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Abstract
Mode division multiplexing has attracted great attention because it can potentially overcome the limitation of single-mode fiber traffic capacity. However, it has been challenging to realize multiple modes controlling and switching due to the intrinsic overlap of the modes in the transmission waveguide. As a solution, we propose a cascaded phase-shifted long-period fiber grating (PS-LPFG) based multiple mode switching scheme. Using the PS-LPFGs, the multiple guided orbital angular momentum (OAM) modes selective controlling and switching at multi-wavelength can be achieved in few-mode fibers by regulating the grating resonance condition. In principle, a N × N mode switch matrix can be realized by cascading $C_{N}^{2}$ gratings, where each grating acts as a mode switch element to achieve a couple selected OAM mode switching and meanwhile the other modes are under nonblocking status. As a proof of the concept, a 2 × 2 mode switching between two OAM modes at different wavelengths based on one PS-LPFG element is demonstrated in our experiments. The switching efficiency of the two modes at two wavelengths 1537nm and 1558nm are ∼98.4% and ∼98.7%, respectively. The proposed multiple OAM mode switch has potential applications in the future hybrid multi-dimensional multiplexing optical fiber communication systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The single-mode fiber (SMF) capacity for transmitting Internet data has increased by several orders of magnitude over the past decades through fully exploiting various dimensions, including time, wavelength, polarization and phase [1]. As the continuously rapid development of the information age and the advent of big data era [2,3], the transmission capacity of SMF in transmission systems is approaching the bottleneck enforced by optical fiber nonlinear effects [4,5]. In order to further increase the transmission capacity per fiber and solve the bottlenecks of the increasingly tight bandwidth resource, mode division multiplexing technology (MDM) has been widely investigated, which provides a new dimension for the future optical communication network by exploiting different spatial modes as signal carriers [6 –9]. The ability to switch such channels over a reconfigurable optical network would offer new functionalities to MDM that effectively reduces the complexity of the network infrastructure [10 –13].
Recently, orbital angular momentum (OAM) mode as a new spatial mode basis has attracted wide attentions [14 –16]. OAM mode has a helical transverse phase structure of $\exp (i \varphi l)$, where $\varphi$ is the transverse azimuthal angle and $l$ denoting the OAM state [17]. In principle, OAM mode has the theoretically unlimited values of $l$, and OAM modes with different $l$ values are mutually orthogonal. Such modes with unlimited topological charge $l$ can be exploited as an additional switching domain for reconfigurable optical network based on MDM [18,19]. OAM switching combined with existing wavelength division multiplexing (WDM) would effectively enhance the scalability of optical interconnection networks [20 –22]. In OAM switching domain, it is vital to switch the multimode channels for subsequent routing. But the dynamic manipulation of these OAM states in transmission waveguides remains challenging due to the intrinsically overlap of the modes. To date, some OAM-based switching methods have been experimentally demonstrated, such as chip-based devices [23,24], spatial light modulators [25 –27] and nonlinear optical interactions [28]. Typically, the most commonly used switching device is spatial light modulator, which dynamically controls the phase with high cost and a limited scalability. Moreover, the coupling loss and accurate optical alignments will be non-ignorable factors, when these devices are combined with optical fiber communication system. In comparison, all-fiber-based OAM mode switching elements would be a promising solution due to its natural compatibility with the fiber system and the all-fiber based switching device without a complicated demultiplexing and multiplexing procedure. However, due to the intrinsically overlap of the modes in transmission fiber, it is difficult to realize the multiple mode switching based on all-fiber device. No works have been reported to achieve all-fiber-based multiple OAM mode switching, as far as our literature review concerns, let alone multiple OAM mode switching is not confined to wavelength domain.
To realize multiple OAM mode switching at multi-wavelength simultaneously in few-mode fiber (FMF), we propose an optical mode switching scheme based on a cascaded phase-shifted long-period fiber grating (PS-LPFG). The PS-LPFGs inscribed and cascaded in FMF can switch the guiding OAM modes by regulating the grating resonance condition at multiple wavelengths. Each grating in the cascaded PS-LPFGs can independently switch a pair of OAM modes, while the cascaded gratings can switch multiple pairs of OAM modes and, in principle, can realize a $N \times N$ mode switch matrix. In addition, the mode switching at any wavelength in accordance with the application requirement can be realized by adjusting the parameters of the PS-LPFGs. As a proof of the multiple OAM mode switching, we experimentally demonstrated the switching between the zero-order OAM mode and the second-order OAM modes with the efficiency of $\sim$98.4% and $\sim$98.7% at two wavelengths (1537nm and 1558nm) based on a PS-LPFG element.
2. Principle
2.1 Scheme of OAM mode switching
Figure 1 shows a schematic of the OAM mode switching at different wavelengths. The OAM degree of freedom is orthogonal to wavelength and can be used as a switching domain, which is independent of the wavelength domain. Thus, the guided OAM modes in FMF can be switched at different wavelengths simultaneously, as shown in Fig. 1(a). To realize the OAM mode-selective switching shown in Fig. 1(b), LPFGs inscribed in FMF are selected as switch elements. In principle, a $N \times N$ mode switch matrix can be realized by cascading $C_{N}^{2}$ LPFGs, where each LPFG acts as a mode switch element and can implement the selected OAM mode pair switching and nonblocking to other modes. For example, a $4 \times 4$ OAM mode selective switch matrix can be implemented by cascading 6 independently designed LPFGs, each of which can switch a pair of OAM modes (any pair selected from the four input OAM modes, such as $l=0, 1, 2, 3)$. In this scheme, the mode-selective coupling and switching is implemented with the special designed LPFGs, and the switching process is reversed by regulating the grating resonance condition. In FMF systems, the maximal switching mode number $N$ is determined by the fiber, which should support the $N$ OAM modes multiplexing and transmission. On the other hand, due to the orthogonality and the large effective refractive index difference between higher-order OAM ($l = 2, 3, 4\cdots$) mode and fundamental mode, it’s very hard to overlap two mode fields and realize their cross-coupling. Here, the $N$ of 4 can be realized, in our point of view, since the first, second and third order OAM modes generation in LPFG has been achieved [29 –31]. In these LPFGs, however, the OAM mode resonance coupling occurs at only one wavelength, it is difficult to support the switching at multiple wavelengths simultaneously. To overcome this limit, as shown in Fig. 1(c), the PS-LPFG is employed to realize multiple wavelengths mode resonance coupling.
Fig. 1. (a) The schematic of OAM mode switching at different wavelengths. (b) OAM mode-selective switch matrix. (c) The schematics of two modes switching at multi-wavelength. PS-LPFG, phase-shifted long-period fiber grating; TPS-LPFG, twisted phase-shifted long-period fiber grating; The output mode field diagram on slice $m$ corresponds to the result of the input of the mode $m$, and slice $n$ corresponds to the result of the mode $n$.
Figure 1(c) illustrates the two OAM mode switching process at multiple wavelengths schematically. The PS-LPFG with multiple phase-shift points (marked by blue arrows) implements mode-selective coupling at multiple wavelengths. The TPS-LPFG (twisted PS-LPFG) represents the grating in a twisted state and has a designed resonance condition. When two selected OAM modes pass through the corresponding grating, the mode conversion can be achieved by the grating, in which one mode can be converted to the other mode and vice-versa. The output mode field diagram in slice $m$ and slice $n$ correspond to the result of the input of the mode $m$ and mode $n$, respectively. When the input light with mode $m$ and mode $n$ pass through the PS-LPFG at different resonance wavelengths $\lambda _1$, $\lambda _3$,…, $\lambda _M$ (odd number corresponds to resonance wavelength), the input mode $m$ is coupled to the another mode $n$ and the input mode $n$ is back-coupled to the mode $m$ due to the mode coupling effect of the grating, as shown in the first row of slice $m$ and in the first row of slice $n$ of the output of Fig. 1(c), respectively. Then, we applied a twist rate to PS-LPFG, the resonance modes of grating will be switched, which is shown in the second row of slice $m$ and in the second row of slice $n$ of the output in Fig. 1(c). This means the mode channels are passively switched between two selective OAM modes at multi-wavelength by twisting the PS-LPFG.
2.2 Extending the switching wavelength from one to multiple
The proposed PS-LPFGs is used to realize the mode resonance coupling between the corresponding transmission OAM modes and to switch them at multiple wavelengths. The PS-LPFGs inscribed in FMF is different from the ordinary LPFG in SMF, which usually couples the fundamental mode to several kinds of cladding modes. The inserted phase-shift points in the PS-LPFG are used to extend the number of resonance wavelengths for compatibility with coarse wavelength division multiplexing (CWDM) system. Generally, the coupling of two modes in FMF LPFG occurs at one resonance wavelength. When $N$ phase-shift points are introduced in the FMF LPFG, the coupling similar with the ordinary phase-shifted LPFGs in SMF will occurs at $N+1$ resonance wavelengths [32].
In PS-LPFG, the resonance wavelength can be extended from two to $N$ ($N = 3,4,\ldots$) by inserting $N-1$ phase-shift points. In order to understand the characteristics of the multi-wavelength mode coupling and the switching element PS-LPFG, we apply the coupled-mode theory to the fiber core mode coupling, and use the transfer matrix method to analyze the mode coupling of the grating. The PS-LPFG inscribed in the FMF can be treated as a combination of multiple uniform LPFGs and phase-shift regions, each uniform grating and each phase-shift region can be described using $2 \times 2$ transfer matrix and phase shift matrix, respectively [33]. The whole PS-LPFG can be expressed as a $2 \times 2$ matrix $F_{P S-L P F G}$ by multiplying all the transfer matrix and phase shift matrix together, the field amplitude after light traversing the PS-LPFG can be expressed as [32,34]
Fig. 2. (a) Spectral responses for different LPFGs. (b) The number of resonance wavelengths, wavelength spacing as a function of the number of phase-shift points.
2.3 Scaling the mode switch using cascaded PS-LPFGs
In FMF, the passing modes in fiber grating can be switched through controlling the resonance condition of the grating, such as applying twist, strain and so on to the grating. Here, we use the twisting effect of the PS-LPFG to adjust its resonance condition and control the mode channels of the light. Twisting a PS-LPFG will introduce a distributed stress along the grating, which causes the propagation constants of both resonant core modes to change with different magnitude [35], so as to achieve the purpose of regulating the mode resonance conditions of this grating. Through the controlling of the mode resonance conditions of the PS-LPFG, the guided modes can be selectively controlled and switched in FMF. In principle, one PS-LPFG can realize a pair of modes switching as shown in Fig. 1(c), and multiple PS-LPFGs cascades can realize multiple mode switching.
In order to clarify the process of multiple mode switching, we take three OAM modes switching by cascading three PS-LPFGs with two phase-shift points as an example to illustrate the switching process. The PS-LPFGs with different periods are employed to switch different pairs of modes, as shown in Fig. 3. The black with circle and blue with triangle curve represent the spectra of the PS-LPFGs in a twist-free state and twisted state. To simplify the description, we use $|l, m>$ to represent an optical flow $m$ transmitted in $l$ order OAM mode, and use $| l_{1}, m_{1} ; l_{2}, m_{2}>$ to represent two optical flows transmitted in two different OAM modes and so on. The OAM beam acts as a spatial channel and $l$ acts as each channel’s label. We use OAM with different $l$ values to label different optical flows and simultaneously manipulate each flow according to their OAM states. Here, the PS-LPFG1, 2 and 3 are used to realize the transmitted state switch between the $| 0,0 ; 1,1>$ and $| 0,1 ; 1,0>$, $| 0,0 ; 2,2>$ and $| 0,2 ; 2,0>$, and $| 1,1 ; 2,2>$ and $| 1,2 ; 2,1>$, respectively. Taking wavelength $\lambda _1$ as an example, a pair of corresponding modes are switched by a PS-LPFG, and the other modes pass through the grating without any changes. If the PS-LPFG is twisted to a designed state, the mode resonance coupling condition is not satisfied at $\lambda _1$, which means that when the grating is switched between the natural state and this twisted state, two modes switching will be achieved. In the twisted state, the grating is equivalent to a segment of FMF and all the modes pass through it and unchanged (identified as the grating turned off). Based on this adjustable property of grating, the switching functions among the three modes can be achieved via cascading the designed PS-LPFGs. In which, each one of the cascaded gratings needs to be controlled independently to realize the switching functions.
Fig. 3. Conceptual diagram of three OAM modes switching by cascading three PS-LPFGs with two phase-shift points.
The switching function of three modes includes three levels: all modes pass, any two modes switch and three modes switch simultaneously. For the all modes pass situation, the modes are not converted and the three cascaded gratings are all twisted to the designed states to turn off their converting function. For the switching between any two of the three modes, one corresponding grating works and the other two gratings turns off. As an example, for the switching between the $| 0,0 ; 1,1>$ and $| 0,1 ; 1,0>$, the PS-LPFG1 works as a mode switching element and is coupled the input OAM mode $l = 0$ ($l = 1$) to mode $l = 1$ ($l = 0$), and the PS-LPFG2 and 3 are all turned off, the input mode $l = 0$ ($l = 1$) is coupled to $l = 1$ ($l = 0$) at $\lambda _1$ by the grating 1, and then pass through grating 2 and 3 staying unchanged. For the three modes switch situations, "work on" or "turn off" state of each grating is determined by the requirement of output states. Under the situation of three spatial modes’ signals multiplexed and transmitted in the FMF, the three optical flows with state of $| 0,0 ; 1,1 ; 2,2>$ transmitted, if we need the transmission state switched into $| 0,2 ; 1,0 ; 2,1>$, the PS-LPFG1 and 3 need to work on and the PS-LPFG2 need to turn off. The input mode $l = 0$ is converted to $l = 1$ by PS-LPFG1, then unchangeably pass the PS-LPFG2, and at last is converted to mode $l = 2$ by the PS-LPFG3; the input mode $l = 1$ is converted to $l = 0$ by PS-LPFG1 and then pass the PS-LPFG2 and 3 with no change; the input mode $l = 2$ passes the PS-LPFG1 and 2 without change and then is converted to the mode $l = 1$ by the PS-LPFG3. This process can be generalized to any required switched output state. Here, the periods of PS-LPFG1, 2 and 3 are calculated to be about 1153$\mu$m, 549$\mu$m and 912$\mu$m, respectively to meet the phase matching condition of the three modes in and near the C band.
3. OAM mode switching demonstration
Since the $2 \times 2$ mode switching at different wavelengths can be extended into $N \times N$ mode switch at multi-wavelength as an elementary unit, we choose to implement a pair of OAM modes switching based on a designed PS-LPFG to prove the above-mentioned concept. The proposed PS-LPFG is fabricated in FMF by using a high-frequency $\mathrm {CO}_{2}$ laser point-to-point ablation technique, which was experimentally explored in [29]. By inserting a very short piece of fiber as phase-shift segment in the middle of the LPFG, the periodic deformation is broken and a strong modulated PS-LPFG is formed with insertion loss $\sim$1.5dB, as shown in Fig. 4(a). Here, the grating period, length of phase-shift and number of periods of the PS-LPFG are 549$\mu$m, 125$\mu$m and 125, the phase-shift point located in the middle of the grating. The FMF employed in this experiment is a step-index four-mode fiber with core and cladding radius of 9.5$\mu$m and 62.5$\mu$m, respectively. To illustrate the OAM mode switching process, we set up an experimental system as shown in Fig. 4. A tunable laser (Keysight N7711A) is used as a light source. Then, the output light from the laser is divided into two branches by an optical coupler with a proportion of 50:50. The upper path is used to switch the passed OAM modes and the down path is used as the reference beam to interfere with the output OAM modes. In the upper path, the spatial light modulator is used as a converter to offer different OAM mode states as input modes for the OAM switching demonstration. Two disks (R and H) are combined to control the rotation of the PS-LPFG. The polarization controllers (PC1 and PC2) are employed to control the polarization state of input light. The PC3 behind the fixed disk H is employed to adjust the relative phase difference of modes switched by PS-LPFG. The beam splitter (BS) is used to combine the OAM beam and reference Gaussian beam to generate the interference patterns, which are recorded on charge-coupled device (CCD) camera.
Fig. 4. Experimental setup for the dynamic mode switching and detection between OAM modes using a PS-LPFG. OC, 50:50 optical coupler; PC, polarization controller; H, holder; R, rotator; Obj, microscope objective; ATT, attenuator; BS, beam splitter; Col, collimator; SLM, spatial light modulator; CCD, charge-coupled device.
In principle, a PS-LPFG with one phase-shift point can achieve a pair of modes switching $\left (| l_{1}, m_{1} ; l_{2}, m_{2}>\right )$ at four wavelengths. Here, we demonstrate the OAM mode switching between the zero-order and the second-order ($| 0,0 ; 2,2>$ and $| 0,2 ; 2,0>$) using a FMF PS-LPFG. Switching between this pair of modes are monitored at two different wavelengths $\lambda _1$ and $\lambda _2$, respectively and the results as shown in Fig. 5. When the input mode $l = 0$ pass through the PS-LPFG, the output mode at two wavelengths is imaged in Figs. 5(a1)-(a2). Then, if we applied a twist rate to PS-LPFG, the results are shown in Figs. 5(c1)-(c2). When the input mode is $l = 2$, the results are shown in Figs. 5(b1)-(b2) and Figs. 5(d1)-(d2). It proves that a pair of modes switching at two wavelengths is achieved. It also means that the mode switching can be realized at four wavelengths by using PS-LPFG with one phase-shift point, just as shown in the transmission spectra in Fig. 6(a). The green and blue curves in Fig. 6(a) represent the transmission spectra of the PS-LPFG with twist angle of $0^{\circ }$ and $240^{\circ }$ (the corresponding twist rate is 34.9 rad/m), respectively. Four red double arrows indicate that the mode $l = 0$ and mode $l = 2$ can be switched to each other at four wavelengths, when twisting PS-LPFG from $0^{\circ }$ to $240^{\circ }$. The relative power difference in transmission spectra between two modes at wavelength 1537nm and 1558nm was $\sim$17.96 dB and $\sim$18.86 dB, respectively, that is, the corresponding mode switching efficiency is $\sim$98.4% and $\sim$98.7%. In addition, we measured the purity of OAM mode at two wavelengths under the condition that the input mode is $l = 0$. The mode purity of the second-order OAM mode at 1537nm and 1558nm are $\sim$96.64% and $\sim$95.98%, respectively. At the same time, we also monitored the mode changes characteristic at the input mode $l = 0$. The mode field image is recorded every 40 degrees with a CCD, as shown in Fig. 6(b). As the torsional angle increased, the mode $l = 0$ gradually changed to mode $l = 2$ at 1537nm, while mode $l = 2$ gradually changed to mode $l = 0$ at 1558 nm.
Fig. 6. (a) The changes of resonance mode at different wavelengths with the twist rate, (b) The mode field intensity changes of mode at different wavelengths with the torsion angle.
In order to further prove the corresponding mode, we verified it through the interference experiment. The results are illustrated in Fig. 7. First, the tunable laser wavelength is set at $\lambda _2$ = 1558nm, and the PS-LPFG is in a twist-free state. When the input mode is selected as mode $l = 0$ through SLM, the most power of mode $l = 0$ is transferred to OAM mode $l = 2$ at resonance wavelength 1558nm due to the mode resonance coupling effect of fiber grating. The mode filed intensity distribution presents as a doughnut shape, i.e. $l$ = $\pm$2 modes, as shown in Figs. 7(c1)-(c2). In order to further verify these modes are $l$ = $\pm$2 modes, the $l$ = $\pm$2 modes interfere with a reference Gaussian beam. The interference patterns are illustrated in Figs. 7(d1)-(d2). The clockwise spiral interference pattern for mode $l = -2$ and the counterclockwise spiral interference for mode $l = +2$ can be clearly shown in these images. When the input mode is selected as mode $l = 2$ through SLM, the mode $l = 2$ is converted to mode $l = 0$ at resonance wavelength by the grating. The mode filed intensity and interference pattern are illustrated in Fig. 7(c4) and Fig. 7(d4) respectively. Then, The PS-LPFG is twisted $240^{\circ }$ by rotating the disk R. The coupling mode of grating changes at wavelength 1558nm due to the transformation of resonance conditions during the process of twisting grating. For different input mode $l = 0$ and mode $l = 2$, the corresponding results at the output side of PS-LPFG are shown in the Fig. 7(c3) and Figs. 7(c5)-(c6) respectively. The Fig. 7(d3) and Figs. 7(d5)-(d6) are the corresponding interference patterns. This proves that the mode switching between second-order and zero-order OAM modes at the wavelength 1558nm is realized.
Fig. 7. The output modes intensity distribution of PS-LPFG and TPS-LPFG under the different input modes.
Then, the wavelength of the tunable laser is adjusted to $\lambda _1$ = 1537nm and the steps above are repeated. The PS-LPFG keep in a twist-free state firstly. When the input mode are mode $l = 0$ and mode $l = 2$, the corresponding results are illustrated in Fig. 7(a1) and Figs. 7(a4)-(a5), respectively. The interference pattern is imaged on the CCD camera as shown in Fig. 7(b1) and Figs. 7(b4)-(b5). We twist the PS-LPFG 240 degrees subsequently, the changes of mode filed profile are illustrated in Figs. 7(a2)-(a3) and Fig. 7(a6), when the input mode are selected as mode $l = 0$ and mode $l = 2$, respectively. The observed interference patterns are illustrated in Figs. 7(b2)-(b3) and Fig. 7(b6). These results prove that the mode switching between modes $l$ = $\pm$2 and mode $l = 0$ at two different wavelengths is realized based on a PS-LPFG.
4. Conclusion
In summary, the mode switching based on the cascaded PS-LPFGs has been proposed to realize multiple OAM mode switching at multi-wavelength simultaneously. In principle, a $N \times N$ mode switch matrix can be realized by cascading $C_{N}^{2}$ gratings, where each grating acts as a mode switch element to achieve a couple selected OAM mode switching and meanwhile the other modes are under nonblocking status. It overcomes the difficulty of multiple mode switching caused by the intrinsically overlap of the modes in fiber. We have experimentally demonstrated a pair of modes switching at multi-wavelength in FMF by employing one PS-LPFG. The switching of the pair of OAM modes are verified by the interference patterns between the OAM modes and a reference Gaussian beam at each wavelength. The proposed multiple OAM mode switching scheme is not confined to wavelength domain and has potential applications in MDM-WDM hybrid multi-dimensional multiplexing optical fiber communication systems.
Funding
National Key Research and Development Program of China (2018YFB1802300); National Natural Science Foundation of China (61525502, 61775085, 61875076, 62035018, U1701661, 61935013, 61705088); Guangzhou Science and Technology Program key projects (201904020048); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121); Science and Technology Planning Project of Guangdong Province (2017B010123005, 2018B010114002); Leading Talents Program of Guangdong Province (00201502).
Disclosures
The authors declare no conflicts of interest.
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