Benjamin G. Ward

Origin of thermal modal instabilities in large mode area fiber amplifiers

We present a dynamic model of thermal modal instability in large mode area fiber amplifiers. This model allows the pump and signal optical intensity distributions to apply a time-varying heat load distribution within the fiber. This influences the temperature distribution that modifies the optical distributions through the thermo-optic effect thus creating a feedback loop that gives rise to time-dependent modal instability. We describe different regimes of operation for a representative fiber design. We find qualitative agreement between simulation results and experimental results obtained with a different fiber including the time-dependent behavior of the instability and the effects of different cooling configurations on the threshold. We describe the physical processes responsible for the onset of the instability and suggest possible mitigation approaches.

Modeling of transient modal instability in fiber amplifiers.

A model of transient modal instability in fiber amplifiers is presented. This model combines an optical beam propagation method that incorporates laser gain through local solution of the rate equations and refractive index perturbations caused by the thermo-optic effect with a time-dependent thermal solver with a quantum defect heating source term. This model predicts modal instability a fiber amplifier operating at 241, 270, and 287 Watts of output power characterized by power coupling to un-seeded modes, the presence of stable and unstable regions within the fiber, and rapid intensity variations along the fiber. The instability becomes more severe as the power is increased.

Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles

A numerical investigation is presented of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles. The equation determining the acoustic displacement in response to the electrostriction caused by the pump and Stokes waves reduces to the non-homogeneous Helmholtz equation for fibers with a uniform acoustic velocity profile. In this special case the acoustic displacement and subsequently the Brillouin gain are calculated using a Greens function. These results are then used to validate a finite-element solution of the same equation. This finite element method is then used to analyze a standard large mode area fiber as well as fibers incorporating four different acoustic velocity profiles with 5% variation in the acoustic velocity across the core. The profiles which suppress the peak Brillouin gain most effectively exhibit a maximum acoustic gradient near the midpoint between the center and boundary of the fiber core. These profiles produce 11 dB of suppression relative to standard large mode area fibers.

Investigations of single-frequency Raman fiber amplifiers operating at 1178 nm

We report on core-pumped single-stage and two-stage polarization-maintaining single-frequency Raman fiber amplifiers (RFAs). For a counter-pumped single-stage RFA, commercial-off-the shelf (COTS) single-mode fiber was utilized to generate 10 W of output power at 1178 nm through the application of a two-step thermal gradient in order to suppress SBS. The relatively high output can be explained by the Brillouin gain spectrum (BGS) of the COTS fiber. A pump-probe characterization of the BGS of the fiber provided a Brillouin gain coefficient of 1.2 × 10(-11) m/W with a FWHM of 78 MHz for the gain bandwidth. A fiber cutback study was also conducted to investigate the signal output at SBS threshold as a function of pump power for optimal length. This study revealed a linear dependence, which is in agreement with the theoretical prediction. Furthermore, we present numerical simulations indicating that substantial power scaling can be achieved by seeding at a higher power. Consequently, we constructed a two-stage RFA in order to achieve seed powers at the 1 W level. By utilizing an acoustically tailored fiber possessing a lower Brillouin gain coefficient than the COTS fiber and by seeding at higher powers, 22 W of single-frequency 1178 nm output was obtained from a counter-pumped two-stage RFA. Finally, we show that the single-frequency spectral bandwidth could not be maintained when a similar co-pumped two-stage RFA was utilized.

Theory and modeling of photodarkening-induced quasi static degradation in fiber amplifiers.

A theory of photodarkening-induced quasi-static degradation in fiber amplifiers is presented. As the doped core of a fiber photodarkens and continues to absorb more power converting it to heat, the intensity grating created by higher order mode interference with the fundamental mode moves toward the input end. This creates a persistent absorption grating that remains phase-shifted from the modal interference pattern. This leads to power transfer from the fundamental mode to a higher order mode with a very small frequency offset that occurs on a time scale of minutes to hours. This process is modeled in large mode area step index and photonic crystal fibers and is found to produce reasonable threshold values.

Gain-tailored SBS suppressing photonic crystal fibers for high power applications

We present experimental studies of PM Yb-doped photonic crystal fibers possessing acoustic and Yb-ion concentration tailoring. In the initial design, the concentration of dopants in two regions of the core were selected such that the corresponding Brillouin shifts were sufficiently separated to allow for further stimulated Brillouin scattering suppression through thermal effects. The Yb-ion concentration was maintained uniformly throughout the entire core. When this fiber was utilized in a counter-pumped amplifier configuration, ~500 W of single-frequency (kHz linewidth) output was obtained in a 10 m long fiber. Further power scaling with good beam quality beyond 500 W was limited by modal instabilities. A second fiber design was developed in which the Yb-ion concentration was modified to have preferential overlap with the fundamental mode as well as reduced pump absorption. The onset of the modal instabilities was sufficiently suppressed to allow for an output of 990 W with a nominal linewidth of 300 MHz and good beam quality.

Maximizing power output from continuous-wave single-frequency fiber amplifiers

This Letter reports on a method of maximizing the power output from highly saturated cladding-pumped continuous-wave single-frequency fiber amplifiers simultaneously, taking into account the stimulated Brillouin scattering and transverse modal instability thresholds. This results in a design figure of merit depending on the fundamental mode overlap with the doping profile, the peak Brillouin gain coefficient, and the peak mode coupling gain coefficient. This figure of merit is then numerically analyzed for three candidate fiber designs including standard, segmented acoustically tailored, and micro-segmented acoustically tailored photonic-crystal fibers. It is found that each of the latter two fibers should enable a 50% higher output power than standard photonic crystal fiber.

Bend performance-enhanced photonic crystal fibers with anisotropic numerical aperture

An error was made in converting the units of bend radius within the computer program used to obtain the reported results. This caused the calculated values of the bending induced stress to be significantly smaller than their true value. Corrected results for stress within the fiber and bend losses are reported. Since bending-induced stresses cause a relatively small correction to the refractive index profile, these corrections result in no changes in the main conclusions of this work.

Brillouin gain suppression in photonic crystal fibers with random acoustically microstructured cores

Finite-element calculations of the Brillouin gain spectrum in photonic crystal fibers (PCFs) with cores incorporating random arrangements of regions with discrete acoustic velocities are presented. The peak Brillouin gain coefficient for PCFs with cores with an acoustic domain size of approximately 0.26 microm(2) and an acoustic velocity variation of 3% was calculated to be 3.3 x 10(-12) m/W with a Brillouin gain spectrum FWHM of 280 MHz. This corresponds to a decrease in the peak Brillouin gain coefficient of 7.4 dB relative to a PCF with an acoustically homogeneous core.

Modeling of inter-modal Brillouin gain in higher-order-mode fibers.

Finite element calculations of inter-modal Brillouin gain between LP(0n) modes in acoustically-inhomogeneous higher order mode (HOM) fibers are presented. When the pump beam is launched in the LP(08) mode, the LP(01) mode of the Stokes beam experiences the highest gain, approximately 6.7 dB higher than the peak LP(08)-LP(08) gain. An LP(01) Stokes beam experiences successively more Brillouin gain when pumped by higher-order LP(0n) modes.