Ultrahigh Purcell factors and Lamb shifts using slow-light metamaterial
  waveguides

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Abstract

Employing a medium-dependent quantum optics formalism and a Green function solution of Maxwell's equations, we study the enhanced spontaneous emission factors (Purcell factors) and Lamb shifts from a quantum dot or atom near the surface of a %embedded in a slow-light metamaterial waveguide. Purcell factors of approximately 250 and 100 are found at optical frequencies for \(p-\)polarized and \(s-\)polarized dipoles respectively placed 28\thinspace nm (0.02\thinspace \(\lambda_{0}\)) above the slab surface, including a realistic metamaterial loss factor of \(\gamma /2\pi =2 \mathrm{THz}\). For smaller loss values, we demonstrate that the slow-light regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately -1 GHz to -6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far field emission spectrum, which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.

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Three-dimensional optical metamaterial with a negative refractive index.

Jason Valentine, Shuang Zhang, Thomas Zentgraf … (2008)

Metamaterials are artificially engineered structures that have properties, such as a negative refractive index, not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies, but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals. Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide. Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction. Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded 'fishnet' structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices, compact resonators and highly directional sources.