We propose and demonstrate an all-fiber laser with LP11 mode output. A transverse mode filter is designed and fabricated to suppress the fundamental mode and enable the fiber laser to oscillate in the second-order (LP11) transverse mode. The mechanism is to introduce relatively low ohmic loss for the TE01 mode and much higher ohmic losses for other modes through the loss of evanescent waves in the metal clad. The fiber laser operates at the center wavelength of 1053.9 nm with a narrow 3 dB linewidth of 0.019 nm. Four states of cylindrical vector mode with high modal purity are obtained through adjusting the intra-cavity polarization controller. This approach has great potentiality and scalability of realizing single high-order mode fiber laser, from which a wide range of applications could benefit.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fiber lasers with higher-order modes output have attracted considerable attention in recent years. The second-order (LP11) set of modes have played important roles in the generation of cylindrical vector beams (CVBs) [1–3] and optical vortex beams (OVBs), which also named as orbital angular momentum (OAM) beams, in optical fibers [4,5]. More importantly, as the optical communication systems will reach their capacity limit over the next decade or so , fiber lasers operating at different transverse modes are expected to find applications in mode-division-multiplexed systems [7,8]. Hence, fiber lasers with higher-order modes output are desirable for all the applications that mentioned above.
Several kinds of methods for the generation of high-order modes based on fiber laser have been proposed and demonstrated in recent few years. The first one is using offset splicing spot (OSS) to generate LP11 mode and few-mode fiber Bragg grating (FM-FBG) to select the transverse-mode. Continuous-wave (CW) CVBs fiber lasers and pulsed CVBs fiber lasers based on mode-locking and Q-switched techniques have been achieved using the OSS method [9,10]. The higher-order modes are excited from the LP01 mode by the misalignment between the single mode fiber and few-mode fiber, which causes large insertion loss. The second method is using the mode selective coupler (MSC) as the mode converter and splitter inside the fiber cavity. It has lower insertion loss and higher slope efficiency as compared with the OSS method . CW and pulsed CVBs fiber lasers are also obtained by using the MSC [12–14]. The third method is using the long period fiber grating (LPFG) to couple the LP01 mode to the LP11 mode. It has the advantages of low insertion loss, high conversion efficiency, and broad working spectrum . Chen et al.  demonstrated an all-fiber CVBs laser with high slope efficiency (>35.41%) by using the LPFG. However, all of those methods that mentioned above are based on the mode conversion between the LP01 mode and the LP11 mode, in which the LP01 mode and the LP11 mode exist simultaneously in the fiber cavity. In 2016, Liu et al.  demonstrated an LP11 mode oscillation fiber laser by employing a pair of few-mode fiber Bragg gratings as an efficient transverse mode selector, whose spectral characteristics are particularly tailored so that only the LP11 mode can oscillate in the laser cavity. In 2018, T. Wang et al.  demonstrated an LP11 mode oscillation fiber laser by using a wavelength division multiplexing (WDM) mode selective coupler (MSC). Our group also demonstrated an LP11 mode oscillation fiber laser based on the polarization dependence of the few-mode fiber Bragg grating .
Using a metal-clad waveguide to select different modes has been reported since the 1970s. In 1972, Y. Suematsu et al.  used an asymmetric dielectric light guide with a metal film outer coating to select TE mode. R. Alonso et al.  reported a metal-clad side polishing fiber device. This device introduced a large attenuation for the TM mode based on the resonant excitation of metal-clad modes, while the TE mode is hardly influenced. In 2012, Dong et al.  demonstrated an in-line fiber polarizer based on surface plasmon in a metal film. The fiber was tapered to a diameter about 1 μm and placed above an Au thin film, the surface plasmon in the metal film can be excited by the TM mode, while the TE mode can propagate freely.
In this letter, we propose and demonstrate an all-fiber laser oscillating on the LP11 mode by using a metal-clad transverse mode filter to suppress the LP01 mode. The four degenerate vector modes, i.e., TE01 (azimuthally polarized), TM01 (radially polarized), and HE21 (even and odd) can all be obtained by adjusting the polarization controller (PC) inside the cavity. Two matched FM-FBGs are used as the cavity reflector and output coupler. The laser operates at a wavelength of 1053.9 nm within a narrow spectrum width of 0.019 nm.
2. Simulation and fabrication of the transverse mode filter
The schematic structure diagram of the mode filter is shown in Fig. 1. It is made from the SMF-28e fiber, which only supports the modes HE11, TE01, TM01, and HE21 (even and odd) near the wavelength of 1064 nm. The modes HE11, TM01, and HE21 (even and odd) would experience large ohmic losses with the existence of the free electrons in the metal coating, while TE01 mode is hardly influenced. The physical mechanism of the mode filter is as follows. In the presence of a good, but not perfect, conductor boundary, there exists a strong normal electric field E⊥ and a small tangential electric field E∥, and would experience ohmic loss inside the conductor . Thus, the modes HE11, TM01, and HE21 (even and odd) will have stronger electromagnetic field distribution near the surface of the metal film than TE01 mode, as shown in Fig. 2, and undergo larger ohmic losses inside the metal film. We used the finite element method (FEM) to calculate the effective refractive index of the modes. Re(neff) and Im(neff) represent the real part and imaginary part of the effective refractive index, respectively. The confinement loss of the mode is given by 
In the simulation, the diameter of the fiber core is set to be 8.2 μm, whereas the diameter of the cladding d and the thickness of the Aluminum coating δ are adjusted to analysis their influence on the confinement losses of the modes. The refractive index of the core n1 and the cladding n2 are set to be 1.455 and 1.45, respectively. Figure 3 shows the dependencies of the Re(neff) and the confinement losses of the modes HE11, TE01, TM01, and HE21 (even and odd) on d and δ. The HE21 (even) and HE21 (odd) degenerate into one curve in Fig. 3.
The results show that the TE01 mode has the lowest confinement loss among the LP01 and LP11 modes. Its confinement loss can be smaller than 0.5 dB/cm, whereas that of the other modes are larger than 20 dB/cm. Meanwhile, the differences of Re(neff) between TE01 and the other modes are larger than when the cladding diameter is smaller than 13 μm and assume the thickness of Aluminum is 200 nm. Thus, the mode TE01 is distinguishable from the other modes (HE11, TM01, and HE21), and will experience a weakly mode coupling and low confinement loss when propagating in the mode filter. In a word, the designed mode filter can make the TE01 mode pass through and the other modes cutoff.
Fabrication of the mode filter is as follows: first, using the fiber optics stripper to remove the fiber coating. Second, putting the fiber into the BOE (6.5% HF) solution for about 7 h and a half under the ultrasonic agitation. Third, after the corrosion process, the sample was put into deionized water at 70°C to remove the residual NH4F crystal on the fiber surface, then the sample was dried at 70°C for 1 h. Finally, the Aluminum film was deposited using the Ebeam Evaporator (KertLeskerLAB 18). A layer of with a thickness of 20 nm was deposited on the Aluminum film to protect the Aluminum from oxidation. The fabricated mode filter has a length of about 1 cm with 20 cm pigtailed fiber in both ends for splicing. The cladding diameter is about 12 μm measured by the optical microscope, and the thickness of the Aluminum coating is 200 nm. Figure 4 shows the scanning electron microscopy (SEM) images of the fiber after corrosion, which has a smooth surface and uniform diameter.
3. Experiments and discussion
The schematic of the high-order mode fiber laser is illustrated in Fig. 5. A length of 30 cm few-mode ytterbium-doped fiber (Nufern, MM-YDF-7/128) is used as the gain medium and pumped by a 980 nm laser diode through a 980/1064 nm wavelength division multiplexing (WDM). A pair of few-mode fiber Bragg grating (FM-FBG) is used as the feedback element, which was written on the SMF-28e fiber with same period but different reflectivity. The high reflective FBG (HR-FBG) acts as the high reflector while the low reflective FBG (LR-FBG) acts as the output coupler. The transmission spectra are measured using an ASE light source when only the LP01 mode is excited, and the peak reflectivity is estimated to be over 99% for HR-FBG and about 67% for LR-FBG. In theoretically, the reflectivity of FBG for LP11 mode is close to the LP01 mode. A polarization controller is used to adjust the output patterns. The output beam property is measured using a CCD camera through a fiber collimator.
Figure 6 shows the spectrum of the fiber laser which is characterized by an optical spectrum analyzer from the LR-FBG end. The fiber operates at the wavelength of 1053.9 nm with a narrow 3 dB linewidth of 0.019 nm, which corresponding to the LP11 intra-modal reflection peak of the FM-FBG, indicating that the fiber laser oscillates at LP11 mode with LP01 mode being suppressed. Figure 7 plots the output power characteristic of the fiber laser. The threshold when the fiber laser starts to oscillate is at approximately 310 mW, and the slope efficiency is 1.5%. This relatively low slope efficiency is due to the high degeneracy of LP11 mode in the SMF-28e fiber and the FM-YDF, which causes the strong mode coupling among the TE01, TM01, and HE21 (even and odd) modes. Once TE01 mode coupled to TM01 and HE21 (even and odd) mode, it would experience a large loss when passing through the mode filter, which causes the high loss inside the laser cavity. This problem could be solved by using the ring-core (vortex) fiber . In vortex fiber, the index separation of two adjacent LP11 modes could reach an order of 1 × 10−4, which is large enough to break the degeneracy within the LP11 modes.
The fiber laser can operate at all the four different LP11 modes through adjusting the intra-cavity PC. The intensity profiles of the four modes (TE01, TM01, HE21 (even), and HE21 (odd)) are measured by the CCD camera as shown in Fig. 8. The state of polarization of the output mode was confirmed by recording the intensity distributions by rotating a linear polarizer inserted between the collimator and the CCD camera. The mode purity of LP11 mode is estimated based on the bending method used in . The fiber of the output end is bent to a circle with a radius of 1.2cm, and the output power decreases from 683 μW to 15.67 μW, which gives a 97.7% loss. In addition, the loss percentage of LP01 mode is 94.5% in the same conditions. Thus, the purity of LP11 mode is estimated to be 97.5%.
In conclusion, we have proposed and demonstrated an all-fiber high-order mode laser experimentally using a transverse mode filter. We show that the fiber laser can stably work on the LP11 mode with a narrow 3 dB spectral width of 0.019 nm at the center wavelength of 1053.9 nm. Four CVB modes (TE01, TM01, HE21 (even), and HE21 (odd)) can all be obtained by adjusting the intra-cavity PC, and the purity of LP11 mode is estimated to excess 97%. More importantly, by substituting vortex fiber for the SMF-28e fiber, a high-purity single-mode (TE01) oscillation fiber laser could be realized by this approach. This high-order mode oscillation fiber laser may find potential applications in areas such as optical trapping, surface plasmon excitation, particle acceleration, laser processing, microscopic imaging and mode-division multiplexed systems.
National Natural Science Foundation of China (NSFC) (No.61675188); Fundamental Research Funds for the Central Universities (WK6030000065); Science and Technology on Plasma Physics Laboratory (No.6142A0403060917); Open Fund of Key Laboratory Pulse Power Laser Technology of China (SKL2016KF03).
This work was partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication, and we thank engineer Yu Wei for his help on micro fabrication.
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