19 research outputs found
Extremal transmission at the Dirac point of a photonic band structure
We calculate the effect of a Dirac point (a conical singularity in the band
structure) on the transmission of monochromatic radiation through a photonic
crystal. The transmission as a function of frequency has an extremum at the
Dirac point, depending on the transparencies of the interfaces with free space.
The extremal transmission is inversely proportional to
the longitudinal dimension of the crystal (for larger than the lattice
constant and smaller than the transverse dimension ). The interface
transparencies affect the proportionality constant , and they
determine whether the extremum is a minimum or a maximum, but they do not
affect the ``pseudo-diffusive'' 1/L dependence of .Comment: 6 pages, 4 figures. Fig. 1 revised, Fig. 4 adde
Hartman effect and spin precession in graphene
Spin precession has been used to measure the transmission time \tau over a
distance L in a graphene sheet. Since conduction electrons in graphene have an
energy-independent velocity v, one would expect \tau > L/v. Here we calculate
that \tau < L/v at the Dirac point (= charge neutrality point) in a clean
graphene sheet, and we interpret this result as a manifestation of the Hartman
effect (apparent superluminality) known from optics.Comment: 6 pages, 4 figures; v2: added a section on the case of
perpendicularly aligned magnetizations; v3: added a figur
How to detect the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum
We propose a method to detect the geometric phase produced by the Dirac-type
band structure of a triangular-lattice photonic crystal. The spectrum is known
to have a conical singularity (= Dirac point) with a pair of nearly degenerate
modes near that singularity described by a spin-1/2 degree of freedom (=
pseudospin). The geometric Berry phase acquired upon rotation of the pseudospin
is in general obscured by a large and unspecified dynamical phase. We use the
analogy with graphene to show how complementary media can eliminate the
dynamical phase. A transmission minimum results as a direct consequence of the
geometric phase shift of pi acquired by rotation of the pseudospin over 360
degrees around a perpendicular axis. We support our analytical theory based on
the Dirac equation by a numerical solution of the full Maxwell equations.Comment: 6 pages, 6 figures; v2: section added, figure adde
Quantum Goos-Hanchen effect in graphene
The Goos-Hanchen (GH) effect is an interference effect on total internal
reflection at an interface, resulting in a shift sigma of the reflected beam
along the interface. We show that the GH effect at a p-n interface in graphene
depends on the pseudospin (sublattice) degree of freedom of the massless Dirac
fermions, and find a sign change of sigma at angle of incidence
alpha*=arcsin[sin alpha_c]^1/2 determined by the critical angle alpha_c for
total reflection. In an n-doped channel with p-doped boundaries the GH effect
doubles the degeneracy of the lowest propagating mode, introducing a two-fold
degeneracy on top of the usual spin and valley degeneracies. This can be
observed as a stepwise increase by 8e^2/h of the conductance with increasing
channel width.Comment: 5 pages, 6 figures; expanded version of the published paper (one
extra page, one extra figure), including also a reference to J.M. Pereira et
al, PRB 74, 045424 (2006
Artificial graphene as a tunable Dirac material
Artificial honeycomb lattices offer a tunable platform to study massless
Dirac quasiparticles and their topological and correlated phases. Here we
review recent progress in the design and fabrication of such synthetic
structures focusing on nanopatterning of two-dimensional electron gases in
semiconductors, molecule-by-molecule assembly by scanning probe methods, and
optical trapping of ultracold atoms in crystals of light. We also discuss
photonic crystals with Dirac cone dispersion and topologically protected edge
states. We emphasize how the interplay between single-particle band structure
engineering and cooperative effects leads to spectacular manifestations in
tunneling and optical spectroscopies.Comment: Review article, 14 pages, 5 figures, 112 Reference
Topological Photonics
Topology is revolutionizing photonics, bringing with it new theoretical
discoveries and a wealth of potential applications. This field was inspired by
the discovery of topological insulators, in which interfacial electrons
transport without dissipation even in the presence of impurities. Similarly,
new optical mirrors of different wave-vector space topologies have been
constructed to support new states of light propagating at their interfaces.
These novel waveguides allow light to flow around large imperfections without
back-reflection. The present review explains the underlying principles and
highlights the major findings in photonic crystals, coupled resonators,
metamaterials and quasicrystals.Comment: progress and review of an emerging field, 12 pages, 6 figures and 1
tabl
Fiber guiding at the Dirac frequency beyond photonic bandgaps
Light trapping within waveguides is a key practice of modern optics, both scientifically and technologically. Photonic crystal fibers traditionally rely on total internal reflection (index-guiding fibers) or a photonic bandgap (photonic-bandgap fibers) to achieve field confinement. Here, we report the discovery of a new light trapping within fibers by the so-called Dirac point of photonic band structures. Our analysis reveals that the Dirac point can establish suppression of radiation losses and consequently a novel guided mode for propagation in photonic crystal fibers. What is known as the Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. We find the unexpected phenomenon of wave localization at this point beyond photonic bandgaps. This guiding relies on the Dirac point rather than total internal reflection or photonic bandgaps, thus providing a sort of advancement in conceptual understanding over the traditional fiber guiding. The result presented here demonstrates the discovery of a new type of photonic crystal fibers, with unique characteristics that could lead to new applications in fiber sensors and lasers. The Dirac equation is a special symbol of relativistic quantum mechanics. Because of the similarity between band structures of a solid and a photonic crystal, the discovery of the Dirac-point-induced wave trapping in photonic crystals could provide novel insights into many relativistic quantum effects of the transport phenomena of photons, phonons, and electrons
Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
Spatial and/or temporal propagation of light waves in periodic optical
structures offers a rather unique possibility to realize in a purely classical
setting the optical analogues of a wide variety of quantum phenomena rooted in
relativistic wave equations. In this work a brief overview of a few optical
analogues of relativistic quantum phenomena, based on either spatial light
transport in engineered photonic lattices or on temporal pulse propagation in
Bragg grating structures, is presented. Examples include spatial and temporal
photonic analogues of the Zitterbewegung of a relativistic electron, Klein
tunneling, vacuum decay and pair-production, the Dirac oscillator, the
relativistic Kronig-Penney model, and optical realizations of non-Hermitian
extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference
Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum
Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin- particle. Here we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal. While constructive interference of a scalar (spin-zero) wave produces a coherent backscattering peak, consisting of a doubling of the disorder-averaged reflected photon flux, the destructive interference caused by the Berry phase suppresses the reflected intensity at an angle which is related to the angle of incidence by time reversal symmetry. We demonstrate this extinction of coherent backscattering by a numerical solution of Maxwell's equations and compare with analytical predictions from the Dirac equation