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Abstract
Mid-infrared fiber combiners have great potential in power and spectral combination. However, studies on mid-infrared transmission optical field distributions using these combiners are limited. In this study, we designed and fabricated a 7 × 1 multimode fiber combiner based on sulfur-based glass fibers and observed approximately 80% per-port transmission efficiency at 4.778 µm wavelength. We investigated the propagation properties of the prepared combiners and explored the effects of transmission wavelength, output fiber length, and fusion deviation on the transmitted optical field and beam quality factor M2. Additionally, we assessed the effect of coupling on the excitation mode and spectral combination of the mid-infrared fiber combiner for multiple light sources. Our results provide an in-depth understanding of the propagation properties of the mid-infrared multimode fiber combiners, which may find applications in high-beam-quality laser devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, mid-infrared (Mid-IR) optics have attracted significant research interest, whereby Mid-IR light sources are useful in many applications, including biosensing, environmental monitoring, homeland security, and medical diagnostics [1–11]. However, only a few high-power sources are available in the Mid-IR range, and most are restricted to narrow wavelength ranges and low power, such as CO and CO2 laser emissions and Mid-IR quantum cascade lasers (QCLs) [12]. For example, QCLs are widely used light sources at Mid-IR wavelengths [13–16] and are currently available at an average power in the low range [17]. The multimode fiber combiner may be the preferred choice for significantly enhancing higher powers in the Mid-IR band. The multimode fiber combiner allows for an incoherent higher-power and spectral combination of multiple light sources, which are particularly attractive in the mid-wave and long-wave IR wavelength ranges [12]. In addition, the multimode fiber combiner, benefiting from a larger core diameter, can support higher laser power compared with its singlemode counterpart, which is more conducive to coupling the Mid-IR free-space laser. However, highly multimode devices have challenges, such as maintaining high laser brightness because a larger number of modes could diminish the brightness. The power combiner must be carefully designed to satisfy the brightness requirements of the light source for directed beam transmission [18]. Therefore, achieving higher power transmission and beam quality in multimode fiber combiners with large diameters remains one of the main challenges.
Additionally, most silica-based fibers have a large absorption loss in the Mid-IR band, which limits the application of such fibers in Mid-IR beam combinations [19]. According to current studies, chalcogenide fibers, such as arsenic sulfide (As2S3), exhibit the advanced properties of long-term environmental stability [20], high-power handling [21,22], and a wide transmission window extending to 6 µm [23,24]. In 2013, Gattass et al. reported a 7 × 1 structured sulfur-based glass fiber combiner using an As2S3 multimode fiber as the input fiber, which is capable of transmission at Mid-IR wavelengths [12]. Fluoride fibers are a mature technology suitable for transmitting light in the Mid-IR spectral range. In 2022, Annunziato et al. designed and characterized a 3 × 1 fused fiber combiner based on multimode step-index fluoroindate optical fibers (InF3), achieving a power transmission efficiency of 1–5 µm [25]. Regarding the beam quality investigation of multimode combiners, Baer et al. fabricated a 7 × 1 multimode fiber combiner, whose beam profiles in the near field for the fabrication steps were measured and analyzed [26]. Majumder et al. investigated the problem of higher-order mode leakage in the tapered region of a multimode pump combiner [27]. However, the underlying understanding of the transmission light optical field distribution and the beam quality of a multimode fiber combiner in the Mid-IR region, which is the objective of this study, is largely unknown.
In this study, we designed and fabricated a 7 × 1 fiber combiner grounded on a low-loss As2S3 multimode step-index fiber developed and measured the corresponding transmission efficiency at Mid-IR wavelengths. The loss spectrum of an As2S3 multimode step-index fiber fabricated in our laboratory is shown in Fig. 1. We numerically simulated the Mid-IR transmission optical field of such fiber combiners, in which the effects of the transmission wavelength, output fiber length, and fusion deviations (off-axis offset and tilt angle) on the optical field performance were systematically and deeply explored and studied theoretically. In addition, the corresponding optical field and beam quality factor M2 of the combiners under various conditions were experimentally measured and analyzed, which partially matched our theoretical simulation results.
2. Design and preparation of multimode mid-infrared fiber combiner
In our experiments, a 7 × 1 multimode fiber combiner was fabricated by inserting seven multimode step-index As2S3 fibers into a low-refractive-index tube that was heated and tapered at a certain temperature. Figure 2(a) shows the fabrication process. By using the fused taper method at a low temperature (200 °C) based on the Vytran processing station (GPX3850), the fiber bundle with a certain taper length was obtained, as shown in Fig. 2(b). Thereafter, a suitable output fiber was fused with the fiber bundle to achieve the completed fiber combiner. Figures 3(a–c) show the multimode fiber combiner with the FC/PC connectors and the end face of the input fiber bundle after the tapering and fusion processes. Table 1 illustrates the measured power transmission efficiency of the combiner at a wavelength of 4.778 µm, and an average transmission efficiency of seven ports of approximately 77.2% was achieved.
Fig. 2. (a) Fibers threaded into a tube and tapered down under tension and heat. (b) Input fiber bundle after tapering.
Fig. 3. (a) Combiner with FC/PC connectors. (b) End of the fiber bundle after tapering. (c) Fusion of input fiber bundle (right) and output fiber (left).
Table 1. Port transmission for 7 × 1 multimode combiner measured at a wavelength of 4.778 µm
3. Simulation of the multimode mid-infrared fiber combiner
3.1 Combiner numerical model
Because the transmission of the optical field in the combiner is closely related to the beam quality of the associated output laser, we built a mathematical model of a 7 × 1 multimode combiner to achieve an in-depth theoretical understanding. The adopted numerical analysis method is the commonly used finite-difference beam propagation method (FD-BPM) [28,29]. This method analyzes the optical field propagation in the waveguide by numerically solving the Helmholtz equation, which has the advantages of high speed and high efficiency and is widely used in numerical studies of fiber taper devices [30–33]. The fundamental principle of FD-BPM is as follows: it divides the waveguide cross-section into many square lattices and expresses the difference equation in each lattice, then adds a transparent boundary condition [34,35], which obtains the field distribution of the entire cross-section. Thus, the final field distribution over the entire waveguide was obtained.
The Scalar Helmholtz equation in column coordinates yields:
The structure of the 7 × 1 multimode fiber combiner is shown in Fig. 4. We assume that the seven fiber claddings are arranged in close proximity to each other and are infinite, and the influence of the cladding boundary on optical field propagation can be ignored. Considering that the taper ratio was small, the laser was confined to the core, and no coupling occurred between the fibers. For the output fiber, the core diameter and numerical aperture (NA) must be sufficiently large to allow the output optical field at the bundle end to maintain brightness conservation. However, such a core diameter must be sufficiently small to obtain better output laser beam quality. The parameters of the input fiber, taper ratio, and optical field are listed in Table 2. Using this model, the transmission optical field in a multimode fiber combiner was numerically investigated. Despite the above model not being able to completely reflect the actual results, the relationship between the optical field and certain combiner parameters can be correctly summarized.
Table 2. Parameters of the input fiber, taper ratio, and optical field
3.2 Numerical simulation results and discussion
In this section, we discuss the calculated results of optical field propagation in a typical multimode fiber combiner with a taper length of 2.5 cm (the taper is not linear). The core diameter of the output fiber is 350 µm, and the wavelengths of the input optical field are in the 4 µm range. The evolution of the optical field power distribution in the TFB is shown in Fig. 5. We assume that the single-mode 4.20 µm laser is ideally inputted into seven ports simultaneously (axial normal incidence), as shown in Fig. 5(a). If the effects of factors such as fiber bending are abandoned, the multimode input fiber only excites the axisymmetric LP0, n modes and outputs an optical field from the fiber bundle, as shown in Fig. 5(b).
Fig. 5. Laser field of the combiner at the following: (a) Input Gaussian light. (b) Final end face of the tapered bundle.
The output optical field from the fiber bundle is then input into the multimode output fiber, where different proportions of higher-order modes are excited, and the corresponding energy distributions on the cross section of the multimode fiber change with the output fiber length. Figures 6(a–d) show the optical fields of the output fibers with lengths of 2, 3, 4, and 5 cm, respectively. Furthermore, the energy distribution is relatively concentrated, and the beam quality remains optimal for an output fiber length of 5 cm. These variations in the optical field with transmission distance may be attributed to mode coupling in the multimode fiber. In addition, the phase of the mode changes periodically with the length during the transmission of the multimode fiber, and the optical field also changes with the transmission distance, whereas the total energy of the fiber cross-section at any position does not change. Therefore, the correct length of the output fiber must be chosen to obtain a good beam quality from the combiner without affecting the package because of its long length.
Fig. 6. Laser field of the combiner at the following: (a), (b), (c), and (d) output fiber with 2, 3, 4, and 5 cm, respectively.
The relationship between the wavelength and the normalized frequency is:
The total number of modes supported by a multimode fiber is approximately ${\textrm{V}^\textrm{2}}\textrm{/2}$, where $V\textrm{}$ is the normalized frequency, $\lambda $ is the transmission wavelength, a is the core radius, and ${n_1}$, ${n_2}$ are the refractive indices of the core and the cladding, respectively. But the actual number and proportion of modes in a multimode fiber are determined by the input field, input conditions, and multimode fiber parameters. Because the transmission constants β of the guided modes and the phase of the transmission field are highly related to the transmission wavelength, different optical fields in multimode fibers will be affected by different transmission wavelengths. Furthermore, the single-mode laser at the input fiber and the bundle end at the output fiber are both ideal inputs. Because both the wavelength and output fiber length affect the phase of the transmission optical field, the output fields of the three wavelengths with a 5 cm output fiber were compared. Figure 7 shows the output optical field of the combiner at transmission wavelengths of 4.25, 4.35, and 4.45 µm. The optical field on the cross-section of the combiner is affected by the transmission wavelength. Considering the complex structure of the combiner, we compute the mode spectrum to determine the modes supported by the multimode combiner at different transmission wavelengths. Figure 8 shows the spectrum of the partial modes in the multimode combiner, indicating that the wavelength is related to the mode composition and proportion of the corresponding output field.
In practice, both the spatial coupling from the single-mode laser to the input fiber and the tapered fiber bundle, which is fused to the output fiber, inevitably exhibit deviations that may significantly destroy the optical field of the combiner. Therefore, we numerically explored the dependence of the deviation parameters (off-axis offset and tilt angle) on fiber combiner performance. When the Gaussian beam is selected as the input source at different off-axis offsets, the proportions of excited modes LP0, 1-4 in the input fiber are as shown in Fig. 9(a). The proportions of LP0, 1-4 decreases gradually and finally transfer to the higher-order modes. The total number of excited modes slightly increased when the off-axis offsets increased, and the output field distribution became chaotic. Furthermore, considering the input Gaussian beam at different tilt angles, the proportions of modes LP0, 1-4 in the input fiber accumulated, as shown in Fig. 9(b). However, as the input angles slowly increase from 0 to 0.349 rad (20°), the proportion of modes LP0,1-4 hardly changes, and modes LP0, 3 and LP0, 4 exhibit a sudden change only when the angle reaches 0.524 rad (30°). Thus, we conclude that the transmission modes in the multimode combiner are more sensitive to the off-axis offset than their counterparts under a tilt angle.
Fig. 9. Proportion of LP0, 1-4 modes excited in the multimode input fiber. (a) Gaussian beam is input at different off-axis offsets. (b) Gaussian beam is input at different tilt angles.
In addition, fusion deviations between the tapered fiber bundle and the output fiber can degrade the transmission field. Compared with the coupling effect of the Gaussian beam, as discussed above, the input optical field, which is the output field of the tapered fiber bundle, is more complex, the diameter of the multimode output fiber becomes larger, and the total number of modes and the proportion of higher-order modes increase accordingly. The computed optical field of the output fiber at different off-axis offset ($\Delta \textrm{x}$) is shown in Fig. 10. Furthermore, the output field features good symmetry when $\Delta \textrm{x = 0}$, while such symmetry becomes worse and worse at a larger off-axis offset, and the output field becomes chaotic. In addition, because of the increase in the off-axis offset, the axisymmetric modes LP0, x are transformed into nonaxisymmetric higher-order modes, which makes the output field complex.
Figure 11 shows the dynamic evolution of the output field with different fusion tilt angles $({\Delta \phi } )$. Displaying is also important because the energy distribution of the output optical field shifts and the beam quality drops with increasing tilt angle. The output field in the multimode combiner was more sensitive to the off-axis offset than to the tilt angle. However, the fusion tilt angle has a greater influence on the transmission modes of the multimode combiner than the coupling angle. Therefore, to reduce the high-order mode and obtain high beam quality, minimization of the fusion deviation (off-axis offset and tilt angle) is critical.
4. Measurements and discussion
4.1 Transmission optical field and beam quality factor M2
Owing to the complicated waveguide structure of the combiner and the lack of high-power Mid-IR sources, several difficulties are encountered in the quantitative measurement and investigation of the transmission optical field of a multimode combiner, and a systematic report on this aspect is currently unavailable. Benefiting from the use of the Mid-IR source and the beam profilers (WinCamD-IR-BB), we successfully measured and characterized the optical field and beam quality factor of the self-developed 7 × 1 multimode fiber combiner in such bands. Figure 12 shows a schematic of the experiments. The input fiber length of the 7 × 1 fiber combiner was approximately 90 cm, the taper length was approximately 2.5 cm, the incident field is a single-mode laser (4.20 µm) and the other relevant parameters are listed in Table 2. Figure 13 shows the far-field distribution of the output optical field at the bundle end when each port is input individually. The measured M2 values of the seven tapered multimode input fibers are listed in Table 3. Furthermore, these are the minimum values measured under the current parameters, including the taper ratio and transmission wavelength. The difference in the optical field distribution and M2 at each port can be attributed to two main reasons. Conversely, because the Mid-IR QCL used was a spatial output light, the different coupling conditions for different multimode input fibers could result in different numbers and proportions of the modes. However, multimode input fibers exhibit different degrees of deformation during the tapering process, leading to the generation of higher-order modes and mode coupling.
Fig. 12. Schematic of the experimental set-up used for 7 × 1 combiner characterization in the Mid-IR.
Table 3. The M2 of seven input fiber after tapering
The final output optical field of the combiner was experimentally measured with changes in the output fiber length. When the input optical field (4.20 µm) is input to one port, the output optical field is shown in Figs. 14(a–d) at output fiber lengths of 2, 3, 4, and 5 cm, respectively. The diameter of output fiber is about 350 µm. The optical field distribution varies significantly, which is mainly caused by mode coupling. When the fiber length is further increased and under the influence of various conditions, such as bending, pressure, vibration, and deformation, the number of modes gradually increases, and the interference among the modes is thus enhanced. To accurately compare the beam quality of the output light, the value of beam quality factor M2 was also measured, which oscillates between 18.81 and 28.60 using the 4σ method to define the beam diameter, as shown in Table 4. M2 reached its maximum value when the output fiber length was 4 cm, indicating the worst beam quality and the most dispersed energy distribution on the fiber cross section. The value of M2 was minimized when the output fiber length was 5 cm, indicating that the energy distribution on the fiber cross section was relatively concentrated. Therefore, selecting an appropriate length of the output fiber can significantly improve the beam quality of the output light.
Table 4. M2 of combiner with different output fiber
We experimentally explored the changes in the output optical field in a multimode combiner with different transmission wavelengths (Mid-IR). The input optical field of one port was tuned at the range of 4.25–4.45 µm and the length of output fiber is 5 cm, the output field of the multimode combiner was measured, as shown in Fig. 15. In the structure of the combiner, the transmission wavelength affects the phase of the multimode transmission fiber and changes the mode composition and proportion. By measuring the value of M2, the most striking result is the emerging of the smallest M2 (M2xy = 23.78/23.05) of the transmission wavelength at 4.35 µm.
To study the relationship between the fusion deviation and the performance of the beam combiner, we further measured the evolution process of the output optical field under certain controllable deviations and two situations: off-axis offset and tilt angle. The transmission wavelength of 4.30 µm, and the length of output fiber of 3 cm were chosen. The input optical field was within the core range throughout the variation, and the effect of the power transfer efficiency was ignored. Figures 16(a) and (b) show the variation in the output optical field with the off-axis offset and tilt angle of the input optical field, respectively. Different off-axis offsets and tilt angles of the input field can stimulate different numbers and proportions of the higher-order modes, ultimately causing changes in the output optical field. The optical field distribution of the combiner was also more sensitive to the off-axis offset than to the tilt angle, and the experimental observations agreed well with the numerical simulation, as shown in Fig. 16.
Fig. 16. Output optical field of combiner (a) with different off-axis offsets of input optical field. (b) with different tilt angles of input optical field.
Despite being limited by the Mid-IR light source, structure of the combiner, preparation defects, and experimental errors, our experimental results still match the numerical simulations to some extent, and our results could further guide and control the fabrication of high beam quality sulfide fiber combiners.
4.2 Spectral combining
In addition to power combining, the multimode fiber combiner has significant application potential in spectral combining, which allows for a wavelength combination of multiple spatially isolated sources with a single emission aperture. In contrast to single-mode wavelength multiplexers, multimode fused-fiber combiners do not display interferometric oscillations of transmitted signals with varying wavelengths [36]. By coupling two distinct QCL sources at Mid-IR wavelengths (4.350 and 4.778µm) and an erbium-doped fiber amplifier at 1.550 µm wavelength, and measuring the output spectrum of the combiner, we have experimentally demonstrated that our self-developed multimode fiber combiner can realize the multi-wavelength beam combination in coverage from near-infrared to Mid-IR. As shown in Fig. 17, three lasers with different wavelengths have achieved an excellent all-fiber integrated spectral beam combination by using the multimode fiber combiner, displaying the advantage of the compact and stable structure of the multimode fiber combiner compared to that of a spatial light structure.
5. Conclusion
In this study, the 7 × 1 arsenic sulfide multimode fiber combiner was fabricated, and the measured power transmission efficiency of the combiner was approximately 80% at 4.778 µm wavelength. The Mid-IR transmission optical field of the fiber combiner was also systematically studied both theoretically and experimentally. We found that the output optical fields of such combiners are greatly influenced by the transmission wavelengths and output fiber lengths; the optimal beam quality was measured with an output fiber length of 5 cm and a transmission wavelength of 4.35 µm. Because of the excitation of higher-order modes in a multimode fiber combiner, fusion deviations (off-axis offset and tilt angle) significantly affect the performance of the combiner. This study can guide and control the fabrication of high-performance Mid-IR sulfide fiber combiners, thereby laying the foundation for possible applications in high-power and multispectral laser devices.
Funding
National Natural Science Foundation of China (61935006, 62005312, 62090065); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022409); Key Research and Development Projects of Shaanxi Province (2022GY-423); Open Research Fund for development of high-end scientific instruments and core components of the Center for Shared Technologies and Facilities, XIOPM, CAS..
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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