749 research outputs found
Foerster resonance energy transfer rate and local density of optical states are uncorrelated in any dielectric nanophotonic medium
Motivated by the ongoing debate about nanophotonic control of Foerster
resonance energy transfer (FRET), notably by the local density of optical
states (LDOS), we study an analytic model system wherein a pair of ideal dipole
emitters - donor and acceptor - exhibit energy transfer in the vicinity of an
ideal mirror. The FRET rate is controlled by the mirror up to distances
comparable to the donor-acceptor distance, that is, the few-nanometer range.
For vanishing distance, we find a complete inhibition or a four-fold
enhancement, depending on dipole orientation. For mirror distances on the
wavelength scale, where the well-known `Drexhage' modification of the
spontaneous-emission rate occurs, the FRET rate is constant. Hence there is no
correlation between the Foerster (or total) energy transfer rate and the LDOS.
At any distance to the mirror, the total energy transfer between a
closely-spaced donor and acceptor is dominated by Foerster transfer, i.e., by
the static dipole-dipole interaction that yields the characteristic
inverse-sixth-power donor-acceptor distance dependence in homogeneous media.
Generalizing to arbitrary inhomogeneous media with weak dispersion and weak
absorption in the frequency overlap range of donor and acceptor, we derive two
main theoretical results. Firstly, the spatially dependent Foerster energy
transfer rate does not depend on frequency, hence not on the LDOS. Secondly the
FRET rate is expressed as a frequency integral of the imaginary part of the
Green function. This leads to an approximate FRET rate in terms of the LDOS
integrated over a huge bandwidth from zero frequency to about 10 times the
donor emission frequency, corresponding to the vacuum-ultraviolet. Even then,
the broadband LDOS hardly contributes to the energy transfer rates. We discuss
practical consequences including quantum information processing.Comment: 17 pages, 9 figure
Light propagation and emission in complex photonic media
We provide an introduction to complex photonic media, that is, composite
materials with spatial inhomogeneities that are distributed over length scales
comparable to or smaller than the wavelength of light. This blossoming field is
firmly rooted in condensed matter physics, in optics, and in materials science.
Many stimulating analogies exist with other wave phenomena such as sound and
seismology, X-rays, neutrons. The field has a rich history, which has led to
many applications in lighting, novel lasers, light harvesting, microscopy, and
bio optics. We provide a brief overview of complex photonic media with
different classes of spatial order, varying from completely random to
long-periodically ordered structures, quasi crystalline and aperiodic
structures, and arrays of cavities. In addition to shaping optical waves by
suitable photonic nanostructures, the realization is quickly arising that the
spatial shaping of optical wavefronts with spatial light modulators
dramatically increases the number of control parameters. As a result, it is
becoming possible for instance to literally see through completely opaque
complex media. We discuss a unified view of complex photonic media by means of
a photonic interaction strength parameter. This parameter gauges the
interaction of light with any complex photonic medium, and allows to compare
complex media from different classes for similar applications.Comment: 8 pages, 2 figures, Light Localisation and Lasing: Random and
Quasi-Random Photonic Structures, Eds. M. Ghulinyan and L. Pavesi, (Cambridge
Univ. Press, Cambridge, 2015) Ch. 1, p.
Optimal control of light propagation through multiple-scattering media in the presence of noise
We study the control of coherent light propagation through
multiple-scattering media in the presence of measurement noise. In our
experiments, we use a two-step optimization procedure to find the optimal
incident wavefront. We conclude that the degree of optimal control of coherent
light propagation through a multiple-scattering medium is only determined by
the number of photoelectrons detected per single speckle spot. The prediction
of our model agrees well with the experimental results. Our results offer
opportunities for imaging applications through scattering media such as
biological tissue in the shot noise limit
Design of a 3D photonic band gap cavity in a diamond-like inverse woodpile photonic crystal
We theoretically investigate the design of cavities in a three-dimensional
(3D) inverse woodpile photonic crystal. This class of cubic diamond-like
crystals has a very broad photonic band gap and consists of two perpendicular
arrays of pores with a rectangular structure. The point defect that acts as a
cavity is centred on the intersection of two intersecting perpendicular pores
with a radius that differs from the ones in the bulk of the crystal. We have
performed supercell bandstructure calculations with up to
unit cells. We find that up to five isolated and dispersionless bands appear
within the 3D photonic band gap. For each isolated band, the electric-field
energy is localized in a volume centred on the point defect, hence the point
defect acts as a 3D photonic band gap cavity. The mode volume of the cavities
resonances is as small as 0.8 (resonance wavelength cubed),
indicating a strong confinement of the light. By varying the radius of the
defect pores we found that only donor-like resonances appear for smaller defect
radius, whereas no acceptor-like resonances appear for greater defect radius.
From a 3D plot of the distribution of the electric-field energy density we
conclude that peaks of energy found in sharp edges situated at the point
defect, similar to how electrons collect at such features. This is different
from what is observed for cavities in non-inverted woodpile structures. Since
inverse woodpile crystals can be fabricated from silicon by CMOS-compatible
means, we project that single cavities and even cavity arrays can be realized,
for wavelength ranges compatible with telecommunication windows in the near
infrared.Comment: 11 figure
Local density of optical states in the band gap of a finite photonic crystal
We study the local density of states (LDOS) in a finite photonic crystal, in
particular in the frequency range of the band gap. We propose a new point of
view on the band gap, which we consider to be the result of vacuum fluctuations
in free space that tunnel in the forbidden range in the crystal. As a result,
we arrive at a model for the LDOS that is in two major items modified compared
to the well-known expression for infinite crystals. Firstly, we modify the
Dirac delta functions to become Lorentzians with a width set by the crystal
size. Secondly, building on characterization of the fields versus frequency and
position we calculated the fields in the band gap. We start from the fields at
the band edges, interpolated in space and position, and incorporating the
exponential damping in the band gap. We compare our proposed model to exact
calculations in one dimension using the transfer matrix method and find very
good agreement. Notably, we find that in finite crystals, the LDOS depends on
frequency, on position, and on crystal size, in stark contrast to the
well-known results for infinite crystals.Comment: 22 pages, 8 figure
Non-exponential spontaneous emission dynamics for emitters in a time-dependent optical cavity
We have theoretically studied the effect of deterministic temporal control of
spontaneous emission in a dynamic optical microcavity. We propose a new
paradigm in light emission: we envision an ensemble of two-level emitters in an
environment where the local density of optical states is modified on a time
scale shorter than the decay time. A rate equation model is developed for the
excited state population of two-level emitters in a time-dependent environment
in the weak coupling regime in quantum electrodynamics. As a realistic
experimental system, we consider emitters in a semiconductor microcavity that
is switched by free-carrier excitation. We demonstrate that a short temporal
increase of the radiative decay rate depletes the excited state and drastically
increases the emission intensity during the switch time. The resulting
time-dependent spontaneous emission shows a distribution of photon arrival
times that strongly deviates from the usual exponential decay: A deterministic
burst of photons is spontaneously emitted during the switch event.Comment: 12 pages, 4 figure
Light exiting from real photonic band gap crystals is diffuse and strongly directional
Any photonic crystal is in practice periodic with some inevitable fabricational imperfections. We have measured angle-resolved transmission of photons that are multiply scattered by this disorder in strongly photonic crystals. Peculiar non-Lambertian distributions occur as a function of frequency: due to internal diffraction, wide angular ranges of strongly reduced diffuse transmission coincide with photonic stop bands, while enhancements occur for directions outside stop gaps. We quantitatively explain the experiment with a model incorporating diffusion and band structure on equal footing. We predict that in the event of a photonic band gap, diffuse light at frequencies near band gap edges can exit only along isolated directions. Angle-resolved diffuse transmission appears to be the photonic equivalent of angle-resolved photoelectron spectroscopy
Controlled light scattering of a single nanoparticle by wavefront shaping
Controlling light scattering by nanoparticles is fundamentally important for
the understanding and the control of light inside photonic nanostructures, as
well as for nanoparticle scattering itself, including Mie scattering. Here, we
theoretically and numerically investigate the possibility to manipulate
nanoparticle scattering through wavefront shaping that was initially developed
to control scattering of light through opaque random media that consist of
large numbers of scattering nanoparticles. We find that even a single
nanoparticle supports multiple strongly scattering eigenchannels, which opens
the opportunity to manipulate scattering with wavefront shaping previously
developed for multiple scattered light through opaque random media. We find
that these scattering eigenchannels are related to different resonant leaky
modes of the scatterer. Moreover, we investigate the spectral correlation of
these highly scattering eigenchannels, and demonstrate the coexistence of short
range and long range correlations. Our work proposes a new tool to control
light-matter interactions with resonant modes via wavefront shaping and
constitutes a step towards exploring novel spectral correlations in the
scattering of light by nano scatterers, including Mie spheres.Comment: 8 pages, 2tables, 3 figure
Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors
This paper discusses free carrier generation by pulsed laser fields as a
mechanism to switch the optical properties of semiconductor photonic crystals
and bulk semiconductors on an ultrafast time scale. Requirements are set for
the switching magnitude, the time-scale, the induced absorption as well as the
spatial homogeneity, in particular for silicon at lambda= 1550 nm. Using a
nonlinear absorption model, we calculate carrier depth profiles and define a
homogeneity length l_hom. Homogeneity length contours are visualized in a plane
spanned by the linear and two-photon absorption coefficients. Such a
generalized homogeneity plot allows us to find optimum switching conditions at
pump frequencies near v/c= 5000 cm^{-1} (lambda= 2000 nm). We discuss the
effect of scattering in photonic crystals on the homogeneity. We experimentally
demonstrate a 10% refractive index switch in bulk silicon within 230 fs with a
lateral homogeneity of more than 30 micrometers. Our results are relevant for
switching of modulators in absence of photonic crystals
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