1. What are the inventions? (1) We have designed and tested the first example of a disordered photonic heterostructure that blocks light equally in all directions. Left: Protocol for mapping point patterns into tessellations for photonic structure designs. Right: Disordered hyperuniform photonic band gap heterostructure fabricated from dielectric polymer. (2) The disordered heterostructure arose from our invention of a new general mathematical protocol for finding structures with optimal band gap properties. The protocol works for crystals, quasicrystals, and disordered heterostructures. How can the heterostructures be distinguished? The different types of heterostructures are distinguished by their symmetries which can be determined from the Fourier transforms of the structures. Hyperuniform Crystal Quasicrystal Disordered What is a hyperuniform disordered structure? Disordered means random positions distributed uniformly in all directions (along two or three-dimensions, depending on the case). Hyperuniform means the density variations are constrained on large distances so that the Fourier transform has zero intensity near the center (wavenumber k=0). The example above is a stealthy hyperuniform pattern with no intensity within a finite radius of the center, one of the invented structures predicted by our mathematical design method to have a complete photonic bandgap. What are the inventions? (1) We have designed and tested the first example of a disordered photonic heterostructure that blocks light equally in all directions. Left: Protocol for mapping point patterns into tessellations for photonic structure designs. Right: Disordered hyperuniform photonic band gap heterostructure fabricated from dielectric polymer. (2) The disordered heterostructure arose from our invention of a new general mathematical protocol for finding structures with optimal band gap properties. The protocol works for crystals, quasicrystals, and disordered heterostructures. How can the heterostructures be distinguished? The different types of heterostructures are distinguished by their symmetries which can be determined from the Fourier transforms of the structures. Hyperuniform Crystal Quasicrystal Disordered What is a hyperuniform disordered structure? Disordered means random positions distributed uniformly in all directions (along two or three-dimensions, depending on the case). Hyperuniform means the density variations are constrained on large distances so that the Fourier transform has zero intensity near the center (wavenumber k=0). The example above is a stealthy hyperuniform pattern with no intensity within a finite radius of the center, one of the invented structures predicted by our mathematical design method to have a complete photonic bandgap. What is the purpose? To design and construct new and improved types of photonic heterostructures, the equivalent of semiconductors for light that can be used to manipulate and control the flow of light in photonic circuits. What is photonics? Photonics refers to the use of light in place of electrons in communication and computer devices and in other applications in which electronics is conventionally used. Fiber-optics replaces wires and photonic heterostructures replace semiconductors.. What are heterostructures? Heterostructures are man-made “designer” materials composed of two or more dielectric materials in an interpenetrating arrangement. The ability of a photonic heterostructure to block and manipulate light depends on the symmetry and geometry of the arrangement. Two examples of non-crystalline heterostructures composed of polymer and air are shown below. Left: Optimal design of a disordered hyperuniform photonic band gap heterostructure. Right: Design for a three-dimensional quasicrystalline photonic heterostructure. What is a photonic band gap? A photonic band gap is the range of frequencies that are blocked (reflected) by a photonic heterostructure no matter the incoming direction or polarization (analogous to the way a semiconductor blocks electrons for a range of energies to form an electronic band gap). By introducing strategically placed defects in the structure, blocked frequencies can be manipulated in various selected ways to enable information communication and computation. What is the purpose? To design and construct new and improved types of photonic heterostructures, the equivalent of semiconductors for light that can be used to manipulate and control the flow of light in photonic circuits. What is photonics? Photonics refers to the use of light in place of electrons in communication and computer devices and in other applications in which electronics is conventionally used. Fiber-optics replaces wires and photonic heterostructures replace semiconductors.. What are heterostructures? Heterostructures are man-made “designer” materials composed of two or more dielectric materials in an interpenetrating arrangement. The ability of a photonic heterostructure to block and manipulate light depends on the symmetry and geometry of the arrangement. Two examples of non-crystalline heterostructures composed of polymer and air are shown below. Left: Optimal design of a disordered hyperuniform photonic band gap heterostructure. Right: Design for a three-dimensional quasicrystalline photonic heterostructure. What is a photonic band gap? A photonic band gap is the range of frequencies that are blocked (reflected) by a photonic heterostructure no matter the incoming direction or polarization (analogous to the way a semiconductor blocks electrons for a range of energies to form an electronic band gap). By introducing strategically placed defects in the structure, blocked frequencies can be manipulated in various selected ways to enable information communication and computation. Does the design work? The design was tested by fabricating the predicted structure from dielectric polymer and air. Below is shown the first-ever disordered photonic heterostructure found to have a complete photonic band gap. Measured transmission as a function of frequency and angle for the disordered hyperuniform structure shown in the middle column, upper right. Why are disordered photonic materials useful? Disordered photonic band gap heterostructures capable of blocking light equally from all directions facilitate a variety of applications, such as waveguides for photonic communication, new types of isotropic light sources and highly-efficient thermophotovoltaic devices. Does the design work? The design was tested by fabricating the predicted structure from dielectric polymer and air. Below is shown the first-ever disordered photonic heterostructure found to have a complete photonic band gap. Measured transmission as a function of frequency and angle for the disordered hyperuniform structure shown in the middle column, upper right. Why are disordered photonic materials useful? Disordered photonic band gap heterostructures capable of blocking light equally from all directions facilitate a variety of applications, such as waveguides for photonic communication, new types of isotropic light sources and highly-efficient thermophotovoltaic devices. Marian Florescu 1, Salvatore Torquato 2,3, Paul J. Steinhardt 1,3 1 Department of Physics 2 Department of Chemistry 3 Princeton Center for Theoretical Science References [1] Marian Florescu, Salvatore Torquato, Paul J Steinhardt, Proceedings of the National Academy of Sciences, 106, 20658 (2009). [2] Marian Florescu, Salvatore Torquato, Paul J Steinhardt, Physical Review B 80, 155112 (2009). [3] Weining Man, Marian Florescu, Kazue Matsuyama, Polin Yadak, Salvatore Torquato, Paul J Steinhardt, and Paul Chaikin, submitted to CLEO/QELS. Acknowledgements This work was supported by the NSF Grant No. DMR-0606415. References [1] Marian Florescu, Salvatore Torquato, Paul J Steinhardt, Proceedings of the National Academy of Sciences, 106, 20658 (2009). [2] Marian Florescu, Salvatore Torquato, Paul J Steinhardt, Physical Review B 80, 155112 (2009). [3] Weining Man, Marian Florescu, Kazue Matsuyama, Polin Yadak, Salvatore Torquato, Paul J Steinhardt, and Paul Chaikin, submitted to CLEO/QELS. Acknowledgements This work was supported by the NSF Grant No. DMR-0606415. Disordered Photonic Band Gap Heterostructures