Conference Paper

# Advanced laser modeling with BLAZE multiphysics

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Article
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The optically pumped rare-gas metastable laser is a chemically inert analogue to three-state optically pumped alkali laser systems. The concept requires efficient generation of electronically excited metastable atoms in a continuous-wave (CW) electric discharge in flowing gas mixtures near atmospheric pressure. We have observed CW optical gain and laser oscillation at 912.3 nm using a linear micro-discharge array to generate metastable Ar(4s, 1s5) atoms at atmospheric pressure. We observed the optical excitation of the 1s5 → 2p9 transition at 811.5 nm and the corresponding fluorescence, optical gain and laser oscillation on the 2p10 ↔ 1s5 transition at 912.3 nm, following 2p9→2p10 collisional energy transfer. A steady-state kinetics model indicates efficient collisional coupling within the Ar(4s) manifold.
Article
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Experiments and modeling have led to continued enhancements in the Electric Oxygen-Iodine Laser (ElectricOIL) system. This continuous wave (cw) laser operating on the 1315 nm transition of atomic iodine is pumped by the production of O 2 (a) in a radio-frequency (RF) discharge in an O 2 /He/NO gas mixture. New discharge geometries and increases in gain length, flow rates, discharge power, and resonator mode volume have improved the peak measured gain to 0.26% cm -1 and the outcoupled laser power to 102 W. The BLAZE model has been used to perform end-to-end (discharge though laser resonator) simulations of the new system configuration to help guide this process. Results are in good agreement with data. Additional measurements of gain recovery downstream of an operating laser cavity for five cases of interest are presented and modeled. The deviation of the gain recovery data from calculations based on presently accepted theory is highlighted. Several potential mechanisms to explain this theory are presented and discussed.
Article
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Experiments[1] with Electric Oxygen-Iodine Laser (ElectricOIL) heat exchanger technology have demonstrated improved control of oxygen atom density and thermal energy, with minimal quenching of O2(a1Δ), and increasing small signal gain from 0.26% cm-1 to 0.30% cm-1. Heat exchanger technological improvements were achieved through both experimental and modeling studies, including estimation of O2(a1Δ) surface quenching coefficients for select ElectricOIL materials downstream of a radio-frequency discharge-driven singlet oxygen generator. Estimation of O2(a1Δ) quenching coefficients is differentiated from previous studies by inclusion of oxygen atoms, historically scrubbed using HgO[2-4] or AgO[5]. High-fidelity, time-dependent and steady-state simulations are presented using the new BLAZE-VI multi-physics simulation suite[6] and compared to data.
Article
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Pulsed lasing from optically pumped rare gas metastable atoms (Ne, Ar, Kr, and Xe) has been demonstrated previously. The laser relies on a three-level scheme, which involves the (n+1)p[5/2]<sub>3</sub> and (n+1)p[1/2]<sub>1</sub> states from the np<sup>5</sup>(n+1)p electronic configuration and the metastable (n+1)s[3/2]<sub>2</sub> level of the np<sup>5</sup>(n+1)s configuration (Racah notation). Population inversions were achieved using relaxation from ((n+1)p[5/2]<sub>3</sub> to (n+1)p[1/2]<sub>1</sub> induced by collisions with helium or argon at pressures near 1 atm. Pulsed lasing was easily achieved using the high instantaneous pump intensities provided by a pulsed optical parametric oscillator excitation laser. In the present study we examine the potential for the development of a continuous wave (CW) optically pumped Ar laser. We report lasing of the 4p[1/2]<sub>1</sub>→4s[3/2]<sub>2</sub> (912.547 nm) transition following CW diode laser excitation of the 4p[5/2]<sub>3</sub>←4s[3/2]<sub>2</sub> line (811.754 nm). A pulsed discharge was used to generate Ar 4s[3/2]<sub>2</sub>, and the time-resolved lasing kinetics provide insights concerning the radiative and collisional relaxation processes.
Article
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Recent experiments have led to continued improvements in the hybrid Electric Oxygen-Iodine Laser (ElectricOIL) system that significantly increased the discharge performance, supersonic cavity gain, and laser power output. Experimental investigations of radio-frequency discharges in O 2 /He/NO mixtures in the pressure range of 10-50 Torr and power range of 0.1-2.0 kW have shown that O 2 (a 1 Δ) production is a strong function of geometry, pressure and diluent ratio. The goal of these investigations was maximization of both the yield and flow rate (power flux) of O 2 (a 1 Δ) in order to produce favorable conditions for subsequent gain and lasing in our ElectricOIL system. Numerous measurements of O 2 (a 1 Δ), oxygen atoms, and discharge excited states are made to characterize the discharge. Results with both molecular iodine injection and partially pre-dissociated iodine are presented. A gain of 0.17% cm -1 was measured with a corresponding outcoupled power of 12.3 W. Modeling with the BLAZE-IV model is in good agreement with data.
Article
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An overview is presented of experimental and theoretical research in the field of physics and engineering of singlet delta oxygen (SDO) production in low-temperature plasma of various electric discharges. Attention is paid mainly to the SDO production with SDO yield adequate for the development of an electric discharge oxygen–iodine laser (DOIL). The review comprises a historical sketch describing the main experimental results on SDO physics in low-temperature plasma obtained since the first detection of SDO in electric discharge in the 1950s and the first attempt to launch a DOIL in the 1970s up to the mid-1980s when several research groups started their activity aimed at DOIL development, stimulated by success in the development of a chemical oxygen–iodine laser (COIL). A detailed analysis of theoretical and experimental research on SDO production in electric discharge from the mid-1980s to the present, when the first DOIL has been launched, is given. Different kinetic models of oxygen low-temperature plasma are compared with the model developed by the authors. The latter comprises electron kinetics based on the accompanying solution of the electron Boltzmann equation, plasma chemistry including reactions of excited molecules and numerous ion–molecular reactions, thermal energy balance and electric circuit equation. The experimental part of the overview is focused on the experimental methods of SDO detection including experiments on the measurements of the Einstein coefficient for SDO transition and experimental procedures of SDO production in self-sustained and non-self-sustained discharges and analysis of different plasma-chemical processes occurring in oxygen low-temperature plasma which brings limitation to the maximum SDO yield and to the lifetime of the SDO in an electric discharge and its afterglow. Quite recently obtained results on gain and output characteristics of DOIL and some projects aimed at the development of high-power DOIL are discussed.
Article
Full-text available
Optically pumped alkali vapor lasers are currently being developed in several laboratories. The objective is to construct high-powered lasers that also exhibit excellent beam quality. Considerable progress has been made, but there are technical challenges associated with the reactivity of the metal atoms. Rare gas atoms (Rg) excited to the np(5)(n+1)s (3)P(2) configuration are metastable and have spectral properties that are closely similar to those of the alkali metals. In principle, optically pumped lasers could be constructed using excitation of the np(5)(n+1)p←np(5)(n+1)s transitions. We have demonstrated this potential by observing gain and lasing for optically pumped Ar(*), Kr(*) and Xe(*). Three-level lasing schemes were used, with He or Ar as the collisional energy transfer agent that established the population inversion. These laser systems have the advantage of using inert reagents that are gases at room temperature.
Conference Paper
Multiple variants of the Diode Pumped Alkali Laser (DPAL) have recently been demonstrated at the Air Force Research Laboratory (AFRL). Highlights of this ongoing research effort include: a) a 571W rubidium (Rb) based Master Oscillator Power Amplifier (MOPA) with a gain (2α) of 0.48 cm⁻¹, b) a rubidium-cesium (Cs) Multi-Alkali Multi-Line (MAML) laser that simultaneously lases at both 795 nm and 895 nm, and c) a 1.5 kW resonantly pumped potassium (K) DPAL with a slope efficiency of 50%. The common factor among these experiments is the use of a flowing alkali test bed.
Article
Optically pumped lasers that use metastable excited states of Ar have been demonstrated using both pulsed and CW excitation. In terms of Paschen labeling of the states of Ar, the laser system uses excitation of the 2p<sub>9</sub>-1s<sub>5</sub> transition, and lases on the 2p<sub>10</sub>-1s<sub>5</sub> line. Collisional transfer of population from 2p<sub>9</sub> to 2p<sub>10</sub> is achieved using He as the buffer gas. For the purpose of modeling and developing this laser, rate constants for state-to-state transfer in Ar(2p<sub>i</sub>)+Ar/He mixtures are needed. As the 2p<sub>10</sub> level can radiate down to 1s<sub>4</sub>, this lower level also plays a significant role in the laser kinetics. Consequently, rate constants for the relaxation of 1s<sub>4</sub> by Ar and He are also required. In the present study we have used pulsed laser excitation techniques to measure rate constants of relevance to the optically pumped metastable Ar laser.
Article
In the last four years, a few research groups worked on the feasibility of compressive sampling (CS) in ultrasound medical imaging and several attempts of applying the CS theory may be found in the recent literature. In particular, it was shown that using iotap-norm minimization with p different from 1 provides interesting RF signal reconstruction results. In this paper, we propose to further improve this technique by processing the reconstruction in the Fourier domain. In addition, alpha -stable distributions are used to model the Fourier transforms of the RF lines. The parameter p used in the optimization process is related to the parameter alpha obtained by modelling the data (in the Fourier domain) as an alpha -stable distribution. The results obtained on experimental US images show significant reconstruction improvement compared to the previously published approach where the reconstruction was performed in the spatial domain.
Article
The complex interactions in a diode pumped alkali laser (DPAL) gain cell provide opportunities for multiple deleterious processes to occur. Effects that may be attributable to deleterious processes have been observed experimentally in a cesium static-cell DPAL at the United States Air Force Academy [B.V. Zhdanov, J. Sell, R.J. Knize, "Multiple laser diode array pumped Cs laser with 48 W output power," Electronics Letters, 44, 9 (2008)]. The power output in the experiment was seen to go through a "roll-over"; the maximum power output was obtained with about 70 W of pump power, then power output decreased as the pump power was increased beyond this point. Research to determine the deleterious processes that caused this result has been done at the Air Force Research Laboratory utilizing physically detailed simulation. The simulations utilized coupled computational fluid dynamics (CFD) and optics solvers, which were three-dimensional and time-dependent. The CFD code used a cell-centered, conservative, finite-volume discretization of the integral form of the Navier-Stokes equations. It included thermal energy transport and mass conservation, which accounted for chemical reactions and state kinetics. Optical models included pumping, lasing, and fluorescence. The deleterious effects investigated were: alkali number density decrease in high temperature regions, convective flow, pressure broadening and shifting of the absorption lineshape including hyperfine structure, radiative decay, quenching, energy pooling, off-resonant absorption, Penning ionization, photoionization, radiative recombination, three-body recombination due to free electron and buffer gas collisions, ambipolar diffusion, thermal aberration, dissociative recombination, multi-photon ionization, alkali-hydrocarbon reactions, and electron impact ionization.
Article
In recent studies, an optically pumped Ar*/He laser has been demonstrated using the Ar 4p[1/2]1→4s[3/2]2 transition at 912.55 nm. Time-resolved data for this system, recorded using CW laser excitation and pulsed discharge production of Ar* 4p[3/2]2, yielded laser output pulses that were of unexpectedly short duration. It was speculated that radiative relaxation from the upper laser level to the 4s[3/2]1 state (607 cm-1 above 4s[3/2]2) caused termination of the laser pulse. In the present study this hypothesis has been tested by observing the energy transfer kinetics of the 4s[3/2]2 and 4s[3/2]1 states in Ar/He gas mixtures. Following pulsed laser excitation out of 4s[3/2]2, population recovery was observed on a μs time scale. Energy transfer from 4s[3/2]1 to 4s[3/2]2, induced by collisions with He, was characterized. The rate constant was found to be (1.0±0.5)x10-13 cm3 s-1. These observations confirmed that radiative transfer to 4s[3/2]1 was responsible for the short duration laser pulses. Modeling of a fully CW optically pumped Ar* laser shows that radiative transfer to 4s[3/2]1 reduces the number density of the Ar* atoms involved in lasing, but is otherwise benign.
Conference Paper
Lasers driven by optical pumping of alkali metal - rare gas collision pairs have been demonstrated recently. Accurate potential energy curves for the alkali metal - rare gas dimers are need to analyze and predict the scaling characteristics of this type of laser system. We are using high-level theoretical methods to obtain these data and predict the absorption spectra. The potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements for MRg (M=Rb,Cs and Rg=Ar,Kr) electronic states converging to the lowest three dissociation limits have been characterized. Quasi-relativistic matrix elements have been obtained for a wide range of internuclear distances using different sets of small core relativistic pseudopotentials. The core-valence correlation was included in a large-scale multi-reference configuration interaction (MR-CI) treatment. Excited state potentials were also examined using multi-reference averaged quadratic coupled cluster (MR-AQCC) methods. The data obtained from these calculations have been used to predict the absorption spectra for the MRg pairs using semi-classical and quantum mechanical models. © 2010 by the American Institute of Aeronautics and Astronautics, Inc.
Article
Continuing experiments with electric oxygen-iodine laser (ElectricOIL) technology have significantly increased laser power output by increasing the product of gain and gain-length, $g_{0}L$. The authors report on progress with recent ElectricOIL devices utilizing a new concentric discharge geometry with improved ${\rm O}_{2}(a^{1}\Delta)$ production at higher discharge operating pressure at higher system flow rates. ${\rm O}_{2}(a^{1}\Delta)$ produced in flowing radio-frequency discharge in ${\rm O}_{2}\hbox{-}{\rm He}\hbox{-}{\rm NO}$ gas mixture is used to pump $I(^{2}P_{1/2})$ by near-resonant energy transfer, and laser power is extracted on the $I(^{2}P_{1/2})\rightarrow I(^{2}P_{3/2})$ transition at 1315 nm. Advancements in heat exchanger design reduce ${\rm O}_{2}(a^{1}\Delta)$ wall loss without sacrificing significant cooling efficiency improving best gain performance from 0.26 to 0.30% ${\rm cm}^{-1}$. Modeling of recent data is presented. By increasing the gain length (system size) by a factor of 3, a 5-fold increase in laser output on the 1315-nm transition of atomic iodine was achieved. Flow conditions with $g_{0}L=0.042$ were used to extract a continuous wave average total laser power of 481 W. A low frequency ${\pm}{11.9\%}$ oscillation in the total power was observed giving a peak outcoupled power of 538 W.
Article
The emergent field of diode pumped alkali lasers (DPALs) is reviewed.
Article
End-pumped alkali vapor lasers excited on their D2 transition and lased on their D1 transition offer a pathway to high average power that potentially competes with diode-pumped solid-state lasers in many applications that require cw or quasi-cw laser operation. We report on the first experimental demonstration of an end-pumped Cs laser using a Ti:sapphire laser for pump excitation. Detailed experimental and model results are presented that indicate our understanding of the underlying physics involved in such systems is complete. Using an extrapolation of our developed model, a discussion is given on power scaling diode-pumped alkali lasers, indicating a potential efficiency advantage over power-scaled diode-pumped solid-state lasers.
Article
Lasing on the D2 (6p 2P3/2→6s 2S1/2) transition of atomic Cs at 852.1 nm has been observed with a four level system in which the Cs 6p 2P3/2 state is pumped by the photoassociation and subsequent dissociation of Cs-rare gas collision pairs. Characterized by a quantum efficiency >98%, this laser requires no atomic precursor to the upper laser level and provides oscillation on an alkali transition inaccessible to three level, photopumped alkali laser systems. Measurements of photoabsorption and pump energy threshold in Cs–Ar–Kr mixtures reveal the influence of three body photoassociation.
Article
The exciplex-pumped alkali laser (XPAL) system has been demonstrated in mixtures of Cs vapour, Ar, and ethane by pumping Cs–Ar atomic collision pairs and subsequent dissociation of diatomic, electronically excited CsAr molecules (exciplexes or excimers). Because of the addition of atomic collision pairs and exciplex states, modelling of the XPAL system is far more complicated than the modelling of the classic diode-pumped alkali laser (DPAL). In this paper, we discuss BLAZE-V time-dependent multi-dimensional modelling of this new laser system including radiative transport and parasitic loss effects. A two-dimensional, time-dependent baseline simulation of a pulsed XPAL is presented and compared to data. Good agreement is achieved on a laser pulse full width at half-maximum and laser pulse rise time. Parametric simulations of pulsed XPAL system configurations similar to that of the baseline case, given both four- and five-level laser operation, are presented in which good agreement is obtained with outcoupled laser energy as a function of absorbed pump energy data. The potential impact of parasitic losses on modelled system configurations is discussed.
Article
Chemical oxygen-iodine lasers are unique in their ability to generate high-power beams with near diffraction limited beam quality. The operating wavelength, 1.315 µm is readily transmitted by the atmosphere and compatible with fiber optics beam delivery systems. However, applications of the laser are severely limited by logistical problems associated with the complex chemistry used to power the device. Electrical or microwave discharge excitation of oxygen-iodine lasers offers an attractive alternative that eliminates the chemical power generation problems and has the possibility of closed-cycle operation. A discharge oxygen-iodine laser was first demonstrated in 2005. Since that time the power of the device has been improved by a factor of 400 and much has been learned concerning the physics and chemistry of the discharge driven system. Although our current understanding of the chemical kinetics is incomplete, parametric studies of laser performance show considerable promise for further scaling. This article reviews the basic principles of the discharge oxygen iodine laser, summarizes the most recent advances, and outlines some of the unresolved questions regarding the production and removal of excited species in the gas flow.
Article
Chemical oxygen-iodine lasers (COIL) are attractive for diverse industrial applications because they are capable of high efficiency, high power operation, and because the 1.315 μ m wavelength can be transmitted through fiber optics and couples efficiently with most metals. Conventional COILs are pumped with O <sub>2</sub>(<sup>1</sup> Δ ) that is generated by reaction of Cl <sub>2</sub> in a basic H <sub>2</sub> O <sub>2</sub> solution. Current trends in pumping COILs involve producing the O <sub>2</sub>(<sup>1</sup> Δ ) in electric discharges, thereby circumventing the hazards, complexity, and weight associated with pumping and storing caustic liquids. In this work, we have investigated the scaling of O <sub>2</sub>(<sup>1</sup> Δ ) yields with specific energy deposition in He / O <sub>2</sub> mixtures in flowing radio frequency (rf) discharges at pressures of a few to tens of Torr using a global plasma kinetics model. We found that O <sub>2</sub>(<sup>1</sup> Δ ) yield increases nearly linearly with specific energy deposition in O <sub>2</sub> molecules up to a few eV per molecule, with yields peaking around 30% by 5–8 eV . Further increases in specific energy deposition serve only to increase O <sub>2</sub> dissociation and gas heating, thereby reducing the O <sub>2</sub>(<sup>1</sup> Δ ) yield. We also found that variations in peak yields at a given specific energy de- position are caused by secondary effects resulting from dilution, pressure, and power level. We show that these secondary effects alter the O <sub>2</sub>(<sup>1</sup> Δ ) yield by shifting the O <sub>2</sub>(<sup>1</sup> Σ )/ O <sub>2</sub>(<sup>1</sup> Δ ) ratio.
Article
In an electric discharge oxygen-iodine laser, laser action at 1315 nm on the I (<sup>2</sup>P<sub>1/2</sub>)→ I (<sup>2</sup>P<sub>3/2</sub>) transition of atomic iodine is obtained by a near resonant energy transfer from O <sub>2</sub>(a <sup>1</sup>Δ) which is produced using a low-pressure electric discharge. The discharge production of atomic oxygen, ozone, and other excited species adds higher levels of complexity to the postdischarge kinetics which are not encountered in a classic purely chemical O <sub>2</sub>(a <sup>1</sup>Δ) generation system. Mixing effects are also present. In this paper we present postdischarge modeling results obtained using a modified version of the BLAZE-II gas laser code. A 28 species, 105 reaction chemical kinetic reaction set for the postdischarge kinetics is presented. Calculations were performed to ascertain the impact of a two stream mixing mechanism on the numerical model and to study gain as a function of reactant mass flow rates. The calculations were compared with experimental data. Agreement with experimental data was improved with the addition of new kinetics and the mixing mechanism.
Article
Laser action at 1315 nm on the I (<sup>2</sup>P<sub>1/2</sub>)→ I (<sup>2</sup>P<sub>3/2</sub>) transition of atomic iodine is conventionally obtained by a near-resonant energy transfer from O <sub>2</sub>(a<sup>1</sup>Δ) which is produced using wet-solution chemistry. The difficulties in chemically producing O <sub>2</sub>(a<sup>1</sup>Δ) has motivated investigations into purely gas phase methods to produce O <sub>2</sub>(a<sup>1</sup>Δ) using low-pressure electric discharges. In this letter, we report on the demonstration of a continuous-wave laser on the 1315 nm transition of atomic iodine where the O <sub>2</sub>(a<sup>1</sup>Δ) used to pump the iodine was produced by a radio-frequency-excited electric discharge. The electric discharge was sustained in a He / O <sub>2</sub> gas mixture upstream of a supersonic cavity which is employed to lower the temperature of the continuous gas flow and shift the equilibrium of atomic iodine in favor of the I (<sup>2</sup>P<sub>1/2</sub>) state. The laser output power was 220 mW in a stable cavity composed of two 99.99% reflective mirrors.
Article
Lasing on the 6<sup>2</sup>P<sub>1/2</sub>rarr6<sup>2</sup>S<sub>1/2</sub> (D<sub>1</sub>) resonance transition of atomic Cs at 894.3 nm has been realised in mixtures of Ar, ethane, and Cs vapour by the photoexcitation of ground state Cs Ar collision pairs and subsequent dissociation of diatomic, electronically-excited CsAr molecules (excimers). The blue satellites of the alkali D<sub>2</sub> lines provide a pathway for optically pumping atomic alkali lasers on the principal series (resonance) transitions with broad linewidth (gsim2 nm) semiconductor diode lasers.
Article
Population inversion of the 2P 1/2 and 2S 1/2 levels and continuous-wave, three-level laser oscillation at 795 nm on the D1 transition of the rubidium atom has been demonstrated. Using a titanium sapphire laser as a pump source, we obtained a slope power efficiency of 54% relative to absorbed pump power, consistent with homogeneous broadening of the rubidium pump and laser transitions. The end-pumped rubidium laser performance was well described by use of literature spectroscopic and kinetic data in a model that takes into account ground-level depletion and a pump spectral bandwidth that is substantially larger than the collisionally broadened pump transition spectral width.
Article
Laser oscillation at 1315 nm on the I(2P1/2)-->I(2P3/2) transition of atomic iodine has been obtained by a near resonant energy transfer from O2(a1Delta) produced using a low-pressure oxygen/helium/nitric oxide discharge. In the electric discharge oxygen-iodine laser (ElectricOIL) the discharge production of atomic oxygen, ozone, and other excited species adds levels of complexity to the singlet oxygen generator (SOG) kinetics which are not encountered in a classic purely chemical O2(a1Delta) generation system. The advanced model BLAZE-IV has been introduced to study the energy-transfer laser system dynamics and kinetics. Levels of singlet oxygen, oxygen atoms, and ozone are measured experimentally and compared with calculations. The new BLAZE-IV model is in reasonable agreement with O3, O atom, and gas temperature measurements but is under-predicting the increase in O2(a1Delta) concentration resulting from the presence of NO in the discharge and under-predicting the O2(b1Sigma) concentrations. A key conclusion is that the removal of oxygen atoms by NOX species leads to a significant increase in O2(a1Delta) concentrations downstream of the discharge in part via a recycling process; however, there are still some important processes related to the NOX discharge kinetics that are missing from the present modeling. Further, the removal of oxygen atoms dramatically inhibits the production of ozone in the downstream kinetics.
Article
Theoretical studies have indicated that sufficient fractions of O<sub>2</sub>(<sup>1</sup>Δ) may be produced in an electrical discharge that will permit lasing of an electric discharge oxygen-iodine laser (ElectriCOIL) system. Results of those studies along with more recent experimental results show that electric excitation is a very complicated process that must be investigated with advanced diagnostics along with modeling to better understand this highly complex system. A kinetic package appropriate for the ElectriCOIL system is presented and implemented in the detailed electrodynamic GlobalKin model and the Blaze II chemical laser modeling code. A parametric study with the Blaze II model establishes that it may be possible to attain positive gain in the ElectriCOIL system, perhaps even with subsonic flow. The Blaze II model is in reasonable agreement with early gain data. Temperature is a critical issue, especially in the subsonic cases, and thus it appears that supersonic flow will be important for the ElectriCOIL system. Simulations of a supersonic ElectriCOIL system indicate that it may be possible to attain reasonable performance levels, even at low yield levels of 20% or less. In addition, pre-dissociation of the iodine is shown to be very important for the supersonic flow situation.
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• D L Carroll
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Carroll D L and Verdeyen J T (2012). "XPAL theory and predictions", SPIE Vol. 8238, 823804. Han, J., and Heaven, M.C. (2012). Opt. Lett. 37, 2157.
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Krupke, W. F., Beach, R. J., Kanz, V. K., and Payne, S. A. (2003). Opt. Lett., 28, 2336. Krupke, W. F. (2012). Prog. Quant. Electronics, 36, 4-28.