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Abstract
In this paper, we propose a stable orbital angular momentum (OAM) mode fiber laser with an all-polarization-maintaining fiber (PMF) structure based on a combination of two linearly polarized modes. The mode intensity ratio between the two linearly polarized modes can be adjusted by adopting a double-pump structure. A pair of polarization-maintaining long-period fiber gratings (PM-LPFGs) are used as a mode converter. The number of topological charges of the OAM mode beam can be tuned between +1 and −1 by stretching the fiber. By adopting an all-PMF structure, we can build an OAM mode fiber laser without a polarization controller and that is resistant to environmental disturbances. The purity of the OAM mode was approximately 93.6%. This stable and compact OAM mode fiber laser can be used as a laser source in practical applications and scientific research.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, orbital angular momentum (OAM) beams laser has developed rapidly, including broadband tunable OAM beams, tunable chirality OAM beams, ultrashort pulse OAM laser and time-varying OAM beams [1–5]. And it has widely applications in material processing [6], quantum informatics [7], mode-division multiplexing [8,9], optical tweezers [10,11], and microscopy [12,13]. OAM is characterized by a helical phase front ${\textrm{e}^{{\pm} \textrm{il}{\mathrm{\varphi}}}}$, where ${\mathrm{\varphi}}$ is the azimuth angle and l is the topological charge [14]. Generally, OAM beams can be obtained by using optical components such as spatial light modulators [15], Q-plates [16,17], and spiral phase plates [18,19]. Compared with OAM beams with a free-space structure, OAM beams with an all-fiber structure are superior in terms of compactness, low cost, and flexibility.
The LP11 modes in a few-mode fiber (FMF) include four vector modes, i.e., TE01, TM01, and HE21 (even and odd). Through the linear combinations of the TE, TM, EH, and HE modes, OAM beams can be generated in an optical fiber [20–24], which provides an attractive way to realize an OAM laser beam with an all-fiber structure. Many methods have been applied to generate OAM beams in an optical fiber. Jin et al. demonstrated OAM laser beams with an all-fiber structure based on offset-splicing technology [25]. Zhao et al. reported a high-purity OAM mode laser with an all-fiber structure generated with FMF long-period gratings [26]. In 2017, Wang et al. presented a femtosecond OAM mode laser with an all-fiber structure by adopting a few-mode selective coupler [27]. However, OAM modes cannot propagate stably in a common fiber owing to severe mode crosstalk [22], and, therefore, an additional polarization controller is usually required. The generation of OAM modes in a polarization-maintaining fiber (PMF) can effectively solve the problem of mode crosstalk owing to its colossal birefringence, which has been proved experimentally with an OAM mode laser with a free structure [28–30].
In this paper, we propose a method to realize an all-PMF ytterbium (Yb)-doped OAM mode fiber laser based on the superposition of linearly polarized LP11 modes obtained from a polarization-maintaining long-period fiber grating (PM-LPFG). Owing to the large birefringence of the PMF, severe mode crosstalk during the transmission process can be significantly reduced. The laser can output a highly stable OAM mode by stretching the fiber to tune the phase difference. Moreover, the PMF is not sensitive to environmental perturbations, which is very important for practical applications. We believe that our scheme is attractive for developing stable OAM mode lasers and may be broadly applied in the field of communication systems and scientific research.
2. Operating principle
Under the weak-guidance approximation, a few-mode polarization-maintaining fiber (FM-PMF) supports LP11 linear polarization mode groups, including LP11ax, LP11bx, LP11ay, and LP11by, by solving a scalar wave equation, as shown in Fig. 1. Generally, the OAM mode can be obtained by superposing the odd and even LPlm modes (where l refers to the azimuthal index and m refers to the radial index) with a ${\pm} \pi /2$ phase difference, as illustrated in Fig. 2. In conventional FMFs, LP11 modes would randomly couple with each other during propagation owing to the extremely small (∼10−5) effective refractive index difference within the LP11 groups, which will cause the OAM mode to become highly unstable [22]. The PMF offers one attractive option: the effective refractive index difference of LP11 in an FM-PMF can reach up to ∼10−4, which largely avoids mode crosstalk. The relative phase difference between two linear polarization modes can be written as ΔΦ=LΔneff (2π/λ), where Δneff is the effective refractive index difference of the mode, L is the length of the fiber, and λ is the operation wavelength. To achieve the OAM mode, we must set ΔΦ to ${\pm} \pi /2\; $+m$\pi $ (m=0,1,2,…), which can be achieved by adjusting the phase delay of different modes (stressing the fiber or changing the operation wavelength [30–32]). The effective refractive index difference of the odd and even LP11 modes in an FM-PMF is calculated as 2.4×10−4 by using the finite element method, as shown in Fig. 3(a). The beating length for LP11 at 1064 nm in an FM-PMF is approximately 4.4 mm, as illustrated in Fig. 3(b), which means that the phase difference between two degenerate odd and even LP11 modes can be adjusted by controlling the fiber length.
Fig. 1. Spatial distribution of the electric vector field for the LP11ax, LP11ay, LP11bx, and LP11by modes.
Fig. 3. (a) Modal effective index for LP11ax, LP11ay, LP11bx, and LP11by in PM1550. (b) Phase difference between the LP11ax and the LP11bx mode vs. the PM1550 length.
3. Experimental result and discussion
Figure 4 shows the experimental configuration of the all-PMF Yb-doped OAM mode fiber laser. A 976-nm laser diode was used to pump the all-PM Yb-doped fiber (Nufern PM-YSF-HI-HP) with a 980/1060-nm PM wavelength division multiplexer (PM-WDM). Two PM-LPFGs were used as a mode converter, which converts from LP01 to LP11ax and LP11ay, respectively. In the experiment, the PM-LPFGs were self-fabricated in a PM1550 fiber by using a CO2 laser. Like in the LPFG fabricated in a common FMF, if the phase-matching condition is satisfied, the LP01 mode will be coupled to the LP11 mode in the grating region of the fiber. The phase-matching condition can be expressed by Λ=λ/Δneff, where Λ is the period of the PM-LPFG, λ is the wavelength of the PM-LPFG, and Δneff is the effective refractive index difference between the LP01 and the LP11 mode. Here, the periods of the PM-LPFG1 and PM-LPFG2 Λ were set to 450 µm and 410 µm, respectively. The transmission spectrum of the PM-LPFG can be seen in Fig. 5(a). The same conversion peak of the PM-LPFG1 and PM-LPFG2 was located at around 1067 nm, which converted LP01 to LP11ax and LP11ay, respectively. A high-reflectivity polarization-maintaining FMF Bragg grating (HR-PM-FMFBG) acts as a reflector with a reflectivity of ∼95%; it is fabricated in a PM1550 fiber by using an ultraviolet excimer laser. The reflection spectrum of the HR-PM-FMFBG is shown in Fig. 5(b); it was measured with hybrid spatial modes by using a broadband amplified spontaneous emission source with offset coupling. Each reflection peak represents a different reflection mode. The four reflection peaks on the left represent the reflections of the LP11 mode. The two central peaks represent the intra-modal reflection between the LP01 and the LP11 mode. The two reflection peaks on the right represent the reflections of the LP01 mode. The LP11ax and LP11ay modes from the left and right arm resonator cavities are superposed by a polarization-maintaining few-mode optical coupler (PM-FMOC), and the insertion loss of PM-FMOC is about 1.31 dB. A fiber stretcher was used to tune the phase difference between the odd and the even LP11x mode. In order to compose linearly polarized OAM beams, when Port 2 is coupled to Port 3 of the PM-FMOC, the direction of the polarization and the mode field distribution is artificially rotated by 90°, which corresponds to the conversion from the LP11ay mode to the LP11bx mode. The operating principle of PM-FMOC is shown in the inset of Fig. 4. The profiles of the mode intensity were imaged by using a CCD camera. Except for the WDM and the Yb-doped fiber, which are a single-mode fiber (PM980), the tail fiber type of the other optical devices is PM1550.
Fig. 4. Experimental setup of the proposed all-PMF Yb-doped OAM mode fiber laser. LD, 976-nm laser diode; PM-WDM, polarization-maintaining wavelength division multiplexer; PM-YDF, polarization-maintaining ytterbium-doped fiber; PM-OC, polarization-maintaining 90:10 optical coupler; PM-LPFG, polarization-maintaining long-period fiber grating; HR-PM-FMFBG, high-reflectivity polarization-maintaining few-mode fiber Bragg grating; PM-FMOC, polarization-maintaining few-mode optical coupler; STRETCHER, fiber stretcher; NPBS, non-polarized beam splitter; COL, collimator; P, linear polarizer; CCD, CCD camera. The inset shows operating principle of PM-FMOC.
The proposed fiber laser operates stably in the fundamental mode (LP01) when the pump power of the left and right arms reaches 10 mW and 20 mW, respectively. The maximum output power of the left and right arms is 67.2 mW and 70.8 mW, respectively; the output is in the LP01 mode. When the laser outputs in this mode, the output wavelength of the left and right arms is 1064.10 nm and 1064.13 nm, respectively, as shown in the red line in Fig. 6. When the pump power of the left and right arms exceeds 157.5 mW and 262.6 mW, respectively, the fiber laser stably outputs in the LP11 mode with a wavelength of 1067.1 nm and 1067.2 nm, respectively, as shown in the blue line in Fig. 6. The inset of Fig. 6 shows the LP11 mode intensity distribution of the outputs of the left and right arms, corresponding to the LP11ax and LP11ay modes, respectively. Figure 7 shows the output power characteristic of the proposed fiber laser, whose left and right arms have a slope efficiency of 22.6% and 30.12%, respectively. When the output mode is switched from LP01 to LP11, the slope efficiency changes slightly owing to different reflectivity of LP01 and LP11.
Fig. 6. (a) Spectrum of the output of the left arm. The red line is the output spectrum of LP01, and the blue line is the output spectrum of LP11. The inset shows the spatial distribution of LP11ax. (b) Spectrum of the output of the right arm. The red line is the output spectrum of LP01, and the blue line is the output spectrum of LP11. The inset shows the spatial distribution of LP11ay.
Two orthogonal linear polarization LP11 modes from the left and right arms are superimposed by a PM-FMOC; The output power of the left and right arms is set to 110 mW, and the final power of the three ports is 83 mW after passing through the PM-FMOC. The phase difference between the LP11ax and the LP11bx mode in port 3 of the PM-FMOC is tuned by a fiber optic stretcher. To confirm the OAM mode, we split the reference beam with power of 28 mW by using a 90:10 coupler. The output mode field distributions of the OAM and Gaussian beams are shown in Figs. 8(a) and 8(b), respectively. The interference pattern was recorded by the CCD camera. By tuning the phase difference, we enabled the forked direction of the interference pattern to evolve from up to down, as illustrated in Figs. 9(a) and 9(c). The spiral interference pattern can be further observed when the reference beam is slightly expanded, which clearly indicates that the topological charge of the OAM beam is ±1, as shown in Figs. 9(b) and 9(d). The purity of the OAM mode was approximately 93.6%, based on the method in [33]. As long as the stretcher is fixed, the last result can be obtained after the laser is restarted. In addition, the fiber laser can operate stably under perturbation conditions as long as the grating remains stationary.
4. Conclusion
In this paper, we proposed a fiber laser to generate OAM beams with an all-PM fiber structure by adopting two PM-LPFGs to excite the LP11ax and LP11ay modes, respectively. The OAM beam can be stably generated because of the significant effective refractive index difference. Moreover, the fiber laser is capable of resisting environmental disturbances owing to the characteristic of the PMF. This method can extend to higher-order OAM beams by replacing the type of PMF. The purity of the OAM mode was measured as approximately 93.6%. By tuning the phase difference with a fiber stretcher, we can switch the topological charge number between +1 and −1. The proposed fiber laser can be used as a source in optical communication systems with mode multiplexing.
Funding
National Natural Science Foundation of China (61675188).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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