We propose and demonstrate an all-fiber passively mode-locked laser with a figure-8 cavity, which generates pulsed cylindrical vector beam output based on a mode selective coupler (MSC). The MSC made of a two mode fiber and a standard single mode fiber is used as both the intracavity transverse mode converter and mode splitter with a low insertion loss of about 0.65 dB. The slope efficiency of the fiber laser is > 3%. Through adjusting the polarization state in the laser cavity, both radially and azimuthally polarized beams have been obtained with high mode purity which are measured to be > 94%. The laser operates at 1556.3 nm with a spectral bandwidth of 3.2 nm. The mode-locked pulses have duration of 17 ns and a repetition rate of 0.66 MHz.
© 2017 Optical Society of America
Due to their polarization and amplitude symmetry, the cylindrical vector beams (CVBs) are receiving increasing attention from various applications, such as optical tweezers , surface plasmon excitation , material processing  and high resolution imaging , etc. CVBs are classified as azimuthally polarized, radially polarized, and hybridly polarized beams according to the spatial distribution of the polarization, especially, tighter focal spots can be obtained by using radial polarization owing to the existence of a strong and localized longitudinal field component .
Various kinds of techniques have been proposed and demonstrated for CVBs generation, such as spatial light modulators, axial birefringent components, angular gratings, and interferometric methods [6–12]. As compared to the solid-state lasers, all-fiber laser has advantages of low cost, high compactness and efficiency [13,14]. In Reference  we demonstrated a single-longitudinal-mode fiber ring laser with continuous wave (CW) CVB emission using a two-mode fiber Bragg grating as a transverse mode selector. Recently, pulsed CVB fiber lasers have been reported, using mode-locking or Q switching method [15–20]. Reference  presented a passively Q-switched single-wavelength all-fiber laser generating CVBs with large pulse energy. Reference  demonstrated a ring cavity actively mode-locked CVB fiber laser that emits a cylindrical vector beam. Most of these research use offset splicing (OSS) method to generate high-order mode and few-mode fiber Bragg grating (FM-FBG) as the transverse-mode selector. The FM-FBG is necessarily used to separate the fundamental mode and the higher order modes since they transmit in the same fiber. However, high order modes are excited by lateral misalignment between single-mode fiber (SMF) and few-mode fiber (FMF) which introduces insertion loss into fiber cavity, limits slope efficiency, the output power and, possibly, the long-term stability. Efforts are still needed to improve the efficiency of fiber lasers with CVB emission.
In this paper, we report a high efficiency, passively mode-locked CVB fiber laser based on an all-fiber mode selective coupler (MSC) with high mode conversion efficiency. The MSC is fabricated by weakly-fusing technique, based on the principle of phase matching, converting the fundamental mode in the SMF to the higher-order mode in the FMF and outputs different modes at different output ports. To the best of our knowledge, this is the first report on using MSC as the transverse mode converter and splitter in a figure-8 fiber laser cavity for generation of mode-locked CVB pulses with high mode purity and slope efficiency.
2. Theoretical analysis and Experimental setup
2.1 MSC simulation and fabrication
Figure 1 shows the schematic of the MSC, composed of a two mode fiber (TMF) and a SMF. The principle of this coupler is to phase match a high order mode in the TMF with the fundamental mode in the SMF, and then to achieve mode conversion .
According to the coupling mode equations :22]:
Suppose β2 is the propagation constant of the LP11 mode in the TMF, only if is zero, the LP01 mode in the SMF and the LP11 mode in the TMF meet the phase match condition. Then, Eqs. (3) and (4) are: and indicating a complete periodic power exchange between the two modes in the lossless case. So, on one hand, the MSC functions as a mode converter (from the LP01 mode in the SMF to the LP11 mode in the TMF), since the power of the two modes exchange periodically. On the other hand, the MSC functions as a mode splitter by outputting different modes at different fiber output ports.
The propagation constant β can be calculated as: , where k0 is the propagation constant in vacuum, neff is the mode effective index, which varies with the diameter of the fiber. Therefore, the diameters of SMF and TMF should be optimized in order to meet phase match condition between the LP01 mode in SMF and the LP11 in the TMF. As shown in Fig. 2, we calculated the mode effective index at different fiber diameters for step index profiles by finite element method (FEM). For phase match condition, the best diameter ratio of the SMF as compared to the TMF is about 0.63, so the diameter of the SMF should be pre-tapered to 79 μm.
Then, we use beam propagation method (BPM) to calculate and confirm the high efficiency modal power exchange under the phase match condition. As shown in Fig. 3, when the diameters of SMF and TMF cores are 5.1 µm and 8 µm, respectively (the diameter ratio is about 0.63), the phase match condition is satisfied and only the LP11 mode is excited in the TMF with high mode conversion efficiency.
Various kinds of mode conversion couplers have been fabricated, such as polished couplers , fused etched multi-mode couplers , and stress induced modal couplers  and weakly-fused coupler . In order to achieve high coupling efficiency and mode purity, we use weak fusion technique for maintaining the geometry of the SMF and the TMF and ensuring accurate modal conversion efficiency. According to our simulation results, the SMF (SMF-28) is pre-tapered to about 79 μm, then carefully aligned with the TMF (core/cladding diameter = 19.7/125μm, NA = 0.12) and fused them together using the modified flame brushing technique . A laser source of 1550 nm is launched into the SMF input, the output power of SMF and TMF are detected simultaneously by power meter. As shown in Fig. 4, the mode field distributions at the TMF output port at different wavelengths are detected by a CCD (CinCam IR). The purity of the LP11 mode is estimated to be about 97% near wavelength of 1550 nm, measured by tight bend approach. The LP01 mode can be efficiently converted to the LP11 mode with a low insertion loss of about 0.65 dB.
2.2 Experimental setup
Figure 5 shows the experimental setup of the proposed all-fiber mode-locked figure-8 cavity CVB laser. The MSC is inserted into the figure-8 cavity (right section) between a 50:50 fiber coupler and a 90:10 fiber coupler. The figure-8 cavity consists of a 980 nm laser diode, a 980/1550 nm wavelength division multiplexer (WDM), a section of Er3+-doped fiber (EDF) of 70 cm, three polarization controllers (PCs), a long section fiber (550 m, SMF28e + ) and an isolator (ISO). The mode-locking mechanism of the laser is Nonlinear Amplifying Loop Mirror (NALM), through adjusting the PC1 in the cavity.
Our proposed fiber laser uses MSC instead of FM-FBG as the transverse mode converter and eliminates extra cavity loss. The insertion loss of the MSC is 0.65 dB with an intra-cavity coupling ratio of 90%. The spectral and temporal properties of the laser are measured at output1, by an optical spectrum analyzer (OSA, YOKOGAWA, AQ6370C) and an oscilloscope (OSC, SDA 6000A). The output beam profiles are captured by a CCD camera placed at output2 through a fiber collimator.
3. Experimental results and discussions
The threshold pump power of the proposed fiber laser is about 130 mW. Long-term stable pulse trains can be observed by adjusting the PC1 in the cavity. For a pump power of 300 mW, the temporal behavior of the pulse train and the single pulse shape are shown in Figs. 6(a) and 6(b), respectively. The duration of pulse is measured to be 17 ns and the pulse repetition rate is about 0.66 MHz.
The mode-locked laser spectrum with a pump power of 300 mW at output1 is measured as Fig. 7(a). The center wavelength of the laser is 1556.3 nm and the 3-dB bandwidth is measured to be 3.2 nm. Figure 7(b) shows the output laser power versus the pump power (output1, black curve and output2, red curve), the slope efficiency of output1 is about 3.1%, which is higher than previous lasers using the offset-splicing method.
In the mode-locked figure-8 cavity, the MSC functions as a mode converter and splitter, the LP01 mode is converted to LP11 mode when the pulse light passes through the coupling region and outputs the LP11 mode at the TMF output port (output2). As for our CVB generation, PC2 and PC3 are used at the input and output port of the MSC in order to filter out TM01 or TE01 mode from superposition of several higher-order modes [27,28]. PC2 is used to control the polarization of the input fundamental mode to adjust the coupling efficiency from the fundamental mode to higher-order modes, PC3 in the few-mode fiber is used to refine final output polarization state to achieve higher purity of TM01 or TE01 modes which can form cylindrical vector beams. Radially polarized and azimuthally polarized beams with a high purity can be obtained at output2 through adjustment of PC2 and PC3. The doughnut-shaped intensity profiles of the radially and azimuthally polarized beams are measured by CCD camera as shown in Figs. 8(a)–8(f). The purity of the radially polarized beam and the azimuthally polarized beam are measured to be 94.2% and 94.3%, respectively [13,29]. The radial polarization and azimuthal polarization of the output mode could be confirmed by recording the intensity distributions by rotating a liner polarizer inserted between the collimator and the CCD camera. Figures 8(b)-8(e) and 8(g)-8(j) show the intensity distributions of the radially polarization beam and azimuthally polarization beam after passing a liner polarizer at different orientations.
In summary, we present an all-fiber passively mode-locked laser producing CVBs with high efficiency and high mode purity. A MSC made by weakly fused technology is incorporated into the figure-8 cavity as the transverse mode converter and mode splitter. The MSC can achieve LP11 mode with a high purity (about 97%) near wavelength of 1550 nm with a low insertion loss of about 0.65 dB. The CVB laser slope efficiency is about 3.1%. The purities of the radially polarized beam and the azimuthally polarized beam are measured to be 94.2% and 94.3%, respectively. The laser is mode-locked within a spectral bandwidth of 3.2 nm at the 1556.3 operating wavelength. The repetition rate of the mode-locked laser is 0.66 MHz and the pulse duration is 17 ns. As compared to previous structure using FM-FBG and offset splicing method, our mode-locked CVB fiber laser has the advantages of higher efficiency, high purity with high stability and simple structure with low lost. Our further work will focus on higher-order mode oscillation in the laser cavity to improve CVB laser efficiency. This simple and novel all-fiber laser source may find applications in many areas such as optical tweezers, optical imaging, and mode-division multiplexed systems.
Natural Science Foundation of Jiangsu Province under Grants BK20150858 and BK20161521; Nanjing University of Posts and Telecommunications (NUPTSF) under Grant NY214059, NY214002, and NY215002; Distinguished Professor Project of Jiangsu under Grant RK002STP14001; Six Talent Peaks Project in Jiangsu Province under Grant 2015-XCL-023.
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