O.A. Ryabushkin - Ph.D. (Phys.-Math.), Associate Professor, Moscow Institute of Physics and Technology, Institute of Radio-engineering and Electronics of RAS Fryazino branch. E-mail: roa228@mail.ru
R.I. Shaidullin - Research Scientist, Moscow Institute of Physics and Technology, Institute of Radio-engineering and Electronics of RAS Fryazino branch. E-mail: rs-mipt@mail.ru
I.A. Zaytsev - Research Scientist, Institute of Radio-engineering and Electronics of RAS Fryazino branch. E-mail: hetziff@mail.ru

In active optical fibers doped with rare earth ions in process of laser generation the part of the optical pumping power is converted into heat. The main mechanisms of heating are quanta exchange between optical pumping and generating photons and nonradiative relaxation of excited rare-earth ions. Rise of the optical fiber core temperature leads to a changes in luminescence and absorption cross sections of rare-earth ions, and changes the lifetime of their excited states. Scaling-up of the fiber lasers increases the fiber heating and therefore requires precise experimental method of the temperature measurements. To date there are several methods of active fiber temperature measurement. To determine the temperature of the fiber core primarily indirect methods are used. Previously, we have developed a method for measuring the temperature in the core of active fibers under lasing regime based on a Mach-Zehnder fiber interferometer. Based on these results, we have proposed a new coaxial model of fiber heating, which claimed that in addition to the quanta exchange an important role in fiber heating plays absorption of scattered radiation of photoluminescence and the pump power in the fiber polymer cladding. By measuring the transmission spectrum of the polymer, we found significant radiation absorption peaks in the polymer at wavelengths that fall within the spectral range of the pump and photoluminescence wavelengths of high-power fiber laser. In this paper we present a simple method for measuring the temperature of the polymer cladding of active fibers based on well-known radio frequency impedance spectroscopy. We have shown that temperature dependence of the dielectric permittivity in radio frequency range of polymers used as a protective coating for silica fibers, several orders of magnitude higher than a similar dependence for the silica. Thus, by using impedance spectroscopy method for an optical fiber with a polymer cladding we can determine the temperature of the polymer, and by resolving the stationary heat conduction equation, we can calculate the temperature of the fiber core. For a more accurate temperature measurement in optical fiber polymer, we have developed the original construction scheme and experimental method of measurement. Experimental setup includes a fiber amplifier with two-wire copper line connected as an oscillating LC-circuit. Two thin metal wires form a flexible two-wire condenser, the fiber consisting of a fused silica core and with the polymer coating is located between them. This structure is wounded on the dielectric glass frame to form an inductor. The result is an oscillating LC-circuit, which is connected to the radiofrequency generator with frequency scanning ability. Admittance measurement is carried out using a radiofrequency spectrum analyzer, recording the frequency response of the resonance circuit. Heating of the fiber resulted in a change of the dielectric constant of the polymer, and this led to the change of the two-wire capacitor capacitance and then to the resonance frequency shift, which was measured by us. Experimental results consisted of three phases: calibration measurements in a thermostat, measuring the temperature of the fibers with a metal core under conditions of core heating by the electric current power and measurement of the temperature of the polymer under conditions of laser radiation amplifying. The coefficient of polymer cladding heating temperature on optical pumping power for the most of the heated area (near the input of pumping power) was measured to be 0,34 ºK/W, i.e. at 120 W of optical pumping equivalent heating temperature of the polymer was about 40 degrees. Thus, it was experimentally established that the radiofrequency impedance spectroscopy technique allows defining heating of the optical fiber polymer coating separately. The combination of interference and impedance methods allows experimental measurement of heating of different fiber claddings and determination of the temperature profile of the fiber. This work confirmed the important role of the optical spectral properties of the polymers used as protective coatings for active fibers. The presented method allows measuring the temperature not only in the polymer coating of passive and active fibers, but also exploring other types of fibers, including polymer optical fibers.