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In this paper we report on the examination of the temperature influence of the effective refractive index and on the dispersion characteristics in air-hole lattice photonic crystal fibers. We use an original method to measure the temperature influence on chromatic dispersion in an optical fiber, where both the thermal expansion of the fiber and its effective group refractive index are taken into account. We present the experimental and modeling results of dispersion characteristics for two types of non-linear fibers, a silica glass fiber and a soft glass fiber in the temperature range from 20°C to 420°C. We measured the zero dispersion wavelength shift of + 0.020 nm/°C for the fused silica fiber and + 0.045 nm/°C for the heavy metal oxide soft glass fiber. Experimental results are in agreement with numerical modeling. Finally, the influence of the temperature-induced change of the dispersion profile on nonlinear performance of the studied fiber structures is investigated numerically. Notable change of parametric gain maxima locations is observed even for small changes of the zero dispersion wavelength in relation to the pump laser wavelength in a four-wave mixing fiber-based wavelength conversion scenario.
© 2016 Optical Society of America
1. Introduction
Nonlinear processes in optical fibers are strongly susceptible to the changes of dispersion properties [1]. In particular temperature stability of soft glass fibers is considered as an issue since these glasses have high attenuation (of the order of few dB/m) and large portion of the absorbed energy is dissipated as heat through a photon-phonon energy transfer [2]. High energy pulsed pumping has been known for decades to influence functional properties of glass optical elements [3,4]. In the nonlinear fiber optics domain, this can be easily related to changes of the frequency conversion performance. The increase of temperature can influence both the geometrical and material parameters of an optical fiber, thus changing the dispersion properties determined by often subtle photonic crystal fiber microstructure.
The phenomena related to the increase of temperature in optical fibers have already been reported by a number of groups, but these results were constrained to fused silica fibers [5–13]. The previous studies of temperature dependence of optical fiber chromatic dispersion have been focused on the telecommunication aspect, where the temperature fluctuation have direct impact on bit error rate (BER) in 40 Gbit/s systems based on standard single mode fibers [10]. Rise of temperature from 20°C to 60°C shifts the G.652 single mode fiber’s zero dispersion wavelength (ZDW) located at 1319.30 nm towards the longer wavelengths with a ratio of 0.026 nm/°C. This results in BER increase in excess of 104. Red-shift of the ZDW have been also observed by A. Kudlinski in air/silica photonic crystal fibers (PCF) with air hole diameter d = 1.9 μm and relative air-hole size of d/Λ = 0.48 [5]. There, the location of ZDW at room temperature was established at 1088 nm and the observed, temperature-induced red-shift was about 10 nm at 250°C. Fiber heat load has also been studied in the context of changes of gain in rare-earth doped silica fibers for laser applications [12] and in the context of mode structure and single mode operation in large mode area silica PCFs [13]. In the earlier, a roughly 100 K temperature range has been considered, corresponding to a range between the room temperature and 120°C. In the latter, the authors studied numerically heat loads corresponding to maximum temperatures at the center of the fiber core just above 300°C.
Temperature influence on fiber parameters was not investigated in soft glass fibers. Some works were dedicated only to determination of the temperature-related change of the refractive index of selected bulk soft glasses [14,15]. In this paper for the first time we study both theoretically and experimentally the influence of temperature change on the dispersion properties of photonic crystal fibers made of a heavy metal oxide glass. As a reference we use a fused silica fiber with similar geometry to distinguish between geometrical and material impacts of the observed dispersion change.
The chromatic dispersion of a nonlinear PCF determines the area of application of the fiber, especially in terms of generation of new optical frequencies such as supercontinuum generation. Most of the nonlinear optical effects are obtained by pumping the nonlinear medium with a high pulse energy ultrafast laser, which is accompanied by release of heat. In χ(2) processes (i.e. second harmonics generation), the nonlinear crystals are routinely temperature-stabilized in order to maintain phase-matching during operation. In this work, we show the context in which thermal effects should be taken in to account when the nonlinear optical phenomena are investigated in optical fibers made from highly nonlinear glasses enabling χ(3)-based frequency conversion. Coupling the high power radiation into the small core of the nonlinear PCF causes the heating of the core and the immediately adjacent area of the cladding, which is covered by the mode area. Increased temperature inside the fiber changes the refractive index of the material and the dimensions of the photonic lattice, which has crucial impact on the mode propagation and its dispersion. We therefore demonstrate experimental (measurement) and theoretical (simulation) results performed to verify the magnitude of dispersion changes in two nonlinear PCFs made of different glasses.
We have modified the standard Mach-Zehnder interferometric setup commonly used for dispersion measurement by adding a furnace, in order to allow measurements of the temperature influence on dispersion. Previously, the method based on the four-wave mixing (FWM) process was used, where the fused silica PCF was pumped in the normal dispersion regime with two Nd:YAG lasers operating at slightly detuned wavelengths [5]. Only the zero dispersion wavelength shift as a function of temperature was measured with this approach. Our method allows to obtain full dispersion characteristics of the fiber at different temperatures.
Having recorded temperature-dependent dispersion profiles for a silica PCF and a soft glass PCF, we performed a series of numerical simulations to assess how the elevated fiber temperature influences the nonlinear performance in each of the fibers. The obtained results enable to evaluate the potential consequences of temperature response of the nonlinear fiber in specific applications, where temperature sensitivity of the dispersion may require e.g. its thermal stabilization during operation or taking into account the temperature response at the fiber design stage. Specifically, we show through numerical simulations, how a highly nonlinear soft glass PCF fiber in a hypothetical parametric conversion scenario yields over 200 nm of shift of the detuned idler component location with a temperature increase from 20°C to 420°C.
2. Material properties and geometrical parameters of the examined fibers
Thermal effect on the effective group index Neff and dispersion D was examined in two types of air-hole photonic crystal fibers, both dedicated to nonlinear optics applications. Both fibers were fabricated in-house using the stack-and-draw method. The photonic lattice of the fibers was formed by air holes arranged in hexagonal lattice with a central defect filled by a glass rod, acting as the fiber core, as shown in scanning electron microscopy (SEM) images in Fig. 1. The first fiber, labeled NL33B1, was made of fused silica glass whereas the second fiber, labeled NL24C4, was made of lead-bismuth-gallate glass labelled PBG08 [16].
Fig. 1 Nonlinear photonic crystal fibers used in this work (SEM images): fused silica fiber NL33B1 (a), and fiber NL24C4 made of lead-bismuth-gallate glass PBG08 (b).
The lattice of this soft glass PCF has two different relative air-hole sizes (the inner most ring air holes have larger diameters than the remaining air-holes). Dispersion properties are optimized by relative air-hole sizes in the first ring of the photonic cladding. A change of the relative air-hole sizes in first ring allows to tune the zero dispersion wavelength into the proximity of the selected pump wavelength at 1550 nm. The relative hole size of the outer rings is decreased in order to increase the modal losses of the higher order modes. We verified numerically, that the fiber guides only a few modes, while losses of higher order modes are significantly higher than the one for the fundamental mode. Experimentally we confirmed an effective single mode performance of the fiber at 1550 nm and that its dispersion properties were optimized for supercontinuum generation with erbium-based ultrafast lasers [17]. The geometrical parameters of the fiber microstructures are given in Table 1. The thermal and optical properties of the used glasses are presented in Table 2 and Table 3.
Table 1. Geometrical parameters of fused silica PCF NL33B1 and lead-bismuth-gallate PCF NL24C4
Table 2. Optical and thermal parameters of used glasses
Table 3. Sellmeier coefficients of fused silica glass and the PBG08 glass, used in this work
3. Measurements of effective group index at different temperatures – description of the method
The used dispersion measurement system, presented in Fig. 2, is based on a Mach-Zehnder interferometer configuration [18]. As a source we used supercontinuum emitting in the spectral range of 400 - 2000 nm with an average output power of 105 mW. Two spectrometers, covering the visible and near-infrared wavelengths, enabled to measure dispersion characteristics in the spectral range of 450 - 1700 nm. The collimated input beam is split with a beamsplitter cube BS1 and next in the measuring arm it is coupled by a microscope objective MO2 to the examined fiber, whereas in the reference arm a parallel beam is reflected from the system of conjugated two silver mirrors M3 and M4, both translatable in one axis. That system of mirrors placed on a platform with micrometer measuring screw enabled to measure the compensation length Δl in the reference arm induced by the optical fiber with the length of Lfiber placed in the measuring arm. The custom-made furnace is located at the measuring arm and allows to set and control the temperature of the examined fiber over its section of a length of LT = 145 mm. The water cooling casing provides ample thermal stability and insulation of the furnace from the rest of the system. A thermocouple was placed inside the furnace positioned and fixed at 2 mm away from the examined fibers. It allowed to measure and control the temperature of the heated fiber by an external controller with high precision and repeatability. The heating system enabled to change the fiber temperature from 20°C to 800°C with 1°C resolution.
Fig. 2 Scheme of the developed system used to measure dispersion in optical fibers at high temperatures.
Using the system we can directly measure the compensation length Δl of optical path length in the reference arm for a wavelength of the interferometer compensation. Knowledge of Δl(λ) enables to determine the group refractive index of the propagating mode in the fiber Neff(λ) using the equation:
where OPD denotes optical path difference as function of wavelength, induced by optical component in the interferometer. The OPDs of microscope objectives MO2, MO3 and neutral density filter NDF have previously been obtained using a Michelson interferometer. If the Neff(λ) is known we can easily calculate the dispersion of the fiber with the standard formula:where c denotes the speed of light in vacuum.The Eq. (1) for Neff(λ) is accurate only for the fiber at room temperature. The situation changes when we insert the fiber into the furnace, and fix the two ends of the fiber in a 3-axis translation stage, followed by the start of heating. It is obvious that the heated fiber increases its length slightly because of thermal expansion of the glass. If we want to know how the effective group index of the heating part of the fiber has changed, the fiber elongation has to be taken into account.
To solve this problem the examined fiber is placed in the furnace by using a ceramic rod with two channels along its length. A thermocouple sensor is placed inside the first channel, while the measured fiber in placed in the second channel. The diameter of internal holes of the ceramic tube is 2 mm which ensures that the fiber cannot bend inside the tube. Therefore, we assume that our fiber can bend only between the clamps and the ends of the ceramic rod, as shown in Fig. 3. A further assumption is that the examined fiber was heated only in the central section of length LT = 145 mm placed inside the furnace. These assumptions give us the following formula describing the optical path length (OPL) introduced by the heated and bent fiber:
In principle, the ceramic rod assures that the part of the fiber experiencing elevated temperature does not change its length during the measurement, since the elongation takes place at the parts extending outside of the furnace. The measuring process begins with evaluation of the characteristics Δl20°C(λ) at room temperature T = 20°C for the straight fiber with length Lfiber, placed inside the furnace. It gives us the possibility to calculate the reference Neff(λ) and the dispersion D(λ) at temperature of 20°C. In the next step the temperature inside the furnace is slowly increased at a rate of 3-5°C/min, up to 120°C. After additional 10 minutes of stabilization, we perform the next measurement of the compensation length ΔlT(λ) at 120°C. This information enables us to calculate the effective group index of heated part of fiber at the higher temperature Neff(λ,T) using the equation:The thermal increase of the fiber length ΔL(T) can be obtain from linear thermal expansion coefficient α of the glass, which the fiber is made of, and the length of heating LT:The same process is realized for 220°C, 320°C and 420°C. Although the furnace enables to heat the part of fiber up to 800°C, we limited the maximum temperature to 420°C due to the low softening temperature of PBG08 glass used for development of the NL24C4 fiber. In the final step, the temperature of the fiber was decreased to 20°C and the measurement of Δl20°C(λ) was repeated in order to check the hysteresis of the effective group index after the entire heating and cooling process. We have performed only a single cycle of heating and cooling for every fiber. We might expect a different response for consecutive heat-cool loops only if fiber had previously frozen internal stress in its structure. We note, that this task requires further experimental study.The example of the movement of the interference fringes indicated by heating of the NL24C4 fiber at fixed position of the linear stage with two mirrors in the reference arm, is shown in Fig. 4(a). It was mentioned that heating changes the refractive index of glass and extends the fiber. Both effects contribute to the change of the compensation length ΔlT(λ) at higher temperatures, as presented in Fig. 4(b).
Fig. 4 Shift of the interference fringes in spectral range due to fiber heating (a). Measurement points of the compensation length Δl as a wavelength function for different temperatures (b). All characteristics obtained for a 212 mm long sample of the NL24C4 fiber.
The dispersion measurement in the standard Mach Zehnder interferometer allows to obtain a normalized characteristic, which is the dispersion D (ps/nm·km) as function of wavelength. The fiber length is selected for measurements such, as to enable obtaining of high contrast interferograms (Fig. 4a), which allow calculation of the effective group index Neff profile, which is normalized with respect to fiber length, as shown e.g. in [1]. Similarly dispersion D is normalized with respect to fiber length used in experiments if the measurements are carried out in various temperatures.
4. Experimental results
Both NL33B1 and NL24C4 fibers were examined in the same way in temperature range of 20°C - 420°C with a step of 100°C. The length of heating (section of fiber inside the furnace) LT was 145 mm, whereas the length Lfiber of used fibers was 303 mm and 212 mm for NL33B1 and NL24C4 fibers, respectively. The results of measurements for the fiber NL33B1 show the increase of the effective group refractive index with temperature increment, as in Fig. 5(a). The changes of Neff(λ,T) with respect to Neff(λ,T = 20°C) are plotted in Fig. 5(b). Except for the short wavelength range (500 - 800 nm), the shape of ΔNeff(λ,T) is nearly linear with a slope of −4.5 × 10−4 1/μm at ΔT = 400°C. The maximum change of Neff(λ,T) reaches 3.8 × 10−3 for a wavelength of 500 nm and at a temperature of 420°C. If we consider the linear part of the characteristic we can calculate the thermal coefficient of the group refractive index Neff. At a wavelength of 1 μm its value is obtained as ΔNeff(λ,T)/ΔT = 7.32 × 10−6 1/°C.
Fig. 5 Thermal influence on characteristics of the effective group refractive index for the fiber NL33B1 (a). Change of effective group refractive index Neff(λ,T) in relation to characteristic at room temperature (b).
Measured dispersion of the NL33B1 fused silica fiber at room temperature is shown in Fig. 6(a). The zero dispersion wavelength ZDW is located on 1.036 μm. The other characteristics of dispersion for higher temperatures are not plotted in Fig. 6(a) for better clarity. The dispersion profiles around the ZDW are presented in Fig. 6(b), whereas the relative changes of dispersion with temperature increase are shown in Fig. 6(c). A shift of the ZDW into the infrared for examined temperatures is listed in Table 4.
Fig. 6 Dispersion of the fiber NL33B1 at room temperature (a). Spectral shift of ZDW caused by the fiber heating (b). Dispersion difference in relation to dispersion at room temperature (c).
Table 4. Shift of the zero dispersion wavelength in the NL33B1 and NL24C4 fibers, in function of fiber temperature
The measured dispersion changes for this type of fused silica non-linear PCF NL33B1, induced by the rise of temperature, are small. Maximum shift of the ZDW of 8 nm was obtained for ΔT = 400°C, which gives the ZDW thermal shift of 0.020 nm/°C. It is a slightly lower value of thermal ZDW shift in comparison to the standard germanium doped telecommunication fiber, in which the ZDW thermal shift of 0.026 nm/°C was reported [10]. Only small changes of dispersion characteristics are observed. The maximum shift of −26 ps/(nm × km) was obtained at 500 nm for temperature difference of ΔT = 400°C. Near the ZDW the change of dispersion does not exceed −1.8 ps/(nm × km) for ΔT = 400°C, therefore the thermal sensitivity coefficient is very small and equals ΔD/ΔT = −4.5 × 10−3 ps/(nm × km × °C).
Figure 7(a) shows the increase of Neff(λ,T) measured for the fiber NL24C4 made of lead-bismuth-gallate glass (PBG08). Due to the higher refractive index and dispersion of this glass in comparison to fused silica glass, the changes of effective group index are more significant, especially in the short wavelength range. The maximum change of effective refractive index ΔNeff(λ,T) = 21 × 10−3 was observed at the short wavelength limit of our measurement range, at 500 nm and for the maximum investigated temperature of 420°C. In the proximity of ZDW, which is located at 1.409 μm at room temperature in the case of NL24C4 fiber, the thermal coefficient of the group refractive index equals ΔNeff(λ,T)/ΔT = 7.0 × 10−6 1/°C. For a wavelength of 1 μm the thermal coefficient increases up to ΔNeff(λ,T)/ΔT = 10.4 × 10−6 1/°C. A small hysteresis of the group index after heating and cooling process was also observed, as shown in Fig. 7(b).
Fig. 7 Thermal influence on effective group refractive index in the fiber NL24C4 (a). Change of effective group refractive index Neff(λ,T) with respect to one at the room temperature (b).
Due to the high dispersion of the PBG08 soft glass, which has a ZDW around 2 μm, the dispersion of the NL24C4 fiber, plotted in Fig. 8(a), is much higher (in absolute values) than for the NL33B1 fiber. The ZDW of the NL24C4 fiber is shifted to 1.409 μm (at 20°C) because of the waveguide dispersion contribution. Thermal impact on the dispersion is significant, mainly in the visible wavelength range. This is presented in Fig. 8(c) as a spectral dependence of dispersion in high temperature in relation to dispersion at room temperature. The maximum change of dispersion equals ΔD = 500 ps/(nm × km) at λ = 500 nm for ΔT = 400°C. Near the ZDW the dispersion change reaches the value of −6.93 ps/(nm × km) at 420°C, which gives the thermal sensitivity coefficient of ΔD/ΔT = −17.3 × 10−3 ps/(nm × km × °C).The heating of the fiber has resulted in a nearly linear shift of ZDW as shown in Fig. 8(b) and summarized in Table 4. The shift of ZDW into the longer wavelengths reaches 18 nm for ΔT = 400°C, which gives the ZDW thermal shift of 0.045 nm/°C and after the entire heating process the ZDW returns very close to the position before heating. A small hysteresis of dispersion is observed only for short wavelengths and it may be the result of glass thermal relaxation during heating and cooling in measurement process. We suppose that during drawing of NL24C4 fiber, made of an in-house glass with relatively high linear thermal expansion coefficient (with respect to silica glass as shown in Tab. 2), some internal stress was frozen in the glass structure. In case of the fused silica based fiber, due to its low thermal expansion coefficient, we did not observe hysteresis in the measurements. Simultaneously it is an evidence of thermal stability and accuracy of the measurement setup.
Fig. 8 Dispersion of the fiber NL24C4 at room temperature (a). Spectral shift of ZDW caused by the fiber heating (b). Dispersion difference in relation to dispersion at room temperature (c).
The low thermal sensitivity necessitates a precise examination method. The main impact on the system accuracy is associated with an error of the compensation length measurement, which equals δ(Δl) = ± 5 μm. If we consider the precision of fiber length δ(Lfiber) = ± 0.5 mm and the accuracy of OPD measurement δ(OPD) = ± 30 μm, we obtain the error of the effective group index at room temperature δ(Neff) = ± 16 × 10−4. However the measurement of Neff(λ,T) at higher temperature is based on the differential technique, in which the errors δ(OPD) and δ(Lfiber) are neglected, but then the uncertainty of heated length LT must be taken into account. We don’t know the temperature distribution inside the furnace, nevertheless the construction of the heating element should provide uniform distribution. We assume the length of heating section LT = 145 mm ± 1 mm, which gives the maximum error of the effective group index at high temperature on the level of δ(Neff(λ,T)) = ± 2 × 10−4. This value is below the result of the effective group index change ΔNeff(λ,T) = 8 × 10−4 for NL33B1 fiber at ΔT = 100°C. The precision of dispersion calculation is estimated at δD = ± 1.5 ps/(nm × km).
5. Modeling of influence of temperature on the effective group index for fused silica fiber – verification of the measurement method
Simulations of temperature influence on the effective group refractive index and dispersion for the fused silica based fiber NL33B1 have been carried out to verify the obtained experimental results. In our model we assumed linear expansion of the fiber α = 5.4 × 10−7 1/K. The thermo-optic effect in fused silica glass is applied as the thermal influence on the phase refractive index n, which is described by equation [19]:
We assume the values of constants based on [20] as shown in Table 5. According to [20] these constants are valid for the spectral and thermal ranges of 365 nm < λ < 1014 nm and −100°C ≤ T ≤ + 140°C. Nevertheless we use it for the range outside of the suggested limit, which may result in possible inaccuracies in the obtained results.Table 5. Constants of formula for dn/dT in vacuum. Valid for 365 nm < λ < 1014 nm and for −100°C ≤ T ≤ + 140°C [20]
Simulations of mode propagation in the fiber NL33B1 have been performed with the Finite Element Method in the COMSOL programming environment. The real fiber structure obtained from SEM image, as shown in Fig. 1, was used in the calculations. Simulations for increased temperature have been carried out for a properly modified structure dimensions, where thermal expansion is taken into account, and for the refractive index corresponding to the higher temperature. Assuming the absence of stress inside the single glass - air structure and no deformation, the piezo- and elasto-optic effects are neglected. Thermal change of the refractive indices of the guided mode is almost identical to the change in the case of bulk fused silica glass. This leads to the conclusion that the main influence on the effective index and dispersion of the heated fiber is associated with the thermo-optic effect in the glass. The measured and calculated dispersion profiles of the silica fiber NL33B1 at room temperature are shown in Fig. 9(a).
Fig. 9 Measured and calculated dispersion characteristics of the fiber NL33B1 at room temperature (a). Calculated shift of ZDW induced by increasing the temperature (b). Calculated relative dispersion difference with respect to dispersion at 20°C (c).
We obtained very good agreement, which means that the measuring technique and the simulation method are correct. A small discrepancy occurs regarding to ZDW at room temperature (measured ZDW = 1.036 μm and calculated ZDW = 1.033 μm). The simulation of thermal influence on dispersion of the fiber around the ZDW are presented in Fig. 9(b) and dispersion difference in relation to dispersion at 20°C in wide spectrum range is shown in Fig. 9(c). We obtain 10 nm redshift of ZDW from 1.033 μm to 1.043 μm for ΔT = 400°C and this result is similar to the measured value. The comparison of calculated and measured ZDW location for temperature range 20°C - 420°C is presented in Table 6. The character of the calculated dispersion difference curves in Fig. 9(c) is close to the characteristics obtained in the measurement, which are presented in Fig. 6(c). There are some discrepancies at wavelengths above 1.0 μm, but it is worth to notice that in this range the dispersion difference does not exceed ΔD < 3 ps/(nm × km) for ΔT = 400°C. This low value of ΔD is close to the resolution capability of our measurement system. Furthermore, the thermo-optic parameters of the silica glass are valid only to λ = 1014 nm, therefore the calculation in the spectral range above 1.0 μm should be considered as approximate. In spite of the mentioned inaccuracies, both the model of thermal impact on dispersion of the fused silica PCF used in simulation and the measurement technique return good agreement.
Table 6. The measured and calculated zero dispersion wavelength of the NL33B1 silicate PCF obtained for temperature range of 20°C - 420°C.
6. Discussion
The obtained results show that the temperature change in the range of 20°C – 420°C has limited influence on the dispersion characteristics in both cases of the silica and heavy metal oxide soft glass fibers. The information on the dispersion-temperature dependence is however of particular important in the case of nonlinear applications of fibers, where any change of characteristics may potentially significantly impair the nonlinear performance of the fiber. In the case of fused silica fibers we expect that the small sensitivity of ZDW on temperature changes + 0.020 nm/°C combined with very low absorption would result in negligible influence of temperature on nonlinear fiber performance.
In the case of heavy metal oxide glass fibers, the sensitivity of ZDW on temperature at + 0.045 nm/°C is only twice higher than what was observed for the fused silica. However if we take into account the high attenuation of this type of glasses, usually at the level of single dB per meter, we can expect increase of temperature up to a few hundred °C. As a consequence, the redshift of the dispersion profile in soft glass fibers can be more meaningful to e.g. supercontinuum spectra obtained in such structures.
The influence of temperature-induced dispersion change in the investigated fibers on their nonlinear performance has been investigated using numerically solved generalized nonlinear Schrödinger equation (GNLSE). We used the model proposed in [21]. One photon per mode noise was added in order to simulate pumping scenarios with 20 ps and 50 ps long laser pulses, where modulation instability related noise amplification is the main contributor to the nonlinear mechanics. The picosecond simulations used 250 ps long numerical time windows with a mesh of 217 points. The femtosecond simulations were performed in a narrower window to facilitate faster calculations. All simulations used a Gaussian shaped pulse, a flat fiber loss characteristic (0.1 dB/m for the silica PCF and 3 dB/m for the soft glass PCF) and fixed effective mode area, approximated with the fiber core area. Raman scattering was included respectively for both glass types – default parameters given in [21] were used for the silica glass fiber simulations and the Raman response of the lead-bismuth-gallate glass fiber parameterized as in our previous work [17]. Obtained numerical spectra have been smoothed with averaging over 50 adjacent numerical points, which corresponded to roughly several nanometers within the covered spectral range.
GNLSE simulations were performed for both the NL33B1 silica fiber and the NL24C4 soft glass fiber for the dispersion profiles measured at 20°C (before heating), 220°C and at 420°C. The simulations involved supercontinuum generation assuming either 100 fs or 20 ps long pump pulses centered at 1064 nm. We verified fiber lengths between 3 m and 6 m in the case of the silica PCF and between 15 cm and 50 cm in the case of the soft glass PCF. As expected, the temperature-induced dispersion modification in this case did not reveal any particular pattern in either femtosecond nor picosecond-pumped supercontinuum generation. In fact, this was in agreement with a general expectation, that due to small attenuation in silica glass fibers, the observed temperature-induced changes of their optical properties should be negligible.
In a final set of numerical simulations, the assumed fiber was the NL24C4 soft glass PCF, the pump pulse duration was extended to 50 ps and its center wavelength was set to 1350 nm. The motivation for such input conditions stemmed from the fact, that pumping in the long pulse regime at a wavelength blue-shifted against the ZDW of a dispersion-increasing fiber, facilitates χ(3) parametric conversion of the pump wavelength without supercontinuum generation [22,23]. Very recently, temperature tuning of parametric idler component in the range of 1200-1700 nm, pumped at 1064 nm, has been demonstrated in an ethanol-filled silica air-glass PCF [24]. The maximum detuning corresponded to a temperature increase from 20°C to 55°C. Influence of the temperature-induced dispersion change on the phase-matching condition is of practical importance also for microstructured fibers designed for far-detuned parametric conversion, since the only experimental demonstration of such a conversion took place with a soft glass fiber [25]. The authors have also pointed out, that parametric converter fibers should have large air-filling fractions, thus heat dissipation in such structures should be expected to be inferior, compared to typical air-glass PCFs or classic step-index fibers. Our results of nonlinear simulations of a parametric conversion scenario for a NL24C4 fiber are shown in Fig. 10, with the three temperature-dependent dispersion profiles shown in Fig. 10(a). Here, the wavelength detuning between the 1350 nm pump and the idler component increased with temperature change from 990 nm (room temperature, detuned idler at 2340 nm) up to 1230 nm (420°C, detuned idler at 2580 nm). The blue-shifted signal components analogically show temperature-dependent detuning and can be observed between 750 nm and 900 nm. The levels of the parametric components shown in Fig. 10(b) is very small at about −50 dB below the pump laser wavelength, which is consistent with experimental results reported in [25]. It has been shown numerically, that seeding with a weak continuous wave signal at the signal parametric wavelength (here the blue-shifted components at about 750-1000 nm) could improve this ratio [22]. In our simulations this was not taken into account, as we used a scalar (single mode) GNLSE model. These changes of wavelength detuning are in agreement with the four-wave mixing phase-matching profiles calculated for each of the investigated temperature-depended dispersion profiles presented in Fig. 10(c), according to the formula [26]:
where κ is the phase mismatch, γ stands for fiber nonlinear coefficient, P0 is the peak power of the laser pump pulse, fR is the Raman contribution to the Kerr nonlinearity characteristic for the fiber glass, ω is the detuning frequency and βi are the even dispersion terms (β2 through β8 were taken into account in this work).Fig. 10 Influence of temperature on parametric conversion properties of nonlinear fibers: assumed pump wavelength of 1350 nm (vertical dashed line) against measured dispersion profiles of NL24C4 fiber (a), numerical simulations of parametric conversion under pumping with 50 ps pulses (b), corresponding calculated phase-matching profiles (c).
At lower temperatures it also can be noticed that the phase matching profile changes in the studied fiber for a limited range of pump laser wavelengths. In particular, the phase matching profiles calculated for dispersions measured at 20°C and at 220°C differ mainly between 1325 nm and 1450 nm pump wavelengths. On the other hand, the phase matching profile for the 420°C dispersion indicates a more detuned red-shifted parametric wavelength, compared to the two lower temperature results, across all investigated pump laser wavelengths from 1300 nm. We note that the NL24C4 fiber was not designed particularly for parametric conversion experiments. Despite this, the obtained results demonstrate potential importance of the temperature-induced dispersion profile changes for practical parametric converter fibers based on soft glasses. In real experimental conditions, a soft glass fiber temperature can be expected to increase with pump power, especially in nonlinear fibers designed for parametric conversion, which typically should have large air-fill fraction and thus high thermal isolation of the core [25]. The change of parametric detuning, related to temperature-induced dispersion changes, shown in our results, can be detrimental, if it leads to shifting of the parametric wavelength over an attenuation band in the fiber. Such attenuation bands can include e.g. O-H absorption at about 3 µm (i.e. tellurite or other heavy metal oxide glass fibers) or S-H absorption at about 4 µm in chalcogenide glass fibers [25].
7. Conclusion
We have experimentally verified influence of temperature change in the in the range of 20°C – 420°C on dispersion characteristics of fused silica and heavy metal oxide glass nonlinear photonic crystal fibers. The correctness of the measurement results was confirmed with linear simulations performed for the fused silica glass fiber. We have shown that ZDW thermal shift is + 0.020 nm/°C for fused silica fibers and + 0.045 nm/°C for the PCF made of lead-bismuth-gallate oxide soft glass. If we take into account the low absorption of fused silica glass, the obtained results show that influence of temperature can be neglected in case of nonlinear performance of PCFs based on fused silica, which was confirmed with numerical simulations based on GNLSE.
The temperature sensitivity coefficient for the soft glass fiber considered in this work was found to be only a factor of 2 higher, than in the silica glass fiber. Likewise, the variability of the supercontinuum spectra obtained under femtosecond pumping did not show any temperature-related pattern. This was even despite the fact that the pump wavelength was assumed such, that the ZDW of the fiber crossed from its blue-shifted side to red-shifted wavelengths at elevated temperatures. Spectra obtained in the soft glass fiber under picosecond pulses revealed noticeable differences in the location of modulation instability maxima, which motivated the final numerical experiment of parametric conversion. With the pump wavelength set a value of 1350 nm, that is to the blue-shifted side of all of the recorded, temperature-dependent dispersion profiles of the soft-glass fiber, a clear pattern of change in the detuned Stokes component was observed. This was explained by the change of the four-wave mixing phase-matching condition as the ZDW of the fiber moved further from the assumed pump pulse wavelength for increasing temperature. The total shift in the red-shifted parametric wavelength was 240 nm, from 2340 nm to 2580 nm over a 400°C temperature range from 20°C to 420°C. The observed property, although related to a relatively small rate of temperature response of the investigated fiber, is of significance in the designing of photonic crystal fibers made from soft glasses. It demonstrates, that the increasing of the fiber temperature by e.g. the increasing pump power, can change the fiber’s dispersive properties in such a way, that at the intended pump power levels, the output wavelength does not match the design wavelength due to temperature-induced change of the parametric phase-matching condition. Therefore, the temperature response of soft glass fibers intended for parametric conversion applications should be taken into account at the microstructure design stage.
Acknowledgments
This work was supported by the project TEAM/2012-9/1 operated within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Fund, Operational Program Innovative Economy 2007-2013 and by the National Science Centre in Poland, projects UMO-2012/06/M/ST2/00479 and UMO-2013/11/D/ST7/03156.
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