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^{2}in flowing-gas Cs DPALs with stable optical resonators and of its dependence on the resonator geometry. The measured results were modeled by multi-transverse-mode model [Auslender et al., Opt. Express 25, 19767 (2017)]. Conditions for substantial improvement of the output laser beam quality, reducing M

^{2}to close to unity, are found. In particular we show how changing the length of the resonator, and/or the radius of curvature of the high reflection mirror, leaving all other parameters of the laser unchanged, makes it possible to control the beam quality.

^{2}predicted by the model are in good agreement with the experimental results for different shapes and powers of the pump beam.

_{4}), flow velocities of 1-4.5 m/s and pump powers of 30-65 W, is reported. For the theoretical part of the study we used a 3D computational fluid dynamics model, solving the gas dynamics and kinetics equations relevant to flowing-gas laser operation. Maximum CW output power of 24 W and slope efficiency of 48% were obtained. The experimental and theoretical dependence of the lasing power on the flow velocity are in good agreement. The gas temperature rise in the laser cell was measured. The lasing power was not affected by the flow velocity at this range of pump powers and flow velocities due to the fact that the gas temperature rise was only several degrees. It was estimated – using a “fitting” method – that the quenching cross-section of the excited levels of Cs to the ground state is ~ 0.05 Å

^{2}.

^{2}on the power and spatial shape of the pump beam is studied. An optical model of multi-transverse mode operation of alkali vapor lasers [Auslender et al, Opt. Express 25, 19767 (2017)] is applied to the experimental results. The values of the laser power and M

^{2}predicted by the model are in good agreement with the experimental results for different shapes and powers of the pump beam We also report, briefly, on our recently published work [Yacoby et al, Opt. Express 26, 17814 (2018)] on flowing-gas Cs-DPAL where the output power and gas temperature rise in the laser cell at different flow velocities were studied and the results analyzed by our three-dimensional computational fluid-dynamics) model.

_{2}H

_{6}gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 6

^{2}S

_{1/2}, (2) 6

^{2}P

_{1/2}and (3) 6

^{2}P

_{3/2}. The kinetic processes include absorption due to the 1→3 D

_{2}transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2→1 D

_{1}transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.

*M*on the maximum achievable power of subsonic and supersonic lasers. For Cs DPAL devices with

*M*= 0.2 - 3 the output power increases with increasing M by only ~20%, implying that supersonic operation mode has only small advantage over subsonic. In contrast, the power achievable in K DPALs strongly depends on M. The output power increases by ~100% when

*M*increases from 0.2 to 4, showing a considerable advantage of supersonic device over subsonic. The reason for the increase of the power with

*M*in both Cs and K DPALs is the decrease of the temperature due to the gas expansion in the flow system. However, the power increase for K lasers is much larger than for the Cs devices mainly due to the much smaller fine-structure splitting of the

^{ 2}

*P*states (~58 cm

^{-1}for K and ~554 cm

^{-1}for Cs), which results in a much stronger effect of the temperature decrease in K DPALs. For pumping by beams of the same rectangular cross section, comparison between end-pumping and transverse-pumping shows that the output power is not affected by the pump geometry. However, the intensity of the output laser beam in the case of transverse-pumped DPALs is strongly non-uniform in the laser beam cross section resulting in higher brightness and better beam quality in the far field for the end-pumping geometry where the intensity of the output beam is uniform.

*et al*, Optics Express 22, 17266 (2014)], where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed. The model shows good agreement between the calculated and measured dependence of the laser power on the incident pump power. In particular, the model reproduces the observed threshold pump power, 22 W (corresponding to pump intensity of 4 kW/cm

^{2}), which is much higher than that predicted by the standard semi-analytical models of the DPAL. The reason for the large values of the threshold power is that the volume occupied by the excited K atoms contributing to the spontaneous emission is much larger than the volumes of the pump and laser beams in the laser cell, resulting in very large energy losses due to the spontaneous emission. To reduce the adverse effect of the high threshold power, high pump power is needed, and therefore gas flow with high gas velocity to avoid heating the gas has to be applied. Thus, for obtaining high power, highly efficient K DPAL, subsonic or supersonic flowing-gas device is needed.

*M*~ 0.2) and transonic (

*M*~ 0.9) diode pumped alkali lasers (DPALs), taking into account fluid dynamics and kinetic processes in the lasing medium is reported. The performance of these lasers is compared with that of supersonic (

*M*~ 2.7 for Cs and M ~ 2.4 for K) DPALs. The motivation for this study stems from the fact that subsonic and transonic DPALs require much simpler hardware than supersonic ones where supersonic nozzle, diffuser and high power mechanical pump (due to a drop in the gas total pressure in the nozzle) are required for continuous closed cycle operation. For Cs DPALs with 5 x 5 cm

^{2}flow cross section pumped by large cross section (5 x 2 cm

^{2}) beam the maximum achievable power of supersonic devices is higher than that of the transonic and subsonic devices by only ~ 3% and ~ 10%, respectively. Thus in this case the supersonic operation mode has no substantial advantage over the transonic one. The main processes limiting the power of Cs supersonic DPALs are saturation of the D2 transition and large ~ 60% losses of alkali atoms due to ionization, whereas the influence of gas heating is negligible. For K transonic DPALs both the gas heating and ionization effects are shown to be unimportant. The maximum values of the power are higher than those in Cs transonic laser by ~ 11%. The power achieved in the supersonic and transonic K DPAL is higher than for the subsonic version, with the same resonator and K density at the inlet, by ~ 84% and ~ 27%, respectively, showing a considerable advantaged of the supersonic device over the transonic one. For pumping by rectangular beams of the same (5 x 2 cm

^{2}) cross section, comparison between end-pumping - where the laser beam and pump beam both propagate at along the same axis, and transverse-pumping - where they propagate perpendicularly to each other, shows that the output power and optical-to-optical efficiency are not affected by the pump geometry. However, the output laser beam in the case of end-pumped DPALs has a homogeneous spatial intensity distribution in the beam cross section, whereas for transverse-pumped DPALs the intensity varies significantly along the pumping axis (perpendicular to the resonator optical axis) and hence is strongly inhomogeneous in the laser beam cross section. Thus, higher brightness and better beam quality in the far field is achieved for the end-pumping geometry. Optimization of the resonator geometry for minimal gas temperature rise and minimal intra-resonator intensity (corresponds to a low ionization rate) is also reported.

^{2}) beam makes it possible to obtain even higher output power, > 250 kW, for ~ 350 kW pumping power. The main processes limiting the power of Cs supersonic DPAL are saturation of the D2 transition and large ~ 40% losses of alkali atoms due to ionization, whereas the influence of gas heating is negligibly small. For supersonic K DPAL both gas heating and ionization effects are shown to be unimportant and the maximum achievable power, ~ 40 kW and 350 kW, for pumping by ~ 100 kW cylindrical and ~ 700 kW rectangular beam, respectively, are higher than those achievable in the Cs supersonic laser. The power achieved in the supersonic K DPAL is two times higher than for the subsonic version with the same resonator and K density at the gas inlet, the maximum optical-to-optical efficiency being 82%.

^{2}

*S*

_{1/2}, (2) n

^{2}

*P*

_{3/2}and (3) n

^{2}

*P*

_{1/2}(where n=4,6 for K and Cs, respectively), three excited alkali states and two alkali ionic states. Using the CFD model, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped CW and pulsed Cs and K DPALs. The DPAL power and medium temperature were calculated as a function of pump power and pump pulse duration. The CFD model results were compared to experimental results of Cs and K DPALs.

^{3}.

^{3}. At high pump power the calculated laser power is higher for the transverse scheme than for the parallel scheme because of a more efficient heat convection from the beam volume in the transverse configuration. The CFD models are applied to experimental devices and the calculated results are in good agreement with the measurements.

_{lase}, for the former was found to be higher than for the latter by 25%. Optimization of the He/CH

_{4}buffer gas composition and flow parameters using 3D CFD modeling shows that for Bogachev et al resonator parameters, extremely high lasing power and optical-to-optical efficiency, 33 kW and 82%, respectively, are achievable in the Cs supersonic device. Comparison between the semi-analytical and the 3D CFD models for Cs shows that the latter predicts much higher maximum achievable laser power than the former. For a supersonic K DPAL the semi-analytical model predicts P

_{lase}= 43 kW, 70% higher than for subsonic with the same resonator and K density at the inlet, the maximum optical-to-optical efficiency being 82%. The paper also includes estimates for closed cycle supersonic systems.

_{p}-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.

**44**, 582 (2008)] and 1-kW flowing-gas [A.V. Bogachev et al., Quantum Electron.

**42**, 95 (2012)] DPALs. It predicts the dependence of power on the flow velocity in flowing-gas DPALs and on the buffer gas composition. The maximum values of the laser power can be substantially increased by optimization of the flowing-gas DPAL parameters. In particular for the aforementioned 1 kW DPAL, 6 kW maximum power is achievable just by increasing the pump power and the temperature of the wall and the gas at the flow inlet (resulting in increase of the alkali saturated vapor density). Dependence of the lasing power on the pump power is non-monotonic: the power first increases, achieves its maximum and then decreases. The decrease of the lasing power with increasing pump power at large values of the latter is due to the rise of the aforementioned losses of the alkali atoms as a result of ionization. Work in progress applying two-dimensional computational fluid dynamics modeling of flowing-gas DPALs is also reported.

**44**, 582 (2008)], (2) predicting the dependence of power on the flow velocity in flowing-gas DPALs and (3) checking the effect of using a buffer gas with high molar heat capacity and large relaxation rate constant between the

^{2}

*P*

_{3/2}and

^{2}

*P*

_{1/2}fine-structure levels of the of the alkali atom. It is found that ionization processes have a small effect on the laser operation, whereas chemical reactions of alkali atoms with hydrocarbons strongly affect the lasing power. The power strongly increases with flow velocity and by replacing, e.g., ethane by propane as a buffer gas the power may be further increased by up to 30%. 8 kW is achievable for 20 kW pump at flow velocity of 20 m/s.

_{2}dissociation in the COIL medium. Since O

_{2}(a) is the energy reservoir of the COIL, it must be involved in the dissociation of I

_{2}. Therefore, understanding the dissociation mechanism may help in finding ways of minimizing the O

_{2}(a) consumption for dissociation and increasing the chemical efficiency of the laser. In the present paper previously suggested mechanisms of I

_{2}dissociation are briefly overviewed and recent measurements and modeling of the gain and the power in supersonic COILs carried out in our laboratory are presented. Our studies employ both an analytical model and numerical calculations which are outlined in the present paper, with more details on the models given in a following paper by Barmashenko et al. To unravel the I

_{2}dissociation mechanism we utilize kinetic-fluid dynamics three-dimensional modeling, where pathways involving the excited species I

_{2}(X, 10 ≤ v < 25), I

_{2}(X, 25 ≤ v ≤ 47), I

_{2}(A, A'), O

_{2}(X, v), O

_{2}(a, v), O

_{2}(b, v) and I(

^{2}P

_{1/2}) as intermediate reactants are included. Both the gain and the power studies show good agreement between calculations and experiments. We believe that future modeling should include the above pathways and additional pathways should be considered when additional kinetic data is available.

_{2}(

*A*'

^{3}Pi

_{2u}), I

_{2}(A

^{3}Pi

_{1u}) and O

_{2}(a

^{1}Delta

_{g}, v) as significant intermediates in the dissociation of I2 [Waichman et al., J. Appl. Phys. 102, 013108 (2007)] reproduced the measured gain and temperature of a low pressure supersonic COIL. The previous model is complemented here by adding the effects of turbulence, which play an important role in high pressure COILs.

_{2}molecules at the optical axis of a supersonic chemical oxygen-iodine laser (COIL) was studied via detailed measurements and three dimensional computational fluid dynamics calculations. Comparing the measurements and the calculations enabled critical examination of previously proposed dissociation mechanisms and suggestion of a mechanism consistent with the experimental and theoretical results obtained in a supersonic COIL for the gain, temperature and I

_{2}dissociation fraction at the optical axis. The suggested mechanism combines the recent scheme of Azyazov and Heaven (AIAA J. 44, 1593 (2006)), where I

_{2}(

*A'*

^{3}Π

_{2u}), I

_{2}(

*A*

^{3}Π

_{1u}) and O

_{2}(

*a*

^{1}&Dgr;

_{g}, v) are significant dissociation intermediates, with the "standard" chain branching mechanism of Heidner et al. (J. Phys. Chem. 87, 2348 (1983)), involving I(

^{2}P

_{1/2}) and I

_{2}(X1&Sgr;

^{+}

_{g}, v). In addition, we examined a new method for enhancement of the gain and power in a COIL by applying DC corona/glow discharge in the transonic section of the secondary flow in the supersonic nozzle, dissociating I

_{2}prior to its mixing with O

_{2}(

^{1}&Dgr;). The loss of O

_{2}(

^{1}&Dgr;) consumed for dissociation was thus reduced and the consequent dissociation rate downstream of the discharge increased, resulting in up to 80% power enhancement. The implication of this method for COILs operating beyond the specific conditions reported here is assessed.

_{2}molecules at the optical axis of a supersonic chemical oxygen-iodine laser (COIL) was studied via detailed measurements and three dimensional computational fluid dynamics calculations. Comparing the measurements and the calculations enabled critical examination of previously proposed dissociation mechanisms and suggestion of a mechanism consistent with the experimental and theoretical results. The gain, I

_{2}dissociation fraction and temperature at the optical axis, calculated using Heidner's model (R.F. Heidner III et al., J. Phys. Chem.

**87**, 2348 (1983)), are much lower than those measured experimentally. Agreement with the experimental results was reached by using Heidner's model supplemented by Azyazov-Heaven's model (V.N. Azyazov and M.C. Heaven, AIAA J.

**44**, 1593 (2006)) where I

_{2}(A') and vibrationally excited O

_{2}(a

^{1}&Dgr;) are significant dissociation intermediates.

_{2}molecules at the optical axis of a supersonic chemical oxygen-iodine laser (COIL) was studied experimentally as a function of I

_{2}flow rate. The measurements revealed that the number of consumed O

_{2}(

^{1}&Dgr;) molecules per dissociated I

_{2}molecule depends on the experimental conditions: it is 4.2 ± 0.4 for typical conditions and I

_{2}densities applied for the operation of the COIL, but increases at lower I

_{2}densities. In addition, a new method for dissociating I

_{2}prior to its mixing with O

_{2}(

^{1}&Dgr;) and thus reducing the loss of O

_{2}(

^{1}&Dgr;) is reported. The method is based on applying corona/glow electrical discharge in the transonic section of the secondary flow in the COIL supersonic nozzle. 1.7% of I

_{2}is dissociated by the discharge resulting in 70% power enhancement at rather high I

_{2}/O

_{2}ratio, 1.6%, close to the optimal value (~ 2.5%) for operation of COILs with supersonic mixing.

*Appl. Phys. Lett*., 85, 5851 (2004)). The power and spatial distributions of the gain and temperature across the flow were measured for different supersonic nozzles with both staggered and non-staggered iodine injection holes, different injection locations along the flow and nozzle throat-heights. 40.0% efficiency was measured for 1 s at the early stage of operation, followed by a sustained 35.5% chemical efficiency for 20 s. By carefully studying and optimizing the operation of the chemical generator, 0.73 yield of singlet oxygen was obtained for conditions corresponding to the highest efficiency.

_{2}and the residence time of the flow in the generator, as well as the heating of the nozzle, are discussed and shown to be crucial in attaining this high efficiency.

_{2}flow rate of 17 mmole/s. 33% efficiency is the highest reported chemical efficiency of any supersonic COIL. Comparison between different mixing schemes shows that for supersonic mixing the output power and chemical efficiency are about 20% higher than for transonic mixing scheme. The optimal conditions for the efficient operation are investigated. Diagnostic measurements of the small-signal gain shows that the value of the gain for the supersonic mixing scheme corresponding to the maximum efficiency is about 0.75%/cm, about 1.5 times larger than for transonic mixing scheme. Studies of different supersonic mixing schemes show that to achieve further power increase the injection location should be moved downstream.

_{2}across the flow were studied for transonic and supersonic schemes of the iodine injection in a slit nozzle supersonic chemical oxygen-iodine laser (COIL) as a function of the iodine and secondary nitrogen flow rate and jet penetration parameter. The mixing efficiency for supersonic injection of iodine (~ 0.85) is found to be much larger than for transonic injection (~ 0.5), the maximum values of the gain being ~ 0.65%/cm for both injection schemes. Spatial distributions of the gain corresponding to the maximum power are found. A simple one-dimensional model is developed for the fluid dynamics and chemical kinetics in the COIL. Two different I

_{2}dissociation mechanisms are tested against the performance of a COIL device in our laboratory. The two mechanisms chosen are the celebrated mechanism of Heidner and the newly suggested mechanism of Heaven. The gain calculated using Heaven’s dissociation mechanism is much lower than the measured one. Employing Heidner’s mechanism, a surprisingly good agreement is obtained between the measured and calculated gain and temperature over a wide range of flow parameters.

_{2}were carried out. For transonic injection the optimal value of nI

_{2}at the flow centerline is smaller than that at the off axis location. The temperature is distributed homogeneously across the flow, increasing only in the narrow boundary layers near the walls. Opening a leak downstream of the cavity in order to decease the Mach number results in a decrease of the gain and increase of the temperature. The mixing efficiency in this case is much larger than for closed leak.

_{2}(

^{1}(Delta) ) yield and water vapor fraction at the exit of a jet type singlet oxygen generator (JSOG) and the gain in the resonator. In addition the chlorine utilization and gas temperature at the generator exit were measured. For conditions corresponding to the maximum chemical efficiency of the supersonic COIL energized by the JSOG the O

_{2}(

^{1}(Delta) ) yield, water vapor fraction, chlorine utilization and temperature at the generator exit are 0.65, 0.08, 0.92 and 30 C. Small signal gain and temperature at the resonant optical axis are 0.25%/cm and 280 K, respectively. Dependence of the yield on the generator pressure and variation of the temperature along the flow in the diagnostic cell are consistent with rate constant of the O

_{2}(

^{1}(Delta) ) energy pooling reaction of 2.7 X 10

^{-17}cm

^{3}s

^{-1}.

_{2}flow rate of 11.8 mmole/s. The power is studied as a function of the distance between the optical axis and the supersonic nozzle exit plane, the molar flow rates of various reagents, the BHP and gas pressures in the generator, the type of the secondary buffer gas (N

_{2}or He) and the stagnation temperature of the gas. It is found that the power under the present operation conditions is almost unaffected by water vapor in the medium. The role of buffer gas under different conditions is discussed.

_{2}flow rate, output power of 132 W with chemical efficiency of 14.5% were obtained without a water vapor trap. One-hundred-sixty- three watts and 18% were achieved when cooled (173 K) He was introduced downstream of the JSOG; under these conditions the small signal gain was estimated to be 0.32% cm

^{-1}. Wattage of 190 and 10.5% were obtained for 20 mmole/s of Cl

_{2}flow rate. Replacing He by N

_{2}as a buffer gas resulted in a 13% power decrease only. The main key for increasing the chemical efficiency of a COIL without a water vapor trap for a given iodine-oxygen mixing system is found to be high oxygen pressure and low water vapor pressure inside the reaction zone of the JSOG. The last goal was achieved by optimizing the composition and temperature of the basic hydrogen peroxide solution (BHP). The experimental results are discussed and related to the composition and flow conditions of the gaseous reactants and of the BHP. We also report on preliminary results of efficient COIL operation without primary buffer gas using rectangular nozzles with iodine injection in the throat.

_{2}(

^{1}(Delta) ) chemical generator and a medium size pumping system. A grid nozzle is used for iodine injection and supersonic expansion. 45 W of CW laser emission at 1315 nm are obtained in the present experiments. The small size and the simple structure of the laser system and its stable operation for long periods make it a convenient tool for studying parameters important for high power supersonic iodine lasers and for comparison to model calculations. The gain and the lasing power are studied as a function of the molar flow rates of the various reagents, and conditions are found for optimal operation. Good agreement is found between the experimental results and calculations based on a simple 1D semi-empirical model, previously developed in our laboratory and modified in the present work. The model is used to predict optimal values for parameters affecting the laser performance that are difficult to examine in the present experimental system.

_{2}(

^{1}(Delta) ) at high pressure. Such generators are especially important for supersonic chemical oxygen-iodine lasers. The model treats different types of generators, e.g., bubble column, film, aerosol, and jet generators. The main factor affecting the O

_{2}(

^{1}(Delta) ) yield under high pressure is liquid-phase quenching enhanced by depletion of HO

_{2}

^{-}ions near the gas/liquid interface. Simple analytical expressions are derived for the O

_{2}(

^{1}(Delta) ) yield at the exit of the generator. Output characteristics of different specific generators are calculated and compared with available experimental results. O

_{2}(

^{1}(Delta) ) yield > 0.5 can be achieved for oxygen pressure up to 50 Torr and flowrates of 3 mmol/cm

^{2}s. For equal velocities of the gas and the liquid the maximum flux of the energy carried by O

_{2}(

^{1}(Delta) ) for jet or aerosol generators reaches 200 W/cm

^{2}. It can be increased by increasing the liquid velocity in the generator.

_{2}. The maximum nI

_{2}for which lasing is possible is less than 1 - 2% of the oxygen flow rate. This is in agreement with experimental data and is not explained by models assuming premixed flows. The present model was applied to calculations of the performance of supersonic COILs.

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