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Abstract
We investigated theoretically and experimentally the cascaded long-period fiber gratings (c-LPFGs) in a few-mode fiber (FMF) for the generation of LP11 core mode in a broad wavelength range. The dependence of the transmission spectra of the c-LPFGs on the spacing between the gratings, and grating periods are studied in detail. The c-LPFGs experimentally generate LP11 core mode in a 10-dB bandwidth of 193.6 nm in 1.55 µm waveband and 447.5 nm in 2 µm waveband, respectively. The first-order orbital angular momentum mode can be converted by the c-LPFGs with the same broadband wavelength range. The 10-dB bandwidth and corresponding wavelength range for mode conversion can be adjusted by changing the grating spacing and grating periods.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mode division multiplexing (MDM) is considered to be one of the most effective methods to increase the capacity of optical communications [1–3]. Mode converter is an essential optical device in the MDM system, which is employed to generate high order modes. Mode converters have been implemented in several ways, such as mode selective couplers [4], spatial light modulators [5], photonics lanterns [6], waveguide gratings [7,8], fiber Bragg gratings [9], and long-period fiber gratings (LPFGs) [10–13]. Among these methods, LPFG based mode converters have been widely used to generate high order core modes in few-mode fibers (FMFs) due to their advantages of simple method, low cost, and flexible design. The different methods have been demonstrated for the fabrication the LPFG mode converter such as CO2 laser writing technique [10,12–14], mechanical microbending [11,15], and acoustically inducing technique [16]. The CO2 laser writing technique has the advantage of flexibility, high repeatability [17]. The LPFGs were fabricated in FMF to generate LP11 and first-order orbital angular momentum (OAM) mode [10]. The second-order optical vortex was successfully stimulated by strong modulated LPFG in FMF [12]. The all-fiber controllable generation and conversion of LP21 mode and OAM mode were generated by cascaded LPFGs [18].
Conventional LPFG usually has a narrow bandwidth of tens nanometers, which is insufficient for broadband applications [10]. Although we could decrease the number of grating periods to write a LPFG with broader bandwidth, the writing efficiency will be quite low, which increases the difficulty of grating fabrication. Several approaches have been developed to increase the bandwidth of the LPFG mode converter. When the LPFG is fabricated with a period near the dispersion turning point of its phase-matching curve, the transmission spectrum will contain dual resonance dips, which increase the bandwidth of the mode converter significantly [19–21]. However, the wavelength range of mode conversion is limited to the waveband closing to the turning point. A phase-shift LPFG could show a broader bandwidth [22,23]. A 3-section phase-shifted LPFG has been inscribed in the FMF to realize mode conversion with a 10-dB bandwidth of ∼182 nm [23]. The LPFG fabricated with chirped periods or apodized grating also show a broader bandwidth than conventional LPFG [15,24]. In the above methods, the bandwidth of the LPFG mode converter was increased, however, the tunability of the wavelength range is not realized. The wavelength ranges of most mode converters reported early were located around the 1.55 µm waveband.
In this paper, we demonstrated the fabrication of bandwidth tunable broadband mode converters based on cascaded LPFGs (c-LPFGs) in both 1.55 µm and 2 µm wavebands. The 2 µm waveband has attracted much attention as a new “window” of next generation optical communications. The performance of the 10-dB bandwidth of the c-LPFGs on different grating periods and spacing between two adjacent gratings are simulated in 1 µm, 1.55 µm, and 2 µm wavebands. The bandwidth tunable broadband mode conversion has been achieved experimentally by c-LPFGs with a maximum 10-dB bandwidth of 193.6 nm and 447.5 nm in 1.55 µm and 2 µm wavebands, respectively. The experimental results are well consistent with the simulation results. The bandwidth and corresponding wavelength range are able to adjust by changing the grating spacing and grating periods. The LP11 mode and ±1st OAM mode can be generated in wide spectral range with high efficiency.
2. Bandwidth optimization of the c-LPFGs
The FMF in the experiment has a core and cladding diameter of 19 µm and 125 µm, respectively. The refractive index (RI) difference between the core and cladding is 0.005. The effective RIs of LP01 mode and LP11 mode and the grating period for mode coupling with respective to the wavelength of launched light is calculated by Finite Element Method with Comsol software. As shown in Fig. 1(a), the FMF can support LP01 mode and LP11 mode within the wavelength up to 2300 nm. The effective RIs and theoretical grating period for mode coupling decrease with wavelength. The grating periods for realizing mode coupling at wavelength of 1000 nm, 1550 nm, and 2000 nm are 1690 µm, 1270 µm, and 1140 µm, respectively. The bandwidth of the LPFG in FMF is proportional to a factor related to resonance wavelength and effective RIs of LP01 mode and LP11 mode, which can be expressed by [25]
Where $n_{eff}^{01}$ and $n_{eff}^{11}$ denote effective RIs of LP01 mode and LP11 mode, $\lambda $ is resonance wavelength of LPFG, L is length of the LPFG. Figure 1(b) shows the dependence of the factor on the resonance wavelength of the LPFG when the grating length is 1 cm. The result shows that the bandwidth of the LPFG increases with resonance wavelength.
Fig. 1. (a) The effective refractive indices of LP01 mode and LP11 mode and theoretical grating period with respective to wavelength of launched light. (b) Dependence of the factor on the resonance wavelength.
Figure 2 shows the schematic structure of the c-LPFG mode converter. The c-LPFG consists of two conventional LPFGs with periods of Λ1, Λ2, and the same number of the period N=10. There is a spacing with length of ΔL between the endpoint of the first LPFG and the beginning point of the second LPFG. By changing the grating periods and grating spacing, an appropriate phase shift can be introduced into the c-LPFGs, resulting in a broad bandwidth mode converter.
Firstly, we investigate the transmission spectra of the c-LPFGs at wavelength near 1.55 µm waveband. The grating periods and the RI modulation depth of the c-LPFG are set as: Λ1=Λ2=1270 µm, Δn=6×10−4. The ΔL is varied from 0 to 4000 µm. As shown in Fig. 3(a), the resonance depth is displayed by shade of color. The resonance dips in transmission spectra appear periodically with the change of ΔL. When the ΔL=0, the transmission spectrum of the c-LPFGs contains two shallow dips with wavelength of approximately 1405 nm and 1738 nm. The transmission spectra appear a deep resonance dip when the ΔL is near 400 µm or 900 µm, with the similar bandwidth as conventional LPFG. Then, the Λ1 is fixed at 1270 µm, and the Λ2 is varied from 1120 µm to 1200 µm. We simulate the transmission spectra of the c-LPFGs with the ΔL varying from 0 to 4000 µm. Figure 3(b) plots the transmission spectra of the c-LPFGs with the Λ2=1170 µm. The dash curves show the dependence of resonance wavelengths of the c-LPFGs on the ΔL. When the ΔL=0, there are two resonance dips (dip1 and dip2) in the spectra with wavelengths of 1531 nm and 1665 nm, respectively. With the ΔL increasing to 600 µm, the contrast of the dip1 decreases, while the contrast of the dip2 increases. As the ΔL increases further, a shallow dip (dip3) will also appear in the spectrum with wavelength near 1800 nm and shift towards the short-wave direction. The transmission spectra change periodically as the ΔL increases. The region enclosed by solid lines in Fig. 3(b) is the wavelength range of the transmission spectra with contrast more than 10 dB with different ΔL, which is to meet the conversion efficiency of more than 90%. Figure 4(a) depicts the dependence of 10-dB bandwidth of the c-LPFGs on the Λ2 and the ΔL when Λ1 is kept constant at 1270 µm. The bandwidth of the c-LPFGs has a maximum value of 210 nm when the Λ2=1170 µm and the ΔL=0. When Λ2 increasing to 1200 µm, the bandwidth decreases suddenly, which resulting from the convex spectrum near the central wavelength. As shown in Fig. 4(b), the resonance depth near the central wavelength is less than 10 dB when the Λ2≥1200 µm. The discontinuous 10-dB bandwidth is treated as 0 nm. The result indicates that, with optimized parameters, the bandwidth of the c-LPFGs can be significantly increased.
Fig. 3. Transmission spectra of the c-LPFGs depending on the spacing between two adjacent gratings. The solid line represents the grating contrast of −10 dB. (a) Λ1=Λ2=1270 µm, (b) Λ1=1270 µm and Λ2=1170 µm
Fig. 4. (a) The 10-dB bandwidth of the c-LPFGs with the ΔL ranging in 0∼4000 µm and the Λ2 ranging in 1120 µm∼1200 µm when Λ1=1270 µm. (b) Transmission spectra of the c-LPFGs with the period Λ2 of 1190 µm, 1200 µm, and 1210 µm when Λ1=1270 µm and ΔL=0.
We keep the difference between two grating periods constant as 100 µm (ΔΛ=Λ1-Λ2=100 µm) and calculated the transmission spectra of the c-LPFGs with varied grating periods. Figure 5(a) plots the transmission spectra of the c-LPFGs with grating periods of 1250 µm-1150 µm, 1260 µm-1160 µm, 1270 µm-1170 µm, 1280 µm-1180 µm, and 1290 µm-1190 µm, respectively. The spectra show a blueshift with the grating periods increasing. Meanwhile, the 10-dB bandwidth can be maintained above 190 nm. When the grating periods are further increased, the spectrum of the c-LPFGs will shift continuously towards the short-wave direction. We further simulated the transmission spectra of the c-LPFGs with same grating periods and the varied ΔL from 250 µm to 350 µm. As plotted in Fig. 5(b), the spectra show flatter bottom but narrower bandwidth compared with the spectra in Fig. 5(a). The maximum 10-dB bandwidth is 161.5 nm in the wavelength range from 1505.3 nm to 1666.8 nm. Moreover, the c-LPFGs simulated in Fig. 5(b) can realize higher mode conversion efficiency. The result indicates that the c-LPFG mode converter can realize an efficient and broadband mode conversion with tunable wavelength range by optimizing the grating periods and the grating spacing.
Fig. 5. Transmission spectra of the c-LPFGs with grating periods of 1250 µm-1150 µm, 1260 µm-1160 µm, 1270 µm-1170 µm, 1280 µm-1180 µm, and 1290 µm-1190 µm. (a) The maximum bandwidth is achieved when the ΔL is kept constant at 0. (b) The flat-bottom resonance dip is achieved with the ΔL varied from 250 µm to 350 µm. The insets are the simulated intensity distributions of the coupled LP11 mode at different wavelengths.
Similarly, the simulation is carried out for the c-LPFGs working in 1 µm and 2 µm wavebands with RI modulation depth of 2.5×10−4 and 8.5×10−4. As depicted in Fig. 6(a) and 6(b), the c-LPFGs achieved broad and tunable wavelength range for mode coupling in both wavebands. With grating periods of 1680 µm-1540 µm, 1690 µm-1550 µm, 1700 µm-1560 µm, 1710 µm-1570 µm, and 1720 µm-1580 µm, the c-LPFGs realize 10-dB bandwidth of 91.7 nm, 90.4 nm, 88.7 nm, 87.6 nm, and 87.5 nm in 1 µm waveband, respectively. The c-LPFGs with grating periods of 1155 µm-1065 µm, 1160 µm-1070 µm, 1165 µm-1075 µm, and 1170 µm-1080 µm can achieve wide bandwidth of 414.0 nm, 387.6 nm, 362.8 nm, and 341.9 nm in 2 µm waveband, respectively. In addition, the c-LPFGs share the same grating period difference of 140 µm in 1 µm waveband and 90 µm in 2 µm waveband. The results indicate that the c-LPFGs possess the ability of broadband mode conversion in wavelength range from 1000 nm to 2200 nm. The bandwidth increases with the wavelength, which is consistent with theoretical analysis.
Fig. 6. (a) Transmission spectra of the c-LPFGs with grating periods of 1680 µm-1540 µm, 1690 µm-1550 µm, 1700 µm-1560 µm, 1710 µm-1570 µm, and 1720 µm-1580 µm in 1 µm waveband and (b) 1155 µm-1065 µm, 1160 µm-1070 µm, 1165 µm-1075 µm, and 1170 µm-1080 µm in 2 µm waveband. The insets are the simulated intensity distributions of the coupled LP11 mode at different wavelengths.
3. Experimental results and discussion
Figure 7(a) shows the experimental setup for the fabrication of the c-LPFG mode converter. The FMF is spliced with single-mode fiber (SMF) at both ends and exposed by a CO2 laser (CO2-H10, Han’s laser) with average power of ∼1 W. The transmission spectra of the c-LPFGs during the fabrication are monitored by an optical spectrum analyzer (OSA, AQ6375, YOKOGAWA) with a supercontinuum source (SCS, SuperK compact, NKT). The laser scans each period of the c-LPFGs points by points. A single scan will cover all the periods of the c-LPFGs and repeat several times to complete the fabrication with high contrast dips. The mode field distribution of the c-LPFGs is captured by a CCD (C10633-23, HAMAMATSU) with a tunable laser (81600B, Agilent), as depicted in Fig. 7(b). The light from the tunable laser is divided into two paths by a 50:50 coupler. Light of one path is converted into LP11 mode or first-order OAM mode by the c-LPFGs, which will interfere with the Gaussian beam from the other path. The polarization controllers (PC1 and PC2) are used to manage the polarization state of input LP01 mode and output high-order modes.
Fig. 7. (a) Experimental setup for fabrication of the c-LPFGs mode converter by CO2 laser. (b) Experimental setup for the characterization of the mode pattern of the c-LPFGs mode converter. SCS: Supercontinuum Source; PC: polarization controller; NPBS: Non-polarization beam splitter.
According to the simulation results, we set Λ1=1270 µm, Λ2=1170 µm, and adjust the ΔL to fabricate the c-LPFGs with broad bandwidth. Figure 8(a) shows the transmission spectra of the c-LPFGs with ΔL of 0, 100, 200, 600, 800, and 1200 µm. When the ΔL=0, the transmission spectrum shows a resonance dip with 10-dB bandwidth from 1502.0 nm to 1694.8 nm. The inset shows the mode pattern of the c-LPFGs at the wavelength of 1550 nm. With the increase of ΔL, the spectra shift towards the short-wave direction. When ΔL=600 µm, the transmission spectrum has a single dip around 1550 nm, and a new dip appears at the wavelength of 1789.4 nm. Then we keep the ΔΛ=100 µm and ΔL=0, and investigate the spectral characteristics of the c-LPFGs with the variation of the grating periods. Figure 8(b) shows the transmission spectra of the c-LPFGs with grating periods of 1250 µm-1150 µm, 1260 µm-1160 µm, 1270 µm-1170 µm, 1280 µm-1180 µm, and 1290 µm-1190 µm. The 10-dB bandwidths are 193.6 nm, 192.4 nm, 192.8 nm, 192.1 nm, and 190.8 nm, respectively, which are maintained above 190 nm. The wavelength ranges corresponding to 10-dB bandwidth are 1539.4 nm∼1733.0 nm, 1524.8 nm∼1717.2 nm, 1502.0 nm∼1691.8 nm, 1480.4 nm∼1672.5 nm, and 1441.6 nm∼1632.4 nm, respectively.
Fig. 8. (a) Transmission spectra of the c-LPFGs with Λ1=1270 µm, Λ2=1170 µm and ΔL vary in 0, 100, 200, 600, 800, and 1200 µm. (b) Transmission spectra of the c-LPFGs with grating periods of 1250 µm-1150 µm, 1260 µm-1160 µm, 1270 µm-1170 µm, 1280 µm-1180 µm, and 1290 µm-1190 µm.
We summarize the experimental and simulated 10-dB bandwidth of the c-LPFGs with a growing ΔL when Λ1=1270 µm and Λ2=1170 µm, as shown in Fig. 9(a). The experimental bandwidth is in good agreement with the simulation results shown in Fig. 3(b). When ΔL=0, the 10-dB bandwidth of the c-LPFGs is 192.8 nm. As the ΔL increasing to 750 µm, the minimum bandwidth is about 84 nm. The variation of bandwidth is periodically repeated with growing of the ΔL. Figure 9(b) shows the comparison of the experimental and simulated wavelength ranges corresponding to 10-dB bandwidth. The resonance wavelength of the c-LPFGs shifts to short-wave direction when both Λ1 and Λ2 increase, on the contrary, the resonance wavelength shows a redshift, indicating that the experimental result is well consistent with the simulation. According to Fig. 1(b), the bandwidth of the c-LPFGs increases with the wavelength of the resonance dip. If the periods of the c-LPFG continue to increase or decrease, the 10-dB bandwidth will show an opposite variation with the changes of the grating period.
Fig. 9. (a) The experimental and simulated 10-dB bandwidth of the c-LPFGs with grating period Λ1=1270 µm, Λ2=1170 µm varies with the ΔL. (b) The comparison of the experimental (in blue) and simulated (in red) wavelength range of 10-dB bandwidth.
We also fabricate the c-LPFGs with grating periods of 1170 µm-1090 µm and 1180 µm-1100 µm with N=10 and ΔL=0. The spectra are plotted in Fig. 10. The insertion losses of two c-LPFGs are about 1.8 dB and 1.2 dB, respectively, which can be attributed to the high energy CO2 laser exposure. The insertion loss could be decreased by increasing the number of scan cycles of CO2 laser with reducing laser power. Increasing the period number of the c-LPFGs is also feasible, but this will reduce the bandwidth. The c-LPFGs show ultra-broad bandwidth of 447.5 nm and 379.4 nm in 2 µm waveband with wavelength range of 1798.9 nm∼2247.1 nm and 1762.8 nm∼2137.7 nm, respectively. The differences between the grating periods are 80 µm, which is slightly smaller than the simulation results in Fig. 6(b). The results indicate the c-LPFGs realize broadband mode conversion with an adjustable wavelength range at both 1.55 µm and 2 µm wavebands.
Fig. 10. Transmission spectra of the c-LPFGs with grating periods of 1170 µm-1090 µm, 1180 µm-1100 µm in 2 µm waveband.
The c-LPFGs with grating periods of 1280 µm-1180 µm is selected to investigate the mode characteristics because the wavelength range of 10-dB bandwidth is close to operating wavelength of the tunable laser. As shown in Fig. 11, the intensity distributions of the c-LPFGs at selected wavelengths from 1460 nm to 1640 nm were captured. The LP11 mode can be generated in wide wavelength range by the c-LPFGs. By managing the polarization state with PC1 and PC2, the π/2 phase difference could be generated between the high-order vector modes, which results in the generation of first order OAM mode. When the wavelength is 1460 nm, the resonance depth of the transmission spectrum is about 5 dB. Although the donut-shaped OAM pattern is not distinct enough, the interference pattern with spiral distribution is still captured. The patterns corresponding to ±1 order OAM modes are captured distinctly with the wavelength from 1480 nm to 1640 nm. The interference patterns with a Gaussian beam are also observed. It can be verified that the ±1 order OAM mode is generated effectively, which indicated that the c-LPFGs could convert the LP11 mode and first-order OAM mode within a wide wavelength range.
Fig. 11. OAM mode intensity distribution of the c-LPFGs and corresponding interference pattern generated in a wide wavelength range.
The torsion characteristic of the c-LPFG with periods of 1280 µm-1180 µm is investigated by fixed the c-LPFG between two fiber rotators. The twist rate of the c-LPFG was varied from −36 rad/m to 36 rad/m. As shown in Fig. 12(a), the spectra show a redshift or blueshift depending on the twist direction. The wavelength shift is about 18 nm, and the bandwidth kept almost unchanged during the twisting. The wavelength range for mode conversion can be slightly adjusted by changing the twist rate of the c-LPFGs. The spectral characteristics of the c-LPFGs under tension is also investigated experimentally. As shown in Fig. 12(b), the axial stress of grating has little effect on its transmission spectrum. The spectral shift is only about 2 nm, and the 10-dB bandwidth remains unchanged. The result indicates that the c-LPFG can keep the stability of mode conversion under tension.
The 10-dB bandwidth of the c-LPFGs has been enlarged to be maximum of 193.6 nm and 447.5 nm in 1.55 µm and 2 µm wavebands, respectively. Compared with the previous work [20–24], broader bandwidth and adjustable wavelength range of mode conversion are experimentally realized by the proposed mode converter. If broadband mode conversion is required in other waveband, the grating periods and grating spacing of the c-LPFG can be optimized by the proposed method. The broadband mode conversion is supposed to be generated in wavelength range of 1000 nm∼2200 nm. Moreover, our research focuses on the increase of the 10-dB bandwidth of the c-LPFGs. If a higher conversion efficiency is needed, for example, 15-dB or 20-dB bandwidth, one only need to pay attention to the corresponding bandwidth in the optimization process.
4. Conclusion
In conclusion, we have proposed the fabrication of a broadband mode converter based on c-LPFGs for efficient generation of LP11 mode in 1.55 µm and 2 µm wavebands. The grating periods and grating spacing of the c-LPFGs are optimized to get broad bandwidth and adjustable wavelength range in ultra-wide waveband based on the simulation analysis. The c-LPFGs achieve a maximum 10-dB bandwidth of 193.6 nm and 447.5 nm in 1.55 µm and 2 µm wavebands, respectively. The wavelength range of the 10-dB bandwidth can be adjusted with different grating periods. The c-LPFGs possess flexible design and high mode conversion efficiency, which provides a new solution to extend the bandwidth of mode converter used to generate high order modes.
Funding
National Natural Science Foundation of China (61875117, 62075124).
Disclosures
The authors declare no conflicts of interest.
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