A theoretical analysis of the pump-induced temperature change and associated thermal phase shift occurring in a pumped doped fiber is presented. Although the primary devices targeted are all-optical switches based on doped fibers, where such effects can be detrimental, this analysis is also applicable to lasers, amplifiers, and other doped fiber devices. The effects of a single pump pulse, multiple pulses and continuous wave (CW) pumping are investigated, both in the dynamic and steady-state regimes. Simple expressions are derived for the thermal relaxation time constant of a fiber, and for its steady-state temperature rise and thermal phase shift under CW pumping. This study predicts that in all-optical fiber switches utilizing a reasonably good dopant the thermal effect due to a single short pulse is negligible in all interferometers, while the steady-state effect can be sizable in a standard fiber Mach-Zehnder but is negligible in a twin-core fiber, a two-mode fiber, and a specially designed Mach-Zehnder interferometer.
M. K. Davis, M. J. F. Digonnet, Richard H. Pantell, and Life Fellow, "Thermal Effects in Doped Fibers," J. Lightwave Technol. 16, 1013- (1998)