25,797 research outputs found
Optical third harmonic generation in black phosphorus
We present a calculation of Third Harmonic Generation (THG) for two-band
systems using the length gauge that avoids unphysical divergences otherwise
present in the evaluation of the third order current density response. The
calculation is applied to bulk and monolayer black Phosphorus (bP) using a
non-orthogonal tight-binding model. Results show that the low energy response
is dominated by mixed inter-intraband processes and estimates of the magnitude
of THG susceptibility are comparable to recent experimental reports for bulk bP
samples.Comment: 9 pages, 5 figure
Harmonic analysis of fractal measures induced by representations of a certain C-algebra
We describe a class of measurable subsets in \br^d such that
has an orthogonal basis of frequencies
indexed by
\lambda\in\Lambda\subset\br^d. We show that such spectral pairs have a self-similarity which may be used to generate associated
fractal measures with Cantor set support. The Hilbert space
does not have a total set of orthogonal frequencies, but a harmonic analysis of
may be built instead from a natural representation of the Cuntz C-
algebra which is constructed from a pair of lattices supporting the given
spectral pair . We show conversely that such a pair may be
reconstructed from a certain Cuntz-representation given to act on .Comment: 7 page
Iterative approach to arbitrary nonlinear optical response functions of graphene
Two-dimensional materials constitute an exciting platform for nonlinear
optics with large nonlinearities that are tunable by gating. Hence,
gate-tunable harmonic generation and intensity-dependent refraction have been
observed in e.g. graphene and transition-metal dichalcogenides, whose
electronic structures are accurately modelled by the (massive) Dirac equation.
We exploit on the simplicity of this model and demonstrate here that arbitrary
nonlinear response functions follow from a simple iterative approach. The power
of this approach is illustrated by analytical expressions for harmonic
generation and intensity-dependent refraction, both computed up to ninth order
in the pump field. Moreover, the results allow for arbitrary band gaps and
gating potentials. As illustrative applications, we consider (i)
gate-dependence of third- and fifth-harmonic generation in gapped and gapless
graphene, (ii) intensity-dependent refractive index of graphene up to ninth
order, and (iii) intensity-dependence of high-harmonic generation.Comment: 6 pages, 5 figures. Supplemental material: 6 pages, 2 figure
Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation
We study the effects of a truncated band structure on the linear and
nonlinear optical response of crystals using four methods. These are
constructed by (i) choosing either length or velocity gauge for the
perturbation and (ii) computing the current density either directly or via the
time-derivative of the polarization density. In the infinite band limit, the
results of all four methods are identical, but basis truncation breaks their
equivalence. In particular, certain response functions vanish identically and
unphysical low-frequency divergences are observed for few-band models in the
velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study,
we analyze the problems associated with all methods and identify the optimal
one. Our results show that the length gauge calculations provide the fastest
convergence rates as well as the most accurate spectra for any basis size and,
moreover, that low-frequency divergences are eliminated.Comment: 11 pages, 7 figure
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