Functional Properties of Photonic Crystals on 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 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.
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 t and form with this layer a structural unit (SU) for nanocrystallization [21–24]. The value of t depends on the total electrolyte concentration in the suspension expressed through the Debye parameter c as t = 1/c. 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 c is a key parameter of the particle interaction and nanocrystallization (this ratio is more conveniently expressed as the product c 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:
(1)
(2)
, (3)
where A is the Hamaker constant, e is the permittivity of the dispersion medium (water, ethyl alcohol, diethyl ether, acetone, etc.), and jo is the surface potential [23], q 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, cr > 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, rc <1, and (b) single crystal opal film grown for Pi =Pm, rc >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 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 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 B sections consist of 16 lattice planes of a close-packed face-centered-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. 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.