Self-optimization of optical confinement in ultraviolet photonic crystal slab laser

We studied numerically and experimentally the effects of structural disorder on the performance of ultraviolet photonic crystal slab lasers. Optical gain selectively amplifies the high-quality modes of the passive system. For these modes, the in-plane and out-of-plane leakage rates may be automatically balanced in the presence of disorder. The spontaneous optimization of in-plane and out-of-plane confinement of light in a photonic crystal slab may lead to a reduction of the lasing threshold.Comment: 5 pages, 5 figure

Immittance Matching for Multi-dimensional Open-system Photonic Crystals

An electromagnetic (EM) Bloch wave propagating in a photonic crystal (PC) is characterized by the immittance (impedance and admittance) of the wave. The immittance is used to investigate transmission and reflection at a surface or an interface of the PC. In particular, the general properties of immittance are useful for clarifying the wave propagation characteristics. We give a general proof that the immittance of EM Bloch waves on a plane in infinite one- and two-dimensional (2D) PCs is real when the plane is a reflection plane of the PC and the Bloch wavevector is perpendicular to the plane. We also show that the pure-real feature of immittance on a reflection plane for an infinite three-dimensional PC is good approximation based on the numerical calculations. The analytical proof indicates that the method used for immittance matching is extremely simplified since only the real part of the immittance function is needed for analysis without numerical verification. As an application of the proof, we describe a method based on immittance matching for qualitatively evaluating the reflection at the surface of a semi-infinite 2D PC, at the interface between a semi-infinite slab waveguide (WG) and a semi-infinite 2D PC line-defect WG, and at the interface between a semi-infinite channel WG and a semi-infinite 2D PC slab line-defect WG.Comment: 8 pages, 6 figure

Magnetic and charge structures in itinerant-electron magnets: Coexistence of multiple SDW and CDW

A theory of Kondo lattices is applied to studying possible magnetic and charge structures of itinerant-electron antiferromagnets. Even helical spin structures can be stabilized when the nesting of the Fermi surface is not sharp and the superexchange interaction, which arises from the virtual exchange of pair excitations across the Mott-Hubbard gap, is mainly responsible for magnetic instability. Sinusoidal spin structures or spin density waves (SDW) are only stabilized when the nesting of the Fermi surface is sharp enough and a novel exchange interaction arising from that of pair excitations of quasi-particles is mainly responsible for magnetic instability. In particular, multiple SDW are stabilized when their incommensurate ordering wave-numbers $\pm{\bf Q}$ are multiple; magnetizations of different $\pm{\bf Q}$ components are orthogonal to each other in double and triple SDW when magnetic anisotropy is weak enough. Unless $\pm 2{\bf Q}$ are commensurate, charge density waves (CDW) with $\pm 2{\bf Q}$ coexist with SDW with $\pm{\bf Q}$. Because the quenching of magnetic moments by the Kondo effect depends on local numbers of electrons, the phase of CDW or electron densities is such that magnetic moments are large where the quenching is weak. It is proposed that the so called stipe order in cuprate-oxide high-temperature superconductors must be the coexisting state of double incommensurate SDW and CDW.Comment: 10 pages, no figure

Theory of itinerant-electron ferromagnetism

A theory of Kondo lattices or a $1/d$ expansion theory, with $d$ spatial dimensionality, is applied to studying itinerant-electron ferromagnetism. Two relevant multi-band models are examined: a band-edge model where the chemical potential is at one of band-edges, the top or bottom of bands, and a flat-band model where one of bands is almost flat or dispersionless and the chemical potential is at the flat band. In both the models, a novel ferromagnetic exchange interaction arises from the virtual exchange of pair excitations of quasiparticles; it has two novel properties such as its strength is in proportion to the effective Fermi energy of quasiparticles and its temperature dependence is responsible for the Curie-Weiss law. When the Hund coupling $J$ is strong enough, the superexchange interaction, which arises from the virtual exchange of pair excitations of electrons across the Mott-Hubbard gap, is ferromagnetic. In particular, it is definitely ferromagnetic for any nonzero $J>0$ in the large limit of band multiplicity. Ferromagnetic instability occurs, when the sum of the two exchange interactions is ferromagnetic and it overcomes the quenching of magnetic moments by the Kondo effect or local quantum spin fluctuations and the suppression of magnetic instability by the mode-mode coupling among intersite spin fluctuations.Comment: 14 pages, 4 figure

Theory of Kondo lattices and its application to high-temperature superconductivity and pseudo-gaps in cuprate oxides

A theory of Kondo lattices is developed for the t-J model on a square lattice. The spin susceptibility is described in a form consistent with a physical picture of Kondo lattices: Local spin fluctuations at different sites interact with each other by a bare intersite exchange interaction, which is mainly composed of two terms such as the superexchange interaction, which arises from the virtual exchange of spin-channel pair excitations of electrons across the Mott-Hubbard gap, and an exchange interaction arising from that of Gutzwiller's quasi-particles. The bare exchange interaction is enhanced by intersite spin fluctuations developed because of itself. The enhanced exchange interaction is responsible for the development of superconducting fluctuations as well as the Cooper pairing between Gutzwiller's quasi-particles. On the basis of the microscopic theory, we develop a phenomenological theory of low-temperature superconductivity and pseudo-gaps in the under-doped region as well as high-temperature superconductivity in the optimal-doped region. Anisotropic pseudo-gaps open mainly because of d\gamma-wave superconducting low-energy fluctuations: Quasi-particle spectra around (\pm\pi/a,0) and (0,\pm\pi/a), with a the lattice constant, or X points at the chemical potential are swept away by strong inelastic scatterings, and quasi-particles are well defined only around (\pm\pi/2a,\pm\pi/2a) on the Fermi surface or line. As temperatures decrease in the vicinity of superconducting critical temperatures, pseudo-gaps become smaller and the well-defined region is extending toward X points. The condensation of d\gamma-wave Cooper pairs eventually occurs at low enough temperatures when the pair breaking by inelastic scatterings becomes small enough.Comment: 15 pages, 14 figure

A working model of stroke recovery from rehabilitation robotics practitioners

We reviewed some of our initial insights about the process of upper-limb behavioral recovery following stroke. Evidence to date indicates that intensity, task specificity, active engagement, and focusing training on motor coordination are key factors enabling efficacious recovery. On modeling, experience with over 400 stroke patients has suggested a working model of recovery similar to implicit motor learning. Ultimately, we plan to apply these insights in the development of customized training paradigms to enhance recovery

Frustrated electron liquids in the Hubbard model

The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy is that of a normal Fermi liquid even if the multisite self-energy is anomalous. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S^3A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S^3A and is further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S^3A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model. It is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the whole Hilbert space by Kondo lattice theory. Even if higher-order multisite terms than the Fock-type term are considered, the ground state cannot be a Mott insulator. It can be merely a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high temperature phase.Comment: 11 pages, no figur

Cognitive loading affects motor awareness and movement kinematics but not locomotor trajectories during goal-directed walking in a virtual reality environment.

The primary purpose of this study was to investigate the effects of cognitive loading on movement kinematics and trajectory formation during goal-directed walking in a virtual reality (VR) environment. The secondary objective was to measure how participants corrected their trajectories for perturbed feedback and how participants' awareness of such perturbations changed under cognitive loading. We asked 14 healthy young adults to walk towards four different target locations in a VR environment while their movements were tracked and played back in real-time on a large projection screen. In 75% of all trials we introduced angular deviations of ±5° to ±30° between the veridical walking trajectory and the visual feedback. Participants performed a second experimental block under cognitive load (serial-7 subtraction, counter-balanced across participants). We measured walking kinematics (joint-angles, velocity profiles) and motor performance (end-point-compensation, trajectory-deviations). Motor awareness was determined by asking participants to rate the veracity of the feedback after every trial. In-line with previous findings in natural settings, participants displayed stereotypical walking trajectories in a VR environment. Our results extend these findings as they demonstrate that taxing cognitive resources did not affect trajectory formation and deviations although it interfered with the participants' movement kinematics, in particular walking velocity. Additionally, we report that motor awareness was selectively impaired by the secondary task in trials with high perceptual uncertainty. Compared with data on eye and arm movements our findings lend support to the hypothesis that the central nervous system (CNS) uses common mechanisms to govern goal-directed movements, including locomotion. We discuss our results with respect to the use of VR methods in gait control and rehabilitation

Electronic control of coherence in a two-dimensional array of photonic crystal surface emitting lasers

We demonstrate a semiconductor PCSEL array that uniquely combines an in-plane waveguide structure with nano-scale patterned PCSEL elements. This novel geometry allows two-dimensional electronically controllable coherent coupling of remote vertically emitting lasers. Mutual coherence of the PCSEL elements is verified through the demonstration of a two-dimensional Young’s Slits experiment. In addition to allowing the all-electronic control of the interference pattern, this type of device offers new routes to power and brightness scaling in semiconductor lasers, and opportunities for all-electronic beam steering

An Inverse-Problem Approach to Designing Photonic Crystals for Cavity QED Experiments

Photonic band gap (PBG) materials are attractive for cavity QED experiments because they provide extremely small mode volumes and are monolithic, integratable structures. As such, PBG cavities are a promising alternative to Fabry-Perot resonators. However, the cavity requirements imposed by QED experiments, such as the need for high Q (low cavity damping) and small mode volumes, present significant design challenges for photonic band gap materials. Here, we pose the PBG design problem as a mathematical inversion and provide an analytical solution for a two-dimensional crystal. We then address a planar (2D crystal with finite thickness) structure using numerical techniques.Comment: 12 pages, 8 figures, preprint available from http://minty.caltech.edu/MabuchiLa