1. Introduction

High-power femtosecond (fs) laser has become a recognized tool for high-precision micromachining of different materials, including transparent ones — amorphous glasses, crystals and polymers. A wide range of devices that can be created by this technology: elements of integrated photonics and fiber optics [1], lab-on-a-chip [2] and lab-in-fiber [3] structures. The mechanism of femtosecond pulse absorption in a volume of transparent material, which is of a non-linear nature [4], allows one to precisely localize the region of modification in volume and achieve a resolution down to 1 μm³ and below [5]. This feature is widely used for direct inscription of point-by-point fiber Bragg gratings (FBGs) in single-mode optical fibers [6]. As compared to interferometric techniques of inscription [7], femtosecond point-by-point technology has a higher degree of flexibility, allowing variation of FBG parameters in a wide range, including length, period, and overlap integral between the fiber mode field and FBG’s transverse cross-section [8].

Optical fiber sensors are promising for various industrial and health-care applications that benefit from advantages providing by fiber optics, such as compactness, mechanical flexibility, insensitivity to electromagnetic interference, and temperature, radiation and chemical resistance. One of such applications is a 3D shape reconstruction using FBG based multicore fiber (MCF) sensors [9–14]. To recover fiber shape from the shifts of FBG reflection peaks with enough spatial resolution continuous or nearly continuous sensing is often required. This, in turn, requires reliable and stable method of FBG inscription to ensure reproducibility during a meters-long sensor fabrication, while it should be flexible enough for operating exactly on a selected core. This becomes even more critical for a twisted (or spun) MCF, which can be used as a free-standing fiber sensor when the applied local twist cannot be neglected. Besides shape sensing, MCF with straight and twisted cores commonly serve as different optic sensors, which measure mechanical impact: bending, twist, and rotation [15]. In comparison with the sensing solutions based on single-core fibers [16], multicore fiber sensors are more compact and flexible that is important for micro-robotics, particularly for minimally invasive surgical manipulations [17].

For these reasons, the inscription of FBGs in multicore fibers is the subject of research in the last decade. The first results on FBG inscription in MCF were achieved using UV radiation: the holographic [18] and the phase mask writing techniques [19]. In these cases, due to the impact of radiation on all the cores simultaneously, FBGs were inscribed in all the cores with the same wavelength. However, many tasks require the FBG inscription in an individual core of MCF, for which two approaches were proposed. The first one is based on the use of special multicore fiber with the cores having different diameters or the effective refractive index; however, the spacing between FBG peaks associated with different cores is not controllable in the inscription process [20,21]. The second one is based on the phase mask inscription method and careful adjustment both the width of the laser beam and the spatial distance between the optical fiber and the phase mask [22]. This approach, combined with the need to replace the mask to inscribe FBGs with different wavelengths, makes the method very complicated for the inscription of FBG arrays in individual core of MCF. As mentioned above, the fs laser micromachining technology enables tight localizing the refractive index modification area in the glass volume and, accordingly, the inscription of FBGs in the selected cores of MCF [23,24]. When using the point-by-point writing method, the period of FBG is set by setting the fiber translation speed, which makes the method very attractive for FBG arrays inscription in selected cores of MCF.

In this paper, we report on the inscription of point-by-point FBG arrays in spun optical fiber by femtosecond IR laser pulses. In particular, we show that the FBGs arrays can be inscribed in transverse and longitudinal directions of a fiber through the acrylate protective coating that is essential for sensing applications, in which the fiber suffers from a mechanical impact. Fabrication of individual FBGs and FBG arrays in multicore spun fiber is of great importance for different research areas where this fiber can be applied: 3D shape sensing [9–14], structural health monitoring, and microwave signal processing [22]. The advantage of this type of fiber, in comparison with fibers with straight cores, for 3D shape sensing is the ability to measure not only the bending deformation of the fiber, but also the twist with the determination of the twist direction [25].

2. Experimental setup

When point-by-point FBGs are inscribed by fs laser pulses, one of the most productive and flexible methods is drawing a coated optical fiber through a channel of transparent ferrule with polished side faces [26]. For this method of inscription, the laser beam is focused in the region of the optical fiber inserted into the ferrule channel, and the linear translation stage draws the fiber with required velocity, as shown in Fig. 1. The choice of the necessary ratio between the frequency of laser pulses ν and the velocity of fiber v_trans makes it possible to select the FBG period Λ = v_trans/f. Moving the ferrule/fiber in the transverse to the fiber axis plane (XY) allows one to set the point of refractive index modification. The method does not require removal of the fiber protective coating and can be adapted for different fiber diameters.

 

Fig. 1 Focusing of fs laser pulses during point-by-point FBGs inscription by drawing a coated optical fiber through a channel of transparent ferrule.

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In this work, we used Light Conversion Pharos 6W (λ = 1030 nm, t_р = 232 fs) as the source of fs laser pulses. For all experiments, the frequency of fs pulses was constant and set to f = 1 kHz. The focusing of fs pulses was performed using a Mitutoyo 50X Plan Apo NIR HR objective (NA = 0.65). A ferrule with side faces at an angle of 90 degrees was attached to a 3-axis mechanical linear stage (Thorlabs MAX313D) and a monitoring system consisting of two CMOS cameras allowed us accurately set the point of refractive index modification in transverse plane of optical fiber [8]. The inner diameter of the used ferrule was 200 µm, and the outer (before polishing) was 3 mm. We used glycerin as an immersion liquid, since it is well retained in the capillary thanks to the relatively high viscosity. The procedure for setting the modification area inside the multicore fiber was as follows. First, we brought the ferrule/fiber to the estimated focal point, and then released several fs pulses, which led to the modification of the refractive index inside the fiber. After that, using the CMOS cameras, we corrected the spatial position of the ferrule/fiber. This procedure allowed us to set the exact position of the modification region in the XY plane. Translation of an optical fiber relative to the fs beam focal point was performed by a high-precision air-bearing translation stage Aerotech ABL1000, having resolution of 0.5 nm, accuracy of ± 0.2 µm, and repeatability of ± 50 nm. Position synchronized output feature, which is integrated in the translation stage controller, allows user to change the state of the fs laser pulse picker in the required coordinates along the fiber axis (Z).

For the experiments on FBGs inscription, we opted for commercially available 7-core spun fiber Fibercore SSM-7C1500(6.1/125) which has straight central core and 6 twisted side cores positioned in the vertices of regular hexagon and making helical turn at the length of L_p = 15.4 mm. All the cores operate in single-mode regime and have mode field diameter (MFD) of 6.3 μm at the wavelength of 1550 nm (see Table 1 for more fiber parameters). When modifying the fiber, the fs laser pulses were focused through a protective acrylate coating, whose thickness is about 30 μm, which made it possible to avoid direct mechanical effect on the material of the fiber during further testing of inscribed FBGs. The focal point of fs laser pulses varied depending on the cores in which the inscription took place. When modifying the central core, the focus of the objective was placed in the center of the fiber. When modifying side cores, the focus was placed on the surface of the cylinder, on which the cores lay on.

Table 1. Specification of 7-core spun fiber SSM-7C1500(6.1/125) manufactured by Fibercore

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To work with FBG arrays in a 7-core spun fiber we assembled the scheme shown in Fig. 2, which enables independent measurement of the reflection and transmission spectra for each individual fiber core. The signal from the broadband light source, Thorlabs SLD1550S-A2 superluminescent diode (SLD), came to the input of a fiber-optic circulator and then, through a FC/APC connection, directed to the input of a specialized Fibercore FAN-7C fan-out, compatible with the used fiber. The selection of the fan-out input channel allowed us to send a signal to the desired core of the fiber. The signal reflected from the FBG (array) was measured using Yokogawa AQ6370D optical spectrum analyzer (OSA). To suppress the level of back reflection, the far end of the 7-core optical fiber was polished at an angle of 7 degrees.

 

Fig. 2 Fiber-optic scheme for interrogation of individual cores of a 7-core spun fiber.

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3. Considerations and estimations

For a better understanding of the further results, as well as the geometry of the inscribed FBGs, it is useful to make some preliminary estimations. So, let us consider the process of inscription of single FBG in the selected side core of 7-core spun fiber. Suppose the focal point of the fs laser beam lies on the surface of the cylinder, on which the side cores lie on (Fig. 3(a)). Next, by irradiating fiber by fs laser pulses and by moving it in the longitudinal direction, an FBG track is inscribed in the region of a side core. When the FBG track crosses the core, the phase-matching condition is satisfied for the core modes propagating in forward and backward directions, resulting in optical signal reflection at Bragg wavelength.

 

Fig. 3 (a) Schematic representation of single FBG inscribed in the side core of a 7-core spun fiber. (b) The cylindrical surface of the FBG-containing section of the fiber put on the plane.

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Now, take the section of a fiber with length L_p/6 = 15.4/6 = 2.567 mm. At this length, each of the side cores turns by 60° and moves along an arc at a distance of P_c/6 = 2πR/6 = 36.65 μm in the XY plane, as shown in Fig. 3(a). By unfolding the cylindrical surface and putting it on a plane where the core and FBG track lie on, the FBG inscription problem can be reduced to a two-dimensional case. Thus, we can build a right triangle, which legs are the above distances L_p/6 and P_c/6, and the hypotenuse is the optical axis of the side core (Fig. 3(b)). Since the FBG track crosses the side core at an angle α = arctan(P_c/L_p) ≈0.8°, the inscribed FBG will have a variable coupling coefficient along the optical axis. With a linear rate of rotation of the side core around the Z axis, the FBG structure will have a longitudinal coupling coefficient apodized by Gaussian function. For straight single-mode optical fibers, a similar inscription mode was implemented in [27], where apodization was achieved due to transverse motion of the fiber during point-by-point FBG inscription by fs laser pulses. Knowing the value of mode field diameter of the fiber core (MFD = 6.3 μm), one can estimate the length of the region where the mode field interacts with the inscribed FBG structure. If we assume that the interaction is realized only within the MFD, when E > E₀/e, we can obtain a lower estimate of the FBG length L_FBG,low = MFD/sin(α) = 441 µm. In fact, the interaction of the FBG with the mode field extends at a greater distance than the MFD. So, assuming that the mode field interacts with the FBG structure within the field level E > E₀/e², one can obtain an upper estimate of the FBG length L_FBG,up = 622 µm.

In general case, multiple fiber cores can be modified in a single-pass inscription procedure. Indeed, at the length of full turn of the side core L_p = 15.4 mm, the FBG track will alternately modify each of the side cores. Moreover, by controlling the speed of the fiber movement, as well as the state of the fs laser pulse picker, the period and the resonant wavelength can be set for each individual core, as shown in Fig. 4. Holding the laser pulse picker in the “closed” state allows one to “skip” the cores in which inscription is not required. Further, it will be shown that the described technique allows one to create FBG arrays with different spatial structure inside a 7-core optical fiber.

 

Fig. 4 The state diagram of the fs laser pulse picker and the velocity profile of the fiber when longitudinal FBG array is inscribed in side cores of 7-core spun fiber. v₁… v₆ denote different velocities defining the periods of the FBG structures Λ₁… Λ₆.

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4. Fiber Bragg gratings inscription

4.1 Single-pass inscription of FBG arrays with length L_p = 15.4 mm at a constant and variable speed

In our case, we choose for FBG inscription the 2nd-order Bragg resonance, at which the period of the structure is Λ ≈1.07 μm for the resonant wavelength λ ≈1550 nm. As a first step, the laser pulse energy was set to E_p = 200 nJ and a test FBG track was inscribed. Next, the FBG-containing fiber section was cleaved at a right angle and its end face was captured with an optical microscope. From the microphotograph provided in Fig. 5, it is seen that the modification region is positioned exactly on the line of rotation of the side cores. The modification area itself has the shape of an ellipse with a height of h = 13 μm and a width of w = 1 μm. Its longitudinal inhomogeneity, namely the more contrast central region, may be associated with the occurrence of a microvoid inside the less contrast surrounding region [28].

 

Fig. 5 Cleavage of the 7-core spun optical fiber made in the FBG-containing section.

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In order to test the repeatability of the inscription in different cores, we fabricated a sample of longitudinal FBG array with length L_p, which corresponds to a full turn of the side cores thus providing sequential inscription of a periodic Bragg structures in them. The focal point of fs pulses was in a fixed position, the structure period remained constant and was equal to Λ = 1.07 μm yielding the resonant wavelength λ ≈1552.4 nm. For the fabricated sample, the reflection spectra (Fig. 6(a)) were measured using the scheme shown in Fig. 2. As can be seen from the spectra, the reflection coefficient ranges from −3.7 to −1.1 dB (43–78%), the central wavelength is 1552.05–1552.8 nm, the FWHM is 2.2–2.95 nm, the side lobe suppression ratio (SLSR) is 12.8–14.9 dB. The difference in the measured parameters may be attributed to the imperfect geometry of the fiber, namely, the error in cores positioning, the error in positioning of the fs modification area in depth, as well as the difference in power of the optical signals coupled to the cores, which is associated with a small loss variation for each measuring channel at the fan-out. The absence of reflection signal in the central core (4) indicates the selectivity of the FBG inscription and negligible cross-coupling with other FBG-containing cores. The transmission spectrum measured for the FBG in the side core 1 (Fig. 6(b)) shows that near the Bragg resonance the loss levels differ in the short- and long- wavelength regions. It is known that the short-wavelength losses arise due to the occurrence of a coupling between the core and the cladding modes of a fiber, while the long-wavelength losses are due to the diffractive scattering [29].

 

Fig. 6 (a) Reflection spectra of the longitudinal FBG array with fixed period Λ = 1.07 μm inscribed in different cores of the 7-core spun optical fiber in the single-pass procedure. (b) Transmission spectrum measured for FBG inscribed in core 1.

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In the next experiment, a longitudinal FBG array was inscribed in the side cores, but different resonant wavelengths were set for individual FBGs. To do this, after inscribing an FBG, the speed of the drawing had been changed, as shown in Fig. 4. The period of the first FBG was Λ₁ = 1.091 μm, the period of the last one was Λ₆ = 1.056 μm, so the period was changed with ΔΛ = 0.07 μm step, which corresponds to the change of resonant wavelength by Δλ ≈10 nm. The reflection spectra measured for the resulting array are shown in Fig. 7. Addressing the performance of this inscription technique, it is worth to mention that the whole array has the length of a spin pitch L_p = 15.4 mm and is written in about 14.3 seconds that leads to an average rate of 1.077 mm/s. Further acceleration of the process is possible by raising the pulse repetition rate and, subsequently, the fiber drawing speed. The process of inscription was captured by one of the used CMOS cameras and is provided as a supplementary material to the paper (see Visualization 1).

 

Fig. 7 Reflection spectra of the longitudinal FBG array with a variable period (Λ = Λ₁, …, Λ₆) inscribed in different side cores of the 7-core spun optical fiber in the single-pass procedure.

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4.2 Inscription of the longitudinal FBG arrays in selected cores: the central and side ones

In order to show the ability of multiple modification of a single selected core we inscribed FBG arrays in central and side cores. At first, the uniform 1-mm long FBGs with periods Λ₁ = 1.084 μm, Λ₂ = 1.07 μm and Λ₃ = 1.056 μm were inscribed in the central core of 7-core spun fiber. Since, the FBGs in the central core lay on a neutral axis of the fiber, it is not sensitive to a bending deformation, and thus, it can be used for longitudinal strain and temperature compensation of a bending sensor. The focal point of the fs laser beam was shifted to the central core, and the inscription was carried out without intersection of the laser radiation with the side cores. Otherwise laser radiation can be absorbed by the side cores material because of high concentration of germanium in them, resulting in pulse energy fluctuation during the inscription process. As in previous experiments, the energy of the laser pulses remained the same (E_p = 200 nJ). The reflection spectra of the array were measured sequentially from the side where FBG with shorter wavelength locates (Fig. 8). Measuring spectra after each following FBG makes it possible to estimate the introduced losses. As can be seen from the figure, the reflection coefficient for the long-wavelength FBG in the array (#3) decreased by 0.88 dB. Such decrease in reflection corresponds to the total losses attained by the propagating optical signal when passing FBGs #1-2 back and forth. Thus, the insertion loss of single FBG is estimated to be about 0.22 dB (4.9%).

 

Fig. 8 Reflection and transmission spectra of the FBG array inscribed in the central core of 7-core spun fiber.

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The similar experiment on FBG inscription was carried out for the selected side core. In this case, the laser pulse picker was held in “closed” state to “skip” the side cores in which inscription is not required and “open” state to inscribe the FBG in the desired core. The reflection spectra of the array (Fig. 9) were measured by the same way as described above for the FBG array in the central core. The periods were set to Λ₁ = 1.091 μm, Λ₂ = 1.084 μm, Λ₃ = 1.077 μm, Λ₄ = 1.07 μm, Λ₅ = 1.063 μm, and Λ₆ = 1.056. As one can see from the figure, the reflection coefficient for the long-wavelength FBG in the array has decreased by 1.27 dB. These losses correspond to the total losses attained by the propagating optical signal when passing the FBGs #1-5 back and forth. Thus, the insertion loss for a single FBG is about 0.127 dB (2.88%). Although the magnitude of insertion losses is higher compared to that for FBGs inscribed by UV radiation, it can be reduced to <1% per FBG by further optimization of the inscription regime [30]. A lower SLSR value (down to 5.2 dB) for the central core, than that of the side ones, is associated with the higher reflectivity and the difference in the refractive index profiles. The usage of interrogation equipment with a wide dynamic range (>40 dB) allows one to significantly increase the number of FBGs in the core (or interrogation channel) that can be registered.

 

Fig. 9 Reflection spectra of the FBG array inscribed in selected side core of 7-core spun fiber.

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4.3 Inscription of the FBG array in the transverse plane of the fiber

The ability to modify selected cores of the 7-core spun fiber with femtosecond point-by-point writing technique opens up the opportunity of FBG array inscription in the transverse plane of the 7-core spun fiber. Such array, due to different spectral response of individual FBGs to the direction and magnitude of the bend, is a key element of the 3D vector/shape sensor. When each FBG is significantly detuned from another one, the array can be used in a sensing system with wavelength-division multiplexing, and interrogated via single optical channel.

The example of the interrogation scheme for transverse FBG arrays with single optical channel is shown in Fig. 10. In contrast to the scheme used earlier (Fig. 2), the reflection signals from four cores were combined and simultaneously analyzed by OSA unit using a 2x4 fiber-optic splitter, which did not require an optical switch to measure the spectra from individual cores separately. To implement this scheme, the transverse FBG array was inscribed in chosen cores of the 7-core spun fiber: one FBG in the central core (4) and three FBGs in the side cores (7, 2, 3), with resonant wavelengths λ₄ = 1522.7 nm, λ₇ = 1542 nm, λ₂ = 1562.4 nm, and λ₃ = 1582.1 nm, respectively. Since these FBGs should be located in limited cross-section of the fiber, parallel to each other, after the inscription of next FBG, the translation stage returned to start point and the fiber was rotated around its axis at angles + 120° and −120° using a graduated high precision fiber rotator mounted on the translation stage.

 

Fig. 10 Single-channel interrogation scheme of 7-core spun fiber with FBGs inscribed in different cores at different resonances wavelengths.

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The reflection spectrum of the inscribed array measured for a straight FBG-containing section is shown in Fig. 11(a) (black line). Then, the optical fiber was winded turn-by-turn round different cylindrical rods with radii R₁ = 7.15 mm and R₂ = 3.75 mm so that the FBG-containing section was in the middle of the winding to reduce the effect of longitudinal stretching. The resulting reflection spectra are shown in Fig. 11(b)-(c) (blue and red colors). There is a significant shift of the FBG resonance wavelengths in the side cores with a maximum values Δλ₂ ≈5.5 nm for R₁ = 7.15 mm and Δλ₂ ≈9.85 nm for R₂ = 3.75 mm. The sign of the wavelength shift indicates the type of the FBG deformation: positive corresponds to extension, negative to compression. At the same time, the wavelength shift value indicates the distance of the FBG from the neutral bend plane and, therefore, allows one to calculate radius of curvature and bending direction.

 

Fig. 11 Single-channel interrogation of 7-core spun fiber with inscribed four FBG at different resonances wavelengths.

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In order to determine the magnitude of the bending deformation, the approach described in [31] was used. In this technique, the bending induced strain ε_i in i-th individual core is related to a partial curvature vector κ_i for this core. This vector points in the direction of the i-th core’s center from the center of the fiber (or to the opposite direction, depending on the sign of ε_i) and has a magnitude proportional to the strain. Then, the sum of vectors κ_i is calculated to find a general apparent curvature vector:

$\kappa =-\frac{1}{r}\left({\displaystyle \sum _{i=1}^N{\epsilon }_i}\cos {\theta }_i{n}_x+{\displaystyle \sum _{i=1}^N{\epsilon }_i}\sin {\theta }_i{n}_y\right),$ [REMOVED MACROBUTTON FIELD]where n_x and n_y are unit vectors aligned with the local axes x and y, respectively, r is the cores separation distance, θ_i is the angle between i-th core and x-axis (see Fig. 12), N = 3 is the number of analyzed side cores. The curvature radius is then $R=N/\left(2\left|\kappa \right|\right)$, and the local bend direction is $\theta =\mathrm{angle}(\kappa )$ [31].

 

Fig. 12 Geometry of fiber cross-section and parameters for bending calculations.

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For the case of R₁ = 7.15 mm, we calculated the sensitivity coefficient of FBG deformation: 1.2 pm/μstrain. This coefficient is approximately equal to the typical value for germanosilicate fibers ≈1 pm/μstrain in telecom window. Having this coefficient and the data of the wavelength shifts for the second case (R₂ = 3.75 mm), we calculated the bending curvature radius R_2,calc = 3.86 mm. Based on the above data, it is possible to estimate the error in determining this value, which is 3% in our case. This error can be attributed to the wavelength measurement errors and some weakening of the fiber after winding resulting in a small increase of bending radius.

It is important to note that the resonant peaks of the inscribed FBGs experience almost no decrease in amplitude even with a substantially small bending radius R₂ = 3.75 mm, which indicates a low bending loss of the proposed sensor.

5. Conclusion

Thus, new versatile method of core-selective FBG inscription by fs laser pulses was demonstrated for a 7-core spun fiber. Various configurations of FBG arrays were inscribed with the presented method — a longitudinal array in all peripheral cores, a longitudinal array in one selected side and central cores, an FBG array in a transverse fiber section. It was shown, that the longitudinal FBG arrays with predefined periods can be inscribed in a single-pass procedure with high productivity (average speed is 1.077 mm/s, or faster than an FBG per second). As compared to commonly used methods of FBGs inscription by UV radiation, our approach enables the FBG inscription through protective polymer coating of the fiber. The vector bend sensor based on the inscribed FBG array in a 7-core spun fiber was demonstrated that allows measurements of small curvature radii using single-channel interrogation scheme. The results open up the possibility of compact and flexible 3D vector/shape sensors development based on multicore fibers for micro-robotics, particularly for minimally invasive surgical manipulations.