Engineering photonic density of states using metamaterials

The photonic density of states (PDOS), like its electronic counterpart, is one of the key physical quantities governing a variety of phenomena and hence PDOS manipulation is the route to new photonic devices. The PDOS is conventionally altered by exploiting the resonance within a device such as a microcavity or a bandgap structure like a photonic crystal. Here we show that nanostructured metamaterials with hyperbolic dispersion can dramatically enhance the photonic density of states paving the way for metamaterial-based PDOS engineering. It was recently predicted that an appropriately designed metamaterial can be used to enhance the PDOS [1] through a nanopatterning route which presents a paradigm shift to PDOS alteration and can give rise to broadband, ultralow mode volume photonic devices, as opposed to conventional Z. Jacob and J.-Y. Kim contributed equally to this work. Electronic supplementary material The online version of this article (http://dx.doi.org/10.1007/s00340-010-4096-5) contains supplementary material, which is available to authorized users. Z. Jacob · J.-Y. Kim · G.V. Naik · A. Boltasseva · E.E. Narimanov · V.M. Shalaev ( ) Birck Nanotechnology Center, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA e-mail: [email protected] A. Boltasseva DTU-Fotonik Technical University of Denmark, DTU Building 343, 2800 Kongens Lyngby, Denmark A. Boltasseva Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universitaät Erlangen-Nuürnberg, 91052 Erlangen, Germany resonant [2–4], diffraction-limited approaches [5, 6]. A simple probe for the local density of states is the spontaneous emission of light in the vicinity of such a metamaterial [7]. In this work, we demonstrate that dye molecules in the near field of a hyperbolic metamaterial spontaneously excite unique electromagnetic states in the metamaterial medium responsible for the enhanced PDOS leading to a decrease in the lifetime of emitters. The photonic density of states is obtained via a mode counting procedure in k-space from the dispersion relation ω(k) and can be simply related to the volume of the shell enclosed between two spheres at ω(k) and ω(k)+ dω (Fig. 1(a)). Here we show that nanostructuring a medium can radically alter the dispersion relation and hence allows the manipulation of the PDOS. Nanostructured metamaterials can have an extreme anisotropic electromagnetic response with x = y < 0 and z > 0 so that the extraordinary waves in this medium obey a hyperbolic dispersion relation [8–12]. While high wavevector modes simply decay away in vacuum, a hyperbolic metamaterial (HMM) allows for bulk propagating waves with unbounded wavevectors (Fig. 1). These spatial modes with large wavevectors have been studied with regards to subwavelength imaging [13–15] and subdiffraction mode confinement [16]. The high wavevector spatial modes not present in vacuum are characteristic of hyperbolic metamaterials (HMMs) and contribute to the photonic density of states causing a divergence in the low loss effective medium limit [17]. The remarkable property which sets it apart from other photonic systems with an enhanced DOS is the bandwidth. Hyperbolic dispersion can be achieved in a large bandwidth [11, 12] which directly implies that the PDOS would in fact, diverge in this entire band of frequencies leading to a host of new physical effects.