A steady-periodic method for modeling mode instability in fiber amplifiers

We present a detailed description of the methods used in our model of mode instability in high-power, rare earth-doped, large-mode-area fiber amplifiers. Our model assumes steady-periodic behavior, so it is appropriate to operation after turn on transients have dissipated. It can be adapted to transient cases as well. We describe our algorithm, which includes propagation of the signal field by fast-Fourier transforms, steady-state solutions of the laser gain equations, and two methods of solving the time-dependent heat equation: alternating-direction-implicit integration, and the Green’s function method for steady-periodic heating. © 2014 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.4370) Nonlinear optics, fibers; (140.6810) Thermal effects; (190.2640) Stimulated scattering, modulation, etc References and links 1. A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180. 2. A.V. Smith and J.J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express 20, 22545–22558 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24545. 3. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20, 11407-11422 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11407. 4. C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20, 1291212925 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12912. 5. M.D. Feit and J.A. Fleck, “Computation of mode properties in optical fiber waveguides by a propagating beam method,” Applied Optics 19, 1154-1164 (1980). 6. M.D. Feit and J.A. Fleck, “Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method,” Applied Optics 19, 2240-2246 (1980). 7. G.P. Agrawal, “Nonlinear fiber optics,” Academic Press, NY, second edition 1995. 8. D. Marcuse, Theory of dielectric optical waveguides, second ed., (Academic Press, NY 1991). 9. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216-220 (1976). 10. K.D. Cole, “Steady-periodic Green’s functions and thermal-measurement applications in rectangular coordinates,” Journal of Heat Transfer 128, 706-716 (2006); DOI: 10.1115/1.2194040 11. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, second ed., (Cambridge Univ. Press, NY, 1992). 12. P. W. Milonni, The quantum vacuum: an introduction to quantum electronics, (Academic Press, CA 1994). 13. M. Frigo, and S. G. Johnson, “FFTW Home Page,” http://www.fftw.org/.