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NASA NTRS1995

Laser diagnostics for microgravity droplet studies

An instrument has been designed, built, and tested for performing laser diagnostic measurements of droplet combustion in low-gravity-flight aircraft. Nonintrusive measurements are of particular importance for droplet combustion (the simplest example of non-premixed combustion) and transport in microgravity environments, where physical contact would introduce an unacceptable level of perturbations. The resolution of these diagnostics can also isolate transport to length scales much smaller than the droplet diameter. These techniques can be configured to instantaneously map an entire flow field in two and three dimensions, providing either qualitative or quantitative information on the distribution of a desired scalar or vector quantity. Detailing the gas-phase flow field and position of the flame front can be achieved using planar laser-induced fluorescence (PLIF) of OH or another flame front marker. An alternative approach is to obtain LIF from a diagnostic seed included in the liquid phase fuel; it would be consumed at the flame front. The main advantage to this approach is that it is easier to choose the wavelength of the molecular absorption which coincides with convenient laser wavelengths rather than finding lasers which can be configured to access OH. Our present method uses a nitrogen-pumped dye laser tuned to a sodium absorption and addition of small concentrations of NaCl to the fuel. Particle image velocimetry (PIV) is a laser-based technique which has recently had its practicality greatly enhanced by the development of high-resolution CCD cameras and the increase in speed and capacity of computer systems. With this technique, a seeded flow is illuminated with a double-pulsed laser sheet to generate a double exposure image on a film or CCD camera. Computer analysis of the image is used to determine the particle velocity vectors and, thus, the gas velocity within the plane of the laser sheet. Our current experiment uses PIV for measuring relative droplet gas-phase velocities in a parabolic flight environment. The results show successful application of PLIF relative to luminosity and radical emission near 308 nm. PIV results are less successful due to gas thermal expansion deflecting the seed particles away from the measurement volume. PIV is applicable for measurements in the absence of combustion.

Winter, Michael↗

NASA NTRS1996

Laser Sources for Generation of Ultrasound

Two laser systems have been built and used to demonstrate enhancements beyond current technology used for laser-based generation and detection of ultrasound. The first system consisted of ten Nd:YAG laser cavities coupled electronically and optically to permit sequential bursts of up to ten laser pulses directed either at a single point or configured into a phased array of sources. Significant enhancements in overall signal-to-noise ratio for laser ultrasound incorporating this new source system was demonstrated, using it first as a source of narrowband ultrasound and secondly as a phased array source producing large enhanced signal displacements. A second laser system was implemented using ultra fast optical pulses from a Ti:Sapphire laser to study a new method for making laser generated ultrasonic measurements of thin films with thicknesses on the order of hundreds of angstroms. Work by prior investigators showed that such measurements could be made based upon fluctuations in the reflectivity of thin films when they are stressed by an arriving elastic pulse. Research performed using equipment purchased under this program showed that a pulsed interferometric system could be used as well as a piezoreflective detection system to measure pulse arrivals even in thin films with very low piezoreflective coefficients.

Wagner, James W.↗

NASA NTRS1995

Laser-Directed Ranging System Implementing Single Camera System for Telerobotics Applications

The invention relates generally to systems for determining the range of an object from a reference point and, in one embodiment, to laser-directed ranging systems useful in telerobotics applications. Digital processing techniques are employed which minimize the complexity and cost of the hardware and software for processing range calculations, thereby enhancing the commercial attractiveness of the system for use in relatively low-cost robotic systems. The system includes a video camera for generating images of the target, image digitizing circuitry, and an associated frame grabber circuit. The circuit first captures one of the pairs of stereo video images of the target, and then captures a second video image of the target as it is partly illuminated by the light beam, suitably generated by a laser. The two video images, taken sufficiently close together in time to minimize camera and scene motion, are converted to digital images and then compared. Common pixels are eliminated, leaving only a digital image of the laser-illuminated spot on the target. Mw centroid of the laser illuminated spot is dm obtained and compared with a predetermined reference point, predetermined by design or calibration, which represents the coordinate at the focal plane of the laser illumination at infinite range. Preferably, the laser and camera are mounted on a servo-driven platform which can be oriented to direct the camera and the laser toward the target. In one embodiment the platform is positioned in response to movement of the operator's head. Position and orientation sensors are used to monitor head movement. The disparity between the digital image of the laser spot and the reference point is calculated for determining range to the target. Commercial applications for the system relate to active range-determination systems, such as those used with robotic systems in which it is necessary to determine the, range to a workpiece or object to be grasped or acted upon by a robot arm end-effector in response to commands generated by an operator. In one embodiment, the system provides a real-time image of the target for the operator as the robot approaches the object. The system is also adapted for use in virtual reality systems in which a remote object or workpiece is to be acted upon by a remote robot arm or other mechanism controlled by an operator.

Wells, Dennis L.↗

NASA NTRS1998

Research Lasers and Air Traffic Safety: Issues, Concerns and Responsibilities of the Research Community

The subject of outdoor use of lasers relative to air traffic has become a diverse and dynamic topic. During the past several decades, the use of lasers in outdoor research activities have increased significantly. Increases in the outdoor use of lasers and increases in air traffic densities have changed the levels of risk involved. To date there have been no documented incidents of air traffic interference from research lasers; however, incidents involving display lasers have shown a marked increase. As a result of the national response to these incidents, new concerns over lasers have arisen. Through the efforts of the SAE G-10T Laser Safety Hazards Subcommittee and the ANSI Z136.6 development committee, potential detrimental effects to air traffic beyond the traditional eye damage concerns have been identified. An increased emphasis from the Federal Aviation Administration (FAA), the Center for Devices and Radiological Hazards (CDRH), and the National Transportation Safety Board (NTSB) along with increased concern by the public have resulted in focused scrutiny of potential hazards presented by lasers. The research community needs to rethink the traditional methods of risk evaluation and application of protective measures. The best current approach to assure adequate protection of air traffic is the application of viable hazard and risk analysis and the use of validated protective measures. Standards making efforts and regulatory development must be supported by the research community to assure that reasonable measures are developed. Without input, standards and regulations can be developed that are not compatible with the needs of the research community. Finally, support is needed for the continued development and validation of protective measures.

Nessler, Phillip J., Jr.↗

NASA NTRS2000

Laser Welding in Electronic Packaging

The laser has proven its worth in numerous high reliability electronic packaging applications ranging from medical to missile electronics. In particular, the pulsed YAG laser is an extremely flexible and versatile too] capable of hermetically sealing microelectronics packages containing sensitive components without damaging them. This paper presents an overview of details that must be considered for successful use of laser welding when addressing electronic package sealing. These include; metallurgical considerations such as alloy and plating selection, weld joint configuration, design of optics, use of protective gases and control of thermal distortions. The primary limitations on use of laser welding electronic for packaging applications are economic ones. The laser itself is a relatively costly device when compared to competing welding equipment. Further, the cost of consumables and repairs can be significant. These facts have relegated laser welding to use only where it presents a distinct quality or reliability advantages over other techniques of electronic package sealing. Because of the unique noncontact and low heat inputs characteristics of laser welding, it is an ideal candidate for sealing electronic packages containing MEMS devices (microelectromechanical systems). This paper addresses how the unique advantages of the pulsed YAG laser can be used to simplify MEMS packaging and deliver a product of improved quality.

Source record↗

NASA NTRS2000

Using Airborne Laser Altimetry to Detect Topographic Change at Long Valley Caldera California

The topography of the Long Valley caldera, California, was sampled using airborne laser altimetry in 1993, 1995, and 1997 to test the feasibility of using airborne laser altimetry for monitoring deformation of volcanic origin. Results show the laser altimeters are able to resolve subtle topographic features such as a gradual slope and to detect small transient changes in lake elevation. Crossover and repeat pass analyses of laser tracks indicate decimeter-level vertical precision is obtained over flat and low-sloped terrain for altimeter systems performing waveform digitization. Comparisons with complementary, ground-based CPS data at a site close to Bishop airport indicate that the laser and GPS-derived elevations agree to within the error inherent in the measurement and that horizontal locations agree to within the radius of the laser footprint. A comparison of the data at two sites, one where no change and the other where the maximum amount of vertical uplift is expected, indicates approximately 10 cm of relative uplift occurred 1993-1997, in line with predictions from continuous CPS measurements in the region. Extensive terrain mapping flights during the 1995 and 1997 missions demonstrate some of the unique abilities of laser altimetry; the straightforward creation of high resolution, high accuracy digital elevation models of overflown terrain, and the ability to determine ground topography in the presence of significant ground cover such as dense tree canopies. These capabilities make laser altimetry an attractive technique for quantifying topographic change of volcanic origin, especially in forested regions of the world where other remote sensing instruments have difficulty detecting the underlying topography.

Hofton, M. A.↗

NASA NTRS1999

Using Airborne Laser Altimetry to Detect Topographic Change at Long Valley Caldera, California

The topography of the Long Valley caldera, California, was sampled using airborne laser altimetry in 1993, 1995, and 1997 to test the feasibility of using airborne laser altimetry for monitoring deformation of volcanic origin. Results show the laser altimeters are able to resolve subtle topographic features such as a gradual slope and to detect small transient changes in lake elevation. Crossover and repeat pass analyses of laser tracks indicate decimeter-level vertical precision is obtained over flat and low-sloped terrain for altimeter systems performing waveform digitization. Comparisons with complementary, ground-based GPS data at a site close to Bishop airport indicate that the laser and GPS-derived elevations agree to within the error inherent in the measurement and that horizontal locations agree to within the radius of the laser footprint. A comparison of the data at two sites, one where no change and the other where the maximum amount of vertical uplift is expected, indicates approximately 10 cm of relative uplift occurred 1993-1997, in line with predictions from continuous GPS measurements in the region. Extensive terrain mapping flights during the 1995 and 1997 missions demonstrate some of the unique abilities of laser altimetry; the straightforward creation of high resolution, high accuracy digital elevation models of overflown terrain, and the ability to determine ground topography in the presence of significant ground cover such as dense tree canopies. These capabilities make laser altimetry an attractive technique for quantifying topographic change of volcanic origin, especially in forested regions of the world where other remote sensing instruments have difficulty detecting the underlying topography.

Hofton, M. A.↗

NASA NTRS2000

Future Applications Using Return-Pulse Correlation from Imaging Laser Altimeters

The Laser Vegetation Imaging Sensor (LVIS) is an airborne, wide-swath, digitization-only laser altimeter capable of collecting full return waveforms (i.e. echoes) from laser footprints ranging in diameter from 1 to 80 m across up to a 1 km wide data swath. The return waveform can be used to enhance the accuracy of laser ranging and to provide information about the vertical structure of vegetation and topography within each laser footprint. Although extremely small laser footprints (< 1 0 cm diameter) generally return simple, impulse responses to their target surface, larger footprints typically exhibit complex returns representing the diverse vertical distributions of surfaces contained in each footprint. Only a handful of airborne and spaceborne laser altimeters record the return echo or return pulse that is reflected from the Earth's surface (i.e. NASA's LVIS, SLA, VCL, and GLAS laser altimeters). Waveforms are currently interpreted to extract a timing or ranging point or points to represent the mean ground elevation or the vertical height of vegetation. But, recent progress using pulse shape correlation techniques shows promise for a variety of science applications involving change detection of surface topography and vegetation as well as potential for improving data processing by correlating images or crossovers to solve systematic biases. We show example correlation images from LVIS and discuss instrument design implications and potential science applications.

Blair, J. Bryan↗

NASA NTRS2001

Laser Ignition Technology for Bi-Propellant Rocket Engine Applications

The fiber optically coupled laser ignition approach summarized is under consideration for use in igniting bi-propellant rocket thrust chambers. This laser ignition approach is based on a novel dual pulse format capable of effectively increasing laser generated plasma life times up to 1000 % over conventional laser ignition methods. In the dual-pulse format tinder consideration here an initial laser pulse is used to generate a small plasma kernel. A second laser pulse that effectively irradiates the plasma kernel follows this pulse. Energy transfer into the kernel is much more efficient because of its absorption characteristics thereby allowing the kernel to develop into a much more effective ignition source for subsequent combustion processes. In this research effort both single and dual-pulse formats were evaluated in a small testbed rocket thrust chamber. The rocket chamber was designed to evaluate several bipropellant combinations. Optical access to the chamber was provided through small sapphire windows. Test results from gaseous oxygen (GOx) and RP-1 propellants are presented here. Several variables were evaluated during the test program, including spark location, pulse timing, and relative pulse energy. These variables were evaluated in an effort to identify the conditions in which laser ignition of bi-propellants is feasible. Preliminary results and analysis indicate that this laser ignition approach may provide superior ignition performance relative to squib and torch igniters, while simultaneously eliminating some of the logistical issues associated with these systems. Further research focused on enhancing the system robustness, multiplexing, and window durability/cleaning and fiber optic enhancements is in progress.

Thomas, Matthew E.↗

NASA NTRS1998

Ultrafast Modulation and Switching of Quantum-Well Lasers using Terahertz Fields

Modulation and switching of semiconductor lasers are important for laser-based information technology. Typically the speed of modulation and switching is limited by interband processes such as stimulated and spontaneous recombinations which occur on a nanosecond time scale. This is why the diode laser modulation has been restricted to tens of GHz. Modulation at higher speed is highly desirable as the information technology enters into the so-called tera-era. In this paper, we study the possibility of utilizing THz-field-induced plasma heating to modulate quantum-well lasers. This is a timely study since, with the advancement of THz solid-state sources and free-electron lasers, THz physics and related technology is currently coming out of its infancy. The investigation of interplaying THz and optical fields is also of intruiging fundamental interest. First, we introduce theoretical plasma heating results for the quantum-well optical amplifier in the presense of an intense half-cycle THz pulse. The heated carrier distributions are then utilized to calculate the THz-pulse-induced change in refractive index and gain profile. Since the electron-hole-plasma is heated using intraband transitions, we circumvent the usual complications due to an overall change in density, and the nonlinear recovery is governed solely by the carrier-LO-phonon interactions, typically 5 ps for a complete recovery. This procedure implies THz and sub-THz switching and recovery rates, respectively; using either gain modulation or index modulation. Plasma heating via steady-state THz fields is also studied. Finally, numerical simulation of a coupled set of equations to investigate the THz modulation based on a simplified model for quantum-well lasers is presented. Our results show that a semiconductor laser can be modulated at up to 1 THz with little distortion with a THz field amplitude at the order of a few kV/cm. Laser responses to a change in THz frequency will be shown. Constraints, practicalities, and applications will be discussed.

Ning, Cun-Zheng↗

NASA NTRS2004

Advanced Receiver/Converter Experiments for Laser Wireless Power Transmission

For several years NASA Marshall Space Flight Center, UAH and ENTECH have been working on various aspects of space solar power systems. The current activity was just begun in January 2004 to further develop this new photovoltaic concentrator laser receiver/converter technology. During the next few months, an improved prototype will be designed, fabricated, and thoroughly tested under laser illumination. The final paper will describe the new concept, present its advantages over other laser receiver/converter approaches (including planar photovoltaic arrays), and provide the latest experiment results on prototype hardware (including the effects of laser irradiance level and cell temperature). With NASA's new human exploration plans to first return to the Moon, and then to proceed to Mars, the new photovoltaic concentrator laser receiver/converter technology could prove to be extremely useful in providing power to the landing sites and other phases of the missions. For example, to explore the scientifically interesting and likely resource-rich poles of the Moon (which may contain water) or the poles of Mars (which definitely contain water and carbon dioxide), laser power beaming could represent the simplest means of providing power to these regions, which receive little or no sunlight, making solar arrays useless there. In summary, the authors propose a paper on definition and experimental results of a novel photovoltaic concentrator approach for collecting and converting laser radiation to electrical power. The new advanced photovoltaic concentrator laser receiver/converter offers higher performance, lighter weight, and lower cost than competing concepts, and early experimental results are confirming the expected excellent Performance levels. After the small prototypes are successfully demonstrated, a larger array with even better performance is planned for the next phase experiments and demonstrations. Thereafter, a near-term flight experiment of the new technology should be developed and flown, to lay the groundwork for future space power applications in the Earth-Moon neighborhood, and ultimately encompassing Mars and its environs.

Howell, Joe T.↗

NASA NTRS2001

Laser High-Cycle Thermal Fatigue of Pulse Detonation Engine Combustor Materials Tested

Pulse detonation engines (PDE's) have received increasing attention for future aerospace propulsion applications. Because the PDE is designed for a high-frequency, intermittent detonation combustion process, extremely high gas temperatures and pressures can be realized under the nearly constant-volume combustion environment. The PDE's can potentially achieve higher thermodynamic cycle efficiency and thrust density in comparison to traditional constant-pressure combustion gas turbine engines (ref. 1). However, the development of these engines requires robust design of the engine components that must endure harsh detonation environments. In particular, the detonation combustor chamber, which is designed to sustain and confine the detonation combustion process, will experience high pressure and temperature pulses with very short durations (refs. 2 and 3). Therefore, it is of great importance to evaluate PDE combustor materials and components under simulated engine temperatures and stress conditions in the laboratory. In this study, a high-cycle thermal fatigue test rig was established at the NASA Glenn Research Center using a 1.5-kW CO2 laser. The high-power laser, operating in the pulsed mode, can be controlled at various pulse energy levels and waveform distributions. The enhanced laser pulses can be used to mimic the time-dependent temperature and pressure waves encountered in a pulsed detonation engine. Under the enhanced laser pulse condition, a maximum 7.5-kW peak power with a duration of approximately 0.1 to 0.2 msec (a spike) can be achieved, followed by a plateau region that has about one-fifth of the maximum power level with several milliseconds duration. The laser thermal fatigue rig has also been developed to adopt flat and rotating tubular specimen configurations for the simulated engine tests. More sophisticated laser optic systems can be used to simulate the spatial distributions of the temperature and shock waves in the engine. Pulse laser high-cycle thermal fatigue behavior has been investigated on a flat Haynes 188 alloy specimen, under the test condition of 30-Hz cycle frequency (33-msec pulse period and 10-msec pulse width including a 0.2-msec pulse spike; ref. 4). Temperature distributions were calculated with one-dimensional finite difference models. The calculations show that that the 0.2-msec pulse spike can cause an additional 40 C temperature fluctuation with an interaction depth of 0.08 mm near the specimen surface region. This temperature swing will be superimposed onto the temperature swing of 80 C that is induced by the 10-msec laser pulse near the 0.53-mm-deep surface interaction region.

Zhu, Dong-Ming↗

NASA NTRS2006

Stretched Lens Array (SLA) for Collection and Conversion of Infrared Laser Light: 45% Efficiency Demonstrated for Near-Term 800 W/kg Space Power System

For the past 2% years, our team has been developing a unique photovoltaic concentrator array for collection and conversion of infrared laser light. This laser-receiving array has evolved from the solar-receiving Stretched Lens Array (SLA). The laser-receiving version of SLA is being developed for space power applications when or where sunlight is not available (e.g., the eternally dark lunar polar craters). The laser-receiving SLA can efficiently collect and convert beamed laser power from orbiting spacecraft or other sources (e.g., solar-powered lasers on the permanently illuminated ridges of lunar polar craters). A dual-use version of SLA can produce power from sunlight during sunlit portions of the mission, and from beamed laser light during dark portions of the mission. SLA minimizes the cost and mass of photovoltaic cells by using gossamer-like Fresnel lenses to capture and focus incoming light (solar or laser) by a factor of 8.5X, thereby providing a cost-effective, ultra-light space power system.

O'Neill, Mark↗

NASA NTRS2006

Advanced 2-micron Solid-state Laser for Wind and CO2 Lidar Applications

Significant advancements in the 2-micron laser development have been made recently. Solid-state 2-micron laser is a key subsystem for a coherent Doppler lidar that measures the horizontal and vertical wind velocities with high precision and resolution. The same laser, after a few modifications, can also be used in a Differential Absorption Lidar (DIAL) system for measuring atmospheric CO2 concentration profiles. The world record 2-micron laser energy is demonstrated with an oscillator and two amplifiers system. It generates more than one joule per pulse energy with excellent beam quality. Based on the successful demonstration of a fully conductive cooled oscillator by using heat pipe technology, an improved fully conductively cooled 2-micron amplifier was designed, manufactured and integrated. It virtually eliminates the running coolant to increase the overall system efficiency and reliability. In addition to technology development and demonstration, a compact and engineering hardened 2-micron laser is under development. It is capable of producing 250 mJ at 10 Hz by an oscillator and one amplifier. This compact laser is expected to be integrated to a lidar system and take field measurements. The recent achievements push forward the readiness of such a laser system for space lidar applications. This paper will review the developments of the state-of-the-art solid-state 2-micron laser.

Yu, Jirong↗

NASA NTRS1993

Solid state laser

A wavelength-tunable, injection-seeded, dispersion-compensated, dispersively-pumped solid state laser includes a lasing medium; a highly reflective mirror; an output coupler; at least one isosceles Brewster prism oriented to the minimum deviation angle between the medium and the mirror for directing light of different wavelengths along different paths; means for varying the angle of the highly reflective mirror relative to the light from at least one Brewster angle for selecting a predetermined laser operating wavelength; a dispersion compensation apparatus associated with the lasing medium; a laser injection seeding port disposed between the dispersion compensation apparatus and one of the mirror and coupler and including a reflective surface at an acute non-Brewster angle to the laser beam for introducing a seed input; a dispersion compensation apparatus associated with the laser medium including opposite chirality optical elements; the lasing medium including a pump surface disposed at an acute angle to the laser beam to define a discrete path for the pumping laser beam separate from the pumped laser beam.

Rines, Glen A.↗

NASA NTRS2009

High Repetition Rate Pulsed 2-Micron Laser Transmitter for Coherent CO2 DIAL Measurement

A high repetition rate, highly efficient, Q-switched 2-micron laser system as the transmitter of a coherent differential absorption lidar for CO2 measurement has been developed at NASA Langley Research Center. Such a laser transmitter is a master-slave laser system. The master laser operates in a single frequency, either on-line or off-line of a selected CO2 absorption line. The slave laser is a Q-switched ring-cavity Ho:YLF laser which is pumped by a Tm:fiber laser. The repetition rate can be adjusted from a few hundred Hz to 10 kHz. The injection seeding success rate is from 99.4% to 99.95%. For 1 kHz operation, the output pulse energy is 5.5mJ with the pulse length of approximately 50 ns. The optical-to-optical efficiency is 39% when the pump power is 14.5W. The measured standard deviation of the laser frequency jitter is about 3 MHz.

Singh, Uprendra N.↗

NASA NTRS2007

Dual-Beam Atom Laser Driven by Spinor Dynamics

An atom laser now undergoing development simultaneously generates two pulsed beams of correlated Rb-87 atoms. (An atom laser is a source of atoms in beams characterized by coherent matter waves, analogous to a conventional laser, which is a source of coherent light waves.) The pumping mechanism of this atom laser is based on spinor dynamics in a Bose-Einstein condensate. By virtue of the angular-momentum conserving collisions that generate the two beams, the number of atoms in one beam is correlated with the number of atoms in the other beam. Such correlations are intimately linked to entanglement and squeezing in atomic ensembles, and atom lasers like this one could be used in exploring related aspects of Bose-Einstein condensates, and as components of future sensors relying on atom interferometry. In this atom-laser apparatus, a Bose-Einstein condensate of about 2 x 10(exp 6) Rb-87 atoms at a temperature of about 120 micro-K is first formed through all-optical means in a relatively weak singlebeam running-wave dipole trap that has been formed by focusing of a CO2-laser beam. By a technique that is established in the art, the trap is loaded from an ultrahigh-vacuum magnetooptical trap that is, itself, loaded via a cold atomic beam from an upstream two-dimensional magneto-optical trap that resides in a rubidium-vapor cell that is differentially pumped from an adjoining vacuum chamber, wherein are performed scientific observations of the beams ultimately generated by the atom laser.

Thompson, Robert↗

NASA NTRS2007

Ring-Down Spectroscopy for Characterizing a CW Raman Laser

.A relatively simple technique for characterizing an all-resonant intracavity continuous-wave (CW) solid-state Raman laser involves the use of ring-down spectroscopy. As used here, characterizing signifies determining such parameters as threshold pump power, Raman gain, conversion efficiency, and quality factors (Q values) of the pump and Stokes cavity modes. Heretofore, in order to characterize resonant-cavity-based Raman lasers, it has usually been necessary to manipulate the frequencies and power levels of pump lasers and, in each case, to take several sets of measurements. In cases involving ultra-high-Q resonators, it also has been desirable to lock pump lasers to resonator modes to ensure the quality of measurement data. Simpler techniques could be useful. In the present ring-down spectroscopic technique, one infers the parameters of interest from the decay of the laser out of its steady state. This technique does not require changing the power or frequency of the pump laser or locking the pump laser to the resonator mode. The technique is based on a theoretical analysis of what happens when the pump laser is abruptly switched off after the Raman generation reaches the steady state. The analysis starts with differential equations for the evolution of the amplitudes of the pump and Stokes electric fields, leading to solutions for the power levels of the pump and Stokes fields as functions of time and of the aforementioned parameters. Among other things, these solutions show how the ring-down time depends, to some extent, on the electromagnetic energy accumulated in the cavity. The solutions are readily converted to relatively simple equations for the parameters as functions of quantities that can be determined from measurements of the time-dependent power levels. For example, the steady-state intracavity conversion efficiency is given by G1/G2 1 and the threshold power is given by Pin(G2/G1)2, where Pin is the steady-state input pump power immediately prior to abrupt switch-off, G1 is the initial rate of decay of the pump field, and G2 is the final rate of decay of the pump field. Hence, it is possible to determine all the parameters from a single ring-down scan, provided that the measurements taken in that scan are sufficiently accurate and complete.

Matsko, Andrey↗