Recently, a new algorithm for wide-angle beam propagation was reported that allowed grid points to move in an arbitrary fashion between propagation planes and was thus capable of modeling waveguides whose widths or centerlines varied with propagation distance. That algorithm was accurate and stable for TE polarization but unstable for wide-angle TM propagation. This deficiency has been found to result from an omission in one of the wide-angle terms in the derivation of the finite-difference equation and is remedied here, resulting in a complete algorithm accurate for both polarizations.
Advanced optically-activated solid-state electrical switch development at Sandia has demonstrated multi-kA/kV switching and the path for scalability to even higher current/power. Realization of this potential requires development of new optical sources/switches based on key Sandia photonic device technologies: vertical-cavity surface-emitting lasers (VCSELs) and photoconductive semiconductor switch (PCSS) devices. The key to increasing the switching capacity of PCSS devices to 5kV/5kA and higher is to distribute the current in multiple parallel line filaments triggered by an array of high-brightness line-shaped illuminators. Commercial mechanically-stacked edge-emitting lasers have been used to trigger multiple filaments, but they are difficult to scale and manufacture with the required uniformity. In VCSEL arrays, adjacent lasers utilize identical semiconductor material and are lithographically patterned to the required dimensions. We have demonstrated multiple-line filament triggering using VCSEL arrays to approximate line generation. These arrays of uncoupled circular-aperture VCSELs have fill factors ranging from 2% to 30%. Using these arrays, we have developed a better understanding of the illumination requirements for stable triggering of multiple-filament PCSS devices. Photoconductive semiconductor switch (PCSS) devices offer advantages of high voltage operation (multi-kV), optical isolation, triggering with laser pulses that cannot occur accidentally in nature, low cost, high speed, small size, and radiation hardness. PCSS devices are candidates for an assortment of potential applications that require multi-kA switching of current. The key to increasing the switching capacity of PCSS devices to 5kV/5kA and higher is to distribute the current in multiple parallel line filaments triggered by an array of high-brightness line-shaped illuminators. Commercial mechanically-stacked edge-emitting lasers have been demonstrated to trigger multiple filaments, but they are difficult to scale and manufacture with the required uniformity. As a promising alternative to multiple discrete edge-emitting lasers, a single wafer of vertical-cavity surface-emitting lasers (VCSELs) can be lithographically patterned to achieve the desired layout of parallel line-shaped emitters, in which adjacent lasers utilize identical semiconductor material and thereby achieve a degree of intrinsic optical uniformity. Under this LDRD project, we have fabricated arrays of uncoupled circular-aperture VCSELs to approximate a line-shaped illumination pattern, achieving optical fill factors ranging from 2% to 30%. We have applied these VCSEL arrays to demonstrate single and dual parallel line-filament triggering of PCSS devices. Moreover, we have developed a better understanding of the illumination requirements for stable triggering of multiple-filament PCSS devices using VCSEL arrays. We have found that reliable triggering of multiple filaments requires matching of the turn-on time of adjacent VCSEL line-shaped-arrays to within approximately 1 ns. Additionally, we discovered that reliable triggering of PCSS devices at low voltages requires more optical power than we obtained with our first generation of VCSEL arrays. A second generation of higher-power VCSEL arrays was designed and fabricated at the end of this LDRD project, and testing with PCSS devices is currently underway (as of September 2008).
We have numerically compared the performance of various designs for the core refractive-index (RI) and rare-earth-dopant distributions of large-mode-area fibers for use in bend-loss-filtered, high-power amplifiers. We first established quantitative targets for the key parameters that determine fiber-amplifier performance, including effective LP01 modal area (Aeff, both straight and coiled), bend sensitivity (for handling and packaging), high-order mode discrimination, mode-field displacement upon coiling, and index contrast (manufacturability). We compared design families based on various power-law and hybrid profiles for the RI and evaluated confined rare-earth doping for hybrid profiles. Step-index fibers with straight-fiber Aeff values > 1000 μm2 exhibit large decreases in Aeff and transverse mode-field displacements upon coiling, in agreement with recent calculations of Hadley et al. [Proc. of SPIE, Vol. 6102, 61021S (2006)] and Fini [Opt. Exp. 14, 69 (2006)]. Triangular-profile fibers substantially mitigate these effects, but suffer from excessive bend sensitivity at Aeff values of interest. Square-law (parabolic) profile fibers are free of modal distortion but are hampered by high bend sensitivity (although to a lesser degree than triangular profiles) and exhibit the largest mode displacements. We find that hybrid (combined power-law) profiles provide some decoupling of these tradeoffs and allow all design goals to be achieved simultaneously. We present optimized fiber designs based on this analysis.
We report results from Yb-doped fiber amplifiers seeded with two microchip lasers having 0.38-ns and 2.3-ns pulse durations. The shorter duration seed resulted in output pulses with a peak power of > 1.2 MW and pulse energy of 0.67 mJ. Peak power was limited by nonlinear processes that caused breakup and broadening of the pulse envelope as the pump power increased. The 2.3-ns duration seed laser resulted in output pulses with a peak power of >300 kW and pulse energy of > 1.1 mJ. Pulse energies were limited by the onset of stimulated Brillouin scattering and ultimately by internal optical damage (fluences in excess of 400 J/cm 2 were generated). In both experiments, nearly diffraction-limited beam profiles were obtained, with M 2 values of < 1.2. Preliminary results of a pulse-amplification model are in excellent agreement with the experimental results of the amplifiers operating in the low-to-moderate gain-depletion regime.
This report describes the research accomplishments achieved under the LDRD Project ''Leaky-mode VCSELs for photonic logic circuits''. Leaky-mode vertical-cavity surface-emitting lasers (VCSELs) offer new possibilities for integration of microcavity lasers to create optical microsystems. A leaky-mode VCSEL output-couples light laterally, in the plane of the semiconductor wafer, which allows the light to interact with adjacent lasers, modulators, and detectors on the same wafer. The fabrication of leaky-mode VCSELs based on effective index modification was proposed and demonstrated at Sandia in 1999 but was not adequately developed for use in applications. The aim of this LDRD has been to advance the design and fabrication of leaky-mode VCSELs to the point where initial applications can be attempted. In the first and second years of this LDRD we concentrated on overcoming previous difficulties in the epitaxial growth and fabrication of these advanced VCSELs. In the third year, we focused on applications of leaky-mode VCSELs, such as all-optical processing circuits based on gain quenching.
We report a fully integrated high-Q factor micro-ring resonator using silicon nitride/dioxide on a silicon wafer. The micro-ring resonator is critically coupled to a low loss straight waveguide. An intrinsic quality factor of 2.4 x 10{sup 5} has been measured.
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.
This SAND report is the final report on Sandia's Grand Challenge LDRD Project 27328, 'A Revolution in Lighting -- Building the Science and Technology Base for Ultra-Efficient Solid-state Lighting.' This project, which for brevity we refer to as the SSL GCLDRD, is considered one of Sandia's most successful GCLDRDs. As a result, this report reviews not only technical highlights, but also the genesis of the idea for Solid-state Lighting (SSL), the initiation of the SSL GCLDRD, and the goals, scope, success metrics, and evolution of the SSL GCLDRD over the course of its life. One way in which the SSL GCLDRD was different from other GCLDRDs was that it coincided with a larger effort by the SSL community - primarily industrial companies investing in SSL, but also universities, trade organizations, and other Department of Energy (DOE) national laboratories - to support a national initiative in SSL R&D. Sandia was a major player in publicizing the tremendous energy savings potential of SSL, and in helping to develop, unify and support community consensus for such an initiative. Hence, our activities in this area, discussed in Chapter 6, were substantial: white papers; SSL technology workshops and roadmaps; support for the Optoelectronics Industry Development Association (OIDA), DOE and Senator Bingaman's office; extensive public relations and media activities; and a worldwide SSL community website. Many science and technology advances and breakthroughs were also enabled under this GCLDRD, resulting in: 55 publications; 124 presentations; 10 book chapters and reports; 5 U.S. patent applications including 1 already issued; and 14 patent disclosures not yet applied for. Twenty-six invited talks were given, at prestigious venues such as the American Physical Society Meeting, the Materials Research Society Meeting, the AVS International Symposium, and the Electrochemical Society Meeting. This report contains a summary of these science and technology advances and breakthroughs, with Chapters 1-5 devoted to the five technical task areas: 1 Fundamental Materials Physics; 2 111-Nitride Growth Chemistry and Substrate Physics; 3 111-Nitride MOCVD Reactor Design and In-Situ Monitoring; 4 Advanced Light-Emitting Devices; and 5 Phosphors and Encapsulants. Chapter 7 (Appendix A) contains a listing of publications, presentations, and patents. Finally, the SSL GCLDRD resulted in numerous actual and pending follow-on programs for Sandia, including multiple grants from DOE and the Defense Advanced Research Projects Agency (DARPA), and Cooperative Research and Development Agreements (CRADAs) with SSL companies. Many of these follow-on programs arose out of contacts developed through our External Advisory Committee (EAC). In h s and other ways, the EAC played a very important role. Chapter 8 (Appendix B) contains the full (unedited) text of the EAC reviews that were held periodically during the course of the project.
Finite difference equations are derived for the simulation of dielectric waveguides using an Hz -Ez formulation defined on a nonuniform triangular grid. The resulting equations may be solved as a banded eigenproblem for waveguide structures of arbitrary shape composed of regions of piecewise constant isotropic dielectric, and all transverse fields then computed from the solutions. Benchmark comparisons are presented for problems with analytic solutions, as well as a sample calculation of the propagation loss of a hollow Bragg fiber.
Artificially structured photonic lattice materials are commonly investigated for their unique ability to block and guide light. However, an exciting aspect of photonic lattices which has received relatively little attention is the extremely high refractive index dispersion within the range of frequencies capable of propagating within the photonic lattice material. In fact, it has been proposed that a negative refractive index may be realized with the correct photonic lattice configuration. This report summarizes our investigation, both numerically and experimentally, into the design and performance of such photonic lattice materials intended to optimize the dispersion of refractive index in order to realize new classes of photonic devices.
This report describes a passive, optical component called resonant subwavelength gratings (RSGs), which can be employed as one element in an RSG array. An RSG functions as an extremely narrow wavelength and angular band reflector, or mode selector. Theoretical studies predict that the infinite, laterally-extended RSG can reflect 100% of the resonant light while transmitting the balance of the other wavelengths. Experimental realization of these remarkable predictions has been impacted primarily by fabrication challenges. Even so, we will present large area (1.0mm) RSG reflectivity as high as 100.2%, normalized to deposited gold. Broad use of the RSG will only truly occur in an accessible micro-optical system. This program at Sandia is a normal incidence array configuration of RSGs where each array element resonates with a distinct wavelength to act as a dense array of wavelength- and mode-selective reflectors. Because of the array configuration, RSGs can be matched to an array of pixels, detectors, or chemical/biological cells for integrated optical sensing. Micro-optical system considerations impact the ideal, large area RSG performance by requiring finite extent devices and robust materials for the appropriate wavelength. Theoretical predictions and experimental measurements are presented that demonstrate the component response as a function of decreasing RSG aperture dimension and off-normal input angular incidence.
Resonant subwavelength gratings (RSGs) may be used as narrow-band wavelength and angular reflectors. Rigorous coupled wave analysis (RCWA) predicts 100% reflectivity at the resonant frequency of an incident plane wave from an RSG of infinite extent. For devices of finite extent or for devices illuminated with a finite beam, the peak reflectivity drops, coupled with a broadening of the peak. More complex numerical methods are required to model these finite effects. We have modeled finite devices and finite beams with a two-dimensional finite difference Helmholtz equation. The effect of finite grating aperture and finite beam size are investigated. Specific cases considered include Gaussian beam illumination of an infinite grating, Gaussian illumination of a finite grating, and plane wave illumination of an apertured grating. For a wide grating with a finite Gaussian beam, it is found that the reflectivity is an exponential function of the grating width. Likewise, for an apertured grating the reflectivity shows an exponential decay with narrowing aperture size. Results are compared to other methods, including plane wave decomposition of Gaussian beams using RCWA for the case of a finite input beam, and a semi-analytical techniques for the case of the apertured grating.
One method of providing the mode selectivity necessary to insure single mode operation in a large diameter VCSEL is to independently control the size of the gain region and that of the optical mode. Numerical simulations quantity this approach by predicting lateral mode discrimination for different sized gain apertures. Calculations are experimentally confirmed by the fabrication and testing of 850 nm VCSELs employing hybrid ion implantation/selective oxidation that produce a single-mode output of more than 5 mW.
Previously, an effective index optical model was introduced for the analysis of lateral waveguiding effects in vertical-cavity surface-emitting lasers. The authors show that the resultant transverse equation is almost identical to the one typically obtained in the analysis of dielectric waveguide problems, such as a step-index optical fiber. The solution to the transverse equation yields the lateral dependence of the optical field and, as is recognized in this paper, the discrete frequencies of the microcavity modes. As an example, they apply this technique to the analysis of vertical-cavity lasers that contain thin-oxide apertures. The model intuitively explains the experimental data and makes quantitative predictions in good agreement with a highly accurate numerical model.
We demonstrate for the first time anti-guided coupling of two adjacent vertical-cavity surface-emitting lasers (VCSEL's), obtaining a 1-by-2 phase-locked array at 869 nm. The lateral index modification required for anti-guiding is achieved by a patterned 3-rim etch performed between two epitaxial growths. In contrast with prior evanescently coupled VCSEL's, adjacent anti-guided VCSEL's can emit in-phase and produce a single on-axis lobe in the far field. Greater than 2 mW of in-phase output power is demonstrated with two VCSEL's separated by 8 {micro}m. Moreover, phase locking of two VCSEL's separated by 20 {micro}m is observed, indicating the possibility of a new class of optical circuits based upon VCSEL's that interact horizontally and emit vertically.
We compare 2 angular regimes for the measurement of changes in the real refractive index of bulk fluid analytes. The measurements are based on the use of the Kretschmann-Raether configuration to sense a change in reflectivity with index. Specifically, we numerically simulate the relative sensitivities of the total internal reflection (TIR) and surface-plasmon resonance (SPR) regimes. For a fixed-angle apparatus, the method which gives the greatest change in reflectivity varies with metal film thickness. For films thicker than the skin depth, the SPR regime is the most sensitive to index changes. For thinner films, however, the TIR angle is then dominant, with increases in sensitivity on the order of 75% for 10 nm gold or silver media.
Progress towards the development of such algorithms as been reported for waveguide analysis'-3and vertical-cavity laser simulation. In all these cases, the higher accuracy order was obtained for a single spatial dimension. More recently, this concept was extended to differencing of the Helmholtz Equation on a 2-D grid, with uniform regions treated to 4th order and dielectric interfaces to 3'd order5. No attempt was made to treat corners properly. In this talk I will describe the extension of this concept to allow differencing of the Helmholtz Equation on a 2-D grid to 6* order in uniform regions and 5* order at dielectric interfaces. In addition, the first known derivation of a finite difference equation for a dielectric comer that allows correct satisfaction of all boundary conditions will be presented. This equation is only accurate to first order, but as will be shown, results in simulations that are third-order-accurate. In contrast to a previous approach3 that utilized a generalized Douglas scheme to increase the accuracy order of the difference second derivative, the present method invokes the Helmholtz Equation itself to convert derivatives of high order in a single direction into mixed
A methodology is presented that allows the derivation of low-truncation-error finite difference equations for photonics simulation. This methodology is applied to the case of wide-angle beam propagation in two dimensions, resulting in finite difference equations for both TE and TM polarization that are quasi-fourth-order accurate even in the presence of interfaces between dissimilar dielectrics. This accuracy is accomplished without an appreciable increase in numerical overhead and is concretely demonstrated for two test problems having known solutions. These finite difference equations facilitate an approach to the ideal of grid-independent computing and should allow the simulation of relevant photonics devices on personal computers.
Recent advances in Vertical-Cavity Surface-Emitting Laser (VCSEL) technology that have led to higher efficiencies and lower thresholds have opened up a new realm of applications for these devices. In particular, phase-locked arrays of VCSELs1, previously thought to be impractical due to thermal considerations, now look extremely attractive as high-power and highbrightness sources. In addition, a new understanding of waveguiding in VCSELs2 has led to practical methods for designing phase-locked arrays employing either evansecent or leaky-mode (antiguided) coupling. The latter type of coupling is particularly attractive in light of previous calculations1 that predict especially strong mode discrimination against higher-order lateral modes. In this paper we report the first detailed simulation of leaky-mode coupling between two VCSEL pixels performed without the use of simplifying assumptions such as the effective index model. The results of this simulation are, however, found to be in good agreement with previously-developed simple theories3 of leaky-mode coupling.
Vertical-cavity surface-emitting lasers (VCSELs) are presently the subject of intense research due to their potential as compact, efficient, astigmatic laser sources for a number of important applications. Of special interest are the selectively-oxidized VCSELs that have recently set records for threshold current and wall-plug efficiency. The onset of higher-order modes at powers of a few milliWatts, however, presently limits the wide utilization of these devices and indicates the need for improvements in design. Unfortunately, their complexity precludes optimization based solely upon empirical methods, and points instead to the need for better numerical models. Modeling the optical field in a vertical-cavity laser, however, is especially difficult due to both the high Q of the optical cavity and the distributed reflectivity of the mirrors. Our approach to this dilemma has been the development of modeling techniques on two complexity scales. We first derived an effective- index model that is numerically efficient and thus can be included together with carrier transport and thermal models to make up a self-consistent modeling package. In addition to its use in the overall VCSEL model, this simplified optical model has been extremely valuable in elucidating the basic principles of waveguiding in VCSELs that in turn have led to new ideas in device design. More specifically, the derived expression for the effective index shows clearly that index guiding in a VCSEL depends only on variations in optical cavity length, and thus can be engineered without the need to alter the material index of refraction. Also, we have designed index- guided and antiguided devices whose cavity lengths are modified in certain regions by etching of the cavity material prior to growth of the second mirror. Fabrication of these new device designs is presently in progress.
The authors present a comprehensive numerical model for vertical-cavity surface-emitting lasers that includes all major processes effecting cw operation of axisymmetric devices. In particular, the model includes a description of the 2D transport of electrons and holes through the cladding layers to the quantum well(s), diffusion and recombination processes of these carriers within the wells, the 2D transport of heat throughout the device, and a multi-lateral-mode effective index optical model. The optical gain acquired by photons traversing the quantum wells is computed including the effects of strained band structure and quantum confinement. They employ the model to predict the behavior of higher-order lateral modes in proton-implanted devices, and to provide an understanding of index-guiding in devices fabricated using selective oxidation.
A numerical solution technique has been presented which solves in one dimension the coupled heat and mass flow equations for water, water vapor, and an inert gas moving through a porous medium. The physical effects included in the resulting computer program PETROS are more complete than for previous simulations, particularly for the gas phase transport. The latter includes effects due to binary gaseous diffusion and Knudsen diffusion as well as Darcy flow. PETROS is thus capable of simulating two-phase flow through porous media.