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Abstract
We propose and demonstrate an all-fiber passively Q-switched laser generating a third-order orbital angular momentum (OAM) pulse by introducing a few-mode long-period fiber grating (LPFG) into the laser cavity. The LPFG with asymmetric cross structure and strong refractive index modulation overcomes the coupling issue between the fundamental and the third-azimuthal-order (LP31 or OAM3) modes and realizes their direct conversion. A homemade graphene-based saturable absorber is used to realize Q-switched operation. The laser operates at a center wavelength of 1548.2nm, with a 3 dB spectral bandwidth of 0.4nm, and the OAM+3 and OAM-3 beams can achieve the purity of 90.0% and 90.2%, respectively. This all-fiber Q-switched laser has simple and compact structure and high purity of OAM±3 beams, which has potential applications in the fields of optical tweezers and material processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Structured lights including cylindrical vector beams and orbital angular momentum (OAM) beams have been widely studied due to their unique characteristics of polarization, phase and intensity distribution [1,2]. In particular, OAM beams with spiral phase factor exp(ilφ) have a phase singularity and zero intensity at the center [3,4], where l is the integer topological charge number and φ is the azimuthal coordinate. Attributed to the unique properties, OAM beams have attracted significant attention in various kinds of research fields, such as atomic manipulation [5,6], data transmission [7], high-dimensional optical communications [8,9], and optical tweezers [10]. With the recent rapid development of ultrafast optics, higher-order OAM pulse is obtained by combining higher-order OAM mode with time-domain control technology. Compared with the traditional fundamental mode pulse, the higher-order OAM pulse brings new physical effects and degrees of freedom when interacting with matter, and provides conditions for special physical experiments [11], and expands new application scenarios [12,13]. Therefore, the generation and applications of higher-order OAM modes have received widespread attention [14,15].
The current methods for generating OAM beams are mainly divided into two types: free space and optical fiber methods. Free space methods include Q-plates [16], spatial light modulators [17], metamaterials [18,19], helical phase plates [20,21]. Comparatively, OAM beam generated in the optical fiber has the advantages of easy integration, low cost, flexibility, convenience and stability. In recent years, a variety of methods for generating OAM beams in fiber laser have been proposed and proved [22–24]. Mode conversion devices outside or inside the laser cavity mainly focus on fiber grating [25,26], mode selective coupler [27,28], photonic lantern [29], etc. The OAM pulses can be obtained by combining the above laser structure with mode-locked and Q-switched techniques [30–33]. For instance, R. Chen et al. proposed the generation of the first-order vortex beam in mode-locked laser by using a two-mode LPFG, where two-mode fiber Bragg grating worked as the output mirror in the ring cavity and Mach-Zehnder intensity modulator served as a mode-locker [34]. T Wang et al. reported a mode-locked fiber laser, which generated the first and second-order vortex beams by using a mode selective coupler, and the nonlinear polarization rotation technique was also employed in laser to produce pulses [35]. However, the previous reports of OAM modes generation based on fiber lasers almost focus on the first and second-order. Due to the difficulty in the fabrication of the higher-order (l > 2) mode converter and selection of the output mirror used to construct the cavity, up to now, the higher-order OAM pulse fiber lasers have not been reported. Although it has been reported that few-mode fiber Bragg gratings were used as the output mirror matching the mode converter, the fabrication process is more complicated for the higher-order mode reflection at a specific wavelength. Higher-order OAM pulse light sources are currently required for many applications, such as material processing [36] and ultrafast nonlinear optics [37,38]. It is essential to develop an all-fiber higher-order OAM pulse laser with simple and universal structure.
In this paper, we propose and demonstrate an all-fiber passively Q-switched third-order OAM mode laser based on a few-mode LPFG. The LPFG with asymmetric cross structure and strong refractive index modulation is inscribed in a seven-mode fiber (7MF), which inserted in the cavity acts as a mode converter between LP01 and LP31 modes. Third-order OAM mode is obtained by the even and odd π/2-phase-shifted superposition of LP31 modes. A homemade graphene-based saturable absorber (SA) is used to realize Q-switched operation. To the best of our knowledge, this is the first report on the efficient generation of third-order OAM pulses with controllable topological charge of $l ={\pm} 3$ in an all-fiber Q-switched laser. The single-mode fiber Bragg grating (SM-FBG) and gold-plated 7MF connector are used as two mirrors of the linear cavity. The laser operates at 1548.2nm, with a 3 dB spectral bandwidth of 0.4nm. The purity of OAM+3 and OAM-3 beams are estimated to be about 90.0% and 90.2%, respectively. This method provides a simple structure of the laser to achieve higher-order OAM pulse.
2. Third-order OAM mode generation in the cavity based on a LPFG
2.1 Principle of LPFG
In a weakly guided few-mode fiber, it is difficult to distinguish fiber eigenmodes owing to the small effective refractive index difference between them. Therefore, the fiber eigenmodes with almost the same propagation constant degenerate into the linearly polarized (LP) modes. 7MF guided modes are designated as LPmn modes, where m and n are the azimuthal and radial indices, respectively. LPmn modes propagate independently in the fiber and not interfere with each other. However, when different positions in fiber are affected by refractive index disturbance, the orthogonality condition between the modes is destroyed, resulting in coupling between the modes in the transmission. The LPFG introduces periodic refractive index modulation in the axial direction of the fiber to achieve mode coupling. According to the coupled mode theory, to achieve the coupling between the fundamental mode and a higher-order mode at a specific wavelength, the following phase matching condition needs to be satisfied [39]:
where Λ is the period of the LPFG, ${\lambda _{res}}$ is the resonant wavelength of the grating, ${n_{01}}$, ${n_{mn}}$ are the effective refractive indexes of LP01 and LPmn modes, respectively. In principle, the energy transfer between the fundamental and target modes can be achieved by choosing the grating period properly. The third-order OAM mode as a form of third-azimuthal-order mode is related to the same azimuthal-order LP31 mode. They have a common set of fiber eigenmodes, hence, they can be transformed to each other. The sketch of the mode conversion in LPFG is shown in Figs. 1(a), the LP01 mode is coupled to the third-azimuthal-order mode. Based on the finite element method, the supported core guided modes in 7MF and the relationship between their effective refractive index and wavelength can be obtained, as shown in Figs. 1(b). It is clearly seen that the refractive index difference (Δ) between the LP01 and the LP31 modes is large, and there is extremely little overlap between the LP01 and LP31 mode fields. In order to achieve the coupling between them, the fiber mode field must be modified by the special refractive index modulation. The introduction of a strong refractive index modulation in fiber can solve the small overlap area of the mode fields [40]. The strong refractive index modulation is not easy to introduce and may damage the waveguide geometric structure of the optical fiber. Fortunately, this can be achieved by optimizing the manufacturing process and special modulation of the fiber. The linearly polarized OAM±3 modes can be obtained by superposition of LP31a (even) and LP31b (odd) modes with ±π/2 phase shift, as illustrated in Figs. 1(c). In the experiment, we fabricate a LPFG to convert the energy from LP01 mode to the LP31 mode.
Fig. 1. (a) Sketch of the mode conversion in LPFG. (b) The mode effective index curves for the seven LP modes supported in the 7MF versus wavelength. (c)Superposition of LP31a and LP31b modes with phase shift results in OAM modes with topological charge of $l ={\pm} 3$. The upper and lower figures present the intensity profiles and phase distributions, respectively.
2.2 Experimental setup
The experimental setup of the all-fiber passively Q-switched laser is shown in Fig. 2. The fiber laser cavity consists of a SM-FBG, a 6-m-long erbium-doped fiber (EDF) with ∼6.2dB/m absorption at 1530nm pumped by a 976nm laser, a homemade SA, a LPFG, a 7MF connector plated with gold film, and two polarization controllers (PC). The SM-FBG is utilized as one linear-cavity mirror with a high reflectivity (>99%) at the wavelength of 1548.2nm. A gold film of appropriate thickness is deposited on the ceramic end of the homemade 7MF flat-ended connector as the output mirror, its reflectivity is about 16%. A 9:1 optical coupler (OC) is inserted into the cavity to extract 10% of the energy as a reference beam (Output1), and the rest part remains in the cavity to generate OAM beam (Output2). The mode conversion is realized by the LPFG in the cavity. The PC1 can adjust polarization states in the cavity. The PC2 is used to introduce ±π/2 phase shift between LP31a and LP31b modes. It is worth mentioning that in order to ensure that the mode transmitted into the LPFG is LP01 mode, the fusion splicing between the SMF and 7MF must be aligned. A slight deviation in the alignment of the cores splicing may introduce other modes into LPFG, which will lead to mode interference and low purity of the target mode.
Fig. 2. Schematic of the passively Q-switched laser for third-order OAM beam generation. FBG, fiber Bragg grating; EDF, erbium-doped fiber; OC, optical coupler; PC, polarization controller; SA, saturable absorber; LPFG, long-period fiber grating; M, fiber mirror (homemade 7MF connector plated with gold film).
As one of the important components of the Q-switched laser, graphene-based SA in the cavity can independently realize Q-switched technique. The manufacturing process: a certain proportion of the graphene dispersion liquid (Nanjing XFNANO Materials Tech Co., Ltd) and the polyvinyl alcohol solution were thoroughly mixed by ultrasonic oscillation and then the mixed liquid was coated on a polystyrene evaporating dish. Finally, we placed it in a drying oven to form a film. The preparation is similar to the previously reported methods [41–43]. The graphene polymer film is placed on the end face of the optical fiber connector, shown in the lower inset of Fig. 2. It is connected to another optical fiber connector by a flange to form a sandwich structure. This optical fiber component is used as a SA.
The LPFG used as a mode converter is a key element to generate OAM beam, which is fabricated by CO2 laser with point-to-point writing technique in a 7MF. In the experiment, in order to monitor the energy transfer between the LP01 and LP31 modes and obtain a LPFG with high conversion efficiency, both ends of the 7MF were carefully spliced with SMFs and connected with a supercontinuum broadband light source (Fianium, WL-MICRO) and an optical spectrum analyzer (OSA, Yokogawa, AQ6370), respectively. The OSA is used to observe the real-time changes of the transmission spectrum. The repetition frequency and the scanning speed of the CO2 laser were set to 5kHz and 27mm/s, respectively. The number of period was set as 100 to enhance the resonance between two modes.
Since the difference of effective refractive index between LP01 and LP31 modes is quite large, in order to achieve the coupling between the two modes, strong refractive index modulation needs to be introduced into the 7MF. Conventional method of multiple low-power scanning is difficult to achieve the corresponding azimuthal refractive index modulation, and multiple high-power scanning will cause serious deformation of the fiber structure and be easy to break the fiber, resulting in no LP31 mode coupling. Therefore, it is hard to fabricate a LPFG that can directly convert LP01 to LP31 modes. In order to solve the above problems, the grating with asymmetric modulation is fabricated by CO2 laser with gradual power single-sided radiation, the power of the CO2 laser increases gradually with the increase of scanning times. Strong refractive index modulation is slowly accumulated by specific gradient power parameters and the residual stress in fiber is slowly released so as not to damage the fiber structure. Under the proper grating period and laser power, a resonance peak appears at the wavelength of 1548.2nm. The transmission spectrum of LPFG is shown in Figs. 3. It can be concluded that the conversion efficiency of the third-order mode is about 90%. The inset of Figs. 3(b) proves that LP31 mode is effectively generated.
Fig. 3. (a) Calculated grating pitch for the LP01-LP31 mode conversion. (b) Transmission spectrum of LPFG.
The output modes intensity profiles of the laser and their interference patterns are recorded on a charge-coupled device (CCD) camera, the laser spectrum is measured by OSA, the time domain waveform is analyzed by a photo-detector (Thorlabs, PDB450C) connected to an oscilloscope (Rigol, DS6104).
3. Experimental results and discussion
The operation mechanism of the laser is described as follows. The fundamental mode oscillates in the resonant cavity and transforms into the LP31 mode when passing the LPFG. The LP31 and LP01 modes reflected from the 7MF connector will be converted into LP01 and LP31 modes respectively when passing the LPFG, and then arrive the splice point between SMF and 7MF. LP01 mode propagates backward in SMF and is reflected back into the cavity by the SM-FBG, while LP31 mode suffers a large loss. The output of the third-order mode depends on the matching of the operating wavelengths of the SM-FBG, 7MF connector and the LPFG. The signal light continuously oscillates and amplifies in the cavity, and by rotating the squeeze PC2 and adjusting the pressure appropriately, third-order OAM beam outputs from the end of gold-plated connector when reaching the laser threshold.
In the absence of SA, the third-order OAM beam appears when the pump power reaches 18mW, no pulse is generated in the laser. Adding SA into the cavity, when the pump power reaches 30mW, self-started Q-switched state is achieved. It confirms that SA plays a major role in realizing the Q-switched technique. The output spectrum of the Q-switched laser at the pump power of 160mW is shown in Figs. 4(a). The center wavelength and 3dB bandwidth are 1548.2nm and 0.4nm, respectively. The spectral bandwidth of the laser is affected by the wavelength range of the reflection peak of the FBG in the cavity. The signal-to-noise (SNR) of the laser is about 40dB, which proves the stability of the laser output. Figures 4(b) shows the Q-switched pulse train, the repetition frequency is 30.7kHz, corresponding to the time interval of 32.5µs. The duration of a single pulse is 5.2µs, as shown in Figs. 4(c). Figures 4(d) shows the output power versus the pump power in the Q-switched laser. It can be seen that output power increases with the pump power. Once the pump power exceeds 200mW, the Q-switched state becomes unstable and changes to the CW state, but the Q-switched state can be recovered by decreasing pump power again. We further measured the stability of fiber laser when it was operating, the spectrum was monitored every 10 minutes with a total time of 1hour. At each time interval, the wavelength fluctuation is no more than 0.1nm and the power fluctuation is also small. It confirms the stability of our laser.
Fig. 4. (a) The output spectrum of the Q-switched fiber laser. (b) Q-switched pulse train. (c) Single pulse shape. (d) Output power versus pump power.
The mode field distributions and interference patterns of the output beam are observed by the experimental setup shown in Fig. 5. The 9:1 OC splits the LP01 mode energy into the upper and lower branches. 10% of the energy extracted to the upper branch is used to be a reference beam, which is used to interfere with the output beam of the lower branch. The PC3 in the upper branch adjusts the polarization state of the reference beam. The intensity distributions and interference patterns are observed by CCD, as shown in Figs. 6.
Fig. 5. Experimental setup to observe the beam profiles and the interference patterns of the laser output beam. Col, collimator; Obj, microscope objective; BS, beam splitter; CCD, charge-coupled device.
Fig. 6. Near-field intensity distributions of the laser. (a)-(b) corresponding LP31 mode. (c)-(d) corresponding OAM±3 modes. (e)-(f) corresponding interference patterns.
The polarization state of LP01 mode can be changed by adjusting PC1. LP01 mode is converted to the LP31 mode through LPFG, and the mode intensity distributions are shown in Figs. 6(a)-(b), where the six-lobe mode profile certifies the order of the guided mode. Adjusting the PC2 on the 7MF, the phase shift of ±π/2 is generated between the LP31a and LP31b modes, and the two modes are superimposed to produce OAM±3 modes. As shown in Figs. 6(c)-(d), the spatial distributions of OAM±3 modes are presented as a dark dot in the center and bright ring around it. Due to the residual inter-modal coupling, the imbalance of optical power between orthogonal LP31 modes appears, which leads to the slight deviation from an ideal donut-shape. The reference beam and the OAM beam are combined through the beam splitter (BS) to produce the interference patterns. The opposite topological charges of OAM can be determined by the spiral fringes with opposite rotation directions, as shown in Figs. 6(e)-(f), which clearly demonstrates the generation of OAM+3 and OAM-3 beams.
In addition, we also measured the purity characteristic of the OAM mode by decomposing the generated OAM beam directly into the constituent OAM modes, based on the method used in [44]. The modal contribution of OAM-4-OAM+4 modes is measured by recording the power in the center of the beam profile in the Fourier plane. The representative data is shown in Figs. 7, the power of each order OAM mode relative to the generated OAM mode is represented by the vertical axis. The mode purity of OAM+3 and OAM-3 are measured to be 90.0% and 90.2%, respectively. Less than 1.5% of the power is in any other order modes.
Fig. 7. Representative data set showing the high mode purity of the generated OAM beams, corresponding to (a) OAM+3 mode, (b) OAM-3 mode.
4. Conclusion
In summary, we have experimentally demonstrated the generation of third-order OAM pulses with controllable topological charge of $l ={\pm} 3$ in an all-fiber Q-switched fiber laser with a LPFG, for the first time to our knowledge. The 7M-LPFG was introduced into the cavity to overcome the coupling problem and realize the conversion between the LP01 and LP31 modes. The OAM±3 modes were obtained by tuning the phase shift of even and odd modes. The homemade graphene-based SA was used to realize the transition of the laser from continuous wave to Q-switched state. Determined by the combination of the FBG and the LPFG, the laser oscillation occurred at 1548.2nm with a spectral width of 0.4nm at 3dB. The purity of the OAM+3 and OAM-3 modes were measured to be 90.0% and 90.2%, respectively. Our approach provides an effective strategy for generating higher-order modes. High power and ultrafast OAM pulses are supposed to be implemented by optimizing the loss of the LPFG, SA and the reflectivity of the output mirror. This simple and high purity OAM fiber laser source may find promising applications in optical tweezers, material processing, etc.
Funding
National Key Research and Development Porgram of China (2018YFB1801800); National Natural Science Foundation of China (U2001601, 62035018, 61875076, 61935013); Guangzhou Science and Technology Program key projects (201904020048); Guangdong Basic and Applied Basic Research Foundation (2021A1515011837).
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.
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