High-Order Modes Suppression in All-Glass Large-Mode Area Rare-Earth Doped Optical Fibers with Modified Cladding

Abstract

In the present work we have developed and realized a high core-to-cladding diameters ratio active optical fibers operated in a single-mode regime due to specially designed structure containing boron-doped and fluorine-doped rods. The beam quality at the output of the realized fibers was studied by three independent methods: near field investigation, M² technique and S² technique. According to the obtained results, the developed approach allows efficient suppression high-order-modes (first of all—LP₁₁ mode) in the core and achieves a diffraction-limited beam at the output of the appropriately bent fiber (suppression of unwanted modes was better than 30 dB). Additionally, it is shown that application of such approach allows for increased bent-resistance of the fundamental mode and realizes polarization-sensitive amplification.

1. Introduction

High-power fiber lasers, including high-average and high-peak-power lasers, have become indispensable tools for applications such as material processing [1], light detection and ranging (LIDAR) [2,3] and development of new light sources for fundamental study [4,5]. The rapid and, in fact, unprecedented spread of fiber optic methods was mainly due to the unique waveguide properties of optical fibers, which guarantee high quality of the output beam, compactness and reliability of laser schemes. At the same time, the growth of the fiber lasers’ output peak power is limited due to relatively small core diameter of standard optical fibers (~6–10 μm), which results in the appearance of nonlinear effects (stimulated Raman scattering, self-phase modulation and so on), which distort the spectrum of the amplified signal and degrade the quality of the pulse in the time domain.

The challenge of developing optical fibers with a high threshold of nonlinear effects can be solved by two independent and at the same time complementary approaches. The first one is based on the decrease of light intensity in the fiber core by increasing its diameter. The second approach relies on a shortened active fiber length by increasing the concentration of the active dopant.

Application of the first approach connects with strong interdependence between the fiber core size, core refractive index and core mode content [6]. In particular, the single-mode propagation regime in step-index fibers with increased core diameter could be achieved by appropriate decreasing of the refractive index of the core to the level close to that of the first fiber cladding. The minimal core-cladding refractive index difference (Δn) is limited by the technological capabilities of the reproducible implementation of the flat-top refractive index profile of the core, as well as by the high fiber sensitivity to bending. For Δn ~ 0.001, the core diameter should be 21 µm to provide single-mode operation at a wavelength of about 1.55 µm. To achieve single-mode operation near 1 µm with the same value of Δn, the core diameter should be less than 13 µm. A further increase in the core size requires utilization of special optical fiber designs, as well as special conditions for their operation. The best results for high-peak-power laser systems based on Yb-doped and Tm-doped fibers were obtained using rod-type photonics crystal fibers (PCFs) [7,8,9,10,11] with unprecedented low numerical aperture, thus the fibers must be kept perfectly straight. For the Er-doped fibers, the best results thus far have been achieved with few-mode step-index fibers [12,13,14] where high-order modes (HOMs) suppression are achieved due to higher bent sensitivity of HOMs as compared to the fundamental mode. Recently, the development of technology for fabrication of tapered optical fibers [15,16,17,18,19], which could be bent with a radius of 10 cm and even less, made it possible to obtain maximum peak power comparable to that achieved in Yb-doped PCFs [7]. In the case of Er-doped fibers this technique allowed for setting a world record in terms of peak power [19]. However, a good output beam quality was achieved thus far only in relatively long tapered fibers of 1–4 m in length and this value cannot be significantly reduced due to peculiarities of the tapered fiber fabrication process.

Recently, great progress in reduction of an active fiber length by doping with an extremely high Yb concentration was shown [20,21,22]. In particular for Yb-doped fibers, when pumped through the cladding, the active fiber length could be reduced down to a couple of tens of centimeters without noticeable reduction of the pump-to-signal conversion efficiency. In this regard, the development of new optical fiber designs with constant diameters of the core and cladding along the fiber length and increased mode field diameter is of great interest, as it is the main way to increase the threshold of nonlinear effects in extremely-high-Yb-doped fibers.

Furthermore, a number of applications require a high core-to-cladding diameters ratio, which allows for increasing cladding pump absorption and shortens the optimum fiber length. Ability to maintain polarization is another typical demand for fibers used in high-peak power lasers. In this case, polarizing fibers are more preferable as it could additionally suppress an unwanted polarization state. Earlier in [23], we demonstrated a design of a passive LMA Bragg fiber (BF), in which HOMs suppression was achieved together with polarizing properties by creation of a microstructured core, containing F-doped and B-doped rods. In this case, delocalization of HOMs and fast-polarization state of the fundamental mode from the central part of the core was due to modes’ deformation and its extremely high bend sensitivity.

Thus, the main motivation of the present work was development and study of a new approach for implementation of flexible large-mode-area (LMA) high core-to-cladding diameters ratio polarization maintaining (end even polarizing) active fiber appropriated for high-power single-mode lasing. In the present work, we developed a double-clad (DC) Yb-doped quasi-Bragg fiber with a mode field diameter of about 24 μm (at 1030 nm) and average clad diameter of about 125 μm with the ability to maintain polarization and slow-polarization-enhanced gain. A technique of inserting two B-doped rods and two F-doped rods into the core was used for HOMs and fast polarization suppression. The fiber was carefully studied: single-mode operation and polarizing properties of the fiber were confirmed. Furthermore, we demonstrate applicability of the proposed technique for usual step-index fibers; and efficient HOMs suppression was achieved in cladding-pumped Er-doped fiber.

2. Fiber Modelling

The main challenge in designing active double-clad fiber as compared to the design developed in [23] is absence of leaky modes in the structure with two reflective claddings. Due to the DC fiber configuration the modes under cutoff could still propagate in the first cladding and will have non-zero intensity in the doped fiber core. Thus, some of the cladding modes can be efficiently amplified, resulting in deterioration of the core mode content. For example, in [7] the achieved output power was limited by dramatical degradation of the beam quality. Another problem is a small core-to-cladding ratio (and a large fiber outer diameter) as in [23], which is not suitable for many applications of active fibers. Increase of the core/clad ratio requires removal of nearly all high-index ring layers except the last one (nearest to the core), which also makes filtering of the unwanted modes more difficult. In this regard, differential mode gain [24] is the only way to filter out undesirable modes, but it requires careful optimization of the fiber design.

The simulation was carried out using the COMSOL Multiphysics software package. Material dispersion was not taken into consideration. The modal content was estimated for the spectral range of 0.8–1.6 µm. In calculations, the doped core diameter was chosen to be 35 µm. The fiber design had core refractive index close to zero (as in the case of conventional LMA Bragg fibers). Additionally, we added two B-doped and two F-doped rods to the fiber (Figure 1) that was necessary to confine the fundamental mode on the fiber axis. Introduction of B-doped rods created anisotropy and defines polarization states of the modes localized in the core (i.e., position of high order modes’ side lobes). Adding of F-doped rods helped to confine the fundamental mode in the central part of the fiber, doped with Yb. Simultaneously, HOMs suffered from distortion of their sidelobes and mode intensity redistribution to the cladding.

Additionally, for effective spatial separation of the core modes, i.e., to create priority condition to the fundamental mode localization in the central core region, we added an appropriately designed high-index ring layer centered on the fiber axis. The inner radius of the high-index ring layer was 40 μm, and the outer was 41.3 μm. With the aim to develop a compact fiber structure, with outer diameter comparable with conventional fibers, we used only one high-index ring layer. At the same time position of the interface between the first and the second cladding and the position of the high index layer were chosen to achieve the maximum fundamental mode confinement in the central core region. As a result, the developed fiber design had extremely small cladding compared with the core and the main principles of mode selection in this case were inevitable. The selective mode amplification technique [24], when only the central part of the core (where the fundamental mode has the maximum intensity) is doped with rare-earth elements, was used as the main mechanism for mode selection. In our calculations to estimate the efficiency of mode selection we compared part of the mode’s power concentrated in the doped region (the mode’s gain will be proportional to this value).

Furthermore, on the outer fiber boundary we added a perfectly-matched layer (PML) eliminating reflections at the interface. Calculation of the similar structure without PML but with outer double clad layer were also performed, and the results reproduced the results of the fiber with PML with good accuracy. Thus, we could conclude that the main principle of mode confinement in the core of the developed structure happens due to coherent Fresnel reflection from the high-index ring layer and small distortion of the outer cladding should not result in dramatic changes of real structure mode content. Besides, it should be stressed that during calculations of double clad fiber, a huge number of waveguiding modes appeared in the structure, mostly propagated in the cladding. As a result we had to calculate about 200 modes for one wavelength to find and identify core modes. The main problem was that all core-guiding modes due to specific mechanism of mode confinement had effective refractive indexes lower than silica cladding. Further calculations for spectral range with reasonable step became even more cumbersome, and more importantly, there were jumbles of modes. Thus, for our final modelling we considered structures with outer PML only.

Despite the fiber design hardly being able to be called a Bragg fiber (only one high-index ring layer retained in the structure), we will name it quasi-BF below due to its similarity to the design proposed in [23]. Due to zero refractive index contrast between the doped core and undoped cladding, the fiber was extremally sensitive to any small refractive index perturbations. Small heterogeneities (dips or peaks) in the core refractive index profile could dramatically impact on the propagation constant and optimal position of the reflecting layers, respectively. By this reason our modelling of the refractive index distribution of the doped area obtained from the real Yb-doped preform available in stock was also taken into account, but we “adjusted” the average level of the doped core to be at the silica level. It was done due to the possibility of precise control of the index difference between the doped core and undoped cladding by selection of fiber tension during its drawing [25]. It allowed us to estimate the mode confinement and mode shape under real conditions.

In Figure 1 the results of the calculation of mode’s power in the Yb-doped region via wavelength are shown for the straight fiber. In our study we considered modes having more than 10% of the total power in the core Yb-doped region. It can be seen that near the 1.03 μm part of the $L{P}_{01}^{slow}$ mode’s power in the doped core is at least two times higher than for other modes, and all modes except the fundamental one dramatically spread across the fiber cross-section. Thus, in our fiber design, due to different mode field intensity distribution, $L{P}_{01}^{slow}$ mode gain will be at least twice as high as compared to other modes, providing 15 dB undesirable modes suppression in the output beam for net gain of 30 dB. Splicing losses for the developed fiber with a matched step-index fiber will also provide suppression of the undesirable modes by at least 3 dB due to modes field distribution mismatch.

Additionally, it is interesting to emphasize that at shorter wavelengths one of the HOMs with non-zero intensity at the axis (according to mode electric field distribution it is analog to the LP₀₂ mode of the conventional step-index fiber) became localized in the core mainly while the fast-polarization state of the fundamental mode, on the contrary, became localized outside the central core region (Figure 1). In the spectral region around 1 μm there is a maximum delocalization of both unwanted modes (fast-polarization state of the fundamental mode—line 2 in Figure 1 and mode shown by line 3), which should provide a perfect single-mode single-polarization operation of the designed fiber.

Fiber bending provided further improvement in the mode selection. In the structure with low-index rods embedded into fiber construction, there are several leaky channels providing mode evacuation from the doped area. In particular, the fast-polarization state of the fundamental mode is significantly more sensitive to bending compared with the slow one. Thus, even slight bending causes the state of fast polarization escaping from the fiber core and in such a way provides the additional polarizing effect of the fiber (Figure 2).

3. Materials and Methods

Based on the fiber design described in Section 2, a double-cladding quasi-Bragg fiber with two B-doped and two F-doped rods was fabricated. The fiber preform was realized by a method combining the modified chemical vapor deposition (MCVD) technique and stack and draw approach. MCVD technology was used to implement cylindrically symmetrical structure elements, as well as to implement the Yb-doped core (only the central part of the fiber preform was doped); the stack and draw approach was applied to introduce low-index rods into the fiber cladding. Since the fiber was made to operate in a cladding-pumped scheme, the cylindrical symmetry of the silica cladding was broken. Taking into account the fiber design features, we chose the octagonal shape of the cladding to provide good pump mixture on the one hand, and to exclude distortion of the shape of the high-index ring layer during the fiber drawing on the other hand [26]. The fiber was drawn in a low-index polymer coating providing a cladding aperture of about 0.46. The drawing tension was carefully controlled to match the Yb-doped region average refractive index to that of undoped silica cladding (as was designed initially). The image of the end-face and the measured profile of the refractive index of the fiber are shown in Figure 3.

The lasing properties were studied in standard cladding-pumped amplifier schemes with co-propagating pump and signal (Figure 4). A wavelength-stabilized multimode diode emitting at 976 nm (LD) was used as a pump source. As seed, we used a narrowband 1030 nm fiber laser (or, in some measurements, ASE fiber laser with smooth spectrum spreading from 1029 up to 1082 nm). The choice of the operating wavelength was dictated by large core-to-cladding diameter ratio of the developed active fiber, which favors amplification of short wavelengths. A pump combiner was used to couple pump and signal into the active fiber-under-test. To eliminate unabsorbed pump power and signal leaked to the cladding we used cladding light stripper (CLS) at the fiber output and, additionally, dichroic mirrors (DM), which reflected the signal and transmitted the pump at 976 nm.

The measurements of the realized fiber core mode content were carried out using three independent methods, which give qualitative and quantitative characteristics. Thus, first of all, we measured near field mode intensity distribution at the active fiber output under the amplification condition. In addition, M²-factor measurements were made [27], which gives an estimate of the quality of the output beam by far-field divergence of the beam from the waist. Additionally, the last technique for mode characterization was S²-parameter (by spatially and spectrally resolved imaging) estimation [28,29], relying on spatial and spectral interference between HOMs and fundamental mode in the output beam. The last method provided us with information of exact mode form and content.

4. Experiment and Results

4.1. Yb-Doped Fiber

To reduce splice loss with the active fiber we used a polarization maintaining (PM) pump and signal combiner based on passive step-index fiber with core size of 20 µm (cladding diameter was 130 µm). The signal power coupled into the active fiber was about 15 mW. The fiber was extremely sensitive to any small stresses (including stresses originating from the holder of the fusion splicing machine). Therefore, to align the active fiber axis during splicing with the PM pump combiner we used a fusion splicer with an end-view option.

In the experiment, the active fiber, bent with a radius of 15 cm, was laid freely on a metal surface. Its optimal length for 976 nm pump was 90 cm. An CLS was built at the output end of the fiber by placement of the bare part of the fiber in high-index immersion liquid. The CLS allowed us to eliminate most of the unabsorbed pump power as well as signal and ASE captured by cladding modes. To prevent backward reflection from the fiber facet, the output fiber end was angle-cleaved. The rest of unabsorbed pump power was additionally removed by dichroic mirror.

Figure 5 shows the measured dependence of the signal power via pump power. The estimated slope conversion efficiency was 65%. The lasing threshold was about 2 W. Polarization extinction ratio (PER) was measured in the amplification regime (gain more than 20 dB). To exclude interference between fast and slow-polarization states that could take place in the case of the narrowband seed laser, we used a broadband Yb-doped ASE single-mode laser source as the seed. First, we measured PER with a polarized seed laser. PER on the active fiber output was measured as being higher than 13 dB. Then, to test the ability of the developed fiber to polarize signal we coupled an unpolarized broadband seed into the active fiber. The difference between the power concentrated in the slow- and fast-polarization states of the fundamental mode was only 2.7 dB, which is much less than was expected from the modelling (~10 for 20 dB gain). To discover the reason for the observed mismatch we studied the near field intensity distribution at different input pump powers (Figure 6). It is evident that in the case of zero pump power, the fast-polarization state dramatically broadens through the fiber cross-section in opposition to the slow-polarization state effectively confined at the fiber axis. However, the situation starts to change after turning on of the pump power. With an increase of the pump power the shape of the fundamental mode fast-polarization state becomes more and more similar to that of the slow-polarization state. It starts concentrating in the central core region (in particular, in the Yb-doped region) and thus becomes efficiently amplified. The measured mode field intensity distribution in the amplifying regime for slow-polarization state was estimated to be MFD_x = 24 μm and MFD_y = 24 μm. We suppose that a thermal load in the central part of the core (which is doped with Yb) results in local increase of the refractive index, distortion of the induced-by-stress refractive index profile and simultaneous capturing and amplification of the fast-polarization state. Indeed, according to the calculations, the value of the induced-by-the stress refractive index is extremely small (Δn_induced~0.0004). Increase in the energy flux density in the core due to signal growth with pump power, and, mainly on the fiber axis, where the fundamental mode has an intensity maximum, leads to heating of the core glass and a corresponding nonuniform increase in the refractive index across the fiber cross-section. Thus, due to increasing waveguiding properties under heat load for the fast-polarization state, it starts being more effectively confined on the fiber Yb-doped axis. Note that we used aluminosilicate glass matrix for the Yb-doped core, which results in increased heat generation inside the Yb-doped region. The problem could partially be solved by utilization of photodarkening-free P₂O₅-SiO₂ or Al₂O₃-P₂O₅-SiO₂ glass matrixes [21].

Furthermore, the quality of the output beam in slow-polarization state was investigated using the M² technique. A narrowband seed laser at 1030 nm was used in the experiment. In order to eliminate the effect of the second polarization state at the fiber output we installed a bulk polarizer at the fiber output. Since the shape of the mode differs from the cylindrically symmetric one, the approximation of the beam divergence with distance from the waist region was carried out by an ellipse along the level of 1/e². The result of the study is shown in Figure 7. Measured M²_x was 1.04 and M²_y was 1.12. Thus, the beam quality was nearly diffraction-limited.

The next step of beam quality characterization was measurement of the S²-factor. For this aim we used ASE source passed through a fiber polarizer as a seed laser. At the active fiber output we used the bulk polarizer to additionally suppress the fast-polarization state of the fundamental mode. Spectrum measurements at various spatial points was carried out by the conventional step-index single mode 6/125 fiber placed on automatized shift with a fixed step. During the experiment, we had to replace the pump combiner with 20/125 signal fiber to 6/125. This action was necessary due to a slightly non-single-mode light propagation in the core of the signal fiber in the 20/125 pump combiner. The few-mode propagation regime induced additional peaks originating from HOMs interference in the signal delivered passive fiber. To exclude this effect, we used a perfectly single-mode delivery fiber. The results of the S² active quasi-BF measurement are depicted in Figure 8. Figure 8a shows the result of Fourier transform of the registered optical spectra measured in different spatial points of the beam, and in Figure 8b,c the retrieved mode intensities and phases at the points defined by the red dots in Figure 8a are presented. It is evident that the HOMs in the developed active fiber are suppressed by more than 30 dB. The peaks lower than 30 dB belong to artificial effects (for example, due to re-reflection from the bulk polarizer surface) and according to the amplitude and phase the profile reproduces the fundamental mode.

4.2. Er-Doped Fiber

In the previous paragraph we demonstrated the possibility of efficiently suppressing HOMs by introduction of low-index B-doped and F-doped rods into the quasi-Bragg fiber core. In that case, both core inclusions, position of the high-index ring and outer silica cladding were matched to suppress HOMs. It is quite interesting to check which of these factors is the most important. For this aim we studied the possibility of suppressing HOMs (mainly LP₁₁ mode) by introduction of low-index rods into silica cladding of classical step-index fiber with non-zero core refractive index. For experiments we fabricated Er-doped fiber with 40 µm core diameter and 125 µm outer cladding; the calculated LP₁₁ mode cutoff wavelength was 2.5 µm. The measured refractive index is shown in Figure 9a. Two fluorine-doped rods with diameter of 20 µm were inserted symmetrically 40 µm off the axis and two similarly sized and positioned boron-doped rods were inserted along the orthogonal axis. The fiber had circular outer surface (efficient pump mixture was achieved by the presence of low-index rods in the cladding). The PER provided by the boron-doped rods was measured to be 23 dB.

We performed the same suite of measurements for the Er-doped fiber to analyze the beam quality and the mode content of the fiber. As seed laser for the Er-doped fiber amplifier we used a broadband laser with central wavelength of 1560 nm. In our experiments the active fiber length was 5 m. The results of M² measurement are presented in Figure 9b. The results of S² measurement are depicted in Figure 10a. It can be seen that in the fiber bent with diameter of 25 cm, the dominant HOM is LP₂₁ (Figure 10d) with a multi-path interference (MPI) value of −16.6 dB followed by the LP₁₁ mode (Figure 10c) with an MPI value of less than −20 dB. We suppose that more effective LP₂₁ mode confinement in the core results from the fiber geometry. Indeed, in the case of LP₁₁ mode, all the polarization states tend to be distorted by the rods and in such a way are evacuated from the fiber core, two polarization states of the LP₂₁ mode with peak intensity reproducing low-index B- and F-doped rods’ positions in the structure can be effectively confined in the core. Interestingly, similar behavior was observed in the passive BF configuration [30]. At the same time, the reduction of the coiling diameter to 7 cm results in complete suppression of the LP₂₁ mode and has no noticeable effect on the LP₁₁ mode. It results in the improvement of the M² value from 1.51/1.6 for 25 cm bend diameter to 1.37/1.33 for 10 cm bend diameter. Smaller bend diameters resulted in the degradation of the beam quality, which was possibly caused by bend-induced distortion.

Thus, the proposed design allowed us to suppress the LP₁₁ mode down to −20 dB in a few-modes fiber. The LP₂₁ mode can be easily suppressed by fiber bending with the diameter of 10 cm. Due to a high core refractive index of 0.002 the fiber bend sensitivity was quite low, which results in only slight output power loss under this bend diameter (from 0.75 down to 0.64 W). It should be noted that a high-quality single-mode operation in the cladding-pumped Er-doped fiber with a large core (35 µm) was achieved previously using fiber bent with diameter as large as 30–70 cm [12,13]. In the present work we achieve a perfect single-mode operation in fiber with an even larger core diameter (40 µm) bend with a few times smaller bend diameter (10 cm), which is of great interest for the design of ultra-compact laser systems.

5. Conclusions

In this paper, we propose and study a simple method for suppressing HOMs in the LMA-active optical fibers, based on the introduction into silica cladding of four low-index rods (two of them were boron-doped to create anisotropy and two others, were doped with fluorine to confine fundamental mode in the core).

Practical applicability of the developed approach was experimentally tested on two example fibers, one of them was doped with Yb and other one was doped with Er ions. The choice of the doping elements was dictated by the most promising practical applications. In particular, Yb-doped fiber lasers (emitting near 1 μm) due to the possibility of achieving the highest output power are used for micromachining aims [1]; Er-doped fiber lasers (covered spectral range near 1.55 μm) are applied for LIDAR systems owing to operation in the “eyes-safe” transparency window of the atmosphere [3].

It was shown that the modification of the fiber cladding allows not only the suppression of unwanted core modes, but it also results in a higher bending stability of the fiber. In this context, it is interesting to compare the realized zero-core refractive index quasi-Bragg fiber with conventional step-index fiber (c-SIF) having the same mode field diameter (24 μm) at 1.06 μm. Truly single-mode operation in such c-SIF is possible only when the numerical aperture (NA) of the fiber does not exceed 0.03 (that is, it corresponds to the core-to-cladding refractive index contrast Δn of about 0.0003). Such low NA c-SIFs are extremely sensitive to bending and microbending and can hardly be used in real laser schemes. Thus, according to c-SIF calculation of the ideal structure of optical fiber with NA of 0.03 and corresponding core diameter under 0.15 cm radius, bending will have optical losses at 1.03 μm of more than 100 dB/m. In contrast, investigation of the quasi-Bragg fiber, developed in the work, showed that even in the case of reduced quantity of high-index ring layers it exhibited acceptable resistance to bending without dramatic impact on the amplifier efficiency under fiber coiling.

The polarizing effect in the fiber design with low-index rods can be easily observed in the case of a zero value for core refractive index contrast, which is due to the extreme low induced by the stress refractive index changes. The polarizing effect in the active LMA fiber configuration dramatically reduces under pump conditions. Anyway, as it was shown, application of such an LMA structure in the real schemes can help to slightly improve the initial PER of the propagating beam.