Open Access
Add to BibSonomy
Abstract
A compact single-polarization (SP) coupler based on a dual-hollow-core anti-resonant fiber (DHC-ARF) is proposed. By introducing a pair of thick-wall tubes into a ten-tube single-ring hollow-core anti-resonant fiber, the core is separated into two cores to form the DHC-ARF. More importantly, by introducing the thick-wall tubes, dielectric modes in the thick wall are excited to inhibit the mode-coupling of secondary eigen-state of polarization (ESOP) between two cores while the mode-coupling of the primary ESOP can be enhanced, and thus the coupling length (Lc) of the secondary ESOP is greatly increased and that of primary ESOP is reduced to several millimeters. Simulation results show that the Lc of the secondary ESOP is up to 5549.26 mm and one of the primary ESOP is only 3.12 mm at 1550 nm through optimizing fiber structure parameters. By using a 1.53-mm-long DHC-ARF, a compact SP coupler can be implemented with a polarization extinction ratio (PER) less than - 20 dB within the wavelength range from 1547 nm to 1551.4 nm, and the lowest PER of - 64.12 dB is achieved at 1550 nm. Its coupling ratio (CR) is stable within 50 ± 2% in the wavelength range from 1547.6 nm to 1551.4 nm. The novel compact SP coupler provides a reference for developing HCF-based polarization-dependent components for use in the high-precision miniaturized resonant fiber optic gyroscope.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The resonator fiber optic gyroscope (RFOG) has great potential in high-accuracy inertial rotation sensors for navigation [1]. Compared with the interferometric fiber-optic gyro, the RFOG features small size, low cost, and good linearity within a wide dynamic range [2]. Over a decade ago, hollow-core fibers (HCFs) is proposed to be used in the fiber ring resonator (FRR) of RFOG instead of conventional solid-core fibers to reduce thermal polarization instability, backscattering, Kerr effect, Shupe effect and Faraday effect [3]. Although HCF has shown great potential in RFOGs, the lack of HCF-based components affects the advantages of the HCF into full play [4,5]. The coupler is one of the fundamental components to close the FRR of the RFOG. HCF-based couplers possess the distinguished advantages of low Fresnel, compactness, and high coupling efficiency over the components based on bulk optics, solid core fibers, or silicon wire waveguides. Therefore, an HCF-based coupler would be an ideal solution in the HCF-based RFOG.
In most RFOGs, the primary eigenstate of polarization (ESOP) is purposely excited. The rotation rate is linearly proportional to the resonant frequency difference between the clockwise and counterclockwise primary ESOP in the FRR [6]. In practice, when the light is coupled from a coupler into the FRR, it is difficult to avoid some power occasionally coupling to the secondary ESOP [7]. The secondary ESOP would cause an excess resonant frequency difference and hence induce errors [8]. To eliminate the secondary ESOP and ensure single ESOP operation of the RFOG, in-line polarizers are integrated into the FRRs [9]. This would increase greatly the system complexity. A single-polarization (SP) coupler only allows the primary ESOP to operate and thus the error induced by the second ESOP can be efficiently reduced by employing the SP coupler [10].
Dual-core fibers provide an attractive and powerful platform for guiding and manipulating polarizations. Various polarization-dependent fiber components can be made of dual-core fibers, such as polarization splitters, coupler, mode converters and comb filters [11–14]. Previously, the coupling mechanism of dual-hollow-core fiber (DHCF) has been studied theoretically and experimentally [15–18]. Therefore, the DHCF is promising in the development of an HCF-based SP coupler. The DHCFs mainly include dual-hollow-core photonic bandgap fibers (DHC-PBGFs) and dual-hollow-core anti-resonant fibers (DHC-ARFs). In 2014, Ma et al. proposed a DHC-PBGF and theoretically studied its coupling characteristic [10]. The coupling length (Lc) of the secondary ESOP is much longer than that of the primary ESOP, that is, the mode-coupling of the secondary ESOP between two cores of the DHC-PBGF can be effectively inhibited while only the primary ESOP can be allowed to be coupled between two cores. By using the DHC-PBGF, a DHC-PBGF-based SP coupler can be developed with a polarization extinct ratio (PER) greater than 30 dB at 1550 nm. However, the DHC-PBGF-based SP coupler shows an obvious wavelength dependence, and the high PER is only obtained at 1550 nm. Besides, the performance of the SP coupler strongly depends on the core diameter, hole pitch, and periodic cladding structure of the DHC-PBGF, which challenges the fabrication of the DHC-PBGF-based SP coupler [19]. Compared with DHC-PBGFs, the DHC-ARFs feature a simple cladding structure and high design freedom, which presents enormous advantages in designing HCF-based components. In the previous reports, various DHC-ARFs have been proposed, including single-ring, nested, and asymmetrical DHC-ARFs [20–23]. Among these DHC-ARFs, two methods have been reported to tune the Lc of two ESOPs. By adjusting the mode-coupling channel width between two cores, or by introducing an asymmetric cladding of two cores, the Lc of two ESOPs can be tuned. However, Lc of the two ESOPs obtained by the two methods are close to each other, and the coupling length ratio (CLR) is lower than 2.3 among these DHC-ARFs [21]. It is not conducive to inhibiting the mode-coupling of secondary ESOP between two cores. Therefore, the absence of the method of inhibiting the mode-coupling of secondary ESOP between two cores becomes a key issue that hinders the development of an SP coupler based on DHC-ARF.
Besides, the diameter of HCF-based FRR in RFOGs is typically 10 cm or smaller [4,24]. To take advantage of the size of HCF-based FRR, a small size is necessary for an SP coupler. The size of a DHC-ARF-based component is usually proportional to Lc. To reduce Lc, the coupling characteristics of DHCFs have been studied for many years [15,16,25,26]. In DHC-PBGFs, there are the cladding walls between two cores causing strong confinement on the mode-coupling, and thus it seems to be difficult to implement a short Lc. In 2009, Argyros et al. experimentally demonstrated only 1% of power can be transferred from one core through the cladding wall to the other core over a 0.5 m transmission length [27]. Therefore, it is uneasy to miniaturize the size of the DHC-PBGF-based component in practice. Different from HC-PBGFs that the core must be constructed by cladding walls, HC-ARFs possess more flexible cladding structures, such as tubular, nested, and conjoined-tube HC-ARFs [28]. The cladding structure of such HC-ARFs shows a periodic arrangement of airgaps and cladding walls, in which the airgap provides a leakage channel for core modes. In 2016, Liu et al. utilized the advantage of airgap to break the inhabitation of the cladding wall on mode-coupling between two cores in a DHC-ARF [26]. Meanwhile, they theoretically proved that the Lc can be as short as several centimeters. In 2017, Huang et al. successfully fabricated an airgap-type DHC-ARF-based coupler [17]. However, the component length of the DHC-ARF-based coupler is up to 40 cm, which is less likely to meet the demand of the miniaturized RFOG. Therefore, the absence of a compact SP coupler based on HCF is a key issue for developing a miniature RFOG based on HCF.
In this paper, a compact SP coupler based on a DHC-ARF is proposed for the first time. By introducing a pair of thick-wall tubes between the two cores of the DHC-ARF, dielectric modes are excited to increase the Lc of the secondary ESOP by an order of magnitude and the Lc of the primary ESOP can be reduced by two orders of magnitude simultaneously. Simulation results show that the Lc of the secondary ESOP is as high as 5549.26 mm, while the Lc of the primary ESOP is only 3.12 mm at 1550 nm. And the corresponding CLR is up to 1778.6. In addition, by adjusting the structural parameters of the DHC-ARF, the mode-coupling of secondary ESOP can be inhibited at the expected wavelength, while the Lc of the primary ESOP is almost unaffected. By using a 1.53 mm long DHC-ARF, a compact SP coupler can be obtained, whose PER is less than - 20 dB within the wavelength range from 1547 nm to 1551.4 nm, and PER can be as low as - 64.12 dB at 1550 nm. Besides, its coupling ratio (CR) can be stable within 50 ± 2% in the wavelength range from 1547.6 nm to 1551.4 nm. The acronyms and abbreviations used in this paper are listed in Table 1.
Table 1. Acronyms and abbreviations
2. Fiber structure and principle
Figure 1(a) illustrates the cross-section of the proposed DHC-ARF. By introducing a pair of thick-wall tubes with a thickness of tg and an inner diameter of dg into a ten-tube single-ring HC-ARF, the DHC-ARF is formed. The introduction of thick-wall tubes is aimed to obtain a DHC-ARF which can inhibit the mode-coupling of the secondary ESOP between two cores and reduce the Lc of the primary ESOP. The other ten tubes have different diameters with an identical wall thickness (tc). Except for two tubes that support the thick-wall tubes possessing an inner diameter of ds, the other eight tubes all have an inner diameter of d. Two cores have the same diameter denoted by D. The resonant wavelengths of the fiber are determined by ${\; }{{\lambda }_{{res}}}{ = 2t}\sqrt {{{n}^{2}}{ - 1}} {/m}$, where t, n, and m are the wall thickness of tubes, the refractive index of dielectric material, and any positive integer, respectively. The material of the DHC-ARF is set to be pure silica whose refractive index is obtained by the Sellmeier formula [29]. The initial parameters of tg, tc, dg, d, ds, and D are set as 785 nm, 550 nm, 15 µm, 20.4 µm, 16.35 µm, and 30 µm, respectively.
The modal characteristics of the DHC-ARF are investigated by using the finite-element method in the software COMSOL Multiphysics. A perfectly matched layer boundary is placed outside the fiber domain to accurately calculate the fiber modal characteristics. The simulations are performed using extremely fine mesh sizes of λ/6 and λ/4 in the silica walls and air regions respectively. Similar to other dual-core fibers, the structural symmetry of an individual fiber is broken and the interaction between two cores leads to the appearance of a pair of even and odd supermodes. Thus, two pairs of fundamental supermodes exist in DHC-ARFs, which are y-polarized (y-pol) odd mode, y-pol even mode, x-polarized (x-pol) odd mode, and x-pol even mode. The electric field distributions of four supermodes are shown in Fig. 1(b).
When x- and y-pol modes are coupled into core A simultaneously, the output power can be calculated by:
To obtain a DHC-ARF-based SP coupler, the coupling characteristics of two polarized modes are very important for designing the DHC-ARF. Here, y-pol mode and x-pol mode are set as the primary ESOP and the secondary ESOP, respectively. The CLR is introduced to evaluate the coupling characteristic of the two polarized modes, which is defined as the ratio of $L_c^x$ to $L_c^y$:
To illustrate the development of the DHC-ARF-based SP coupler, we compare the evolutions of normalized power of x- and y-pol modes in two DHC-ARFs, whose tg are 785 nm and 550 nm under other parameters fixed as the initial value. The normalized power is calculated by Eqs. (1-2). To obtain a compact component, the component length is usually selected in the first propagation distance Lc. Since the y-pol mode is the primary ESOP, Fig. 2 shows the evolutions of normalized power in the two DHC-ARFs are under a propagation distance $L_c^y$ at 1550 nm. When tg is 785 nm, $L_c^x$, $L_c^y$ and CLR are 5549.26 mm, 3.12 mm and 1778.6 at 1550 nm, respectively. Figure 2(a) gives the normalized power of the two polarization modes in core A and core B. It can be seen that x-pol mode is difficult to be coupled between two cores, while y-pol mode can couple between two cores. Therefore, by using a DHC-ARF with a high CLR, the mode-coupling of the secondary ESOP between two cores can be effectively inhibited. When tg is 550 nm, $L_c^x$, $L_c^y$ and CLR are 342.76 mm, 374.96 mm and 0.914 at 1550 nm, respectively. Figure 2(b) shows the normalized power of the two polarization modes in core A and core B. It can be seen that two polarized modes can be coupled between two cores at the same time. It is difficult for the DHC-ARF to inhibit the mode-coupling of one of polarized modes. Therefore, when DHC-ARF has a high CLR, it can be used to develop an SP coupler.
Fig. 2. Under tg = 785 nm (a) and tg = 550 nm (b), the evolutions of normalized power of x- and y-pol modes in core A and core B at 1550 nm.
3. Impact of structure parameters
To obtain a high-CLR DHC-ARF with a short $L_c^y$, the mode-coupling region between two cores is of importance for the design. The region includes the airgap and cladding tubes between two cores. Since the guidance mechanisms of HC-ARFs mainly depend on the wall of cladding tube, we focus on the impact of the wall thickness tg of cladding tubes between two cores on $L_c^{x,y}$. In addition, the impact of other structure parameters on $L_c^{x,y}$ are also analyzed, including dg, D, d and tc.
3.1 Impact of wall thickness tg
First, the impact of tg on $L_c^x$ is analyzed. When tg = 550 nm and 785 nm, Fig. 3(a) shows that the changes of $L_c^x$ within the wavelength range from 1540 nm to 1555 nm. When tg = 550 nm, the $L_c^x$ remains around 342 mm in the wavelength range. Besides, the modal field at 1550 nm is shown in the inset of Fig. 3(a). Even if $L_c^x$ is up to 342 mm, it is seen that x-pol mode can still be coupled between two cores. When tg = 785 nm, a peak occurs in curve $L_c^x$ at 1550 nm, and the corresponding $L_c^x$ is up to 5549.26 mm. The $L_c^x$ under tg =785 nm is one order of magnitude higher than that under tg = 550 nm at 1550 nm. Meanwhile, the modal field of tg =785 nm at 1550 nm is shown in the inset of Fig. 3(a). It is seen that x-pol mode is well confined in one core, which means that decoupling occurs for x-pol mode at 1550 nm, and thus it is difficult to be coupled into the other core. To explain the decoupling phenomenon, Fig. 3(b) gives the neff curves of x-pol mode and dielectric mode (TE3,2). The modal field of the TE3,2 mode is also shown in the inset of Fig. 3(b). It can be seen that x-pol even mode couples with TE3,2 mode at 1551.95 nm, which causes the neff of x-pol even mode to decrease slowly with the wavelength until 1553 nm and then increase rapidly. When neff of x-pol even mode decreases slowly from 1540 nm to 1553 nm, the neff of x-pol odd and neff of x-pol even modes cross with each other at 1550 nm. This causes $\mathrm{\Delta }{n^x}$ close to 0 at 1550 nm and thus there is a rapid increase in $L_c^x$. Therefore, the mode-coupling of x-pol mode between two cores can be effectively inhibited by introducing a thick wall.
Fig. 3. The variation of $L_c^x$ with wavelength under tg = 550 nm and 785 nm (a) with the insets of modal fields of x-pol supermodes and the curve of the neff of x-pol supermodes and TE3,2 mode (b) with the insets of the modal fields of x-pol supermodes and TE3,2 mode.
Next, the impact of tg on $L_c^y$ is analyzed. When tg = 550 nm and 785 nm, Fig. 4(a) shows the change of $L_c^y$ in the wavelength range from 1535 nm to 1565 nm. When tg = 550 nm, $L_c^y$ is about 375 mm in the wavelength range. It is due to that a thin wall of cladding tube strongly inhibits the mode-coupling between two cores, and the airgap acts as the main mode-coupling channel to transmit power, as shown in inset i of Fig. 4(a). When tg is increased to 785 nm, $L_c^y$ is only 3.12 mm at 1550 nm. It can be seen that $L_c^y$ under tg = 785 nm is reduced by two orders of magnitude than the one under tg = 550 nm at 1550 nm. It is thanks to dielectric modes that provides a resonant coupling channel to enhance the mode-coupling of y-pol mode between two cores, as shown in inset ii of Fig. 4(a). Therefore, $L_c^y$ can be reduced significantly. To analyze the phenomenon, Fig. 4(b) shows the neff curves of y-pol mode and dielectric modes. There are two dielectric modes TE3,2 and TM3,2 in the wavelength range from 1535 nm to 1565 nm, and their corresponding modal fields are shown in the inset of Fig. 4(b). It is seen that TE3,2 mode couples with y-pol even mode at 1543 nm, and TM3,2 mode couples with y-pol odd mode at 1559 nm, respectively. The modal fields of the coupled modes are also shown in the inset of Fig. 4 (b). The coupling of dielectric modes and the y-pol supermodes results in $\mathrm{\Delta }{n^y}$ increasing in the wavelength range from 1543 nm to 1559 nm, and thus $L_c^y$ decreases significantly. Therefore, by introducing a thick wall of cladding tube, $L_c^y$ can be reduced greatly.
Fig. 4. The variation of $L_c^y$ with wavelength under tg = 550 nm and 785 nm (a) with the insets of modal fields of y-pol even mode for tg = 550 nm and 785 nm at 1550 nm, and the curve of the neff of y-pol supermodes, TE3,2 and TM3,2 modes (b) with the insets of modal fields of TE3,2, TM3,2 and y-pol supermodes.
Subsequently, the impact of tg on $L_c^{x,y}$ and CLR at 1550 nm is analyzed. Figure 5(a) shows the variation of $L_c^{x,y}$ with tg. It is seen that three peaks occur in $L_c^x$ curve at tg = 779.6 nm, 785 nm and 792.3 nm. At these three peaks, $L_c^x$ can reach up to 3123.64 mm, 5549.26 mm and 642.61 mm, respectively, which are much higher than $L_c^x$ = 342 mm under tg = 550 nm. Besides, $L_c^y$ varies slowly between 3.14 mm and 2.55 mm when tg changes from 780.3 nm to 789.3 nm, which are far lower than $L_c^x$ = 375 mm under tg = 550 nm. So, by tuning tg, $L_c^x$ can be increased significantly while $L_c^y$ can be reduced greatly. Figure 5(b) shows the changes of CLR with tg. It is seen that the CLR is as high as 792.8, 1778.6, and 642.6 at tg = 779.6 nm, 785 nm and 792.3 nm, respectively, which exceeds CLR = 0.914 under tg =550 nm. Therefore, by adjusting tg, a high CLR can be obtained for a DHC-ARF and $L_c^y$ can be reduced to several millimeters.
3.2 Impact of other structural parameters
The impact of dg, D, d and tc on $L_c^{x,y}$ will be analyzed in this subsection. First, when dg changes -5%, 0% and +5%, Fig. 6(a) gives the variation of $L_c^{x,y}$ in the wavelength from 1545 nm to 1556 nm. It is seen that the three $L_c^x$ curves show a similar trend, and a peak occurs in three $L_c^x$ curves. The peak in $L_c^x$ curve is caused by decoupling phenomenon. When dg is changed from -5%, 0% to +5%, the peak in $L_c^x$ curve is shifted from 1546.2 nm to 1550 nm and 1553.5 nm, respectively, while the $L_c^x$ is up to 5257.5 mm, 5549.26 mm and 5651.07 mm, respectively. To explain the impact of dg on the peak in the $L_c^x$ curve, the neff curves of x-pol supermodes and TE3,2 mode are given in Fig. 6(b). When dg is changed from -5%, 0% and +5%, it can be seen that neff of TE3,2 mode is shifted towards long wavelength and thus the mode-coupling point between x-pol evenmode and TE3,2 mode is moved to long wavelength. Therefore, when dg increases, the peak in $L_c^x$ curve is shifted to long wavelength. It indicates that the peak in $L_c^x$ curve can be adjusted to the expected wavelength by controlling the cladding tube diameter dg.
Fig. 6. The variation of $L_c^x$ with wavelength under dg changing from -5%, 0% and 5% (a), and the curve of the neff of x-pol supermodes and TE3,2 mode (b).
Next, when dg is changed from -5%, 0% to +5%, Fig. 7 shows the variation of $L_c^y$ with the wavelength from 1546 nm to 1554 nm. It is seen that $L_c^y$ decreases slightly at short wavelength while it is almost unchanged at long wavelength. When dg is changed from -5%, 0% to +5%, $L_c^y$ is decreased from 3.26 mm, 3.12 mm to 2.70 mm at 1550 nm. It is due to that the change of dg has little effect on the mode-coupling between the y-pol supermodes and dielectric modes. Meanwhile, $L_c^y$ remains below 3.3 mm. Therefore, by tuning dg, a short $L_c^y$ can still be obtained to develop a compact SPC.
When structural parameter D, d or tc change ±5%, respectively, the impact on $L_c^x$ and $L_c^y$ is shown in Fig. 8. It is seen from Figs. 8(a), 8(c) and 8(e) that the peak of $L_c^x$ curve is shifted toward longer wavelength region when D increases, d decreases or tc increases. Under D changed -5%, 0%, 5%, the peak of $L_c^x$ curve is shifted from 1549.3 nm, 1550.0 nm to 1550.4 nm; under d changed 5%, 0%, -5%, the peak of $L_c^x$ curve is shifted from 1550.4 nm, 1550.0 nm to 1549.5 nm; under tc changed -5%, 0%, 5%, the peak of $L_c^x$ curve is shifted from 1549.5 nm, 1550.0 nm to 1550.5 nm. Because the increase of D, the decrease of d or the increase of tc will weaken the confinement of the cladding on the core mode, the mode-coupling point of x-pol supermodes and dielectric modes is shifted towards longer wavelength region. Therefore, the peak of $L_c^x$ curve is shifted towards longer wavelength as D increases, d decreases or tc increases. Besides, the variations of $L_c^y$ with D, d and tc is shown in Figs. 8(b), 8(d) and 8(f). It can be seen from Fig. 8(b) that $L_c^y$ is 2.63 mm at 1549.3 nm, 3.12 mm at 1550.0 nm and 3.60 mm at 1550.4 nm when D is changed from -5%, 0% to +5%. It is attributed to that the distance between the two cores will be increased when the D is enlarged, and thus $L_c^y$ is increased. However, $L_c^y$ remains at serval millimeters. As shown in Figs. 8(d) and 8(e), when d decreases or tc increases, $L_c^x$ is almost unchanged. It means that the change of tc and d has little effect on the mode-coupling point of y-pol supermodes and dielectric modes. Therefore, by increasing D, decreasing d, or increasing tc, the peak of $L_c^x$ curve can be adjusted towards longer wavelength while a short $L_c^y$ and a high CLR at the wavelength of the peak of $L_c^x$ curve still can be maintained.
Fig. 8. The variations of $L_c^x$ with wavelength under Dc (a), d (c) and t (e) changing -5%, 0% and 5%. And the variations of $L_c^y$ with wavelength under Dc (b), d (d) and t (f) changing -5%, 0% and 5%.
4. DHC-ARF-based SP coupler
To ensure the single-polarization operation of the SP coupler, PER is supposed to be less than -20 dB. Here, in order to implement a 3 dB coupler, the CR of the coupler is expected to be limited in the range from 48% to 52%. PER denotes the suppression of the secondary ESOP at the output end of the SP coupler; CR represents the power ratio of the primary ESOP at the output end of the SP coupler. In our design, since y-pol mode and x-pol mode are set to be the primary ESOP and secondary ESOP, respectively, PER and CR are expressed as:
According to the above analysis, the structural parameters tg, dg, D, d and tc of the fiber are set as 785 nm and 15 µm, 30 µm, 20.4 µm and 550 nm, respectively. To ensure the operating bandwidth where the fiber can be developed as an SP coupler, the relationship between the fiber performance ($L_c^{x,y}$ and CLR) and the SP coupler performance (component length L0, CR and PER) are analyzed. Firstly, the L0 of the SP coupler is investigated. When CR is stable at 50 ± 2%, the L0 is determined in terms of $L_c^y$, which can be obtained by submitting Eqs. (1-2) into Eq. (6):
4.1 Bandwidth of the DHC-ARF-based SP coupler
The CLR and $L_c^y$ of the DHC-ARF in the wavelength ranges from 1546.5 nm to 1551.5 nm is shown in Fig. 9. It can be seen that CLR increases with the wavelength until 1550.0 nm and then decreases. At 1550 nm, the maximum CLR of 1778.6 is achieved. In the wavelength range from 1547 nm to 1551.4 nm, marked by the gray shaded area, CLR exceeds 11. Meanwhile, $L_c^y$ curve changes around 3 mm in the wavelength ranges from 1547 nm to 1551.4 nm, in which $L_c^y$ is only 3.12 mm at 1550 nm. It means that the DHC-ARF is very promising in developing a compact SP coupler in the wavelength range from 1547 nm to 1551.4 nm, where CLR of fiber exceeds 11 with a ∼3 mm long $L_c^y$.
4.2 Performance of the DHC-ARF-based SP coupler
When the light is coupled into core A at 1550 nm, Figs. 10(a) and 10(b) show the normalized propagation power in two cores with a propagation distance $L_c^y$ = 3.12 mm. The normalized power is calculated by using Eqs. (1) and (2). It can be seen that the y-pol mode can be coupled between two cores, but x-pol mode is hard to be coupled between two cores. The grey area indicates that CRA and CRB are stable at 50 ± 2% when fiber length ranges from 1.52 mm to 1.60 mm. Figure 10(c) shows the change of PER with propagation distance. When the light is coupled to core A and propagates after the distance of $L_c^y$, PER is increased from - 65.00 dB to - 61.16 dB, which indicates that the fiber can effectively inhibit the mode-coupling of x-pol mode between two cores. Therefore, when the fiber length is fixed in the range from 1.52 mm to 1.60 mm, an SP coupler can be obtained at 1550 nm.
Fig. 10. Evolution of normalized power of x- and y-pol modes in incident core A (a) and coupled core B (b), and PER (c) at 1550.0 nm.
Then, the performance of the DHC-ARF-based SP coupler is analyzed in the wavelength range from 1547 nm to 1551.4 nm, which is obtained in subsection 4.1. The component length L0 can be calculated by Eq. (8), that is, L0 = 1.53 mm. When the light is coupled into core A, the corresponding PER and CR can be obtained by Eqs. (7) and (5-6), respectively. Figure 11(a) shows the PER of the DHC-ARF-based SP coupler, where the black solid line indicates PER = - 20 dB. It can be seen that PER is less than - 20 dB in the wavelength range from 1547 nm to 1551.4 nm. Especially at 1550 nm, PER is as low as -64.12 dB. Therefore, the SP coupler shows high performance of single-polarization operation characteristic in the wavelength range from 1547 nm to 1551.4 nm. Figure 11(b) shows CR of the SP coupler. Within the wavelength region from 1547 nm to 1551.4 nm, CRA range is reduced from 46.73% to 52% and CRB is reduced from 53.27% to 48%. The CRA and CRB of the SP coupler can be stable at 50 ± 2% within the wavelength ranges from 1547.6 nm to 1551.4 nm marked by the gray shaded area. This gives the evidence that a 1.53 mm long DHC-ARF can be developed as an SP coupler whose PER is lower than - 20 dB in the wavelength range from 1547 nm to 1551.4 nm, and CR can be stable at 50 ± 2% in the wavelength range from 1547.6 nm to 1551.4 nm.
Fig. 11. The variation of PER (a) and CR (b) with wavelength for the SP coupler based on a 1.53 mm long DHC-ARF.
4.3 Fabrication of the DHC-ARF-based SP coupler
Although we focus on investigate how to design a DHC-ARF-based SP coupler in the current stage, the feasibility of fabricating the SP coupler is also being taken into consideration during the design process. The main challenge for our proposed DHC-ARF-bsed SP coupler is that the fiber consists of two identical cores and different-wall cladding tubes. The designed DHC-ARF has not yet been fabricated, but the HC-ARFs with features, i.e., two identical cores or different-wall cladding tubes, have been successfully fabricated up to now. In 2016, Wheeler et al. successfully fabricated a kagome DHC-ARF with two identical cores and high structural uniformity [26]. In 2017, Huang et al. reported the first DHC-ARF with airgap coupling channel [17], in which there is two identical cores as our designed DHC-ARF. The high structural uniformity of these fabricated DHC-ARFs demonstrated the feasibility of fabricating a DHC-ARF with two identical cores. In 2020, Stępniewski et al. fabricated a single-core six-tube HC-ARF, in which the cladding was composed of two pairs of thick-wall tubes and two thin-wall tubes [30]. In 2022, Zang et al. fabricated another single-core different-wall tube HC-ARF [31]. These HC-ARFs strongly proved the potential of introducing different-wall cladding tubes into the DHC-ARF. Therefore, by combining the fabrication technology of DHC-ARFs with two identical cores and HC-ARFs with different-wall cladding tubes, it is possible to develop the proposed DHC-ARF-based SP coupler.
5. Conclusion
In conclusion, an SP coupler based on a DHC-ARF is proposed. By introducing a pair of thick-wall tubes in the DHC-ARF, dielectric modes are excited to inhibit the mode-coupling of x-pol mode with a significantly increased $L_c^x$, while mode-coupling of y-pol mode can be enhanced by dielectric modes. As a result, $L_c^y$ is reduced to several millimeters. Simulation results show that $L_c^x$ can be raised to 5549.26 mm and $L_c^y$ is only 3.12 mm at 1550 nm. In addition, by adjusting other structural parameters of the fiber, the mode-coupling of x-pol mode can be inhibited at expected wavelength while y-pol mode is almost unchanged. Using a 1.53 mm long DHC-ARF, an SP coupler can be implemented. PER is less than - 20 dB from 1547 nm to 1551.4 nm, and the lowest PER of - 64.12 dB can be achieved at 1550 nm. Thus, the SP coupler shows high performance in single-polarization operation. Besides, CR can be stabilized at 50 ± 2% from 1547.6 nm to 1551.4 nm. Our research can offer a guidance in the design of DHC-ARF-based SP coupler and provide a novel solution for developing the high-precision miniaturized HCF-based RFOG by using the proposed component.
Funding
Beijing Municipal Natural Science Foundation (1232028); National Natural Science Foundation of China (12174022).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
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.
References
1. G. A. Sanders, A. A. Taranta, C. Narayanan, E. Numkam Fokoua, S. Abokhamis Mousavi, L. K. Strandjord, M. Smiciklas, T. D. Bradley, J. Hayes, G. T. Jasion, T. Qiu, W. Williams, F. Poletti, and D. N. Payne, “Hollow-core resonator fiber optic gyroscope using nodeless anti-resonant fiber,” Opt. Lett. 46(1), 46–49 (2021). [CrossRef]
2. R. Carroll, C. Coccoli, D. Cardarelli, and G. Coate, “The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro,” Fiber Optic Gyros: 10th Anniversary Conf., Vol. 0719 (SPIE, 1987).
3. G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in Optical Fiber Sensors, ME6 (2006).
4. X. Suo, H. Yu, J. Li, and X. Wu, “Transmissive resonant fiber-optic gyroscope employing Kagome hollow-core photonic crystal fiber resonator,” Opt. Lett. 45(8), 2227–2230 (2020). [CrossRef]
5. H. Jiao, L. Feng, N. Liu, and Z. Yang, “Improvement of long-term stability of hollow-core photonic-crystal fiber optic gyro based on single-polarization resonator,” Opt. Express 26(7), 8645–8655 (2018). [CrossRef]
6. R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8(12), 644–646 (1983). [CrossRef]
7. A. M. Smith, “Birefringence induced by bends and twists in single-mode optical fiber,” Appl. Opt. 19(15), 2606–2611 (1980). [CrossRef]
8. L. Strandjord and G. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” Fiber Optic Gyros: 15th Anniversary Conf., Vol. 1585 (SPIE, 1992).
9. H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett. 37(16), 3342–3344 (2012). [CrossRef]
10. H. Ma, Z. Chen, and Z. Jin, “Single-polarization coupler based on air-core photonic bandgap fibers and implications for resonant fiber optic gyro,” J. Lightwave Technol. 32(1), 46–54 (2014). [CrossRef]
11. T. Zhao, S. Lou, X. Wang, M. Zhou, and Z. Lian, “Ultrabroadband polarization splitter based on three-core photonic crystal fiber with a modulation core,” Appl. Opt. 55(23), 6428–6434 (2016). [CrossRef]
12. D. Drolet and R. Vallée, “Dual-core fiber as a tunable directional coupler,” Opt. Lett. 18(6), 408–410 (1993). [CrossRef]
13. S. Han, Z. Wang, Y. Liu, H. Li, H. Liang, and Z. Wang, “Mode couplers and converters based on dual-core hollow-core photonic bandgap fiber,” IEEE Photonics J. 10, 1–8 (2018). [CrossRef]
14. H. Zou, S. Lou, and G. Yin, “A wavelength-tunable fiber laser based on a twin-core fiber comb filter,” Opt. Laser Technol. 45, 629–633 (2013). [CrossRef]
15. M. Skorobogatiy, K. Saitoh, and M. Koshiba, “Transverse lightwave circuits in microstructured optical fibers: waveguides,” Opt. Express 13(19), 7506–7515 (2005). [CrossRef]
16. X. Liu, Z. Fan, Z. Shi, Y. Ma, J. Yu, and J. Zhang, “Dual-core antiresonant hollow core fibers,” Opt. Express 24(15), 17453–17458 (2016). [CrossRef]
17. X. Huang, J. Ma, D. Tang, and S. Yoo, “Hollow-core air-gap anti-resonant fiber couplers,” Opt. Express 25(23), 29296–29306 (2017). [CrossRef]
18. K. Naeem, Y. Chung, and B. H. Kim, “Sagnac interferometer based on a highly-birefringent two-core PCF: theory, experiment, and sensing characteristics,” J. Lightwave Technol. 38(18), 5177–5190 (2020). [CrossRef]
19. Z. Wang, G. Kai, Y. Liu, J. Liu, C. Zhang, T. Sun, C. Wang, W. Zhang, S. Yuan, and X. Dong, “Coupling and decoupling of dual-core photonic bandgap fibers,” Opt. Lett. 30(19), 2542–2544 (2005). [CrossRef]
20. T. Zhao, H. Jia, Z. Lian, T. Benson, and S. Lou, “Ultra-broadband dual hollow-core anti-resonant fiber polarization splitter,” Opt. Fiber Technol. 53, 102005 (2019). [CrossRef]
21. H. I. Stawska and M. A. Popenda, “A dual hollow core antiresonant optical fiber coupler based on a highly birefringent structure-numerical design and analysis,” Fibers 7(12), 109 (2019). [CrossRef]
22. H. Jia, X. Wang, T. M. Benson, S. Gu, S. Lou, and X. Sheng, “Ultrawide bandwidth dual sakura hollow-core antiresonant fiber polarization beam splitter,” J. Opt. Soc. Am. B 38(11), 3395–3402 (2021). [CrossRef]
23. H. Jia, X. Wang, T. Zhao, Z. Tang, Z. Lian, S. Lou, and X. Sheng, “Ultrawide bandwidth single-mode polarization beam splitter based on dual-hollow-core antiresonant fiber,” Appl. Opt. 60(31), 9781–9789 (2021). [CrossRef]
24. M. A. Terrel, M. J. F. Digonnet, and S. Fan, “Resonant fiber optic gyroscope using an air-core fiber,” J. Lightwave Technol. 30(7), 931–937 (2012). [CrossRef]
25. L. Meng, J. Fini, J. Nicholson, R. Windeler, A. DeSantolo, E. Monberg, F. DiMarcello, M. Hassan, and R. Ortiz, “Bend tunable coupling in dual-hollow-core photonic bandgap fiber,” in OFC/NFOEC, 1–3 (2012).
26. N. Wheeler, T. Bradley, J. Hayes, G. Jasion, Y. Chen, S. Sandoghchi, P. Horak, F. Poletti, M. Petrovich, and D. Richardson, “Dual hollow-core anti-resonant fibres,” SPIE Photonics Europe, Vol. 9886 (2016).
27. A. Argyros, S. G. Leon-Saval, and M. A. van Eijkelenborg, “Twin-hollow-core optical fibres,” Opt. Commun. 282(9), 1785–1788 (2009). [CrossRef]
28. W. Ding, Y. Wang, S. Gao, M. Wang, and P. Wang, “Recent progress in low-loss hollow-core anti-resonant fibers and their applications,” IEEE J. Sel. Top. Quantum Electron. 26(4), 1–12 (2020). [CrossRef]
29. F. Gan, “Optical properties of fluoride glasses: a review,” J. Non-Cryst. Solids 184, 9–20 (1995). [CrossRef]
30. G. Stępniewski, D. Dobrakowski, D. Pysz, R. Kasztelanic, R. Buczyński, and M. Klimczak, “Birefringent large-mode-area anti-resonant hollow core fiber in the 1.9 µm wavelength window,” Opt. Lett. 45(15), 4280–4283 (2020). [CrossRef]
31. J. Zang, C. Goel, M. R. A. Hassan, W. Chang, and S. Yoo, “Antiresonant hollow-core inline fiber polarizer,” J. Lightwave Technol. 40(16), 5689–5697 (2022). [CrossRef]
