1 Introduction

Metal-coated silica fibers are widely used as robust waveguides and special optical sensors due to its augmented resistance to mechanical stresses, high temperatures, aggressive environments and other extreme conditions [1,2,3].

For example, the authors of the paper [2] used a metallized optical fiber for the development of a highly sensitive sensor of laser radiation power operating in a wide dynamic range. Unlike many other approaches, the application of such sensor made it possible both to avoid attenuation of radiation and to retain its beam quality. In this article, [2] authors proposed a possibility of optical loss measurement using the calorimetric method, which turned out to be more convenient and accurate for these measurements compared to conventional ones.

In the paper [3] it was proposed to measure the intensity profiles of laser radiation using the detector represented by a matrix of fibers coated with copper. The main advantage of this detector is that the preliminary attenuation of the measured high-power laser beam is not necessary. The estimated value of the maximum intensity that can be measured using such a technique is ~ 400 kW/cm2.

Many fiber sensors are based on the application of Fiber Bragg Gratings (FBG). There are several reports where the improvements of the sensitivity and increase of upper limits of an operation temperature were demonstrated for the sensors based on the optical fibers coated with metal [4,5,6]. Another advantage of a metal coating is the feasibility of embedding fiber sensors inside investigated metal objects [7].

Furthermore, the high heat resistance of metal-coated optical fibers makes it possible to use them for the development of compact high-power fiber laser sources without employing any bulky and complex cooling systems [8, 9]. The authors of the paper [8] reported about the fiber laser based on an Yb-doped active fiber coated with aluminum that yielded 405 W of continuous radiation power with 74% efficiency. Good thermal conductivity, as well as high-temperature degradation threshold of the aluminum coating allowed the application of only passive aluminum heatsink weighing just 100 g.

In the paper [9] the Yb-doped fiber amplifier based on a gold-coated fiber with 3.1 kW output power and 90% optical-to-optical efficiency was demonstrated. The diffraction-limited beam quality (M2 < 1.15), as well as the narrow spectral width of 12 GHz were obtained. The latter was achieved by the increase of the thresholds of both Stimulated Brillouin Scattering (SBS) and Multimode Instability (MMI) due to the high thermal stability of the gold coating what allowed the use of fibers with a shorter length and high concentration of Yb ions. In addition, due to the high thermal conductivity of gold the MMI effect was suppressed since the overheating of the active fiber was reduced leading to the diminishing of the temperature-induced difference between the refractive indices of the fiber core and silica cladding.

Also, it should be noted that the absorption and emission cross sections of active fibers are strongly temperature dependent [10]. As a rule, the emission cross section decreases with the increase of temperature resulting in the efficiency impairing of laser generators and amplifiers. Obviously, due to its good thermal conduction properties the metal-coated fibers facilitate maintaining the generation efficiency.

However, despite many advantages of metallized optical fibers, it is well known, that its optical losses are considerably higher compared to conventional polymer-coated fibers [11]. The level of losses highly depends on the radiation wavelength and the geometry of the metal-coated fibers. However, there is a lack of information in the literature concerning the spectral behavior of optical losses in different types of metal-coated fibers. Overall, despite the higher attenuation it is evident that metallized optical fibers can be better suited for some applications than polymer-coated fibers, especially as sensors. Therefore, during the development and optimization of certain devices based on optical fibers one should carefully compare characteristics of different coating materials.

Obviously, for different applications of metal-coated fibers different parameters (fiber geometry, source wavelength, etc.) should be addressed to obtain optimal level of optical losses. For example, fiber sensors usually benefit from high optical losses. In contrast, for the development of radiation sources high losses are completely intolerable. As follows, an accurate determination of attenuation coefficients of different fiber types at different wavelengths is necessary to optimize the performance of various devices and sensors based on metal-coated optical fibers.

It should be noted that the application of conventional methods for measurement of optical loss in metal-coated fibers have serious drawbacks. The most widely used technique for measuring transmission loss in optical fibers is a cutback method [12]. However, aforementioned method is destructive and provides accurate results only if a sufficient length of fiber is cut back (usually around 10 m and even more in case of low attenuation coefficients). In addition, the use of the cutback method relies heavily on the quality of fiber cleaves. That could be an issue with metal-coated fibers due to the fact that the silica cladding of the fiber becomes fragile after the removal of copper and carbon layers by means of etching and heat treatment. For this reason, it is difficult to obtain high-quality cleaves with good repeatability even for thin fibers.

The other frequently used method is OTDR (Optical Time-Domain Reflectometry) [12]. OTDR is usually used in fiber-optic links to locate spots with abnormally high optical loss. OTDR method allows one to measure accurately optical losses in fiber sections. However, like the case of the cutback method, it is necessary to use long fiber lengths. In addition, the investigated fiber section should be located away from connectors and fiber splices. As follows, conventional methods are not always convenient for attenuation measurements of metallized optical fibers, so an alternative approach is required.

In the current article, we have considerably expanded the application limits of the previously introduced method [2] by applying it to different fibers and laser sources with different radiation wavelengths and mode compositions. Thus, the goal of the article is the characterization of the optical radiation loss of metal-coated optical fibers by means of the calorimetric method.

2 Optical fibers with metal coating

For the conventional optical fibers with a polymer coating the main mechanisms of radiation attenuation in the visible and near-infrared wavelength ranges are: Rayleigh and Mie scattering, molecular absorption, weak absorption tail (WAT) and absorption by OH ions and other impurities. The cross-section of Rayleigh scattering is governed by the properties of the medium in which the radiation propagates, and is proportional to λ−4, where λ is the radiation wavelength. An optical loss spectrum for a polymer-coated fiber is well known [13]. Overall, at shorter wavelengths (< 0.8 μm) Rayleigh scattering and WAT contribute most to the attenuation, whereas multiphonon absorption and absorption on OH bands are dominant at longer wavelengths (> 1.6 μm).

Optical losses of metal-coated optical fibers are usually significantly higher compared to optical fibers with a polymer coating (about 3 dB/km at 1550 nm in metallized fibers [14] versus 0.18 dB/km at the same wavelength in ultralow loss SMF-28 fibers). The main reason for this difference is that in the process of cooling of a drawn-out fiber the mechanical stresses occur in its core due to the significant difference between linear thermal expansion coefficients of the silica claddings and the metal coating (βcopper ≈ 16.6 × 10− 6 K−1, βsilica ≈ 0.5 × 10–6 K−1), which can lead to the formation of microcracks and defects [14]. Random deformations of a fiber lead to the scattering of radiation and the coupling of the modes propagating inside its core into higher modes or cladding modes, which exhibit considerably greater losses.

It is well known that the polymer-coated optical fibers are designed for a long-term operation at temperatures up to 85 °C. At higher temperatures the external polymer coatings degrade and, as a consequence, the optical fibers can be damaged [15]. Therefore, for high-temperature applications it is recommended to use fibers with metal coatings. In the case of copper-coated optical fibers temperatures over 600 °C lead to the decrease of the fiber strength and the irreversible increase of optical losses associated with the formation of crystalline clusters at the silica–carbon interface, as well as the diffusion of copper ions into the silica cladding and core [14].

It should be noted that metal-coated fibers can suffer temperature-induced increase of optical losses even at temperatures much lower than 600 °C [16, 17]. First, microbending losses in metal-coated fibers start to increase when its temperature reaches ~ 200 °C [17]. Second, at temperatures over 250 °C some metal-coated fibers demonstrate an increase in the optical loss related to the OH groups [16]. In our case the maximum heating of the metal coating of the fibers was less than 10 °C, therefore, the dependence of losses on temperature can be neglected.

In this paper, we investigated several types of copper-coated silica fibers, which will be referred further as Type-A (thick multimode fiber), Type-B (thin multimode fiber), Type-C (thin single-mode fiber). Main parameters of these fibers are listed in Table 1, and its common structure is schematically shown in Fig. 1.

Table 1 The main parameters of the studied optical fibers with a copper coating
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Fig. 1
figure 1

Structure of a silica fiber coated with copper. 1—waveguiding core, 2 – silica cladding, 3—thin carbon layer, 4—copper coating

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The fused silica waveguiding core 1 is surrounded by the silica cladding 2 with a lower refractive index. An intermediate carbon layer 3 with the thickness of about 0.1 μm serves to improve the adhesion of the copper coating to the fiber. In addition, the carbon layer reduces the effect of the diffusion of copper into the silica cladding. It should be noted that the Type-C single-mode fiber did not have a carbon layer due to the technological features of the production of the specified fiber. This fact also helped us to estimate the influence of the carbon layer on optical losses.

3 Theoretical basis

In this article, we present a novel approach to accurate measurements of optical losses in metallized optical fibers, employing the temperature dependence of the electrical resistance of its metal coatings [2]. When laser radiation propagates through the core of an optical fiber the small part of it, which is directly proportional to the total optical power, is scattered. Subsequently, the scattered radiation is absorbed by the carbon and copper layers resulting in fiber heating. Besides, the absorption of laser radiation inside the fiber core also contributes to its heating. The electrical resistance of copper R linearly depends on temperature T:

$$ R(T) = R(T_{0} ) \cdot [1 + \gamma \cdot (T - T_{0} )] $$
(1)

Here γ ≈ 0.0039 К−1 is the coefficient of thermal resistance of copper, T0 is the initial temperature of the coating. Using this relation, the temperature of the fiber can be determined by measuring the electrical resistance of the copper coating.

The heating of metallized fibers can be described using the heat conduction equation taking into account the Newton law of cooling:

$$ cm\frac{dT}{{dt}} = hS(T_{0} - T)\alpha lP. $$
(2)

Here α is the optical loss coefficient; c, m, S are specific heat, mass and total surface area of the copper coating, respectively; P is the power of the radiation transmitted through the fiber under test, h is the heat transfer coefficient, l is the length of the fiber’s measured section (see Fig. 2). In this case, only the presence of the convective heat transfer is considered. The use of this approximation is justified by the small Biot numbers [18] of the fibers under test (Bi ≈ 10–5). Therefore, we can neglect the nonuniform temperature distribution inside the fiber. We also neglected thermal radiation losses due to a relatively low heating.

Fig. 2
figure 2

Block scheme of the experimental setup with an enlarged layout of the studied fiber (all dimensions are indicated in cm). CMS cladding mode stripper

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The solution of Eq. (2) is the exponential function:

$$ T(t) = T_{1} - (T_{1} - T_{0} ) \cdot \exp ( - \frac{hS}{{mc}}t). $$
(3)

Here T1 is the temperature of the metal coating in a state of thermodynamic equilibrium.

Upon reaching a thermal equilibrium state, the first term in Eq. (2) becomes equal to zero, and the optical loss coefficient is determined as follows:

$$ \alpha (\lambda ) = \frac{{hS(T_{1} (\lambda ) - T_{0} )}}{lP}, $$
(4)

4 Experimental setup

In our experiments, we have used several sources of visible and near-IR laser radiation with the most common wavelengths in laser optics. The main parameters of the laser radiation sources are presented in Table 2.

Table 2 Main parameters of the employed laser radiation sources
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A simplified block scheme of the experimental setup is shown in Fig. 2.

The laser sources had different radiation outputs and, therefore, required different coupling of the radiation into the fibers under test. The Yb, Yb/Er and Tm-doped lasers had single-mode fiber outputs. The blue laser diode had a pig-tailed multimode fiber output. Second harmonic radiation (SHG) from the Raman fiber laser was a collimated beam. Thin Type-B and Type-C fibers were coupled to the fiber laser outputs using an electric arc fusion splicing. However, due to the different diameters of the waveguiding cores of the studied fibers, it was impossible to couple laser radiation into all the studied fibers using a fusion splicing joint. For this reason, when working with Type-A fiber, the laser radiation was focused into its core using a fused silica lens. The waist diameter at the end of the input fiber was about 200–350 µm, depending on the laser source. The estimated value of the radiation insertion loss into the Type-A fiber was less than 10%. In the case of a fusion splicing, the area around the joint was surrounded by a polymer with a refractive index higher than that of a fused silica. This polymer was used to eliminate cladding modes arising due to splicing of the fibers with different mode field diameters (MFD). Since dissimilar fibers were spliced, the splicing losses turned out to be relatively high (about 5% or 0.25 dB).

The length of the studied fiber sections was about 40 cm (see Fig. 2). The copper coating was etched from the initial segment of the test fibers (about 5 cm) to facilitate the input of radiation. Copper etching was performed using the solution of a ferric chloride (FeCl3). The intermediate carbon layer was removed from the fiber surface with the flame of the gas-burner. As it was already mentioned, the imperfect coupling of laser radiation into the fiber under test could lead to the excitation of the cladding modes in that fiber. It is well known that these modes have significantly higher loss coefficients compared to the core modes. To eliminate the influence of the cladding modes on the measurement process, a 15 cm long copper coating was left after the etched segment of the fiber. Here the cladding modes decayed due to the extremely high loss of radiation interacting with carbon and copper. In other words, this fiber segment served as a cladding mode stripper (CMS). The CMS segment was followed by another section with an etched coating (10 cm), which was supposed to prevent the heat transfer from the CMS to the measurement section, since the thermal conductivity of a fused silica is much lower than that one of a copper. The length of the measured section was chosen in accordance with the ohmmeter sensitivity to provide the best accuracy, especially when measuring low optical loss coefficients. The coating at the outlet of the tested fibers was also etched, for a convenient fiber end face cleaving. Two copper wires with diameters of 200 μm were soldered to the surface of the copper coating and served as the ohmmeter electrodes. Such a small diameter of the wire was specifically chosen to make the heat transfer from the copper coating of the fiber through the electrodes negligibly small. At the same time, thin fibers have very high convective heat transfer coefficients due to the large ratio of surface area to volume, so the contribution of the thermal conductivity of contact wires was negligible in comparison to convective cooling. Besides, any dependence of the experimental results on the lengths of the measured sections was not observed, what means that these wires didn’t have a notable impact on the heat sink. Before measurements, the investigated fiber section was straightened to exclude macrobending losses, and was fixed in the air using two holders with poor heat conductivity. Thus, the heat transfer from the fiber was considered to be purely convective. The temperature of the environment was controlled by means of a thermal controller, but was not rigorously stabilized, so the temperature fluctuations were about 0,1 К during the experiment.

Preliminary experiments were carried out in order to determine the CMS-section length that was sufficient for the complete attenuation of the cladding modes. It was revealed that 15 cm long CMS-section is sufficient for an almost complete attenuation of the cladding modes.

5 Determination of optical losses

The first step for the determination of the optical loss was to measure the heating kinetics of the fiber under test when the laser radiation of the given power and wavelength passed through it. Figure 3 shows the temperature kinetics measured for the Type-B fiber for the case of 7 W of transmitting radiation power at 1550 nm wavelength. The black curve corresponds to the measured kinetics of the electrical resistance/temperature of the metal coating of the optical fiber heated by laser radiation. The red curve corresponds to the approximation of the measured dependence using the Eq. (3).

Fig. 3
figure 3

Heating kinetics of the Type-B fiber during the transmission of 7 W radiation at 1550 nm wavelength

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For all fibers and laser radiation wavelengths the linear dependencies of coating temperature measured after reaching stationary state on transmitted optical power were observed. These dependencies measured for the Type-A, Type-B, and Type-C fibers are shown in Figs. 4, 5 and 6, respectively. The power stability of each radiation source was investigated before conducting the measurements. The instability did not exceed 1.5% in terms of standard deviation. The main contributor to the data error shown in Fig. 4 is the determination accuracy of the electrical resistance of copper coatings limited by the ohmmeter sensitivity: ± (7 least significant digits + 0.03%) i.e. about 7 μOhm in the used measurement range.

Fig. 4
figure 4

Dependencies of the copper coating temperature of the Type-A fiber on the transmitted optical power at different wavelengths

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Fig. 5
figure 5

Dependencies of the copper coating temperature of the Type-B fiber on the transmitted optical power at different wavelengths

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Fig. 6
figure 6

Dependencies of the copper coating temperature of the Type-C fiber on the transmitted optical power at different wavelengths

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Since the convective heat transfer increases with temperature, this can lead to the deviations from the linearity at higher optical power. However, in general, these graphs can be considered linear within the margin of the estimated error. The thermo-optical coefficients k that represents the linear slopes of the measured dependencies of the coating temperature on transmitted optical power are presented in Table 3.

Table 3 Thermo-optical coefficients k values
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Via an approximation of the measured kinetics of fibers heating using the function (3), it is possible to determine the convective heat transfer coefficients h. The obtained values are listed in Table 4.

Table 4 Heat transfer coefficients h
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As mentioned above, the errors were determined mainly by the sensitivity of the ohmmeter: the relative error increased with the thickness of the copper cladding as its electrical resistance became lower. Also, the errors were noticeably influenced by temperature fluctuations of the external environment, especially in the case of low optical loss coefficients as the fiber heating was relatively small. Therefore, the errors were calculated individually for each point.

The theoretical values of the heat transfer coefficients were obtained using the Churchill-Chu equation for a long horizontally oriented cylinder [18]:

$$ h = \frac{k}{D}\left[ {0.6 + \frac{{0.387 \cdot R_{{a_{D} }}^{1/6} }}{{(1 + (0.559/\Pr )^{9/16} )^{8/27} }}} \right] $$
(5)

Here κ is the thermal conductivity of air, D is the fiber diameter, RaD is the Rayleigh number, Pr is the Prandtl number. The experimentally measured coefficients h and calculated ones coincide within the margin of error.

The optical loss coefficients α were obtained using Eq. (4). The spectral dependencies of the optical loss measured for the Type-A, Type-B, and Type-C fibers are shown in Figs. 7, 8 and 9, respectively.

Fig. 7
figure 7

Spectral dependence of optical loss of the Type-A fiber (semi-logarithmic scale)

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Fig. 8
figure 8

Spectral dependence of optical loss of the Type-B fiber (semi-logarithmic scale)

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Fig. 9
figure 9

Spectral dependence of optical loss of the Type-C fiber (semi-logarithmic scale)

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The spectral dependencies of the optical loss for all three tested types of fibers are shown in Fig. 10.

Fig. 10
figure 10

Spectral dependence of optical loss for the three fibers under test (semi-logarithmic scale)

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Optical losses of the Type-C fiber were measured only at three wavelengths. The output fiber of the blue laser diode was multimode and had a much higher numerical aperture compared to the Type-C fiber. So, it was impossible to couple the radiation from this source into the single-mode Type-C fiber due to the destruction of the fusion splicing joint between the fibers. Measurements at 589 nm wavelength were not performed, since it was not possible to adequately focus the collimated radiation into the single-mode Type-C fiber core. Therefore, these data points are not shown in Figs. 9 and 10.

Obtained values of the optical loss coefficients are presented in Table 5. Statistical measurement errors of the optical loss coefficients are associated with the fluctuations of the environment conditions during the experiments. Error associated with the measurement of h is also included in the final error for optical loss coefficients.

Table 5 Values of the optical loss coefficients of the investigated fibers
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The dashed curves in Figs. 7, 8, 9, 10 show the characteristic dependencies of the optical loss on the wavelength that are in a good agreement with the empirical approximation (6) for Type-A and Type-B fibers (Type-C fiber has insufficient experimental data for such approximation):

$$ \alpha (\lambda ) = E + F \cdot \exp (G \cdot \lambda ) + \frac{H}{{\lambda^{4} }} $$
(6)

Here E, F, G and H are the constants determined as a result of the fitting of the obtained data. The first term describes the intrinsic wavelength-independent optical losses. The second term describes the microbending losses in single-mode fiber, as well as the increase of losses in the long-wavelength region due to absorption by molecular hydrogen and OH groups in MM fibers. The third term describes optical losses associated with Rayleigh scattering. These fits are purely qualitative, the precise details of the loss spectra, such as absorption peaks associated with the presence of the molecular hydrogen (H2) or hydroxyl groups (OH), are not taken into account. More details can be found in the Discussion section.

To compare the proposed method with the conventional one, as well as to determine the finer structure of the optical loss spectrum, we implemented the cutback method at least for a single-mode Type-C fiber. The schematic of the experiment is shown in Fig. 11. The supercontinuum single-mode pulsed fiber laser operating in the 600–1800 nm wavelength range was used as a broadband laser source. The core diameter of the output single-mode fiber was 2.5 μm. The output optical power of 25 mW was low enough not to cause considerable fiber heating. The spectrum analyzer Yokogawa AQ3670C with a single-mode input (9/125 µm) operating in the 600–1700 nm range was used as an optical detector.

Fig. 11
figure 11

Experimental setup for cutback measurements

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Since the optical losses of the investigated fiber were small enough, to avoid the influence of losses on splices of fibers with different MFD the SMF-28 fibers with a polymer cladding were preliminary connected to the laser output and the spectrum analyzer input. Its silica core was identical to the core of the Type-C copper-coated fiber. The length of these sections was chosen to be sufficient (> 50 cm) for establishing the stable distribution of radiation in the fiber cross section. Sections of the investigated Type-C fiber with different lengths were spliced to these fibers and the spectrum of the transmitted radiation was measured. Since the optical loss coefficient was very small, the maximum fiber length was 500 m, so the fiber was wound on a spool with a diameter of 15 cm. This winding has led to the additional bending losses, however, since the bending diameter was large, the distortions of the results were considered negligible for the fundamental mode. Comparing to the results obtained in the work [2], we can roughly estimate the additional bending loss of the fundamental mode to be less than 0.1 dB/km.

Knowing the difference between the measured spectra for different lengths of the fiber under study, the optical loss spectrum was obtained (see Fig. 12). It can be seen, that below 1.3 µm (the cutoff wavelength for the Type-C fiber), there is a lot of noise since the fiber is no longer single-mode at these wavelengths. Therefore, the mode interference leads to the fluctuations of the transmitted optical radiation power.

Fig. 12
figure 12

Spectral dependence of optical loss of the Type-C fiber measured by cutback method (blue) and calorimetric method (red)

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We also separately measured the optical loss at the wavelength of the thulium-doped laser radiation (1940 nm), since the spectrum analyzer can’t be used in this range. The experimental scheme was identical to the previous one with the exceptions that the thulium superluminescent source with 60 mW power operating at 1940 nm wavelength was taken as the radiation source and the optical power meter was used as detector. The optical losses coefficient was measured to be 55 dB/km, which is in a qualitative agreement with the results obtained using the proposed calorimetric method. The largest discrepancy observed at 1070 nm wavelength is attributed to the radiation transfer from the fundamental mode to higher-order modes that have much higher bending losses due to the winding. It can also be assumed that at such long fiber lengths there may be some local defects or irregularities, which can lead to increased losses. The benefit of measurements on short sections is that there are no such disadvantages.

6 Discussion

It is well known that the preform manufacturing and fiber drawing processes may lead to contamination of produced fibers with hydrogen and OH groups [19]. During the manufacturing process, the fiber is saturated with molecular hydrogen directly from a hydrogen burner, as well as from ambient air due to the high temperature of the fiber. It is known that molecular hydrogen continues to penetrate into the fiber until reaching the equilibrium concentration with the hydrogen outside the fiber. For this reason, when the fiber is removed from the medium with a high concentration of molecular hydrogen it starts to leave the fiber [20]. For a long-term protection of the fiber from H2 penetration, a sealed carbon coating is usually used. In the paper [21] it was demonstrated that at temperatures below 150 °C the molecular hydrogen cannot leak through the carbon layer. In addition, in [21] it was revealed that at room temperature and 1 atm of H2 pressure a carbon coating is 6 orders of magnitude more effective in blocking molecular hydrogen than a copper coating. The inefficiency of the barrier properties of copper coatings against molecular hydrogen was also emphasized in the paper [22].

Comparing the losses of three investigated fiber types (see Fig. 10) we can deduce that the lowest optical loss coefficients were obtained for the Type-C single-mode fiber. This can be explained by the absence of a carbon layer that made it possible for the molecular hydrogen to leave the fiber after it was removed from the hydrogen-saturated atmosphere. However, due to the influence of high temperatures during the fiber production the molecular hydrogen can react with the fused silica or dopants thus creating stable molecular bonds that induce irreversible optical loss [20]. The reason for the higher losses of multimode fibers is the presence of carbon layers under copper coatings that prevent the residual molecular hydrogen from leaving the fibers. As it can be seen from the Fig. 12 the Type-C fiber actually has a small loss peak at 1.24 μm, associated with the hydrogen absorption [20]. However, it gives small contribution to the total loss that is consistent with the assumption that there is a very little amount of the residual hydrogen in fibers without a carbon layer.

Fiber geometry also plays an important role. Comparing two types of the investigated multimode fibers we can see that the thin multimode fiber (Type-B) exhibits higher losses. The optical losses conditioned by hydrogen and hydroxyl groups do not have an explicit dependence on the fiber geometry. However, it is known that microbending optical losses of metallized optical fibers decrease with the diameter of a silica cladding and increase with the thickness of a metal coating [23]. A smaller thickness of a metal coating corresponds to a lower level of mechanical stress, which is caused by the difference of the thermal expansion coefficients of copper and fused silica, and as follows to lower microbending loss. For the convenience, we introduce the characteristic parameter ζ = hcop/ dsil, where hcop is the thickness of a copper coating, dsil is the diameter of a silica cladding. Comparing the studied multimode fibers using the parameter ζ (ζType-A = 0.18, ζType-B = 0.28) we can see that it is higher for the Type-B fiber. Also, it is known, that microbending losses decrease with the numerical aperture of the fiber [24]. The imperfection of the metal cladding of the optical fiber, e.g. inhomogeneity of the coating thickness along the length, can also take place. This can be the cause of the relatively high discrepancy of the results obtained for different investigated segments. By measuring long fiber segments using conventional methods, we obtain only a length-averaged optical loss coefficient. The advantage of our method is that it allows one to measure the exact value of optical loss in short sections, which has less fluctuations.

The behavior of the spectral dependencies of optical losses in the region of short wavelengths can be explained by the fact that for λ < 1 μm the radiation experiences Rayleigh scattering proportional to λ−4. However, there is another reason for the increasing of losses in the short wavelength region. If the waveguiding core of the fiber is doped with GeO2 to increase its refractive index, then the molecular hydrogen could interact with these ligands at high temperatures during fiber drawing leading to the rise of absorption in the wavelength region below 1 μm [20]. However, it was not possible to observe this effect since only Type-C fiber had germanium-doped core, for which measurements at short wavelengths were not carried out. Type-A and Type-B fibers had pure silica cores with the outer cladding doped with fluorine.

In the long-wavelength region, the loss mechanisms for single-mode and multimode fibers are different. As it is known, single-mode fibers are characterized by a strong power-law dependence of microbending losses on the wavelength [25, 26]. Therefore, the main contribution to the losses in the long-wavelength region for single-mode fibers is made by microbending losses. In contrast, microbending losses of multimode fibers are independent of wavelength [27]. Therefore, losses in the long-wavelength region (λ > 1.7 μm) are mainly conditioned by the presence of the molecular hydrogen in multimode fibers. As it was reported in a number of papers [19, 20, 28] the losses associated with absorption by molecular hydrogen increase very rapidly with the wavelength for λ > 1.5 μm. Besides, for both single-mode and multimode fibers the tails of the absorption peaks of OH groups at 1.39 and 1.41 μm can lead to an increase of losses in the region from 1.45 to 1.7 μm [20].

The common property of all investigated fibers is that minimal optical losses were observed near the wavelength λ = 1 μm. Measurements that were conducted using the cutback method confirmed this assumption, although the values of measured optical losses were higher than that measured by the proposed method. Among other reasons, this region corresponds to the minimum losses conditioned by the molecular hydrogen [22]. In addition, it should be noted that in the vicinity of 1910 nm wavelength the absorption due to molecular vibrations in fused silica begins to play the main role and the losses become significantly higher.

Comparing the loss spectra of multimode metal-coated and an SWU (Low-OH) specialty fiber preform (see Fig. 13) we can notice that the minimal optical losses in it are observed near 1 μm and 1.55 μm wavelengths, respectively. It should be noted, that the spectral dependence of metal-coated fiber on the graph is a characteristic approximation and does not display narrow absorption peaks due to OH and other molecular groups. The magnitude of losses at 1 μm and below is almost the same for multimode metal- and polymer-coated fibers. But at longer wavelengths, optical losses in metallized fibers increase dramatically compared to common fibers. Optical losses of polymer-coated fibers at longer wavelengths [13] (~ 1.8 μm) are approximately 5 dB/km. In turn, the loss approximation for the metal-coated Type-A and Type-B fibers gives loss values of ~ 200 dB/km and ~ 370 dB/km, respectively, and almost 25 dB/km for the Type-C fiber. Therefore, we can assert that the contribution of the molecular absorption in metallized fibers in the wavelength range from 1.5 to 1.91 μm is negligibly small. So that in this region the losses are mainly associated with the microbending for single-mode fibers and the contamination with molecular hydrogen and hydroxyl groups for the multi-mode fibers.

Fig. 13
figure 13

Optical loss spectra of the Type-B fiber (black dots and dashed curve) and a SWU specialty fiber preform [13] (solid curve)

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It was verified that by measuring the electric resistance change of the metal coating of fibers in our configuration of the experimental setup it was possible to detect the temperature change of at least 0.05 °C that is equivalent to the optical loss of approximately 0.1 dB/km. In practice, the lowest limit of losses that can be measured is associated with the sensitivity of the ohmmeter used and the instabilities of an environment condition. It is worth noting that the introduced approach has a significant advantage over the cutback method conventionally used for measurements of optical losses [12]. Employing the proposed technique, it is possible to measure optical losses using the fiber sections of several cm long without sacrificing measurement accuracy.

7 Conclusion

We have demonstrated a novel method for measurements of optical losses of different types of fibers with metal coatings at different laser radiation wavelengths. The optical losses of single-mode and multimode copper-coated fibers were determined by measuring the temperature-induced change of the electrical resistance of its metal coatings. It was discovered that the optical loss spectra were highly dependent on a fiber type. This dissimilarity occurs due to the domination of different loss mechanisms for different fibers and laser wavelengths. Losses at the long-wavelength range (λ > 1.5 μm) for the multimode fibers were attributed to the absorption on the tails of the absorption peaks of the hydrogen molecules and hydroxyl groups. In the case of the single-mode fibers the microbending losses made a dominant contribution to the optical loss in this wavelength range. In the region of short wavelengths all metallized fibers demonstrated roughly the same spectral loss behavior associated with Rayleigh scattering and absorption on the compounds of hydrogen with intrinsic molecular groups.

The presented method is primarily applicable for the accurate determination of the optical loss factors for specific laser sources operating at certain wavelengths. Loss spectrum data alone are not always sufficient, since in real applications the optical losses not only depend on the wavelength but, as well, on the parameters of the employed laser sources (such as mode composition or beam divergence) and on the way of radiation coupling into the particular fiber.

The main advantage of the presented method is the possibility of its application for the correct measurements of low radiation losses using relatively short fiber sections, which are independent of macrobending losses. We have conducted measurements for the most commonly used laser sources in visible in near-IR wavelength range. Introduced results can help to select appropriate types of metalized fibers and laser source for optimization of different applications. For example, in the case of fiber sensors that benefit from high optical losses the thin multimode fibers operating at wavelengths λ ≥ 1.5 μm can be used. In turn, for the development of radiation sources based on active metal-coated fibers operational wavelength range near 1 μm and single-mode fibers with low coating thickness are preferable.