Modeling of photonic band gap crystals and applications

In this work, we have undertaken a theoretical approach to the complex problem of modeling the flow of electromagnetic waves in photonic crystals. Our focus to address the feasibility of using the exciting phenomena of photonic gaps (PBG) in actual applications.;We start by providing analytical derivations, as well as the underlying physical principles, of the computational electromagnetic methods used in our work. A comparative study of the strengths and weaknesses of each method is provided. The Plane Wave expansion, Transfer Matrix, and Finite Difference Time Domain Methods are addressed. We also introduce a new theoretical approach, the Modal Expansion Method.;We then shift our attention to actual applications. We begin with a discussion of 2D photonic crystal wave guides. The structure addressed consists of a 2D hexagonal structure of air cylinders in a layered dielectric background. Comparison with the performance of a conventional guide is made, as well as suggestions for enhancing it. Our studies provide an upper theoretical limit on the performance of such guides.;Next, we study 3D metallic PBG materials at near infrared and optical wavelengths. Our main objective is to study the importance of absorption in the metal and the suitability of observing photonic band gaps in such structures. We study simple cubic structures where the metallic scatterers are either cubes or interconnected metallic rods. The effect of topology is also addressed. Our results reveal that the best performance is obtained by choosing metals with a large negative real part of the dielectric function, together with a relatively small imaginary part. Finally, we point out a new direction in photonic crystal research that involves the interplay of metallic-PBG rejection and photonic band edge absorption. We propose that an absolute metallic-PBG may be used to suppress the infrared part of the blackbody emission and, emit its energy only through a sharp absorption band. Potential applications of this new PBG mechanism include highly efficient incandescent lamps and enhanced thermophotovoltaic energy conversion. The suggested lamp would be able to recycle the energy that would otherwise go into the unwanted resulting in a 40% increase in efficiency

Extraordinary optical transmission through patterned subwavelength apertures.

Light propagating through a subwavelength aperture can be dramatically increased by etching a grating in the metal around the hole. Moreover, light that would typically broadly diverge when passing through an unpatterned subwavelength hole can be directed into a narrow beam by utilizing a specific pattern around the aperture. While the increased transmission and narrowed angular emission appear to defy far-field diffraction theory, they are consistent with a fortuitous plasmon/photon coupling. In addition, the coupling between photons and surface plasmons affects the emissivity of a surface comprised of such structures. These properties are useful across several strategic areas of interest to Sandia. A controllable emission spectrum could benefit satellite and military application areas. Photolithography and near-field microscopy are natural applications for a system that controls light beyond the diffraction limit in a manner that is easily parallelizable. Over the one year of this LDRD, we have built or modified the numerical tools necessary to model such structures. These numerical codes and the knowledge base for using them appropriately will be available in the future for modeling work on surface plasmons or other optical modeling at Sandia. Using these tools, we have designed and optimized structures for various transmission or emission properties. We demonstrate the ability to design a metallic skin with an emissivity peak at a pre-determined wavelength in the spectrum. We optimize structures for maximum light transmission and show transmitted beams that beat the far-field diffraction limit

3D Active photonic crystal devices for integrated photonics and silicon photonics.

Over the past 15 years, basic photonic crystals operating in optical wavelengths have been theoretically investigated and experimentally realized. New directions must now be set to understand fundamental photon-matter interactions and thus realize active photonic components for integrated and silicon-based photonic applications. This proposal aims at two key areas to study. They are: (1) Thermal emission and silicon photonic crystal lasers--an aspect of photon-phonon interaction. (2) Optical interconnects--an aspect of photonic transport and mutual interaction. Understanding the underlining photon-phonon interaction, blackbody radiation can be altered, and wasted thermal energy recycled. Furthermore, we intend to build SOI based optical components, and study their mutual interaction for achieving complex optical functionality. Two examples are waveguide-cavity and cavity-cavity interaction for channel dropping filter applications. Indeed, the next challenge in photonic crystal research is in material integration, in on-chip integration of photonic components, and lastly the realization of silicon lasers

Mid-infrared quantum dot emitters utilizing planar photonic crystal technology.

The three-dimensional confinement inherent in InAs self-assembled quantum dots (SAQDs) yields vastly different optical properties compared to one-dimensionally confined quantum well systems. Intersubband transitions in quantum dots can emit light normal to the growth surface, whereas transitions in quantum wells emit only parallel to the surface. This is a key difference that can be exploited to create a variety of quantum dot devices that have no quantum well analog. Two significant problems limit the utilization of the beneficial features of SAQDs as mid-infrared emitters. One is the lack of understanding concerning how to electrically inject carriers into electronic states that allow optical transitions to occur efficiently. Engineering of an injector stage leading into the dot can provide current injection into an upper dot state; however, to increase the likelihood of an optical transition, the lower dot states must be emptied faster than upper states are occupied. The second issue is that SAQDs have significant inhomogeneous broadening due to the random size distribution. While this may not be a problem in the long term, this issue can be circumvented by using planar photonic crystal or plasmonic approaches to provide wavelength selectivity or other useful functionality

Modeling of Photonic Band Gap Crystals and Applications

In this work, the authors have undertaken a theoretical approach to the complex problem of modeling the flow of electromagnetic waves in photonic crystals. The focus is to address the feasibility of using the exciting phenomena of photonic gaps (PBG) in actual applications. The authors start by providing analytical derivations of the computational electromagnetic methods used in their work. They also present a detailed explanation of the physics underlying each approach, as well as a comparative study of the strengths and weaknesses of each method. The Plane Wave expansion, Transfer Matrix, and Finite Difference time Domain Methods are addressed. They also introduce a new theoretical approach, the Modal Expansion Method. They then shift the attention to actual applications. They begin with a discussion of 2D photonic crystal wave guides. The structure addressed consists of a 2D hexagonal structure of air cylinders in a layered dielectric background. Comparison with the performance of a conventional guide is made, as well as suggestions for enhancing it. The studies provide an upper theoretical limit on the performance of such guides, as they assumed no crystal imperfections and non-absorbing media. Next, they study 3D metallic PBG materials at near infrared and optical wavelengths. The main objective is to study the importance of absorption in the metal and the suitability of observing photonic band gaps in such structures. They study simple cubic structures where the metallic scatters are either cubes or interconnected metallic rods. Several metals are studied (aluminum, gold, copper, and silver). The effect of topology is addressed and isolated metallic cubes are found to be less lossy than the connected rod structures. The results reveal that the best performance is obtained by choosing metals with a large negative real part of the dielectric function, together with a relatively small imaginary part. Finally, they point out a new direction in photonic crystal research that involves the interplay of metallic-PBG rejection and photonic band edge absorption. They propose that an absolute metallic-PBG may be used to suppress the infrared part of the blackbody emission and, emit its energy only through a sharp absorption band. Potential applications of this new PBG mechanism include highly efficient incandescent lamps and enhanced thermophotovoltaic energy conversion. The suggested lamp would be able to recycle the energy that would otherwise go into the unwanted heat associated with usual lamps, into light emitted in the visible spectrum. It is estimated this would increase the efficiency over conventional lamps by about 40%

Research on micro-sized acoustic bandgap structures.

Phononic crystals (or acoustic crystals) are the acoustic wave analogue of photonic crystals. Here a periodic array of scattering inclusions located in a homogeneous host material forbids certain ranges of acoustic frequencies from existence within the crystal, thus creating what are known as acoustic (or phononic) bandgaps. The vast majority of phononic crystal devices reported prior to this LDRD were constructed by hand assembling scattering inclusions in a lossy viscoelastic medium, predominantly air, water or epoxy, resulting in large structures limited to frequencies below 1 MHz. Under this LDRD, phononic crystals and devices were scaled to very (VHF: 30-300 MHz) and ultra (UHF: 300-3000 MHz) high frequencies utilizing finite difference time domain (FDTD) modeling, microfabrication and micromachining technologies. This LDRD developed key breakthroughs in the areas of micro-phononic crystals including physical origins of phononic crystals, advanced FDTD modeling and design techniques, material considerations, microfabrication processes, characterization methods and device structures. Micro-phononic crystal devices realized in low-loss solid materials were emphasized in this work due to their potential applications in radio frequency communications and acoustic imaging for medical ultrasound and nondestructive testing. The results of the advanced modeling, fabrication and integrated transducer designs were that this LDRD produced the 1st measured phononic crystals and phononic crystal devices (waveguides) operating in the VHF (67 MHz) and UHF (937 MHz) frequency bands and established Sandia as a world leader in the area of micro-phononic crystals

Phonon manipulation with phononic crystals.

In this work, we demonstrated engineered modification of propagation of thermal phonons, i.e. at THz frequencies, using phononic crystals. This work combined theoretical work at Sandia National Laboratories, the University of New Mexico, the University of Colorado Boulder, and Carnegie Mellon University; the MESA fabrication facilities at Sandia; and the microfabrication facilities at UNM to produce world-leading control of phonon propagation in silicon at frequencies up to 3 THz. These efforts culminated in a dramatic reduction in the thermal conductivity of silicon using phononic crystals by a factor of almost 30 as compared with the bulk value, and about 6 as compared with an unpatterned slab of the same thickness. This work represents a revolutionary advance in the engineering of thermoelectric materials for optimal, high-ZT performance. We have demonstrated the significant reduction of the thermal conductivity of silicon using phononic crystal structuring using MEMS-compatible fabrication techniques and in a planar platform that is amenable to integration with typical microelectronic systems. The measured reduction in thermal conductivity as compared to bulk silicon was about a factor of 20 in the cross-plane direction [26], and a factor of 6 in the in-plane direction. Since the electrical conductivity was only reduced by a corresponding factor of about 3 due to the removal of conductive material (i.e., porosity), and the Seebeck coefficient should remain constant as an intrinsic material property, this corresponds to an effective enhancement in ZT by a factor of 2. Given the number of papers in literature devoted to only a small, incremental change in ZT, the ability to boost the ZT of a material by a factor of 2 simply by reducing thermal conductivity is groundbreaking. The results in this work were obtained using silicon, a material that has benefitted from enormous interest in the microelectronics industry and that has a fairly large thermoelectric power factor. In addition, the techniques and scientific understanding developed in the research can be applied to a wide range of materials, with the caveat that the thermal conductivity of such a material be dominated by phonon, rather than electron, transport. In particular, this includes several thermoelectric materials with attractive properties at elevated temperatures (i.e., greater than room temperature), such as silicon germanium and silicon carbide. It is reasonable that phononic crystal patterning could be used for high-temperature thermoelectric devices using such materials, with applications in energy scavenging via waste-heat recovery and thermoelectric cooling for high-performance microelectronic circuits. The only part of the ZT picture missing in this work was the experimental measurement of the Seebeck coefficient of our phononic crystal devices. While a first-order approximation indicates that the Seebeck coefficient should not change significantly from that of bulk silicon, we were not able to actually verify this assumption within the timeframe of the project. Additionally, with regards to future high-temperature applications of this technology, we plan to measure the thermal conductivity reduction factor of our phononic crystals as elevated temperatures to confirm that it does not diminish, given that the nominal thermal conductivity of most semiconductors, including silicon, decreases with temperature above room temperature. We hope to have the opportunity to address these concerns and further advance the state-of-the-art of thermoelectric materials in future projects