We have experimentally studied fundamental mode propagation in few meters long, adiabatically tapered step-index fibers with high numerical aperture, core diameter up to 117 μm (V = 38) and tapering ratio up to 18. The single fundamental mode propagation was confirmed by several techniques that reveal no signature of higher-order mode excitation. It can be, therefore, concluded that adiabatic tapering is a powerful method for selective excitation of the fundamental mode in highly multimode large-mode-area fibers. Annular near field distortion observed for large output core diameters was attributed to built-in stress due to thermal expansion mismatch between core and cladding materials. The mechanical stress could be avoided by an appropriate technique of fiber preform fabrication and drawing, which would prevent the mode field deformation and lead to reliable diffraction-limited fundamental mode guiding for very large core diameters.
©2012 Optical Society of America
Fiber mode area enlargement is one of the key means for power scaling and nonlinearity mitigation. Currently, there are three main approaches for development of near single mode (SM) large mode area (LMA) fibers, namely, low numerical aperture (NA) fibers, microstructured fibers such as large-pitch photonic crystal fibers (PCF) and leakage-channel fibers (LCF), and selective mode excitation in multi-mode (MM) fibers.
In low-NA fibers, controlled bending is often utilized to induce large losses for the high-order modes (HOM) , and the method was used to realize the first kW laser  and recently a 10-kW amplifier . However, the core diameter usually remains limited to below 50 μm due to the minimum core/cladding refractive index difference (typically NA = 0.05-0.06) achievable by modified chemical vapor deposition (MCVD) technology. In addition, the guiding properties of these fibers are weak due to the low NA, making them highly sensitive to environmental perturbations, especially uncontrolled bends.
An alternative technology for mode area scaling is based on different types of microstructured fibers. Active PCF with small hole-diameter-to-pitch ratio d/Λ (< 0.1) was demonstrated in , and core diameter as large as 70 μm has been achieved . Recently, the core diameter of a large-pitch PCF was further increased to 135 μm . Similarly to low-NA fibers, PCFs of this type possess weak guiding properties, and they are realized as unbendable rod-type fibers; furthermore, their mode content is strongly dependent on pump power . The basic principle of these fibers, the delocalization of higher order modes out of the guiding core, is also utilized in the LCF design . In LCFs, the single mode LMA core is formed by channels introduced in the cladding to make the core waveguide leaky for all modes. Such fibers can potentially be several meters long and bendable to a small diameter, although high-power experimental results are yet to be demonstrated.
Finally, mode area scaling can be achieved by selective excitation of a certain mode in a multimode fiber. Using a lens system for selective excitation of the fundamental mode in a multimode fiber with a core diameter of 45 μm and NA of 0.13, single-mode propagation over 23.5 m was demonstrated in . The excitation of the single LP07 mode by using a long period fiber Bragg grating (LPG) in a multimode fiber with an 86-μm core was demonstrated in . Furthermore, fundamental mode propagation through a 20-cm straight fiber with 300 μm core diameter and NA = 0.39 was demonstrated in , and propagation through 2 m in 100-μm core fiber was demonstrated in  with output M2 of 1.6. The results of [8–11] allow concluding that mode coupling induced by macro-bends in fibers with a sufficiently large cladding diameter is small, and after excitation of a single mode (fundamental or another), the lone mode can propagate in a highly multimode core over long distances without significant mode conversion.
In addition to the free-space [8, 10, 11] and LPG  approaches, adiabatic tapering can be used for fundamental mode excitation in multimode fibers by using the SM end as a launching port. In this paper, we investigate the fundamental mode evolution in long, adiabatic, high-NA tapers with high tapering ratio. Although mode area scaling by tapering a multimode optical fiber has been reported [12–14], only short (few-cm) tapers with up to ~50 μm core diameters have been studied experimentally. Previously, we have proposed the use of long active tapered fiber as a gain medium for fiber lasers and amplifiers . Experimentally, we have shown that the wide side core diameter can be scaled up to 40-60 μm (NA 0.11) with a diffraction-limited beam, whereas further increasing the core diameter often leads to deterioration of the output beam quality [16–18]. The main aim of this paper is a detailed experimental study of the evolution of the beam characteristics (modal composition, state of polarization, transversal mode field distribution, and beam quality) after mode area expansion in a long (several meters) tapered passive fiber with high NA, high tapering ratio, and core diameter up to 117 μm.
2. Experimental results
The longitudinal profiles of the tapered fibers are shown in Fig. 1 . The 7-m and 20-m fibers have tapered lengths of approximately 5 m and 13 m, tapering ratios of 18 and 12, and maximum core diameters of 117 μm and 86 μm, respectively. Both tapers had a W-profile with core NA of 0.11, core to cladding diameter ratio of 1:6, and core diameter to outer diameter ratio of 1:14. The narrow end core diameter was approximately 6.5 μm, strictly single-mode for the 1 μm wavelength used in most measurements. Special attention was paid to the uniformity of the core refractive index, as the maximum core diameter in the 100 wavelengths range renders the mode field sensitive to any perturbation of the transversal index profile. Therefore, the rod-in-tube technology was used for preform fabrication to ensure a uniform index profile of the core. The preform core was a pure silica glass rod (type F-300), and the cladding was formed by fluoro-silicate glass layers deposited inside an F-300 tube by MCVD technique. After deposition of the cladding layers, the core rod was inserted into the tube, and the tapered fibers were pulled directly from the aggregate. The tapers were coated by a high-index polymer to remove cladding modes, and the diameters of the pulled fibers were controlled and measured at several locations during the drawing.
2.1 Mode field distribution and beam quality
A cut-back measurement was used to determine the modal evolution during propagation in the 7-m tapered fiber. A 1060-nm SM diode source was launched by splicing the diode pigtail in the narrow end of the taper. For several cutting locations, the fiber diameter, 1-D and 2-D beam profiles, divergence, and M2-parameter were measured for both straight and coiled (R = 15 cm) fiber. The first 50 cm in the wide side were kept approximately straight also in the coiled case. Figures 2(a) and 2(b) show the beam profiles in the near field and far field at the wide side output after propagation through several cut lengths of the shorter taper, respectively, and Fig. 2(c) shows the near and far field profiles after propagation through the entire 20-m taper.
The dependence of output beam quality on the cut-back was characterized by measuring the output beam divergence and M2 (4σ-method, average of two measured orthogonal axes) at various cut lengths for both coiled and straight 7-m taper, with the results shown as a function of core diameter shown in Fig. 3 . For the 20-m taper, the beam quality was measured for the uncut fiber with output core diameter 86 μm, with the results M2 = 1.31 for R = 100 cm and M2 = 1.42 for R = 15 cm. The output beam profiles are shown in Fig. 2(c).
Prior to the cut-back measurement, 532-nm and 1064-nm emission were launched into the narrow end of the 7-m taper from a frequency-doubled diode laser. At the wide end output, a dichroic filter was used to separate the two wavelengths. Figure 4(a) shows the wide output far field distribution for both wavelengths. As evident from Fig. 4(a), green excitation of the narrow input core (few-mode for green) led to apparent multi-mode output, whereas for the 1-μm excitation the far field had a Gaussian shape. The output divergence for both wavelengths was measured to be 10 mrad.
Furthermore, 1060-nm SM diode emission was launched into a highly multi-mode 30-cm taper section cut from the wide end with core diameter increasing from 90 μm to 117 μm. The SM diode pigtail was butt-coupled to the 90-μm core and the beam profiles, divergence, and polarization state were measured at the output. The output beam distributions are shown in Fig. 4(b) for centered and arbitrary excitation of the large core. The 1/e2 divergence measured after the 30 cm propagation was found to be 50 mrad and 86 mrad for centered and off-centered excitation, respectively.
2.2. State of polarization
The evolution of the state of polarization (SOP) during narrow-to-wide propagation through the long tapered fibers was studied with the 1060-nm SM diode emission. The Stokes parameters were determined after propagation through different taper sections shown in Table 1 , and the degree of polarization (DOP), ellipticity ε, and azimuth θ of the SOP were calculated from the measured parameters. It should be noted that although ellipticity and azimuth are sensitive to perturbations such as bending of the pigtail, the DOP is not. The transmission through a polarizer for the 1060-nm SM diode pigtail output (99% DOP) and for the 7-m taper output is shown in Fig. 5 . The degradation of DOP during propagation through the entire length of either taper was found negligible, whereas propagation through the 30-cm MM taper piece with core diameter 90 μm to 117 μm excited by butt-coupled SM fiber caused significant depolarization (Table 1).
2.3. Mode content
Changes in mode content were experimentally studied for propagation through the entire 20-m taper based on the S2-method . Emission from a 1-μm broadband source was launched into the narrow end of the fiber, and a SM fiber acting as a spatial filter was butt-coupled to the wide output core. The SM fiber was not scanned over the entire output field, but only a few aperture locations were studied. The optical spectra at the source and at the output of the spatial filter were Fourier transformed to derive an intermodal group delay spectrum. The measurement was performed for various taper coiling radii and for different locations of the spatial aperture at the output core; however, coiling and aperture location had little effect on the beat spectrum. A typical group delay spectrum (R = 15 cm) is shown in Fig. 6 . The spectrum of the broadband source exhibited some initial modulation resulting in harmonics in the Fourier domain; however, significant new harmonics could not be observed in the spectrum after propagation through the taper for any bending or aperture location.
2.4. Impact of built-in mechanical stress
Built-in mechanical stresses in optical fibers may lead to significant changes in the refractive index profile of the core [20, 21]. We investigated the existence of such stresses in the studied tapers and their possible influence on the transverse field distribution of the output beam. A 37 mm long section with 1.6 mm outer diameter cut from the wide end of the 7-m taper was excited with a white light source to study the presence of mechanical stress. White light was launched into the fiber piece through a linear polarizer, and the output beam profile was measured as is, and through another (crossed) polarizer. The same measurement was performed after annealing the taper section for 4 h at 1000 °C. The observed output beam profiles are shown in Fig. 7 .
The cross-like structure resulting from mechanical stress is clearly visible in the spatial distribution at the taper output (Fig. 7, top left). The top right image in Fig. 7 shows the same output after transmission through a cross-state polarizer, illustrating the spatial distribution of mechanical stress in the transversal plane of the fiber. Two ring-shaped stress zones can be identified: a broad zone in the cladding, and a narrow zone at the core-cladding boundary. Thermal annealing led to almost complete elimination of the stress (Fig. 7, bottom row).
Furthermore, a quantitative measurement of the intrinsic stress in the taper was carried out. A 1.6-mm diameter fiber segment was cut from the wide part of the 7-m taper and longitudinal mechanical stress was measured directly using a polarimetric setup [21, 22] with a spatial resolution of 20 μm. The result of this measurement shown in Fig. 8 reveals two ring-like stress areas: a broad one in the cladding and a narrower one with an opposite sign at the core-cladding boundary, in agreement with the pictorial result presented in Fig. 7.
It should be noted that the stress measurement in Fig. 8 could only determine the axial (longitudinal) stress. The relevant radial refractive index change in an optical fiber in cylindrical coordinates is defined as Δnr = -B2*Sr-B1*(Sθ + Sz), where B1 and B2 are the stress-optical coefficients for fused silica, and Sr, Sθ, Sz are the radial, tangential, and axial stress components, respectively . Because B1, B2 > 0, B2 << B1, and the three stress components are of the same order of magnitude, B1*Sz can be taken as a reasonable lower limit estimate for Δnr (Fig. 8, right axis).
The mode composition of multimode fiber output is determined mainly by three factors: initial mode excitation, local (e.g. due to a splice) or distributed (e.g. due to microbending) mode coupling, and differential modal attenuation or amplification. Thus, high-quality initial excitation and absence of significant mode coupling sources are essential for robust single-mode propagation. Adiabatic, splice-free fiber tapering is an excellent method for fundamental mode excitation in a large-core, highly-MM fiber. In an ideal taper, significant mode coupling can be caused either by changes of the core diameter [23, 24] or by local bending [25, 26]. Mode coupling in the tapered fiber due to varying core radius has been considered theoretically in [23, 24], and found negligible in long adiabatic tapers with small tapering angle. Furthermore, mode coupling in tapered fibers caused by local bends was studied in [25, 26], and the effect was shown to be strong only for local bends with radii of a few millimeters. This allows assuming that mode coupling in a long adiabatically tapered fiber is insignificant for practical coiling radii of tens of centimeters, given that the taper is free from imperfections such as abrupt diameter changes. In the present work, robust propagation of the solitary fundamental mode in long, step-index, highly-MM fiber tapers has been demonstrated for the first time with V up to 38 and fiber lengths of several meters. This became possible by the record tapering ratio (up to 18), and the absence of any significant structural flaws and splicing points, although some variation of core diameter due to small oscillation of the pull speed regulation system remains possible.
The solitary fundamental mode propagation has been confirmed by several experiments. First, the measured large-diameter output beam divergence of 10 mrad (Fig. 3a) closely corresponds to the theoretical limit 1.22λ/D, where λ is the wavelength and D is the output core diameter. Second, the propagation of SM diode emission through the studied tapers did not cause noticeable degradation of DOP (Table 1). For comparison, propagation through a 30-cm highly-MM taper section caused up to 20% depolarization and increased divergence to 86 mrad for arbitrary excitation. Third, the 7-m taper was simultaneously excited in the narrow end by 1064-nm (V = 1.5) and 532-nm (V = 4.6) emission, revealing apparent MM output for green and a Gaussian far field for infrared. The output divergence for both wavelengths was the same (10 mrad), although the theoretical limit for green is 50% less. Finally, the near constancy of the mode composition of the 1060-nm SM input propagating through the 20-m taper was confirmed by a simplified S2 method.
With increasing core size, the originally Gaussian field distribution gradually assumed a top-hat shape (~50 μm core), followed by an annular profile at larger diameters (Fig. 2(a)). The evolution of the near field distribution is accompanied by moderate increase in M2 (Fig. 3(b)). Interestingly, the progressive mode field distribution change is characteristic only to the near field, whereas far field distribution remains nearly Gaussian for any core diameter (Fig. 2(b), 2(c)). Usually, such an annular near field shape is associated with a higher order mode (LP02) excitation or a central dip in the core index profile. Since the mode content did not change, and the core index profile was uniform, this behavior was ascribed to built-in mechanical stress, which has a ring structure (Figs. 7, 8), modulates the magnitude of the refractive index by several percent, and distorts the fundamental mode field.
The internal mechanical stress associated with inhomogeneous cooling of the fiber structure during drawing (quenching stress), the mismatch of the thermal expansion coefficients of core and cladding materials  or external stress due to bends  can lead to a distortion of the mode field and finally limit the output beam quality. Furthermore, it was recently shown that the presence of rare-earth dopants may lead to additional stress . As can be seen from Fig. 2(a), the distortion of the mode shape becomes significant around 700 μm outer diameter (~50 μm core diameter), likely determined by the magnitude of built-in stress induced by the specific dynamics of fiber cooling during the drawing process. Although the preform of the studied fibers was ensured to have a uniform core index profile, stress compensation or mitigation methods were not applied. By utilizing annealing procedures, modifying the chemical composition of the core and cladding to match their thermal expansion coefficients, and varying the geometry of the pulled fibers, it should be possible to avoid the observed deformation of the fundamental mode field.
In addition to the built-in stress, mechanical stresses due to bending exist in a long fiber which inevitably needs to be coiled for practical purposes . As shown by our experiments, bending of the studied tapers leads to an asymmetric deformation of the beam. Whereas the cross-section of the beam after propagation through a straight taper has a symmetric ring structure (Fig. 2(a)), propagation through a coiled taper leads to a crescent-shaped near field profile (Fig. 2(c)) and results in moderate degradation of the beam quality (Fig. 3(b)). However, coiling did not induce changes in the output divergence (Fig. 3(a)), the DOP (Table 1), or mode composition (Fig. 6), which allows concluding that although the bend-induced stress in a coiled taper distorts the fundamental mode field, its effect on mode coupling is small. As in any LMA fiber, small-radius bending of the taper will eventually limit the achievable mode area  even if the built-in stress can be avoided, unless bend-compensation methods are utilized. However, with the single fundamental mode guiding, additional complications associated with HOM content can be avoided.
In this paper, robust single-mode propagation without depolarization in few-meter long, step-index, high-NA adiabatic tapers with core diameter up to 117 μm (V = 38) and tapering ratio up to 18 was experimentally demonstrated. Nevertheless, the field distribution of the fundamental mode was found to exhibit annular distortion in the near field for large core size. The distortion was attributed mainly to built-in stress in the cladding and at the core-cladding boundary, likely due to inhomogeneous cooling during drawing and mismatched thermal expansion coefficients of the core and cladding materials.
The robust fundamental mode propagation practically without mode coupling illustrates the potential of long adiabatic tapers particularly for traveling-wave LMA amplifiers and high power delivery. Avoiding the built-in stress by careful design of core and cladding materials, doping, and fiber geometry is expected to allow scaling to very high core diameters with diffraction-limited output.
The authors would like to thank O. E. Shushpanov for measurements of mechanical stresses in the fiber and G. A. Ivanov and I. L. Vorob’ev for help with the preform preparation. This research was supported in part by the Finnish Funding Agency for Technology and Innovation (Tekes) project MARTEC, the Graduate School in Electronics, Telecommunications and Automation (GETA), and the Walter Ahlstrom Foundation.
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