Functional Properties of Photonic Crystalson the Basis of Single-Crystal 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 photoniccrystal 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 heterostructuresopal 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.
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 potential-forming 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 , 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 Uiof 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:
(1)
(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 structureswas 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 (PiPm) 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 PiPm, 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.
At the partial deionization and subsequent neutralizationof the freshly prepared alkaline (pH≈10) MSSPsuspension with an HCl solution and the replacement ofOH–groups by Cl–, the total counterion concentrationremains high whileτis small (i.e.,rχ>1). However,because the new NH4Cl electrolyte is indifferent ratherthan potential forming, the particle chargeθdecreasesand, accordingly, the surface potentialϕ0decreasesdown to a value of about50 mV (at pH =4–4.5). Then, according to Eq. (1), themagnitude ofPidecreases to approach Pm. This state isclose to equilibrium and favors the nanocrystallizationof MSSPs in the meniscus region with the formation ofa homogeneous film structure that has a long-rangeorder and is free of domains. The uniformity of stackingof the MSSP rows (single-crystal structure) is maintainedover a large film area (Fig. 1b). The above considerationsrefer to the direct interaction of particles atsmall distances of about 2r when the MSSPs approacheach 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 orientation of the [111] crystalline axis is preserved. The reflection spectra AB of double-layer 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 Bsections consist of 16 lattice planes of a close-packed face-centered-cubic (fcc) colloidal single-crystal composed of 260-nm diameter spheres. The middle Asection is 23planes of an fcc crystal, with sphere diameter of 235 nm.
From comparison of spectrumВАin Fig. 2a and spectrum ВАВin 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. 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 I1 MW/cm2 (0.23 J)(see inset) (2) Below threshold emission I0.3 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 anew effect appearing in the displacement of the PBG on the background of the spectrumof backward diffracted and reflected Bragg waves at the grazing incident of white-lightbeam on the (glass - opal thin film) interface [32]. The physical basis for observable effect issuch characteristics of the PhCs as a strong angular dispersion and the dependence of thespectral position of PBG on the type of analyte.
PhC films were grown by the movable meniscus methodfrom 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 reflectedBragg waves for which the directions of tangential projections of wave vectors are opposite to the corresponding projection of the wave vector of the incidentwave. Refracted (2) and backward reflected (3) waveswere observed after the incidence of the white lightbeam (1) from the glass with the reflective index ng=1.51 at the interface between this medium and thethreedimensional PhC film deposited onits surface.
Fig.4. Spectrum of the refracted Bragg wave with the stopband (solid line) before and (dashed line) after the actionof ammonia vapors with a density of 2 mg/m3. Inset shows scheme of the interaction of light with the opal filmPhC on the glass substrate. The explanation is given in the main text.
It is revealed that the spectrum of the Bragg backward reflection and refractionmanifested the PBG, which changes its position under insignificant change of the concentrationof vapor of a range of substances (isopropyl alcohol, dibutylamine, tributylamine, water,ammonia), filling the PhC (see Fig.4). Theeffect was reversible. After the termination of action of theanalyte vapor under room conditions the PBG returned to original spectral position during10-15 seconds. The spectral shift of the PBG depends on the polarity of the analyte andincreases with their dipole momenta and the concentration of vapors. Specifically, werevealed 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 ofthe center of the stop band by about 1 nm. However, itshould be taken into account that silica balls can consist of globulesand their specific surface can belarger by an order of magnitude, which was not takeninto 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, 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 thestop band of PhCs against the chromaticrefraction background is well described by the Braggrefraction and the reflection of waves at the (glass–PhC) interface. At the same time, the observed effectof the shift of the stop band of PhCs withrespect to the unchanged angular spectrum under asmall change in the refractive index of the medium filling space between the PhC balls can beused in the schemes of optical sensors, as well as forcontrolling the spectrum of refracted and reflectedlight in an optical demultiplexer by an external field.