Plasmonic Bloch oscillations in chirped metal-dielectric structures

We study the propagation of plasmon polaritons in one-dimensional chirped metal-dielectric layered structures. We find an optical Wannier‐Stark ladder in the mode spectrum and analyze Bloch oscillations associated with the coupling of surface plasmons localized at the metal-dielectric interfaces. For long structures, we find that the energy flow may dramatically change its direction, thus providing possibilities for the beam steering in the transmission band. © 2009 American Institute of Physics. DOI: 10.1063/1.3119666 Recent technological advances opened up many opportunities for nanofabrication allowing one to study the fundamental effects earlier predicted only theoretically. As an example, electronic Bloch oscillations predicted in 1928 Ref. 1 were observed almost 50 years later, 2 when semiconductor superlattices with nanometer-scale thick layers were manufactured. Nowadays, one of the most intriguing directions of research is associated with plasmon-polariton excitations and light manipulation at nanoscales 3,4 in various metal-dielectric structures, including multilayered periodic metal film stacks. Periodic metal-dielectric stacks have been studied in a number of papers. 5‐7 The studies of the transmission properties 6,7 revealed that such structures may exhibit resonant transmission due to plasmon tunneling through the structure. This effect by itself is quite remarkable, since every second layer in the structure is made of metal, i.e., it is opaque. It was suggested that these structures can be used as spatial filters. 7 Optical Bloch oscillations in periodic dielectric structures represent an analog of the electronic Bloch oscillations in crystals. Such oscillations were observed in different dielectric structures, 8‐11 and they were also predicted to occur in metal-dielectric structures 12,13 where it was shown that the structures with spatially modulated refractive index of dielectric layers can exhibit optical Bloch oscillations. 12 More complex heterostructures containing coupled dielectric cavities sandwiched between the metal-dielectric waveguides were also shown to exhibit Bloch oscillations, 13 somewhat similar to those observed in dielectric superlattices. 11 In this letter we study the beam propagation in structures with linearly varying chirped thickness of the dielectric layers and uniform thickness of metallic layers. We predict the possibility of plasmonic Bloch oscillations arising due to the excitation and coupling of plasmon polaritons. We show that the energy flow can change its direction within one period of oscillations, leading to the beam curling similar to that predicted for layered structures with left-handed metamaterials. 14 Such flexibility of beam control can open up opportunities of the light manipulation on nanoscales. We start our analysis by studying periodic onedimensional stack consisting of thin metal layers of the width h separated by layers of conventional dielectric of the width l, so that the period of the structure is defined as =h+l. The refractive index in one unit-cell of the structure is written as