Timothy J. Madden

Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations

We present detailed numerical simulations of modal instabilities in high-power Yb-doped fiber amplifiers using a time-dependent temperature solver coupled to the optical fields and population inversion equations. The temperature is computed by solving the heat equation in polar coordinates using a 2D second-order alternating direction implicit method. We show that the higher-order modal content rises dramatically in the vicinity of the threshold and we recover the three power-dependent regions that are characteristic of the transfer of energy. We also investigate the dependence of the threshold on the seed power and the modal content ratio of the seed. The latter has a minimal effect on the threshold while it is shown that for the fiber configuration investigated, the modal instability threshold scales linearly over a wide range with the seed power. In addition, two different gain-tailored core designs are investigated and are shown to have higher thresholds than that of a uniformly doped core. Finally, we show that this full time-dependent model which does not assume a frequency offset between the modes a priori, predicts a reduced threshold when the seed is modulated at the KHz level. This is in agreement with the steady-periodic approach to this phenomenon.

A new energy transfer chemical laser at 1.315 μm

Abstract : CW laser action has been demonstrated on the electronic I(*) - I transition of atomic iodine at 1.315 microns from the NCL(a) + I energy transfer reaction. The stimulated emission was generated in a transverse subsonic flow device when hydrogen azide, HN3, was injected into a flow of iodine and chlorine atoms. The measured laser output power was 180 mW.

The Measurement of Gain on the 1.315 Micrometers Transition of Atomic Iodine in a Subsonic Flow of Chemically Generated NCl(a(1) delta)

Abstract Gain is measured on the electronic I( 2 P 3/2 )– I ∗ ( 2 P 1/2 ) transition of atomic iodine at 1.315 μm when hydrazoic acid HN 3 is injected into a flow of iodine and chlorine atoms. The inversion was generated in a transverse subsonic flow device that produced electronically excited I ∗ ( 2 P 1/2 ) atoms from the efficient energy transfer reaction between NCl(a 1 Δ ) metastable and ground state I ( 2 P 3/2 ) atoms. The population inversion was directly observed using a 1.315 μm tunable diode laser that scanned the entire line shape of the (3,4) hyperfine transition of iodine.

Simulation of deleterious processes in a static-cell diode pumped alkali laser

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.

Characterizing Fluorine and Chlorine Atom Flow Rates Using Iodine Atom Spectrometry

The production of F and Cl atoms in an electrical discharge of F 2 or Cl 2 has been examined in a flow reactor. A tunable diode laser was used to probe the concentration and translational temperature of I atoms produced by F and Cl atom reactions with HI. Kinetic modeling codes were used to determine the discharge efficiencies from the titration plots and the observed trends for atom concentration as a function of F 2 or Cl 2 and pressure. These calculations indicate that the de discharge used in these experiments is 100% efficient for F 2 flow rates ≤0.5 mmol s -1 and reactor pressure ≤20 torr. The highest F 2 -free F atom flow rate that we can generate is 1.0 mmol s -1 . Preliminary data for the Cl 2 discharge indicate that this is a much less efficient source of Cl atoms with yields of less than 50%.

Theoretical and numerical treatment of modal instability in high-power core and cladding-pumped Raman fiber amplifiers

Raman fiber lasers have been proposed as potential candidates for scaling beyond the power limitations imposed on near diffraction-limited rare-earth doped fiber lasers. One limitation is the modal instability (MI) and we explore the physics of this phenomenon in Raman fiber amplifiers (RFAs). By utilizing the conservation of number of photons and conservation of energy in the absence of loss, the 3 × 3 governing system of nonlinear equations describing the pump and the signal modal content are decoupled and solved analytically for cladding-pumped RFAs. By comparing the extracted signal at MI threshold for the same step index-fiber, it is found that the MI threshold is independent of the length of the amplifier or whether the amplifier is co-pumped or counter-pumped; dictated by the integrated heat load along the length of fiber. We extend our treatment to gain-tailored RFAs and show that this approach is of limited utility in suppressing MI. Finally, we formulate the physics of MI in core-pumped RFAs where both pump and signal interferences participate in writing the time-dependent index of refraction grating.

Time developing 3-D simulation of chemical oxygen-iodine lasers (COILs)

A theoretical model for the chemically reacting flow within a chemical laser is employed to conduct 3-D simulations of the laser flowfield for operational conditions. Issues regarding flow unsteadiness are explored in light of their impact on the optical field to gas coupling.

Aspects of 3D chemical oxygen-iodine laser simulation

Theoretical models for the chemical oxygen-iodine laser (COIL) depend on a variety of assumptions and empirical data to provide closure and simplify solution of the governing equations. Among the various assumptions and empirical data built into models for COIL are assumptions regarding steadiness in the time domain and which kinetic processes are significant in addition to the measured values for the rates at which the kinetic processes occur. The work discussed here is directed toward elucidating and increasing the understanding of the assumptions underlying COIL models and the implications for the modeled physical processes underlying the COIL, driven by current directions in the development of this technology. This is directly linked to efforts to achieve improved COIL efficiencies and performance, since excursions well outside traditional operational parameter space are necessary. As such excursions are made, the distance from the traditional parameter space where COIL models have been baselined and validated becomes much greater, increasing the importance for understanding the factors that influence the accuracy of the simulations. In this role of increasing the level of understanding regarding the limits to the accuracy of COIL models, these simulations provide information important to current work investigating configurations and operating conditions well outside of the traditional parameter space.

Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers

We present, using numerical simulations, investigations of the modal instability thresholds in high-power Yb-doped fiber amplifiers. We use a time-dependent temperature solver coupled to the optical fields and population inversion equations to determine the temporal dynamics of the modal content of the signal as well as the modal instability threshold. Our numerical code is optimized to achieve fast computations; thus allowing us to perform efficient detailed numerical studies of fiber amplifiers ranging in lengths from 1-20 meters using various pump and seeding wavelengths. Simulation results indicate promising modal instability suppression through gain tailoring, tandem pumping, or through seeding at an appropriate wavelength. We examine the threshold of an amplifier pumped using fiber lasers operating at 1018 nm; similar to the multi-kilowatt single-mode fiber laser demonstrated by IPG. In this case, we show an increase in threshold of 370%. By simply seeding at other wavelengths, as low as 1030 nm, a 60% suppression of the modal instability threshold can also be realized. Furthermore, we show that gain tailoring is an effective mitigation technique leading to an appreciable suppression of the instability in a fiber design that has already been experimentally tested.

PLIF Flow Visualization of a Supersonic Injection COIL Nozzle

This paper describes Planar Laser-Induced Fluorescence (PLIF) flow visualization of a supersonic nozzle with supersonic injection. The nozzle simulates Chemical Oxygen Iodine Laser (COIL) flow conditions with non-reacting, cold flows, where the injected flow was seeded with iodine. A laser sheet near 565nm excited the iodine, and the fluorescence was imaged with a gated, CCD camera. Spanwise and streamwise images were taken, where the relative concentration of the injected to primary flow, turbulent structures, and penetration distance of the injected flow were identified. These images qualitatively revealed a lack of mixing of the secondary (injected) and primary flows at the centerline of the nozzle, even far downstream of the throat. Quantitative data of the penetration of the secondary flow, with varying primary to secondary flow rate ratios, helped identify the shallow angle of the injectors as an inhibiter of secondary penetration even at relatively low primary flow rates. From the PLIF results, this nozzle is characterized as a poor mixer and would not be recommended as a nozzle that produces a well-mixed medium, as required with chemical lasers. This work precedes a project that will use PLIF results to design a well-mixed supersonic nozzle with supersonic injection. The results will be compared to and enable validation of computational fluid dynamics (CFD) predictions of the designed nozzle.