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We report, through numerical simulations and experimental data, the first successful fabrication of a polarization maintaining single-mode fiber delivering a flat top intensity profile at 1.05 µm. A high quality flat mode was obtained and single-mode behavior was checked by shifting the injection and by S2 imaging method. Numerical investigations were performed to show that it would be possible to increase further the 0.6x10−4 experimental group birefringence.
© 2015 Optical Society of America
1. Introduction
Fiber lasers are widespread amongst industrial and academic communities because of their benefits such as compactness, long term stability and reliability, good heat dissipation and no free-space alignment to name a few. Usually, these fiber lasers deliver a Gaussian-like beam which is fine for many applications. However it would be interesting to obtain a homogeneous intensity for several industrial processes (marking, drilling, cutting, heat treatment…), for biological tissue interactions or for seeding large-scale laser facilities like the Laser MegaJoule (LMJ). Several solutions to shape the beam in free-space have already been used [1] but they lead to alignment difficulties and/or high losses. Obviously an all fiber system would be preferable. A multimode fiber can deliver a top hat intensity profile by mixing higher-order modes [2], but it exhibits a low depth of focus and spatial incoherence. New fiber designs [3,4] have been proposed so as to flatten the fundamental mode (FM) as early as 1999 through the use of a well-tailored index profile. However the first report on such fiber fabrication was done only in 2004 [5] and the beam was still quite far from the ideal top hat profile because of technological difficulties to get the right index profile. It is only in 2012 that our group managed to obtain the first convincing realization of such fiber design [6]. Nevertheless, these top hat single-mode fibers did not enable polarization control. As this feature is required for several applications [7], we had to use a very short length (~few mm) of the fiber [8] to preserve polarization. In this paper, we remove this limitation by realizing the first polarization maintaining (PM) single-mode fiber delivering a top hat profile, the PM property being obtained by adding soundly into the cladding stress applying parts (SAPs).
To report on our findings, we first present the fiber design and fabrication process, followed by results of the optical characterization and conclude on a numerical investigation of the stress effect due to the SAP.
2. Fiber fabrication
To produce the PM top hat fiber, we used the same strategy described in our previous design [6] and added boron doped silica rods as SAPs. More precisely, the fiber has been designed as follows (Fig. 1):
Fig. 1 (a) Optical microscope image of the Ge doped ring and the first air hole ring of a cane. (b) Scanning electron micrograph image of the PM top hat fiber.
- - An undoped silica core (HSQ330-Hereaus) with a refractive index slightly lower than the silica used in the cladding in order to facilitate the single-mode behavior of the fiber as explained in [6].
- - A Ge-doped silica ring deposited by the Outside Vapor Deposition process [9] that allows us to accurately control its thickness (ΔR) and its refractive index. In our case the refractive index difference between this high index ring and the silica used in the cladding is estimated at 4x10−3.
- - An air-silica cladding realized by stacking undoped silica tubes (F300-Heraeus) and characterized by its pitch (Λ) and the air hole diameter (d1). This allows us to finely control the effective index of the cladding up to the final drawing process in order to facilitate the single-mode behavior of the fiber as explained in [10].
- - Six B-doped silica rods (16% mol. B2O3 from Prysmian) on each side of the core to induce stress birefringence.
Note that in order to decrease confinement losses (CL) of the straight and bent fiber, larger air holes (d2) are added after the 4 rings of very small air holes (d1) (required for single-mode behavior). The effect of this extra layer is similar to the F-doped tube used in [6] and its position as well as the diameter d2 have been chosen to insure low enough CL for the fundamental while preserving the single-mode behavior of the fiber.
To assemble the structure, we used the standard stack and draw technique: the different materials were first drawn to realize a stack of about 25 mm of outside diameter (OD), this stack was then drawn into canes of 4 mm [Fig. 1(a)] and finally these canes, jacketed into 10 mm OD tubes, were drawn into fiber using pressurization system to adjust the air hole diameters (and so the cladding refractive index).Among the different birefringent fibers made from this design, the one enabling a top hat profile and single-mode behavior around 1050 nm (see next section) has the following parameters:
3. Optical characterization
To validate the fiber design and fabrication, we first checked that a top hat profile could still be obtained in the presence of the SAPs. Then an 18µm diameter Gaussian-like beam at 1050 nm was injected in 1 m of straight fiber and the near field pattern at the fiber output was imaged on a camera. Figure 2 shows a typical result demonstrating that a flat mode of very good quality could indeed be obtained. The mode field diameter was measured to be 18.8 µm.
Fig. 2 (a) Near field image of the intensity distribution and (b) associated x-cut and (c) y-cut profile at 1050nm.
Secondly, in order to verify the single-mode behavior, the injection was shifted from centered up to 7 µm (ie 100% of the core radius). As expected the output power decreased but the output profile did not change significantly for both polarization axes (Fig. 3) such that the fiber effectively operates in single-mode regime.
Fig. 3 Near field images of the intensity distribution for both polarization axes with an injection offset (Δx) of 0 µm, 5 µm and 7 µm corresponding respectively to 0%, 71% and 100% of the core radius.
In order to demonstrate this quantitatively, the advanced S2 method was utilized as described in [11,12] on a 3 m fiber length kept as straight as possible (to avoid HOM filtering by bending the fiber). The S2 measurement data were analyzed using multivariate statistical analysis methods, taking full advantage of correlations in the data set, both spatially and spectrally (through the group delay difference), as detailed in [12], allowing us to fully separate the modal interference profiles and characteristic group index differences and to retrieve the relative mode power distribution. In a first set of experiments, a linearly polarized Gaussian-like laser beam whose polarization is oriented along one of the fiber birefringence axes was injected with an offset to favor higher-order modes emergence. Beatings between modes were then detected on the camera through an analyzer with the same orientation as the input beam in order to observe one polarization at a time. The spatial beat profiles between the LP01-LP11A and LP01-LP11B could be clearly observed after data processing [Fig. 4(a)] whereas the total intensity looks like a top hat profile as in Fig. 2. These results show that our fiber is not strictly speaking single-mode. However, the power difference between fundamental mode and the most powerful higher order mode (HOM) is very high (more than 15 dB) even for an offset of 5 µm (70% of core radius). It is thus clear that in practice, this fiber can be still considered as single-mode.
Fig. 4 (a) S2 results showing the spatial beat profiles,(b) associated spectra and (c) the reconstructed spatial profiles of LP01, LP11A and LP11B modes with (d) power distribution in the case of an offset of 5µm.
To observe the polarization lifting of degeneracy, a second set of S2 data was acquired, similarly to the previous one except that the two polarizers were turned at 45° from the fiber birefringence axes. The spatial beat profile of the two fundamental polarization modes is shown on Fig. 5(a) and the group birefringence, deduced from the associated spectrum [Fig. 5(b)], is evaluated at 0.61x10−4.
Fig. 5 (a) S2 results with the spatial beat profile between the two polarization fundamental modes and (b) the associated spectrum. (c) Another birefringence measurement method using the polarization beat spectrum.
In order to confirm this birefringence value, a second method [13] was used: a polarized supercontinuum laser was injected at 45° from the birefringence axes of the fiber under test (fiber length L = 2 m) and the output spectrum was analyzed through a polarizer also oriented at 45° of the birefringence axes. The group birefringence (B) was deduced from the modulation pitch of the output spectrum [Fig. 5(c)] using the well-known formula:
This method leads to a group birefringence value of 0.6x10−4 at 1050 nm, confirming the estimated value from the above S2 measurement. Note that the Polarization Extinction Ratio (PER) was also measured at 1050 nm and was better than 20 dB even for a long fiber length (~20 m).Finally the fiber loss has been estimated to 0.1dB/m by cutting back the fiber from 27.5m to 3.6m, the fiber being rolled on a bobbin of 31.8cm radius. The current fiber is relatively bent sensitive: the loss increases to almost 1dB/m for a radius R of 15 cm but for R = 20cm the extra losses have been estimated to be only about 0.1dB/m.
4. Numerical investigations
4.1 Model
Alongside the fabrication and optical characterization of this first PM top hat fiber, we have implemented a simulation code to take into account the birefringence caused by the SAPs. The mechanical stress induced by the fiber drawing and the hydrostatic stress are generally negligible compared to the thermal stress [14], thus they were overlooked to simplify the model. Moreover, the thermal history of the glass should in principle be taken into account to model accurately the thermal stress. However, as the glass history and the temperature dependence of the Young’s modulus (E), Poisson’s ratio (ν) and thermal expansion coefficients (α) of the different materials are not well known, we decided to use the standard simpler approach [14–20] consisting in using thermal average coefficients and the silica Young’s modulus, density and Poisson’s ratio for all materials. There are also some disagreements on values of setting temperatures and thermal expansion coefficients in the literature on Boron SAPs [14,17–19] and on Ge-doped silica [14,17,19]. We chose the same values as in Ref [14,18] leading to a temperature change ΔT of −980 K and a SAP’s expansion coefficient of 2x10−6 K−1 for the 16% doped Boron silica. Note that, we don’t take into account the stress contribution of the Ge-doped silica ring in the model due to its cylindrical symmetry and its thinness.
We then first compute the stress induced profile by using the structural mechanics module of Comsol Multiphysics® software which calculates Von Mises stresses [15]. Subsequently, we calculate the modified index profile and finally obtain the modal content and effective indices of the fundamental and higher-order modes using the wave optics module of this software. A perfectly matched layer (PML) was added to calculate confinement losses of each mode [21,22].
4.2 Numerical results
First to validate our modeling, we used the opto-geometrical parameters of Table 1 (corresponding to the fabricated fiber) and the thermo-mechanical parameters summarized in Table 2.
Table 1. Parameters of the fiber
Table 2. Simulation parameters: d corresponds to the material density, ν the Poisson ratio, E the Young modulus, ΔT the temperature change and αSi, and αSiB2O3 are thermal expansion coefficients respectively for pure silica and 16% mol. Boron doped silica.
Figure 6 shows the index profile used as well as the spatial profiles of the two FMs that present a top hat profile as expected. The first HOMs have their effective indices just below the Space Filling Mode index (nFSM) of the air-silica cladding, which explains that their CL are about 2 orders of magnitude higher than the FMs ones (~0.1 dB/m), in good agreement with our experimental results. Moreover, the group birefringence obtained for these fiber parameters is B = 0.6x10−4, a value very close to the experimental one of section 3.
Fig. 6 (a) 2D index profile (in order to increase the figure clarity, the minimum index scale has been fixed to 1.4396, the air holes refractive index being set to 1), (b1) 2D intensity profile and (b2) its intensity cut along x and y axis for polarization x, (c1) 2D intensity profile and (c2) its intensity cut along x and y axis for polarization y.
We then used the numerical tool previously described to study new designs with the aim of increasing the birefringence value without perturbing too much the mode profile.
First we checked that the birefringence could be increased by simply adding the same SAPs closer to the core. The structure shown on Fig. 7(a) leads indeed to a higher group birefringence (1x10−4) but unfortunately the FM profiles are far too much perturbed [Fig. 7(b1-c2)] making this structure useless as anticipated in section 2.
Fig. 7 (a) 2D index profile, (b1) 2D index profile, 2D intensity profile and (b2) its intensity cut along x and y axis for polarization x, (c1) 2D intensity profile and (c2) its intensity cut along x and y axis for polarization y.
Note that for both polarizations the intensity profiles along x and y directions are very different: the profile in the x direction has a Gaussian-like shape whereas a clear dip is observed along the y axis. These two different shapes rule out the possibility to retrieve a flat mode by simply scaling the fiber structure (or working at another wavelength). Indeed the intensity cut along the x axis could be flattened by increasing the fiber pitch (in a standard top hat structure [6], the Gaussian-like shape is observed at long wavelengths as the light cannot resolve the high index ring) but then the profile along the y axis would have an even deeper central dip, the light being even more localized into the high index ring that would be thicker (in a standard top hat structure [6], the ring like shape is observed at short wavelengths as the light can resolve the high index ring).
In order to enhance the birefringence while preserving a top hat intensity profile, the number of SAP was increased from 12 to 20 and positioned relatively far from the core to keep a flat mode.
With such design, we obtain not only a group birefringence as high as 1x10−4 but also a very good flatness of the FMs [Fig. 8(b1-c2)]. Note that, although this birefringence value is high enough for most applications, even larger values could be simply obtained by increasing the boron concentration in the SAPs (from 16% mol to 20% mol for example [23]) or by reducing the silica around each B-doped inclusion.
Fig. 8 (a) 2D index profile, (b1) 2D index profile, 2D intensity profile and (b2) its intensity cut along x and y axis for polarization x, (c1) 2D intensity profile and (c2) its intensity cut along x and y axis for polarization y.
5. Conclusion and outlook
We report on the realization and characterization of the first PM top hat fiber. This fiber delivers a flattened intensity profile and we proved that, thanks to an advanced characterization by the S2 imaging technique, it can be used as a single-mode fiber. Its birefringence has been measured to 0.6x10−4 and the PER is better than 20 dB even for a long fiber length making this fiber already useful for the community working on lasers. Our numerical investigations are in good agreement with experimental results and ways to further increase the fiber birefringence have been given. These results could be of great interest for industrial process like marking and cutting or for large-scale laser facilities. Future works will aim at increasing the fiber effective area and realizing an active version of this new design.
Acknowledgments
This work was supported by French National Research Agency through Labex CEMPI (ANR-11-LABX-0007) and Equipex FLUX (ANR-11-EQPX-0017), through Contrat de Projets Etat Région (CPER) “Photonics for Society” and by the Aquitaine Regional Council through the CATHARE and HELIAM projects.
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