ACTIVE FIBERS: Self-focusing effects important in high-power fiber amplifiers
The increasing output-power levels of rare-earth-doped fiber lasers and amplifiers are enabling these sources to displace conventional lasers in a growing variety of applications.
The increasing output-power levels of rare-earth-doped fiber lasers and amplifiers are enabling these sources to displace conventional lasers in a growing variety of applications. At the same time, experimentally demonstrated pulsed fiber amplifiers with multimegawatt peak powers are approaching ultimate power limits on fiber amplifiers imposed by self-focusing within the fiber (see figure). Therefore, accurate and reliable modeling of this behavior becomes increasingly essential to the design of practical devices in which self-focusing can significantly influence not only attainable peak power (and hence pulse energy), but also the spectrum (via nonlinear processes in the fiber), the damage threshold, and the beam quality.
Even though self-focusing (SF) is a well-known nonlinear process, significant confusion exists in the literature, according to Dahv Kliner and fellow researchers at Sandia National Laboratories (Livermore, CA, and Albuquerque, NM). For example, some authors have reported that a high-power beam propagating in a fiber will undergo large oscillations in diameter as it propagates, which would substantially lower the threshold power for nonlinear processes and optical damage. Some calculations have shown that the self-focusing limit in a fiber is significantly different from that in a bulk medium, while others have shown little difference.
All previous calculations were performed for passive fibers (that is, fibers without gain), not for fiber amplifiers. And although it is now known that coiling of the fiber (for packaging or for high-order mode suppression) dramatically distorts the fiber modes, all previous calculations treated only straight fibers. To address these issues, Kliner and colleagues set out to answer three questions.1
First, what are the effects of amplification on the propagation of the fundamental mode of a step-index fiber at optical powers approaching the SF limit (also known as the critical power, Pcrit)? In particular, are longitudinal oscillations in beam diameter necessarily present? Second, how does coiling of the fiber affect propagation of amplified and unamplified beams at powers approaching Pcrit? And finally, how does Pcrit compare between straight and coiled step-index fibers and a similar bulk material?
Bend-loss-induced mode filtering, in which a highly multimode large-mode-area fiber is coiled with a radius of curvature chosen to introduce substantial loss for high-order modes and relatively little loss for the fundamental mode, is a widely used method for suppressing higher-order modes in power-scaling of pulsed and continuous-wave fiber sources because it provides near-diffraction-limited beam quality with little or no decrease in slope efficiency. For standard step-index fibers, this coiling results in substantial distortion of the fiber modes, including loss of azimuthal symmetry. So the Sandia analysis included the effects of gain and bending (applicable to coiled fiber amplifiers). The researchers used an eigenmode solver and a beam propagation code (since both methods are applicable to fibers with arbitrary refractive-index profiles, with gain and/or loss, and with any bend radius) to numerically investigate the behavior of the fundamental mode of a step-index, multimode fiber as the optical power approaches Pcrit.
The researchers found that at high powers below Pcrit (around 3 MW), nonoscillatory (stationary) modes exist that propagate unchanged in step-index fibers. In a fiber amplifier seeded with the fundamental mode, the transverse spatial profile will evolve adiabatically into that of the stationary mode as the beam is amplified; that is, the beam will not undergo longitudinal oscillations. These conclusions hold whether the fiber amplifier is straight or coiled, although the quantitative details are somewhat different. For a given value of the nonlinear index, Pcrit is nearly the same in the bulk material and in a step-index fiber, either straight or bent.
Hassaun A. Jones-Bey
1. R.L. Farrow et al., Optics Letters, in press.