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TOPOLOGY OPTIMIZATION OF 1.5 μm ALL-OPTICAL NARROW-BAND LIGHT MODULATOR BASED ON SEMICONDUCTOR NANOHETEROSTRUCTURES
The efficiency of such type light modulator depends on how great
modification of the reflector optical properties could be achieved by insignificant
change of refractive index. Thus the topology of layers of the light modulator is
an object of optimization.
2. Calculations and results
For modeling the data of  were used. GaAs and AlxOy were used as
components of the light modulator. Since these materials posses large refractive
index difference it becomes possible to design structures with low layers
number. The low layer number has two principal advantages: technological
simplicity of making and excitation intensity reduction. GaAs is a nonlinear
material in such structures. Typical nonlinear response time obtained in  is
3 ps. Apparently this feature could lead to creation of light modulators with
operating rate of hundreds gigahertz.
In this contribution four different structures consisting of 16 and 18 GaAs
and AlxOy layers are presented (Fig. 1, here and after A denotes GaAs layer, B
denotes AlxOy layer). The structures consist of quarter-wave layers of GaAs and
AlxOy for wavelength 1.55 µm (n(GaAs)=3.35, n(AlxOy)=1.71, thickness GaAs
of layers is 116 nm, AlxOy – 226 nm), Reflection spectra of these structures
represent a stopband at 1.2-2.0 µm with defect at 1.55 µm. Transmission at
1.55 µm is near 100 %. All spectra were calculated using transfer matrix method.
As one can see from Fig. 1 structures (AB)4(BA)4 and A(BA)4(AB)4A have the
lowest line width (2.5 and 1 nm, correspondingly). An advantage of the lower
line width lies in a possibility of excitation intensity decreasing to achieve
considerable modification of transmission/reflection coefficient at a certain
at half height
a - 2,5 nm
b - 15 nm
c - 8 nm
d - 1 nm
Figure 1. Reflection spectra of the following
structures: a – (AB)4(BA)4, b – (BA)4(AB)4,
c – B(AB)4(BA)4B, d – A(BA)4(AB)4A.
Figure 2. Differential reflection spectra
of the following excited structures:
a – (AB)4(BA)4, b – (BA)4(AB)4,
c – B(AB)4(BA)4B, d – A(BA)4(AB)4A.
Qualitative estimation of GaAs refractive index modification under the
conditions of intense laser excitation generating dense e-h plasma
(6.6×1018 cm-3) with cooling time τ = 10-11 s have been made in accordance with
ε = ε ( 0 ) + iε′ ( 0 ) −
≡ ( n + ik ) ,
4πεε0 µ ω +
where ε(0)+iε'(0) is the crystal dielectric constant at the frequency ω, n+ik is the
sample refraction index in the presence of the e-h plasma, N is the concentration
of free carries, µ is the electron effective mass.
Fig. 2 presents results of calculations of differential reflection spectra under
intensive laser excitation. Uniform excitation of all GaAs layers is supposed.
Spectra of excited structures shift to the shorter wavelength spectral range.
Structures (AB)4(BA)4 and A(BA)4(AB)4A have near 100 % reflection
modification at 1.55 µm.
The condition of uniform excitation of all GaAs layer is hardly realized in
practice and requires high excitation intensity. Therefore calculations of the
reflection spectra modification under the condition of nonuniform layer
excitation have been made. Excitation intensity was chosen in such a way that
modification of refractive index in the first GaAs layer was the same
modification in case of uniform excitation. All subsequent GaAs layers were
excited in accordance with Bouguer law. Comparison of cases of uniform and
nonuniform excitations for (AB)4(BA)4 and A(BA)4(AB)4A structures is
presented in Figs. 3 and 4, correspondingly.
Figure 3. Differential reflection spectra of
(AB)4(BA)4 structures under uniform (solid)
and nonuniform (dotted) excitations.
Figure 4. Differential reflection spectra of
A(BA)4(AB)4A structures under uniform
(solid) and nonuniform (dotted) excitations.
In case of both structures the shift of the reflection spectrum is smaller under
the condition of nonuniform excitation, nevertheless spectrum modification
at 1.55 µm is near 100 %. This fact means that even changes only in the first
layers drastically modify interference pattern due to electromagnetic field
redistribution. It is evident that operating range of such type light modulators is
approximately 3 nm. So, narrow operation range makes it possible to increase
capacity of data transfer due to multiwavelength data links.
1.5 µm all-optical narrowband light modulator based on GaAs/AlxOy multilayer
structures was demonstrated. It was shown that plane structure with a thickness
less than 3 µm could effectively modulate the light at 1.5 µm, operation range
being equal to 3 nm. The structures GaAs/AlxOy)4(AlxOy/GaAs)4 and
GaAs(AlxOy/GaAs)4(GaAs/AlxOy)4GaAs have great potential to be very
promising for light modulators.
1. D. A. B. Miller, IEEE J. Selected Topics in Quantum Electronics 6, 1312
2. A. Y. Elezzabi, Z. Han, S. Sederberg, V. Van, Opt. Express 17, 11045
3. R. S. Jacobsen,
K. N. Andersen,
P. I. Borel,
L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin,
H. Ou, C. Peucheret, B.Zsigri, A. Bjarklev, Nature 441, 199 (2006).
4. V. R. Almeida, Q. Xu, M. Lipson, Opt. Lett. 30, 2403 (2005).
5. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen,
R. Nicolaescu, M. Paniccia, Nature 427, 615 (2004).
6. M. V. Ermolenko, O. V. Buganov, S. A. Tikhomirov, V. V. Stankevich,
S. V. Gaponenko, A. S. Shulenkov, Appl. Phys. Lett. 97, 073113 (2010).
7. M. Combescot, J. Bok, J. Luminesc. 30, 1 (1985).
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IN ENERGY CONVERSION
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PHYSICS, CHEMISTRY AND APPLICATION OF NANOSTRUCTURES, 2011
NANOSCALE SIMULATIONS FOR ENERGY STORAGE
RELATED ENGINEERING PROBLEMS: THE CASE STUDY OF
NANOPOROUS CARBONS UNDER THE NANOSCOPE
R. J.-M. PELLENQ
Centre Interdisciplinaire des Nanosciences de Marseille (CNRS et Université de
Marseille) Campus de Luminy, 13288 Marseille, France
Departement of Civil and Environmental Engineering (1-382)
Massachusetts Institute of Technology
Massachusetts Ave. 77, 02139, Cambridge, MA, USA
Micro and nanoporous carbon materials are critical for many innovative engineering
applications. Such complex multi-scale porous materials have a confined fluid in the
pore void: an electrolyte in the case of batteries and super-capacitors, molecular fluids
(CH4, water, CO2) in the case of charcoal. The question that engineering scientists need
to address today is how to integrate the physics of the fluid and solid behavior and their
interactions into predictive engineering approaches. In this paper, I present how quantum
and statistical physics concepts and methods can be used to put such porous carbon
materials "under the nanoscope"; that is, allowing the assessment of the sought behavior
at nanoscales aiming at bridging to engineering applications. I first illustrate this
approach by showing how to get realistic samples of porous carbon replica from porous
oxides (zeolites) as new forms of porous carbons with ordered texture along with
disordered forms such as saccharose cokes. Then I go on with presenting how quantum
chemistry methods can be used to nail down fundamentals interaction processes for H2
adsorption. Once these relevant interactions are known, I will show their implementation
in a grand canonical Monte-Carlo approach and their application in the case of H2
storage in alkaline doped version of these porous carbons. These are also experimentally
and industrially considered as electrode materials in electrochemical energy storing
devices (supercapacitor and batteries). I will present the first results on electronic
conductivity of these new forms of porous carbons for different polarization conditions
and show the importance of texture properties on ē-conductivity. Finally, addressing the
influence of simple gases adsorption on the mechanical properties of these porous
matrices, I will show how CO2 adsorption process significantly competes with the matrix
elastic energy and can affectively reduce CO2 sequestration in charcoal mines.
1. Producing from computer simulation
1.1. Carbon replica of zeolites
The procedure used to generate the models of carbon replica of zeolite faujasite
(Y) and EMT, C-FAU and C-EMT respectively, is detailed in reference . The
C-FAU and C-EMT structures were prepared by adsorbing carbon from the
vapor phase onto a model of zeolite Y using the grand canonical Monte Carlo
method (GCMC). Carbon-carbon bond formation and destruction was described
using the reactive empirical bond-order potential of Brenner and the C-zeolite
interactions were modeled using the PN-TraZ potential. The zeolite atoms were
then removed and the remaining carbon skeleton was relaxed using a thermal
annealing procedure. The final carbon replica consisted entirely of
sp2-hybridized C atoms and had the same cubic Fd3m space group and pore
morphology as the zeolite Y template (lattice constant a = 2.485 nm). C-FAU
can be seen as a set of tetrahedrally interconnected single wall nanotubes. Its unit
cell contains 629 atoms. By duplicating some unit cells, we can observe a very
well hexagonal distribution of spherical interconnected pores along all the 
directions. On the other hand, C-EMT structure can be considered as a pillared
bundle of single wall undulated nanotubes hexagonally interconnected. It is
denser than the former cubic structure since its unit cell contains 744 atoms for a
similar volume. Densities of C-FAU and C-EMT are 0.81 and 0.96 g/cm3. The
pore size distribution of C-FAU shows peaks at 11-12 Å, while C-EMT structure
shows somewhat smaller interconnected pores. Both structures represent new
allotropic phases of carbon. The extreme curvature is stabilized by the presence
of five and seven member rings. The proportions of six-member rings are on the
order of 60 % and 40 % are shared by five-, seven-, and some eight-member
rings. It is noticeable that these structures do not have dangling bonds or sp3
carbon atoms. The cohesive energy of both structures is around 7.2 eV/atom.
1.2. Disordered saccharose cokes
Most of simplistic (slit like) models do not provide a realistic description of the
disordered carbons. Reconstruction methods, in which a 3D structural model is
built that is consistent with a set of experimental structure data, offer the most
promising route to realistic models of such carbons at the present time. Reverse
Monte Carlo (RMC) is one such reconstruction method, in which an atomistic
model is built that matches experimental structure factor data from X-ray or
neutron diffraction. However, for covalently bonded materials, such as carbons,
there is a nonuniqueness problem associated with the direct application of RMC.
According to the uniqueness theorem of statistical mechanics, if the
intermolecular potential for the material is pairwise additive, the pair correlation
function, g(r) (and hence the structure factor), and all higher correlation
functions are uniquely determined for a given pair potential. Thus, in this case
RMC should give the exact (within the experimental accuracy of the data)
unique structure. However, most materials do not exhibit pairwise additivity.
Chemical bonding is intrinsically a multibody process, as in carbons. In such
cases, the structures obtained from unconstrained RMC are nonunique. Many
molecular structures can match the experimental structure factor. To overcome
this nonuniqueness problem, constraints are needed in the fitting procedure.
These constraints may be physical or chemical and are based upon the
understanding of the material being modeled. RMC has been used before in
modeling amorphous nonporous carbons incorporating different constraints,
such as the ratio of sp2 to sp3 sites, coordination number constraints, bond angle
constraints. A new approach has been introduced in which an energy term is
included in the acceptance probability for atomic moves, so the simulation seeks
to simultaneously minimize the total energy of the system and also the error in
the radial distribution function. The presence of the energy term greatly
decreases the presence of unrealistic, high-energy structures in the resulting
models while simultaneously matching the experimental data. This approach is
called hybrid reverse Monte Carlo (HRMC), since it combines the features of the
regular Monte Carlo and reverse Monte Carlo methods. The use of the energy
constraint term helps alleviate the problem of the presence of unrealistic features
(such as three- and four-membered carbon rings), reported in previous RMC
studies of carbons, and also correctly describes the local environment of carbon
atoms. Figs. 1a and 1b present atomic configurations of two of these saccharose
coke porous carbons.
Figure 1. Snapshots of models of CS400 (a) and CS1000 (b) obtained from the HRMC method.
The gray rods represent C-C bonds, and the black rods represent C-H or H-H bonds.
The simulation box size used is 25 Å.
From GCMC simulation of H2 adsorption, we found that these disordered
nanoporous carbons are not good H2 dockers for a filling pressure of 300 bars
and at room temperature. As all nanoporous carbons including the carbon replica
from zeolite introduced above, they do not show advantageous performances
compared to a classical gas cylinder despite of their crystalline micropore
network. This is why we have made to considering their doped form with
2. H2 storage in alkaline-doped nanoporous carbons
Molecular hydrogen adsorption between two Li, K-doped coronene molecules,
taken as local environment of carbon microporous materials was then studied by
first-principles DFT-B3LYP calculations. These cluster calculations are
complemented with periodic DFT LDA/GGA calculations on extended Li- and
K-doped structures . In all cases, energy minimization calculations unravel
that there is a stable adsorption site for molecular hydrogen in these Li- and
K-doped sp2 carbon structures with large adsorption energies. This is the direct
consequence of the significant charge transfer from the doping agents on
neighboring slab carbon atoms, which allows the coupling of the molecular H2
polarizability with the resulting substrate electric field (polarization interaction)
that in turn induces the stabilization of molecular hydrogen. These calculations
also give an insight on the atomic configurations of interlayer species (H2 and
Li/K) as the interlayer spacing increases.
It can be shown that large positional changes correlate with electronic
properties of interlayer species. The confined hydrogen molecule does not show
any tendency for dissociation and adopts a position in the interlayer void that is
deeply related to that of doping ions. Note that the ab initio Li partial charge is
0.7 and that the adsorption energy is -15 kJ/mol. Further calculations for the
same system in the LDA approximation give an adsorption energy of -24 kJ/mol.
These two values are the lower and upper bounds of the DFT-B3LYP
calculations. For a LiC6 doped molecular system, it gives adsorption energy of
-21 kJ/mol. Similar charge transfer is observed in the case of potassium as a
doping agent but a significantly lower adsorption energy (~ -10 kJ/mol, see
Coming back to our carbon replica of zeolites, positions of Li ions for the
LiC6 composition (that is experimentally attainable) were obtained by energy
minimization at 0 K using the GULP program  assuming ab initio electric
charges for Coulombic interactions, plus a shorter range Lennard-Jones term.
Charges were distributed over all carbon atoms and so chosen to ensure the
electroneutrality of the system. We first generate an initial configuration
consisting of a homogenously spread monoatomic lithium gas phase. Then, we
minimize the energy of the system at 0 K considering the carbon matrix rigid.
We assume here that lithium atoms will remain ionic and not tend to form
metallic clusters. This assumption is consistent with our ab initio calculations.
Figure 2. 0 K adsorption energy versus interlayer distance for the Li-doped (a)
and K-doped (b) systems.
After relaxation, Li ions are decorating the carbon pore wall (see Fig. 3),
leaving enough free room in the pore core to still adsorb H2. Note that the inner
part of the carbon wall is essentially not accessible to lithium atoms, unless a few
of them found enough free space in the case of C-EMT in the channels along
 direction. For the sake of simplicity and transferability in the case of the
doped system, we retain the Lennard-Jones form and parameters as they are for
the H2-C interactions in the case of the undoped matrix and keep the hydrogen
molecular polarizability as a disposable parameter in order to fit ab initio results.
GCMC atomistic simulations of hydrogen adsorption isotherms in these
Li-doped versions of the two carbon structures C-FAU and C-EMT were carried
out to determine their storage capacities at 298 K. We found that these new
forms of carbon solids in their Li-doped versions, show very attractive hydrogen
storage capacities at 298 K close to the US-DOE 2010 target (Fig. 4).
Li-doped nanostructures provide reversible gravimetric and volumetric
hydrogen storage capacities twice larger (3.75 wt.% and 33.7 kg/m3). The
extreme lattice stiffness of their skeleton will prevent them from collapsing
under large external applied pressure, an interesting property compared to soft
compliant materials such as carbon nanotubes bundles or metal organic
frameworks MOFs. These new ordered nanoporous carbon composites are thus
very promising materials for hydrogen storage.