Broadband flat-top second-order OAM mode converter based on a phase-modulated helical long-period fiber grating

Hua Zhao; Zhen Zhang; Miaomiao Zhang; Yuanyuan Hao; Peng Wang; Hongpu Li

doi:10.1364/OE.435951

1. Introduction

Optical orbital-angular-momentum (OAM) beams, also known as optical vortices [1], have been extensively studied and reported to have wide range of applications in optical manipulation, optical trapping, quantum information processing, optical measurement, and optical communications [2–6]. The OAM mode multiplexing technology, which supports the OAM mode propagation in a few-mode fiber, is an effective way to increase the fiber communication capacity [5–7]. The OAM mode converter is a key component in the OAM mode multiplexing system, which can convert the fundamental mode to a specific OAM mode [8]. To date, various methods enabling to realize the OAM mode conversions have been developed, such as the ones including the cylindrical lens [1], the q-plate [9], the integrated silicon device [10], the helical fiber grating [11] based converters, and so on [12]. Owing to their unique properties, such as compact size, low loss, high conversion efficiency, and inherent compatibility with the fiber, helical long-period fiber grating (HLPG)-based OAM mode generators have recently attracted significant research interest [11,13–28]. The concept of using the HLPG as an OAM mode converter was originally proposed by Alexeyev et al. [13] in 2008. Since then, particularly in recent years, HLPG-based OAM mode converters have earned great development both experimentally and theoretically [14]. For example, the HLPG-based OAM mode converters, including first-order (OAM-1) [15], second-order (OAM-2) [16], simultaneous first- and second-order OAM-1 [17], and simultaneous second- and third-order (OAM-3) [18] ones written in single-mode fibers (SMFs) or few-mode fibers (FMFs), respectively, have been experimentally demonstrated. It has been established that the passive OAM mode generator can be achieved using only one HLPG, which could be the simplest of all fiber-based OAM mode converters. However, most of the HLPG-based OAM converters mentioned above are limited to those that have a high conversion efficiency, but lack a wide operating bandwidth, particularly those with a flat-top spectrum have rarely been obtained, which are essential to the wavelength-division multiplexing (WDM) and the OAM mode-division multiplexing (MDM) system whenever they are practically used as WDM OAM mode multiplexers [5,6].

To further expand the bandwidth of HLPF-based OAM mode converters to cover the entire C or L band of optical fiber communication, multichannel HLPGs [19,20], and broad-band HLPGs have also been explored and developed [21–24]. Ren et al. recently proposed and numerically demonstrated an ultra-broadband OAM mode converter based on a linearly chirped and length-apodized HLPG operating at wavelengths near the so-called dispersion-turning point (DTP) [21]. The HLPG-based OAM-1 mode converter with a conversion efficiency of 99.9% and a broad bandwidth of approximately100 nm was numerically demonstrated. Using the same method on a two-mode fiber, Zhao et al. experimentally demonstrated an HLPG-based OAM mode converter, where a rejection filter with a bandwidth of approximately 297 nm and rejection depth of 10 dB (corresponding to a conversion efficiency of 90%) was experimentally obtained [22]. However, the fluctuations in the intra-band depth are rather large (> 15 dB), and thus, HLPGs with a flat-top spectrum have not been achieved. Most recently, we proposed and demonstrated a flat-top filter that was achieved based on a phase-modulated HLPG grating [23]. Using such a phase-modulation method combined with the DTP method, Zhu et al. numerically demonstrated an ultra-broadband OAM mode generator with a bandwidth of approximately 469 nm and a conversion efficiency of approximately 100% [24]. However, only the first-order OAM mode converter is considered there [21–24], and moreover, the OAM mode was produced in the cladding region, which are susceptible to changes in the environment parameters such as the temperature and the surrounding refractive index etc. [21,24]. More importantly, the required length for the designed HLPG is too long (approximately 10 cm) to be difficult to achieve based on the current fabrication technique [25,26].

In this study, a broadband flat-top second-order OAM mode (OAM) converter was proposed and demonstrated using a second-order HLPG written in a thinned four-mode fiber (FMF). The proposed HLPG was operated at wavelengths near the dispersion turning point (DTP). As an example, an OAM-2 mode converter with a flat-top bandwidth of 113 nm @ -20 dB (ranging from 1530 nm-1643 nm) and a depth fluctuation of less than 3 dB @-26 dB has been successfully demonstrated. The fabrication feasibility of the designed HLPG was also discussed.

2. Principle to produce the HLPG-based flat-top broadband second-order OAM mode converter

2.1 Principle for generation of the high-order OAM modes in a single-helix HLPG

Because of either the eccentric core of the originally utilized fiber or the imperfect cylindrical symmetry of the HLPG created during the twisted processing [27,28], the refractive index modulation $\Delta {n_s}$ for l-helix HLPGs can be expressed as follows:

(1)$$\varDelta {n_s}(r,\phi ,z) = \Delta {n_0}(r)\sum\limits_{m ={-} \infty }^\infty {{s_m}\exp \{{i \cdot m \cdot l \cdot \sigma (\phi - 2\pi z/\varLambda )} \}} , $$

where z represents the axial position along the HLPG, and r and φ represent the radial and azimuthal angles, respectively. Δn₀ represents the maximum index modulation, σ represents the helicity of the HLPG, and σ =1 and -1 represent the left-and right-hand helicities, respectively, l represents the helix or the number of angular symmetries in the HLPGs, Λ denotes the pitch of HLPG, and m and S_m represent the order and Fourier coefficients of the harmonics, respectively. To efficiently produce the OAM-2 mode by a resonant coupling between the fundamental mode and the LP₂₁ mode, the utilized single-helix HLPG (l=1) requires to work in its second diffraction order, that is, m=2 in Eq. (1) [16,27]. This means that the following equation should also be satisfied [28],

(2)$${\beta _p} - {\beta _\textrm{q}} - 2 \cdot 2\pi /\varLambda = 0$$

where β_p (=2πn_p/λ) and β_q (=2πn_q/λ) are the propagation constants of these two modes, n_p and n_q represent the effective indices of these two modes, and λ represents the resonant wavelength of the HLPG. The above concepts were experimentally validated by the authors’ research group in [16], where the OAM-2 mode was successfully demonstrated using the single-helix HLPG.

2.2 Principle to enhance bandwidth of the HLPG by using a thinned four-mode fiber

It is generally known that for long-period fiber gratings (LPGs) as well as the HLPGs, the modal dispersion and its effects cannot be neglected, which strongly affect the spectral performance of the grating, particularly for the bandwidth of the rejection filter. It is known that the notch bandwidth for an HLPG can be approximately expressed as follows [29]:

(3)$$\varDelta {\lambda _B} \approx \frac{{\varDelta {\lambda _0}}}{{1 - \varLambda (\lambda )\cdot \frac{{d({\varDelta {n_{eff}}} )}}{{d\lambda }}}} = \frac{{\varDelta {\lambda _0}}}{{({\varDelta {n_{eff}}} )\frac{{d\varLambda }}{{d\lambda }}}}, $$

where $\Delta {\lambda _B}$ and $\Delta {\lambda _0}$ denote the notch bandwidth with and without considering the mode dispersion effect, respectively. λ represents the wavelength, and $\Lambda (\lambda )$ represents the pitch of the HLPG. $\Delta {n_{eff}}$ represents the difference in the effective indices between the two coupling modes. The 20 dB bandwidth $\Delta {\lambda _0}$ of a uniform HLPG of length L that offers 30 dB maximal coupling can be approximately expressed as follows [30]:

(4)$$\varDelta {\lambda _0} \approx 0.0955\frac{{{\lambda _0}^2}}{{\varDelta {n_{eff}} \cdot L}}, $$

where ${\lambda _0}$ and L represent the central wavelength and total length of the HLPG, respectively. Substituting Eq. (4) into Eq. (3), the following equation can be obtained:

(5)$$\varDelta {\lambda _B} \approx 0.0955\frac{{{\varLambda ^2}}}{{L \cdot \frac{{d\varLambda }}{{d\lambda }}}}. $$

From this equation, it can be clearly seen that for a fixed-length HLPG, the bandwidth of the resulting notch is inversely proportional to the magnitude of ${{d\varLambda } / {d\lambda }}$, which is equivalent to the difference in group indices between the fundamental mode LP₀₁ and the coupled modes [24]. Therefore, the broadband spectrum can be expected to be obtained as long as the HLPGs are arranged to work at a nominal wavelength where the condition ${{d\varLambda } / {d\lambda }} \approx 0$ (generally called the dispersion turning point (DTP)) is satisfied.

At beginning, a conventional four-mode fibers (FMF) provided by YOFC Inc. was considered in this study, where the core radius, the refractive indexes of the core and cladding are 9.25 um, 1.4499, and 1.4440, respectively. The required pitch and the DTP wavelength for the paired modes of LP₀₁ and LP₂₁ can be numerically determined by using the finite element method (FEM) and the phase matching condition (Eq. 2)). In concrete, first, we numerically calculated the dispersion spectra of the modes LP₀₁ and LP₂₁ (i.e., the effective refractive indices of the modes LP₀₁ and LP₂₁ vs. the wavelengths) by using the FEM. Then we can obtain the pitch spectrum (i.e., the required pitches vs. wavelengths) by using the Eq. (2) directly. Lastly, by analyzing the pitch spectrum, the DTP wavelength (where the slope is infinite) for the modes of LP₀₁ and LP₂₁ can easily be determined. The similar procedures for determining the DTP wavelengths above could also be found in [21–24]. However, it is found that the DTP wavelengths for the paired LP₀₁ and LP₂₁ are generally longer than 2000nm, which is beyond the bands of the fiber communication. Therefore, the DTP method proposed above cannot be directly used to the HLPG fabricated in a conventional FMF.

To overcome the above issue, the dependence of the pitches was calculated on wavelengths under different core radii, whereas the other parameters of the four-mode fiber provided above remained unchanged. The results for the thinned fiber with different core radii are shown in Fig. 1. From this figure, it can be observed that when the core radii were adopted as 8.74, 8.55, and 8.36 μm, the corresponding DTP wavelengths become 1830, 1780, and 1750nm, respectively, that is, the DTP wavelength decreases with a decrease in the core radius, which means that it is possible to shift the DTP wavelength of the conventional FMF into the communication C or L bands using a thinned FMF and, in fact, the thinned FMF with different core radii can be practically obtained by drawing the conventional FMF under the exposure of the CO₂ laser [26], where the core and the cladding radii are assumed to be adiabatically changed during the drawing process, which have been reasonably proved in Ref. [31].

Fig. 1. Dependence of the HLPG’s pitch on the wavelength under three different values of the core radiuses.

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2.3 Principle to obtain a flat-top rejection filter by using the phase-modulated HLPG

To obtain an HLPG with a flat-top rejection band, the phase-modulation technique, which was demonstrated in [23], where a polarization-independent band-rejection filter with a bandwidth of approximately 10 nm@-20 dB was successfully achieved using phase-modulated HLPG was used. The phase-modulated HLPG is a uniform HLPG whose amplitude is axially modulated by a phase function $S(z )= \exp ({i\varphi (z )} )$. Then from Eq. (1), the refractive index modulation for the second-order HLPG can be expressed as follows:

(6)$$\varDelta n(r,\phi ,z) = S(z )\cdot \Delta {n_0}(r){s_2}\exp \{{i \cdot 2(\phi - 2\pi z/\varLambda )} \}, $$

where the HLPG is assumed to have left-hand helicity, that is, σ =1 in Eq. (1). Without loss of any generalities, the phase $\varphi (z )$ is assumed to be the one that has one harmonic term, and in accordance, the phase-modulated function $S(z )$ can be simply expressed as follows:

(7)$$S(z )= \exp ({i\varphi (z )} )= \exp \{{iA \cdot \sin ({B \cdot 2\pi z/L} )} \}, $$

where L represents the length of the HLPG. A and B represent the two free parameters, which are optimally selected as such the transmission spectrum of the phase-modulated HLPG shown in Eq. (6) has the desired flat-top band for the transmission [23]. For practical fabrication of the phase-modulated HLPG, the optimized phase $\varphi (z )$ is encoded into grating pitches, whose local pitch is expressed as follows:

(8)$${\varLambda _j} = {\varLambda _0}({1 - \Delta {\varphi_j}/({2\pi } )} ),\begin{array}{cc} {}&{} \end{array}1 \le j \le N,$$

where Λ_j represents the pitch of the j-th grating part, Λ₀ represents the normal pitch of the HLPG, and Δϕ_j=ϕ_j-ϕ_j-1 is the phase difference between the neighborhood local pitch. N represents the period number of the grating.

3. Optimization results for the flat-top broadband OAM-2 mode converter based on a thinned phase-modulated HLPG

In view of the design principles, the proposed HLPG-based OAM-2 converter can be schematically given in Fig. 2, where the core radius of the thinned FMF is adopted as R=7.6 μm, whereas the cladding radius of the thinned FMF is accordingly assumed to be 51.4 μm, which is supposed to be fabricated by drawing the conventional FMF (with original radii of 9.25 and 62.5 μm for the core and the cladding, respectively) with the method like that demonstrated in [26]. The local pitches at different grating’s position are non-identical, which are discretely selected according to the Eq. (8). The local pitches required in the phase-modulated HLPG can be realized by using the same method as that reported in [23], where nearly the same kind of phase-only functions were utilized to realize HLPG-based flat-top band-rejection filter. Moreover, it must be pointed that in Fig. 2, the pitches Λ₁, Λ₂, …, Λ_N are only used to show the fact of the non-identical pitches, their actual magnitudes adopted are about 730 μmm which are much larger than the core radius of the thinned FMF. As is shown that after passing through the proposed HLPG, the incident Gaussian mode will be completely converted to the OAM-2 mode.

Fig. 2. The schematic diagram for the proposed phase-modulated HLPG inscribed in a thinned four-mode fiber.

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The dispersion spectra for modes LP₀₁ and LP₂₁ in a thinned FMF and the corresponding resonant pitch spectrum are shown in Fig. 3(a) and 3(b), respectively, where the core radius R of the utilized FMF is assumed to be 7.6 μm and the other parameters remain unchanged. It can be observed that the condition ${{d\Lambda } / {d\lambda }} = 0$ is satisfied at a wavelength near 1595 nm, where the pitch of the HLPG is approximately 726.8 μm.

Fig. 3. (a) Dispersion spectra for modes LP₀₁ and LP₂₁ modes in a thinned four-mode fiber. (b) Pitch spectrum for resonant coupling between LP₀₁ and LP₂₁ modes.

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Figure 4 shows the calculated transmission spectra for one design example of the proposed phase-modulated HLPG, where the core radius R is adopted as 7.6 μm, the normal pitch is selected as 732 μm exactly similar to the one shown in Fig. 3(a). The maximum index-modulation is adopted as 2.75 × 10⁻⁵, and the free parameters A and B for the phase-modulation function S(z) (as shown in Eq. (7)) are adopted as 0.84, and 1.81, respectively. More importantly, the total length of the HLPG is approximately 3.0 cm (40 periods), which is considerably shorter than that required in Ref. [19], and would be acceptable for real fabrication. From Fig. 4, it can be observed that a flat-top rejection filter with a bandwidth of 113 nm @-20 dB (ranging from 1530—1643 nm) was successfully obtained, which completely covered the entire C + L bands. Moreover, the depth fluctuation @-26 dB is less than 3 dB, which represents the best results of the HLPGs reported to date. For LPG/HLPG-based OAM mode converter, the cross-transmission spectrum may be more important than the bar-transmission spectrum, which can show the conversion efficiency directly. Because the HLPG presented in this study is of the second order, the results shown in Fig. 4 implicitly indicate that a flat-top OAM-2 converter with a bandwidth of 113 nm and mode conversion efficiency of 99% can be achieved.

Fig. 4. The simulation spectra for OAM-2 mode generator based on a phase-sampled HLPG inscribed in a thinned four-mode fiber working near the DTP.

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4. Tolerance analyses on spectra of the designed OAM-2 mode converter

Finally, the spectral analyses of the designed HLPG were performed under the assumptions of several different deviations in both the nominal pitch and nominal strength of the HLPG. Figure 5 shows the calculated bar- and cross-transmission spectra of the HLPG, where the nominal pitches are assumed to be 730, 732, and 734 μm, respectively. Note that the curve corresponding to the pitch of 732 μm is ideal in the design of this study, which is exactly the copy of Fig. 4, whereas the curves labeled by 730 and 734 μm, respectively, represent the cases where the deviation in nominal pitch is -2 μm and 2 μm, respectively. From this figure, it can be clearly observed that even small changes, such as ±2 μm in normal pitch will lead to a significant change in the flatness and bandwidth of the obtained spectrum, however the obtained bandwidth is still wide enough to cover the C + L bands at a depth of -15 dB (corresponding to a conversion efficiency of approximately 97%). Therefore to obtain the OAM-2 mode converter with performances similar to the design ones, a fabrication setup that enables precise control of the pitch with a resolution at least higher than ±2 μm is required, which is believed to be realized according to the current HLPG’s fabrication technique [23] although much more efforts and the cares must be made and considered in the future.

Fig. 5. Simulation results showing the effects of the grating’s pitch on the resulted spectrum.

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On the contrary, in the real fabrication of the designed HLPG, the maximum index-modulation obtained can hardly be the same value as what we pre-assumed in the design, which inevitably would result in some changes in the resulting spectrum. Figure 6 shows the calculated bar- and cross-transmission spectra of the designed HLPG, which were assumed to be 2.5×10⁻⁵, 2.75×10⁻⁵, and 3.0×10⁻⁵, respectively. From this figure, it can be seen that, except for the changes in rejection depth, the changes in the index modulation nearly have no effect on the flatness and bandwidth of the obtained HLPG spectrum, which in return means the proposed HLPG-based OAM-2 mode converter HLPG is rather robust to the fluctuations in the index-modulation of the designed HLPG.

Fig. 6. Simulation results showing effects of the maximum index-modulation on the resulted spectrum.

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More importantly, since the proposed HLPGs are fabricated in FMFs and all the mode couplings occur only in the core region, thus the proposed converter is insensitive to the changes in ambient temperature and surrounding refractive index [32,33]. Whereas the spectral changes due to the external torsion and tension can be avoided by using appropriate mechanical protection means.

5. Conclusion

In this study, a broadband flat-top second-order orbital angular momentum mode (OAM) converter is proposed and demonstrated using a phase-modulated second-order helical long-period fiber grating (HLPG). The proposed HLPG is designed to be inscribed in a thinned four-mode fiber and operated at wavelengths near the dispersion turning point (DTP). In contrast to most of the HLPG-based OAM mode generators reported to date, where the high-order OAM mode and flat-top broadband have rarely been achieved simultaneously, a second-order OAM(OAM-2) mode converter with a flat-top bandwidth of 113 nm @ -20 dB (ranging from 1530 nm-1643 nm) and a depth fluctuation of less than 3 dB @-26 dB has been successfully demonstrated in this study, such flat-top bandwidth covers the entire C + L bands and represents the best result of the HLPGs reported to date. Tolerance analyses for the fabrication of the designed HLPG were also performed. It is believed that the proposed HLPG may find applications in all-fiber vortex lasers as well as the OAM mode division multiplex (MDM) system.

Funding

Yazaki Memorial Foundation for Science and Technology; KDDI Foundation; Natural Science Research of Jiangsu Higher Education Institutions of China (19KJD510004); Basic Research Program of Jiangsu Province (BK20201370).

Disclosures

The authors declare no conflicts of interest.

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. L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]

2. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]

3. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329(5992), 662–665 (2010). [CrossRef]

4. M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013). [CrossRef]

5. J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]

6. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013). [CrossRef]

7. P. Sillard, M. Bigot-Astruc, and D. Molin, “Few-mode fibers for mode-division-multiplexed systems,” J. Lightwave Technol. 32(16), 2824–2829 (2014). [CrossRef]

8. L. Fang and J. Wang, “Flexible generation/conversion/exchange of fiber-guided orbital angular momentum modes using helical gratings,” Opt. Lett. 40(17), 4010–4013 (2015). [CrossRef]

9. D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nature Photon 10(5), 327–332 (2016). [CrossRef]

10. X. L. Cai, J. Wang, M. J. Strain, B. J. Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012). [CrossRef]

11. G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012). [CrossRef]

12. A.M. Yao and M. T. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]

13. C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78(4), 043828 (2008). [CrossRef]

14. H. Xu and L. Yang, “Conversion of orbital angular momentum of light in chiral fiber gratings,” Opt. Lett. 38(11), 1978–1980 (2013). [CrossRef]

15. C. Fu, S. Liu, Z. Bai, J. He, C. Liao, Y. Wang, Z. Li, Y. Zhang, K. Yang, B. Yu, and Y. Wang, “Orbital angular momentum mode converter based on helical long period fiber grating inscribed by hydrogen–oxygen flame,” J. Lightwave Technol. 36(9), 1683–1688 (2018). [CrossRef]

16. H. Zhao, P. Wang, T. Yamakawa, and H. Li, “All-fiber second-order orbital angular momentum generator based on a single-helix helical fiber grating,” Opt. Lett. 44(21), 5370–5373 (2019). [CrossRef]

17. P. Wang, H. Zhao, T. Detani, and H. Li, “Simultaneous generation of the first- and second-order OAM using the cascaded HLPGs,” IEEE Photonics Technol. Lett. 32(12), 685–688 (2020). [CrossRef]

18. T. Detani, H. Zhao, P. Wang, T. Suzuki, and H. Li, “Simultaneous generation of the second- and third-order OAM modes by using a high-order helical long-period fiber grating,” Opt. Lett. 46(5), 949–952 (2021). [CrossRef]

19. C. Zhu, P. Wang, H. Zhao, S. Ishikami, R. Mizushima, and H. Li, “DC-sampled helical long-period fiber grating and its application to the multichannel OAM generator,” IEEE Photonics Technol. Lett. 31(17), 1445–1448 (2019). [CrossRef]

20. R. Mizushima, T. Detani, C. Zhu, P. Wang, H. Zhao, and H. Li, “The superimposed multi-channel helical long-period fiber grating and its application to multi-channel OAM mode generator,” J. Lightwave Technol. 39(10), 3269–3275 (2021). [CrossRef]

21. K. Ren, M. Cheng, L. Ren, Y. Jiang, D. Han, Y. Wang, J. Dong, J. Liu, L. Yang, and Z. Xi, “Ultra-broadband conversion of OAM mode near the dispersion turning point in helical fiber gratings,” OSA Continuum 3(1), 77–87 (2020). [CrossRef]

22. X. Zhao, Y. Liu, Z. Liu, and C. Mou, “All-fiber bandwidth tunable ultra-broadband mode converters based on long-period fiber gratings and helical long-period gratings,” Opt. Express 28(8), 11990–12000 (2020). [CrossRef]

23. P. Wang, H. Zhao, T. Yamakawa, and H. Li, “Polarization-independent flat-top band-rejection filter based on the phase-modulated HLPG,” IEEE Photonics Technol. Lett. 32(3), 170–173 (2020). [CrossRef]

24. C. Zhu, L. Wang, Z. Bing, R. Tong, M. Chen, S. Hu, Y. Zhao, and H. Li, “Ultra-broadband OAM mode generator based on a phase-modulated helical grating working at a high radial-order of cladding mode,” IEEE J. Quantum Electron. 57(4), 6800307 (2021). [CrossRef]

25. O. V. Ivanov, “Fabrication of long-period fiber gratings by twisting a standard single-mode fiber,” Opt. Lett. 30(24), 3290–3292 (2005). [CrossRef]

26. P. Wang and H. Li, “Helical long-period grating formed in a thinned fiber and its application to a refractometric sensor,” Appl. Opt. 55(6), 1430–1434 (2016). [CrossRef]

27. H. Zhao and H. Li, “Advances on mode-coupling theories, fabrication techniques, and applications of the helical long-period fiber gratings: a review,” Photonics 8(4), 106 (2021). [CrossRef]

28. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

29. H. Zhao, M. Zhang, and H. Li, “Modal-dispersion effects on the spectra of the helical long-period fibre grating-based components,” Opt. Commun. 457, 124708 (2020). [CrossRef]

30. S. Ramachandran, Z. Wang, and M. Yan, “Bandwidth control of long-period grating-based mode converters in few-mode fibers,” Opt. Lett. 27(9), 698–700 (2002). [CrossRef]

31. H. Xuan, W. Jin, and M. Zhang, “CO₂ laser induced long period gratings in optical microfibers,” Opt. Express 17(24), 21882–21890 (2009). [CrossRef]

32. J. Dong and K. S. Chiang, “Temperature-insensitive mode converters with CO₂-laser written long-period fiber gratings,” IEEE Photonics Technol. Lett. 27(9), 1006–1009 (2015). [CrossRef]

33. X. Cao, Y. Liu, L. Zhang, Y. Zhao, and T. Yun, “Characteristics of chiral long-period fiber gratings written in the twisted two-mode fiber by CO₂ laser,” Appl. Opt. 56(18), 5167–5171 (2017). [CrossRef]

Broadband flat-top second-order OAM mode converter based on a phase-modulated helical long-period fiber grating

Abstract

1. Introduction

2. Principle to produce the HLPG-based flat-top broadband second-order OAM mode converter

2.1 Principle for generation of the high-order OAM modes in a single-helix HLPG

2.2 Principle to enhance bandwidth of the HLPG by using a thinned four-mode fiber

2.3 Principle to obtain a flat-top rejection filter by using the phase-modulated HLPG

3. Optimization results for the flat-top broadband OAM-2 mode converter based on a thinned phase-modulated HLPG

4. Tolerance analyses on spectra of the designed OAM-2 mode converter

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Equations (8)

Optics Express