1972
OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Radio-frequency spectroscopy of the active fiber heating under condition of high-power lasing generation O. A. Ryabushkin,1,2 R. I. Shaidullin,1,2,* and I. A. Zaytsev2 1
2
Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region 141700, Russian Federation Kotelnikov Institute of Radio Engineering and Electronics of RAS, Vvedensky Sq. 1, Fryazino, Moscow region 141120, Russian Federation *Corresponding author: rs‑[email protected] Received November 21, 2014; revised March 25, 2015; accepted April 3, 2015; posted April 3, 2015 (Doc. ID 228321); published April 21, 2015 A novel method for the precise temperature measurement of active fibers in high-power fiber lasers and amplifiers is introduced. This method allows the determination of active fiber longitudinal temperature distribution at different optical pump powers. © 2015 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.5625) Radio frequency photonics; (120.6780) Temperature; (160.5470) Polymers. http://dx.doi.org/10.1364/OL.40.001972
Output power of modern commercial CW low-ordermode fiber laser reached 50 kW [1]. Most efficient conversion of multimode pump radiation of laser diodes, based on semiconductor heterostructures, into singlemode laser radiation is achieved in active ytterbiumdoped cylindrical silica fibers. Ytterbium fiber lasers have high efficiency (up to 80%), and radiation losses in high-power lasers can lead to the hundreds degrees of temperature rise of the active medium. This requires careful study of changes in the properties of the laser medium on temperature. It was shown that fiber heating leads to decrease of the pump power conversion efficiency and can cause thermal lensing and thermal degradation of the fiber [2]. It was discovered soon that due to the active medium heating, the output radiation power of the fiber laser decreases [3]. The wavelength of free generation changes as well [4]. The mode structure and the beam quality of the fiber laser radiation are also affected [5]. Significant theoretical model of fiber heating was proposed in 1998 [6]. In this work, quantum defect caused by difference of the pump and generation wavelength was assumed to be the only mechanism responsible for heating of the active fiber core. Following this assumption, temperature distribution in fiber cross-section was calculated for CW and pulse operating modes of the fiber laser. More comprehensive study of the thermal effects in active optical fibers was introduced in [7], where necessity of full analysis of mechanisms that are responsible for fiber core temperature change, especially at laser power scaling, was discussed. First experimental realizations of active fiber core temperature measurement were made using interferometric method [8]. At present, some other primarily indirect techniques are also applied. For example, in [9], the temperature of the contiguous fiber with written Bragg gratings, being in thermal contact with the active Yb/Erdoped fiber under test, was measured. In [10], infrared camera was used to determine the temperature of the active fiber. It should be noted that in this Letter, thermodynamic properties of the polymer coating were taken into account there for the calculation of the fiber temperature profile. Susceptibility to the thermal damage of different layers (core, silica cladding, and polymer 0146-9592/15/091972-04$15.00/0
cladding) of the active fiber strongly varies. This fact should be taken into account when one considers limiting factors of fiber power scaling. In 2006, we developed method for the active fiber core temperature determination in lasing conditions. It was based on the Mach–Zehnder interferometer [8] and gave measurement accuracy better than 0.1 K. In order to explain experimental results, we proposed a novel model of coaxial fiber heating. We claimed that besides the quantum defect, which occurs in fiber core, absorption of scattered radiation in the fiber polymer cladding plays a significant role [11]. Thus, it was demonstrated that characteristics of the polymer cladding were important in fiber lasers and amplifiers heating. Furthermore, we have experimentally measured transmission spectra of several polymers, usually used as fiber coatings. We found out that all these polymers have strong absorption peaks at wavelengths of 908 and 1020 nm that lie in operating range of the ytterbium fiber laser pump and luminescence radiation [12]. Thus we faced the problem of independent temperature measurement of the fiber core and protective polymer coating. It is well known that radiofrequency impedance spectroscopy is widely used for determination of thermal properties of various dielectric materials [13]. In this Letter, we present a novel method, based on radio-frequency impedance spectroscopy, for temperature measurement of active fibers. We have found that temperature dependence of the dielectric permittivity in radio-frequency range of the polymers, used as protective coatings for silica fibers, is several orders of magnitude higher than it is for fused silica [14]. Thus, applying impedance spectroscopy for optical fiber coated with polymer, we can independently determine the polymer temperature. If we are also interested in fiber core temperature value, it can be calculated then by solving stationary heat conduction equation. Original experimental setup was developed for precise temperature measurements of the fiber polymer cladding. For this purpose, resonance frequency of the electric oscillating LC-circuit, composed of inductor and the capacitor with active fiber as dielectric medium, is measured. © 2015 Optical Society of America
May 1, 2015 / Vol. 40, No. 9 / OPTICS LETTERS
Block scheme of the experimental setup used for optical fiber temperature measurement is shown in Fig. 1(a). It consists of induction coil, formed by copper wire (500 μm in diameter) that is reeled on the cylindrical silica glass tube, and a single-turn double-wire capacitor connected in series. This configuration represents the oscillatory LC-circuit. Segment (15 cm length) of the active fiber that is the part of the high-power fiber amplifier (3 m length) is placed between the plates of a capacitor. In order to achieve higher stability and measurement precision, the capacitor is filled with the additional polymer Sylgard-182, the same used for fiber coating [see Fig. 1(b)]. Network analyzer with build-in variable RF generator is used for measurement of resonance characteristics of LC-circuit. Fiber amplifier is based on dual-clad fiber consisting of fiber with Yb3 -doped active core (core diameter is 20 μm) and adjacent multimode pump fiber both 125 μm in diameter. Diameter of the polymer cladding is 550 μm. Fiber master oscillator provides 5 W of CW output power at 1070 nm wavelength. Seed power is then amplified in active fiber using multimode semiconductor laser diodes (wavelength 955–965 nm) as a pump source. Absorption coefficient of the pump radiation is 3.4 dB/m. Maximum amplifier output power reached 95 W at 120 W pump level with 5 W residual unabsorbed pump. This corresponds to 13 dB amplification factor and 78% conversion efficiency. Spectral dependences of the LC-circuit response I (electric current amplitude in LC-circuit) on frequency
1973
f near resonance measured in thermostat at different temperatures are shown in Fig. 2. Using these results at each temperature T, we determined resonance frequency Rf(T) that corresponds to I maximum. It was verified that inductance L value does not depend on temperature. Capacitance change with temperature C(T) occurs primarily due to variation of polymer dielectric permittivity. Using conventional expression for the resonant frequency of the serial oscillation circuit, we can determine the resonant-thermal coefficient K rt as follows: K rt
∂Rf ∂ 1 1 ∂C p − p · : ∂T ∂T 2π LC 4πC LC ∂T
(1)
Calibration dependence of the resonance frequency on uniform temperature was obtained in experiment when thermostat temperature was changed [see Fig. 3(a)]. In the second stage of the experiment, the resonance frequency shift of LC-circuit was measured at room temperature in process of laser radiation amplification inside optically pumped active fiber. The dependence of the resonance frequency on pump power P pump measured for the hottest segment of the active fiber, i.e. initial segment where most part of pump power is absorbed, is shown in Fig. 3(b). According to pump absorption coefficient and radiation losses, the pump power absorbed in this segment was about 12 W. As follows we can determine the equivalent temperature change of the active fiber polymer cladding with pump power as Δθeq K ro
ΔP βΔP. K rt
(2)
Dependence of the polymer equivalent temperature change on pump power is shown in Fig. 4. It should be noted that equivalent temperature of the polymer coating differs from its inhomogeneous thermodynamic temperature. It is some kind of average temperature of the polymer coating of the investigated fiber segment. More details concerning concept of equivalent temperature can be found elsewhere [13]. Value of the coefficient β was determined to be 0.34 K/W. So for
Fig. 1. (a) Block scheme of experimental setup (PLD—pump laser diodes, master oscillator–ytterbium-doped fiber laser). (b) Cross-section of the capacitor: 1, 2, 3—dual-clad fiber [1— fiber with ytterbium-doped active core, 2—multimode pump fiber, 3—polymer cladding (Sylgard-182)], 4—additional polymer (Sylgard-182).
Fig. 2. Resonance response of the LC-circuit at different temperatures.
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OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Fig. 3. (a) Resonance frequency dependence on temperature in the thermostat. (b) Dependence of the resonance frequency on pump power. Experimental data are linearly fitted using a least squares method.
120 W of pump power, the output laser power was 95 W, and equivalent heating temperature of the polymer was about 40 K. In comparison, heating temperature measured for the output segment of the fiber amplifier at the same pumping level (residual pump at the output is about 5 W) was only 6 K. In order to establish correspondence between the measured resonance frequency and the actual temperature of the fused silica cladding of the active fiber, we conducted additional experiments [15]. In the same experimental setup, instead of optical dual-clad fiber, we used copper
Fig. 4. Dependences of amplifier output power (filled circle) and polymer equivalent temperature (filled square) on pump power. Experimental data are linearly fitted using a least squares method.
wire (100 μm in diameter) of identical length with the identical polymer coating. This wire was heated by transmitting DC electric current. Copper core temperature was determined by measuring its resistance change simultaneously with polymer equivalent temperature at different electrical current values. Consequently, correspondence between polymer equivalent temperature and the copper wire temperature can be found. Taking into account that power of the electric current flowing through the wire is totally converted into heat, it is possible to estimate the fraction of optical power converted into heat in the optical fiber. Polymer equivalent temperature rise was 25.2 K per 1 W of electrical (thermal) power. On the other hand, 12 W of absorbed optical pump power in fiber amplifier segment caused 40.8 K of polymer equivalent temperature rise. Comparison of these experimental results reveals that the fraction of optical power converted into heat was about 14%. It is an estimated value, the exact value requiring further physical interpretation. This value was higher than the expected 10% due to quantum defect between pump and generation. Then instead of active dual-clad fiber, the passive fiber with the same geometry was investigated. It was found that even in the absence of pump conversion into laser radiation, the 120 W of optical pump resulted in 9 K temperature rise of the passive fiber initial segment. These results give us reason to consider additional heating mechanisms conditioned by absorption of pump and luminescence radiation inside the polymer coating. According to the conventional model taking into account only quantum defect [6,7], the temperature rise of polymer ΔT pol at the radius r from fiber axis can be calculated using equation: ln br η dP abs 1 : ΔT pol r 2π dl hb kpol
(3)
Here η is the part of absorbed pump power P abs , converted into heat, b—outer radius of the polymer coating, kpol —thermal conductivity of the polymer, l—fiber length, and h—heat transfer coefficient. Usually the main problem here is correct estimation of heat transfer coefficient that can significantly vary depending on the geometry, temperature, and material properties. By means of experimental measurements of fiber cooling kinetics and theoretical approximation, we determined that coefficient h for our system lies in the range 65 10 W∕m2 K. Thus at 120 W pump level, the average polymer heating theoretically estimated using (3) is 35 5 K. This value lies slightly below experimental results. Such discrepancy can be explained by presence of additional heating mechanisms. In order to compare our results with those obtained using other measurement techniques, it is convenient to compare temperature rise depending on heat load (heat power generated per fiber length unit). In our experiment, heat load for the hottest segment at maximum pump power was about 8 W/m, and corresponding temperature rise of the segment was about 40 K. For example, in [10], the fiber temperature rise measured by thermal IR camera at heat load of about 3.5 W/m was 18–30 K (8–9 K with interstitial material), depending
May 1, 2015 / Vol. 40, No. 9 / OPTICS LETTERS
on heat sink configuration. In [9], for Yb/Er laser, the calculated outer polymer temperature rise was about 200 K at heat load of about 25 W/m. All these temperatures refer to outer cladding of the fiber. It should be noted that experimental results depend on heat sink conditions, which strongly vary in different experimental setups. Radio-frequency impedance spectroscopy allows precise temperature measurement of polymer coating of an active fiber. Presented technique can be successfully applied in processes of generation and amplification of radiation in active fibers. Other types of fiber waveguides, including passive silica fibers and polymer fibers, can be investigated as well. Advantages of this method also include ability to measure the longitudinal temperature distribution of fibers. Impedance spectroscopy in combination with interferometric methods [8] will allow separate temperature analysis of fiber claddings and therefore constructing its 3D temperature distribution accurately. This will help to clarify heating mechanisms responsible for temperature change of different claddings of fibers in lasers and amplifiers and improve theoretical model of active fiber heating including kW-class fiber laser. The authors express their acknowledgement for the assistance provided by Alexey Konyashkin from Moscow Institute of Physics and Technology.
1975
References 1. http://www.ipgphotonics.com/apps_materials.htm. 2. L. Zenteno, J. Lightwave Technol. 11, 1435 (1993). 3. N. A. Brilliant and K. Lagonik, Opt. Lett. 26, 1669 (2001). 4. M. Y. Vyatkin, S. P. Grabarnik, and O. A. Ryabushkin, Quantum Electron. 35, 323 (2005). 5. W. W. Ke, X. J. Wang, X. F. Bao, and X. J. Shu, Opt. Express 21, 14272 (2013). 6. M. K. Davis, M. J. F. Digonnet, and R. H. Pantell, J. Lightwave Technol. 16, 1013 (1998). 7. D. C. Brown and H. J. Hoffman, IEEE J. Quantum Electron. 37, 207 (2001). 8. V. V. Gainov, D. T. Demyankov, and O. A. Ryabushkin, Trudy 49 Nauchnoi Konferencii MFTI, Dolgoprudnyy (2006), Vol. 5, p. 50 (in Russian). 9. Y. Jeong, S. Baek, P. Dupriez, J.-N. Maran, J. K. Sahu, J. Nilsson, and B. Lee, Opt. Express 16, 19865 (2008). 10. M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, Proc. SPIE 7195, 719511 (2009). 11. V. V. Gainov, R. I. Shaidullin, and O. A. Ryabushkin, Quantum Electron. 41, 637 (2011). 12. O. A. Ryabushkin, R. I. Shaidullin, and I. A. Zaytsev, Usp. Sov. Radioelek. 9, 57 (2014). 13. O. A. Ryabushkin, D. V. Myasnikov, A. V. Konyashkin, and V. A. Tyrtyshnyy, J. Eur. Opt. Soc. 6, 11032 (2011). 14. R. I. Shaidullin and O. A. Ryabushkin, Tech. Phys. Lett. 39, 576 (2013). 15. R. Shaidullin, I. Zaytsev, and O. A. Ryabushkin, in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper JW2A.24.
OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Radio-frequency spectroscopy of the active fiber heating under condition of high-power lasing generation O. A. Ryabushkin,1,2 R. I. Shaidullin,1,2,* and I. A. Zaytsev2 1
2
Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region 141700, Russian Federation Kotelnikov Institute of Radio Engineering and Electronics of RAS, Vvedensky Sq. 1, Fryazino, Moscow region 141120, Russian Federation *Corresponding author: rs‑[email protected] Received November 21, 2014; revised March 25, 2015; accepted April 3, 2015; posted April 3, 2015 (Doc. ID 228321); published April 21, 2015 A novel method for the precise temperature measurement of active fibers in high-power fiber lasers and amplifiers is introduced. This method allows the determination of active fiber longitudinal temperature distribution at different optical pump powers. © 2015 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.5625) Radio frequency photonics; (120.6780) Temperature; (160.5470) Polymers. http://dx.doi.org/10.1364/OL.40.001972
Output power of modern commercial CW low-ordermode fiber laser reached 50 kW [1]. Most efficient conversion of multimode pump radiation of laser diodes, based on semiconductor heterostructures, into singlemode laser radiation is achieved in active ytterbiumdoped cylindrical silica fibers. Ytterbium fiber lasers have high efficiency (up to 80%), and radiation losses in high-power lasers can lead to the hundreds degrees of temperature rise of the active medium. This requires careful study of changes in the properties of the laser medium on temperature. It was shown that fiber heating leads to decrease of the pump power conversion efficiency and can cause thermal lensing and thermal degradation of the fiber [2]. It was discovered soon that due to the active medium heating, the output radiation power of the fiber laser decreases [3]. The wavelength of free generation changes as well [4]. The mode structure and the beam quality of the fiber laser radiation are also affected [5]. Significant theoretical model of fiber heating was proposed in 1998 [6]. In this work, quantum defect caused by difference of the pump and generation wavelength was assumed to be the only mechanism responsible for heating of the active fiber core. Following this assumption, temperature distribution in fiber cross-section was calculated for CW and pulse operating modes of the fiber laser. More comprehensive study of the thermal effects in active optical fibers was introduced in [7], where necessity of full analysis of mechanisms that are responsible for fiber core temperature change, especially at laser power scaling, was discussed. First experimental realizations of active fiber core temperature measurement were made using interferometric method [8]. At present, some other primarily indirect techniques are also applied. For example, in [9], the temperature of the contiguous fiber with written Bragg gratings, being in thermal contact with the active Yb/Erdoped fiber under test, was measured. In [10], infrared camera was used to determine the temperature of the active fiber. It should be noted that in this Letter, thermodynamic properties of the polymer coating were taken into account there for the calculation of the fiber temperature profile. Susceptibility to the thermal damage of different layers (core, silica cladding, and polymer 0146-9592/15/091972-04$15.00/0
cladding) of the active fiber strongly varies. This fact should be taken into account when one considers limiting factors of fiber power scaling. In 2006, we developed method for the active fiber core temperature determination in lasing conditions. It was based on the Mach–Zehnder interferometer [8] and gave measurement accuracy better than 0.1 K. In order to explain experimental results, we proposed a novel model of coaxial fiber heating. We claimed that besides the quantum defect, which occurs in fiber core, absorption of scattered radiation in the fiber polymer cladding plays a significant role [11]. Thus, it was demonstrated that characteristics of the polymer cladding were important in fiber lasers and amplifiers heating. Furthermore, we have experimentally measured transmission spectra of several polymers, usually used as fiber coatings. We found out that all these polymers have strong absorption peaks at wavelengths of 908 and 1020 nm that lie in operating range of the ytterbium fiber laser pump and luminescence radiation [12]. Thus we faced the problem of independent temperature measurement of the fiber core and protective polymer coating. It is well known that radiofrequency impedance spectroscopy is widely used for determination of thermal properties of various dielectric materials [13]. In this Letter, we present a novel method, based on radio-frequency impedance spectroscopy, for temperature measurement of active fibers. We have found that temperature dependence of the dielectric permittivity in radio-frequency range of the polymers, used as protective coatings for silica fibers, is several orders of magnitude higher than it is for fused silica [14]. Thus, applying impedance spectroscopy for optical fiber coated with polymer, we can independently determine the polymer temperature. If we are also interested in fiber core temperature value, it can be calculated then by solving stationary heat conduction equation. Original experimental setup was developed for precise temperature measurements of the fiber polymer cladding. For this purpose, resonance frequency of the electric oscillating LC-circuit, composed of inductor and the capacitor with active fiber as dielectric medium, is measured. © 2015 Optical Society of America
May 1, 2015 / Vol. 40, No. 9 / OPTICS LETTERS
Block scheme of the experimental setup used for optical fiber temperature measurement is shown in Fig. 1(a). It consists of induction coil, formed by copper wire (500 μm in diameter) that is reeled on the cylindrical silica glass tube, and a single-turn double-wire capacitor connected in series. This configuration represents the oscillatory LC-circuit. Segment (15 cm length) of the active fiber that is the part of the high-power fiber amplifier (3 m length) is placed between the plates of a capacitor. In order to achieve higher stability and measurement precision, the capacitor is filled with the additional polymer Sylgard-182, the same used for fiber coating [see Fig. 1(b)]. Network analyzer with build-in variable RF generator is used for measurement of resonance characteristics of LC-circuit. Fiber amplifier is based on dual-clad fiber consisting of fiber with Yb3 -doped active core (core diameter is 20 μm) and adjacent multimode pump fiber both 125 μm in diameter. Diameter of the polymer cladding is 550 μm. Fiber master oscillator provides 5 W of CW output power at 1070 nm wavelength. Seed power is then amplified in active fiber using multimode semiconductor laser diodes (wavelength 955–965 nm) as a pump source. Absorption coefficient of the pump radiation is 3.4 dB/m. Maximum amplifier output power reached 95 W at 120 W pump level with 5 W residual unabsorbed pump. This corresponds to 13 dB amplification factor and 78% conversion efficiency. Spectral dependences of the LC-circuit response I (electric current amplitude in LC-circuit) on frequency
1973
f near resonance measured in thermostat at different temperatures are shown in Fig. 2. Using these results at each temperature T, we determined resonance frequency Rf(T) that corresponds to I maximum. It was verified that inductance L value does not depend on temperature. Capacitance change with temperature C(T) occurs primarily due to variation of polymer dielectric permittivity. Using conventional expression for the resonant frequency of the serial oscillation circuit, we can determine the resonant-thermal coefficient K rt as follows: K rt
∂Rf ∂ 1 1 ∂C p − p · : ∂T ∂T 2π LC 4πC LC ∂T
(1)
Calibration dependence of the resonance frequency on uniform temperature was obtained in experiment when thermostat temperature was changed [see Fig. 3(a)]. In the second stage of the experiment, the resonance frequency shift of LC-circuit was measured at room temperature in process of laser radiation amplification inside optically pumped active fiber. The dependence of the resonance frequency on pump power P pump measured for the hottest segment of the active fiber, i.e. initial segment where most part of pump power is absorbed, is shown in Fig. 3(b). According to pump absorption coefficient and radiation losses, the pump power absorbed in this segment was about 12 W. As follows we can determine the equivalent temperature change of the active fiber polymer cladding with pump power as Δθeq K ro
ΔP βΔP. K rt
(2)
Dependence of the polymer equivalent temperature change on pump power is shown in Fig. 4. It should be noted that equivalent temperature of the polymer coating differs from its inhomogeneous thermodynamic temperature. It is some kind of average temperature of the polymer coating of the investigated fiber segment. More details concerning concept of equivalent temperature can be found elsewhere [13]. Value of the coefficient β was determined to be 0.34 K/W. So for
Fig. 1. (a) Block scheme of experimental setup (PLD—pump laser diodes, master oscillator–ytterbium-doped fiber laser). (b) Cross-section of the capacitor: 1, 2, 3—dual-clad fiber [1— fiber with ytterbium-doped active core, 2—multimode pump fiber, 3—polymer cladding (Sylgard-182)], 4—additional polymer (Sylgard-182).
Fig. 2. Resonance response of the LC-circuit at different temperatures.
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OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Fig. 3. (a) Resonance frequency dependence on temperature in the thermostat. (b) Dependence of the resonance frequency on pump power. Experimental data are linearly fitted using a least squares method.
120 W of pump power, the output laser power was 95 W, and equivalent heating temperature of the polymer was about 40 K. In comparison, heating temperature measured for the output segment of the fiber amplifier at the same pumping level (residual pump at the output is about 5 W) was only 6 K. In order to establish correspondence between the measured resonance frequency and the actual temperature of the fused silica cladding of the active fiber, we conducted additional experiments [15]. In the same experimental setup, instead of optical dual-clad fiber, we used copper
Fig. 4. Dependences of amplifier output power (filled circle) and polymer equivalent temperature (filled square) on pump power. Experimental data are linearly fitted using a least squares method.
wire (100 μm in diameter) of identical length with the identical polymer coating. This wire was heated by transmitting DC electric current. Copper core temperature was determined by measuring its resistance change simultaneously with polymer equivalent temperature at different electrical current values. Consequently, correspondence between polymer equivalent temperature and the copper wire temperature can be found. Taking into account that power of the electric current flowing through the wire is totally converted into heat, it is possible to estimate the fraction of optical power converted into heat in the optical fiber. Polymer equivalent temperature rise was 25.2 K per 1 W of electrical (thermal) power. On the other hand, 12 W of absorbed optical pump power in fiber amplifier segment caused 40.8 K of polymer equivalent temperature rise. Comparison of these experimental results reveals that the fraction of optical power converted into heat was about 14%. It is an estimated value, the exact value requiring further physical interpretation. This value was higher than the expected 10% due to quantum defect between pump and generation. Then instead of active dual-clad fiber, the passive fiber with the same geometry was investigated. It was found that even in the absence of pump conversion into laser radiation, the 120 W of optical pump resulted in 9 K temperature rise of the passive fiber initial segment. These results give us reason to consider additional heating mechanisms conditioned by absorption of pump and luminescence radiation inside the polymer coating. According to the conventional model taking into account only quantum defect [6,7], the temperature rise of polymer ΔT pol at the radius r from fiber axis can be calculated using equation: ln br η dP abs 1 : ΔT pol r 2π dl hb kpol
(3)
Here η is the part of absorbed pump power P abs , converted into heat, b—outer radius of the polymer coating, kpol —thermal conductivity of the polymer, l—fiber length, and h—heat transfer coefficient. Usually the main problem here is correct estimation of heat transfer coefficient that can significantly vary depending on the geometry, temperature, and material properties. By means of experimental measurements of fiber cooling kinetics and theoretical approximation, we determined that coefficient h for our system lies in the range 65 10 W∕m2 K. Thus at 120 W pump level, the average polymer heating theoretically estimated using (3) is 35 5 K. This value lies slightly below experimental results. Such discrepancy can be explained by presence of additional heating mechanisms. In order to compare our results with those obtained using other measurement techniques, it is convenient to compare temperature rise depending on heat load (heat power generated per fiber length unit). In our experiment, heat load for the hottest segment at maximum pump power was about 8 W/m, and corresponding temperature rise of the segment was about 40 K. For example, in [10], the fiber temperature rise measured by thermal IR camera at heat load of about 3.5 W/m was 18–30 K (8–9 K with interstitial material), depending
May 1, 2015 / Vol. 40, No. 9 / OPTICS LETTERS
on heat sink configuration. In [9], for Yb/Er laser, the calculated outer polymer temperature rise was about 200 K at heat load of about 25 W/m. All these temperatures refer to outer cladding of the fiber. It should be noted that experimental results depend on heat sink conditions, which strongly vary in different experimental setups. Radio-frequency impedance spectroscopy allows precise temperature measurement of polymer coating of an active fiber. Presented technique can be successfully applied in processes of generation and amplification of radiation in active fibers. Other types of fiber waveguides, including passive silica fibers and polymer fibers, can be investigated as well. Advantages of this method also include ability to measure the longitudinal temperature distribution of fibers. Impedance spectroscopy in combination with interferometric methods [8] will allow separate temperature analysis of fiber claddings and therefore constructing its 3D temperature distribution accurately. This will help to clarify heating mechanisms responsible for temperature change of different claddings of fibers in lasers and amplifiers and improve theoretical model of active fiber heating including kW-class fiber laser. The authors express their acknowledgement for the assistance provided by Alexey Konyashkin from Moscow Institute of Physics and Technology.
1975
References 1. http://www.ipgphotonics.com/apps_materials.htm. 2. L. Zenteno, J. Lightwave Technol. 11, 1435 (1993). 3. N. A. Brilliant and K. Lagonik, Opt. Lett. 26, 1669 (2001). 4. M. Y. Vyatkin, S. P. Grabarnik, and O. A. Ryabushkin, Quantum Electron. 35, 323 (2005). 5. W. W. Ke, X. J. Wang, X. F. Bao, and X. J. Shu, Opt. Express 21, 14272 (2013). 6. M. K. Davis, M. J. F. Digonnet, and R. H. Pantell, J. Lightwave Technol. 16, 1013 (1998). 7. D. C. Brown and H. J. Hoffman, IEEE J. Quantum Electron. 37, 207 (2001). 8. V. V. Gainov, D. T. Demyankov, and O. A. Ryabushkin, Trudy 49 Nauchnoi Konferencii MFTI, Dolgoprudnyy (2006), Vol. 5, p. 50 (in Russian). 9. Y. Jeong, S. Baek, P. Dupriez, J.-N. Maran, J. K. Sahu, J. Nilsson, and B. Lee, Opt. Express 16, 19865 (2008). 10. M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, Proc. SPIE 7195, 719511 (2009). 11. V. V. Gainov, R. I. Shaidullin, and O. A. Ryabushkin, Quantum Electron. 41, 637 (2011). 12. O. A. Ryabushkin, R. I. Shaidullin, and I. A. Zaytsev, Usp. Sov. Radioelek. 9, 57 (2014). 13. O. A. Ryabushkin, D. V. Myasnikov, A. V. Konyashkin, and V. A. Tyrtyshnyy, J. Eur. Opt. Soc. 6, 11032 (2011). 14. R. I. Shaidullin and O. A. Ryabushkin, Tech. Phys. Lett. 39, 576 (2013). 15. R. Shaidullin, I. Zaytsev, and O. A. Ryabushkin, in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper JW2A.24.
