Functional Properties of Photonic Crystals on the Basis of SingleCrystal Opal Films
A.I. Plekhanov
Institute of Automation and Electrometry SB RAS,
Pros. Koptuyg, 1, Novosibirsk, 630090 Russia
ABSTRACT
Formation of single-crystal opal films from a suspension of monodisperse spherical silica
particles in a dynamic meniscus area is treated as nanocrystallization involving
interparticle interaction forces. Preparation of high-quality photonic crystal films with a
reflection coefficient in the photonic band gap up to 95% is based on the concept of
equilibrium crystallization. Two- and three-layer heterostructures have been produced
from single-crystal films with various sizes of silica spheres. Well-resolved allowed
ranges within photonic band gaps have been detected for three-layer heterostructures,
suggesting interesting applications of photonic crystals. We have observed a low
threshold lasing in three-layer heterostructures opal films. The diffraction of light passing
through a glass plate coated by an artificial single-crystal opal film has been analyzed. It
has been shown that the stop band of a photonic crystal is manifested against the
background of the unchanged spectrum of reflected and refracted Bragg waves. The
position of this stop band can be changed under a small change in the concentration of a
number of substances filling the photonic crystal. The application of such an optical
system as an optical chemical sensor has been demonstrated.
INTRODUCTION
Regularities of the permolecular crystallization in suspensions of charged
monodisperse spherical silica particles (MSSP) and the consequent formation of
polycrystalline noble opal have been sufficiently well studied to date [1–5]. The internal
structure of crystals is not ideal, but the understanding of the nature of defects [6] allows
us to avoid the appearance of many defects and improve results of photonic crystalline
measurements. A single-crystalline opal film of the required thickness precipitated on a
wide supporting substrate (plate) is more technological. Mechanism of the preparation of
such film using surface tension and capillary suction as forces governing the MSSP
packing into a regular structure is considered in [7]. The fact that the growth of such films
involves interaction between MSSPs and the nanocrystallization process has not been
discussed in the literature, the investigations were mainly empirical [8–12], and the
appearance of regular structures was explained merely by their self-assembling.
We have treated the formation of single-crystal opal films from a suspension of
MSSPs in a dynamic meniscus area as nanocrystallization involving interparticle
interaction forces. This process allows to occur through the correction of oppositely
directed interparticle interaction forces down to a quasi-equilibrium state. Two- and
three-layer heterostructures have been produced from single-crystal films with various
sizes of MSSPs.
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Well-resolved allowed ranges within photonic band gaps (PBGs) have been detected
for three-layer heterostructures, suggesting interesting applications of photonic crystals
(PhCs). In this paper, we have studied the lasing from artificial opal, thin single-crystal
opal films and opal heterostructures doped with Rhodamine 6G and excited by
picosecond pulses of second harmonic of a Nd:YAG-laser.
A number of unusual properties of the propagation of light in PhCs such as the
refraction of light in negative media [13] and the effect of a superprism and the
selfcollimation of light [14] were recently revealed. It was proposed to use these effects
for creating a supersensitive light beam splitter [15, 16] and for controlling an optical flux
[17]. Moreover, schemes with PhCs can underlie supersensitive optical chemical sensors
[18, 19]. For such applications, it is important to determine and analyze regions with a
strong angular dispersion in optical systems with PhCs and to study the behavior of light
at the interface of PhCs with other optical media.
In this work, we also report the results of the investigation of a new effect of the
displacement of the PBG (stop band) against the unchanged spectrum of diffracted white
light at the (glass–thin opal film) interface and the possibilities of using this effect to
create optical chemical sensors.
SINGLE-CRYSTAL OPAL FILMS
Methodology
Coagulation-resistant nanosize MSSP suspensions are obtained by the hydrolysis of
tetraethoxysilane (Si[OC2H5]4) in an alcohol solution in the presence of ammonia [20]
playing the role of the process catalyst and, then, of an electrolyte, which is a potentialforming and suspension-stabilizing factor. In the suspension, negatively charged MSSPs
are surrounded with a double diffusion layer of NH4+ counterions with a thickness  and
form with this layer a structural unit (SU) for nanocrystallization [21–24]. The value of 
depends on the total electrolyte concentration in the suspension expressed through the
Debye parameter  as  = 1/. The Debye parameter is defined as   8e 2 Z 2 n  kT ,
where e is the elementary charge, Z is the counterion valence, n is the ion concentration,
and ε is the permittivity of a dispersion medium. In turn, the ratio between the MSSP
radius r and  is a key parameter of the particle interaction and nanocrystallization (this
ratio is more conveniently expressed as the product  r).
The DLVO (Deryagin, Landau, Verwey, and Overbeek) theory considers the pair
interaction energy of negatively charged MSSPs in a suspension. During volume
spontaneous nanocrystallization in a concentrated suspension under constrained
conditions, there are the molecular attraction Um of particles and the electrostatic
repulsion Ui of their counterion atmospheres. Differentiating the energies Um and Ui with
respect to a distance H between MSSPs in the suspension or in the growing nanocrystal,
we can pass to counteracting molecular and ion forces Pm and Pi , respectively:
Pm 
Ar
,
12 H 2
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(1)
Pi 
0 
o r  exp(   H )
21  exp(  H ) 

 r (1  r )
(2)
,
(3)
where A is the Hamaker constant,  is the permittivity of the dispersion medium (water,
ethyl alcohol, diethyl ether, acetone, etc.), and o is the surface potential [23],  is the
particle charge. The sum of counteracting forces between particles in equilibrium
growing crystal should be equal to zero [24, 25]. Under the conditions of spontaneous
crystallization from a concentrated suspension under constrained conditions, nanocrystals
are a result of the balance of forces acting between SUs: Pm , Pi , and gravitational forces
Pg as an equivalent of Pm. In freshly prepared alkaline stabilized NH4OH (pH = 9.5–10,
r >> 1) suspensions, Pi > Pm during crystallization under constrained conditions, and an
additional force Pg (Pi = Pm + Pg) is necessary to provide for the balance of forces. The
situation is different when growing thin film nanocrystals.
A mechanism realized in the most promising method of growing thin-film structures
was considered recently in [26]. The main idea is that the film grows in the vicinity of a
meniscus in the dispersion medium, but the formation of a regular structure is also the
result of nanocrystallization. This method rules out the manifestation of Pg forces, so that
only the surface tension of the dispersion medium acts as a macroscopic force with
respect to the particle interaction forces, which provides the constrained conditions
necessary for the nanocrystallization process.
We have obtained the separate single-crystals of opal film on the plate surface in the
case of nonequilibrium nanocrystallization (Pi >> Pm) in the vicinity of a meniscus in the
ethyl alcohol as a dispersion medium (Fig. 1a). As in the case of 3D growth of crystals,
their size depends on the degree of suspension deionization, which may be accomplished
with the help of ion-exchange resin.
a)
b)
Fig. 1. SEM images of (a) an opal film surface with a domain structure grown for Pi >Pm,
r <1, and (b) single crystal opal film grown for Pi =Pm, r >>1. The insets show the
results of two-dimensional discrete Fourier transform of the images, demonstrating the
degree of ordering of the structure. The diameter of MSSP is 280 nm.
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At the partial deionization and subsequent neutralization of the freshly prepared
alkaline (pH ≈ 10) MSSP suspension with an HCl solution and the replacement of OH–
groups by Cl– , the total counterion concentration remains high while τ is small (i.e., rχ
>>1). However, because the new NH4Cl electrolyte is indifferent rather than potential
forming, the particle charge θ decreases and, accordingly, the surface potential ϕ0
decreases down to a value of about 50 mV (at pH = 4–4.5). Then, according to Eq. (1),
the magnitude of Pi decreases to approach Pm. This state is close to equilibrium and
favors the nanocrystallization of MSSPs in the meniscus region with the formation of a
homogeneous film structure that has a long-range order and is free of domains. The
uniformity of stacking of the MSSP rows (single-crystal structure) is maintained over a
large film area (Fig. 1b). The above considerations refer to the direct interaction of
particles at small distances of about 2r when the MSSPs approach each other at these
distances in the region of nanocrystallization.
A serious problem in growing single crystal opal films is related to cracks, which
appear when the thin film nanocrystals are drying and the structure is compressed under
the action of capillary forces. This “shrinkage” is proportional to the initial distance
between MSSPs in a nanocrystal, which is equal to ~2τ. Therefore, the smaller τ, the
lower the probability of cracking; hence, the best growth conditions correspond to rχ>>1,
which takes place either in a strongly alkaline region or in the acid region with pH ~ 4.
In view of the aforesaid, nanocrystalline opal films grown on a flat substrate are
transparent, have a brilliant “varnish” appearance, and cause a bright homogeneous
diffraction of incident light. Their thickness can be controlled from 0.5 to 2–8 μm (from
2–3 to 10–15 MSSP layers) by varying the MSSP concentration in the suspension. Such a
film represents a single-crystal over the entire area, which is corroborated by scanning
electron microscopy (SEM) examination. The MSSPs in the film are stacked in
hexagonal close-packed layers corresponding to the [111] plane of the face-centered
cubic lattice (fcc) and are parallel to the substrate surface. The film surface area reaches
1–2 cm2.
Heterostructures on the base of single-crystal opal films
From the practical state point it is very important to produce the extended defects in
PhC. Such defects give rise to propagating modes lying within the forbidden PBG. These
modes are a crucial element in the development of PhCs as waveguides, resonant cavities
for low-threshold lasers, or as other photonic devices.
The controlled formation of states within the forbidden gap is to use an extended
periodicity, in the form of an optical superlattice. The general properties of such systems
were first described theoretically by Russell [27]. Examples have been experimentally
realized in one-dimensional structures, in both semiconductor multilayers and in optical
fiber gratings [28]. The fabrication of a three-dimensional optical superlattice structure
from sequential depositions of silica colloidal crystals by convective self-assembly was
obtained in [29].
We have used single-crystal opal films to fabricate the colloidal crystal
heterostructures. One of such structures made of composed of two different single-crystal
films with various diameters of MSSP. The inset in Fig. 2a shows that both of A and B
layers are planar and uniform thickness throughout the structure. The preferred vertical
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orientation of the [111] crystalline axis is preserved. The reflection spectra AB of doublelayer opal consisting of single-crystal films clearly demonstrated the presence of different
stop-bands as a consequence of stop-band superposition of individual compositional
colloidal crystals.
a)
b)
Fig. 2. Reflection spectra of opal-based heterostructure assembling from two (solid line
BA) (a) and three opal films (solid line BAB) (b). The dashed line in Fig.2a is the
calculated reflection spectra of two layer heterostructure The lines A and B in Fig.2b are
the reflection spectra of single-crystal opal films made of spheres with different diameter.
The inset in Fig. 2a shows the SEM image of a cleft edge of an artificial opal
heterostucture.
We have fabricated structures as thick as three layers BAB and ABA. The solid curve
BAB in Fig. 2b shows the normal-incidence reflection spectrum of BAB three layer
heterostructure. The two B sections consist of 16 lattice planes of a close-packed facecentered-cubic (fcc) colloidal single-crystal composed of 260-nm diameter spheres. The
middle A section is 23 planes of an fcc crystal, with sphere diameter of 235 nm.
From comparison of spectrum ВА in Fig. 2a and spectrum ВАВ in Fig. 2b it is
possible to draw a conclusion that an additional layer reinforces the long-range
periodicity of the superlattice, resulting in significant modifications to the observed stop
bands. In the three layer sample BAB as well as for structure ABA, the broad photonic
stop bands exhibit pronounced modulation. The experimental result provides convincing
evidence that the observed structure does indeed arise from superlattice effects. Thus, the
controlled formation of states within the forbidden gap has obtained due to an extended
periodicity, in the form of an optical superlattice.
LOW THRESHOLD LASING IN SINGLE-CRYSTAL FILMS AND
HETEROSTRUCTURES
We have studied the lasing from volume artificial opal, single-crystal opal films and
opal heterostructures doped with Rhodamine 6G and excited by picosecond pulses of
second harmonic of a Nd:YAG-laser. Noble opal samples with crystal sizes greater than
the beam diameter were obtained by the crystallization in suspensions of charged MSSPs.
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Structural defects inevitably present in artificial opals introduce disorder that leads to
strong scattering and random lasing [30]. In such case we have observed the appearance
of multiple emission lines. These lines laid within the region of the maximum dye gain,
are unrelated to the opal PBG and had high threshold intensity I  13-15 MW/cm2.
In contrast, the single-crystal films and three-layer opal heterostructures enable to
obtain laser emission in a relatively narrow solid angle (200) with a lower threshold
intensity of I  2,5 MW/cm2 for a single-crystal film infiltrated with Rodamin 6G and I 
0,85 MW/cm2 for an heterostructure on the base of single-crystal opal films. (see Fig. 3,
curve (1)) The heterostructures as thick as three layers BAB. The solid curve (3) in Fig. 3
shows the normal-incidence transmission spectrum of BAB three layer heterostructure.
The optical feedback in the case of single-crystal opal film lasers is provided via Bragg
scattering of light from crystallographic planes at the first pseudogap edge in the direction
of Γ-L. The two B sections provide additional optical feedback in the heterostructure
laser.
Fig. 3. Emission spectra of opal heterostructure infiltrated with Rhodamin 6G solution.
(1) Well-developed laser emission at the excitation intensity I  1 MW/cm2 (0.23 J) (see
inset) (2) Below threshold emission I  0.3 MW/cm2 spectrum shows a wide
photoluminescence band. (3) Transmittance spectrum for three-layer opal heterostructure.
NEGATIVE LIGHT DIFFRACTION AND REFRACTION AT A GLASS-OPAL
INTERFACE
We have investigated a new effect appearing in the displacement of the PBG on the
background of the spectrum of backward diffracted and reflected Bragg waves at the
grazing incident of white-light beam on the (glass - opal thin film) interface [32]. The
physical basis for observable effect is such characteristics of the PhCs as a strong angular
dispersion and the dependence of the spectral position of PBG on the type of analyte.
PhC films were grown by the movable meniscus method from the suspension of
MSSPs on a glass prism. A white light beam from a halogen lamp was incident on a face
of a glass prism and, then, on the (glass–PhC) interface. The inset in Fig.4 shows the
interaction scheme. Here, we consider refracted and reflected Bragg waves for which the
directions of tangential projections of wave vectors are opposite to the corresponding
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projection of the wave vector of the incident wave. Refracted (2) and backward reflected
(3) waves were observed after the incidence of the white light beam (1) from the glass
with the reflective index ng = 1.51 at the interface between this medium and the three
dimensional PhC film deposited on its surface.
Fig.4. Spectrum of the refracted Bragg wave with the stop band (solid line) before and
(dashed line) after the action of ammonia vapors with a density of 2 mg/m3. Inset shows
scheme of the interaction of light with the opal film PhC on the glass substrate. The
explanation is given in the main text.
It is revealed that the spectrum of the Bragg backward reflection and refraction
manifested the PBG, which changes its position under insignificant change of the
concentration of vapor of a range of substances (isopropyl alcohol, dibutyl amine, tributyl
amine, water, ammonia), filling the PhC (see Fig.4). The effect was reversible. After the
termination of action of the analyte vapor under room conditions the PBG returned to
original spectral position during 10-15 seconds. The spectral shift of the PBG depends on
the polarity of the analyte and increases with their dipole momenta and the concentration
of vapors. Specifically, we revealed that for the concentration of NH3 (2 mg/m3 the PBG
spectral shift of the diffracted light was about 8 nm.
It is well known that siloxane (Si–O–Si) and silanol (Si–OH) groups are present on
the surface of silica nanoparticles [33]. Their extremal density can reach five OH groups
per nanometer squared. The presence of a mobile hydrogen atom in polar hydroxyl
groups gives rise to the effective interaction with the molecules of the gas and liquid
phases. The estimates show that the ammonia molecular monolayer uniformly covering
the surface of the opal balls gives rise to a change in neff in ammonia vapors by Δneff ≈
0.004, which corresponds to the spectral shift of the center of the stop band by about 1
nm. However, it should be taken into account that silica balls can consist of globules and
their specific surface can be larger by an order of magnitude, which was not taken into
account in the estimates.
CONCLUSIONS
Thus, correct allowance for the mechanisms of the PhC film growth in the vicinity of
the meniscus in the dispersion medium leads to the formation of a regular structure,
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which is the result of a nanocrystallization process. Using this method, it is possible to
grow single crystal opal films of a desirable size on a flat substrate, two- and three-layer
heterostructures produced from the single-crystal films with various sizes of silica
spheres.
The lasing from artificial opal, thin single-crystal opal films and opal heterostructures
infiltrated with Rhodamine 6G is studied. In the case of volume opal, we have observed
random lasing. In contrast to this case, single-crystal opal films show lasing caused by
distributed feedback inside PBG structure.
The revealed effect of the spectral shift of the stop band of PhCs against the
chromatic refraction background is well described by the Bragg refraction and the
reflection of waves at the (glass–PhC) interface. At the same time, the observed effect of
the shift of the stop band of PhCs with respect to the unchanged angular spectrum under a
small change in the refractive index of the medium filling space between the PhC balls
can be used in the schemes of optical sensors, as well as for controlling the spectrum of
refracted and reflected light in an optical demultiplexer by an external field.
I am grateful to D.V. Kalinin, V.V. Serdobintseva, A.S.Kuch’yanov, and A.A.
Zabolotskii for collaboration.
This work was supported by the Siberian Branch, Russian Academy of Sciences
(interdisciplinary integration project no. 17) and by the Branch of Physical Sciences,
Russian Academy of Sciences (project no. 8, Basic Research Program).
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