Abstract

A fiber coupler for low-crosstalk orbital angular momentum mode beam splitter is proposed with the structure of two separate and parallel microfibers. By properly setting the center-to-center distance between microfibers, the crosstalk is less than −20 dB, which means that the purity of the needed OAM mode in output port is higher than 99%. For a fixed overlapping length, high coupling efficiency (>97%) is achieved in 1545-1560 nm. The operating wavelength is tuned to the whole C-band by using the thermosensitive liquid. So the designed coupler can achieve the tunable coupling ratio over the whole C-band, which is a prospective component for the further OAM fiber system.

© 2017 Optical Society of America

1. Introduction

In recent years, the orbital angular momentum (OAM) beam has attracted much attention because of its great potentiality for scaling the transmission capacity of the classical [1–5] and quantum communication system [6]. The data transmission based on multiple light beams with different value of OAM has been successfully demonstrated in both free space [1–3] and fiber networks [4, 5]. The fiber system is more attractive than the bulk optics system due to the considerable flexibility and reliability. However, there are still some challenges in the OAM fiber communication system [7, 8]. For example, the OAM beams are hardly manipulated in the OAM fiber. There is inevitable high insertion loss when the OAM beams are coupled between the spatial light components and the OAM fiber. So it is of great important significance to design the fiber devices for manipulating the OAM beams.

The basic OAM fiber devices include OAM mode generators [9–12], couplers [13–15], filters [16], and multiplexers [17] and so on. The focus here is the coupler, which splits the OAM beam from one channel to multiple channels and is the one of the most common components in optical fiber links. Two OAM fiber coupler designs have been proposed with the ring fiber [13] and the few-mode fiber [14]. However, the crosstalk is ignored in both designs. The crosstalk is induced because of that other modes will be excited during the coupling process. Due to the non-cylindrical symmetry of the refractive index distribution of the coupling region, firstly, the horizontal and vertical polarization components of the OAM mode have different propagation constants and coupling coefficients, which will excite other modes besides the input OAM mode. Secondly, the asynchronous coupling feature of the even eigenmode and odd eigenmode will inverse the topological charge of the input OAM mode [14]. The crosstalk will result in transmission errors and increase complexity of the decoding module in communication system. So the crosstalk level should also be the key indicator for the OAM coupler. Furthermore, above two coupler designs are fixed structure. Such structure is inherently limited to specific coupling ratio and will sensitive to optical wavelength.

Toward the problems mentioned, we proposed a tunable OAM coupler design based on two separate and parallel microfibers. This OAM coupler design adopts the mode match method [18], which is appropriate for finding the optimum trade-off between the crosstalk and the coupling length. The crosstalk less than −20 dB is achieved by properly setting the center-to-center distance between microfibers. The designed coupler could achieve tunable coupling efficiency over the whole C-band, which is a prospective component for OAM fiber communication system.

2. Theoretical model

As shown in Fig. 1, the tunable OAM coupler consists of two separate and parallel microfibers, which are mounted in the specially designed box with the center-to-center distance d between two microfibers and the overlapping length L. The microfiber structure is submerged in the refractive index liquid for achieving the tunable characteristic and better protection the coupler from the external disturbance. Compared with traditional fused-type coupler, the major difference is that the coupling region is still two separate microfibers instead of one single 8-shaped waveguide, which is conducive to the low crosstalk level of the OAM coupler.

 figure: Fig. 1

Fig. 1 Schematic diagram of the tunable OAM coupler coupler; insets are the refractive index profile of each part. The red arrows represent the direction of the OAM beam travel.

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Since the tunable OAM coupler is composed of microfibers, the weak-guidance approximation and the perturbation method no longer apply. So the coupled mode theory, supermode theory, and beam propagation method are unsuitable for calculating the coupling interaction in this coupler. The mode match method [18] is selected because it is a universal and efficient method for both the strong and the weak coupling situations. This method divides the coupling model into several parts and uses the interference of local eigenmodes in each part to calculate the electromagnetic field. So the designed coupler is divided into three parts: the input port, the coupling region, and the output ports, as shown in Fig. 1. Each part is assumed as the uniform and lossless waveguide. The local eigenmodes are calculated by the finite element method with the corresponding refractive index (RI) profile, as shown in the insets of the Fig. 1. The electric fields in three parts are expressed as the following:

E1=i=1N1aie1iexp(jβ1iz)
E2=i=1N2bie2iexp(jβ2iz)
E3=i=1N3cie3iexp(jβ3iz)
where E is the electric field, e is the normalized local eigenmode, β and N are the propagation constant and the number of the local eigenmodes in each part, the subscrip 1, 2, and 3 represent the parameter of three parts, respectively. ai, bi, and ci are the expansion coefficients of the i-th local eigenmodes in three parts, respectively.

In order to simplify the calculation, the length of the input port and output port are set to be zero. So the output optical field of the input port is

E1=p=1N1ape1p

Using the Maxwell equations at the interface between two adjacent waveguides, the tangential electric field should be continuous. So the input optical field of the coupling region should be

E2_t=E1_t
where the subscript _t represents the tangential electric field.

From Eq. (3) and the orthogonality of the local eigenmodes, we have

bi=E2e2i*dse2ie2i*ds

By substituting Eqs. (4) and (5) in Eq. (6),

bi=(p=1N1ape1p_t)e2i_t*dse2i_te2i_t*ds

Here, the parameter Γmode1_mode2 was defined to estimate the overlapping rate between two modes.

Γmode1_mode2=emode1emode2*dsemode2emode2*ds

So bi is expressed as

bi=p=1N1apΓ1p_2i

The light in the coupling region is considered as the interference of the local eigenmodes. So the output optical field of the coupling region is

E2=i=1N2bie2iexp(jβ2iL)
where L is the length of the coupling region.

At the interface between the coupling region and the output port, the procedures are the same as Eqs. (5)-(9).

E3_t=E2_t
cq=(i=1N2bie2i_texp(jβ2iL))e3q_t*dse3q_te3q_t*ds=i=1N2biexp(jβ2iL)Γ2i_3q

By substituting Eq. (9) in Eq. (12),

cq=i=1N2p=1N1apΓ1p_2iexp(jβ2iL)Γ2i_3q

So when the p-th local eigenmode is launched in the input port, the coupling efficiency of the q-th local eigenmode in the output port is

ηpq=|cqe3qcq*e3q*ds||ape1pap*e1p*ds|=|cqcq*ds||apap*ds|

Usually, the coupling results of the OAM modes can be obtained by the superposition of the coupling results of the corresponding vector modes in fiber. It is inconvenient that both the power and the phase have to be dealt with. In fact, due to the orthogonality, the OAM modes can directly act as the eigenstates of the microfiber in the input/output ports. So the calculations of the coupling OAM modes are simplified and became faster and more convenient by using the mode matching method.

Considering that only the p-th OAM mode is launched in the input port,

ai=δip
ηpq=|[i=1N2Γ1p_2iexp(jβ2iL)Γ2i_3q][i=1N2Γ1p_2iexp(jβ2iL)Γ2i_3q]*|

Based on Eq. (16), the relationship between the coupling efficiency and the length can be very complex and has no periodicity. However, some physical rules still could be concluded from Eq. (16). For example, the maximum coupling efficiency would be achieved at a shorter coupling length with larger propagation constant difference between the excited local eigenmodes in the coupling region.

In our coupler design, two microfibers are identical. According to symmetry, the local eigenmodes in the input port and the output port are the same relative to the local eigenmodes in the coupling region, i.e., Γ2i_3q=Γ1q_2i.

ηpq=|[i=1N2Γ1p_2iΓ1q_2iexp(jβ2iL)][i=1N2Γ1p_2iΓ1q_2iexp(jβ2iL)]*|

Based on Eq. (17), when Γ1p_2iΓ1q_2i0, ηpq0 (pq), the new mode will be excited and the crosstalk is induced during the coupling process. The crosstalk will decrease with decreasing the value of Γ1p_2iΓ1q_2i. Here, Γ1p_2iΓ1q_2i=0means that no common local eigenmodes are excited by different input mode, which can be achieved under the weak coupling situations. So the crosstalk will decrease with decreasing the coupling strength between two microfibers, which is related with the radius and the refractive index of microfiber, the refractive index of liquid, the interval between two microfibers and the input wavelength. In our paper, the crosstalk is improved noticeably by increasing the interval between two microfibers, which is a simple and effective way to decrease the coupling strength. More detailed discussions are shown in Section 3.

3. Results and discussion

In the following part, we design a low crosstalk OAM coupler for the first order OAM mode, which is represented as ±1,±1 and +1,+1=HE21e+jHE21o. The symbol ±1,±1 represents the left (right) circularly polarized OAM mode with topological charge +1 (-1). The symbol HE21 represents the second order vector mode in the microfiber. There are two orthogonal field distributions for the HE21 mode, which are represented with the superscript e and o, respectively. The refractive index liquid (the Cargille Laboratories) is selected to be RI = 1.2962 for 1550 nm at 25 °C and has a thermal-optic coefficient of 3.33×104 refractive index unit per centigrade (RIU/°C) and a boiling point of 250 °C. The RI of the liquid can be regarded as a constant over the C-band (1520-1580 nm). The material of microfiber is set to be the silicon dioxide and the dependence of the RI of the microfiber on the wavelength is calculated by the Sellmeier equation [19]. In order to shorten coupling length, the diameter of microfiber is optimized to be as small as possible until HE21 mode is cutoff at the C-band. Based on the calculation of the finite element method, the diameter of the microfiber is set to be 3.1 μm. The ±1,±1 mode can propagate steadily in both the straight and bending microfiber, as shown in Appendix.

In order to obtain a high OAM mode purity and high maximum coupling efficiency, it is important to control the center-to-center distance d between two microfibers. Figure 2 shows the mode distributions, phase distributions and the coupling efficiency of +1,+1mode at 1550 nm and room temperature (25 °C) in the cross output port with the different interval d. When two microfibers are close together (d=3.1μm, i.e., the traditional 8-shaped waveguide), the input +1,+1 mode is greatly deteriorated. As show in Fig. 2(a), the phase distributions at different coupling length Lare no longer the spiral shape, which means that other modes are excited under such strong coupling state. More specifically, TE01 mode, TM01 mode and 1,1mode will be excited, which lowered the mode purity and coupling efficiency of the +1,+1 mode and induced the crosstalk, as shown in Fig. 2(b). However, when two microfibers are set with a proper interval (e.g., d=6.35μm), the mode distributions and phase distributions at the both output ports of the different coupling length are all clear to recognize as the +1,+1 mode, as shown in Fig. 2(c). Figure 2(d) shows that the maximum coupling efficiency 97.59% with the crosstalk −20.8 dB is achieved at L=2.315cm. The crosstalk is improved noticeably by increasing the interval between two microfibers. Because the proportion of the input mode field distribution in the adjacent microfiber is greatly lowered and the coupling effect between two microfibers is weaken. As shown in Fig. 2(e), the greater the interval, the higher mode purity and maximum coupling efficiency, and the longer the coupling length. There is a critical value of d for balancing the performance and the size of the coupler. Typically, the critical value of d is about twice the diameter of the microfiber, which makes the lowest purity of the +1,+1mode is 99% and the crosstalk level is lower than −20 dB. This crosstalk value should be perfectly adequate for the mostly OAM fiber systems. The critical value of d is smaller while the evanescent wave of the input mode is more concentrated. So the critical value of d will decrease with increasing the refractive index of microfiber, decreasing the refractive index of liquid, and decreasing input wavelength. For example, at room temperature (25 °C), the calculated critical value of d for this +1,+1 mode coupler at 1520 nm and 1580 nm are 6.1 μm and 6.6 μm, respectively. Incidentally, only increasing the diameter of microfiber is not enough to decrease the coupling strength between two microfibers for achieving the low crosstalk level.

 figure: Fig. 2

Fig. 2 When +1,+1 mode is launched at 1550 nm: (a) the mode distributions and phase distributions at the different coupling length withd=3.1μm; (b) the coupling efficiencies of modes in the cross output port with d=3.1μm; (c) and (d) are the coupling results with d=6.35μm; (e) the coupling efficiency of +1,+1 mode in the cross output port with the different interval d between two microfibers.

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Figure 3(a) shows the wavelength dependence of the OAM couple with a fix center-to-center distance (d=6.6μm) and a fix overlapping length (L=3.535cm), where +1,+1 mode achieves the maximum coupling efficiency 99.19% with the crosstalk −24.9 dB. This coupler only achieves high coupling efficiency (less than 1% energy in the collinear output port) in 1545-1560 nm, which is not enough for the needs of the C-band communication. The bandwidth is difficult to expand by adjusting the microfiber’s diameter carefully. When the radius of the microfiber is comparable to the wavelength, the coupling efficiency, which is closely related to the mode distributions and the mode effective index, is highly sensitive to optical wavelength. Here, we propose to change the refractive index of liquid for tuning the operating wavelength and expanding the operating bandwidth. As shown in Fig. 3(b), the coupling curve of the operating wavelength 1580 nm (RI = 1.2878) and 1520 nm (RI = 1.3042) is almost overlapped with that of 1550 nm (RI = 1.2962). Also, this tuning method can achieve different coupling ratio. Figure 4(a) shows that the 1550 nm +1,+1 coupler (L=3.885cm) achieves the coupling ratio 10:90, 50:50, and 70:30 when the liquid RI is 1.2837, 1.2778, and 1.2748, respectively. By using the thermosensitive liquid (the Cargille Laboratories), the +1,+1coupler with d=6.1μm can achieve different coupling efficiency over the wholeC-band at L=3.885cm when the temperatures is tuning from 25 to 150 °C, as shown in Fig. 4(b).

 figure: Fig. 3

Fig. 3 (a) The wavelength dependence of +1,+1 mode in the output ports (at 3.535 cm); (b) the coupling efficiency of +1,+1 mode in the cross output port with (the refractive index of liquid, the input wavelength).

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 figure: Fig. 4

Fig. 4 (a) The different coupling ratios achieved at 3.885 cm; (b) the tunable coupling efficiency over the C-band within 25-150 °C.

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From the results mentioned above, a tunable +1,+1 mode fiber coupler with adjustable coupling ratio over the whole C-band is effectively designed. It is worth nothing that this coupler is also suitable for the coupling of 1,1 mode. Compared with +1,+1 mode, the synthesis of 1,1 mode only has a different sign, i.e., 1,1=HE21ejHE21o. So the coupled results of 1,1 mode and +1,+1 mode are the similar linear combination of the same eigenmodes in output ports and only have a different sign, which means that the coupling results of 1,1 mode in the output ports are exactly the same as Fig. 3 and Fig. 4.

Based on the similar designing process, this tunable fiber coupler can be extended to higher order OAM modes with thicker microfiber. By proper setting the critical value of d, high OAM mode purity and high maximum coupling efficiency can also be achieved. The coupling length may be increased because of the coupling interaction is decreased with the larger diameter and distance of microfibers. Fortunately, such problem can be alleviated by increasing the refractive index of microfiber, which can optimize the diameter and distance of microfibers to the smaller values.

4. Conclusion

In conclusion, the tunable OAM fiber coupler designs have been proposed and simulated for ±1,±1 mode. The designed coupler consists of two separate and parallel microfibers. Based on the mode match method, low crosstalk (< −20 dB) is achieved by optimizing the center-to-center distance d between the microfibers. Over the whole C-band, arbitrary coupling ratio can be achieved by adjusting the temperatures proper. The designed coupler can be potentially used for the OAM optical communication system and expand the application of OAM mode in fiber lasers, sensors and other various fiber systems.

Appendix

The OAM mode can propagate steadily in both the straight microfiber and the bending microfiber with proper curvature radius (1mm). Here is an example: the diameter of the microfiber is set to be 3.1 μm with the refractive index 1.444 at 1550 nm, and the refractive index liquid (the Cargille Laboratories) is selected to be RI=1.2962 for 1550 nm at 25 °C. For the bending microfiber, the radius of curvature is 1 mm. The effective refractive indices of the eigenmodes in the straight and bending microfibers are shown in Table 1. For both the straight and bending microfiber, the refractive index difference between HE21e and HE21o is less than 1×106, and the minimum refractive index difference of different modes in microfiber is larger than 1×104. Furthermore, the mode distribution and phase distribution of the +1,+1 mode in both the straight and bending microfiber are shown in Fig. 5. So the OAM mode can propagate steadily in both the straight and bending microfiber.

Tables Icon

Table 1. The effective refractive indices of the eigenmodes in the microfiber.

 figure: Fig. 5

Fig. 5 The mode distributions and phase distributions of the +1,+1 mode in the straight microfiber (a) and (b), and the bending microbiber (c) and (d).

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Funding

National Natural Science Foundation of China (NSFC) (61575064, U1609219); Science and Technology Project of Guangdong (2015B090926010); Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2015TQ01X322); Fundamental Research Funds for Central Universities (2015ZP019); High-level Personnel Special Support Program of Guangdong Province (2014TX01C087); the National Science Fund for Distinguished Young Scholars of China (61325024).

References and links

1. J. Wang, J. Y. 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]  

2. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014). [CrossRef]  

3. T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015). [CrossRef]  

4. 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]   [PubMed]  

5. P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 267–270 (2015). [CrossRef]  

6. X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015). [CrossRef]   [PubMed]  

7. S. Ramachandran, P. Gregg, P. Kristensen, and S. E. Golowich, “On the scalability of ring fiber designs for OAM multiplexing,” Opt. Express 23(3), 3721–3730 (2015). [CrossRef]   [PubMed]  

8. Z. Zhang, J. Gan, X. Heng, Y. Wu, Q. Li, Q. Qian, D. Chen, and Z. Yang, “Optical fiber design with orbital angular momentum light purity higher than 99.9,” Opt. Express 23(23), 29331–29341 (2015). [CrossRef]   [PubMed]  

9. P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006). [CrossRef]   [PubMed]  

10. Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36(21), 4269–4271 (2011). [CrossRef]   [PubMed]  

11. Y. Yan, L. Zhang, J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, A. E. Willner, and S. J. Dolinar, “Fiber structure to convert a Gaussian beam to higher-order optical orbital angular momentum modes,” Opt. Lett. 37(16), 3294–3296 (2012). [CrossRef]   [PubMed]  

12. S. Li, Q. Mo, X. Hu, C. Du, and J. Wang, “Controllable all-fiber orbital angular momentum mode converter,” Opt. Lett. 40(18), 4376–4379 (2015). [CrossRef]   [PubMed]  

13. Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015). [CrossRef]  

14. N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011). [CrossRef]  

15. C. N. Alexeyev, A. V. Milodan, M. C. Alexeyeva, and M. A. Yavorsky, “Inversion of the topological charge of optical vortices in a coil fiber resonator,” Opt. Lett. 41(7), 1526–1529 (2016). [CrossRef]   [PubMed]  

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

17. 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]   [PubMed]  

18. G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993). [CrossRef]  

19. I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965). [CrossRef]  

References

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  1. J. Wang, J. Y. 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]
  2. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
    [Crossref]
  3. T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
    [Crossref]
  4. 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] [PubMed]
  5. P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 267–270 (2015).
    [Crossref]
  6. X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
    [Crossref] [PubMed]
  7. S. Ramachandran, P. Gregg, P. Kristensen, and S. E. Golowich, “On the scalability of ring fiber designs for OAM multiplexing,” Opt. Express 23(3), 3721–3730 (2015).
    [Crossref] [PubMed]
  8. Z. Zhang, J. Gan, X. Heng, Y. Wu, Q. Li, Q. Qian, D. Chen, and Z. Yang, “Optical fiber design with orbital angular momentum light purity higher than 99.9,” Opt. Express 23(23), 29331–29341 (2015).
    [Crossref] [PubMed]
  9. P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
    [Crossref] [PubMed]
  10. Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36(21), 4269–4271 (2011).
    [Crossref] [PubMed]
  11. Y. Yan, L. Zhang, J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, A. E. Willner, and S. J. Dolinar, “Fiber structure to convert a Gaussian beam to higher-order optical orbital angular momentum modes,” Opt. Lett. 37(16), 3294–3296 (2012).
    [Crossref] [PubMed]
  12. S. Li, Q. Mo, X. Hu, C. Du, and J. Wang, “Controllable all-fiber orbital angular momentum mode converter,” Opt. Lett. 40(18), 4376–4379 (2015).
    [Crossref] [PubMed]
  13. Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
    [Crossref]
  14. N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
    [Crossref]
  15. C. N. Alexeyev, A. V. Milodan, M. C. Alexeyeva, and M. A. Yavorsky, “Inversion of the topological charge of optical vortices in a coil fiber resonator,” Opt. Lett. 41(7), 1526–1529 (2016).
    [Crossref] [PubMed]
  16. H. Xu and L. Yang, “Conversion of orbital angular momentum of light in chiral fiber gratings,” Opt. Lett. 38(11), 1978–1980 (2013).
    [Crossref] [PubMed]
  17. 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] [PubMed]
  18. G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993).
    [Crossref]
  19. I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965).
    [Crossref]

2016 (1)

2015 (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] [PubMed]

S. Li, Q. Mo, X. Hu, C. Du, and J. Wang, “Controllable all-fiber orbital angular momentum mode converter,” Opt. Lett. 40(18), 4376–4379 (2015).
[Crossref] [PubMed]

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 267–270 (2015).
[Crossref]

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

S. Ramachandran, P. Gregg, P. Kristensen, and S. E. Golowich, “On the scalability of ring fiber designs for OAM multiplexing,” Opt. Express 23(3), 3721–3730 (2015).
[Crossref] [PubMed]

Z. Zhang, J. Gan, X. Heng, Y. Wu, Q. Li, Q. Qian, D. Chen, and Z. Yang, “Optical fiber design with orbital angular momentum light purity higher than 99.9,” Opt. Express 23(23), 29331–29341 (2015).
[Crossref] [PubMed]

2014 (1)

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

2013 (2)

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] [PubMed]

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

2012 (2)

Y. Yan, L. Zhang, J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, A. E. Willner, and S. J. Dolinar, “Fiber structure to convert a Gaussian beam to higher-order optical orbital angular momentum modes,” Opt. Lett. 37(16), 3294–3296 (2012).
[Crossref] [PubMed]

J. Wang, J. Y. 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]

2011 (2)

Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36(21), 4269–4271 (2011).
[Crossref] [PubMed]

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

2006 (1)

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

1993 (1)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993).
[Crossref]

1965 (1)

Ahmed, N.

Alexeyev, C. N.

Alexeyev, N.

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

Alexeyeva, M. C.

Alhassen, F.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Birnbaum, K.

Boklag, N. A.

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

Bozinovic, N.

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] [PubMed]

Cai, X. D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Chen, D.

Chen, H.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Chen, M. C.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Chen, Y.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Dolinar, S.

J. Wang, J. Y. 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]

Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36(21), 4269–4271 (2011).
[Crossref] [PubMed]

Dolinar, S. J.

Du, C.

Fadeyeva, T. A.

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

Fang, L.

Fazal, I. M.

Fickler, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Fink, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Gan, J.

Golowich, S. E.

Gregg, P.

Handsteiner, J.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Heng, X.

Hu, X.

Huang, H.

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] [PubMed]

J. Wang, J. Y. 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]

Jia, P.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Krenn, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Kristensen, P.

Lee, H. P.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Lei, T.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Li, Q.

Li, S.

Li, Y.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, Z.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Lin, J.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Liu, G. N.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Liu, N. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Lu, C. Y.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Malik, M.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Malitson, I.

Milodan, A. V.

Min, C.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Mo, Q.

Niu, H.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Nolting, H. P.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993).
[Crossref]

Pan, J. W.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Qian, Q.

Ramachandran, S.

Ren, Y.

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] [PubMed]

J. Wang, J. Y. 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]

Scheidl, T.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Shamee, B.

Su, Z. E.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Sztefka, G.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993).
[Crossref]

Tur, M.

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] [PubMed]

J. Wang, J. Y. 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]

Ursin, R.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Wang, J.

Wang, X. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Willner, A. E.

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] [PubMed]

J. Wang, J. Y. 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]

Y. Yan, L. Zhang, J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, A. E. Willner, and S. J. Dolinar, “Fiber structure to convert a Gaussian beam to higher-order optical orbital angular momentum modes,” Opt. Lett. 37(16), 3294–3296 (2012).
[Crossref] [PubMed]

Y. Yan, J. Wang, L. Zhang, J. Y. Yang, I. M. Fazal, N. Ahmed, B. Shamee, A. E. Willner, K. Birnbaum, and S. Dolinar, “Fiber coupler for generating orbital angular momentum modes,” Opt. Lett. 36(21), 4269–4271 (2011).
[Crossref] [PubMed]

Wu, D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

Wu, Y.

Xu, H.

Xu, P.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Xu, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yan, Y.

Yang, J. Y.

Yang, L.

Yang, Z.

Yavorsky, M. A.

C. N. Alexeyev, A. V. Milodan, M. C. Alexeyeva, and M. A. Yavorsky, “Inversion of the topological charge of optical vortices in a coil fiber resonator,” Opt. Lett. 41(7), 1526–1529 (2016).
[Crossref] [PubMed]

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

Yu, C.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yu, S.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Yuan, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yue, Y.

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] [PubMed]

J. Wang, J. Y. 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]

Zeilinger, A.

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Zhang, L.

Zhang, M.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Zhang, Y.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Zhang, Z.

Zhong, Z.

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett. 5(5), 554–557 (1993).
[Crossref]

J. Opt. (1)

N. Alexeyev, N. A. Boklag, T. A. Fadeyeva, and M. A. Yavorsky, “Tunnelling of orbital angular momentum in parallel optical waveguides,” J. Opt. 13(6), 064012 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

Light Sci. Appl. (1)

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Nat. Photonics (1)

J. Wang, J. Y. 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]

Nature (1)

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref] [PubMed]

New J. Phys. (1)

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across Vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

Opt. Commun. (1)

Y. Zhang, Y. Chen, Z. Zhong, P. Xu, H. Chen, and S. Yu, “Orbital angular momentum (OAM) modes routing in a ring fiber based directional coupler,” Opt. Commun. 350(1), 160–164 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (6)

Optica (1)

Phys. Rev. Lett. (1)

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Science (1)

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] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the tunable OAM coupler coupler; insets are the refractive index profile of each part. The red arrows represent the direction of the OAM beam travel.
Fig. 2
Fig. 2 When + 1 , + 1 mode is launched at 1550 nm: (a) the mode distributions and phase distributions at the different coupling length with d = 3.1 μ m ; (b) the coupling efficiencies of modes in the cross output port with d = 3.1 μ m ; (c) and (d) are the coupling results with d = 6.35 μ m ; (e) the coupling efficiency of + 1 , + 1 mode in the cross output port with the different interval d between two microfibers.
Fig. 3
Fig. 3 (a) The wavelength dependence of + 1 , + 1 mode in the output ports (at 3.535 cm); (b) the coupling efficiency of + 1 , + 1 mode in the cross output port with (the refractive index of liquid, the input wavelength).
Fig. 4
Fig. 4 (a) The different coupling ratios achieved at 3.885 cm; (b) the tunable coupling efficiency over the C-band within 25-150 °C.
Fig. 5
Fig. 5 The mode distributions and phase distributions of the + 1 , + 1 mode in the straight microfiber (a) and (b), and the bending microbiber (c) and (d).

Tables (1)

Tables Icon

Table 1 The effective refractive indices of the eigenmodes in the microfiber.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E 1 = i = 1 N 1 a i e 1 i exp ( j β 1 i z )
E 2 = i = 1 N 2 b i e 2 i exp ( j β 2 i z )
E 3 = i = 1 N 3 c i e 3 i exp ( j β 3 i z )
E 1 = p = 1 N 1 a p e 1 p
E 2 _ t = E 1 _ t
b i = E 2 e 2 i * d s e 2 i e 2 i * d s
b i = ( p = 1 N 1 a p e 1 p _ t ) e 2 i _ t * d s e 2 i _ t e 2 i _ t * d s
Γ mode 1 _ mode 2 = e mode 1 e mode 2 * d s e mode 2 e mode 2 * d s
b i = p = 1 N 1 a p Γ 1 p _ 2 i
E 2 = i = 1 N 2 b i e 2 i exp ( j β 2 i L )
E 3 _ t = E 2 _ t
c q = ( i = 1 N 2 b i e 2 i _ t exp ( j β 2 i L ) ) e 3 q _ t * d s e 3 q _ t e 3 q _ t * d s = i = 1 N 2 b i exp ( j β 2 i L ) Γ 2 i _ 3 q
c q = i = 1 N 2 p = 1 N 1 a p Γ 1 p _ 2 i exp ( j β 2 i L ) Γ 2 i _ 3 q
η p q = | c q e 3 q c q * e 3 q * d s | | a p e 1 p a p * e 1 p * d s | = | c q c q * d s | | a p a p * d s |
a i = δ i p
η p q = | [ i = 1 N 2 Γ 1 p _ 2 i exp ( j β 2 i L ) Γ 2 i _ 3 q ] [ i = 1 N 2 Γ 1 p _ 2 i exp ( j β 2 i L ) Γ 2 i _ 3 q ] * |
η p q = | [ i = 1 N 2 Γ 1 p _ 2 i Γ 1 q _ 2 i exp ( j β 2 i L ) ] [ i = 1 N 2 Γ 1 p _ 2 i Γ 1 q _ 2 i exp ( j β 2 i L ) ] * |

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