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Abstract
Due to the large core diameter and high number of guided modes in fibers with large core diameters, increasing the reflectivity of Fiber-Bragg-Gratings (FBG) in these multimode (MM) fibers is technically challenging. To increase the homogeneity and reflectivity of FBG in MM fibers, we analyze the impact of laser inscription parameters onto the FBG dimensions. Limitations of the processable core volume due to the cylindrical fiber geometry are observed. A new inscription strategy is developed, utilizing the rotational symmetry of the fiber to make a larger core volume accessible. In combination with a chirp of the FBG’s grating period a maximum reflectivity of 61% is archived in a 105 µm core diameter fiber.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Today, Fiber-Bragg-Gratings (FBG) in single mode (SM) fibers are commercially available for several Bragg-wavelengths and reflection coefficients from R < 0.01 up to R = 0.99 [1] and used for sensing applications like temperature sensing [2] or setup of monolithic fiber resonators [3,4]. A widely used approach to inscribe FBG in single mode fibers is by use of ultra-fast laser systems and a two-beam interference [5,6].
Transferring this technology from SM fibers with core diameters of about 10 µm to larger multimode (MM) fibers with core diameters >60 µm is state of research [7]. One common approach for grating inscription is a phase mask scanning technique, which is described in detail in [6,7]. FBG in multimode fibers manufactured this way, already have been applied as a low reflective (LR) mirror of a high power fiber laser [8]. Another demonstrated application is the frequency stabilization of diode lasers [9].
As shown in theory (section 2.2) the FBG reflectivity increases with increasing overlap of propagating modes with the grating cross.section. Additionally, since each propagation mode has a individual propagation constant, a grating chirp [10] is necessary to cover the Bragg condition for each resulting mode dependent effective refractive index [11] to maximize the FBG reflectivity [12]. Using a similar approach with a chirped FBG in a 25 µm core diameter fiber, a monolithic multimode fiber laser was demonstrated [11].
To realize a high reflective (HR) fiber-integrated mirror for a MM fiber resonator by an FBG, the processable cross section area needs to be increased. Due to the high diameter of MM fibers and mode propagation characteristics compared to a SM fiber, new writing schemes with scanning techniques have to be taken into account to significantly increase the grating cross-section and thereby increase the reflectivity further than approximately 10% [8].
Since the area covered by the focused beam is smaller than the cross-section area of the core, a translation of the core relative to the laser focus (“scanning”) is necessary. The resulting transverse homogeneity of the refractive index modifications that form the FBG depends on the combination of used laser pulse energy, pulse duration, number of pulses and transverse scanning steps during inscription. To determine the scan parameters, the area processed with a single inscription step without scanning is analyzed in bulk SiO2. Afterwards, the determined scan and laser parameters are used in combination with a chirped phase mask to demonstrate an HR-FBG.
2. Methods
2.1 Experimental setup for FBG inscription and characterization
The used setup for grating inscription consists of an ultra-fast laser system, emitting at a wavelength of 800 nm, with a maximum available pulse energy of 2 mJ and a minimum pulse duration of 100 fs at a repetition rate of frep = 1 kHz. The collimated circular beam, with a diameter of 6 mm, is focused collinearly to the fiber core by a cylindrical lens with a focal length of 20 mm (Fig. 1(b)). This setup results in a Rayleigh length of 19 µm and a beam waist of 2.2 µm. For creation of the periodic grating pattern, a phase mask operating as a transmission grating is placed between the focusing lens and the fiber. Right behind the phase mask substrate the +1 and −1 orders of diffraction overlap and hence create the interference modulation of the intensity (Fig. 1(a)).. The zero-order transmission of the phase mask is suppressed to below 2%.
The fiber itself is mounted on the “Nanomax 300” three axes translation stage which has two rotation axes attached (Fig. 2). These rotational and translational degrees of freedom allow the positioning of the fiber relative to the inscription beam focus and the adjustment of line focus collinearly to the fiber core. A scanning technique has been established, translating the fiber in discrete steps Δy perpendicular to the inscription beam to inscribe the FBG into the core, having a larger transverse diameter than the beam waist [7]. During every inscription step the fiber is exposed to the inscription laser for an exposure time texp. With the repetition rate the total number of pulses per step Nexp is calculated via ${N_{\textrm{exp}}} = {t_{\textrm{exp}}}{f_{\textrm{rep}}}$.
Fig. 1. Schematic illustration of the phase mask inscription technique, a) top view, showing the phase mask operating as a beam splitter, b) side view showing the focusing of the laser beam collinear to the fiber core and c) schematic illustration of the spectral transmission measurement setup consisting of a broadband light source coupled into a fiber with FBG and an Optical Spectrum Analyzer (OSA).
The FBG produced in this way are characterized by a spectral transmission measurement. A broadband white light source (350 nm-2000 nm) is coupled into the fiber containing the FBG to measure the transmission spectrum (Fig. 1(c)). To evaluate exclusively the spectral characteristics of the FBG, a transmission spectrum without FBG is subtracted for normalization. The maximum reflectivity R of the FBG is calculated at the minimum transmission TBragg at the Bragg wavelength, divided by the transmittance T at a wavelength without influence of the FBG:
Fig. 2. Picture of the FBG inscription setup in different configurations: a) to inscribe FBG with linear scanning strategy, b) for bulk material, c) with rotation mounts to inscribe rotational symmetrical FBG.
2.2 Methods and theoretical background for HR-FBG
The FBG reflectivity strongly depends on the transverse extend of the FBG. Every guided mode has a different spatial distribution inside the fiber core [13]. Assuming that the Bragg condition is fulfilled, the overlap between the extend of the FBG and each mode defines if a mode is affected by the grating [10]. When an FBG is extending homogeneously over the whole cross section area of the fiber core, every guided mode is reflected equally, and the total reflectivity rises.
For increasing the homogeneity of the FBG, the refractive index changes induced by the inscription process are analyzed in bulk SiO2. The refractive index modulation is visualized qualitatively with polarization-contrast-microscopy, which images the mechanical strain being correlated with the refractive index change. Therefore, a Leica DMLM light microscope with linear polarizers before and after the sample and a 10x magnification objective lens is used. The absolute change of refractive index is not measured. For this purpose, the fiber is replaced by bulk material with a plane entrance surface. Being able to measure the transverse extend of an FBG with respect to the used pulse energy and number of process pulses allows the adaption of the scan parameters to increase the homogeneity and thereby the maximum reflectivity.
Furthermore, the homogeneous overlap of the FBG with all guided modes is not the only condition to be met for achieving a high reflectivity in a multimode fiber. Because of the large number of guided modes and a constant grating period, the Bragg condition (Eq. (3)) is not fulfilled for every single mode at the same wavelength, since every mode has an individual index of refraction. Concluding a HR-FBG cannot be realized with a constant period phase mask [11]. To maximize the reflectivity of the FBG, the Bragg condition must be fulfilled for every guided mode. This can be achieved with a chirped phase mask, having a position dependent grating period.
The range of the effective refractive indices of modes propagating in a step-index fiber is defined by the refractive index of the core ncore and the cladding nclad, and fulfills:
The total change of the grating period $\mathrm{\Delta }{\mathrm{\Lambda }_{\textrm{PM}}}$, that is needed to cover all wavelengths in a fiber with NA = 0.1 is calculated by using the effective index range and the Bragg equation:
Here ΛPM is the grating period, λ the reflected Bragg wavelength and m an integer defining the order of Bragg-diffraction in the fiber. Here the second order is used. The cladding consists of pure fused silica with a refractive index of nclad = 1.45. To match the NA of 0.1 the doped core has the refractive index of ncore = 1.4534.
Assuming an FBG length of at least L = 11 mm, the chirp rate needs to ensure that the Bragg condisiton is met for every guided is 3.43 nm/cm. Our experimental setup mechanically limits the maximum FBG length to L < 20 mm. The width of the phase mask is chosen to be 25 mm. With the phase mask being slightly larger than the mechanic limitation, diffraction at the phase mask boundary is avoided. The phase mask’s center grating period ΛPM of 1477.3 nm results in a second order diffraction at 1071 nm for n = 1.45.
In our experimental setup a modular concept allows the exchange of the phase mask, fiber mounts and focusing optics. A second phase mask without chirp (grating period of 1345.5 nm) resulting in a second order diffraction at 975 nm (n = 1.45) is used for non-chirped grating inscription. Additionally, to allow the inscription of FBG longer than the 6 mm beam diameter of the inscription laser, the beam is scanned along the fiber axis if necessary.
3. Results and discussion
3.1 Increasing transverse FBG homogeneity
For determination of the influence of the laser parameters on the shape of the processed area, gratings are produced under variation of the pulse energy and the number of process pulses, while the focal length of the cylindrical lens, beam diameter and pulse duration remain constant. As explained in chapter 2.2, bulk SiO2 is used here to allow the analysis with polarization contrast microscopy. Note that the following figures in false color representation do not deliver any quantitative information about refractive index change. Each figure is normalized to enhance visibility of the processed area.
The pulse duration is fixed to 100 fs, following the state of research for single mode FBG [5,6]. Figure 3 shows two dominant effects that decrease the homogeneity of the processed area. First, exposing the sample to 300,000 pulses per step with a pulse energy of 0.75 mJ with a pulse duration of 100 fs, leads to self-focusing and defocusing effects [14,15], resulting in a inhomogeneous periodic structure along the inscription beam propagation axis (Fig. 3(a)). Self-focusing occurs when a material dependent intensity threshold is exceeded. In this parameter combination, this threshold is exceeded several micrometers in front of the actual focusing volume. At this volume the intensity is higher than the threshold for nonlinear absorption, resulting in a refractive index change. When processing a fiber with this parameter set, this may result in an unwanted structuring of the cladding volume. Transmission losses will occur due to cladding mode -coupling. Because of this the pulse energy is reduced to 0.5 mJ in the following investigations.
Fig. 3. False color representation of a polarization contrast microscopy measurement of a structured area: a) with 0.75 mJ pulse energy, and 300,000 process pulses in bulk SiO2. Inscription is repeated five times with the same parameters to show reproducibility of the effect. b) with 0.5 mJ pulse energy, varying the number of process pulses, in bulk SiO2.
Fig. 4. False color representation of a polarization contrast microscopy measurement of a structured area with 0.35 mJ pulse energy and 300,000 process pulses in bulk SiO2.
Second, increasing the exposure time creates artefacts around the structured area (Fig. 3(b)) and therefore this effect also reduces the homogeneity of the produced structure. These artefacts are created by refraction of pulses at previously inscribed refractive index modulations. Since a repetition rate of 1 kHz with a pulse duration of 100 fs is used, thermal effects do not contribute. The relaxation of the electrons at the induced plasma takes places at time scales of 150 fs [16]. When scanning along the y-axis these undesirable artefacts would overlap and create a periodic inhomogeneity. To avoid this effect, we limit the applied process pulses per step to 106 pulses for a pulse energy of 0.5 mJ.
In conclusion these effects limit the laser parameters to
The lower limit of the pulse energy density is caused by the minimum intensity needed to induce nonlinear absorption processes in SiO2 [17]. The maximum number of process pulses, avoiding the formation of the described artefacts, depends on the pulse energy. Increasing the pulse energy leads to a reduction of the maximum number of pulses and vice versa.
Operating in this parameter range with reduced pulse energy and process pulses, a homogeneous elliptic refractive index change is produced, as shown in Fig. 4. The number of process pulses is chosen to 300,000 for increasing the visibility of the refractive index change. The processed area is approximately 25×3 µm2.
In Fig. 5 is shown that the reflectivity is increased by decreasing the scan step size from 9 µm to 3 µm while the total processed transverse diameter remains 35 µm. Here, the amount of scan steps is adapted to cover the same transverse diameter. The knowledge about the dimension of the processed area enables a scan proceeding increasing the homogeneity of the grating.
Fig. 5. a) Maximum reflectivity and transmittance. b) Spectral transmission of FBG with different Δy without chirp of the grating period.
With a step size of 3 µm effectively more the area is covered since the individual modifications are closer to each other, than with a step size of 5 µm. In comparison of 3 µm and 5 µm steps, the reflectivity is increased by a factor of two, with a constant transmittance of 88%. Losses around 10% are observed for the FBG shown in Fig. 5. The loss is caused by scattering due to strain caused by the energy deposition as well as possible cladding mode coupling. At previously iterations of LR-FBG fabrication using a pulse energy of only 0.35 mJ yielded a maximum transmittance of 98%. In the following iterations of FBG production a pulse energy of 0.35 mJ is used to avoid the 10% loss.
3.2 Processing larger core volumes and chirp of grating period
Since the focus cross section is sufficiently smaller than the core diameter, a scanning strategy must be applied to process more core volume. The accessible core volume using the linear scan method is limited by refraction. For investigating this effect, the system consisting of the f = 20 mm focusing lens and the fiber is simulated with Zemax Optic Studio. The Wavelength of 800 nm and the beam diameter of 6 mm is matching the ultra-fast laser.
Translating the fiber along the y-axis in the simulation changes the angle of incidence between laser beam and fiber surface normal due to the fiber’s curvature. As a result, especially the edge area in direction of the scanning is not accessible (Fig. 6(b). This effect is not dominant for inscription close to the center. Approximating this area with two circular segments, about 15% of the core volume is not processable. Taking the tilted beam path through the fiber into account, the modification pattern becomes inhomogeneous in these areas.
Fig. 6. Raytracing model of the refraction at the fiber surface with the incident beam a) centered in y-direction, b) translated by 50 µm in y-direction. Focusing lens and phase mask are not shown. c) Illustration of the scan strategy utilizing the rotation symmetry of the fiber. Orange ellipses represent the processed area (not to scale) and the arrows the fiber rotation.
To overcome this limiting effect, a new scan strategy is developed, using the rotational symmetry of the fiber. By rotating the fiber around its symmetry axis and not translating it in y-direction the incident beam hits the fiber surface perpendicular (Fig. 6(a,c)). The used fiber rotation stages eccentricity is specified with ±10 µm [18]. According to that a readjustment of the fiber is necessary after every rotation step.
The presented scan strategy gives access for processing the complete fiber core. For structuring the core volume at the center, the linear scan strategy with competently low translation can be combined with the rotation scan strategy to avoid overlap of structured areas.
In addition to the largest possible cross section of modified volume, the Bragg wavelength has to be the met for every propagating fiber mode to maximize the reflectivity, as shown in section 2.2. Thus, in the following this advanced scan strategy is combined with the chirp of the grating period. The length of the FBG is increased to 16 mm by scanning the beam in longitudinal direction over the phase mask. The length of the FBG is estimated by measuring the visible scattered stray light during characterization, attributable to core-cladding-coupling. The length L of an FBG, written with a pulse energy of 0.35 mJ, without scanning in longitudinal direction, is approximately 4 mm.
The FBG with a length of 16 mm reaches a maximum reflectivity of 61% at 1068 nm (Fig. 7(b)). The transmittance of 77% at 1080 nm is attributed to the increased processed area and accompanying scatter losses. Therefore, an angular step size of 10° is chosen with an offset from the center of $\mathrm{\Delta }z = 30\; \mathrm{\mu} m$. A scaled illustration of the scanning is shown in (Fig. 7(a)). The pulse energy is chosen to 0.35 mJ with 60,000 pulses per step to a create homogeneous refractive index modulation with a extend in z-direction of roughly 25 µm.
Fig. 7. a) Scaled illustration of the final pattern of FBG inscription combining the linear scanning method and rotational scanning. b) Measured spectral transmission of an FBG at 1068 nm with different length L and chirped grating period.
The inscription of HR-FBG is right now limited by the total production time. With an inscription laser repetition rate of 1 kHz it takes 60 s for each of the 156 inscription steps. Additionally, the fiber must be realigned after every inscription step.
4. Conclusion and outlook
In this paper the development of a scan strategy enabling the production of high reflective FBG is presented. First, the refractive index modification’s dimensions in Si02 are analyzed, depending on the pulse energy and the number of process pulses per scanning step. If the chosen energy or the amount of process pulses is too high, the modulation becomes inhomogeneous because of self-focusing effects or diffraction artefacts.
The process parameters are set the way a homogeneous elliptic refractive index change is produced. The determination of the transverse dimensions and shape of the processed area enables an adjustment of the linear scan step size to cover the core cross-section more effectively, and thus increase the homogeneity and reflectivity of the FBG.
Due to the mode propagation properties of multimode fibers a chirp of the grating period is necessary to further increase the FBG reflectivity. This is realized by inscribing the FBG with a chirped phase mask while simultaneously applying the rot-symmetrical technique to cover a large core cross-section.
The linear scan process is limited in the accessible core volume, due to refraction of the incident inscription beam at the curved fiber surface, when scanning. A new scanning technique is developed, avoiding this issue. By rotating the fiber along its symmetry axis, the inscription beam always hits the fiber centered and even the edge of the fiber core is accessible.
Combining the chirp with the new scanning technique an FBG in a NA = 0.1, 105/125 µm MM fiber is produced. With this inscription process a reflectivity of 61% at 1068 nm and a transmittance of 77% at 1080 nm is archived in comparison to just around 10% with the linear scanning strategy. While this rotation strategy is beneficial for HR-FBG, it takes significant more process time, due to necessary readjustment of the fiber after every scanning step because of an offset between fiber and rotation axis. Therefore, the conventional technique is still preferable for LR-FBG with reflectivity below 10%.
The next steps are the demonstration of an all in-fiber monolithic multimode fiber laser and further improvement of the reflectivity and transmittance. For this application a reflectivity of 100% without any losses would be the ideal case. To further increase the maximum reflectivity towards 100%, the total processed area needs to be increased. By increasing the focal length of focusing lens and adapting the pulse energy, the processed area per process step can be increased. An approach for increasing transmittance is to decrease the used pulse energy for decreasing the strain induced to the fiber core. A thermal post processing of the FBG to heal out the strain, without vanishing the FBG itself, also may be used to increase transmittance.
Funding
Fraunhofer-Gesellschaft (MEF 602590).
Acknowledgments
This work was supported by Fraunhofer Internal Programmes. We thank RWTH Aachen University LLT - Chair for Laser Technology for providing the ultra-fast laser system.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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