1. Introduction

Spatial division multiplexing (SDM) is a widely accepted approach for scaling the transmission capacity of optical communication networks beyond the limits of single-mode fiber (SMF) [1–3]. As an approach of SDM, few-mode fiber (FMF) based mode division multiplexing (MDM) system, which utilizes individual modes within FMF as communication channels, offers the potential to open up the spatial dimension as a means to increase the transmission capacity. One of the fundamental components in an MDM system is a mode converter, which serves to couple light between the fundamental core mode and a selected high-order core mode. Mode converters have been demonstrated with different approaches. The most well-known technique is spatial light modulator (SLM) [4,5] which is based on the hologram and adjust spatial intensity and phase distribution of the light beam to obtain the higher order modes, but the configuration is complex and the spatial resolution of the SLM pixel is limited, which will reduce the coupling efficiency. A simpler bulk component is phase plate [6,7], which has been used widely recently, and it just manipulates the phase distribution of the light beam, but the loss of mode coupling is large. Due to the complication and complex of optical alignment, it is difficult for the bulk mode converters to build low-loss systems. Another kind of mode converter is based on the mode coupling. By using tapered velocity coupler [8, 9], mode conversion can be realized with low loss and low crosstalk. Waveguide coupler [10,11] has been recently reported to be efficient mode converter with low crosstalk. The photonic lantern [12,13], which has attracted wide attention, converts multiple beams into the super-mode in FMF, but the multiple-input multiple-output process is needed due to the large crosstalk. Fiber Bragg gratings [14,15], which couple light between specific modes with an external mode selector, can be used as reflective mode converter. Waveguide grating [16], as a mode switch, has a simpler waveguide structure and can be fabricated with simpler conventional protonexchange process. Compared to the other techniques, long-period fiber grating (LPFG) [17–19] mode converters have the advantages of smaller size, lower loss and easier fabrication. The LPFGs can be fabricated by several methods including ultra-violet (UV) laser [20], arc technique [21], mechanical micro-bending [17], CO₂ laser [18,19,22–24]. Thanks to the advantages of the CO₂ laser writing technique, the LPFGs can be successfully written in various types of specialty fibers [22,23] and different types of LPFGs can also be achieved [24].

In this paper, we demonstrate the fabrication of the LPFG mode converters written in the two-mode fiber (TMF) using CO₂ laser. Two kinds of gratings including the uniform and tilted LPFGs were fabricated, and the writing efficiency and the bandwidth of the LPFG mode converter could be adjusted by changing the tilt angle of tilted TMF-LPFGs. The mode conversion can be achieved for the light coupling between LP₀₁ mode and LP₁₁ mode with a coupling efficiency more than 99%. The refractive index (RI), polarization and torsion characteristics of the LPFG mode converters have been investigated experimentally. The high polarization sensitive characteristic is consistent with the polarization sensitivity of LP₁₁ mode. We can obtain two orthogonal vector modes (the HEeven 21and HEodd 21 modes) at the resonance wavelength by adjusting the polarization state of the LP₀₁ mode launched into the LPFG mode converter. Moreover, the orbital angular momentum (OAM) state, can be generated from the LPFG mode converter, which could be useful for the MDM of optical communication.

2. Principle and simulation

Figure 1(a) shows the transverse RI profile of the TMF (two-mode step-index fiber, OFS) measured by a RI profiler (S14, Photon Kinetics) at the wavelength of 1550 nm. The TMF has a core diameter of 19 μm, a cladding diameter of 125 μm, a cladding index of 1.444 and a core index of 1.449, which can support LP₀₁ and LP₁₁ modes. We performed numerical simulations based on the finite-element method (FEM) with commercial software (COMSOL) [15]. The field profiles of the constitutive vector modes are shown in Fig. 1(b), which indicating that the TMF supports 6 vector modes. And the effective indices of the vector modes were calculated to be 1.446758 (TM₀₁), 1.446759 (HEeven 21and HEodd 21), 1.446761 (TE₀₁) and 1.4481 (HEx 11 and HEy 11) at the wavelength of 1550 nm.

 

Fig. 1 (a) The transverse RI profile of TMF measured by S14; (b) transverse electric field of the guided vector modes at $\lambda =1550nm$ in the TMF. The graph shows the fields of the fundamental HE₁₁ mode (LP₀₁) and the TE₀₁, HE₂₁, and TM₀₁ modes (LP₁₁ group) calculated with FEM.

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We wrote the LPFGs in the TMF by irradiating the fiber from one side with a CO₂ laser (CO₂-H10, Han’s Laser). The average power of the CO₂ laser and the frequency of the laser pulses were 0.6 W and 5 kHz, respectively. The laser beam was focused on the exposed fiber (with its jacket removed) to a spot with a diameter of ~30 µm, which was computer programmed to scan across the fiber point wise in the transverse direction at a controlled particular speed. Transverse scanning was advanced along the fiber with each step equal to the grating period. Because the TMF was exposed to the CO₂-laser beam on one side, the laser beam induced an asymmetric index distribution across the core, which could excite the mode conversion between the LP₀₁ mode and the LP₁₁ mode. The pitch of the LPFG mode converter can be governed by $\Lambda ={\lambda }_{res}/(n_{eff,01}-n_{eff,11}),$, where the ${\lambda }_{res}$ is the resonance wavelength, and the $n_{eff,01}$ and $n_{eff,11}$ are the effective indices of the LP₀₁ mode and LP₁₁ mode, respectively. The effective indices of the vector modes based on the measured index profile were calculated and the result is plotted in Fig. 2(a). By choosing the grating parameters properly, the LP₀₁ mode launched into the fiber can be converted into the higher order core mode with high conversion efficiency. The calculated grating pitch for the mode coupling between LP₀₁ mode and LP₁₁ mode on the grating resonance wavelength is shown in Fig. 2(b).

 

Fig. 2 (a) The calculated effective indices of the fiber vector modes based on the measured RI profile, (b) dependence of the calculated grating pitches for core mode coupling on resonance wavelength.

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The TMF was spliced with SMF to construct SMF-TMF-SMF (STS) structure, which can work as a Mach-Zender interferometer, and the schematic diagram of STS structure is shown in Fig. 3. The small part of the incident light (LP₀₁ mode) excite the LP₁₁ mode at the SMF-TMF splicing point. When a LPFG is written in the TMF, the light of LP₀₁ mode can be coupled into LP₁₁ mode. Due to the difference of the fiber core diameters, there is a small part of the light from the LP₁₁ mode could be coulped back into the output SMF. To ensure the light of LP₀₁ mode launched into the TMF-LPFG and detected at output with a high purity, two mode strippers (FM-1, Newport) were added on the TMF at the two sides of TMF-LPFG. The transmission dip can be observed in the spectra of the LPFGs, which corresponds to the light coupling to LP₁₁ mode. Compared with the TMF-LPFG, the tilted TMF-LPFG is optimized to achieve effective mode coupling between LP₀₁ mode and LP₁₁ mode with azimuthal symmetry. The tilted LPFG is one of the special gratings, whose wave vector K of the grating planes are tilted an angle $\theta$ with the Z axis, as shown in Fig. 3, and ${\Lambda }_T=\Lambda \times \cos \theta$ is the actual pitch. The more effective mode coupling between LP₀₁ mode and LP₁₁ modes can be achieved using the tilted TMF-LPFG.

 

Fig. 3 The schematic diagram of the STS structure with a tilted TMF-LPFG.

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3. Fabrication and characteristics of TMF-LPFG mode converter

The transmission spectra of the LPFG were measured with a supercontinuum broadband source (BBS, NKT Photonics) and an optical spectrum analyzer (OSA, AQ6375, YOKOGAWA). Several TMF-LPFGs with grating pitches of 1140 μm, 1160 μm, 1170 μm, 1180 μm, 1190 μm, 1200 μm, 1220 μm and 1240 μm were fabricated, and the resonance wavelength was shifted toward a shorter wavelength with the increasing grating pitch, as shown in Fig. 4, which is consistent with the theoretical analysis. The small difference of the grating pitches between experimental results and theory may be caused by the asymmetric index distribution induced by CO₂ laser.

 

Fig. 4 Dependence of the resonance wavelength on the grating pitch, and the inset shows the transmission spectra of TMF-LPFGs fabricated with different pitches.

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Figure 5(a) shows the transmission spectra of TMF-LPFG with the increasing laser scanning cycles. The pitch of the TMF-LPFG used in our experiment is 1190 μm and the grating number is 20. The energy density of the CO₂ laser used during the fabrication was 4.862 J/mm². The grating has a resonance dip with a grating contrast of ~30 dB at ∼1544.8 nm and a 20-dB bandwidth of 6.0 nm. The mode conversion efficiency is high to be ~99%. In order to improve the fabrication efficiency of the LPFG mode converter, we wrote the tilted TMF-LPFGs for the conversion of the modes with different azimuthally symmetry. The tilt angles of tilted LPFGs increase the asymmetry of index modulation and change the strength of coupling between the fundamental core mode and higher-order core mode. The tilted TMF-LPFG was fabricated with a period of 600 μm, a tilted angle of 60°and a grating number of 20. The energy density of the CO₂ laser used was 2.778 J/mm², which is much lower than that for the fabrication of the TMF-LPFG. The transmission spectra of the tilted TMF-LPFG with the increasing laser scanning cycles is shown in Fig. 5(b). The grating has a resonance dip with a grating contrast of ~27 dB at 1507 nm and a 20-dB bandwidth of 14.8 nm.

 

Fig. 5 The transmission spectra of TMF-LPFG with the increasing scanning cycles (a) TMF-LPFG; (b) tilted TMF-LPFG.

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The tilted TMF-LPFGs with the same grating number of 20, grating length of 24 mm and different tilt angles range from 0° to 80° with a step of 10° were fabricated. All the gratings have the similar grating contrast of ~30dB. The 20dB-bandwidth of the resonance dips were measured to be 9.6 nm, 10.4 nm, 11.6 nm, 12.6 nm, 13.6 nm, 17.8 nm, 14.8 nm, 13.4 nm, and 12.6 nm, respectively, as shown in Fig. 6. It can be found that the tilted TMF-LPFG with the tilt angle with 50° has the largest 20dB-bandwidth (17.8 nm). Therefore the writing efficiency and the bandwidth of the LPFG mode converter could be adjusted by changing the tilt angle of the tilted TMF-LPFGs.

 

Fig. 6 The variations of the 20-dB bandwidth of the resonance dip with different tilt angle.

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To ensure the mode corresponding to the resonance dip of the TMF-LPFG is pure LP₁₁ mode, we first studied the RI characteristics of the TMF-LPFG. Figure 7 shows the transmission spectra of the TMF-LPFG with different surrounding RI. The index range of the RI liquid used in the experiment was from 1.335 to 1.443. It can be found that the resonance dip is insensitive to the surrounding RI changes, which are consistent with that the LPFG mainly couples light between core modes of the TMF. Based on the measured grating contrast of ~30 dB at the resonance wavelength, the mode conversion efficiency from LP₀₁ mode to LP₁₁ mode is ~99.9%. And the RI characteristics of tilted TMF-LPFG confirms the same result.

 

Fig. 7 The transmission spectrum of the TMF-LPFG with different surrounding RI range from 1.335 to 1.443.

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We also studied the polarization characteristics of the TMF-LPFG mode converter using the optical component analyzer (N7788BD, Agilent) with a tunable laser (81600B, Agilent). Figure 8 shows the transmission spectra of both gratings corresponding to two input polarizations and the correspondent spectral polarization dependent loss (PDL), the input state of polarization was modified using an automated polarization controller and the maximum and minimum amplitudes were recorded for every wavelength. The wavelength separation between the minimum and the maximum resonance wavelengths is equal to 1.8 nm and 3.5 nm. The wavelength separation is given by $\Delta {\lambda }_{res}=\Lambda (\Delta n_{11}^{\max }-\Delta n_{11}^{\min })$, where $\Delta {\lambda }_{res}$ is the largest resonance wavelength separation for LP₁₁ mode resonance and $\Delta n_{11}^{\max }$ and $\Delta n_{11}^{\min }$ are corresponding maximum and minimum effective indices difference between LP₀₁ mode and LP₁₁ mode. From this value, we can estimate that the modal birefringence generated in the fiber core is equal to 1.5 × 10⁻⁶ and 2.9 × 10⁻⁶, respectively. The blue lines in Fig. 8 display the PDL evolution with wavelength, which was obtained from the difference of the correspondent two polarization transmission spectra. It’s well known that the peak–trough–peak nature of the grating PDL over the wavelength range is due to crossover of the transmission spectra associated with the minimum and maximum resonance wavelengths [25] and it happens more absolutely in case of tilted TMF-LPFG, as shown in Fig. 8(b). And the two peaks of the PDL graph are not equal, which is similar to that of the LPFG with the energy deposition strongly asymmetric in relation to the fiber core recorded by a CO₂ laser [25]. The maximum PDL of the TMF-LPFG and tilted TMF-LPFG were both measured to be ~6 dB, which is much higher than those reported previously for the conventional LPFGs written by CO₂ laser heating (1.2 dB [25]). The higher PDL of TMF-LPFG mode converter is consistent with the polarization sensitivity of LP₁₁ mode. Compared with the TMF-LPFG, the tilted TMF-LPFG with smaller index modulation performed better polarization characteristics, which is induced by the azimuthal symmetry of index modulation.

 

Fig. 8 The transmission spectra of the LPFG mode converter corresponding to two orthogonal input polarizations and the correspondent spectral PDL (a) TMF-LPFG; (b) tilted TMF-LPFG (θ = 60°).

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We studied the torsion characteristics of the TMF-LPFGs and tilted TMF-LPFGs with a tilt angle of 70°, and both gratings have the same grating number and grating length. The grating contrast is not less than 20 dB. As shown in Fig. 9(a) and 9(b), the resonance wavelengths of both gratings shift linearly toward a longer wavelength as the TMF-LPFGs are twisted clockwise and shift linearly toward a shorter wavelength as the gratings are twisted anticlockwise, which are opposite with that of the SMF-LPFG with the same grating number and grating length, as shown in Fig. 9(c). And the torsion sensitivity of TMF-LPFGs and tilted TMF-LPFGs were measured to be 0.37 nm/(rad/m) and 0.50 nm/(rad/m), respectively. The tilted TMF-LPFGs show a much higher sensitivity than that of the SMF-LPFG, which was measured to be ~0.049 nm/(rad/m). Therefore, the tilted TMF-LPFG can be used as not only a high efficiency wavelength tunable mode converter in the MDM system but also a high sensitive torsion sensor in the optical sensing field. By changing the tilt angle and the applied torsion of the tilted TMF-LPFGs, both the bandwidth and resonance wavelength of the mode converter can be tuned, which can be useful for the application in the MDM optical communications.

 

Fig. 9 Dependence of resonance wavelength on twist rate (a) TMF-LPFG (b) tilted TMF-LPFG (c) SMF-LPFG, and the tansmission spectra of resonance dips on different twist rate are shown in the insert, respectively.

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4. Vector mode and OAM state measurements

A schematic diagram of the experimental setup used to generate vector beams of the TMF-LPFG mode converter is shown in the Fig. 10(a). The input port of the TMF was spliced to SMF with a polarization controller (PC) inserted between the tunable laser and the TMF-LPFG mode converter so that the light launching into TMF was in the fundamental core mode. The wavelength of the tunable laser was set to be the resonance wavelength of the grating. Thereafter, the TMF-LPFG converters the light to the higher-order core mode. The lens (focal length: 13.8 mm) was used to adjust the size of the beam and a CCD camera (InGaAs camera, Model C10633-23 from Hamamtsu Photonics) was used to record the mode patterns. Figure 10(b) shows experimental near-field pattern at the output of the TMF with TMF-LPFG mode converter. The vector modes excited by the TMF-LPFG mode converter was generated by adjusting the PC. With the polarizer in the beam path, only the projection of the mode which were aligned with the polarizer were transmitted, resulting in the LP₁₁-like intensity profile rotating with the polarizer. And the polarizer orientation combined with the simulation field profile confirms that the pattern of the vector modes of the TMF-LPFG mode converter to be HEeven 21mode. As shown in the Fig. 10(c), the HEodd 21 mode of the TMF-LPFG mode converter can be generated by adjusting the PC, and the LP₁₁-like intensity profile confirms an orthogonal polarization state compared with the HEeven 21mode. The near-field pattern of the tilted TMF-LPFG mode converter can also be obtained as shown in Fig. 10(d) and Fig. 10(e).

 

Fig. 10 (a) Experimental setup used to generate vector beams of the TMF-LPFG mode converter; (b-d) experimental near-field pattern at the output TMF and pattern rotation with polarizer in beam path consistent with expected polarization orientation for the HEeven 21and HEodd 21 mode of TMF-LPFG (b) (c) and tilted TMF-LPFG (d) (e).

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OAM of light is represented by an electrical field with a helical phase proportional to $e^{iL\phi }$ where L is topological charge and $\phi$ is the azimuthal angle [26]. Based on the numerical simulation, the TMF theoretically supports two $OA{M}_{\pm L,M}^{\pm S}$ states through coherent combinations of the vector modes: ${\text{OAM}}_{\pm 1,1}^{\pm }={\text{HE}}_{21}^{\text{even}}\pm {\text{iHE}}_{21}^{\text{odd}}$, where the $\pm \text{S}$ indicates the circular polarization state of the OAM mode, $\text{M}$ denotes the radial mode number. We now turn our attention to the generation of OAM modes in the TMF-LPFG mode converter (MC), which is feasible by exciting HEeven 21and HEodd 21 modes. It is notable that OAM modes generated in a fiber requires that two HE₂₁ modes generated with the appropriate phase shift. The schematic of experimental setup used to excite and characterize OAM states is shown in Fig. 11(a). Light from the tunable laser was split into two branches by a 3 dB coupler. The OAM modes can be generated in the lower branch, and the near field patterns at the output of the TMF were the vector mode propagated through the TMF with a length of 3 m and PC 2, and then expanded via Len 1. To confirm that the monitored vector mode is an OAM mode, the measurement of helical phase was needed. It was achieved when the OAM beams in the lower branch combined and interfered with the reference beam obtained from an SMF in the upper branch through a non-polarization beam splitter (NPBS). In the upper branch, Len 2 was used to adjust the size of the reference beam and a polarizer was used to adjust the power at the output of the mirror. The beam profiles and interference patterns of beams transmitted through the TMF-LPFG and tilted TMF-LPFG are displayed in Fig. 11(b) and Fig. 11(c), respectively. The reference beam interfered with a beam with different topological charge $\text{L}$ ($\text{L}=+1$ and $\text{L}=-1$, respectively), indicating that the OAM modes were generated in the lower branch in Fig. 11(a). Moreover, the topological charge ($\text{L}$) of the OAM state generated in the TMF can be tuned easily by adjusting the PC 2 to control the phase between the the HEeven 21and HEodd 21 modes after propagating through 3 m TMF. The experimental results comfirm that the TMF-LPFG mode converter can generate the $\text{L}=\pm 1$ OAM modes successfully, which could be useful for the OAM mode division multiplexing optical communications.

 

Fig. 11 (a) Experimental setup used to excite and characterize OAM states; (b-c) profiles and interference patterns at output of TMF with (b) TMF-LPFG and (c) tilted TMF-LPFG.

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5. Conclusion

In conclusion, we have demonstrated the fabrication of TMF-LPFG mode converters by CO₂ laser. Two kinds of LPFG mode converters, which are the uniform and tilted TMF-LPFG mode converters, have been fabricated. Both TMF-LPFG mode converters can provide the light coupling between LP₀₁ mode and LP₁₁ mode with a coupling efficiency of more than 99%. The writing efficiency and the bandwidth of the LPFG mode converter can be adjusted by changing the tilt angle of the tilted TMF-LPFGs. With a high torsion sensitivity of 0.50 nm/(rad/m), the tilted TMF-LPFG can be used as not only a high efficiency wavelength tunable mode converter in the MDM system but also a high sensitive torsion sensor in the optical sensing field. The orthogonal vector modes and OAM state were measured experimentally for the characterization of the TMF-LPFG mode converter. The proposed TMF-LPFG mode converter is a convenient component for achieving the mode conversion between LP₀₁ mode and LP₁₁ mode, characterizing the vector modes and the corresponding OAM states. It is believable that the TMF-LPFG mode converter can have potential applications in the all fiber based MDM system.