical second harmonic at each surface/interface is characterized by multiple components of chi(2)-tensor [6].

In case of multiple interfaces intrinsic to the hybrid multilayer structures an effective interface approximation (EIA) would be highly desirable as well.

Here we present an EMA for the magneto-plasmonic metal-ferromagnet multilayers [4]. Whereas EMA for the diagonal components of the (linear) dielectric succeptibility tensor can be used to predict the propagation length of surface plasmon polaritons (SPPs), the EMA for its non-diagonal components accurately describes the magnetic modulation of SPP wave vector [1,2]. The EMA displays a good agreement with transfer-matrix calculations. In the nonlinear magneto-plasmonics the phenomenological nonlinear EIA is applied to quantitatively model the angular dependence of second harmonic generation in Kretschmann configuration.

In addition to static multilayer structures we can also generate “transient multilayer structures”. Here, the nano-scaled (a few picoseconds long) acoustic pulse creates a layer with a modified electron density propagating at the speed of sound through the layer of a noble metal. The linear EMA can be applied to characterize ultrashort acoustic pulses from the dynamic modulation of SPP wave vector, which is measured by femtosecond time-resolved plasmonic interferometry [2].

References:
[1] V.V. Temnov, Nature Phot. 6, 728 (2012)
[2] V.V. Temnov et al., Nature Comm. 4, 1468 (2013)
[3] I. Razdolski et al., ACS Photonics 3, 179 (2016)
[4] V.V. Temnov et al., J. Opt. 18, 093002 (2016)
[5] J. F. Torrado et al., New J. Phys. 15, 075025 (2013)
[6] V.V. Pavlov et al., Appl. Phys. Lett. 75, 190 (1999)