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Abstract
A helical Yb3+-doped three-core microstructure fiber (YTMF) amplifier is proposed in this paper, so as to solve the problem of generation and transmission of the orbital angular momentum (OAM) beams. The fiber is composed of three Yb3+-doped cores with a regular triangle shape and a longitudinal helical structure. The experimental results show that the 1064nm laser can be amplified due to the fluorescence amplification characteristics of the doped material Yb3+. Furthermore, theoretical analysis indicates the modes in YTMF at 1064nm, which is located in the amplified wavelength, can support nine modes carrying OAM. Therefore, the related experiments were performed and verified that the transmission modes can respectively carry 1, 2, and 3-order OAM at 1064nm in different coupling cases. These excellent properties indicate that the combination of doped materials and helical fiber provide favorable conditions for the generation and amplification of OAM, which provides a basis for the further development of OAM beams in the field of quantum communication and dense space division multiplexing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The data-carrying capacity of the single-mode fiber has increased by four orders of magnitudes over the past three decades. The main reason is that the wavelength, amplitude, phase, and polarization of light are used in multiplexing technologies to encode information [1–4]. As the capacity of the current optical fiber system reaches the limit of nonlinear effect, multicore fibers have been widely explored by many researchers. However, multicore fibers can only limited increase the number of communication channels [5,6]. Meanwhile, OAM optical communication technology with theoretically infinite high-order multiplexing dimension is gradually being paid attention to, and has become one of the research hotspots used to break Shannon limit in the field of ultra-high-speed optical communication [7–10].
Although the transmission test of OAM channel of 1 km in special optical fiber has been realized in some reports [7], the system is composed of discrete optical diffractive devices, and the coupling process of optical fiber-free space and free space-optical fiber is bound to introduce unnecessary insertion loss. Moreover, the system is too complex and huge, and is with poor flexibility and stability, which is not easy to adjust, and is not conducive to the realization of integration. Furthermore, as a recent research hotspot, metasurface is widely used to generate OAM beams [11–13], which may be directly combined with optical fiber in the later stage [14], and then integrated with optical fiber. However, high technology and large cost are required for the preparation of metasurface, and it is relatively difficult to realize commercialization currently. Therefore, how to directly generate OAM beams in optical fiber has become a difficulty of research. At the beginning, traditional fiber bragg grating was used to generate OAM beams [15]. However, on the one hand, this method not only has a high cost of writing based on the grating. On the other hand, OAM beams generated based on the coupling and superposition between modes is of poor quality and unstable. Meanwhile, in 2012, Wong et al. reported the optical characteristics of OAM in helical microstructure fiber, and proposed that light of OAM mode could be existed in the cladding of helical microstructure fiber [16]. Napiorkowski et al. in Japan theoretically studied the interaction between the light transmitted by the core of helical fiber and the clad OAM beams, and further revealed the light-guiding mechanism of OAM in helical fiber [17]. In 2018, Roth et al. demonstrated experimentally for the first time that OAM beams could be transmitted in the helical photonic crystal fiber [18]. In order to further study the generation of OAM in helical fiber, Fu et al. reported the generator of OAM in helical photonic crystal fiber with standard regular hexagonal arrangement in 2019, and proved that the cladding can produce a first-order OAM beams [19].
Nevertheless, the helical photonic crystal fiber reported currently is basically a single-fiber core structure [16–19], and the orbital angular momentum generated is located in the cladding, with high transmission loss. Although the optical fiber proposed by Russel et al. have taken into account the Bloch orbital angular momentum of the fiber core [20]. It is easy to generate supermodes due to the three-bladed Y-shaped core with low crosstalk, which is not conducive to the transmission of signals. Besides, for further increasing the capacity, multicore fibers have been used to transmit the multi-OAM beams [21,22]. However, the lack of generation of multi-OAM beams in fiber makes the transmission of multi-OAM beams difficult. Meanwhile, the amplification of OAM beams in long distance transmission is also a key problem. Some reports have studied the OAM amplification and tried to solve the problems [23,24]. However, the insertion loss caused by different optical path coupling increases the difficulty of practicality because the generation and amplification of OAM are not in the same type of optical fiber.
Therefore, based on the integration consideration of multi-OAM beams amplification and generation, a helical YTMF is proposed in this paper. Through high-concentration doping of the fiber core, not only the gain efficiency is improved, but also the signal crosstalk is reduced due to the increase of refractive index of the doped fiber core, which is beneficial to space division multiplexing. What’s more, due to the twist modification of the fiber structure, the corresponding experiments show the light is transmitted in the fiber core carrying OAM. Moreover, due to the relatively long period of twist, the spectral transmission characteristics are basically unchanged compared with those of the original fiber, which also shows that, after rationally setting the fiber structure to reduce waveguide loss, twisted rare-earth doped fiber is expected to integrate the generation, amplification and transmission of OAM into a single fiber. All these excellent properties show that rare-earth-doped multi-core fiber combined with helical modification of fiber can be used to generate and amplify OAM beams have the potential application value in biological imaging, optical quantum communication and other fields.
2. Fabrication of Yb3+-doped three-core twisted micro-structured fiber
In order to improve the refractive index of fiber core and obtain uniformly Yb3+ ion-doped fiber core material, the laser sintering technology [25] was used to prepare the Yb3+-doped quartz glass with a refractive index of 1.625. Figure 1(a) shows the three-core Yb3+-doped photonic crystal fiber successfully drawn by the arrangement drawing process. The diameter of the fiber is 135 $\mu m$; and the spacing and diameter of the air holes is 8.2 and 3.6 $\mu m$, respectively. Due to the large refractive index difference between the fiber core material and the clad silica glass, compared with the literature [20], 1 Moreover, the interference between fiber cores can be decreased, which provides the possibility for the later research on the generation and amplification of multi-channel OAM beams. The CO2 splicer is used to twist the drawn three-core Yb3+-doped photonic crystal fiber, as shown in Fig. 1(b). In order to take into account the balance between optical fiber transmission loss and OAM generation, the twist cycle length of 10 $mm$ is obtained by setting the twist speed of holder, as shown in Fig. 1(c). It can be seen that the straight line formed by the air hole becomes an oblique line, which also means the air holes in YTMF are twisted.
Fig. 1. Sample preparation diagram. (a) Fiber-drawing cross-section diagram. (b) Twist machining diagram. The difference in twisting speed between the left and right motors causes the microstructure fiber to be twisted. (c) Lateral view of the twist sample. The white lines on the side of the microstructure fiber are projections of the internal air holes. Obviously, the air holes change from the straight line to the diagonal line, which proves that the fiber is twisted.
3. Results and discussions
Figure 2 shows the transmission spectra before and after the twist of the microstructure fiber. Both of twisted sample and untwisted sample are 20cm in length. It is obvious that the two transmission spectra are basically consistent between 1000nm and 1100nm. It is proved that weak twist has little effect on the transmission band characteristics of the fiber between 1000nm and 1100nm. Furthermore, it can be clearly seen two transmission valleys at 976nm and 915nm in Fig. 2, respectively. This is due to the material absorption caused by the energy level transition of Yb3+ from 2F7/2 to 2F5/2 [26]. Moreover, the transmittance between 1000nm and 1100nm is higher compared with other bands, and the fluorescence loss generated by the pump is small, which facilitates the amplification of this wave band.
Fig. 2. Test result of sample transmission. The normalized transmission spectra of the sample before and after twist. It can be seen that the transmission spectra are basically consistent.
Figure 3(a) shows that when pumping with the laser with wavelength of 976 nm and power of 0.77w. The sample is 20cm in length. Strong fluorescence can be observed in the wave band of 1000-1100nm, which means this band signal can be effectively amplified. The optical fiber amplification device in Fig. 3(b) is used to take 1064nm wavelength as the signal light and 976nm wavelength laser as the pump light. Then, beam splitter (BS) can gather two beams of light into the sample through the objective lens (OL). In order to eliminate the influence of the pump light with wavelength of 976nm, a filter is added to the output of the fiber (the light below 1000nm can be filtered). From the amplified spectrum in Fig. 3(c), it can be concluded that the signal light at 1064nm is counted at approximately 7000 when there is no pump light. When the pump light is gradually increased to 0.77w from 0.32w, the light at 1064nm is increased to 60000 from 7000, and the signal light was amplified more than 8 times.
Fig. 3. Results of sample amplification characterization. (a) Fluorescence characteristics of the sample. (b) Experimental setup diagram for amplification characteristic testing. (c) Amplification test result of the spectrum. (d) Amplification test results of different power.
To verify the stability of power amplification, we pump the sample at different input signals of 1W, 2W and 3W. It can be seen that the power of the output signal gradually increases as the pump power increases. When the pump light is less than 2W, the small-signal gain is approximately exponential; and when it is greater than 2W, the amplification gradually becomes linear. Moreover, the slope of power amplification curve is consistent with different input power. It is proved that the magnification characteristic of the sample is basically unchanged for different signal light.
In order to further study the interference and modes characteristics between three cores in the Yb3+-doped microstructure fiber in the process of amplifying light transmission. Based on the coupled mode theory, the crosstalk between the optical fiber cores of the three cores should be analyzed. According to [27], for achieving the crosstalk between three cores in the fiber, the coupling coefficient can be firstly calculated as follows:
Furthermore, due to the numbers of core in fiber are three, we have made some deformation on the basis of Ref. [28], and finally derivative the crosstalk as follows:
Here, L is coupling length, and it equals $\frac{\pi }{{2\sqrt 2 C}}$.
In addition, when fiber is twisted, the coupling of the twisted three-core fiber needs to be analyzed in the helical coordinate frame of the Ref. [29]. Firstly, a twisted co-ordinate system $({\xi _1},{\xi _2},{\xi _3})$ deduced from rectangular Cartesian co-ordinates $({x_1},{x_2},{x_3})$ is introduced as following:
In Eq. (3), $\alpha$ is a parameter that characterizes the torsion of the structure. It equals to $2\pi /P$. Here, P is twist cycle, and it is 10mm. Maxwell’s equations take the same form in any coordinate system. But when the ${x_3}$-dependent material permittivity and permeability tensor $[\varepsilon ]$ and $[\mu ]$ in the Cartesian co-ordinates are transformed into the helical frame, they become axially invariant, developing off-diagonal elements as follows:
Because of the circular symmetric structure of three cores and low crosstalk between the fiber-cores, the mode analysis of each core of three cores can be simplified to that of one core. $V = ka{n_c}\sqrt {2({n_c} - {n_s})/{n_c}}$ is the dimensionless V number involved in the eigenvalue problem describing the modes of the waveguide. ${n_c}$ and ${n_s}$ are the core and cladding refractive indices, respectively. k is the wave vector in vacuum. a is corresponding core radius [30]. After twist, the corresponding eigenmode field distribution and refractive index of YTMF could be calculated in the helical coordinate system according to Eqs. (3),(4). Then, the related results were brought into $V = ka{n_c}\sqrt {2({n_c} - {n_s})/{n_c}}$. The V value of YTMF after twist will achieved. As shown in Fig. 4(b), the normalized frequency, V value, before and after twist was calculated for a single fiber core, so as to analyze the mode of each fiber core. After twist, the V value of the fiber core increased slightly. In the wave band of 920 nm to 1100 nm, the V value of the core before and after twist is within the range of 5.4 to 5.6. It demonstrates 9 modes including HE11, TE01, HE21, TM01, EH11, HE31, HE12, EH21 and HE41 are supported for the optical fiber.
Fig. 4. Crosstalk and normalized frequency diagrams of three-core doped microstructure fiber (a) Crosstalk of the fundamental and second-order modes before and after twist. The TF mode and TT mode represent the twist fundamental mode and twist second-order mode, respectively. The NTF mode and NTT mode represent untwist fundamental mode and untwist second-order mode, respectively. (b) Change of normalized frequency before and after twist.
Figure 5 shows the mode diagram and phase changes of the 9 supported modes transmitted at 1064 nm in the amplified waveband before and after twist, where Figs. 5(a) and 5(c) represent the z component of the electric field in the corresponding mode, indicating that the z component of TE01 varies significantly. This is due to the fact that the field line of the TE01 mode is in the plane. Therefore, with the twist of the structure, the TE01 mode does helical motion with the fiber axis, resulting in different propagation constants of the distribution near the axis and away from the axis [31], and then the internal coupling of the mode occurs. However, electric fields of all the other modes have components along the z axis, they don't change much. Furthermore, Figs. 5(b) and 5(d) show the phase changes of the corresponding modes before and after twist. The change of phase distribution of TE01 mode may also be explained as the above. The reason why TM01 mode has been not changed is that there is electric field along the z axis in TM01, and the wavefront is less affected by the transverse modulation of the helical structure.
Fig. 5. The mode and corresponding phase diagrams supported by three-core doped microstructure fiber. (a) Schematic diagram of the z-component of the electric field for the mode supported before twist (b) The corresponding phase characteristics of the mode supported before twist. (c) Schematic diagram of the z-component of the electric field for the mode supported after twist. (d) The corresponding phase characteristics of the mode supported after twist.
The other HE21, EH11, HE31, EH21 and HE41 modes carry OAM of order ‘1’, ‘2’, ‘2’, ‘3’ and ‘3’ respectively. It shows that HEl+1 or EHl-1 mode can directly carry the l-order OAM after twist when the radial number m = l. Meanwhile, the relationship generated by fiber OAM may be obtained as follows:
where $HOAM$ represents the OAM in the twisted fiber core, “l” represents the order number of OAM. It can be seen that the order of OAM beams under the helix core is consistent with the angular number of traditional mode superposition mode, but no additional phase superposition is required. This phenomenon can be understood by photo behavior as shown in Fig. 6. In the process of transmission, the light is modified by the spiral structure, and the corresponding photon will rotate around the z-axis along the transmission direction. Then, the photon has the corresponding OAM, $J = \varepsilon \int\!\!\!\int {r \times \left\langle {E \times B} \right\rangle } dxdy$. $\varepsilon$ is the dielectric constant in medium, E and B are the corresponding electric and magnetic field vectors of photons. Naturally, photons carry first-order OAM. Because different modes have different transverse energy distributions, the OAM of the corresponding modes is equal to the sum of the OAM of each part of the energy. Finally, the HE21, EH11, HE31, EH21 and HE41 modes carry OAM of order ‘1’, ‘2’, ‘2’, ‘3’ and ‘3’ respectively. In conclusion, it is proved that the transmission modes of twist YTMF amplification at 1064 nm are carried OAM.The universal experimental device in Fig. 7(a) is used to verify the transmitted OAM light [18,19]. After the laser passes through the polarization controller (PC), the state of incident light is adjusted. At the same time, light is collimated and expanded through an OL. Subsequently, beam splitter (BS) is divided into two paths, one of which passes through the sample fiber and the other passes through the attenuator to control the light intensity. Finally, the two paths of light interfere in BS and are collected by camera. P1 and P2 are two lens, which can be used to make the plane wave become spherical wave. For easier modulation of the optical path, the length of three-core Yb3+-doped fiber is 10cm. When the reference arm is a three-core Yb3+-doped fiber without twist, the phase collected in Fig. 7(a) is interfered with the spherical wave to obtain the experiment results shown in Fig. 7(b). The results are the interference pattern of two common spherical waves. It is proved that the optical fiber without twist will not generate the beams of OAM, and the light amplified by 976nm pump is also the ordinary light. When the reference arm is a three-core Yb3+ fiber after twist, and the phase collected in Fig. 7(a) is interfered with the spherical wave to obtain the experiment results shown in Fig. 7(c). The red circle indicates that there are one, two and three phase singularities in the interference phase. When the objective lens at one end of the sample is aligned with the sample at the center, the interferogram of a singularity can be obtained. When there is a small angle between a core of the sample and the incident light from the objective lens, the higher-order modes in the core are excited. In this case, we can obtain an interferogram with two and three singularities by changing the angle of the incident sample core.
Fig. 6. Schematic diagram of photon transmission in twist structure at r from z-axis. The related OAM can be represented as $J = \varepsilon \int\!\!\!\int {r \times \left\langle {E \times B} \right\rangle } dxdy$. $\varepsilon$ is the dielectric constant in medium, E and B are the corresponding electric and magnetic field vectors of photons.
Fig. 7. Phase analysis of three-core doped microstructure fiber (a) the experimental device detection diagram of phase characterization. M1 and M2 represent two reflecting mirrors. (b) The experimental results of the interference between three core doped microstructure fiber and the spherical waves before twist (c) The experimental results of the interference between the three-core doped microstructure fiber and the spherical waves after twist.
The bifurcation of the fringes from the spherical wave interference show that the light in a single fiber core carries a first-order, second-order and third-order OAM. It proves the transmission beams in Yb3+-doped three-core twisted microstructure fiber carry OAM. Furthermore, combined with the experimental results of light amplification in Fig. 3, the Yb3+-doped three-core twisted microstructure fiber can realize the generation and amplification of OAM beams at 1064nm.
4. Conclusion
In summary, a kind of three-core helical photonic crystal fiber based on Yb3+ doping is proposed in this paper. After weak twist, loss characteristics do not change. Furthermore, 976 nm laser pump is used to observe fluorescence, which may be effectively used to amplify the 1064 nm laser. Through theoretical analysis, it is proved that the mode crosswalk of transmission and amplification between fiber cores is relatively weak and independent. Further analysis of beams modes at 1064 nm show that OAM beams are generated in the transmission process of helically Yb3+-doped three-core photonic crystal fiber, and HE21, EH11, HE31, EH21 and HE41 can carry ‘1’, ‘2’, ‘2’, ‘3’ and ‘3’-order OAM respectively through twist. It is also proved that the amplified fluorescence transmission is provided with OAM beams, that is, the amplification of OAM beams is realized. Finally, it was verified experimentally that the twisted YTMF carried first-order to third-order OAM. These results show that, with the multi-core twisted photonic crystal fiber doped with rare earth, the transmission and amplification and multiplexing of multiple OAM beams can be realized. Besides, it is expected to realize the generation, transmission and amplification of OAM into a single fiber for OAM quantum communication in the space division multiplexing. Meanwhile, it is provided with potential application value in biomedical imaging, functional devices and other fields.
Funding
National Key Research and Development Program of China (2019YFB2204002, 2018YFB0407400); National Natural Science Foundation of China (61527822, 61735005, 61935007, 61935010); GDUPS (2017); Innovation Project of Graduate School of South China Normal University (2019LKXM001); Guangdong Provincial Applied Science and Technology Research and Development Program (2018B010114002).
Disclosures
The authors declare no conflicts of interest.
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