1. Introduction

Lasers have become important and versatile tools with a great diversity of both scientific and industrial applications. Fiber lasers constitute one of the newest types of lasers, which over the last decade have experienced an extensive development and rapid expansion in commercial applications, in defense applications, and in research laboratories. The main cause of fiber lasers’ rise has been associated with the significant practical advantages and revolutionarily increased output powers [1, 2], which established fiber lasers as one of the laser technologies with the highest laser power. Further increase in optical power remains one of the most important directions of fiber laser development, and it is primarily associated with further enlarging the core size of the fibers while maintaining the diffraction-limited output-beam quality and other technological advantages of conventional single-mode optical fibers.

Indeed, the high power fiber laser revolution occurred due to reversing the decades-long technological trend in fiber technology of using only small-core single-mode fibers, and instead using the so-called Large-Mode-Area (LMA) fibers with core sizes greater than single-mode limit [3]. LMA fibers are broadly defined as large, nominally multimode core fibers in which the mode quality close to diffraction-limit is achieved by “external” means of either carefully exciting fundamental-mode [4] or employing fiber coiling to produce higher-order spatial mode (HOM) filtering effect [5]. Up to now, conventional index-guiding LMA fibers are predominantly used in industrial fiber lasers due to their compatibility with standard fiber splicing techniques and compact-coiling for packaging, both of which are critical for monolithic integration of practical fiber lasers. In fact, the majority of high power fiber laser records so far have been achieved with these conventional LMA fibers, which includes 10kW fiber laser demonstration [6] constituting the highest single-mode CW fiber laser to date. However, due to their multimode nature set by the lowest 0.06 NA limit from the conventional MCVD technique, conventional LMA fibers in monolithically-integrated systems are restricted to the core sizes below approximately 25μm, which in fact sets the current limit on power (or energy) scalability of this technology in practical laser systems. As an alternative, photonic-crystal LMA fibers (PCF LMA) have been proposed [7], whose air-hole based PCF microstructure allows for precise control of the core-cladding refractive index difference. Thus, much lower NA than 0.06 can be achieved. The PCF LMA fibers primarily rely on lowering of core NA to reduce the number of modes in the core and to extend LMA operation to larger core sizes. For flexible (bendable) PCF LMA fibers the largest core size possible is approximately around 40μm diameter, since further increasing the PCF LMA core size requires lowering the core NA to the extent that in-core guidance becomes susceptible to weak external perturbations such as package bending and micro-bending, thus making it necessary to resort to the stiff-rod geometry. Consequently, rod-type PCF LMA with core sizes close to 100μm has been demonstrated [8]. Due to their large core size, PCF LMA fibers and PCF rods have found extensive use in laboratory. However, their adoption by industry has been slow due to the difficulty of splicing structures that contain air-holes and due to practical disadvantages of rod-type geometry in terms of integration, limitations in beam robustness [9], and increased susceptibility to thermal effects [10]. Overall, the PCF rods offer large core sizes but lose some essential advantages of conventional fibers for monolithic integration and power scaling.

Therefore, the key of further developing practical higher power laser technology relies on the development of optical fibers with the robust single-mode output at core sizes well beyond the conventional LMA fibers’ limit, as well as the seamless compatibility with monolithic integration including the abilities of being spliced using standard splicing equipment and being coiled for packaging purposes. As a response to this critical need, there has been a burst of creativity in the field, and multiple solutions from diverse directions of how to increase the fiber core size have been proposed, such as chirally-coupled-core (CCC) fibers [11], leaky-channel fibers [12], large-pitch PCF fibers [13], gain-guiding fibers [14], higher-order-mode(HOM) fibers [15], SHARC fibers [16], all-solid photonic bandgap fiber [17] and many others. The underlying basic principle of these approaches (except HOM approach of ref [15].) is to design such fiber structures that introduce significant higher-order-mode (HOM) loss by extracting HOM from the core into the cladding, while ensuring that the fundamental mode experiences only negligible loss. The critical parameter that determines the robustness of the single-mode performance in such fibers is the magnitude of the HOM suppression. It can be shown that when HOM suppression becomes sufficiently high, the performance would approach that of a truly single-mode fiber, i.e. it produces single-mode output irrespective of input modal excitation or fiber coiling conditions, so the sensitivity of fiber output to external perturbations becomes low. In fact, single-mode operation of a fiber can be quantitatively defined based on TIA-455-80-C standard, stating that the HOM in a single-mode fiber should be suppressed by more than 19.3dB at the fiber output [18]. From the perspective of advancing practical high power fiber laser technology, it is essential that increasing fiber core size is achieved with simultaneously maintaining robust single-mode characteristics of the fiber.

At present, however, practically all published results on novel core-scalable fibers are predominantly concerned with core diameter increase, but not the degree of modal purity. In the majority of published papers, the only presented evidence of the beam quality at the output is based on the near-field image or the measured M² value of the output beam. However, it is well understood by now that M² measurement cannot determine the single-mode characteristics of a large core fiber [19]. As it has been shown in ref [19], even with relatively large ratio of HOM content, the output beam can still yield low M² values. The only reliable way to verify single-mode characteristics is to measure HOM content and, most importantly, the robustness of the modes has to be quantified by showing how this content changes under different fiber excitation conditions. HOM content can be measured, for example, by using so-called spectrally and spatially resolved imaging (S2) method [20]. It also provides a way to qualitatively confirm single-mode performance by observing the absence of spectral beating in spatially-filtered spectral measurement of the test-fiber output under different excitation conditions [11]. So far, rigorous single-mode quantification and proof of robust single-mode performance have been reported for 35μm core CCC fibers [11], 40μm core PCF LMA fibers [21], 34µm all-solid photonic bandgap fibers [22], and 50µm leaky channel fibers [23].

In this paper we report further advance in CCC fibers geometry, which enables increasing fiber core sizes to beyond 50μm diameter with effectively single mode operation. Structure of the paper is the following. It starts with the description of the geometrical structure, operation, principle, design parameters and numerical simulations of polygonal CCC fibers in Section 2. In Section 3 and 4, qualitative and quantitative measurements demonstrating the robust performance of such effective single mode CCC fibers are presented, which include detailed modal beating and S² measurements as well as referencing CCC fiber performance against that of industry-standard 20µm core LMA fibers. Demonstrations of 55μm core Yb doped P-CCC fibers are presented in Section 5. The conclusions are given in Section 6.

2. Large core polygonal CCC fibers

Chirally Coupled Core (CCC) fibers belong to the category of effectively single mode (E-SM) fibers, whose operation is based on selective leakage of higher order modes from the fiber core into its cladding, while transmitting the fundamental mode with a small (practically negligible) loss. Achieving E-SM operation requires HOM leakage-loss from the central core to be at least in the 10’s of dB range, with the fundamental-mode loss to be < 1 dB/m. Previously reported CCC fibers with a single side core are achieving this E-SM operation by selectively coupling HOM from the central into a helically-wound side core through an angular-momentum assisted quasi-phase-matching, and then radiating this coupled light into the cladding due to the curvature of the side core. With this single-side approach, excellent performance of E-SM CCC fibers with core sizes of up to 40μm diameter for both “passive” Ge-doped, and “active” double-clad Yb-doped have been achieved [11]. Further increase of the central core size with this approach is limited by the decrease in the modal overlap between central core and side core with the increasing size of the central core, which leads to weaker HOM coupling into the side core.

Here, we report a further advance of this CCC technique, demonstrating 8-side and octagon-shaped central core CCC fibers operating as effectively single-mode with core sizes larger than 50µm diameter. As we show further, operation of these new CCC structures include an additional interaction channel: apart from coupling central-core higher-order modes to side-core leaky modes, it also couples central-core HOM into central-core leaky modes, thus radiating HOM directly into the cladding. Since modal overlap between central-core guided and leaky modes does not decline with the central-core size, which allows significantly increasing E-SM core size of CCC fibers.

The new chirally-coupled core structure is shown in Fig. 1. There are two major features that distinguish this structure from the previously reported CCC geometry [11]: 1. Polygon-shaped (octagon-shaped in this particular case) transverse profile of the main core positioned on the fiber axis; 2. Multiple off-axis side cores which are helically winding around the main core. It is fabricated by spinning a fiber preform containing a straight on-axis main core and straight off-axis side cores during fiber drawing process. As a result of this spinning, the on-axis polygon-shaped main core acquires a twisted polygon shape, with a twisting period Λ, while the off-axis side cores become helically winding around this main core with the same period Λ. Therefore, we can label this structure as “Polygonal-CCC” (P-CCC) fiber to distinguish it from the previously reported CCC fibers as “Single-side CCC” (S-CCC) fibers [11].

 

Fig. 1 Polygonal-CCC Fiber Structure: In this structure on-axis central core has a polygonal shape (octagon in this example), with side cores (8 side cores in this case) positioned at the corners of this polygon.

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Both S-CCC structure and P-CCC structure are helically symmetric, since they remain invariant with respect to a simultaneous translation along the axis z of the fiber and a rotation with a period Λ around the axis. This is a lower-degree symmetry compared to the linear translational symmetry of a conventional cylindrical fiber. Consequently, as it is shown in ref [11], all modal interactions in such a CCC structure can only occur between helically-symmetric modes of propagation. These helically symmetric modes possess optical angular momentum, consisting from orbital (due to modal field-distribution rotation) and spin (due to modal field vector rotation) angular momentum components, leading to symmetry-based distinction between modes. As shown in ref [11], this leads to E-SM operation for S-CCC structure due to selective coupling between central-core HOM and side-core leaky modes through angular-momentum assisted quasi-phase-matching conditions:

We have designed and fabricated a series of large-core Ge-doped and Yb-doped P-CCC fibers, which include 50μm, 55μm, 60μm and 64μm core fibers with different helix periods for exploring different design variations and their effects on single-mode performance. P-CCC fibers with Ge-doped cores have central-core NA = 0.068 and side core NA = 0.088, and different helix periods in the range from 5mm to 6.3mm. Fabricated Yb-doped P-CCC fibers are based on the Ge-doped design which is identified to have best performance and have core size of 55μm with central-core NA 0.072, side-core NA 0.088 and helix period of 5.3mm. For facilitating high-power pumping, these Yb-doped CCC fibers have an octagonally-shaped triple-clad structure with all-glass inner cladding of 330μm diameter and NA 0.22, and an outer 390μm cladding with polymer coating and NA 0.45. Using rigorous modal characterization methods (to be shown in next section), we demonstrated robust single-mode operation in ~1μm Yb-doped fiber range of all 55μm, 60μm core fibers and with lengths of only ~1.5m. Some of tested 50μm-core experimental design variations were also tested to show single-mode performance, but only at lengths longer than ~2m. In addition, CCC fiber with a core diameter of 64μm has shown highly-robust single-mode performance at ~1.4μm wavelengths, indicating potential of CCC large-core fibers of operating single-mode in different wavelength ranges. An example of a cross section of a fabricated Ge-doped 60μm core P-CCC and its comparison to a conventional 125μm telecom-grade single-mode fiber is shown in Fig. 2(a), and the cross section of a fabricated 55μm core triple-clad Yb-doped fiber is shown in Fig. 2(b).

 

Fig. 2 Image of fabricated P-CCC fibers: (a) Cross-section of 60µm-core P-CCC fiber (left-hand image) and comparison to a standard 125μm clad single-mode fiber (right-hand image). (b) Cross-section of 55μm core Yb-doped triple-clad fiber. The structure has all-glass (fluorine-doped silica) second cladding with 0.22NA, and fluoro-acrylate-polymer third cladding with 0.45NA.

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Numerically simulated performance of a 55μm core P-CCC fiber is shown in Fig. 3. Parameters of the fiber structure in this simulation example correspond to one of the fabricated fibers and are the following: central core NA = 0.068, side core NA = 0.088, central core diameter (inscribed into octagon) 55μm, helix period 5.3mm, side-core size 10μm, side-center core separation 6.8μm. We used here a self-developed algorithm based on finite difference beam propagation method to simulate the performance of such CCC fibers with linear and torsional stress, which is reported in [24] and will be discussed in further publications. In Fig. 3(a), solid blue line and solid red line show the calculated LP₀₁ and LP₁₁ mode losses as a function of optical wavelength for such a P-CCC structure. It shows that, over ~100nm range extending from ~1020nm to 1120nm, solid blue line of LP₀₁ mode exhibits low loss (~0.2dB/m) and solid red line of LP₁₁ mode exhibits high loss (>20dB/m). In addition, it is also labeled that, the high loss region of LP₀₁ mode comes from the modal coupling from LP₀₁ mode to central core LP₈₁ mode, and the high loss performance of LP₁₁ mode comes from the modal coupling from LP₀₁ mode to central core LP₇₁ mode and central core LP₉₁ mode, which will be explained in Fig. 4. To reveal the role of the polygonal shape of the central core and the role of polygonally placed side cores, we also simulated the two hypothetical cases: (1) P-CCC structure consists of only a polygonal (octagonal) central core without presence of side cores (thick dash lines); (2) P-CCC structure consists of a round central core and 8 side cores (thin dash lines). Looking at all solid and dash lines, one can see that the overall performance of such a P-CCC structure comes from the combination of polygonal shape effect (thick dash lines) and side core effect (thin dash lines). It shows that a P-CCC structure without either a polygonal core or polygonally-placed side cores would not produce the required HOM suppressing performance, and both features are critically important. In Fig. 3(b), lowest-order modes from LP₀₁ through LP₄₁ in such a P-CCC fiber structure are simulated and shown with colored solid lines. It confirms that all modes higher than the fundamental are well suppressed in the entire E-SM wavelength range of this P-CCC fiber.

 

Fig. 3 Numerical simulation of P-CCC fibers: Simulated parameters are: central core diameter (inscribed into octagon) 55µm, central core NA = 0.068, side core diameter 10µm, side core NA = 0.088, side-center core separation 6.8µm, and helix period 5.3mm. (a) Simulated modal loss vs. wavelength for central core LP₀₁ and LP₁₁ mode are shown with blue solid line and red solid line respectively, which indicates low loss performance (~0.2dB/m) for fundamental mode and high loss performance (>20dB/m) for higher order modes from ~1020nm to ~1120nm. The simulation for only octagonal central core and no side cores is shown with thick dash lines, and the simulation for round central core with side cores is shown with thin dash lines. The phase matching points between central core modes are also marked. (b) Numerical simulation for lowest order modes from LP₀₁ through LP₄₁ in such a P-CCC fiber structure are shown with colored solid lines. It indicates E-SM performance of this P-CCC structure.

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Fig. 4 Quasi-phase matching between central-core guided modes and central-core leaky modes: The dispersion curves are shown as calculated modal propagation constant as function of optical wavelength. Due to quasi-phase matching mechanism of helically-symmetric CCC structures, each propagation constant is accompanied by its corresponding quasi-phase matching additions (product of modal number l and 2π/Λ), which is labeled in the figure. Each crossing point is below the cutoff of each higher order modes (950nm, 1050nm, and 1170nm for LP₉₁, LP₈₁, and LP₇₁ respectively), so these higher order modes are leaky modes with high propagation loss. These crossing points explained the origin of wavelength-dependent loss of central core guided modes, which also agree with the numerical simulation in Fig. 3(a).

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Figure 4 shows modal coupling between central-core guided modes and central core leaky modes. The dispersion curves (calculated modal propagation constant as function of optical wavelength) are shown to be crossing between central core guided modes LP₀₁ and LP₁₁ and central core higher order modes LP₉₁, LP₈₁, and LP₇₁ due to quasi-phase matching shown in Eq. (2). As known, when a certain fiber mode is around or below its cutoff, it becomes a “half-guided” mode with a radiating tail in the cladding and therefore presenting wavelength-dependent loss, which is usually referred as “leaky mode”. Since the higher order mode LP₉₁, LP₈₁, and LP₇₁ here have cutoff wavelengths at 950nm, 1050nm, and 1170nm respectively, they are actually behaving as leaky modes around the phase matching points (dispersion curve crossing points shown in Fig. 4). Therefore, it explains the origin of the wavelength-dependent loss of central core guided modes LP₀₁ and LP₁₁. Comparing Fig. 4 with the numerical simulation results of Fig. 3(a), we can conclude that a broad LP₀₁ loss peak extending from λ = 1150nm towards longer wavelength is associated with the LP₀₁ coupling into LP₈₁ leaky mode. Likewise, LP₁₁ loss peak at around 1030nm is unambiguously attributable to the LP₁₁ mode coupling into LP₉₁ leaky mode. One can also discern a broad loss feature centered at approximately 1200nm, and corresponding to LP₁₁ coupling into LP₇₁ leaky mode.

3. Qualitative measurements of robust single mode performance

Rigorous characterization of single-mode performance is the key for demonstrating CCC technology, since our objective is not only to increase the core size but also to achieve it with pure and robust single-mode performance independent from excitation and packaging conditions. Our modal characterization did not rely on M² measurements of the fiber output beam to characterize the robust single mode performance of CCC fibers, since it is well understood by now [19] that such beam-quality measurement is ambiguous with respect to single-mode performance of a fiber and cannot be used as an accurate criterion to define single-mode performance of a fiber. Instead, we based our CCC fiber modal characterization on the so-called spatially and spectrally (S²) resolved measurements [20]. We used this approach in two different ways. First, we used broad-band spatially resolved spectral measurement with optical spectrum analyzer (OSA) to qualitatively observe single mode performance by observing the presence or absence of spectral beating patterns. The absence of beating patterns indicates the pure single-mode performance, whereas the presence of beating patterns indicates HOM presence in the fiber output [20], as described in more detail below. Second, by using S² measurement, we quantitatively measured the HOM content at the fiber output, thus providing a solid reference for comparing performance of different fibers. For example, we could compare the performance of a large-core CCC with that of a standard LMA, as described in more detail further in the text.

Measurement setup for this modal-content characterization is shown in Fig. 5. In the setup, a standard single-mode fiber (SMF) with ~5μm core size (MFD = 6.2μm at ~1μm wavelength) is used to launch the broadband amplified spontaneous emission (ASE) signal into the input end of a test fiber at “Input Excitation” position shown in Fig. 5. Another standard SMF fiber with output end connected to an OSA is used as a spatial filter for sampling different portions of the test-fiber’s output beam at “SMF Reception” position, for which the test-fiber output beam was deliberately focused to a spot much larger than single-mode sampling-fiber MFD of 6.2μm. If the beam is multimode, then the interference between spatial modes can be observed with the SMF sampling fiber at any transverse position of the beam as spectral beating of the transmitted ASE signal measured by the OSA [20]. The flip mirror M1 in the setup is used to redirect the beam into a CCD camera for observing the near field image of the test fiber output.

 

Fig. 5 Setup for modal beating measurement used to characterize the modal output of the test fiber: Broadband ASE source is launched through SMF into the test fiber at “Input Excitation” position, where the modal excitation can be adjusted by translation stages T1 and T2. Another SMF is used to receive the beam coming out of the test fiber at “SMF Reception” position, so that T3 and T4 can adjust the SMF transverse position for sampling different parts of the beam. By adding an automatic 2-dimensional scan on T4, this setup can perform S² measurement. Flip mirror M1 and mirror M2 are used to record the near field image of the output beam with the CCD camera. L1, L2, L3, L4, L5 are collimating and focusing aspherical lenses. OSA is an optical spectrum analyzer which receives the broadband signal captured by the sampling-SMF.

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The qualitative demonstration of a pure SM output from a 55μm core Ge-doped P-CCC fiber is shown in Fig. 6. If the test beam is single mode, there will be no observable spectral beating at any transverse position of the sampling fiber. If the beam is multimode, this should manifest itself as a transverse-position dependent spectral beating. For comparison, we also used a standard 20μm LMA fiber as a reference-test fiber. This LMA is currently an industrial standard for monolithic commercial systems. Measured modal performance of this reference LMA fiber is shown in Fig. 6(a), and of the P-CCC fiber is shown in Fig. 6(b). Both tested samples were of equal length of 1.5m. Structure parameters of the tested two samples are the following:

 

Fig. 6 Varying sampling position at fiber output: Performance comparison between industry-standard 20µm LMA fiber and 55µm CCC fiber, both less than 50cm diameter loosely coiled condition. A 6µm mode field diameter sampling-SMF is used to receive light at different parts of a beam with around 40µm mode field diameter. 20µm LMA fiber is under single mode excitation condition and 55µm CCC fiber under maximum transmission condition. Blue curve corresponds to the signal received by the SMF at the peak center of the beam profile. The CCD images shown at upper-right position of each sub-plot are acquired at blue curve conditions. Red curve corresponds to the signal received by the SMF at intensity −3dB down position comparing to the peak center of the beam profile, and the black curve corresponds to the intensity −10dB down position. (a) Transmission spectrum of 20µm LMA fiber at different parts of the beam profile. It shows the further away from the peak center of the beam profile, the more pronounced spectral beating observed, which is consistent with the fact that the fundamental mode has more distribution in the center whereas the HOM have more distribution in the wings of the modal profile. (b) Despite slightly octagonal shape of the 55µm CCC fiber output modal profile (due to the shape of the central core), there are no modal beating across the entire beam profile, which indicates that it is a pure single mode beam.

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The test result is apparent that, the standard 20μm LMA fiber’s output, even when its input excitation is optimized for a fundamental mode throughput, does contain traces of the higher-order LP₁₁ mode that this fiber supports. In contrast, 55μm core CCC test shows that, when its input is optimized for maximum transmission, no higher-order modal content is observable for this length, despite the fact that the central-core nominally should support 17 modes.

An additional interesting observation worth noting here is that, a good near field image cannot guarantee a single fundamental mode output as shown in Fig. 6(a), where the near field image shows a nearly perfect Gaussian profile but the broadband spectra received by the SMF at different positions of the near field modal profile show clear modal spectral beating, which is a convincing evidence of HOM contents in this beam. Therefore, as pointed out above, just looking at the near-field image cannot indicate how good the beam is.

The qualitative demonstration of robustness of single-mode output from the same sample of the 55µm core CCC fiber and its comparison to industry-standard 20μm LMA fiber is shown in the following Fig. 7. By varying the beam-launching offset into the test fiber at “Input Excitation” position shown in Fig. 5, we can observe the sensitivity and evolution of the beam output from the test fiber with respect to the external perturbation, which is modal excitation here but could also be tested with other mode-perturbing effects such as external pressure and fiber bending. In Fig. 7(a), the recorded transmission spectra and CCD beam profiles at different excitation offsets clearly show excitation-dependent spectral beating and beam quality degradation for 1.5 meter 20μm LMA fiber, indicating its dual-mode nature and the resulting sensitivity to modal excitation conditions. This becomes much more pronounced for larger core size LMA fibers, as has been reported for 30μm core diameter LMA in [11]. In contrast, since CCC fibers have strong HOM suppression, the same test presented in Fig. 4(b) clearly shows complete absence of such spectral beating for any transverse-excitation offset. This is consistent with the near field images which always remain the same while the transmitted power decreases at increasing offset, clearly indicating that this 1.5 meter-long 55um CCC fiber behaves as a single mode fiber.

 

Fig. 7 Varying excitation position at fiber input: Experimental demonstration of robust effectively-single-mode output from 1.5 m long 55µm core CCC fiber at different lateral offset excitation positions. Figure (a) shows broad band spectra and the near-field beam images measured for four different misalignment positions (relative transverse positions of the fiber input) of the 1.5 meter 20µm LMA fiber. Figure (b) shows the same test performed with 1.5 meter 55µm CCC fiber. All transmission spectra are obtained with the sampling-SMF positioned at the peak center of the beam. (a) At 0µm position, 20µm LMA fiber is under the single mode excitation condition. At 5, 10, and 15 microns offset positions, both the beating spectra and the near-field images show the increase in HOM contents. (b) At 0µm position, 55µm CCC fiber is under the maximum transmission condition. At 20, 30, and 40 microns offset positions, no beating is observed in the transmission spectra, and the near-field images remain the same shape with only the intensity decreasing with the increasing offset, indicating that CCC fiber behaves as a single mode fiber. (See Media 1.)

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To better show the robust single mode performance of this 55um P-CCC fiber, we recorded a video of the output near field image while changing the excitation in real time at “Input Excitation” in Fig. 5. Please see Media 1 for details. It basically renders the same evidence as Fig. 7 that, this 55um P-CCC fiber truly behaves as a single mode fiber. It is worth noting that, other types of perturbations such as touching and twisting this P-CCC fiber during the measurement also showed no traces of frequency beating on the OSA.

4. Quantitative characterization of single mode performance using S² measurements

The quantitative characterization of 55μm core P-CCC fiber and the reference 20μm LMA fiber modal performance using the S² measurement is shown in Fig. 8. The two top panes, namely (a) and (b), show the modal-content measurement results under the conditions when single-mode excitation is optimized for each test fiber. The two lower panes, namely (c) and (d), show the two cases when approximately 50% of the incident power is excited to HOM at the input of each test fiber. Such S² measurements in Figs. 8(a), 8(b), and 8(d) have been obtained by scanning transversely the position of the sampling SM fiber over the complete focal-plane profile of the test beam (at the position marked as “SMF reception” in Fig. 5) and then taking the Fourier transform of each spectrum measured at each transverse-sampling point [20]. Each spatial fiber mode produces a distinct peak in this Fourier-transform spectrum, corresponding to a different group delay of each mode, and LP₀₁ modal peak is always at the zero group-delay position. For easily comparing different cases, Figs. 8(a), 8(b), and 8(d) are plotted with modal group delay per unit length. Note that all graphs shown here are raw Fourier transform data, which means there should be a difference between the HOM beating content ratio and HOM modal content ratio, because the beating is in fact composed by the electric field of both fundamental mode and HOM. As shown in Ref [20], for a peak whose peak value is α, the intensity or power ratio of this mode over fundamental mode is α², because the interference term of two electric field beating is proportional to$\left|{\tilde{E}}_1\right|\cdot \left|{\tilde{E}}_2\right|$. Simply put, the peak value on the plot represents the electric-field amplitude ratio between the HOM and the fundamental mode, so the suppression of the peak in dB should be 2 times of the value of the peak on the raw Fourier transform data.

 

Fig. 8 S² measurement for 3meter 20µm-core 0.065NA LMA fiber and 1.5meter 55µm-core 0.068NA CCC fiber with corresponding near field image taken with CCD camera: (a) Fourier transform of the beating spectrum obtained with the S² measurement of 20µm-core LMA fiber under the condition of single mode excitation and the near field image taken at fiber output. A prominent peak indicating LP₁₁ appearance in the fiber output, even though the near field image is so round and Gaussian-like, which his consistent with Fig. 6(a). (b) Fourier transform of the beating spectrum obtained with the S² measurement of 55µm CCC fiber under the condition of maximum transmission, and the near field image taken at fiber output. It is clear that all HOM are well suppressed in this case, which is consistent with Fig. 6(b). (c) 20µm LMA fiber with −3dB transmission comparing to the optimum single mode excitation condition, and the near field image taken at fiber output. Obviously, the LP11 mode is actually excited more than fundamental mode in this case, which can be verified by using the least square fitting method on the near field image. This is consistent with Fig. 7(a). (d) Fourier transform of the beating spectrum obtained with the S² measurement of 55µm CCC fiber under the condition of −3dB transmission comparing to the maximum transmission condition, and the near field image taken at fiber output. All HOM excited at this offset condition are well suppressed, and near field image looks the same except carrying less power output. This is consistent with Fig. 7(b).

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Figure 8(a) shows the result of S² measurement for 3 meter long 20µm-core 0.065NA LMA fiber, whose input alignment has been optimized to achieve the best possible single-mode output. The LP₁₁’ group delay difference per unit length relative to LP₀₁ mode is calculated to be around 0.66ps/m, which indicates the prominent peak shown to be around ~0.6ps/m can be recognized as LP₁₁ beating with LP₀₁. The group delay value of LP₂₁ and LP₀₂ relative to LP₀₁ are difficult to calculate because they are around modal cutoff, but one can validly consider the other two weak peaks in Fig. 5(a) as signatures of LP₂₁ and LP₀₂. We can see that the value of LP₁₁ and LP₀₁ beating peak is −13dB, which means the amplitude ratio of LP₁₁ relative to LP₀₁ is roughly 5%. This 5% amount of LP₁₁ electric field amplitude over fundamental mode amplitude explains why the spectrum beating measurement shows a little bit beating wiggles in Fig. 6(a). Based on the above analysis, −13dB peak value means the LP₁₁ mode is roughly −26dB in intensity.

Figure 8(b) shows the S² measurement result for 1.5 meter long 55µm 0.068NA P-CCC fiber with input excitation optimized for maximum power transmission. Based on step-index weakly guiding fiber assumption, the modal group delay differences per unit length for LP₁₁, LP₂₁, and LP₀₂ relative to LP₀₁ are calculated to be around 0.25ps/m, 0.6ps/m, and 0.73ps/m for 55µm 0.068NA step-index fibers. We believe, the little bump around 0.2ps/m is from the LP₁₁ beating peak. Since the zero-group-delay peak LP₀₁ and beating peak LP₁₁ are almost overlap with each other, the peak value of LP₁₁ should be a bit lower than it appears to be, so a reasonable estimate of the LP₁₁’s peak value should be below −15dB, which means the intensity ratio of LP₁₁ mode is below −30dB. The fact that Fig. 6(b) shows no trace of spectrum beating means the amplitude ratio of LP₁₁ mode most likely below −15dB, but we cannot prove that since it is not well resolved. It is true that using long length of fiber can hopefully resolve LP₁₁ mode better, but experiments show that this fiber is stripping out HOM so efficiently that longer than 2 meter fiber is too long for the HOM to be correctly detected. We believe the two peaks around 0.4ps/m and 0.65ps/m are contributions from LP₂₁ and LP₀₂, and we do not know why they deviate from the step-index modal group delay difference values, which may be the results of polygonal shape or quasi-phase-matching resonances all over the detecting wavelength range. Basically, we see all HOM contents are well suppressed below −30dB. Up to now, the comparison between Figs. 8(a) and 8(b) is not that distinguishing, but we will see the huge difference when comparing Figs. 8(c) and 8(d) in the following.

Figure 8(c) shows output beam intensity distribution for the 3m long reference 20μm core LMA fiber with its input misaligned for −3dB lower power throughput compared to single-mode excitation. The data is taken through a SM “sampling” fiber at the output of the test fiber (see the experimental setup in Fig. 5). In this case, the −3dB misalignment for the LMA fiber produces so large ratio of LP₁₁ mode output that S² algorithm would fail to work properly. Instead, we used least square best fitting method to obtain the estimate of modal content ratio to be 45% LP₀₁ and 55% LP₁₁. This observation is consistent with the spectrum beating measurement and corresponding near field image on Fig. 7(a). Obviously, misalignment of the fiber launching condition can produce more HOM than the fundamental mode, which is expected for multimode fiber behaviors. Then, the question is whether or not the E-SM large core P-CCC fibers can still only output fundamental mode at HOM-preferred launching positions, which is illustrated in Fig. 8(d).

Figure 8(d) shows S² measurement for the 1.5m long 55µm P-CCC fiber sample with input misaligned at −3dB power transmission compared with the maximum transmission, which means ~50% HOM excitation at the input is ensured. One can see that fiber output still has no prominent HOM content, which is a consequence of HOM stripping along the CCC fibers. This observation is consistent with the spectrum beating measurement in Fig. 7(b) and Media 1. Even though Fig. 8(d) shows a bit more HOM content than Fig. 8(b) because of the fact that more HOM is intentionally excited, one can see that HOM contents are suppressed below −15dB of amplitude ratio and thus −30dB of intensity ratio. It means that this 55μm core P-CCC fiber passes TIA-455-80-C Industrial Standard for SM operation [18], which requires that HOM content at the fiber output would be below −19.3dB level though a 2 meter piece of fiber, so this large core fiber is single-mode fiber according to the industry-accepted definition. For all the measurements in Figs. 8(b) and 8(d), the CCC fiber is coiled to 50cm diameter. However, coiling to 30cm diameter or keeping fiber straight produces the identical results.

5. Laser demonstration using Yb doped 55μm core polygonal CCC fiber

Modal characterization described above requires broadband test signal. This makes it difficult to apply these techniques to an operating CW or pulsed fiber laser, which is typically having a relatively narrow-band signal. Therefore, for modal characterization of an operating fiber laser with such an Yb-doped 55μm triple-clad P-CCC fiber, we resorted to measuring M² of the output beam.

A simple CW laser configuration is set up with a 3.5 meter long sample of 55µm Yb-doped triple-clad P-CCC fiber coiled at 50cm coiling diameter, whose geometry is shown in Fig. 2(b). One fiber end facet is straight cleaved to provide ~3.5% Fresnel back-reflection, and other end facet is aligned with an external mirror for a complete ~100% back-reflection. This fiber is end-pumped at 976nm with up to 49W of pump power. The pump power coupling efficiency is about 90%, and the measured residual pump transmission is about ~10%. The laser emission wavelength is centered at 1030nm, and the measured laser slope efficiency versus absorbed pump power is 57.1% as shown in Fig. 9. The relative low slope efficiency might be due to the rough alignment of the high-reflection end mirror.

 

Fig. 9 Lasing performance of 55µm P-CCC fiber samples: The blue dash line represents the data of laser power versus absorbed power. The red solid line represents the linear fit of the blue dash line, which indicates the slope efficiency with this fiber sample is 57.1%. The M² is measured to be 1.12.

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Nevertheless, we preformed the M² measurement and the measured M² value is 1.12. This is consistent with the anticipated effectively single-mode performance for this Yb-doped P-CCC fiber. Further work of using this 55um core P-CCC fiber in high energy pulsed laser systems has been reported [25], where single mode 9.1mJ and 10ns pulses are generated through a Master Oscillator Power Amplifier (MOPA) configuration.

6. Conclusions

In this paper we have demonstrated that, for fibers with core diameters exceeding ~50μm, it is possible to achieve modal performance practically equivalent to a single-mode operation using all-glass index-guiding CCC fiber structures. We have shown the geometrical configuration, numerical simulation, and working principle of multiple-side-core Polygonal CCC fibers with 55μm and up to 60μm core diameters. By performing series of rigorous modal-content measurement and comparing measured performance of these fibers to that of an industry-standard 20μm core LMA fibers, we have verified the robust single-mode operation of these fibers. More specifically, these large-core P-CCC fibers can pass the TIA-455-80-C Industrial Standard for SM operation and show far superior modal performance than conventional 20μm LMA fibers. Furthermore, as known, CCC fibers are completely compatible with the monolithic integration due to their all-glass fiber structure suitable for standard laser fusion techniques and fiber flexibility due to relatively large NA (i.e. >0.06) of the central core to maintain fiber packaging advantages. In addition, CCC fibers also offer other experimentally shown advantages such as design options to provide SRS suppression [26–28] and polarization maintenance without stress rods [29, 30]. Therefore, large-core CCC fibers offer a practical approach for building high-power/high-energy integrated fiber laser systems.