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Abstract
Optical properties of conventional polysiloxane polymers used in fiber optics were analyzed. Transmission spectra and absorption coefficients of polymers in the operating wavelength range of Yb and Er doped fiber lasers were measured. Heating of Yb-doped active fiber inside the industrial laser unit poured with a silicone polymer protective layer was investigated. A part of the pump power converted into heat during laser generation was evaluated using experimental data obtained by substituting the active fiber with an electrically heated copper wire. Mathematical model of fiber laser unit heating was developed.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays high-power fiber lasers are widely used in fields of science, industry and medicine. Output optical power of continuous wave single-mode fiber lasers exceeds 10 kW level. Certain part of optical power (about 10% for Yb-doped active medium) inevitably converts into heat mainly due to the energy difference between the pump and generated photons, leading to considerable heating of the active fibers. High temperatures result in deterioration of laser radiation properties and lead to the thermal degradation of active fibers. Thermal stability of polysiloxane (PS) polymers (or silicones) used in fiber optics is considerably lower compared to quartz silica cladding. It was demonstrated that one of the main limiting factors of fiber lasers power scaling is the thermal degradation of protective polymer coatings of active silica waveguides [1]. PS polymers have suitable optical, thermal and mechanical properties, so they are widely used in fiber optics. In industrial fiber laser units active fibers coated with protective polymer claddings are additionally poured with a thick polymer layer, which plays both heat dissipation and mechanical protection roles. Polymer heating occurs mainly due to heat transfer from an active fiber core. However, it was shown [2] that polymer layers can be also heated due to absorption of pump, photoluminescence and scattered laser radiation. This additional heat source speeds up polymer degradation, leading to the failure of fiber laser operation.
Polymer absorption in the visible and near-IR ranges is conditioned by the transitions between the vibration and rotation levels of the fundamental molecular groups, such as CH3, Si-O and OH [3]. Absorption peaks, that lie in the operating wavelength range of Yb- (1030-1100 nm) and Er (1450-1600 nm) doped fiber lasers, are associated with higher overtones of CH3 vibrations. Optical transmission spectra measured for some PS polymers were reported [4]. However, specific values of absorption coefficients cannot be determined simply using the transmission spectra due to a relatively high scattering in the polymer volume.
Therefore, we have performed more accurate measurements of absorption of PS polymers for the most important wavelengths: optical pumping (960-970 nm) and lasing of Yb (1064 nm) and Er (1550 nm) doped fiber lasers. Temperature dependence of the polymer optical absorption was also investigated. Several polymers conventionally used in fiber optics were studied: Dow Corning Sylgard polymer used for protective coating of active fibers, Wacker Silgel polymer used for filling of commercial fiber laser units, and special FSX polymer with low refractive index used as a wave guiding material. Another part of this work is devoted to the investigation of the heating of the fiber laser unit during the operation. Both surface and volume temperatures of the Silgel polymer layer were measured. The part of optical power converted into heat under laser generation conditions was evaluated as a result of simulations.
2. Polymers transmission and absorption measurements
Polymer samples were prepared by mixing two components (main polymer and crosslinker agent) in the required proportion inside the glass cuvette with internal volume 3.4 × 1.8 × 1 cm3 and optical path length of 1 cm. Transmission spectra of the polymer samples were measured using Perkin Elmer Lambda 950 spectrometer in the 800-1100 nm wavelength range. The spectral pattern of all polymer samples turned out to be similar. The absorption bands were observed in the following wavelength ranges: 890-925 nm, 980-1040 nm and 1080-1100 nm, corresponding to the CH3 vibration levels [3]. However, for different polymers the absorption peak depths were slightly different because of different concentrations of methyl groups in polymer chains. Typical transmission spectrum of PS polymer (on the example of Silgel) measured at room temperature is shown in Fig. 1(a).
Fig. 1 Transmission spectra of Silgel polymer at room temperature in the ranges of 800-1100 nm (a) and 1-2.3 μm (b). Yellow stripes denote typical operating wavelength ranges of fiber lasers with different dopants.
Polymer transmission spectra were also measured in the near-IR range of 1-2.3 μm, wherein the large number of deep absorption peaks were observed (Fig. 1(b)). As can be seen, the absorption of PS polymers in the emission wavelength ranges of Er- and Tm-doped fiber lasers are significantly higher compared to that of Yb-doped laser. In addition, PS polymers are almost opaque to optical radiation at wavelengths greater than 2.2 μm. Some absorption is present even in the relatively transparent range of 1040-1080 nm.
As it was mentioned earlier, it is impossible to determine exact values of optical absorption coefficient relying on the transmission data, because bulk polymers have a significant radiation scattering, primarily conditioned by the refractive index heterogeneities (Rayleigh and Mie scattering). One of the ways for measuring the absorption is to use the laser calorimetry, i.e. to measure the polymer heating depending on transmitting optical power. According to Beer’s law, absorbed power can be determined as Pabs = P0(1-e-αl), where P0 is an initial laser radiation power, l is an optical path length and α [cm−1] is an absorption coefficient. A block scheme of experimental setup is shown in Fig. 2(a).
Fig. 2 (a) Block scheme of the experimental setup for the measurement of polymers optical absorption coefficients; (b) Dependences of the Silgel sample heating on transmitted laser power measured for different radiation wavelengths.
The following radiation sources were used in the experiments: GaAs/InGaAs laser diode (960 nm), Yb (1064 nm) and Er (1550 nm) doped fiber lasers. Collimated laser radiation with 3 mm beam diameter was transmitted through the polymer sample inside the glass cuvette. Polymer temperature was measured using a thermocouple sensor that was submerged into the polymer at the corner of the cuvette. A small mirror was used for shielding the temperature sensor from laser radiation. Dependences of the Silgel polymer heating on transmitted optical power at investigated radiation wavelengths are shown in Fig. 2(b).
In order to determine optical absorption coefficient we have developed a mathematical model of the polymer heating inside the cuvette. It was based on the solution of the stationary heat conduction equation [Eq. (1)] with corresponding boundary conditions [Eq. (2)].
where k is coefficient of thermal conductivity, Q is heat density power, Tout is an ambient temperature. The convective heat transfer coefficient h was obtained by measuring the cooling kinetics of the cuvette after laser radiation switching off. It is known, that the temperature of a convectively cooled object T(t) follows the Newton’s law of cooling:where C is the sample heat capacity, S is an area of the convectively cooled surface, T0 – sample initial temperature. The measured heat transfer coefficient was h = 9 ± 1 W/(m2·K). The temperature distribution inside the polymer volume was calculated for the appropriate thermal power, proportional to the absorption coefficient value. Using the developed model we obtained the temperature dependence of the absorption coefficients of all polymers at the wavelengths 960 nm, 1064 nm and 1550 nm. Relatively high errors of the simulation results are due to the uncertainties of the thermal conductivity values of the polymers. The presence of impurities and air micro bubbles lead to the variations of the polymer thermal conductivity in the range of 0.15-0.25 W/(m·K) [5]. Typical temperature dependences of the absorption coefficients of different polymers at 1064 nm are shown in Fig. 3(a). Temperature dependences of the Silgel absorption at different wavelengths are presented in Fig. 3(b).Fig. 3 Temperature dependences of the absorption coefficients of (a) all polymers at λ = 1064 nm, (b) the Silgel polymer at different wavelengths.
The averaged values of the absorption coefficients of investigated polymers are listed in Table 1. It can be seen that the absorption at 1550 nm wavelength is several times higher compared to other two wavelengths. This stays in agreement with the measured transmission spectra (Fig. 1(b)). Absorption of the Silgel polymer is also noticeably higher compared with other types.
Table 1. Temperature-averaged values of the absorption coefficients α of the studied polymers at different wavelengths (cm– 1)
3. Simulations of the fiber laser unit heating
In the industrial fiber units the active fiber coils are additionally poured by a thick layer of Silgel polymer in order to improve the mechanical stability and heat removal. Due to the fact that its thickness is an order of magnitude greater than that of Sylgard and FSX fiber coatings, and it also has higher absorption coefficient (see Table 1), it makes the main contribution to additional heating due to the absorption of spontaneous luminescence, scattered laser radiation and any other radiation losses occurring inside the laser unit.
We have studied heating of the Yb-doped fiber laser unit in lasing conditions. The output power of the investigated fiber laser operating at 1064 nm wavelength reached 100 W level. The optical to optical conversion efficiency was 76.4%. An overall length of the active fiber with 1 dB/m pump absorption was 20 m.
First, surface temperature of the polymer layer of the fiber unit was measured. We proposed to use the segments of the copper wire connected to a highly sensitive milliohmmeter as the temperature sensors. It is well known that the electrical resistance R of the conducting material depends on its temperature T. In the investigated temperature range the heating of the sensor wire can be determined directly by measuring its resistance change as ΔT = ΔR/(αrR0), where αr is a temperature coefficient of the resistance (3.9·10−3 K−1 for copper).
Therefore, it is possible to determine the temperature of the polymer contacting with the wire sensor. A block scheme of the experimental setup is shown in Fig. 4(a). A circular segment of the thin copper wire (100 μm in diameter) was placed at the hottest place of the Silgel polymer surface (right above the active fiber ring) and covered with a thin layer of the same polymer for better thermal contact. Measured dependence of the polymer surface heating on the output laser power is shown in Fig. 4(b). The line slope was 0.105 ± 0.003 K/W.
Fig. 4 (a) Block scheme of the experimental setup for measurement of the polymer surface temperature in a fiber unit. Dark and light gray lines indicate metal wires and optical fiber, respectively. (b) Dependence of the Silgel polymer surface heating on the laser output power.
In order to determine the temperature inside the polymer volume an additional experiment was conducted. A replica of the laser unit was assembled in which the active fiber was substituted with the copper wire coated with Sylgard polymer with the same length. This inner wire was heated by transmitting the electric current through it, thus simulating heating of an active fiber core under the same heat sink conditions. The advantage of this design is that the temperature change of the inner metal wire can be accurately determined from the change of its resistance and released thermal power can be obtained according to the Joule-Lenz law from the parameters of the flowing electric current. As in the previous experiment the surface temperature was measured simultaneously using the same copper wire temperature sensor. It served as a reference point for comparison between two experimental setups.
Measured dependences of the polymer surface and inner wire heating on the released thermal power are shown in Fig. 5.
The heating of the inner wire replacing an active fiber turned out to be ~23% higher compared to the surface of Silgel polymer layer (0.74 K/W versus 0.60 K/W). This temperature ratio should be the same for the fiber laser unit because of the equal heating conditions. It is worth noting that knowledge of this ratio allows using of an infrared thermal camera, which usually can measure only the surface temperature, to determine the temperature of the active fiber inside the polymer.
Taking into account the total heat power released in the experiment with electric heating and using the temperature of the surface wire as reference point between two experiments (blue line in Fig. 5), we calculated that the fraction of the optical pump power converted into heat in the studied fiber laser was about 14%. Since for our Yb-doped active medium the quantum defect (energy difference between the pumping and generating photons) is only 10%, we can conclude that about 4% of the pump power was absorbed in the surrounding polymer layers.
To compare the experimental data with theoretical calculations three-dimensional mathematical model of fiber laser unit heating was elaborated using Eqs. (1) and (2). The convective heat transfer coefficient of the fiber unit was measured experimentally from Eq. (3) in the same way as for the cuvette filled with a polymer and was h = 11 ± 1 W/(m·K). In order to specify correctly the boundary conditions for modeling, experimental measurements were carried out in different cooling conditions, i.e. for the fiber unit placed onto the heat conductive optical table and onto the thermally insulating racks. The simulation results of the fiber unit heating under lasing conditions are presented in Fig. 6.
Fig. 6 3D view and a cross section of the temperature distribution (in °C) calculated for the Yb-doped fiber unit generating 100 W of output optical power and placed onto the optical table. Initial and ambient temperature was 20 °C.
The simulation results showed good agreement with the experiment, taking into account the model errors. Applying the thermal power corresponding to the generation of 100 W of laser radiation (considering only quantum defect) the temperature change of the surface copper wire was 7.7 K and heating of the fiber core was 9.4 K, which is much less than what was observed in the experiment (10.5 K and 12.9 K, respectively). But adding absorption of 4% of the pump radiation in the polymer layer led to an increase in heating of surface wire up to 10,7 K and of fiber core up to 12.5 K, that better corresponds to the measured values.
Approximating the experimental conditions to the 1 kW of laser output power (optical pumping ~1,3 kW), it was evaluated that the active core temperature reaches 142 °C and the polymer temperature varies from 140 °C near the fiber to 125°C on the surface, that is beyond the limits of long-term thermal stability of PS polymers [1].
4. Conclusions
In the present research optical and thermal properties of three polymers conventionally used in fiber optics were investigated. Measured optical transmission spectra of polymers revealed the presence of absorption bands in the wavelength ranges of optical pumping and generation of fiber lasers doped with Yb and Er ions. Absorption coefficients of these polymers at corresponding wavelengths were measured using laser calorimetry. Its values varied from 0.02 to 0.2 cm−1 depending on the polymer type, radiation wavelength and temperature. Also heating of high-power Yb-doped fiber laser unit, representing the metal case with an active fiber coil placed inside and filled with a thick polymer layer, was investigated. Relying on the experiment with an electrically heated copper wire substituting the active fiber it was obtained that heating of the active fiber core was ~23% higher compared to the surface of the polymer layer. Furthermore, experimental results revealed that about 4% of the pump power was absorbed in the surrounding polymer additionally heating the fiber laser. Mathematical model of fiber laser unit heating was developed and showed a good agreement with experimental data.
References
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