25th anniversary article: ordered polymer structures for the engineering of photons and phonons

Abstract

The engineering of optical and acoustic material functionalities via construction of ordered local and global architectures on various length scales commensurate with and well below the characteristic length scales of photons and phonons in the material is an indispensable and powerful means to develop novel materials. In the current mature status of photonics, polymers hold a pivotal role in various application areas such as light-emission, sensing, energy, and displays, with exclusive advantages despite their relatively low dielectric constants. Moreover, in the nascent field of phononics, polymers are expected to be a superior material platform due to the ability for readily fabricated complex polymer structures possessing a wide range of mechanical behaviors, complete phononic bandgaps, and resonant architectures. In this review, polymer-centric photonic and phononic crystals and metamaterials are highlighted, and basic concepts, fabrication techniques, selected functional polymers, applications, and emerging ideas are introduced.

Keywords: metamaterial; phononic crystal; photonic crystal; polymers.

Figure 1

The versatility, flexibility, and multi-functionality of a periodic polymer/fluid structure is illustrated. The functional polymer represented by a double-gyroid structure (red, blue networks) is simultaneously interacting with phonon (Ω) and photon (ω) waves while the material's interaction parameters (periodicity, dielectric constant, impedance, etc.) continuously respond to a broad range of physical and chemical stimuli, resulting in tunable photonic and phononic behavior.

Figure 2

(a) Annual photonic crystal research papers produced by different disciplines. (b) Annual photonic crystal research papers featuring lasers, sensors, and solar applications. (c) Annual research papers on phononic crystals and acoustic metamaterials. Note the factor of 10 difference in scale compared to figures (a) and (b). Data from Web of Knowledge, ISI.

Figure 3

(a1) The 2D photonic band diagram of a typical polymeric solid having a permittivity of with embedded air cylinders in a square lattice. The air cylinders have a radius , where is the lattice constant of the structure (inset). The partial PBG for TE-polarization is shown in red for the Γ−X and the Γ−M directions, respectively. (a2) The 2D photonic band diagram of the same structure with a higher permittivity of exhibiting a PBG for TM-polarized waves and for TE-polarized waves. However, since the TE and TM gaps do not overlap, there is no polarization-independent complete gap. (a3) The 2D photonic band diagram in (a2) is folded along the boundary of the irreducible BZ. (b) The phononic band diagram of the same structure with typical polymer solid density of = 1190 kg m⁻³, transverse sound speed = 1800 m/s, and longitudinal sound speed = 3100 m/s, respectively, for in-plane (solid lines) and out-of-plane (dashed lines) elastic waves.

Figure 4

(a) Schematic of double exposure PMIL and a scanning electron microscope (SEM) image of a fabricated woodpile structure. Reproduced with permission. Copyright 2010, American Vacuum Society. (b) Schematic of dip-in 3D-DW and SEM images of patterned 200 μm tall negative Poisson ratio structure. Reproduced with permission. (c) Schematic of a combinatory approach (IL + FLaSk DW). SEM (top) and optical (bottom) images of a fabricated hierarchical photonic structure containing 3D-DW designer waveguide defects. Reproduced with permission. Copyright 2011, The Royal Society of Chemistry.

Figure 5

(a) SEM images of two-layer graphoepitaxy structure of a cylindrical BCP thin film revealed by etching. Order is controlled in both layers independently by the positioning of photoresist pillars (visible as bright dots) previously patterned by e-beam DW. Reproduced with permission. Copyright 2012, American Association for the Advancement of Science (AAAS). (b) Transmission electron microscope (TEM) image of a section of a thick film (>1 mm) of lamellar BCP perpendicular to an applied in-plane external magnetic field is shown with small-angle X-ray scattering data (left). Hexagonally-packed cylindrical BCP aligned along the magnetic field directed normal to the film with fast Fourier transform (FFT) data (inset right). Reproduced with permission. Copyright 2011, American Chemical Society.

Figure 6

(a) Solid core polymer fiber preform and a resultant PhC fiber showing different colors of leaky light. Reproduced with permission. Copyright 2008, Optical Society of America. (b) Electrospun fiber of bulk double gyroid BCP microdomains demonstrating through both simulations and TEM images the ability for the cylindrical confinement to induce new microphase morphologies. Reproduced with permission. Copyright 2010, American Chemical Society.

Figure 7

(a) Schematic of the director patterns in LC-polymer films fabricated with tangential and radial alignments. The red arrows show heat-induced deformation directions. (b) Heating of the film by IR absorption causes reversible out of plane deformation dependent on the mesogen alignment. Photographs show actual LC-polymer films deformed under IR irradiation. Reproduced with permission.

Figure 8

Structural colors from PhCs made of polymeric materials. (a) A decorative bow made of multilayer polymer film. (b) Light transport tubes made of giant birefringent multilayer polymer film are superior to those made of aluminum and silver mirrors. Reproduced with permission. Copyright 2000, American Association for the Advancement of Science.

Figure 9

(a) Projected photonic band structure of a 1D PhC made of PS (n₁ = 1.6) and tellurium (n₂ = 4.6) layers with a thicknesses ratio of d₁/d₂ = 2. The red lines are the light lines having a slope corresponding to the speed of light in air. Reproduced with permission. Copyright 1998, American Association for the Advancement of Science. (b) 2D plot of calculated reflectance spectra of a PhC consisting of 10 pairs of PS and tellurium layers with thicknesses of 1.0 μm and 0.5 μm, respectively for TE- and TM-polarizations as a function of the incident angle from air. The grey scale indicates the value of the reflectivity (white = 100% reflection). The relatively low reflectivity of TM-polarized light for incident angles ranging from 60 to 80° is due to the Brewster angle effect. (c) Reflectance spectra of 20 pairs of dielectric layers calculated by transfer matrix method as a function of refractive index ratios with a fixed thickness of 100 nm for each layer. (d) The peak reflectivity vs. the ratio between high and low refractive indices is plotted for several different numbers of pairs of high and low refractive index layers.

Figure 10

(a) A 3D PhC comprised of close packed spheres (the opal structure). A cubic lattice is represented by a red box. (b) Wigner-Seitz cell of the fcc latice showing the BZ boundaries. Two paths of wavevectors are represented in red and blue lines for the 3D band diagrams. (c) A 3D PhC made by inversion of the close packed fcc structure (the inverse opal structure). (d) A 3D photonic band diagram of the opal structure made of silicon (n = 3.5). The partial gap along [111] direction (Γ-L) is represented in a red gap. (e) A 3D photonic band diagram of the inverse opal structure made of silicon (n = 3.5). A wider partial gap (a red gap) along [111] direction (Γ-L) and a complete gap (a green gap) between 8th and 9th bands are shown.

Figure 11

(a) Bright-field TEM image of a phase-separated blend of polyisoprene (PI)-PS-P2VP star terpolymer and a PS homopolymer showing a 2D quasi-crystalline structure. The red lines show the structure is comprised of a packing of equilateral triangles and squares. Reproduced with permission. Copyright 2007, American Physical Society (b) SEM image of the spongy keratin structure of a scarlet macaw blue feather (inset). Reproduced with permission. Copyright 2012, National Academy of Science of the USA. (c) 6-valent polymer particles created by IL and UV/ozonolysis. Reproduced with permission. Copyright 2007, American Chemical Society.

Figure 12

(a) Protein-based multilayer reflector of Loligo pealeii squid and the corresponding electrochemically tunable BCP lamellar structure using a voltage to create H⁺ in a PS-b-P2VP system that triggers large swelling of the P2VP domains. Inset a1) TEM cross section of a squid iridophore showing periodic layers, a2) electrically tunable BCP, a3) TEM of 1D lamellar BCP layer. (b) Single gyroid chitin network and a model constant mean curvature surface clipped to a truncated octahedron shape and SEM images of a wing scale of Callophrys rubi butterfly. The network's single type of 3-coordinated vertices are at Wyckoff sites 8a in space group I4₁32 (no. 214 in ref.226) Reproduced with permission. Copyright 2011, American Physical Society (c) Schematic of hierarchical photonic structure of butterfly wing scales and their tunable reflectivity corresponding to uptake of vapor.

Figure 13

(a) Photograph of an operating PhC laser shown with the atomic force microscope (AFM) image of a surface of the PhC structure with lattice constants, a and b. Reproduced with permission. Copyright 2008, American Institute of Physics. (b) Photograph of the 410 nm lasing from the BCP-based laser is shown with a schematic of its structure. A highly directional lasing output in the backward direction was observed. Reproduced with permission. Copyright 2006, American Chemical Society. (c1) A photograph of the laser action of the all polymer film laser shows excellent mechanical flexibility. (c2) A cross sectional SEM image shows the gain medium cavity confined by colloidal 3D PhCs. (c3) The emission spectra below and above the lasing threshold. The inset represents the high-resolution spectrum of the laser emission. Reproduced with permission. (d) Reflectance spectrum of a 1D PhC comprised of 30 unit cells showing the electric field intensity profiles for four selected wavelengths within and outside the PBG. Reproduced with permission. Copyright 2012, Optical Society of America.

Figure 14

Schematic illustration of various strategies to enhance the power-conversion efficiency of a single-junction PV cell. (a) Concentrators (luminescent and geometric) (b) Anode patterning for antireflection and self-cleaning and introduction of (metallic) gratings for enhanced light trapping. (c) pn-junction interface engineering for efficient exciton harvesting and for enhanced photon absorption via a PhC interface. (d) Cathode patterning.

Figure 15

(a) Cross sectional schematic of 2D PhC and SEM image of hexagonal array of active polymer columns prior to backfilling with nanocrystalline-ZnO. Reproduced with permission. Copyright 2009, American Chemical Society. (b) AFM images of linearly and hexagonally patterned PET substrate. Reproduced with permission.

Figure 16

The simplified seven cases of solvent swelling for a 1D bilayer stack. Changes of reflectance peak wavelength, λ_peak, and maximum reflectance, R_max, of a lamellar PhC structure corresponding to small variations of refractive index (±2%), and thickness (+5%). The initial lamellar PhC consists of 40 pairs with high ( = 1.60) and low ( = 1.45) indices and with the layer thickness equal to a quarter-wave optical thickness (). Depending on the refractive index of the solvent () and the preference of the solvent for each type of polymer layer, a wide range of responses can occur.

Figure 17

(a) Schematic illustration of the PSS-b-PMB BCP humidity sensor at low and high RH and photographs of sensors at different RH. Reproduced with permission. Copyright 2012, American Chemical Society. (b) Schematic representation of the mechanism for color change in the PS-b-QP2VP photonic lamellar gels by a direct exchange of counter-ions in the QP2VP layers and photographs of the films showing different colors with increasing hydration energy of the counter-anions. Reproduced with permission. Copyright 2012, American Chemical Society.

Figure 18

(a) Photographs of blast injury dosimeters using 3D PhCs made by IL before and after exposure to blast waves having peak overpressures of 655 and 1,090 kPa. The SEM images allow identification of changes in the structural features of the blast injury dosimeter after the shock. Reproduced with permission. Copyright 2010, Elsevier Inc. (b) Photograph of a transparent PhC shows colors at elevated temperature and its temperature-dependent optical scattering spectra. Depending on a viewing angle, different colors are observed from the PhC at 100 °C, as shown by the spectra below. Reproduced with permission. Copyright 2009, American Institute of Physics.

Figure 19

(a) Schematic of the electric field driven swelling of a silica-PFS PhC composite. (b) Optical responses of the PS-b-QP2VP photonic gel film (left) depending on UV irradiation dose and multicolor patterns created using a photomask having gradient pattern density to control local crosslink density (right). Reproduced with permission. (c) Schematic of writing and erasing of opal photonic paper by UV induced ring-opening and temperature induced ring-closing reaction of RhBMA dye 3 (top) and optical images of a patterned elastomeric opal film after activation of RhBMA-labeled beads (right) and temperature-induced reversible erasing (left). Reproduced with permission. Copyright 2013, American Chemical Society.

Figure 20

(a) Ray trajectory of light entering the spherical transformation space is guided smoothly around any object within the inner spherical region. Reproduced with permission. Copyright 2006, American Association for the Advancement of Science. (b) Calculated photon trapping by a photon black hole created by designing a spatial varying silicon-silica composite. Reproduced with permission. Copyright 2009, American Institute of Physics. (c) The photonic band diagram of a metallic double gyroid structure enabling negative refraction of light. The local energy flux vectors (the inset) of the negative refraction mode (thick red line in the band diagram) is in the opposite direction to the wavevector. Reproduced with permission. (d) SEM image of BCP derived gold gyroid network with a = 35 nm and filling fraction of 30%. Reproduced with permission.

Figure 21

(a) Diagram of the modulation space of real index vs. imaginary index for various photonic systems. (b) Schematic of a 1D periodic material having PT-symmetry requiring even and odd functions of and , respectively. The non-reciprocal behavior of the PT-symmetric system for the two different input beams (solid and dashed arrows) is illustrated.

Figure 22

Behavior of PnBGs (a1) Transverse plane wave of a frequency () inside the PnBG propagates through a solid and is completely reflected by a solid/solid 2D PnC made of cylinders arranged in a triangular lattice embedded in a matrix. (a2) The sound wave of a frequency () outside the PnBG is transmitted through the PnC to the other side solid. Adapted from. (b1) An illustration of a 3D PnC consisting of lead spheres () arranged on a fcc lattice embedded in epoxy matrix. (b2) A phononic band diagram of the 3D PnC shows a large complete PnBG. Adapted with permission. (c) A mechanically switchable phononic device. The PnBG shifts due to the dramatic change in symmetry.

Figure 23

(a1) Two-component PnC comprised of a square lattice of hard cylinders embedded in a softer polymer matrix and (a2) its phononic band structure with displacement fields corresponding to the two eigenmodes, A and B. A PnBG ( = 0.53) is created from Bragg scattering of the impedance contrast of 6. (b1) Three-component PnC having an additional concentric very soft layer that serves to weakly couple the cylinders and the matrix and (b2) its band structure with displacement fields corresponding to the eigenmodes, C and D. A low frequency resonant PnBG ( = 0.7) is created by using a soft shell () with impedance contrasts of of 50 and of 9. Adapted from. The color map for each mode indicates zero (blue) to a maximum displacement amplitude (red) with local directions and magnitudes of the displacements given by the arrows.

Figure 24

Polymer based acoustic “super absorbers” and reflectors. (a) Locally resonant 3D PnC comprised of rubber-coated lead spheres on a simple cubic lattice in an epoxy matrix and (b) its measured transmission spectra with (solid circles) and without (open square) resonators. Reproduced with permission. Copyright 2000, American Association for the Advancement of Science. (c) Bubble meta-screen made of air voids (R = 39 μm) in a PDMS matrix and (d) transmission spectra of a one-layer (circles) and four-layer crystals (squares) with lines of theoretical predictions. Reproduced with permission. Copyright 2009, American Institute of Physics.

Figure 25

Tunable PnCs with polymer-based systems. (a) SEM images show the instability induced pattern transformation in hexagonal SU8 based photo-patterned polymer with displacement fields for the modes near the tunable PnBG. Reproduced with permission. Copyright 2009, American Chemical Society. (b) BLS spectra of PDMS microframe undergoing large strains (30%) along the direction, showing clear shifts in the peaks of modes 1 and 3, indicating a change in the propagation modes. The corresponding AFM images and Fourier transformed images (insets) indicate the breaking of the hexagonal symmetry due to the stretching. Reproduced with permission. Copyright 2006, American Chemical Society. (c) Tilted SEM image of AAO template without polymers (inset: top view). Experimental in-plane phononic dispersion relations of polyethylene glycol (PEG)- filled AAO (black symbols) and PDMS-filled AAO (red symbols) for the longitudinal acoustic branch 1 (open circles) and the weak flat branch 2 (open triangles). Reproduced with permission. Copyright 2010, American Chemical Society.

Figure 26

(a) Calculated pressure map for a planar longitudinal wave incident on a rigid cylindrical scatterer surrounded by a multilayered acoustic shell made up of 200 layers (see inset). Reproduced with permission. Copyright 2008, IOP Publishing Ltd. (b) Oblique-view photograph of a cloaking device made of PVC before filling with PDMS and experimentally measured displacement fields passing by a solid disk with and without the cloak device at 200 Hz. Reproduced with permission. Copyright 2012, American Physical Society. (c) Photographs of a ground cloaking cover consisting of perforated plates are shown with the unit cell and simulated acoustic signatures of a triangular object with and without the cloaking cover. Reproduced with permission. Copyright 2011, American Physical Society.