Shadi Naderi

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 theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light

Beam combining of phase-modulated kilowatt fiber amplifiers has generated considerable interest recently. We describe in the time domain how stimulated Brillouin scattering (SBS) is generated in an optical fiber under phase-modulated laser conditions, and we analyze different phase modulation techniques. The temporal and spatial evolutions of the acoustic phonon, laser, and Stokes fields are determined by solving the coupled three-wave interaction system. Numerical accuracy is verified through agreement with the analytical solution for the un-modulated case and through the standard photon conservation relation for counter-propagating optical fields. As a test for a modulated laser, a sinusoidal phase modulation is examined for a broad range of modulation amplitudes and frequencies. We show that, at high modulation frequencies, our simulations agree with the analytical results obtained from decomposing the optical power into its frequency components. At low modulation frequencies, there is a significant departure due to the appreciable cross talk among the laser and Stokes sidebands. We also examine SBS suppression for a white noise source and show significant departures for short fibers from analytically derived formulas. Finally, SBS suppression through the application of pseudo-random bit sequence modulation is examined for various patterns. It is shown that for a fiber length of 9 m the patterns at or near n=7 provide the best mitigation of SBS with suppression factors approaching 17 dB at a modulation frequency of 5 GHz.

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.

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.

Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers

We present detailed studies of the effect of sinusoidal phase modulation on stimulated Brillouin scattering (SBS) in ytterbium-doped fiber amplifiers. Based on a time-dependent SBS model, SBS enhancement factor versus pump linewidth for different modulation depths ranging from 0 to π , and modulation frequencies ranging from 30 MHz to 500 MHz were analyzed. In addition, experimental validation of SBS suppression via sinusoidal phase modulation is presented with experimental results agreeing well with the model and simulations. Furthermore, narrow linewidth coherent beam combining (CBC) of 5 sinusoidal phase modulated lasers is demonstrated via LOCSET.

Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers

Cladding-pumped Raman fiber amplifiers (RFA) have been proposed as gain media to achieve power scaling. It is well-known that the onset of the modal instability (MI) phenomenon is a limiting factor for achieving higher output powers in Yb-doped fiber amplifiers with good beam quality. In this paper, we present an analytical approach to the investigation of the MI phenomenon in high-power, cladding-pumped RFAs. By utilizing the conservation of the number of photons and the conservation of energy in the absence of loss, the nonlinear equations for the propagation of the pump power and the total signal power can be decoupled from one another. Decoupling lead to exact solutions for the pump power and transverse modes signal powers. Further we investigate various MI suppression techniques including increasing the seed power and gain-tailored design.

Pseudo-random binary sequency phase modulation in high power Yb-doped fiber amplifiers

We present experimental and theoretical studies on the stimulated Brillouin scattering (SBS) threshold in fiber amplifiers seeded with a spectrally broadened single-frequency laser source. An electro-optic phase modulator is driven with various pseudo-random binary sequence (PRBS) patterns to highlight the unique characteristics of this linewidth broadening technique and its facility in SBS mitigation. Theoretical predictions show a variation in SBS suppression based on PRBS pattern and modulation frequency. These predictions are experimentally investigated in a kilowatt level monolithic fiber amplifier operating with near diffraction-limited beam quality. We also show Rayleigh scattering and other sources of back reflected light in phase modulated signals can seed the SBS process and significantly reduce the nonlinear threshold.

Numerical investigations of self- and cross-phase modulation effects in high-power fiber amplifiers (Conference Presentation)

The development of high-power fiber lasers is of great interest due to the advantages they offer relative to other laser technologies. Currently, the maximum power from a reportedly single-mode fiber amplifier stands at 10 kW. Though impressive, this power level was achieved at the cost of a large spectral linewidth, making the laser unsuitable for coherent or spectral beam combination techniques required to reach power levels necessary for airborne tactical applications. An effective approach in limiting the SBS effect is to insert an electro-optic phase modulator at the low-power end of a master oscillator power amplifier (MOPA) system. As a result, the optical power is spread among spectral sidebands; thus raising the overall SBS threshold of the amplifier. It is the purpose of this work to present a comprehensive numerical scheme that is based on the extended nonlinear Schrodinger equations that allows for accurate analysis of phase modulated fiber amplifier systems in relation to the group velocity dispersion and Kerr nonlinearities and their effect on the coherent beam combining efficiency. As such, we have simulated a high-power MOPA system modulated via filtered pseudo-random bit sequence format for different clock rates and power levels. We show that at clock rates of ≥30 GHz, the combination of GVD and self-phase modulation may lead to a drastic drop in beam combining efficiency at the multi-kW level. Furthermore, we extend our work to study the effect of cross-phase modulation where an amplifier is seeded with two laser sources.

Numerical studies of modal instabilities in high-power fiber amplifiers

We present a detailed time-dependent numerical model of the modal instability phenomenon observed in Yb-doped fiber amplifiers. The thermal effects are captured by solving the heat equation in polar coordinate using a 2D, second-order, time-dependent, alternating direction implicit (ADI) method. The model captures the three power-dependent regions that are characteristic of the transfer of energy between the fundamental mode and the higherorder mode as a function of time. It is also shown that for the fiber configuration investigated, the modal instability threshold scales linearly over a wide range with the seed power. Furthermore, we present numerical results indicating that gain tailoring can increase the threshold. Two different gain-tailored fiber designs are simulated and compared.

Experimental and theoretical investigations of single-frequency Raman fiber amplifiers operating at 1178 nm

We present a detailed study of power scaling in polarization-maintaining Raman fiber amplifiers operating at 1178 nm since this wavelength can be frequency doubled into 589 nm for sodium guide star applications. We confirm experimentally that the optimized output signal at SBS threshold scales linearly with the pump power. We also present results from numerical and experimental studies investigating the scalability of Raman fiber amplifiers with seed power. Both co-pumped and counter pumped two-stage amplifiers utilizing acoustically tailored fiber for SBS suppression were constructed and studied. For the former configuration spectral broadening was observed, while the latter configuration provided 22 W of single-frequency output. Finally, we show results of a phase-modulated amplifier generating multiple spectral lines separated by 886 MHz, which corresponds to the spectral separation of the sodium D2a, and D2b lines after frequency doubling in a nonlinear cavity.