Electrically switchable photonic crystals are simply and rapidly formed by holographic polymerization-induced phase separation of liquid crystal from a monomer-liquid crystal mixture. We report the fabrication and electro-optical properties of liquid-crystal-filled polymer photonic crystals of orthorhombic F symmetry. Inverse opal and fcc structures can also be obtained. The crystals exhibit electrically switchable Bragg diffraction at ~8–10 V/μm with crystal structure in good agreement with theoretical expectations. These photonic crystals compare favorably with liquid-crystal-imbibed colloidal crystal arrays.
© 2002 Optical Society of America
Photonic crystals (PCs) have generated much interest from the points of view of both fundamental physics and practical applications . The periodic lattice of a PC is formed from a composite material, typically air and a high dielectric material, e.g., close-packed silica or polystyrene spheres with air gaps in the interstitial volume . This is known as the opal structure. An inverse opal structure, such as spherical air inclusions in silicon, makes a much more efficient scattering system exhibiting a complete photonic band gap (photon density-of-states equals zero) . Applications requiring some degree of tunability of the band gap have led to the consideration of filling or partially filling the air voids in a PC with liquid crystal (LC), forming pseudo gaps under certain circumstances . The photonic band structure could then be modulated either thermally or by applying an electric field, potentially yielding an electro-optic shutter by opening a complete three-dimensional (3D) photonic band gap.
Opal or inverse opal structures in silicon are difficult to make. Therefore, synthetic opals made with silica spheres and imbided with LC have been studied. Colloidal crystals are formed by slow sedimentation of sub-micrometer size spheres in water. The composition is then dried and imbibed with LC. Although these structures do not exhibit a complete band gap, thermal and electric field modulation of pseudo gaps has been demonstrated [5,6]. A LC-filled inverse opal has also been studied . These are interesting systems for studying the nature of LC-filled photonic crystals, but they are time consuming to fabricate and invariably suffer from several defects when the colloidal crystal is dried.
To facilitate these types of studies, a simple fabrication technique is desired that yields high quality PCs with few defects. We recently fabricated switchable PCs of orthorhombic P symmetry by holographic polymerization-induced phase separation of LC from a monomer-LC mixture . In that procedure three pairs of mutually incoherent laser beams were used to record three orthogonal gratings. Here we present a study of a simpler technique using only four mutually coherent beams in a simple two-prism geometry for fabricating switchable PCs having orthorhombic F or fcc lattices. Compared to colloidal crystals, our method greatly simplifies the formation of LC-filled PCs having structures analogous to opal or inverse opal configurations, as the polymer PC formation and LC filling occur simultaneously in a single step. It takes only a few seconds to fabricate a sample. The process is also interesting in its own right for the study of liquid crystal-polymer phase separation in well-controlled 3D patterns.
2. Holographic methods and photonic crystals
Previous work has established the principle of recording electrically switchable 1D volume holograms in photopolymer-LC mixtures [9,10]. These holograms exhibit well known Bragg diffraction of light in both transmission and reflection gratings typical of volume holograms in polymers and other media. The gratings in this case, however, consist of small LC droplets dispersed in periodic channels within solid polymer. Although LC droplets condense in well defined 1D periodic arrays, their spatial distribution within the grating planes is random. Conventionally, 1D holograms are recorded by the interference of two coherent beams in a photosensitive medium. Recently, we generalized this concept to the simultaneous recording of three orthogonal gratings using three mutually incoherent pairs of laser beams, each pair being coherent . In this case, a spatially ordered 3D array of individual LC droplets in solid polymer is produced with a structure that is analogous to an orthorhombic P crystal, confirmed by Bragg diffraction measurements as well as atomic force and scanning electron microscope images. In the limit of equal lattice constants, this is the familiar simple cubic (sc) structure. In other words, the 3D intensity pattern has forced a spatial ordering of phase-separated LC droplets in all three dimensions.
Campbell et al. have reported the holographic fabrication of photonic crystals in photopolymers using a four-beam technique . They have established the relationship of the reciprocal lattice vectors of a photonic crystal with linear combinations of the laser wave vectors used in the holographic process. For example, various combinations of four laser beams yield wave vector combinations that are identical with bcc reciprocal lattice vectors. The corresponding intensity pattern in real space is then a fcc lattice, which in their case produced a fcc lattice of polymer “atoms” connected by polymer “bonds” and surrounded by air voids . Cai et al. have recently shown that all 14 Bravais lattices can be formed by the interference of four noncoplanar beams . Here we show how to apply this technique to holographic polymerization-induced phase separation of liquid crystal to obtain LC-filled polymer photonic crystals, i.e., the air voids of the Campbell et al. structures are replaced with liquid crystal. This accomplishes in a single step the goal of LC-filled photonic crystals others have achieved by more complex methods using colloidal crystal arrays [5–7].
X-ray diffraction has long been used to study the structure of crystals in solid state physics . Kogelnik established the relation of Bragg diffraction of light in thick holographic gratings to the dynamical theory of X-ray diffraction in solids . The work of Campbell et al. has closed the loop on this by making photonic crystals using 3D holography. Bragg diffraction of light in these structures is analogous to X-ray diffraction in ordinary crystals. Thus, we use the term “photonic crystals” in the sense of being a regular periodic array of optical scatterers having lattice constants comparable with the wavelength of visible or near infrared light. Depending on the strength of the optical scattering, the structure can yield photonic band gaps or psuedo gaps [3,4]. The electro-optical modification of psuedo gaps has been the object of study with LC-filled colloidal crystal arrays [5–7]. Here we show that similar results are obtainable with periodic arrays of LC droplets in polymer formed by holographic polymerization-induced phase separation of liquid crystal.
3. Experimental method and holographic crystal formation
The basic experimental configuration is illustrated schematically in Fig. 1. A sample is sandwiched between two 45–45–90 prisms with their apexes orthogonal to one another. Two horizontally spaced laser beams are incident on the vertically oriented prism, while two vertically spaced beams are incident on the other prism. A 3D perspective of the configuration is given in Fig. 1a. Details of the recording geometry can be seen in Fig. 1b. Two combinations of beam polarization are included in this study. In one, all incident beams are polarized along y. This is called the sp configuration since one set of beams is s-polarized while the other is p-polarized. In the second set, the beams on the left in Fig. 1b are polarized along x while the beams on the right remain polarized along y. This is called the pp configuration. A variety of other combinations are possible, but these are the simplest from an experimental point of view. The beams are incident at an angle θi with respect to the normal to the prism faces, then cross the z axis at an angle θ.
The detailed experimental setup is illustrated in Fig. 2. The stable, Gaussian TEM00 output beam from a frequency-doubled, diode-pumped Nd:YVO4 laser is focused through a 25-μm pinhole by a 10× objective, expanded to a 3.8-cm (FW1/e2M) diameter, and collimated using a 2-inch (5-cm) achromatic lens. It is then passed through a 1-cm aperture to yield a collimated optical beam with <15% variation of intensity across the beam. From our experience, the photocuring process in our hologram recipe is relatively insensitive to this amount of beam intensity variation. We estimate the diffraction-limited beam divergence (for a Gaussian beam) to be ~10 μrad. Although the achromats are designed to eliminate spherical aberration, any imperfections in the design can lead to increased beam divergence. Thus, we collimated the beams by observing the output of a shear-plate interferometer placed near the sample position. The resolution of the shear plate is 75 μrad. Hence, the beams are collimated to within an error of Δθ~75 μrad. Divergent or convergent beams will produce a chirp in the interference pattern across the sample. Along the z axis the chirp is ~Λ(Δθ)2 while along the x or y axis it is ~ΛΔθ, where Λ is a typical fringe spacing. We thus expect the chirp to be negligible. No evidence of chirp was seen in the data.
The prisms in our setup facilitate coupling of the beams to the sample, particularly for a large angle of incidence θ on the sample (see Fig. 1). Note that all four beams must be present simultaneously to produce the 3D interference patterns discussed below. At the sample, the beam-diameter-to-sample-thickness ratio is ~103, while the beam-diameter-to-lattice-constant ratio is ~105. As long as the sample thickness is small compared to the region of beam overlap, the intensity pattern in the sample will be uniform. Sample thickness is typically ~10 μm, but can be as large as 25 μm. Thicker samples are difficult to record, and the switching voltage generally becomes prohibitive.
The recipe for our prepolymer syrup is similar to that reported previously [9,10]. It consists of a penta acrylate monomer (Aldrich Chemical Company) at 50% by weight, Rose Bengal dye (Spectra Group) as the initiator (0.6 wt-%), and N-phenylglycine (Aldrich) as the coinitiator (1.9 wt-%). N-vinylpyrrolidinone (Aldrich) is added at 10 wt-% to increase solubility and homogenize the components in the formulation. Octanoic acid (Aldrich, 6 wt-%) is added to increase sample conductivity and facilitate more favorable phase separation. The liquid crystal is TL213 (Merck) at a concentration of 31.5% by weight. The syrup is sonicated for 30 minutes at 32 °C and subsequently sandwiched between two ITO-coated glass slides using precision glass fiber spacers. Typical sample thickness is 8–10 μm. The beams are derived from a frequency-doubled cw Nd:YVO4 laser (532 nm). A single shutter controls the experiment, and the total exposure time is 20 seconds.
Following a nomenclature similar to that of Campbell et al. , we write the intensity pattern in the recording volume as
where G mn (m,n = 0…3) are reciprocal lattice vectors given by G mn = k m - k n, and the wave vectors k m are defined in Fig. 1b. There are a total of six vectors; three can be selected to form the basis of the reciprocal lattice, while the other three are linear combinations of the basis vectors. We choose the basis vectors to be -G 03, G 02, and G 13. These become the basis of a bcc reciprocal lattice when θ = tan-1 (2). The reciprocal basis vectors form equal angles θG = tan-1(2-1/2tanθ) with respect to the z axis. The basis vectors of the crystal lattice are determined to be a′ = (a/2)(x̂ + ŷ), b′ = (a/2)(ŷ + ½tanθẑ), c′ = (a/2)(x̂ + ½tanθẑ), where a = λ/nsinθ is the dimension of the conventional unit cube , λ is the recording wavelength, and n is the refractive index. The structure factors are given by Smn = ê m ∙ ê n, where ê m is the unit polarization vector of the m-th beam. For the sp configuration, S 01 = 1, S 02 = S 03 = S 12 = S 13 = cosθ, S 23 = cos2θ - sin2θ. The pp configuration has a more symmetric form, yielding S 01 = S 23 = cos2θ - sin2θ while -S 02 = S 03 = S 12= -S 13= sin2θ.
We give some examples in Fig. 3 of the intensity patterns generated by Eq. (1). The xy plane is tilted in perspective to aid viewing the intensity peaks and valleys. We emphasize that these plots are made for comparison and are not all drawn to the same scale. Figure 3a represents the case of sp polarization configuration, with θi= 45° and θ = 17.28°, and shows the intensity pattern in the base plane (z = 0). Figure 3b gives the pattern in the plane at z = (a/4)tanθ, illustrating the orthorhombic F symmetry. The pattern repeats itself at increments of (a/2)tanθ along the z axis. This structure is analogous to the fcc lattice in colloidal crystals [5,6], becoming fcc when θ = tan-1 (2). Polymerization is favored at regions of peak intensity, and monomer diffuses to bright regions to replace consumed monomers. LC molecules are excluded by chemical potential forces and diffuse to the dark areas. Hence the low intensity regions appear to act as potential wells that attract LC molecules. At a critical concentration the miscibility gap is breached and the LC separates as a distinct phase. For Figs. 3a and 3b, this would be in the interstitial volume of the crystal. Note that the PC structure can be easily visualized, with LC droplets situated in the dark regions and polymer forming in the bright regions.
Figure 3c illustrates an interesting case for the pp configuration with θi= 14.9° and θ = tan-1 (2-1/2). Under this condition all the structure factors have equal magnitude. Note that this yields the inverse structure of that shown in Fig. 3a, which would give a polymer backbone with LC droplets in the symmetric “potential wells” of the lattice. This is analogous to the inverse opal structure [3,7]. Figure 3d (pp) gives the pattern obtained with θi= 0° (θ = 45°). In this case a binary lattice appears to form, one of polymer and one of LC droplets in the symmetric “potential wells”. For sp configurations (Fig. 3a, and particularly for a fcc lattice, not shown), the intensity peaks are broader and more asymmetric, and the valleys have a bowtie shape.
4. Results and discussion
We show in Fig. 4 the results of a sample recorded according to the geometry specified for Fig. 3a. The lattice constants for this PC are theoretically a′ = 833 nm and b′ = c′ = 596 nm. White light is incident along the z axis, forming four symmetrically spaced green diffraction spots as shown in the photograph of Fig. 4a. Light will diffract in directions and at the wavelength determined by the Bragg condition,
where k d, k i are the diffracted and incident wave vectors, respectively, and G is a reciprocal lattice vector. The reciprocal lattice vectors are plotted in Fig. 4b along with the wave vectors that satisfy the Bragg condition. The wave vectors form equal azimuth angles (45°) in the four quadrants and equal polar angles of θd = 2θG = 24.8°. This corresponds to an external angle (after refraction) of 39.6°, in close agreement to 38° measured experimentally. We calculate the diffracted wavelength to be λd = 531 nm, which agrees well with the experimental value of 524 nm. Normally there is a small blueshift due to polymer shrinkage, which in this case amounts to 1.3%.
We show a scanning electron micrograph (SEM) of this sample in Fig. 5. Figure 5a gives a 3D perspective, illustrating cleavage planes. Figure 5b is a top view of the crystal and reveals the close packing structure. The arrow gives the  direction. The small holes near the corners of the square polymer regions comprise the interstitial volume where LC would reside. From this SEM we estimate a′ = 765 nm, which is about 8% shorter than expected theoretically. However, there is ~10% contraction of the sample when the LC is extracted for SEM analysis . Consequently, this estimate is in good agreement with the theoretical value.
We studied the electro-optical behavior of these PCs by applying an electric field along the z axis and observing the light back-scattered from the (111) planes. We direct s-polarized white light at a small angle with respect to the  direction and collect the Bragg diffracted light with an optical fiber that is coupled to an Ocean Optics spectrometer . The spectrometer measures reflection in counts. We have calibrated the system in the transmission mode, and the peak reflectance at zero volts (2835 counts) corresponds to a diffraction efficiency of approximately 10%. This is comparable to the efficiencies reported for liquid-crystal-filled colloidal crystals [5,6]. The diffracted light spectrum is measured as a function of the amplitude of a bipolar 2-kHz square-wave voltage. Results for an orthorhombic F PC recorded with θi = 0° (θ = 45°) are shown in Fig. 6. The geometry of the experiment is shown as an inset to Fig. 6. As can be seen, a field of 8–10 V/μm closes the band gap completely. For sufficiently large field strength, the LC molecules will align with the z axis, a direction perpendicular to the optical polarization which is in the xy plane. The optical field then sees a refractive index for the LC droplets that is approximately equal to the ordinary refractive index of the bulk LC, which is closely matched to the polymer index. Hence the scattering from the (111) planes is minimized.
The theoretical lattice constants for this PC are a′ = 350 nm and b′ = c′= 277 nm. This yields a value of θG = tan-1(2-1/2) = 35.26° for the reciprocal lattice basis vectors. The expected Bragg wavelength for the small angle of incidence (4.25°) in our experiment is 613 nm, whereas the peak diffracted wavelength measured at zero field is 588 nm. This amounts to a blueshift of about 4%.
As noted in previous work , these photonic crystal samples exhibit excellent electro-optical stability when stored at room temperature for several months after recording, yielding consistent diffraction efficiency and switching curves. No appreciable change in diffraction efficiency with temperature is observed until about 40 °C. As in all acrylate polymers, there is an initial creep in the switching voltage that stabilizes after about 48 hours. The switching voltage increases by about 50% over this period. Current research is focused on recipes incorporating monomers that eliminate this voltage creep. Environmental stress tests of 1D reflection gratings, made with the same recipe as reported here, have shown that samples are fairly robust. Although shrinkage is always present in photopolymers, after annealing, samples exhibited a blue shift of the Bragg diffraction peak of only ~2% after 2000 hours of heating at 85 °C. Diffraction efficiency (measured at room temperature) changed at most by ~4% after 2000 hours at 85 °C, and typically <1% under other more benign conditions. For samples experiencing continuous switching at room temperature for 500 hours, Bragg wavelength, diffraction efficiency, and switching voltage all remained constant. Although diffraction efficiency in these photonic crystal samples is relatively low, diffraction efficiency can exceed 70% in 1D reflection gratings and 90% in 1D transmission gratings. Clearly, to be viable for applications, methods to increase phase separation in 3D samples must be developed. This is an area of ongoing research.
In the theoretical analysis of LC photonic band gap materials by Busch and John , silicon (n = 3.4) was considered for the backbone material of an inverse opal structure, with a total volume fraction of 24.5%. This leaves a 75.5% volume fraction of air voids that is available for filling with LC. In our material n = 1.52, and the total volume fraction of phase-separated LC is about 30%. Consequently, one cannot expect to achieve a complete photonic band gap with present LC-polymer composites (note the relatively low diffraction efficiency). However, the results compare favorably with systems consisting of colloidal crystalline arrays imbibed with LC [5–7]. Hence, the holographic LC-polymer composites make attractive alternatives for studying the properties of these types of PC, due to their fabrication simplicity and the wide variety of lattice constants, lattice types , and structure factors which can be readily obtained. Current research is focused on achieving wider stop bands by obtaining higher volume fraction phase-separated LC in other types of polymers with different refractive indices.
We have demonstrated a simple and rapid method for fabricating switchable photonic crystals of orthorhombic F symmetry. The technique exploits holographic polymerization-induced phase separation of liquid crystal from a monomer-liquid crystal mixture. LC molecules naturally diffuse to minima in the 3D intensity pattern. The crystals exhibit Bragg diffraction and can be switched with an electric field of ~8–10 V/μm. Inverse opal structures and fcc lattices can theoretically be obtained by simply adjusting beam polarization and angles of incidence. The resulting structures compare favorably with colloidal crystals imbibed with LC. They therefore make interesting prototypes for the study of tunable band gap photonic crystals.
This research is supported by a contract with the U.S. Air Force. The work was performed at the Materials and Manufacturing Directorate of the Air Force Research Laboratory (AFRL/MLPJ), Wright-Patterson Air Force Base, Ohio.
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