389 research outputs found
Nonhermitian transport effects in coupled-resonator optical waveguides
Coupled-resonator optical waveguides (CROWs) are known to have interesting
and useful dispersion properties. Here, we study the transport in these
waveguides in the general case where each resonator is open and asymmetric,
i.e., is leaky and possesses no mirror-reflection symmetry. Each individual
resonator then exhibits asymmetric backscattering between clockwise and
counterclockwise propagating waves, which in combination with the losses
induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling
between the resonators induces an additional source of non-hermiticity, and a
complex band structure arises. We show that in this situation the group
velocity of wave packets differs from the velocity associated with the
probability density flux, with the difference arising from a non-hermitian
correction to the Hellmann-Feynman theorem. Exploring these features
numerically in a realistic scenario, we find that the complex band structure
comprises almost-real branches and complex branches, which are joined by
exceptional points, i.e., nonhermitian degeneracies at which not only the
frequencies and decay rates coalesce but also the eigenmodes themselves. The
non-hermitian corrections to the group velocity are largest in the regions
around the exceptional points.Comment: 11 pages, 9 figure
Revisiting the hierarchical construction of higher-order exceptional points
Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians
describing open quantum or wave systems have a variety of potential
applications in particular in optics and photonics. However, the experimental
realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev.
Lett. 125, 203602 (2020)] have introduced a robust construction where a
unidirectional coupling of two subsystems having exceptional points of the same
order leads generically to a single exceptional point of twice the order. Here,
we investigate this scheme in a different manner by exploiting the nilpotency
of the traceless part of the involved Hamiltonians. We generalize the scheme
and derive a simple formula for the spectral response strength of the composite
system hosting a higher-order exceptional point. Its relation to the spectral
response strengths of the subsystems is discussed. Moreover, we investigate
nongeneric perturbations. The results are illustrated with an example.Comment: 6 pages, 2 figure
Designing coupled microcavity lasers for high-Q modes with unidirectional light emission
We design coupled optical microcavities and report directional light emission
from high- modes for a broad range of refractive indices. The system
consists of a circular cavity that provides a high- mode in form of a
whispering gallery mode, whereas an adjacent deformed microcavity plays the
role of a waveguide or collimator of the light transmitted from the circular
cavity. As a result of this very simple, yet robust, concept we obtain high-
modes with promising directional emission characteristics. No information about
phase space is required, and the proposed scheme can be easily realized in
experiments.Comment: 3 pages, 3 figure
Rotating optical microcavities with broken chiral symmetry
We demonstrate in open microcavities with broken chiral symmetry,
quasi-degenerate pairs of co-propagating modes in a non-rotating cavity evolve
to counter-propagating modes with rotation. The emission patterns change
dramatically by rotation, due to distinct output directions of CW and CCW
waves. By tuning the degree of spatial chirality, we maximize the sensitivity
of microcavity emission to rotation. The rotation-induced change of emission is
orders of magnitude larger than the Sagnac effect, pointing to a promising
direction for ultrasmall optical gyroscopes.Comment: 5 pages, 5 figure
On a solution functor for D-cap-modules via -adic Hodge theory
This article aims to formulate the main technical input for the construction
of a solution functor in a still hypothetical -adic analytic Riemann-Hilbert
correspondence. Our approach relies on a novel period sheaf
, which is a certain ind-Banach completion of
along the kernel of Fontaine's map . We
relate the ind-continuous -linear endomorphisms of
a corresponding period structure sheaf to the sheaf of infinite order
differential operators D-cap introduced by Ardakov-Wadsley. Locally on the
cotangent bundle, this yields a definition of a solution functor. The main
result computes that significant information about a perfect complex can be
reconstructed out of its solutions, which hints strongly towards a
reconstruction theorem for a large category of complexes of D-cap-modules
Pitfalls in the theory of carrier dynamics in semiconductor quantum dots: the single-particle basis vs. the many-particle configuration basis
We analyze quantum dot models used in current research for misconceptions
that arise from the choice of basis states for the carriers. The examined
models originate from semiconductor quantum optics, but the illustrated
conceptional problems are not limited to this field. We demonstrate how the
choice of basis states can imply a factorization scheme that leads to an
artificial dependency between two, actually independent, quantities.
Furthermore, we consider an open quantum dot-cavity system and show how the
dephasing, generated by the dissipator in the von Neumann Lindblad equation,
depends on the choice of basis states that are used to construct the collapse
operators. We find that the Rabi oscillations of the s-shell exciton are either
dephased by the dissipative decay of the p-shell exciton or remain unaffected,
depending on the choice of basis states. In a last step we resolve this
discrepancy by taking the full system-reservoir interaction Hamiltonian into
account
Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity
The effect of a Kerr nonlinearity on dynamical tunneling is studied, using
coupled whispering gallery modes in an optical microcavity. The model system
that we have chosen is the 'add-drop filter', which comprises an optical
microcavity and two waveguide coupled to the cavity. Due to the evanescent
field's scattering on the waveguide, the whispering gallery modes in the
microcavity form doublets, which manifest themselves as splittings in the
spectrum. As these doublets can be regarded as a spectral feature of dynamical
tunneling between two different dynamical states with a spatial overlap, the
effect of a Kerr nonlinearity on the doublets is numerically investigated in
the more general context of the relationship between cubic nonlinearity and
dynamical tunneling. Within the numerical realization of the model system, it
is observed that the doublets shows a bistable transition in its transmission
curve as the Kerr-nonlinearity in the cavity is increased. At the same time,
one rotational mode gets dominant over the other one in the transmission, since
the two states in the doublet have uneven linewidths. By using coupled mode
theory, the underlying mode dynamics of the phenomena is theoretically modelled
and clarified.Comment: 7 pages, 5 figure
- …