Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model

A numerical analysis of surface plasmon dispersion, propagation, and localization on smooth lossy films is presented. Particular attention is given to determining wavelength-dependent behavior of thin Ag slab waveguides embedded in a symmetric SiO2 environment. Rather than considering Ag as a damped free electron gas, the metal is defined by the experimentally determined optical constants of Johnson and Christy and Palik. As in free electron gas models, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric field distributions—as film thickness is decreased below 50 nm. However, unlike free electron gas models, the surface plasmon wave vector remains finite at resonance with the antisymmetric-field plasmon converging to a pure photon mode for very thin films. In addition, allowed excitation modes are found to exist between the bound and radiative branches of the dispersion curve. The propagation characteristics of all modes are determined, and for thin films (depending upon electric field symmetry), propagation distances range from microns to centimeters in the near infrared. Propagation distances are correlated with both the field decay (skin depth) and energy density distribution in the metal and surrounding dielectric. While the energy density of most long-range surface plasmons exhibits a broad spatial extent with limited confinement in the waveguide, it is found that high-field confinement does not necessarily limit propagation. In fact, enhanced propagation is observed for silver films at ultraviolet wavelengths despite strong field localization in the metal. The surface plasmon characteristics described in this paper provide a numerical springboard for engineering nanoscale metal plasmon waveguides, and the results may provide a new avenue for integrated optoelectronic applications

Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles

Linear arrays of very small Ag nanoparticles (diameter ~10 nm, spacing 0–4 nm) were fabricated in sodalime glass using an ion irradiation technique. Optical extinction spectroscopy of the arrays reveals a large polarization-dependent splitting of the collective plasmon extinction band. Depending on the preparation condition, a redshift of the longitudinal resonance as large as 1.5 eV is observed. Simulations of the three-dimensional electromagnetic field evolution are used to determine the resonance energy of idealized nanoparticle arrays with different interparticle spacings and array lengths. Using these data, the experimentally observed redshift is attributed to collective plasmon coupling in touching particles and/or in long arrays of strongly coupled particles. The simulations also indicate that for closely coupled nanoparticles (1–2 nm spacing) the electromagnetic field is concentrated in nanoscale regions (10 dB radius: 3 nm) between the particles, with a 5000-fold local field intensity enhancement. In arrays of 1-nm-spaced particles the dipolar particle interaction extends to over 10 particles, while for larger spacing the interaction length decreases. Spatial images of the local field distribution in 12-particle arrays of touching particles reveal a particlelike coupled mode with a resonance at 1.8 eV and a wirelike mode at 0.4 eV

Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization

We present a numerical analysis of surface plasmon waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength. Attention is given to characterizing the dispersion relations, wavelength-dependent propagation, and energy density decay in two-dimensional Ag/SiO2/Ag structures with waveguide thicknesses ranging from 12 nm to 250 nm. As in conventional planar insulator-metal-insulator (IMI) surface plasmon waveguides, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric electric field distributions—as SiO2 core thickness is decreased below 100 nm. However, unlike IMI structures, surface plasmon momentum of the symmetric mode does not always exceed photon momentum, with thicker films (d~50 nm) achieving effective indices as low as n=0.15. In addition, antisymmetric mode dispersion exhibits a cutoff for films thinner than d=20 nm, terminating at least 0.25 eV below resonance. From visible to near infrared wavelengths, plasmon propagation exceeds tens of microns with fields confined to within 20 nm of the structure. As the SiO2 core thickness is increased, propagation distances also increase with localization remaining constant. Conventional waveguiding modes of the structure are not observed until the core thickness approaches 100 nm. At such thicknesses, both transverse magnetic and transverse electric modes can be observed. Interestingly, for nonpropagating modes (i.e., modes where propagation does not exceed the micron scale), considerable field enhancement in the waveguide core is observed, rivaling the intensities reported in resonantly excited metallic nanoparticle waveguides

Mega-electron-volt ion beam induced anisotropic plasmon resonance of silver nanocrystals in glass

30 MeV Si ion beam irradiation of silica glass containing Ag nanocrystals causes alignment of Ag nanocrystals in arrays along the ion tracks. Optical transmission measurements show a large splitting of the surface plasmon resonance bands for polarizations longitudinal and transversal to the arrays. The splitting is in qualitative agreement with a model for near-field electromagnetic plasmon coupling within the arrays. Resonance shifts as large as 1.5 eV are observed, well into the near-infrared.

Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule

We discuss how the bath's memory affects the dynamics of a swap gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi Golden Rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: I) collapsed resonances that split at an exceptional point in II) two resolved resonances ; III) out-of-band resonances; IV) virtual states; and V) pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion and localized dynamics respectively. The frequency of the swap gate depends differently on the unperturbed Rabi frequency. In region I) there is no oscillation at all, while in the regions III) and IV) the oscillation frequency is particularly stable because it is determined by environment's band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.Comment: 11 pages 8 figure

Nanoscale waveguiding methods

While 32 nm lithography technology is on the horizon for integrated circuit (IC) fabrication, matching the pace for miniaturization with optics has been hampered by the diffraction limit. However, development of nanoscale components and guiding methods is burgeoning through advances in fabrication techniques and materials processing. As waveguiding presents the fundamental issue and cornerstone for ultra-high density photonic ICs, we examine the current state of methods in the field. Namely, plasmonic, metal slot and negative dielectric based waveguides as well as a few sub-micrometer techniques such as nanoribbons, high-index contrast and photonic crystals waveguides are investigated in terms of construction, transmission, and limitations. Furthermore, we discuss in detail quantum dot (QD) arrays as a gain-enabled and flexible means to transmit energy through straight paths and sharp bends. Modeling, fabrication and test results are provided and show that the QD waveguide may be effective as an alternate means to transfer light on sub-diffraction dimensions