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Physical Review A

Third-harmonic generation in resonant-metamaterial-based photonic-band-gap materials

Jolly Jose

Published Oct 31, 2013• 1 citation
Publisher

Abstract

We present large enhancement of the nonlinear wave mixing process (third-harmonic generation) in photonic-band-gap materials made of negative and positive index media, at the band edge of the zero-$\overline{n}$ band gap. Incorporating metamaterial-based, electromagnetically induced transparency (EIT)--like resonance in the nonlinear layer leads to unprecedented line narrowing of the generated third harmonic. This scheme permits the mapping of the narrow EIT resonance at the fundamental frequency to the generated third-harmonic frequency with even narrower line shape.

DOI
10.1103/physreva.88.043849

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We present large enhancement of the nonlinear wave mixing process (third-harmonic generation) in photonic-band-gap materials made of negative and positive index media, at the band edge of the zero-n‾\overline{n}n band gap. Incorporating metamaterial-based, electromagnetically induced transparency (EIT)--like resonance in the nonlinear layer leads to unprecedented line narrowing of the generated third harmonic. This scheme permits the mapping of the narrow EIT resonance at the fundamental frequency to the generated third-harmonic frequency with even narrower line shape.
The dressed four-wave mixing (FWM) in a four-level 85 Rb atomic system, experimentally demonstrated in this paper, is comprised by two coexisting processes. One is emission signal due to enhanced nonlinear via electromagnetically induced transparency (EIT). The other is the Bragg reflection of probe beam because of the created photonic band gap (PBG), which is affected by both linear and third-order nonlinear susceptibility. Moreover, we have demonstrated that different experimental parameters can significantly influence the measured signal with flexibly controlled PBG. These studies are found useful for understanding the fundamental mechanisms in generated FWM processing.
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.
In this review, we describe recent developments in functional metamaterials based on coupled resonators. We first consider coupled resonator metamaterials that mimic electromagnetically induced transparency (EIT). We present a circuit model for EIT-like metamaterials and introduce a new coupled resonator in which the coupling is provided by a field gradient so that the group velocity can be varied by varying the incident angle. We then describe the principles for enhancing second harmonic generation (SHG) in nonlinear resonant metamaterials. Optical and microwave experiments of SHG in singly resonant metamaterials are presented. A method for further enhancing SHG using a doubly resonant metamaterial is also described.
Optical materials exhibit significant losses over the resonance frequency of their constituent atoms and so they are practically implemented at frequencies far from resonances. Electromagnetically induced transparency (EIT) provides a method for effective suppression of optical loss in a narrow window over the resonance, where the medium exhibits significant dispersion but at the expense of zero susceptibility. The classical or plasmonic analogs of the EIT effect are introduced and widely used in the context of electromagnetic or optical metamaterials (MMs). In another interesting phenomenon in quantum optics known as enhancement of index of refraction (EIR), the optical loss of the medium can be zero or even negative at the region of maximal susceptibility and negligible dispersion. This condition is interesting for applications where a strong electromagnetic response of the medium with negligible loss is required, such as zero- or negative-index metamaterials (MMs). Here we introduce a plasmonic analog of the EIR which allows for coherent control over the polarizability and absorption of plasmonic nanoantennas. It can open up the way for loss-compensated propagation of optical waves in zero-index to high-refractive-index plasmonic MMs. The scheme also offers an approach to all-optical switching and coherent control of transmission, diffraction, and polarization conversion properties of plasmonic nanostructures, as well as propagation properties of surface plasmon polaritons on metasurfaces.