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NASA NTRS2001

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Li, Jianzhong↗

NASA NTRS1998

A Coupled Plasma Dynamics and Gas Flow Model for Semiconductor Processing

A continuum modeling approach by self-consistently coupling plasma dynamics and gas flow will be presented for the analysis of high density plasma reactors. Experimental data shows that gas flow distribution affects the etch rate uniformity even at low pressures (6-20 mTorr) and flow rates (20-70 sccm). This study will investigate the effects of gas flow and gas energy on bulk plasma densities and temperatures using a continuum model. The model solves multidimensional equations of mass balance for neutrals and ions, gas momentum, separate energy equations for electrons and neutrals and Maxwell's equations for power coupling. A test case of N2 plasma in a 300mm TCP etch reactor, for which hybrid model and Langmuir probe data are available, is chosen for this analysis. Our preliminary results show that modeling gas flow and energy improves the predictions of electron density and its spatial variation in the reactor when compared with the experimental data. The aim of this study is to identify the operating conditions for the TCP reactor when a self-consistent modeling of gas flow is important.

Bose, Deepak↗

NASA NTRS1998

A Transport Model for Non-Local Heating of Electrons in ICP Reactors

A new model has been developed for non-local heating of electrons in ICP reactors, based on a hydrodynamic approach. The model has been derived using the electron momentum conservation in azimuthal direction with electromagnetic and frictional forces respectively as driving force and damper of harmonic oscillatory motion of electrons. The resulting transport equations include the convection of azimuthal electron momentum in radial and axial directions, thereby accounting for the non-local effects. The azimuthal velocity of electrons and the resulting electrical current are coupled to the Maxwell's relations, thus forming a self-consistent model for non-local heating. This model is being implemented along with a set of Navier-Stokes equations for plasma dynamics and gas flow to simulate low-pressure (few mTorr's) ICP discharges. Characteristics of nitrogen plasma in a TCP 300mm etch reactor is being studied. The results will be compared against the available Langmuir probe measurements.

Chang, C. H.↗

NASA NTRS1998

Computational Modeling of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the hewn. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗

NASA NTRS1998

Simulation of Transverse Modes in Vertical-Cavity Surface-Emitting Lasers

An approximation to the Maxwell-Semiconductor Bloch equations is solved for the transverse modes of vertical-cavity surface-emitting lasers. A finite-difference algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. Effects of pumping current and refractive index profiles will be investigated.

Goorjian, Peter M. P.↗

NASA NTRS1998

Computational Nonlinear of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the beam. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗

NASA NTRS1991

Power Supply

Maxwell Laboratories capacitor charging power supply is the first commercial spinoff from the NASA CCDS program - a consortia of industries and government establishments to accelerate development of ground and space based commercial applications of NASA technology. The power supply transforms and conditions large voltages to charge capacitors used in x-ray sources, medical accelerators, etc. It is lighter, more reliable, more compact and efficient. Originally developed for space lasers, its commercial potential was soon recognized.

Source record↗

NASA NTRS2002

Investigation of Venus Surface Properties

Strong localized radar echoes have been observed at decimeter wavelengths from the highlands of Venus since the earliest radar maps were obtained over 30 years ago. These echoes are some five to ten times stronger than those from the presumably basaltic rocks seen at lower altitudes elsewhere on Venus. Observations of thermal emission from the visible disk of Venus at wavelengths corresponding to those used in the radar mapping confirm that the regions of high reflectivity also exhibit low emissivity, as expected from considerations of detailed thermodynamic balance. Two possibilities have been put forward to explain this unexpected aspect of the Venus highlands: 1) surface materials of high effective dielectric constant, probably associated with finite electrical conductivity, and 2) volume scattering associated with multiple scattering from a layer of very-low-loss material containing voids and extending down a few hundred wavelengths beneath the surface. Analogs to these two mechanisms are found elsewhere in the solar system, and each is capable of explaining the basic observations. as of the early 1990's. In 1993, however, it became possible to carry out a bistatic observation of the anomalous highland regions using the Magellan spacecraft, then in orbit about Venus. In this experiment the on-board telemetry transmitter was aimed at the planet's surface with its linear S-band polarization vector oriented at 45 deg to the spacecraft-Venus-Earth scattering plane. The pointing of the transmitting antenna was adjusted so that the spacecraft-to-illuminated-surface incidence angle equalled the Earth-to-Venus-surface incidence angle. In this way, the experiment emphasized the specular scattering component. A full Stokes-Vector analysis of the reflected signal as received on Earth was carried out as the illuminated region scanned across the highland regions of Venus. From the observed position angle of the echo, it was possible to calculate the Fresnel reflectivity of a number of regions on Venus, including the high-altitude Maxwell Montes, and to show unequivocally that the complex dielectric constant of that anomalous area was 100 +/- 50i, as compared to 4.0 (real) for the typical lowland area. Thus this experiment was able to rule out definitively an hypothesis of volume scattering as the explanation for the anomalous scattering in the Venus highlands.

Ford, Peter G.↗

NASA NTRS2002

User's Manual for FEM-BEM Method

A user's manual for using FORTRAN code to perform electromagnetic analysis of arbitrarily shaped material cylinders using a hybrid method that combines the finite element method (FEM) and the boundary element method (BEM). In this method, the material cylinder is enclosed by a fictitious boundary and the Maxwell's equations are solved by FEM inside the boundary and by BEM outside the boundary. The electromagnetic scattering on several arbitrarily shaped material cylinders using this FORTRAN code is computed to as examples.

Butler, Theresa↗

NASA NTRS2002

Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers

A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.

Li, J.↗

NASA NTRS2003

An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses

Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.

Johnson, Arthur R.↗

NASA NTRS2003

An Introduction to Atmospheric Radiation: Review for the Bulletin of AMS

Whether you like a certain geophysical book or not, largely depends on your background. The field of radiative transfer and atmospheric radiation, in particular, combines people with a wide range of mathematical skills: from theoretical astrophysicists and nuclear physicists to meteorologists and ecologists. There is always a delicate balance between physical explanations and their mathematical interpretations. This balance is very personal and is based on your background. I came to the field of atmospheric radiative transfer as a mathematician with little knowledge of atmospheric physics. After being in the field for more than a decade, I still have gaps in my atmospheric science education. Thus I assess a radiative transfer book fi-om two main criteria: how well does it describe the material that is familiar to me (the radiative transfer equation and its numerical solutions) and how well does it help me to fill the gaps in my personal knowledge. So I present this review fi-om the perspective of a former mathematician working in the field of atmospheric radiation. . After being asked to review the book, my first intention was to compare the new edition with the previous one (Liou, 1980). In doing so, you can clearly follow the progress made in the field of atmospheric radiation over the past two decades. If there are few changes (as in Fundamental Radiative Transfer) or no changes at all (as in the Maxwell s equations), then the field has not seen much development. To the contrary, many differences between the two editions illustrate areas of major progress in the field, such as evidenced in Thermal Ineared Radiative Transfer and even in the creations of completely new fields like Three-Dimensional Radiative Transfer or Light Scattering by Nonspherical Particles. Obviously, the major changes happened not in the theory, which is at least half a century old, but in data quality and completely new measurements (mostly due to new satellite data) with higher accuracy and more reliability. The new edition illustrates this progress well.

Marshak, Alexander↗

NASA NTRS2003

Fundamentals of Polarized Light

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Mishchenko, Michael↗

NASA NTRS2003

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗

NASA NTRS2004

SQUID Multiplexers for Cryogenic Detector Arrays

SQUID multiplexers make it possible to build arrays of thousands of cryogenic detectors with a manageable number of readout channels. We are developing time-division SQUID multiplexers based on Nb trilayer SQUIDs to read arrays of superconducting transition-edge sensors. Our first-generation, 8-channel SQUID multiplexer was used in FIBRE, a one-dimensional TES array for submillimeter astronomy. Our second-generation 32-pixel multiplexer, based on an improved architecture, has been developed for instruments including Constellation-X, SCUBA-2, and solar x-ray astronomy missions. SCUBA-2, which is being developed for the James Clerk Maxwell Telescope, will have more than 10,000 pixels. We are now developing a third-generation architecture based on superconducting hot-electron switches. The use of SQUID multiplexers in instruments operating at above 2 K will also be discussed.

Irwin, Kent↗

NASA NTRS2004

Enhanced Damping for Capillary Bridge Oscillation Using Velocity Feedback

The stability of cylindrical liquid bridges in reduced gravity is affected by ambient vibrations of the spacecraft. Such vibrations are expected to excite capillary modes of the bridge. The lowest-order unstable mode is particularly susceptible to vibration as the length of the bridge approaches the stability limit. This low-order mode is known as the (2,0) mode and is an axisymmetric varicose mode of one wavelength in the axial direction. In this work, an optical system is used to detect the (2,0)-mode amplitude. The derivative of the error signal produced by this detector is used to produce the appropriate voltages on a pair of ring electrodes which are concentric with the bridge. A mode-coupled Maxwell stress profile is thus generated in proportional to the modal velocity. Depending on the sign of the gain, the damping of the capillary oscillation can be either increased or decreased. This effect has been demonstrated in Plateau-tank experiments. Increasing the damping of the capillary modes on free liquid surfaces in space could be beneficial for containerless processing and other novel technologies. [work supported by NASA]

Wei, Wei↗

NASA NTRS2001

An Implicit LU/AF FDTD Method

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗

NASA NTRS1999

Envelope structure of deeply embedded young stellar objects in the Serpens Molecular Cloud

Aperture-synthesis and single-dish (sub-) millimeter molecular-line and continuum observations reveal in great detail the envelope structure of deeply embedded young stellar objects (SMM 1 = FIRS 1, SMM 2, SMM 3, SMM 4) in the densely star-forming Serpens Molecular Cloud. SMM 1, 3, and 4 show partially resolved (>2" = 800 AU) continuum emission in the beam of the Owens Valley Millimeter Array at lambda = 3.4-1.4 mm. The continuum visibilities accurately constrain the density structure in the envelopes, which can be described by a radial power law with slope -2.0 +/- 0.5 on scales of 300 to 8000 AU. Inferred envelope masses within a radius of 8000 AU are 8.7, 3.0, and 5.3 Msolar for SMM 1, 3, and 4, respectively. A point source with 20%-30% of the total flux at 1.1 mm is required to fit the observations on long baselines, corresponding to warm envelope material within approximately 100 AU or a circumstellar disk. No continuum emission is detected interferometrically toward SMM 2, corresponding to an upper limit of 0.2 Msolar assuming Td = 24 K. The lack of any compact dust emission suggests that the SMM 2 core does not contain a central protostar. Aperture-synthesis observations of the 13CO, C18O, HCO+, H13CO+, HCN, H13CN, N2H+ 1-0, SiO 2-1, and SO 2(2)-1(1) transitions reveal compact emission toward SMM 1, 3, and 4. SMM 2 shows only a number of clumps scattered throughout the primary field of view, supporting the conclusion that this core does not contain a central star. The compact molecular emission around SMM 1, 3, and 4 traces 5"-10" (2000-4000 AU) diameter cores that correspond to the densest regions of the envelopes, as well as material directly associated with the molecular outflow. Especially prominent are the optically thick HCN and HCO+ lines that show up brightly along the walls of the outflow cavities. SO and SiO trace shocked material, where their abundances may be enhanced by 1-2 orders of magnitude over dark-cloud values. A total of 31 molecular transitions have been observed with the James Clerk Maxwell and Caltech Submillimeter telescopes in the 230, 345, 490, and 690 GHz atmospheric windows toward all four sources, containing, among others, lines of CO, HCO+, HCN, H2CO, SiO, SO, and their isotopomers. These lines show 20-30 km s-1 wide line wings, deep and narrow (1-2 km s-1) self-absorption, and 2-3 km s-1 FWHM line cores. The presence of highly excited lines like 12CO 4-3 and 6-5, 13CO 6-5, and several H2CO transitions indicates the presence of material with temperatures > or approximately 100 K. Monte Carlo calculations of the molecular excitation and line transfer show that the envelope model derived from the dust emission can successfully reproduce the observed line intensities. The depletion of CO in the cold gas is modest compared to values inferred in objects like NGC 1333 IRAS 4, suggesting that the phase of large depletions through the entire envelope is short lived and may be influenced by the local star formation density. Emission in high-excitation lines of CO and H2CO requires the presence of a small amount of approximately 100 K material, comprising less than 1% of the total envelope mass and probably associated with the outflow or the innermost region of the envelope. The derived molecular abundances in the warm (Tkin > 20 K) envelope are similar to those found toward other class 0 YSOs like IRAS 16293-2422, though some species appear enhanced toward SMM 1. Taken together, the presented observations and analysis provide the first comprehensive view of the physical and chemical structure of the envelopes of deeply embedded young stellar objects in a clustered environment on scales between 1000 and 10,000 AU.

NASA Discipline Exobiology↗