Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Coupled resonators”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Damage Detection Response Characteristics of Open Circuit Resonant (SansEC) Sensors

The capability to assess the current or future state of the health of an aircraft to improve safety, availability, and reliability while reducing maintenance costs has been a continuous goal for decades. Many companies, commercial entities, and academic institutions have become interested in Integrated Vehicle Health Management (IVHM) and a growing effort of research into "smart" vehicle sensing systems has emerged. Methods to detect damage to aircraft materials and structures have historically relied on visual inspection during pre-flight or post-flight operations by flight and ground crews. More quantitative non-destructive investigations with various instruments and sensors have traditionally been performed when the aircraft is out of operational service during major scheduled maintenance. Through the use of reliable sensors coupled with data monitoring, data mining, and data analysis techniques, the health state of a vehicle can be detected in-situ. NASA Langley Research Center (LaRC) is developing a composite aircraft skin damage detection method and system based on open circuit SansEC (Sans Electric Connection) sensor technology. Composite materials are increasingly used in modern aircraft for reducing weight, improving fuel efficiency, and enhancing the overall design, performance, and manufacturability of airborne vehicles. Materials such as fiberglass reinforced composites (FRC) and carbon-fiber-reinforced polymers (CFRP) are being used to great advantage in airframes, wings, engine nacelles, turbine blades, fairings, fuselage structures, empennage structures, control surfaces and aircraft skins. SansEC sensor technology is a new technical framework for designing, powering, and interrogating sensors to detect various types of damage in composite materials. The source cause of the in-service damage (lightning strike, impact damage, material fatigue, etc.) to the aircraft composite is not relevant. The sensor will detect damage independent of the cause. Damage in composite material is generally associated with a localized change in material permittivity and/or conductivity. These changes are sensed using SansEC. The unique electrical signatures (amplitude, frequency, bandwidth, and phase) are used for damage detection and diagnosis. An operational system and method would incorporate a SansEC sensor array on select areas of the aircraft exterior surfaces to form a "Smart skin" sensing surface. In this paper a new method and system for aircraft in-situ damage detection and diagnosis is presented. Experimental test results on seeded fault damage coupons and computational modeling simulation results are presented. NASA LaRC has demonstrated with individual sensors that SansEC sensors can be effectively used for in-situ composite damage detection of delamination, voids, fractures, and rips. Keywords: Damage Detection, Composites, Integrated Vehicle Health Monitoring (IVHM), Aviation Safety, SansEC Sensors

Dudley, Kenneth L.↗
NASA NTRS2008

Optimized Geometry for Superconducting Sensing Coils

An optimized geometry has been proposed for superconducting sensing coils that are used in conjunction with superconducting quantum interference devices (SQUIDs) in magnetic resonance imaging (MRI), magnetoencephalography (MEG), and related applications in which magnetic fields of small dipoles are detected. In designing a coil of this type, as in designing other sensing coils, one seeks to maximize the sensitivity of the detector of which the coil is a part, subject to geometric constraints arising from the proximity of other required equipment. In MRI or MEG, the main benefit of maximizing the sensitivity would be to enable minimization of measurement time. In general, to maximize the sensitivity of a detector based on a sensing coil coupled with a SQUID sensor, it is necessary to maximize the magnetic flux enclosed by the sensing coil while minimizing the self-inductance of this coil. Simply making the coil larger may increase its self-inductance and does not necessarily increase sensitivity because it also effectively increases the distance from the sample that contains the source of the signal that one seeks to detect. Additional constraints on the size and shape of the coil and on the distance from the sample arise from the fact that the sample is at room temperature but the coil and the SQUID sensor must be enclosed within a cryogenic shield to maintain superconductivity.

Eom, Byeong Ho↗
NASA NTRS1999

Quantum Computation by Optically Coupled Steady Atoms/Quantum-Dots Inside a Quantum Cavity

We present a model for quantum computation using $n$ steady 3-level atoms kept inside a quantum cavity, or using $n$ quantum-dots (QDs) kept inside a quantum cavity. In this model one external laser is pointed towards all the atoms/QDs, and $n$ pairs of electrodes are addressing the atoms/QDs, so that each atom is addressed by one pair. The energy levels of each atom/QD are controlled by an external Stark field given to the atom/QD by its external pair of electrodes. Transition between two energy levels of an individual atom/ QD are controlled by the voltage on its electrodes, and by the external laser. Interactions between two atoms/ QDs are performed with the additional help of the cavity mode (using on-resonance condition). Laser frequency, cavity frequency, and energy levels are far off-resonance most of the time, and they are brought to the resonance (using the Stark effect) only at the time of operations. Steps for a controlled-NOT gate between any two atoms/QDs have been described for this model. Our model demands some challenging technological efforts, such as manufacturing single-electron QDs inside a cavity. However, it promises big advantages over other existing models which are currently implemented, and might enable a much easier scale-up, to compute with many more qubits.

Pradhan, P.↗
NASA NTRS2009

A Finite Element Theory for Predicting the Attenuation of Extended-Reacting Liners

A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

Watson, W. R.↗
NASA NTRS2003

[13C]-Specific labeling of 8-2' linked (-)-cis-blechnic, (-)-trans-blechnic and (-)-brainic acids in the fern Blechnum spicant

In vivo administration experiments using stable (13C) and radio (14C) labeled precursors established that the optically active 8-2' linked lignans, (-)-cis-blechnic, (-)-trans-blechnic and (-)-trans-brainic acids, were directly derived from L-phenylalanine, cinnamate, and p-coumarate but not either from tyrosine or acetate. The radiochemical time course data suggest that the initial coupling product is (-)-cis-blechnic acid, which is then apparently converted into both (-)-trans-blechnic and (-)-trans-brainic acids in vivo. These findings provide additional evidence for vascular plant proteins engendering distinct but specific phenolic radical-radical coupling modes, i.e., for full control over phenylpropanoid coupling in vivo, whether stereoselective or regiospecific.

NASA Discipline Plant Biology↗
NASA NTRS1989

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Hoshino, M.↗
NASA NTRS1961

Some Recent Studies in Structural Dynamics of Rotor Aircraft

This paper presents a summary of four recent studies relating to the structural-dynamics problems of rotor-powered aircraft. The first study concerns the measurement by means of dynamic models of the forces and moments at the hubs of various rotor configurations. The results of this study show that the periodic components of the forces and moments are highly dependent on both the rotor configuration and the flight condition. The second study treats the problem of resonance amplifications of rotor-blade stress and shows that by using multiple flapping hinges or flex-joints it is possible to control the natural frequencies of the rotor blade so that conditions of resonance between the frequencies of the aerodynamic input forces and the natural frequencies of the lower blade modes are avoided for all rotor speeds. Two studies of the stability of rotor aircraft axe also discussed. One of these involves the mechanical instability or ground resonance of rotorcraft wherein the rotor support in each of two mutually perpendicular directions in the rotor plane is represented as a multiple-degree-of-freedom system in contrast to the system having a "single" degree of freedom normally used in helicopter analysis. The consideration of the rotor support system as a two-degree-of-freedom system predicts additional unstable ranges of rotor speed not predicted by former analyses. The other instability treated is propeller whirl for which the significant motions are the pitching and yawing motions of the propeller disk which are coupled together by gyroscopic forces. The effect of the significant variables on the instability is presented and shows that the speed at which the instability occurs can be increased by increasing the relative stiffness of the propeller in the pitch and yaw directions or by increasing the effective structural damping of the nacelle.

George W Brooks↗
NASA NTRS1984

Kinetics of the reaction Cl + NO2 + M

Using atomic chlorine resonance fluorescence at 140 nm to detect the decay of atomic chlorine in the presence of an excess of NO2, the rate constant for the reaction Cl + NO2 + M, where M is the total gas concentration, is measured over the temperature range 264 to 417 K and at a pressure 1 to 7 torr in a discharge flow system. The rate constants for M= He and M= N2 are measured and the results are summarized in a table. The systematic error of the rate constants is estimated to be about 15 percent. A static photolysis system coupled with an FTIR spectrophotometer is used to determine the branching ratio for the formation of two possible isomers. The ratio is concluded to be ClONO (greater than or equal 75 percent) and ClNO2 (less than or equal 25 percent) which is in agreement with the results of Niki et al. (1978).

Leu, M.-T.↗
NASA NTRS1972

Design and testing of a magnetic suspension and damping system for a space telescope

The basic equations of motion are derived for a two dimensional, three degree of freedom simulation of a space telescope coupled to a spacecraft by means of a magnetic suspension and isolation system. The system consists of paramagnetic or ferromagnetic discs confined to the magnetic field between two Helmholtz coils. Damping is introduced by varying the magnetic field in proportion to a velocity signal derived from the telescope. The equations of motion are nonlinear, similar in behavior to the one-dimensional Van der Pol equation. The computer simulation was verified by testing a 264-kilogram air bearing platform which simulates the telescope in a frictionless environment. The simulation demonstrated effective isolation capabilities for disturbance frequencies above resonance. Damping in the system improved the response near resonance and prevented the build-up of large oscillatory amplitudes.

Ockman, N. J.↗
NASA NTRS1988

The influence of and the identification of nonlinearity in flexible structures

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Zavodney, Lawrence D.↗
NASA NTRS1990

Solar Activity and the Sea-surface Temperature Record-evidence of a Long-period Variation in Solar Total Irradiance

There have been many suggestions over the years of a connection between solar activity and the Earth's climate on time scales long compared to the 11-year sunspot cycle. They have remained little more than suggestions largely because of the major uncertainties in the climate record itself, and the difficulty in trying to compile a global average from an assembly of measurements that are uneven in both quality and distribution. Different climate time response to solar activity, some suggesting a positive correlation, some a negative correlation, and some no correlation at all. The only excuse for making yet another such suggestion is that much effort has been devoted in recent years to compiling climate records for the past century or more that are internally consistent and believable, and that a decadal-scale record of solar total irradiance is emerging from spacecraft measurements, and can be used to set limits on the variation that is likely to have occurred on these time scales. The work described here was originally inspired by the observation that the time series of globally averaged sea-surface temperatures over the past 120 years or so, as compiled by the British Meteorological Office group (Folland and Kates, 1984), bore a resonable similarity to the long-term average sunspot number, which is an indicator of the secular variability of solar activity. The two time series are shown where the sunspot number is shown as the 135-month running mean, and the SST variation is shown as the departure from an arbitrary average value. The simplest explanation of the similarity, if one accepts it as other than coincidental, is that the sun's luminosity may have been varying more or less in step with the level of solar activity, or in other words that there is a close coupling between the sun's magnetic condition and its radiative output on time scales longer than the 11-year cycle. Such an idea is not new, and in fact the time series shown can be regarded as a modern extension of the proposal put forward by Eddy (1977) to explain the covariance between various global climate indicators and solar activity as revealed by the C-14 record over the past millenium.

Reid, George C.↗
NASA NTRS1995

Uncooled tunneling infrared sensor

An uncooled infrared tunneling sensor in which the only moving part is a diaphragm which is deflected into contact with a micromachined silicon tip electrode prepared by a novel lithographic process. Similarly prepared deflection electrodes employ electrostatic force to control the deflection of a silicon nitride, flat diaphragm membrane. The diaphragm exhibits a high resonant frequency which reduces the sensor's sensitivity to vibration. A high bandwidth feedback circuit controls the tunneling current by adjusting the deflection voltage to maintain a constant deflection of the membrane. The resulting infrared sensor can be miniaturized to pixel dimensions smaller than 100 .mu.m. An alternative embodiment is implemented using a corrugated membrane to permit large deflection without complicated clamping and high deflection voltages. The alternative embodiment also employs a pinhole aperture in a membrane to accommodate environmental temperature variation and a sealed chamber to eliminate environmental contamination of the tunneling electrodes and undesireable accoustic coupling to the sensor.

Kenny, Thomas W.↗
NASA NTRS2011

Analytical Solution and Physics of a Propellant Damping Device

NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.

Yang, H. Q.↗
NASA NTRS1984

Decennial Specialists' Meeting on Rotorcraft Dynamics, 2nd, Moffett Field, CA, November 7-9, 1984, Proceedings

Various papers on helicopter rotor technology are presented. The subjects considered include: ground resonance analysis using a substructure modelling approach, aerolastic stability of a bearingless rotor, experimentally determined flutter from two and three-bladed model bearingless rotors in hover, lifting surface theory for a helicopter rotor in forward flight, aeroelastic considerations for torsionally soft rotors, and restructuring of a rotor analysis program. Also discussed are: dynamic inflow and its effect on experimental correlations, flap-lag-torsion instability in forward flight, dynamic stability of a bearingless circulation control rotor blade in hover, dynamic response characteristics of a circulation control rotor model pneumatic system, the relations between vibratory loads and airframe vibrations, coupled rotor body vibrations with in-plane degrees of freedom, helicopter vibration reduction concepts.

Source record↗
NASA NTRS2001

Quantum Mechanical Study of Nanoscale MOSFET

The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.

Svizhenko, Alexei↗
NASA NTRS2013

Estimating the Concentration of Large Raindrops from Polarimetric Radar and Disdrometer Observations

Estimation of rainfall integral parameters, including radar observables, and empirical relations between them are sensitive to the truncation of the drop size distribution (DSD), particularly at the large drop end. The sensitivity of rainfall integral parameters to the maximum drop diameter (D(sub max)) is exacerbated at C‐band since resonance effects are pronounced for large drops in excess of 5 mm diameter (D). Due to sampling limitations, it is often difficult to reliably estimate D(sub max) with disdrometers. The resulting uncertainties in D(sub max0 potentially increase errors in radar retrieval methods, particularly at C‐band, that rely on disdrometer observations for DSD input to radar models. In fact, D(sub max) is typically an assumed DSD parameter in the development of radar retrieval methods. Because of these very uncertainties, it is difficult to independently confirm disdrometer estimates of D(sub max) with polarimetric radar observations. A couple of approaches can be taken to reduce uncertainty in large drop measurement. Longer integration times can be used for the collection of larger disdrometer samples. However, integration periods must be consistent with a radar resolution volume (RRV) and the temporal and spatial scales of the physical processes affecting the DSD therein. Multiple co‐located disdrometers can be combined into a network to increase the sample size within a RRV. However, over a reasonable integration period, a single disdrometer sample volume is many orders of magnitudes less than a RRV so it is not practical to devise a network of disdrometers that has an equivalent volume to a typical RRV. Since knowledge of DSD heterogeneity and large drop occurrence in time and space is lacking, the specific accuracy or even general representativeness of disdrometer based D(sub max) and large drop concentration estimates within a RRV are currently unknown. To address this complex issue, we begin with a simpler question. Is the frequency of occurrence of large rain drops (D > 5 mm) in disdrometer observations, either stand alone or networked, generally representative and consistent with polarimetric radar observations? We first show from simulations that the concentration of large (D > 5 mm) rain drops (N(sub T5)) can be estimated from polarimetric observations of specific differential phase (K(sub dp)) and differential reflectivity (Z(sub dr)), N(sub T5)=F(K(sub dp),Z(sub dr)), or horizontal reflectivity (Z(sub h)) and Z(sub dr), N(sub T5)=(Z(sub h),Z(sub dr)). We assess the error associated with polarimetric retrieval of N(sub T5), including sensitivity to D(sub max) parameterization assumptions and measurement error in the radar simulations. Polarimetric measurements at S‐band and C‐band will then be used to retrieve estimates of N(sub T5) and compared to disdrometer estimates of N(sub T5). After careful consideration of retrieval error, we will check consistency between disdrometer and polarimetric radar estimates of N(sub T5) and the frequency of occurrence of large rain drops in a variety of precipitating regimes using data from NASA's Global Precipitation Measurement (GPM) Ground Validation (GV) program, including field campaigns such as MC3E (Oklahoma) and IFloodS (Iowa) and extended measurements over Huntsville, Alabama and NASA Wallops Flight Facility in coastal Virginia.

Carey, Lawrence D.↗
NASA NTRS2006

Stabilizing Microwave Frequency of a Photonic Oscillator

A scheme for stabilizing the frequency of a microwave signal is proposed that exploits the operational characteristics of a coupled optoelectronic oscillator (COEO) and related optoelectronic equipment. An essential element in the scheme is a fiber mode-locked laser (MLL), the optical frequency of which is locked to an atomic transition. In this scheme, the optical frequency stability of the mode-locked laser is transferred to that of the microwave in the same device. Relative to prior schemes for using wideband optical frequency comb to stabilize microwave signals, this scheme is simpler and lends itself more readily to implementation in relatively compact, rugged equipment. The anticipated development of small, low-power, lightweight, highly stable microwave oscillators based on this scheme would afford great benefits in communication, navigation, metrology, and fundamental sciences. COEOs of various designs, at various stages of development, in some cases called by different names, have been described in a number of prior NASA Tech Briefs articles. A COEO is an optoelectronic apparatus that generates both short (picosecond) optical pulses and a steady microwave signal having an ultrahigh degree of spectral purity. The term "coupled optoelectronic" in the full name of such an apparatus signifies that its optical and electronic oscillations are coupled to each other in a single device. The present frequency-stabilization scheme is best described indirectly by describing the laboratory apparatus used to demonstrate it. The apparatus (see figure) includes a COEO that generates a comb-like optical spectrum, the various frequency components of which interfere, producing short optical pulses. This spectrum is centered at a nominal wavelength of 1,560 nm. The spectrum separation of this comb is about 10 GHz, as determined primarily by the length of an optical loop and the bandpass filter in the microwave feedback loop. The optical loop serves as microwave resonator having a very high value of the resonance quality factor (Q). The optical frequency of MLL is then stabilized by locking it to an atomic transition as described below. The COEO contains a tunable 1-nm band-pass optical filter and a piezoelectric-transducer (PZT) drum over which a stretch of fiber is wound. The 1-nm-wide pass band of the filter provides coarse tuning to overlap the frequency comb with the atomic transition frequency. Controlled stretching of the fiber by means of the PZT drum can be used in conjunction with temperature control for locking the laser frequency. To reference to an atomic resonance at 780 nm in this demonstration setup, the optical output of the COEO at 1,560 nm is fed through an erbium-doped-fiber amplifier (EDFA) to a frequency doubler in the form of a periodically poled lithium niobate (PPLN) crystal. The frequency-doubled output is combined with the output of a separate frequency-stabilized diode laser at a photodetector. As described thus far, the two 780-nm laser subsystems are nominally independent of each other and can, therefore, operate at different frequencies. Hence, at the photodetector, the two laser beams interfere, so that the output of the photodetector includes a beat note (a component at the difference between the two laser frequencies).

Maleki, Lute↗
NASA NTRS1986

Theoretical studies of Resonance Enhance Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

It is well known that the presence of a real atomic level which is nearly resonant with the pump field can greatly enhance the Raman emission cross section. In order to accurately calculate the Raman gain in systems where resonance enhancement plays a dominant role, expressions for the pump and signal susceptibilities must be derived. These expressions should be valid for arbitrary field strengths in order to allow for pump and signal saturation. In addition, the theory should allow for arbitrary longitudinal and transverse relaxation rates. This latter point is extremely vital for three level atomic systems such as the alkali earth metals since they do not have population reservoirs and can have widely varying spontaneous lifetimes on the three pertinent transitions. Moreover, the dephasing rates are strong functions of electron states and are therefore also different for the three coupled pairs of levels. These considerations are not as important when molecular systems are concerned since the large reservoir of rotational states serve to produce essentially equal longitudinal recovery rates for the population of the three levels. The three level system with three arbitrary longitudinal and transverse relaxation rates was solved. There is no need for setting either pair of rates equal and the expressions are valid for arbitrarily strong fields.

Lawandy, N. M.↗