Three Dimensional Photonic Crystals Corey Ulmer

Outline What are Photonic Crystals/Why Important? How They Work Manufacturing Challenges Manufacturing Techniques –Layer by layer techs. –Serial tech. –Mass production tech. Conclusions Image from S. G. Johnson et al., Nature. 429, 538 (2004) SEM Micrograph of a photonic crystal made with a layer by layer E-Beam lithography technique

What Are They? Photonic crystals analogous to semiconductors Crystal structure gives rise to band gap Photons inside band gap reflect off material Electron band gap in semiconductorPhoton band gap in photonic crystal Images from and modified from initio.mit.edu/photons/tutorial/ lecture 3

Why Do They Matter? Used in –Lossless reflective coatings on mirrors/lenses –Iridescent paint –Low threshold laser diode Images from and Paint makes use of photonic crystals Potential Uses –Replace fiber optic cable – higher energy light, different wavelengths –Optical computers – theoretically can be thousands of times faster than electronic computers SEM Micrograph of photonic crystal fiber cross section

How Does it Work? Alternating dielectrics – high contrast Repeating periodic structure gives rise to forbidden zones Band gap size dependent primarily on a diff in dielectric constant, frequency dependent primarily on cell size Example here is 1D (layers) – 1D always has a complete band gap (gap covers all phase, k) Image modified from

How Does it Work? In 3D, allowed energies MUCH more complicated Not all geometries have complete band gap (does not block in all directions) However! If all it does is block light, it’s not useful Intentional defects allow control of light – waveguides, logic gates Rough schematic of 1, 2, and 3 dimensional photonic crystals. 1D very easy – already has widespread application. 2D moderately difficult. 3D very hard. Image from lecture 2 Energy structure for 3D system

Manufacturing Challenges Technique must produce repeating structure accurately Must be able to introduce controlled defects accurately Band gap must be at useful wavelength (feature size) Cost and speed of production help Larger band gap makes system more fault-tolerant (dielectric constants and geometry) Images from S.-Y. Lin et al., JOSA B 18, 32 (2001) and F. Garcia-Santamaria et al., Adv. Mater. 14 (16), 1144 (2002) This simple cubic structure may be relatively easy to make, but it has a very small band gap Looks good, but assembled 1 sphere at a time w/ nanorobotics 5µm

Layer by Layer: Electron Beam Lithography E-Beam PMMA pattern, Reactive Ion Etch Si, fill w/ dielectric, mechanically smooth, spin on PMMA, repeat Defects are introduced by over-etching individual cylinders Method produces large band gap, can be adapted for other materials Images from S. G. Johnson et al., Appl. Phys. Lett. 77, 3490 (2000) and modified from S. G. Johnson et al., Nature. 429, 538 (2004) Side (a) and top (b) view of process

Layer by Layer: Woodpile Process very similar to previous method Grooves etched in substrate, filled with dielectric, mechanically smoothed, repeat with groves at 90° 3 rd layer offset by ½ unit cell Many different variations on tech. – repeat layers, wafer press Fair sized band gap, has been developed for many materials Images from and S. Noda et al., Science 289, 604 (2000) SEM Micrographs of woodpile structure and introduction of defect

Serial: 2 Photon Polymerization Focused laser light polymerizes bulk monomer with photoinitiator Polymerization occurs only at beam focus Allows for cheap prototyping vs. other systems, but accuracy not as good Polymer Monomer, Photoinitiator Lens Laser Light Image from B. H. Cumpston et al., Nature 398, 51 (1999) Woodpile structure created via 2 Photon Polymerization

All-at-Once: Inverse Opals Self assembling microspheres create FCC matrix Spheres cannot create complete band gap, but a dielectric filler with hollow spheres can 3 photon polymerization used to create defects after sedimentation of microspheres Defects and microspheres removed, but dielectric filler remains Sensitive to defects Image modified from L. Wonmok, Adv. Materials 14, 271 (2002) and from Y. A. Vlasov, et al., Nature 15, 289 (2001)

Conclusions Many techniques exist for creation of photonic crystals, and development continues to improve The most promising techniques seem to be layer by layer woodpile, and layer by layer e-beam lithography Development of technology for optical computers is a very active field Image modified from S. Ogawa Science 305, 227 (2004) SEM Micrographs of point defects added to woodpile structures

References S. G. Johnson et al., Nature. 429, 538 (2004) S.-Y. Lin et al., JOSA B 18, 32 (2001) F. Garcia-Santamaria et al., Adv. Mater. 14 (16), 1144 (2002) S. G. Johnson et al., Appl. Phys. Lett. 77, 3490 (2000) S. Noda et al., Science 289, 604 (2000) B. H. Cumpston et al., Nature 398, 51 (1999) L. Wonmok, Adv. Materials 14, 271 (2002) Y. A. Vlasov, et al., Nature 15, 289 (2001) S. Ogawa Science 305, 227 (2004)