Ultralong-range plasmonic waveguides using quasi-two-dimensional metallic layers

Abstract

We calculate the bound plasmonic modes of a "quantum metamaterial" slab, comprised of multiple quasi-two-dimensional electron gas (Q2DEG) layers, whose thickness is much smaller than the optical wavelength. For the first order transverse magnetic (TM) optical and the surface plasmonic modes we find propagation constants which are independent of both the electron density and of the scattering rates in the Q2DEG's. This leads to extremely long propagation distances. In a detailed case study of a structure comprising a slab of GaAs/AlGaAs multiple-quantum-well (MQW) material, we find propagation lengths of 100's of mm. In addition, the electric field enhancement associated with the plasmonic resonance is found to be sufficient to induce the condition of 'strong coupling' between the slab modes and the intersubband transitions in the MQW's. IntroductionSurface plasmon polaritons (SPPs) are evanescent waves which travel along the boundary between two materials whose dielectric tensors differ in sign 1 . It has long been known that two such SPPs can couple across a thin metal layer, thus producing a single coupled mode whose propagation length is much longer than an individual SPP 2 . These coupled SPPs can be put into the larger framework of bound modes in slab waveguides for dielectric and weakly absorbing thin films 3 . The coupling across the thin metallic layer hybridises the SPP modes into symmetric and or anti-symmetric admixtures, giving modes known as long and short range plasmons respectively (LRP/SRP). For the LRP the mean Poynting vector within the metallic layer is screened out by the large real part of the dielectric tensor of the metal, which leads to long propagation lengths. Even longer LRP propagation lengths can be attained if the real part of the dielectric constant of the metallic layer is exactly equal to zero 4 ; in this case the mean Poynting vector inside the metallic layer is zero and the absorption vanishes. The SRP, on the other hand, always has a large fraction of its power within the metallic layer, and is therefore always heavily damped.Semiconductor structures have a mature growth and fabrication technology. Nano-engineering in semiconductors can lead to quantum confinement and low dimensional structures such as quantum dots, quantum wires, and quantum wells. Moreover, one can accurately control the electron density, and hence the dielectric constant, by doping the semiconductor with donor atoms. The optical response of a quantum well is strongly anisotropic, and can be well described 5 as a quasi-twodimensional electron gas (Q2DEG): the electrons are free to move as a gas in the plane of the quantum well, but they are restricted to an atomic-like transition (intersubband transition, ISBT) in the perpendicular direction.When quantum wells are stacked in layers to form a multiple quantum well structure (MQW), they form a "quantum metamaterial" slab, comprised of Q2DEG material which has a finite optical thickness but has a similar dielectric tensor to the individual Q2DEGs which ...

Ultra-strong coupling effects with quantum metamaterials

“…The broad positive excursions, just to the red of the highest energy CPR modes are due absorption from a damped s-polarised mode, which does not couple to the ISBT. This assignment can be confirmed by analysing the field profiles at those energies in the TM model, and by an independent analytical treatment 7 . With this present, non-optimised sample the TM model predicts propagation distances of 2.1mm and 1.34 mm at photon energies (wavelengths) of 88meV (14μm) and 315 meV (3.94 μm) respectively.…”

“…At a given MQW doping level the plasma frequency,  p , determines the frequency at which the in-plane dielectric constant flips from negative to positive. The critical point to note though is that when the MQW slab is thin compared with the optical wavelength, mode volumes, dispersion curves and propagation distances are completely unaffected by this sign change 7 . However, because the E-field in the thin slab is only in the zdirection, we can use the quantum metamaterial approach to design out the losses, enabling the CPR mode to propagate for centimetres 7 .…”

“…The critical point to note though is that when the MQW slab is thin compared with the optical wavelength, mode volumes, dispersion curves and propagation distances are completely unaffected by this sign change 7 . However, because the E-field in the thin slab is only in the zdirection, we can use the quantum metamaterial approach to design out the losses, enabling the CPR mode to propagate for centimetres 7 . The ISBT energy is dispersionless and is governed by the nanoscopic QW thicknesses (its oscillator strength is determined by the QW doping).…”

“…With "Quantum Metamaterials", we exploit not only the wavelike nature of EM radiation but also we exploit the wavelike nature of matter; we control the electrons' behaviour at the quantum level and instead of using just Maxwell's equations to design-in the resonances, we also use Schroedinger's 7 . At a given MQW doping level the plasma frequency,  p , determines the frequency at which the in-plane dielectric constant flips from negative to positive.…”

Quantum metamaterials in the microwave and optical ranges

“…In refs. [15][16][17] it was applied to the plasmonic properties of a stack of 2D layers, each of them thin enough for the motion of electrons in the normal direction to be completely quantized.…”