Open AccessCommunication

Optimization Design and Simulation of Coin-Slot-Type Anti-Resonant Fiber Structure for 2 μm Transmission

Boyue Zhang

^1,2,

Zhaoyang Tian

¹,

Yu Li

¹,

Xinyang Su

^1,*

Hongxiang Chi

¹,

Zikun Nie

¹,

Xiaoyu Luo

¹,

Bohan Li

¹,

Tianran Sun

Sergey Sarkisov

⁴

and

Sergey Kobtsev

⁵

School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China

Research Institute for Road Safety of the Ministry of Public Security, Beijing 100062, China

Beihang-Goertek Joint Microelectronics Institute, Beihang University, Qingdao 266000, China

⁴

Synchrotron Radiation Detector Laboratory, R&D Center “Advanced Electronic Technologies”, Tomsk State University, Tomsk 634050, Russia

⁵

Division of Laser Physics and Innovative Technologies, Novosibirsk State University, Novosibirsk 630090, Russia

Author to whom correspondence should be addressed.

Photonics 2024, 11(12), 1109; https://doi.org/10.3390/photonics11121109

Submission received: 21 October 2024 / Revised: 20 November 2024 / Accepted: 22 November 2024 / Published: 23 November 2024

(This article belongs to the Special Issue Advanced Fiber Laser Technology and Its Application)

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Abstract

In this work, we propose a new type of hollow-core anti-resonant fiber (HC-ARF) structure called a coin-slot structure. In this type of structure, two more layers of glass walls are added into the outer cladding capillary, which can effectively prevent light from leaking out of the fiber. In aiming to explore the influence of the outer resonant tube on loss at a wavelength of 2 μm, the fundamental mode loss, high-order mode loss, and higher-order mode extinction ratio (HOMER) under different geometric parameters are studied.

Keywords:

hollow-core anti-resonant fiber (HC-ARF); higher-order mode extinction ratio (HOMER); high-order mode (HOM)

1. Introduction

Different types of optical fiber have their unique advantages and disadvantages. The earliest developed type of optical fiber, traditional solid-core optical fiber, is the most mature in terms of its technology and is used in a wide range of applications, including optical communications, defense, medical surgery, etc. The light-guiding principle of solid-core optical fiber is based on total internal reflection, confining light within the highly refractive index core material. However, the nonlinearity, dispersion, and light damage of solid-core optical fiber materials also limit their development, which makes researchers have to turn their attention to other types of fiber such as hollow-core optical fiber. Compared with traditional solid-core optical fiber, hollow-core optical fiber can ensure that light is transmitted in an air core. To obtain a fiber with better performance, researchers have conducted in-depth research on the design of hollow-core fiber structure. Thus, the structure of the hollow-core fiber now comes in various forms. In 1986, a one-dimensional anti-resonant reflective optical waveguide model was proposed by Duguay et al. [1]. This was a completely new optical waveguide model at the time, and it enabled light to propagate through the material in the core region. In 1996, photonic crystal fiber was first reported, which greatly promoted the development of hollow-core fiber [2]. Since the first photonic-bandgap hollow-core fiber (HCF) was successfully drawn in 1999 [3], its structure has been improved, and Kagome-type hollow-core fiber has also been proposed [4]. The structure of this fiber is similar to that of photonic-bandgap fiber, but it does not support photonic-bandgap transmission. Furthermore, compared with photonic-bandgap fiber, Kagome fiber can simultaneously transmit several optical frequency bands over a wider spectral range. After that, researchers also proposed a light-guiding mechanism for the anti-resonant reflective optical waveguide (ARROW) [5]. As a newly developed type of fiber, hollow-core anti-resonant fiber (HC-ARF) has since become a new focus of research. When the inner structure of the resonant tube of HC-ARF has a negative curvature, its light-guiding efficiency is higher, and the outer tubular structure has little effect on the performance of the fiber [6,7]. The loss of Kagome HCF has reportedly dropped dramatically from a few dB/m to tens of dB/km with a negative curvature shape [7]. Therefore, HC-ARF has gradually become the focus of research.

The study of HC-ARF is mainly focused on loss reduction, and its structure has experienced a development process from simplicity to complexity. Pryamikov et al. achieved ultralow-loss transmission in HC-ARF for the first time [8]. At the same time, they also proposed a core profile with negative curvature for the first time, which can reduce the confinement loss to a small order of magnitude. Kolyadin et al. proposed that the intersection between cladding resonant tubes generates corresponding resonance losses based on the previously designed HC-ARF, thereby increasing the loss of optical fiber transmission. Therefore, the structure of hollow-core fiber is mainly designed as a node-free negative curvature type in the drawing process [9]. Belardi et al. created double-layer nested cladding resonant tubes in HC-ARF for the first time; by adding a layer to ordinary single-layer resonant tubes, the limiting loss and bending loss were greatly reduced [10]. An important next step was performed by Poletti et al., who introduced nodeless HC-ARF, combining the advantages of photonic-bandgap fiber and anti-resonant fiber (ARF) to achieve ultralow loss, wide bandwidth, and effective single-mode operation [11]. Gao et al. proposed a conjoined tubular HC-ARF structure, which achieved a minimum loss of 2 dB/km when transmitting light near 1500 nm [12]. Bradley et al. prepared a new type of nested structure fiber that can achieve a minimum loss of 1.3 dB/km when propagating 1450 nm light [13]. They also reduced the loss of nested optical fiber from 0.65 dB/km to 0.28 dB/km with transmission wavelengths in the 1530~1625 nm band, achieving a reduction in loss and optimization of the structure [14]. Sun et al. systematically studied several of the most traditional HC-ARF structures, with the aim of achieving low confinement loss, single-mode performance, and high insensitivity to bending in the 2 µm band [15]. Also, a much more systematic, complete, comprehensive, and relevant analysis of the performance of HCF was conducted in work by Fokoua et al. [16], where they reviewed and analyzed various physical mechanisms driving the attenuation of hollow-core optical fiber. Habib et al. improved the five-tube nested HC-ARF fiber, which reduced the propagation loss to a lower bending loss [17]. Zhang et al. tested the transmission of five-tube nested HC-ARF with high-power lasers and realized the transmission of high-power lasers of 60.5 W, with a coupling efficiency of 86.7% [18]. The delivery of 1 kW average power has been demonstrated over a 1 km long HC-ARF at a wavelength of 1 µm [19]. Most recently, HC-ARF with a loss level as low as 0.1 dB/km has been fabricated [20,21], and the idea of cladding capillary truncation has been implemented in Reference [21]. Furthermore, interconnection loss in HC-ARF with common standard single-mode fiber has been reported to be 0.15 dB based on gluing, which means the application of this type of HC-ARF has become more and more practical [22].

Furthermore, the 2 µm region is an eye-safe band due to the absorption properties of liquid water and other important substances [23]. Lasers in this band have less atmospheric scatter, atmospheric distortion, and thermal blooming, enabling more efficient work in light detection and ranging, high-energy laser weapons, sensing systems, and optical communications. They are also well suited for non-metallic material processing applications such as cutting, welding, and drilling [24]. Thus, there is a demand for using low-loss HC-ARF to transmit a high-power 2 µm fiber laser with high beam quality and low transmission loss. However, there is little work about the design of HC-ARF for the 2 μm region.

Based on the traditional classic double-layer nodeless nested structure, the inner nested structure is transformed so that new types of HC-ARF with lower loss and better single-mode performance for 2 μm transmission can be proposed. A coin-slot-type anti-resonant fiber structure was designed, which can effectively prevent light from leaking out of the fiber.

2. Parameter Optimization of Circular Coin-Slot-Type HC-ARF

2.1. Design of Circular Coin-Slot-Type Optical Fiber Structure

In this section, we will follow the principles of negative curvature and no node. It is found that when the number of cladding capillaries is 6, the transmission performance of its bending radius is the best in the multiple simulations of multi-tube double-layer nested structure [15]. Therefore, in this work, we will adopt the structure of six resonant tubes.

In the principle of anti-resonance, the more layers of glass in the cladding capillary, the stronger its ability to prevent light waves from leaking out [10]. The guiding principle of anti-resonant fiber can be explained by the ARROW principle in planar waveguides. When light is transmitted to the interface between the core and cladding, the light that meets the resonant conditions is directly transmitted out of the cladding, while other light that does not meet the resonant conditions will be reflected back to the core region. Based on this principle, a fiber structure similar to a coin slot was proposed. From the fiber core to the outer fiber surface, there are four layers of glass walls; thus, the chances of light resonating and overflowing from the fiber core can be greatly reduced.

As shown in Figure 1, referring to previous work [15], we set the core diameter

D_{c} = 50 μ m

. S is the width of the gap in the middle of the coin slot, D is the diameter of the circular cladding capillary, and two semicircular ends of the coin slot with a radius of d are inscribed onto the outer resonant tube. The thickness of the glass wall is still set to the optimal thickness

t = 1.46 μ m

, and the material is fused silica, which is calculated by the Sellmeier equation. The Sellmeier equation can be shown as follows [25]:

n (λ) = \sqrt{1 + \frac{0.6961663 λ^{2}}{λ^{2} - {0.0684943}^{2}} + \frac{0.4079426 λ^{2}}{λ^{2} - {0.1162414}^{2}} + \frac{0.8974794 λ^{2}}{λ^{2} - {9.896161}^{2}}},

where λ is expressed in microns.

For the results of the newly designed HC-ARF, it is necessary to simulate its structural characteristics and parameters to find an optimal structure with minimum transmission loss. This requires sweeping simulation calculations for each structural parameter.

For the simplification of variables, we set the normalized nested cladding tube diameter (

d / D

) and the normalized anti-resonant tube diameter (

D / D_{c}

) as two independent variables. The normalized nested coin slot diameter indicates the proportion of the middle coin slot to the entire circle. The larger the ratio is, the larger the diameter and width of the semicircle at both ends of the coin slot are and the larger the proportion of the area of the coin slot to that of the entire circular resonant tube is.

When it comes to the study of the transmission loss of the HC-ARF, its structural parameters are adjusted firstly, and after repeated attempts, the value of the ratio

D / D_{c}

is set between 0.6 and 0.9 to ensure its structure is within a reasonable range, and the scan step is set to 0.01. A calculation is performed every time the ratio is increased by 0.01 from 0.6. The ratio

d / D

is set between 0.05 and 0.3, and the scan step is set to 0.01. Every time the ratio is increased by 0.01 from 0.05, one time calculation is performed. Figure 2 shows a comparison of all the calculation results.

Figure 2a shows the transmission loss of the fundamental mode (FM). In this contour map, the bluer a region is, the lower the transmission loss value is, and the redder a region is, the higher the loss value is. It can be seen from the color distribution in the figure that the structure has the lowest FM transmission loss when

D / D_{c}

ranges from 0.8 to 0.9 and

d / D

ranges from 0.05 to 0.15.

As shown in Figure 2b, for the high-order mode (HOM) transmission loss of this structure, there is a minimum loss value for HOM transmission when

D / D_{c}

is in the range between 0.75 and 0.85 and

d / D

is in the range between 0.13 and 0.17. As shown in Figure 2c, the large areas inside the surrounding pink area are all areas that meet the pseudo-single-mode transmission conditions, and their higher-order mode extinction ratios (HOMERs) are all higher than 100. The calculation results show that the FM loss of this structure is the lowest when

D / D_{c} = 0.84

and

d / D = 0.12

, and the minimum FM transmission loss is

6.9 \times 10^{- 6} d B / m

. The HOM loss corresponding to the minimum FM loss is

2.9 \times 10^{- 3} d B / m

. Based on the above two values, the HOMER is calculated to be 421, which is far greater than 100, meeting the conditions of pseudo-single-mode transmission. Figure 2d shows the transmission loss at different wavelengths for optimal structure (

D / D_{c} = 0.84

and

d / D = 0.12

). It can be seen that when the structure is adjusted to the optimum, a detailed scanned calculation of the wavelength can be obtained. When this structure transmits light with a wavelength of 2 μm, its FM loss is the lowest, and the difference between the HOM loss and the FM loss is the largest; thus, this structure is the most suitable for transmitting light at a wavelength of 2 μm.

As shown in Figure 3a, under different bending radii, there is a big difference in the bending loss between the higher-order mode and the FM, and it can be seen that the loss of the FM is significantly smaller than the loss of the higher-order mode. Regardless of the HOM or FM, the smaller the bending radius, the greater the bending loss. However, when the bending radius is 6.5 cm, there are two obvious peaks in the FM bending loss at wavelengths of 1.9 μm and 1.95 μm, and the FM loss and HOM loss will appear in the same magnitude. At a wavelength of 2 μm, there is a minimum bending loss regardless of the bending radius. Therefore, this kind of structure is suitable for propagating a 2 μm laser source. As shown in Figure 3b, the bending loss of the FM is much lower than that of the HOM. At a bending radius of 4 cm, there is a higher peak loss in the HOM, which results in better single-mode transmission.

2.2. Design of Cut Circular Coin-Slot Optical Fiber Structure

As shown in Figure 4, we enlarged the diameter of the outermost circle of the optical fiber, so that the six resonant tubes inside were cut by the outer circle, and the green area is the part reserved in the HC-ARF. To explore the influence of the size of the outermost cladding circular resonant tube on the transmission loss, the original circular coin hole structure was transformed. The diameter of the cladding resonant tube and the width of the coin slot horizontal glass tube were kept constant, the outer circular tube was made to continuously cut the cladding resonant tube, and its losses were calculated at different cutting depths. The cutting depths can be expressed as

l = d_{circle tube} + r_{tube} - r_{outer circle}

d_{circle tube}

is the distance between the centers of the outer circle and the centers of the cladding resonant tube.

r_{tube}

is the radius of the cladding resonant tube, and

r_{outer circle}

is the radius of the outer circle.

As shown in Figure 5a, it can be seen that the loss increases with the cutting depth. Furthermore, when the cutting depth is 0.65 μm, the lowest FM loss is

5.8 \times 10^{- 6} d B / m

. As shown in Figure 5b, HOMERs are also shown at different cutting depths, and the corresponding HOMER is 517 when the cutting depth is set to 0.65 μm, which shows good pseudo-single-mode transmission characteristics. Figure 5c shows transmission losses corresponding to different wavelengths at the optimal cutting depth, which shows the same performance with the previous untransformed one in Section 2.1.

3. Conclusions and Discussion

In this paper, in order to reduce transmission loss and achieve single-mode transmission performance at a wavelength of 2 μm, a new type of HC-ARF structure called the coin-slot structure is proposed, and the optimal transmission performance is found by adjusting the geometric parameters of the inner structures. Firstly, based on the traditional classic double-layer nodeless nested structure, the inner nested structure was transformed to show a new HC-ARF structure with lower loss and better single-mode performance for 2 μm transmission. A coin-slot structure was added to the single-layer resonant tube, and the overflow of light was greatly reduced by adding two layers of glass walls. The normalized anti-resonant tube diameter (

D / D_{c}

) and the normalized nested cladding tube diameter width (

d / D

) were set as variables, and the fiber core diameter were set to 50 μm. To maintain good single-mode transmission characteristics, an HOMER above 100 is ensured; the minimum loss of the FM at 2 μm is calculated to be

6.9 \times 10^{- 6} d B / m

, and the corresponding HOMER is 421, which conforms to pseudo-single-mode transmission characteristics. Secondly, we enlarged the circular resonant tube structure, and they were cut by the outermost cladding tube so that the shape of the resonant tubes became an incomplete circle. It is now known that, when the other variables are consistent with the uniform circular coin slot and when the cutting depth is 0.65 μm, the lowest FM loss is

5.8 \times 10^{- 6} d B / m

, and the corresponding HOMER is 517, which reflects good pseudo-single-mode transmission characteristics. Through all the simulation results, theoretical guidance is provided for the design of HC-ARF with low transmission loss and high single-mode performance for 2 μm transmission.

Author Contributions

Conceptualization, B.Z. and X.S.; methodology, B.Z. and T.S.; software, B.Z., Z.T. and T.S; validation, B.Z., Z.T. and T.S.; formal analysis, B.Z., Z.T., X.S. and T.S; investigation, B.Z., Z.T. and X.S.; resources, B.Z.; data curation, B.Z. and Z.T.; writing—original draft preparation, B.Z. and X.S.; writing—review and editing, B.Z., Z.T., Y.L., H.C., Z.N., X.L., B.L., T.S., S.S., S.K. and X.S.; visualization, B.Z. and Z.T.; supervision, X.S.; project administration, X.S.; funding acquisition, X.S. and S.S. All authors have read and agreed to the published version of the manuscript.

Funding

This study was funded by the National Natural Science Foundation of China (62405017, 61935010, and 12275017), High-end Foreign Experts Recruitment Plan of China (G2023104003L), and the Ministry of Science and Higher Education of the Russian Federation under project no. FSWM-2020-0038.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

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.

Conflicts of Interest

The authors declare that no conflict of interest.

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Figure 1. Schematic diagram of circular coin-slot-type HC-ARF optical fiber structure.

Figure 2. Transmission loss diagram of circular coin-slot HC-ARF.

Figure 3. (a) Transmission loss spectra of coin-slot-type HC-ARF at different bending radii; (b) the transmission loss of coin-slot-type HC-ARF under different bending radii at a wavelength of 2 μm.

Figure 4. Schematic diagram of the structure of the coin-slot-type HC-ARF.

Figure 5. (a) Transmission loss at different cutting depths; (b) HOMER at different cutting depths; (c) Transmission losses corresponding to different wavelengths at the optimal cutting depth.

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MDPI and ACS Style

Zhang, B.; Tian, Z.; Li, Y.; Su, X.; Chi, H.; Nie, Z.; Luo, X.; Li, B.; Sun, T.; Sarkisov, S.; et al. Optimization Design and Simulation of Coin-Slot-Type Anti-Resonant Fiber Structure for 2 μm Transmission. Photonics 2024, 11, 1109. https://doi.org/10.3390/photonics11121109

AMA Style

Zhang B, Tian Z, Li Y, Su X, Chi H, Nie Z, Luo X, Li B, Sun T, Sarkisov S, et al. Optimization Design and Simulation of Coin-Slot-Type Anti-Resonant Fiber Structure for 2 μm Transmission. Photonics. 2024; 11(12):1109. https://doi.org/10.3390/photonics11121109

Chicago/Turabian Style

Zhang, Boyue, Zhaoyang Tian, Yu Li, Xinyang Su, Hongxiang Chi, Zikun Nie, Xiaoyu Luo, Bohan Li, Tianran Sun, Sergey Sarkisov, and et al. 2024. "Optimization Design and Simulation of Coin-Slot-Type Anti-Resonant Fiber Structure for 2 μm Transmission" Photonics 11, no. 12: 1109. https://doi.org/10.3390/photonics11121109

APA Style

Zhang, B., Tian, Z., Li, Y., Su, X., Chi, H., Nie, Z., Luo, X., Li, B., Sun, T., Sarkisov, S., & Kobtsev, S. (2024). Optimization Design and Simulation of Coin-Slot-Type Anti-Resonant Fiber Structure for 2 μm Transmission. Photonics, 11(12), 1109. https://doi.org/10.3390/photonics11121109

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