Abstract
1. Introduction
Large-mode-area (LMA) fibers working with advanced mechanisms have been established as promising candidates for next-generation high-power fiber lasers, benefitting from their potentials in mode area scaling, higher nonlinear threshold, and feasibilities for some functional applications[
SM operation with near-diffraction-limited output places further requirements on the performances of the LMA fiber. With the development of characterization techniques, a large quantity of researches have been focused on spatiotemporal analysis of the modal characteristics[
In this Letter, by employing an in-house fabricated multi-resonant AS-PBGF, the guidance property of AS-PBGF within the entire third PBG is thoroughly investigated and analyzed in detail. Under the premise that the SM behavior is quantified by the spatially and spectrally resolved imaging () method, the wavelength dependence of the beam quality covering the third PBG is simulated and experimentally measured. The evolution of exhibits similar band-spread (U-shaped) distribution to the PBG distribution. Further theoretical calculations also extend the U-shaped tendency from the third PBG to other PBGs. In addition, by comparing with the representative results in the AS-PBGF field, the universality of the findings in this work is demonstrated profoundly.
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2. Experimental Results
The fiber to be investigated is an in-house fabricated multi-resonant AS-PBGF, whose cross-section image is shown in the inset of Fig. 1. In this fiber, multiple-cladding-resonance defect cores are employed to enhance the HOMs leakage[
Figure 1.Relative losses of the 5-m-length fiber. Inset shows the cross section of our multi-resonant fiber.
The schematics of our experimental setups for measurement and SM performance evaluation are depicted in Figs. 2(a) and 2(b), respectively. As illustrated in Fig. 2(a), the tunable source used for evaluation integrates a supercontinuum light source (YSL Photonics, SC-OEM) and an acousto-optic tunable filter (AOFT). By adjusting the working frequency of the AOFT, the output wavelength can be artificially controlled to cover the third PBG. Light from the tunable source is launched into the fiber under test by using a butt coupled SM fiber (SMF). To achieve the optimized FM excitation, the SMF is spliced with the AS-PBGF under test directly. In this case, the bending radius of the AS-PBGF is coiled to about 40 cm, so the spectral compression at the high-frequency edge can be avoided to some extent whilst imposing effective HOMs suppression.
Figure 2.Experimental configurations constructed for (a) M2 and (b) S2 measurements, respectively. SMF, single-mode fiber; FUT, AS-PBGF under test; L, L1, and L2, aspherical lens; M1 and M2, reflective mirror; BQA, beam quality analysis; ASE source, amplified spontaneous emission source; PBS, polarizing beam splitter; CF, collecting fiber; OSA, optical spectrum analyzer.
The evolution of beam quality factor versus wavelength in the third PBG is measured firstly based on the setup shown in Fig. 3(a). As represented in Fig. 3(a), we can see the significantly varies with the wavelength in the whole transmission band, especially for the edge regions of the working PBG. The left ordinate scale of Fig. 3(a) has the same definition as the one in Fig. 1. The relative loss curve (black curve) of the third PBG in Fig. 3(a) is a subset of Fig. 1, which represents the third PBG data that is extracted from Fig. 1 specially. Similar to the distribution of PBG curves, the wavelength dependence of exhibits the band-spread (U-shaped) feature, but the two curves are not fit entirely. Overall, according to the variation character, the evolution curve of in Fig. 3(a) can be divided into three parts, labeled as short-wave anomalous edge (SAE), normal band (NB), and long-wave anomalous edge (LAE), respectively. The above three regions cover 982 nm to 1000 nm, 1000 nm to 1070 nm, and 1070 nm to 1185 nm, respectively. At the high-frequency edge of the third PBG, a sharp increment of appears with the wavelength shifting to a shorter wavelength in the SAE region. The measured rapidly increases to over 2.0 after passing the critical wavelength of near 984 nm, and more details are shown in Fig. 3(b). Within the region of NB, the measured keeps relatively stable at the level of less than 1.2, which is similar to the conventional perception in SIF with SM operation[
Figure 3.Measured M2 results under different wavelengths. (a) The U-shaped curve covering the third PBG and (b) partial magnification of the results in the SAE region.
Based on the knowledge of modal characteristics in SIF, the poor value normally means considerable contents of HOMs. To monitor the modal contents of the output profile, the method is employed to verify the mode spectrum of the output. The setup for performing measurements[
Figure 4 represents the results of the measurements within the different regions of Fig. 3(a). The Fourier transform extracts and averages all spectrum data results in the curve of Fig. 4. The inset shows the reconstructed beam profile of the fundamental frequency, in which the FM characteristic is well identified. For the first measurement within the NB region, the wavelength sweeping range is between 1035 and 1050 nm. This wavelength window results in a high time differential resolution, which is more than sufficient to allow the characterization of the 5-m-length AS-PBGF sample. Similarly, the second measurement in the LAE region selects the wavelength range from 1070 nm to 1085 nm. On the basis of the Fourier transform results, we found no HOMs peaks, so we can only reconstruct the FM profile, demonstrating the SM behavior of the realized fiber under current test conditions. For the SAE region, the loss is too high to collect the signal with reasonable signal-to-noise ratio, even if we try to utilize the supercontinuum source with higher power than the ASE source. However, according to the leakage guidance mechanism of the HOMs, we can reasonably expect that the FM operation is also valid in the SAE region when the other ranges of the whole working PBG are verified to be operated in the FM.
Figure 4.S2 data analysis within the NB and LAE regions with a 5-m-length fiber when the coiled diameter Φ = 80 cm.
The U-shaped profile of the beam propagation factor in AS-PBGF indicates a potential obstacle in maintaining a lower beam quality factor while pursuing the SM operation. According to the evolution tendency demonstrated here, robust SM operation with a lower value is more convenient to be achieved in the NB, which is near the short-wave edge of the third PBG. For the future designs of AS-PBGF, by controlling the PBG bandwidth appropriately, it is possible for us to locate the operating wavelength within the NB region. On the one hand, the beam quality factor of the signal emitting from AS-PBGF should be optimized by selecting a suitable wavelength range, even if the SM operation is guaranteed. On the other hand, if the beam quality factor of the light from the AS-PBGF is measured to far outweigh one, we should be careful enough to draw a conclusion that there should be many HOM contents if we do not have the mode decomposition results.
3. Simulation and Discussion
Furthermore, according to the measured structural parameters, we reconstruct the structure of the fabricated AS-PBGF for simulation. Theoretical distributions of PBGs and beam quality factor of the FM are calculated by using the finite element method (FEM) and free-space transfer function[
Figure 5.Theoretical calculations of PBGs distribution and beam quality factor M2 based on the measured structural parameters.
Figure 6.Theoretical calculations of FM profile and wavefront distribution at 870 nm, 1030 nm, and 1140 nm, respectively.
In view of the unusual modal characteristics of the AS-PBGF compared to conventional SIF, we will further discuss the influence of the FM electric field on the beam propagation property. The FM electric field in the conventional SIF normally maintains a near Gaussian intensity distribution with a flat wavefront, and the value of is related to the normalized frequency V to some extent. To be specific, the is considered to be close to one when V is greater than 1.5[
To extend the universality of the wavelength dependence for in the AS-PBGF, two representative results in this field are selected for comparison. The first structure is the “mixed-cell” scheme reported by Gu et al.[
Figure 7.Beam propagation property of the two representative structures. (a) The “mixed-cell” structure reported in Ref. [
4. Conclusion
We have theoretically and experimentally verified the spectrally U-shaped profile of the beam propagation factor in the AS-PBGF. The measurement result of in the third PBG shows a band-spread (U-shaped) feature that is similar to the PBG distribution. In the different regions of the third PBG, the measured evolves with different trends. According to the simulation results, the same conclusion is portable when extended to other PBGs. By comparing with two representative structures in this field, the universality of the wavelength dependence of in the AS-PBGF is further verified to some extent. In view of the future designs of AS-PBGF or other PBG-guided fibers, this finding seems essential to instruct a scheme for maintaining the beam quality factor while optimizing its SM behavior.
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