Synthesis and photonic band gap characterization of polymer inverse opals

From a practical point of
view the polymer infiltration in opals, whether silica or otherwise, is
relatively easy and efficient. Host matrices are also easily removed by means
of either a chemical attack or optically induced degradation, both procedures
being highly selective. In this fashion an exact replica of the starting
material can be obtained.

Even though the dielectric
contrast in empty inverse opals is not very high (epolymer/eair=2.5 or
thereabouts) it is higher than that of bare silica opals (esilica/eair=2.1). This
is not the only advantage inasmuch as, the topology being inverse, the filling
ratio for the scattering material is low (f=0.26) as required to enhance the
photonic band gap properties. Other properties, inherent to polymers in general,
such as their eventual elasticity, add to the wealth of possible applications
of these systems. A precise and controlled variation of the optical signatures
of these inverse opals can be achieved by the application of strain to the
structure as was demonstrated on latex direct opals. Strong modifications of
dye emission have been observed in these sort of systems when dyes are embedded
in the photonic structure. From a fundamental point of view these systems are
interesting since they permit, as shown here, the analysis and direct
comparison of the effects of topology and index contrast in photonic crystals
for the visible and near infrared. Actually, they have already been used to
analyse the dependence of the diffraction properties on the crystal thickness.

Figure 1. Polymer infiltrated opal viewed under the SEM. Images of internal
{111} type facets with a higher magnification inset of the same kind of face
after polishing.

The polymer infiltrated is obtained by polymerization of an epoxy resin in the
presence of catalizer. In this way a viscous fluid is obtained in which the
opals is immersed. The liquid soaks the opal and when the diffusion is total the
opal turns transparent as a consequence of partial index matching between silica
and polymer. In about 12 hours polymerization completes and the shrinkage
between the liquid and the solid is less than 5%. This allows a good filling and
a very good connection of the infiltrated material. The polymer refractive index
was measured by the prism minimum deviation angle and resulted to be n=1.609±0.005.

Once the sample is embedded and the polymer solid, the block is cut and polished
till the original outer facet of the opal is brought to the surface of the
block. The same is done on the rear surface to finally obtain a sample about 200
thick. The polishing is done with alumina powder down to 0.05 mm roughness.
Fig. 1 shows scanning electron microscope (SEM) images of cleft edges of a
sample in this stage of production. The composite regular structure can be seen
where some of the silica spheres were detached on cleaving. The inset shows a
detail of the surface after polishing. Where the sphere is missing the windows
connecting neighbouring voids can be appreciated. Some spheres are sectioned on
polishing revealing its internal structure which tells about the processes of
growth. The number of shells indicates the number of regrowth processes.


Figure 2. SEM image of a polymer inverse opal
revealing the perfection of the replication process. The inset shows a detail of
one cavity where the channels (a) communicating with the spheres in same layer
and those three (b) communicating with the underlying layer can be seen.

Finally the silica is removed from the composite material by means of a 1 wt %
HF aqueous solution. It was found that 12 hours in this solution completely
dissolves the silica leaving a neat inverse polymer opal. The polymer is not
affected by the silica etching. The necks connecting the silica spheres
(resulting from the sintering process) act as channels through which the etchant
flows. The good connectivity provided by the sintering allows it to reach the
whole structure and fully etch away the silica skeleton. Fig. 2 shows and
example of the resultant structure after the etching has been performed. The
internal {111} type planes are identified by the symmetry and the quality of the
replica can be appreciated in the cleaved edges. The inset displays the
structure of these channels, that for the (111) facet are three in number,
connecting the layer underneath plus six connecting the surrounding spheres. Of
course, the latter six can only be seen in sections through the equatorial plane
of the spheres. It is worth mentioning here that all the silica disappears in
the etching process none being left in the whole structure. The perfection of
this structure is enticing as far as its use as template for the growth of fine
monodisperse spherical particles is concerned. Some materials can be grown
herein that otherwise would not grow in this shape due to its crystallinity.

Important optical changes due to the infiltration and subsequent inversion can
be appreciated even by naked eye. In Fig. 3 near normal incidence reflection and
transmission images are displayed. The chief feature to be observed is the blue
shift of the reflected colour that will be explained next.

For the optical characterisation of the different stages of inverse opal
synthesis we have employed both reflectance and transmission spectroscopy. The
samples are always oriented with its (111) direction on the optical axis so that
the reflection observed corresponds to light k-vectors crossing
the Brillouin zone boundaries in the vicinity of the L point.

example can be seen in Fig. 4 where both transmission and angle integrated
reflectance are plotted for three opals of 390 nm spheres. The doted line
corresponds to the bare opal (74% silica, 26% air); the dashed line to the fully
infiltrated opal (74% silica, 26% polymer) and the solid line to the inverse
opal (74% air, 26% polymer). It can be readily seen that both the attenuation
and the diffuse reflection increase as the dielectric contrast does and the
filling fraction of the higher refractive index component decreases. This
accounts for the reduction in attenuation and reflectance attained when the bare
opal is filled with polymer since the dielectric constants of polymer and silica
are closer than those of silica and air. On this line of reasoning the increase
in scattering observed on inversion is due to the enhanced contrast between
polymer and air. The propagation along different crystalline directions were
also studied. Transmission experiments at different incidence angles with
respect to the (111) planes were performed.

Figure 3. Reflection (upper) and transmission
(lower) images obtained with an optical microscope of 500 × 200 mm2 regions of
an opal made of 230 nm spheres prior (left) and after (right) infiltration and

The optical properties, as far as positions and widths of the pseudogaps are
concerned, can be accounted for by photonic band calculations. Theory and
experiments are summarized in Fig. 5 for a sample of 390 nm sphere diameter. In
the left panel of Fig. 5 experimental reflectance spectra obtained at normal
incidence with respect to the (111) planes are shown for the three systems
(dotted line for the bare opal; dashed lines for the polymer-silica composite
and solid lines for the polymer inverse opal). The centre panel plots, with the
same convention, those bands that lie in the corresponding direction, G-L. The
agreement theory-experiment is fairly good not only regarding positions but also
widths. Finally, in the right hand side panel, we have plotted the energy of the
reflection peak on top of the bands along the L-U path as a function of the
internal angle measured with respect to the L direction. Here squares, diamonds
and circles stand for reflectance peak position as the sample is tilted off the
(111) direction for bare opal, composite and inverse structure respectively. In
view of the fact that the photonic band structure is rather isotropic around the
L point, we have chosen the L-U direction as representative of the behaviour of
energy bands, the points W and K being very much the same as U. Inspection of
the energy diagram around the L point reveals that states near those points are
very similar irrespective of their particular wavevector.

4. Transmission (A) and angle integrated reflectance (B) from a 390 nm sphere
opal before (dotted line), after infiltration (dashed line) and after inversion
(solid line).

Since the underlying structure is unchanged upon infilling or inversion the
lattice parameter remains the same and, as a consequence, the energy position of
the L pseudogap is, fundamentally, determined by the average dielectric
constant. This explains the relative positions in Fig. 5. For the bare opal the
average dielectric constant áeñ
= 1.94 that grows to áeñ
= 2.22 in the infiltrated one (reducing the contrast at the same time). Under
inversion the mean dielectric constant decreases to áeñ = 1.41 and,
accordingly, the L pseudogap energy shifts upwards (see Fig. 5).

Peak width is a function of both the dielectric contrast and the filling factor
of the structure. Bare opals present a contrast eSiO2/
which shifts to epolymer/
=1.24 when infiltration takes place. So, the pseudogap width is largely
decreased, as is observed in both the experiment and band structure calculation.
When inversion occurs, contrast is increased up to epolymer/
It has to be noticed that, although bare and inverse opal have similar values of
the refractive index contrast, inverse opals show a much broader pseudogap than
the direct opal structure which reflects the fact that inverse structures are
more powerful scatterers. (see Fig. 5(A))

Figure 5.(A) Experimental reflectance spectra.
Dotted, dashed and solid lines correspond to the bare, composite and inverse
opals respectively. The diffuse background has been subtracted and the intensity
normalized to its maximum. (B) Calculated band diagrams along G-L direction for
the bare, the infiltrated and the inverse opal. Different line types have the
same meaning as in (A). (C) Band diagram for L-U path together with the
experimental pseudogap centre represented as symbols (see text).

When the sample is tilted with respect to normal incidence, the k vector ceases
to be collinear with G-L.
For a given direction (tilt angle) at some point of the energy scan, k
crosses the Bragg plane and a reflection is obtained. Since L is the closest
(to G)
point of the Bragg plane, tilting increases both the wavevector length and the
energy for which reflection occurs. This pseudogap energy position, can be
followed along the L-U (or L-K or L-W) line in the Brillouin zone. In Fig. 5 (C)
experimental data are superimposed on the band structure diagram by using Snell
law with an average refractive index for calculating the internal angle (with
respect to the G-L
direction). The theory gives a good account of the behaviour of the pseudogap