An all-fiber scheme for stable orbital angular momentum (OAM) beam generation and propagation is proposed and demonstrated. This scheme is based on a self-designed and manufactured graded-index few mode fiber (GI-FMF) and compatible mode selection coupler (MSC). The MSC, which consists of a conventional single mode fiber (SMF) and the GI-FMF, can effectively couple the fundamental mode in the SMF to the desired OAM mode in the GI-FMF based on phase matching condition. Meanwhile, the GI-FMF breaks the degeneracy between the desired eigenmodes and neighboring vector modes, thereby allowing the preservation and propagation of the selectively excited OAM modes. As a proof-of-principle, we have implemented an all-fiber device operating in stable OAM modes with |l| = 1. The experimental results show stable propagation of OAM beams with the mode purity of ∼95% and bandwidth of 100 nm. This all fiber device could be useful for further development of wide bandwidth OAM mode division multiplexed application.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Orbital-angular-momentum (OAM) beam, characterized by a helical phase front exp(ilϕ) (where l is the topological charge and ϕ is the azimuthal angle around the optical axis, respectively), has generated considerable interest for a variety of fundamental research studies and modern applications, such as quantum and nano optics [1, 2], optical manipulation , super-resolution microscopy  and laser material processing . In addition to these application areas, OAM beam has the potential to tremendously increase the capacity of communication systems due to the topological charge l could be used as an additional degree of freedom for light . Several proof-of-concept experimental demonstrations of OAM modes multiplexing and de-multiplexing for data rate record-breaking optical communications have been reported both in free space [7, 8] and optical fiber . To fully access the benefits of the OAM degree of freedom, the devices that can efficiently generate the OAM mode are highly desirable. As for the free-space optical communication system, many approaches for generating OAM beams have been studied and applied, such as cylindrical lens mode convertors , spiral phase plates , q-plates , or spatial light modulators (SLMs) . Compared with the free-space optical communication, which is seriously affected by transmission loss and atmospheric turbulence, the fiber optic network is much more suitable for ultra-long distance communication. The OAM beams multiplexing and transmission over a 50-km few mode fiber (FMF) has been demonstrated, where the OAM beams have been generated by SLMs in free-space and then coupled into the optical fiber by conventional free-space focusing method . Although the information has been successfully transmitted with OAM modes in FMF, this system strictly relies on free-space OAM generation and high-precision fiber coupling, which obviously increase the complexity and reduce the practicality of the system. Therefore, it is highly desirable for the all fiber devices which could achieve stable OAM beam generation and propagation.
Recently, several all fiber schemes for OAM beam generation have been proposed and demonstrated, such as fiber mode converter , fiber gratings , and all-fiber mode selective couplers (MSCs) . However, these all fiber OAM beam generation schemes have been achieved based on conventional FMFs which meet the weak-guidance approximation conditions. In these conventional FMFs, the eigenmodes which could carry OAM always coexist with other vector modes in the same mode group, which causes modes crosstalk and restricts the stable OAM beam propagation. Therefore, the stable OAM beam propagation supported fiber, which could break the degeneracy of eigenmodes and vector mode within a mode group, is the basic element of all fiber OAM beam generation device. Till now, only limited schemes have been proposed and developed for supporting stable OAM beam propagation in fiber, such as the ring-core fiber [18–20], inverse-parabolic graded-index fiber  and large refractive index difference graded-index few mode fiber (GI-FMF) . From a practical standpoint, OAM beam generation based on exactly the OAM propagation supported fiber would be the optimal scheme. The only related research has been reported by S. Pidishety et.al , where the OAM beam has been excited using an all-fiber weakly fused mode selective coupler consisting of a single-mode fiber and a OAM mode propagation supported ring-core fiber. Hence, the all-fiber OAM beam generation and propagation devices which offer the potential for direct integration with existing optical communication system are highly desirable and deeply significant.
In this paper, a self-designed and manufactured GI-FMF, which could support stable OAM beam propagation, is adopted as the base fiber for the OAM beam generation. It is important to note that this specially designed GI-FMF owns the merit of breaking the degeneracy between the desired HE21 eigenmode and neighboring TE01/TM01 vector modes, thereby allowing the preservation of the selectively excited OAM modes. Based on the phase matching condition and weakly fused technology, an all-fiber MSC composed of a conventional SMF and our specially designed GI-FMF has been fabricated. Based on this all-fiber MSC, OAM beams (|l| = 1) with the mode purity of ∼95% has been generated. Also, stable OAM beam generation and propagation in this GI-FMF with 100 nm bandwidth has been experimental demonstrated.
2. Principle and design
Here the refractive index profile of our specially designed GI-FMF is supposed as , where ∆n, r0, n1 and α are the maximum refractive index difference between core and cladding, the core radius, the cladding index and the shape factor, respectively. The key design of stable OAM propagation supported fiber is to introduce a relative large refractive index difference ∆n to obtain effective mode separation, which obviously breaks the weakly guiding approximation. The relationship between the fiber structure and the purity of synthesized OAM light have been theoretically explored in our previous work . The plasma enhanced chemical vapor deposition (PECVD) is adopted to ensure that the refractive index profile of fiber is the same as that of the design. Figure 1(a) shows the refractive index profile of our fabricated GI-FMF, where ∆n = 0.0363, r0 = 4.8 μm, n1 = 1.4306 and α = 1.98. A fluorine doped low refractive index layer is added between the germanium doped gradient index core and the silica cladding for achieving high refractive index contrast. The effective refractive indices of the fiber eigenmodes are calculated at C-band. According to simulation, this specially designed GI-FMF could support 6 vector modes ( and ) over the whole C-band. As we all know, OAM states with l = ± 1 can be represented as π/2-phase-shifted linear combinations of the eigenmodes and , and expressed as . This indicates that our specially designed GI-FMF is expected to support 2 different OAM modes, i.e. l = + 1 and l = −1. The minimum difference of effective refractive index neff between TE01/TM01 mode and mode is 0.9 × 10−4 as shown in Fig. 1(b), which breaks modal degeneracy and decreases inter-mode crosstalk to be very low level. The relative large effective index separation between TE01/TM01 mode and mode allows selective excitation and stable propagation of the desired OAM mode in our GI-FMF. However, due to the restriction of the current process condition, the preliminary fabricated GI-FMF can only support the OAM beams with |l| = 1. Of course, if we continue to increase the refractive index difference between the core and cladding, this type of optical fiber will steadily support much more high orders of OAM beams.
The schematic of all fiber MSC which could generate OAM modes with |l| = 1 is shown in Fig. 2(a). The MSC is composed of a SMF arm and our specially fabricated GI-FMF arm, and its function is to realize the selective mode coupling between the HE11 mode in the SMF and the HE21 mode in our specially fabricated GI-FMF. The circular polarization HE21 mode in the GI-FMF, i.e. the |l| = 1 OAM modes, could be selectively excited when the circular polarization HE11 mode is launched into the SMF. The principle of this MSC is to phase match the HE11 mode in SMF with the HE21 mode in GI-FMF in coupling region, that is, the effective refractive index of the HE11 mode in SMF is the same as that of the HE21 mode in GI-FMF. As shown in Fig. 2(b), the effective refractive indexes of the HE11 mode in SMF and the HE21 mode in GI-FMF as a function of fiber diameter are simulated to find the phase matching condition. For specially fabricated GI-FMF, a three-layer structure consisting of the germanium doped gradient index core, fluorine doped low refractive index layer and air regions is adopted in the simulations as the core guided mode could be influenced by the surrounding environment at the smaller taper diameters . Similarly, for the SMF (SMF-28 from Corning Inc., 8.2 μm core, 125 μm silica cladding and 0.36% refractive index difference), a three-layer structure including the core, silica cladding and air regions is adopted in the simulations. As indicated with the blue dashed lines in Fig. 2(b), when the HE11 mode in SMF and the HE21 mode in GI-FMF have the same effective refractive index of 1.38, the diameter of the SMF and GI-FMF is 2.45 μm and 4.49 μm, respectively. Consequently, in order to satisfy the phase matching condition, the target diameter ratio between the SMF and GI-FMF should be 0.55. The effective refractive index differences ∆neff of neighboring modes i.e., and in GI-FMF as a function of fiber diameter are also shown in Fig. 2(c). The ∆neff of phase matching points are 3.1 × 10−3 and 0.9 × 10−3, respectively. These results indicate that the TE01/TM01 modes are sufficiently separated from the desired HE21 mode so as to enable directional coupling only to the HE21 mode in coupling region.
The all fiber MSC is fabricated based on weakly fused technique. First a section of GI-FMF is etched using HF solution to be 22 μm diameter, where the silica cladding of GI-FMF is completely corroded. To achieve the phase matching condition, the SMF arm is prepared by tapering a section of the SMF-28 to the diameter of 12 μm. Then the pre-tapered SMF-28 is carefully aligned with the etched GI-FMF. Finally, the all fiber MSC has been fabricated by standard fused biconical taper technique . During the fused tapering process, a laser diode operating at 1550 nm wavelength is injected into the input SMF port of MSC, the optical power and intensity pattern from the output ports are real-time monitored and the fused tapering process won’t stop until the coupled power reaches the maximum.
3. Experimental setup
The experimental setup used for characterization of the OAM beam generation is shown in Fig. 3. The output beam from a narrow-linewidth tunable laser is divided into two branches by an optical coupler with a proportion of 10:90. The lower branch is injected into the fabricated all fiber MSC to generate OAM beam, and the upper branch is used as a reference beam to interfere with the generated OAM beam. The output beams from the reference SMF and the GI-FMF output of the MSC are collimated using 10 × objective lens. In order to record the interference pattern and estimate the mode purity synchronously, the collimated OAM beams are also split into two branches by a non-polarizing beam splitter (NPBS). One branch is split into horizontal and vertical polarization projections through a polarizing beam displacing prism (PBDP) directly. The vertical polarization projection and the reference beam are combined using a NPBS to form the interference patterns. The other branch is split into left circular (LC) and right circular (RC) polarization projections through a quarter wave plate (QWP) and a PBDP to analyze the mode purity. All these patterns are recorded by a CCD camera (Goldeye G-033, Allied Vision).
4. Experimental results and discussion
By properly adjusting the polarization controllers, a perfect annular intensity profile and its corresponding interference pattern are observed as shown in Fig. 4(a). The characteristic fork interference pattern confirms the presence of OAM in the generated beam. The number of forks represents the topological charge of the OAM beam, which is |l| = 1. To further estimate the mode purity, the intensity patterns of LC and RC polarization states are deconstructed into an azimuthal Fourier series, from which relative modal weights could be determined . The purity measurement results of the output OAM beam at 1550 nm are displayed in Fig. 4(b). It is important to note that, since the entire output intensity pattern is divided into LC and RC polarization states, as illustrated in Fig. 4(b), the two polarization states should be calculated together to estimate the mode occupation ratio in the whole output, rather than the proportion of the mode in one polarization state. It can be seen that the maximum modal purity of ∼95% is obtained in our fabricated all fiber MSC. The mode purity of OAM beam is affected by the excitation of unwanted neighboring modes (TE01/TM01). This is probably due to the slight deviation of the diameter of the two fibers in fused biconical process.
To measure the wavelength dependence of our fabricated all fiber MSC, a tunable laser source (81606A, Keysight) is injected into the input port of SMF arm, and the wavelength is tuned from 1490 nm to 1610nm with 5 nm interval step. The mode purity is measured at different wavelengths. As can be seen in Fig. 5(a), the bandwidth for 80% coupling around the peak coupling wavelength is about 60 nm, and 3 dB bandwidth is about 100 nm. The mode purity decreases as the operating wavelength gradually deviates from the target wavelength. The main reason of wavelength dependence is the phase-mismatch between the HE11 and the HE21 modes at different wavelengths in the tapered coupling region. The 3 dB bandwidth of 100 nm far exceeds that of the reported all fiber OAM generators, such as long-period fiber gratings  and helical fiber Bragg gratings . Also, the temperature stability of this all fiber MSCs are far better than fiber grating based devices.
Additionally, the polarization dependence of our fabricated all fiber MSC is investigated. The operation wavelength of the tunable laser source is fixed at 1550 nm. The collimated output beam from laser source passes through a polarizer and a half wave plate sequentially in space, and then focusing couples into the SMF input port of the MSC. The polarization state of the input fundamental transverse mode can be adjusted by accurately rotating the angle of the half-wave plate. The mode purity of the OAM light beam is measured at different polarization angles. As shown in Fig. 5(b), the mode purity is highly dependent on polarization, which is mainly attribute to the asymmetry induced birefringence in the coupling area of the MSC. OAM modes l = −1 and l = + 1 have the reverse correlation with the polarization angle. However, it is not easy to tune the OAM completely from l = −1 to l = + 1 by only varying the polarization. For generating stable OAM light with high mode purity, it is necessary to adjust the polarization of the input light and avoid bending or twisting the fiber.
Furthermore, the stable propagation of the generated OAM beam is verified by cutting off a section of the output GI-FMF of the MSC with different length L while monitoring the far-field intensity profiles of the output. As shown in the top row of Fig. 6, the OAM beam are kept steady in GI-FMF after cutting off different fiber length. It is need to note that the measurement is implemented without modifying the input polarization state. As a contrast, the conventional commercial FMF (OFS-Fitel, Two Mode Step-Index Fiber), which meet the weak-guidance approximation conditions and could not break the degeneracy of eigenmodes and vector mode within a mode group, has been used for replacing our designed GI-FMF in the MSC. Based on the same design and fabrication process, this SMF-FMF MSC is fabricated for the comparison. Before the characterization of this SMF-FMF MSC, it needs to adjust the polarization states of input SMF arm and output FMF arm synchronously so as to obtain OAM beam at the output port. However, the OAM beam from this SMF-FMF MSC could not kept steady in the output FMF arm after cutting off different fiber length, as shown in the bottom row of Fig. 6, which is consistent with the previous theoretical analysis. Additionally, the transmission loss of generated OAM beam in our GI-FMF is ∼2.8 dB/km, which is measured by truncation method. According to the above results, our SMF GI-FMF MSC is a good solution to achieve stable OAM generation and propagation in optical fiber.
The all-fiber OAM generation and propagation scheme will contribute to the realization of all-fiber OAM mode multiplexing and demultiplexing system. This not only avoids the high precision coupling of OAM modes to optical fiber, but also has the advantages of higher compactness, flexibility and practicability. Additionally, thanks to its 100 nm bandwidth, it can be combined with mature wavelength division multiplexing to further improve the transmission capacity and spectral efficiency of the OAM based optical fiber communication system.
In summary, we demonstrate an all fiber MSC for highly stable and efficient generation OAM beams in fiber. OAM beams (|l| = 1) with the mode purity of ∼95% is achieved in our SMF GI-FMF MSC. The mode purity of OAM beam can be further optimized by improving the technological parameters of the fused biconical process. Stable OAM beam generation and propagation in fiber with 100 nm bandwidth has been experimental demonstrated. Additionally, by employing a GI-FMF which supports more higher order vector modes, this all-fiber SMF GI-FMF MSC scheme can be extended to generate OAM beams with |l|>1. These results show that the all fiber OAM generator will greatly promote the OAM mode multiplexing application in practical fiber communication system.
National Natural Science Foundation of China (61575064, U1609219, U1766220), the Science and Technology Project of Guangdong (2015B090926010, 2016B090925004, and 2017B090911005), Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2015TQ01X322), and Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X137).
We thank Dr. Wenyong Luo and Dr. Cheng Du in Fiberhome Telecommunication Technologies Limited Company for their help in the fabrication of this graded-index few mode fiber.
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