Quantum transport in cylindrical semiconductor nanowires with constrictions

The energy dependence of the tunneling coefficient for a cylindrical semiconductor nanowire, i.e. a one-dimensional electron gas, with one or two constrictions is studied. Using the R-matrix formalism the localization probabilities at the resonant energies can be computed. They give decisive information about the physical meaning of the resonant peaks and dips that appear. The nanowire with two constrictions yields a well-defined system for the experimental evidence of the quasi-bound states of the evanescent channels. Clearly marked dips due to them should appear in the linear conductance at low temperatures

Gradient Optics of subwavelength nanofilms

Propagation and tunneling of light through subwavelength photonic barriers, formed by dielectric layers with continuous spatial variations of dielectric susceptibility across the film are considered. Effects of giant heterogeneity-induced non-local dispersion, both normal and anomalous, are examined by means of a series of exact analytical solutions of Maxwell equations for gradient media. Generalized Fresnel formulae, visualizing a profound influence of gradient and curvature of dielectric susceptibility profiles on reflectance/transmittance of periodical photonic heterostructures are presented. Depending on the cutoff frequency of the barrier, governed by technologically managed spatial profile of its refractive index, propagation or tunneling of light through these barriers are examined. Nonattenuative transfer of EM energy by evanescent waves, tunneling through dielectric gradient barriers, characterized by real values of refractive index, decreasing in the depth of medium, is shown. Scaling of the obtained results for different spectral ranges of visible, IR and THz waves is illustrated. Potential of gradient optical structures for design of miniaturized filters, polarizers and frequency-selective interfaces of subwavelength thickness is considered

Norm resolvent convergence of singularly scaled Schr\"odinger operators and \delta'-potentials

For a real-valued function V from the Faddeev-Marchenko class, we prove the norm resolvent convergence, as \epsilon goes to 0, of a family S_\epsilon of one-dimensional Schr\"odinger operators on the line of the form S_\epsilon:= -D^2 + \epsilon^{-2} V(x/\epsilon). Under certain conditions the family of potentials converges in the sense of distributions to the first derivative of the Dirac delta-function, and then the limit of S_\epsilon might be considered as a "physically motivated" interpretation of the one-dimensional Schr\"odinger operator with potential \delta'.Comment: 30 pages, 2 figure; submitted to Proceedings of the Royal Society of Edinburg

Characterization of wave transport in non-conservative media with random and correlated disorder

Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description --Abstract, page iv

Towards Faster Data Transfer by Spoof Plasmonics

With the emergence of complex architectures in modern electronics such as multi-chip modules, the increasing electromagnetic cross-talk in the circuitry causes a serious issue for high-speed, reliable data transfer among the chips. This thesis aims at developing a cross-talk resilient communication technology by utilizing a special form of electromagnetic mode, called spoof surface plasmon polariton for information transfer. The technique is based on the fact that a metal wire with periodic sub-wavelength patterns can support the propagation of confined electromagnetic mode, which can suppress cross-talk noise among the adjacent channels; and thus outperform conventional electrical interconnects in a parallel, high channel density data-bus. My developed model shows that, with 1 THz carrier frequency, the optimal design of cross-talk resilient spoof plasmon data-bus would allow each channel to support as high as 300 Gbps data, the bandwidth density can reach 1 Tbps per millimeter width of data-bus, and the digital pulse modulated carrier can travel more than 5 mm distance on the substrate. I have demonstrated that spoof plasmonic interconnects, comprised of patterned metallic conductors, can simultaneously accommodate electronic TEM mode, which is superior in cross-talk suppression at low-frequencies; and spoof plasmon mode, which is superior at high-frequencies. The research work is divided into two complementary parts: developing a theory for electromagnetic property analysis of spoof plasmon waveguide, and manipulating these properties for high-speed data transfer. Based on the theory developed, I investigated the complex interplay among various figure-of-merits of data transfer in spoof plasmonics, such as bandwidth density, propagation loss, thermal noise, speed of modulation, etc. My developed model predicts that with the availability of 1 THz carrier, the bit-error-rate of spoof plasmon data bus, subject to thermal noise would be $sim10^{-8}$ while the Shannon information capacity of the bus would be $10$ Tbps/mm. The model also predicts that, by proper designing of the modulator, it can be possible to alter the transmission property of the waveguide over one-fifth ($1/5$) of the spoof plasmon band which spans from DC frequency to the frequency of spoof plasmon resonance. To exemplify, if the spoof plasmon resonance is set at $1$ THz, then we can achieve more than $200$ Gbps speed of modulation with a very high extinction ratio, assuming the switching latency of the transistors at our disposal is negligible to the time-resolution of interest. We envision spoof plasmonic interconnects to constitute the next generation communication technology that will be transferring data at hundreds of Gigabit per second (Gbps) speed among different chips on a multi-chip module (MCM) carrier or system-on-chip (SoC) packaging.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163041/1/srjoy_1.pd