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Abstract
A fiber-based beam shaper to adjust the distribution of spatial modes in a few-mode fiber (FMF) is theoretically and experimentally investigated in this work. A compact and robust device, composed with a single mode fiber-graded index multimode fiber-few mode fiber (SMF-GIMF-FMF), is fabricated by simply fusion splicing of the fibers. Switchable spatial modes and multi-wavelength comb are obtained by the combination of the beam shaper and the few-mode fiber Bragg grating (FM-FBG). This combination acts as a filter to select the wavelength and spatial mode in the laser. A spatial mode switchable fiber laser with high mode purity is extended among LP01, LP11 and cylindrical vector beam (CVB) by adjusting the pressure applied on the beam shaper. Five-discrete wavelengths and their free combination wavelength comb are emitted with a slope efficiency higher than 10%. The fiber laser can be used in the spatial- and wavelength-division multiplexing (SWDM) fiber communication networks requiring particular structure light field.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-order mode (HOM) fiber lasers have attracted tremendous interest in the past few years due to their unique distribution of spatial intensity, phase and polarization. The doughnut beams including CVB [1–3] and orbital angular momentum (OAM) beams [4] are often used in optical tweezer [5], optical communication [6] and super-resolution imaging [7]. HOMs can be converted from the fundamental mode in fiber by various optical devices including long period fiber grating [2,3], fiber mode coupler [8–10], geometric phase plate [11], spatial light modulator [12] and offset splicing spot [13]. Internet data traffic capacity is rapidly reaching the limit imposed by optical fiber nonlinear effects. The possibility to enhance data capacity is now being explored using spatial modes of fibers. Spatial-and wavelength-division multiplexing (SWDM) fiber communication network is an excellent choice for high-speed optical communication [14]. Therefore, switchable HOM lasers are necessary for the development of future fiber communication networks.
In the area of HOM fiber lasers, the mechanism to obtain the switchable output is mainly based on the lateral offset splicing spot between a FM-FBG and a tunable filter [13,15–19]. The symmetric mode LP01 and antisymmetric mode LP11 are both excited in the section when the single-mode fiber was slightly laterally offset to the FMF [20]. The relative excitation coefficient of transverse modes is determined by the value of axial misalignment (or lateral offset value) which is generally controllable at the fusion splice spot between the optical fibers [21]. The FM-FBG with modal dependent multi-reflection peaks has been proposed as an all-fiberized modal discriminator in the HOM fiber laser. The fiber laser with a tunable filter and FM-FBG could emit switchable HOMs [16,17]. However, it could not realize the HOMs and wavelength switching simultaneously. With the assistance of axial misalignment, the FM-FBG shows controllable multi-reflection peaks which is corresponding to different transverse modes. Using the FM-FBG as a feedback element and mode filter, the all-fiber lasers emitting adjustable pure HOM and multi-wavelength comb have been demonstrated [22–24]. However, the offset splicing spot limited the performance of the HOM laser. The excitation coefficients of higher-order modes rely on the value of axial misalignment which bring huge insertion loss. In addition, it is difficult to change the operation modes of the fiber laser if the fusion splicing is fixed.
In this work, we presented a new approach to realize an erbium-doped fiber laser operating in switchable HOMs and wavelength. A SMF-GIMF-FMF structure was used as a beam shaper which could be instead of the offset splicing spot to excite the HOMs. The multimodal interference in GIMF gave tunable field profiles at the end face [25,26]. The field injected into the FMF could excite the HOMs with a controllable mode proportion. The FM-FBG fabricated in a four-mode fiber was used as a mode discriminator and a multi-wavelength filter. The fiber laser using the cooperation of the beam shaper and the FM-FBG emitted various transverse modes and multi-wavelength comb with stability.
2. Experimental method and schematic
2.1 Beam shaper fabrication and operation principle
A novel SMF-GIMF-FMF structure with unilateral pressure was fabricated to act as the beam shaper as shown in Fig. 1. A fundamental mode generated from the input SMF, which was spliced to the input facet of the GIMF. The multimode interference effect occurs in the GIMF, which can create a diffused or centralized field profiles in the end face of the GIMF. The FMF supports four linear polarized (LP) modes including LP01, LP11, LP02 and LP21 mode around the wavelength of 1.55 µm. A manual controlled fiber squeezer was applied on one side of the GIMF fiber. The pressure was adjusted by a hand-operated rotary screw of the fiber squeezer. The screw could be fixed to resist environmental disturbance. The unilateral pressure induced the deformation of the GIMF. The deformation induced the variation of the bending radius and fiber length in the GIMF. The variation of the fiber length influenced the multimodal interference to modulate the spatial distribution at the end of the GIMF. Light propagating along the input SMF enters the GIMF with an approximate Gaussian-shaped field distribution. The bend radius can break azimuthal symmetry of the Gaussian beam to excite more HOMs. Therefore, the excitation coefficient of different transverse modes can be controlled by the carefully manual adjustment of the fiber squeezer when the GIMF is spliced to the FMF.
The finite difference beam propagation method (FD-BPM) has been employed for numerical calculation of the light propagation in the beam shaper [27]. This technique uses finite difference methods to solve the well-known parabolic or paraxial approximation of the Helmholtz equation. In our numerical model, the SMF core diameter has been set as 8.2 µm. The length of GIMF and the FMF have been taken as 50 µm and 20 µm. The length of the SMF was set to 200 µm to launch the light field. The GIMF length was a variable within the range of hundreds of micrometers which was estimated according to the fiber squeezer. The bend radius of the GIMF imposed by the squeezer has been considered in the simulation. It was set to be millimeter scale in a small segment of the GIMF. The FMF length was set to 5000 µm to obtain a stable result. The detailed geometry is presented in the Fig. S1 of the Supplement 1.
Figure 2(a) presents the amplitude distribution of the calculated field in the X-Z cross section of the beam shaper. The GIMF section in Fig. 2(a) is from 200 µm to 2450 µm. Light spreads and converges along the GIMF and is re-imaged with the distance of 710 µm, as shown in Fig. 2 (a). The light twisted and deviated from the center of the fiber core appears at the Z position of 1500 µm due to the bend radius. The bend radius contributes to break the azimuthal symmetry of the launch field and excites more HOMs as is shown in Fig. 2 (a). The value of the GIMF length and the bend radius modulate the spatial distribution of the field at the end of the GIMF; the field launched into the FMF excited different HOMs. Intermodal interference occurs among the four modes occurs in the FMF. The FMF section in Fig. 2(a) is from 2450 µm to 7450 µm. Figure 2(b) presents the total power distribution within the fiber core which denotes the insertion loss of the beam shaper. The calculated insertion loss is about 0.86 dB as shown in Fig. 2. The simulated insertion loss versus the value of bend radius and GIMF length is shown in Fig. S2 of the Supplement 1.
Fig. 2. (a) Amplitude distribution of the light in the SMF-GIMF-FMF structure calculated by the FD-BPM method when the GIMF length is 2250 µm and the bend radius is 2 mm. (b) Normalized power is the overlap integral between the fiber core geometry and the mode field.
In the simulated model, we searched for the suitable value of the GIMF length and the bend radius to obtain the LP11 and LP21 mode-like profiles output from the beam shaper. Figures 3(a) and 3(b) presents the numerically simulated intensity images output from the beam shaper with different GIMF lengths and bend radius. It can be seen from Figs. 3(a) and 3(b) which demonstrate typical characteristics of the LP11 and LP21 mode distribution. Though it is hard to calculate the exact LP11 and LP21 mode excitation coefficient from the image, hybrid modes including the LP11 and LP21 are indeed excited by the beam shaper. Figures 3(a) and 3(b) demonstrate that the mode proportions can be adjusted by the length of GIMF and the bend radius. Though the small bend radius contributes to excite more HOMs, it would bring huge insertion loss. The simulated insertion loss is 0.86 dB for Fig. 3(a) and 1.31 dB for Fig. 3(b).
Fig. 3. Numerically simulated mode field distribution of the output from the beam shaper with different GIMF lengths and bend radii. (a) GIMF: 2250 µm, Bend radius: 20 mm. (b) GIMF: 2050µm, Bend radius: 6500 µm. (c) and (d) are the experimentally captured fiber end-face profiles correspond to (a) and (b) with different pressures.
We fabricated the beam shaper structure for exciting the LP11 and LP21 mode experimentally in the FMF to validate the simulated results. Adjustable pressure was added at one side of the GIMF by the fiber squeezer. The distributed feedback (DFB) laser with narrow linewidth at 1550 nm was coupled into the SMF as the exciting field. The output intensity profiles were captured from a CCD after beam alignment, as shown in Figs. 3(c) and 3(d). With the adjustable pressure on the GIMF, the hybrid mode with different mode excitation coefficient was obtained, which is similar to the numerically simulated results. The insertion loss is measured to be 0.75 dB for Fig. 3(c) and 1.57 dB for Fig. 3(d). The experimental results agree well with the simulated results.
2.2 Mode switchable operation based on FM-FBG
A FM-FBG was used to further test the beam shaper experimentally. The FM-FBG was fabricated on a four-mode FMF which is the same as the FMF in the beam shaper. The core and cladding diameters of the FMF are 20 and 125 µm, respectively.
The FMF can support four LP modes including LP01, LP11, LP02 and LP21 mode around the wavelength of 1.55 µm. The Bragg wavelength of an FBG is determined by the grating function as [28]
where ${\beta _1}$ and ${\beta _2}$ represent the propagation constants of the forward and backward propagating modes, respectively. In the four-mode fiber, ${\beta _j}$($j = 1,2$) of the Nth-order principal mode of the fiber could be approximated by where $V = (2\pi aNA)/\lambda $ is the normalized frequency, $a$ and NA are the fiber core radius and numerical aperture, ${n_{core}}$ is the reflective index of the core and $\Delta = ({n_{core}} - {n_{cladding}})/{n_{core}}$ is the normalized core-cladding index difference. The multi-reflection peaks appear at particular wavelength once the phase matching condition is satisfied.The propagation constants of the LP01, LP11, LP02, and LP21 modes were calculated by analyzing the FMF using finite element method, as shown in Fig. 4(b). The grating period was set at 537 nm. The hybrid mode was obtained by putting the beam shaper before the FM-FBG. An amplified spontaneous emission (ASE) was used as the broadband light source. The reflection spectrum of the FM-FBG was measured through a optical fiber circulator, as shown in Fig. 4(a). The five peaks in Fig. 4(a) are consistent with the theoretical calculated propagation constants in Fig. 4(b), which proved that the HOM was inspired effectively by the beam shaper. From the right to left side in Fig. 4(a), the high reflection peaks represent the self-coupling of LP01 (1550.4 nm), LP11 (1548.8 nm) and LP21 modes (1546.8 nm); the lower reflection peaks represent the cross-coupling between LP01, LP02 modes (1548.35 nm) and the self-coupling of LP02 (1546.3 nm). The cross-coupling between the LP01, LP11 and LP21 mode does not appeared in Fig. 4 due to the manufacturing method of the FM-FBG.
Fig. 4. (a) Measured reflection spectrum of the FM-FBG with the beam shaper injected. (b) Propagation constants of LP01, LP11, LP02 and LP21 modes and the dashed lines represent the average propagation constant of the neighboring modes.
As shown in Fig. 5, controllable reflection spectra of the FM-FBG were obtained experimentally by tuning the fiber squeezer on the beam shaper. The HOMs were excited with different proportions which changed the reflection spectrum of the FM-FBG. The dominant reflection peaks correspond to the three self-coupling reflection peaks. The side-mode suppression ratio (SMSR) of the dominant reflection peaks is higher than 2 dB. It means that the three modes can be switched to get their own highest proportion in the FMF. The adjusted dominant peaks in Fig. 5 validate experimentally the reliability and the sensitivity of the FM-FBG to the HOMs excited by the beam shaper. The measured transmission spectra of the beam shaper are shown in the Fig. S3 of the Supplement 1. The spectra in Fig. S3 demonstrated that the filter effect of the beam shaper is weak comparing to the combination of the beam shaper and the FM-FBG.
Fig. 5. Adjustable reflection spectrum of the FM-FBG by the beam shaper. (a) LP01-LP01 reflection peak dominated; (b) LP11-LP11 reflection peak dominated; (c) LP21-LP21 reflection peak dominated.
3. Experimental results and discussion
3.1 Spatial mode switchable output
Figure 6 presents the schematic of the mode switchable fiber laser based on the beam shaper and the FM-FBG. The gain section of the fiber laser is a 75 cm EDF (Liekki Er110-8/125) pumped by a 1480 nm Laser Diode (LD) with the maximal average power of 400 mW. A fiber Sagnac loop based on a 5:5 fiber coupler was used as a broadband reflector. The FM-FBG fabricated on a four-mode fiber was added as another reflector and output end. The beam shaper consisted of a SMF-28e (8/125), a GIMF (50/125) and a four-mode fiber (20/125).
There was only the fundamental mode (LP01) running in the single mode part of the cavity as shown in Fig. 6. The spatial-mode distribution was changed in the FMF with tuning the micro-pressure applied on the beam shaper. The side reflection peaks with low reflectivity in the FM-FBG as shown in Fig. 5(a) were successfully suppressed and the dominant reflection peak with highest reflectivity won the competition. The laser mode (e.g. LP01) with the dominant reflection peak (1550.4 nm) oscillated in the laser cavity, where the opposite modes (e.g. LP11) output from the cavity due to the mismatched wavelength (1550.4 nm) with the FM-FBG, as shown in Fig. 7. The beam shaper was adjusted finely to ensure only two modes excited in the FMF. The laser emitted switchable modes (LP01 and LP11) with high purity and single wavelength.
Fig. 7. Measured profiles of the oscillated mode of (a) LP01 and (b) LP11. (c) Measured output spectra of the LP11 and LP01 lasing. (d) Output power of the LP01 and LP11 mode versus pump power.
The experimentally measured output profile of the LP01 mode (1548.8 nm) and LP11 mode (1550.4 nm) are shown in Figs. 7(a) and 7(b). The 3-dB linewidths of the two modes are both less than 0.02 nm and the SMSRs are higher than 60 dB as shown in Fig. 7(c). The relationship between the output power and the pump power for the two states in Fig. 7(d). It demonstrates that the laser could work in the LP11 and LP01 mode with two sets of threshold as 42 mW and 52 mW with the corresponding slope efficiency of 12.27% and 11.87%, respectively.The insertion loss of the beam shaper was measured to be 0.75 dB. The differences of threshold and slope efficiency are mainly caused by the different reflectivities of the LP11 and LP01 mode in the FM-FBG.
A polarization controller was added at the out port FMF to remove the degeneracy of the LP11 mode. As presented in Fig. 8, four distinctively different vector eigen-modes ($\textrm{T}{\textrm{M}_{01}}$, $\textrm{T}{\textrm{E}_{01}}$, $\textrm{HE}_{21}^{even}$ and $\textrm{HE}_{21}^{odd}$ modes) can be obtained from the LP11 mode. The polarization state of the four modes were confirmed by rotating a linear polarizer inserted between the collimator and the CCD. The mode purity of the LP11 mode was estimated by the method as in [13]. The FMF was bent to a circle with a radius of 1.5 cm, where the output power of the LP11 mode decreased from 38 mW to 2.4 mW which resulted in a 93.7% loss. In addition, the bent loss of LP01 mode is 5.4% in the same condition as LP11 mode. Considering the loss percentage of the two modes, the purity of the LP11 mode was estimated to be ∼93%.
Fig. 8. Measured intensity profiles of the generated CVBs and the distribution after passing through a linear polarizer. The black arrows represent the orientation of the linear polarizer.
When the pressure was slightly increased, the third-order mode (LP21) was excited in the FMF due to the increased bend radius of the GIMF. Three modes including LP01, LP11 and LP21 were excited in the FMF. The fiber laser oscillated with the dual-wavelength corresponding to the two self-coupling peaks (LP01 and LP11) of the FM-FBG when the proportion of the two modes are both higher than the LP21. The two modes were reflected by the FM-FBG; the LP21 mode with the dual-wavelength could be emitted due to the mismatched phase condition. The experimentally measured output profile of the LP21 mode with the dual-wavelength (1548.8 nm and 1550.4 nm) is shown in Fig. 9(a). The 3-dB linewidths of the two modes are both less than 0.02 nm and the SMSRs are both higher than 50 dB as shown in Fig. 9(b). The slope efficiency was measured to be 10.39% as shown in Fig. 9 (c). The purity of the LP21 mode is slightly low as shown in Fig. 9(a) due to the residual LP01 and LP11 modes.
Fig. 9. Measured output when the laser emitted the LP21 mode. (a) LP21 profile. (b) Output spectrum. (c) Output power versus pump power.
3.2 Wavelength switchable and multi-wavelength output
Erbium-doped fiber lasers (EDFLs) with switchable wavelength output has been extensively used in optical fiber sensing and dense wavelength division-multiplexing (DWDM) fiber networks due to their flexible lasing performance. To attain wavelength switchable fiber lasers, a tunable fiber filter is usually used, e.g: pressure tuning an FBG, fiber etalons, external diffractions grating and fiber coupled acoustic optical tunable filters. All of them have their own advantages and drawbacks. However, the mechanism to obtain the switchable output is always random or inflexible. With the setup as shown in Fig. 6, an EDFL emitted single or several wavelengths can be switched freely by tuning the beam shaper.
The operation principle of the laser is described as follows. The beam shaper adjusted the proportion of transverse modes in the FMF; the transverse modes have their own reflection peak in the FM-FBG as illustrated in the section 2.2. The cooperation of the beam shaper and the FM-FBG acted as a tunable filter as shown in Fig. 5. For example, the 1550.4 nm wavelength reflects the LP01 self-coupling peak when the LP01 mode take the majority in the FMF. In other words, the wavelength dependent loss can be controlled by the beam shaper. It is possible to realize the balance between the inhomogeneous loss and the mode competition effect of the EDFL by the beam shaper. The balance leads to stable multi-wavelength oscillation. Therefore, the laser with the setup in Fig. 6 can be switched among single-wavelength operation, dual-wavelengths operation and triple-wavelengths operation, as shown in Fig. 10.
Fig. 10. Measured spectra for lasing at multi-wavelength switchable modes. (a) single-wavelength, (b) and (c) dual-wavelengths, (d) triple-wavelength.
When the EDF is pumped with 400 mW of 1480 nm LD, five switchable single-wavelength (peaks 1-5) and their combination formed a comb-type structure, as shown in Fig. 10. The five operating wavelengths corresponding to the reflection peaks of the FM-FBG are 1550.4 nm, 1548.8 nm, 1548.35 nm, 1546.8 nm and 1546.3 nm, respectively. The SMSRs of single-wavelength operation are all higher than 50 dB for peaks 1-5, as shown in Fig. 10 (a). The 3-dB linewidth of the five peaks were less than 0.02 nm. When the fiber laser switched to dual-wavelength and triple-wavelengths output mode, the SMSRs were reduced to 45 dB, as shown in Figs. 10(b)–10(d). The output power versus pump power at three operation modes were measured as shown in Fig. 11, where the corresponding slope efficiencies are 12.31%, 10.59% and 9.67%. We found that the combination of different peaks with the same number of wavelengths almost have the same slope efficiency in the experiment. The reduction of the SMSR and the slope efficiency are attributed to two kinds of insertion loss. On one hand, the HOMs are usually excited with the increased pressure applied on the GIMF. The fraction power coupled to the radiation modes lost due to the increased bend radius as shown in Fig. S2. On the other hand, the power of HOMs lost because their phase-matching condition in the FM-FBG cannot be satisfied simultaneously. The intensity profiles of the three operation modes were also measured. The images were the superposition of the two or three transverse modes, which agreed well with the analysis in the section 3.1. However, the output power and wavelength were found to be very stable at different modes. No significant power and wavelength fluctuation was observed at room temperature and humidity.
4. Conclusion
We have reported a GIMF based beam shaper to adjust the spatial mode power distribution in the FMF. Based on the beam shaper and the FM-FBG, the wavelength and spatial modes switchable EDFL was achieved by tuning the pressure applied on the GIMF. With the simple SMF-GIMF-FMF structure, the laser spatial modes can be switched among LP01, LP11 and CVB transverse modes. The lasing wavelength can be selected in five peaks or their free combinations. The controllable multi-mode and multi-wavelength laser in C-band potentially enable key application for future communication networks with SWDM technique.
Funding
National Key Research and Development Program of China (2022YFB2903102); National Natural Science Foundation of China (51972317, 61875052, 61905059, 62105087, 62105088); Anhui Provincial Key Research and Development (202104a07020010); Natural Science Foundation of Anhui Province (1908085QF273, 2108085QF282); Fundamental Research Funds for the Central Universities (JZ2020HGTB0065, JZ2021HGQA0255, JZ2021HGTA0145, JZ2021HGTA0148).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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