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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 [6] 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 [6] 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









Line width

at half height

a - 2,5 nm

b - 15 nm

c - 8 nm

d - 1 nm










Wavelength, µm

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.










Wavelength, µm


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 ) −

Ne 2


≡ ( n + ik ) ,

 2 iω 

4πεε0 µ  ω + 

τ 









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.








Wavelength, µm

Figure 3. Differential reflection spectra of

(AB)4(BA)4 structures under uniform (solid)

and nonuniform (dotted) excitations.



Wavelength, µm


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.

3. Conclusion

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,

J. Fage-Pedersen,

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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Belarusian-French Seminar

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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 [1]. 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 [110]

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

alkaline species.

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 [2]. 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

Fig. 2).

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 [1] 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

[001] 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.

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