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Abstract
We propose and demonstrate an all-polarization-maintaining (PM) high-power cylindrical vector beam (CVB) fiber laser based on the principle of mode superposition. The non-degenerated LPy 11a is generated from the oscillator with the maximum power of 11.9W, whose slope efficiency is 24.4%. Then the stable single TE01 vector beam is achieved by the superposition of LPy 11a and LPx 11b in an all-PM architecture, its output power is 3.1W and mode purity of 91.2%. Due to the all-PM architecture, our configuration is free of adjusting polarization controller (PC) and reliable during long-term operation. This laser could be used as a high-power CVBs source for a wide range of applications towards scientific research and industrial field.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cylindrical vector beams (CVBs) have attracted extensive attention due to their axisymmetric polarization distribution and annular mode field distribution [1]. The typical CVBs include radially polarized (TM01) and azimuthally polarized (TE01) beams. CVBs have wide applications such as surface Plasmon excitation [2], super-resolution imaging [3,4], optical communication [5–8], optical sensing (surface Raman spectroscopy enhancement) [9,10], particle acceleration [11], optical manipulation [12] and laser processing [13–16]. Generally, the generation of CVBs can be classified into two categories: spatial optics scheme and optical fiber scheme. Spatial optics scheme includes photonic crystal gratings [17], q-wave plate [18,19], S-wave plate [20]. Compared with spatial optics scheme, optical fiber scheme has the advantages of high compactness, simple operation and flexibility. A lot of CVBs fiber lasers have been developed based on method like : offset splicing spot (OSS) [21] between two fibers, few-mode fiber Bragg grating (FM-FBG) [22–25], long-period fiber grating (LPFG) [26–30] and mode selective coupler (MSC) [31,32]. In the field of material processing, high-power CVBs laser has become a good candidate for the reason of enhancement of machining efficiency and precision [15,16]. Recently many high-power CVBs fiber lasers have been demonstrated experimentally. For example, in 2017 [33], a high-power LP11 fiber laser was realized based on fiber Bragg grating pairs. In 2018, X.Yang et al. reported the high power LP11 mode supercontinuum based on mechanical LPFG [34]. In 2021, L.Wang et al. demonstrated high-order mode (HOM) dissipative soliton resonance pulse at high average power by nonlinear optical loop mirror (NOLM) [35]. In the same year, M. Huang et al. realized high-power Raman CVBs by using a nonlinear polarization rotation (NPR) structure based on MSC [36]. However, most of the previous works were based on non-PM fiber and thus usually lead to poor stability and careful adjustment on PC.
In this work, an all-PM high-power CVBs fiber laser is demonstrated based on the principle of mode superposition. The mode crosstalk can be inhibited effectively for our case as the difference of effective refractive index between slow and fast axes is larger than 10−4 in PM fiber [37,38], and thus the stability will be improved significantly. It is worth mentioning that our architecture is free of tedious adjustment on PC as none of it is used. The maximum output power of our compact all-PM fiber laser is 3.1W with a mode purity of 91.2% for TE01. To the best of our knowledge, this is the highest output power of CVBs in all-PM fiber laser. The center wavelength is 1063.9 nm with a 3 dB bandwidth of 0.23 nm. The high-power CVBs laser can be self-started and operate stably under certain disturbances of environment. Our laser will be appealing for practical application in laser machining and scientific research.
2. Principle analysis
The mechanism of generating CVBs in our work is based on the mode superposition in few mode PM-fiber. The polarization-maintaining fiber (PLMA fiber) in our work has a core diameter of 15 µm and an inner-cladding diameter of 130 µm. The PLMA fiber supports four polarized modes at 1064nm, which are written as LPx 11a, LPy 11a, LPx 11b, LPy 11b (Subscript a/b indicates the spatial distribution of the light field, and superscript x/y indicates the polarization direction of the light field). We can call them vector LP11 modes collectively in this paper. The results of the calculation of the effective refractive index versus wavelength for different modes by finite element method is shown in Fig. 1(a). The dotted line marks the operation wavelength of our laser at 1064nm. The effective refractive indexes (Δneff) between LPy 11a and LPy 11b is larger than 1×10−4, on the other hand, although the Δneff between LPx 11a and LPx 11b is less than 10−4, the overlap mode areas of them are small for their spatial distributions are orthogonal. As a result, all four non-degenerated LP11 modes can transmit stably, and the crosstalk among the four LP11 modes could be greatly inhibited because of the effective index difference and the characteristics of mode distribution.
Fig. 1. (a) Modal effective refractive index of LP11 groups in PLMA-GDF-15-130; (b) the relative phase shift between LPy 11a and LPx 11b mode versus the length of PLMA-GDF-15-130.
The CVBs can be achieved by linear superposition of two related LP11 modes [1]:
The phase difference Δφ between LPx 11a (LPy 11a) and LPy 11b (LPx 11b) should satisfy:
Δneff is the effective refractive index difference between the two related LP11 modes, k is the wave vector, L is the fiber length. As illustrated in Fig. 1(b), the beating length for orthogonal LP11 at 1064 nm in PLMA fiber is approximately 2.5 mm. Thus, we can obtain the desired phase difference by simply stretching the optical fiber for the generation of CVBs by the method of mode superposition. In fact, several methods could be used to adjust the phase difference, such as time delay line, stretching fiber, changing operation wavelength [39–42].Due to the all-PM architecture, our scheme do not require polarization controller, which make the fiber laser insensitive to the environmental disturbance. In summary, we take three steps to achieve CVBs output: 1. Use fiber-based device to convert fundamental mode into HOM. 2. Devide vector LP11 modes into two optical paths. 3. Adjust the relative phase shift to obtain CVBs laser.
3. Experimental setup
The schematic of the proposed CVBs fiber laser is shown in Fig. 2. The experiment setup comprises an oscillator and a mode superposition setup. The oscillator is utilized to generate vector LP11 modes, and the mode superposition setup is used to composite CVBs. The oscillator includes two high reflectivity Bragg gratings (FBG1, FBG2) written on PLMA fiber. FBG1 acts as a reflecting mirror of the cavity with the reflectivity of about 99%. The reflection spectrum is depicted in Fig. 3(a). Two high-power multi-mode semiconductor laser diodes (LD) taken as pump sources inject the laser oscillator through the pump beam combiner ((2 + 1) ×1COM). A 4.5m long double-cladding pumped large-mode area PM Ytterbium-doped fiber (PLMA-DC-YDF) served as gain medium. Then the residual cladding light is filtered out by a cladding pump stripper (CPS). The LPFG inscribed into PLMA-fiber (PLMA-LPFG) transform the fundamental mode beam into targeted HOM modes. According to the phase-matching condition, the resonant wavelength λres=Λ·Δneff [29], the period (Λ) of PLMA-LPFG in our work is 1500 µm at the resonant wavelength (λres) of 1064nm. Δneff refers to the effective refractive index difference between target vector modes, herein the mode of LPy 01 and LPy 11a. The period number of the grating is 30 and the duty cycle is 0.5 by using the point-by-point scanning inscription of the CO2 laser. A mode stripper (MS) is in charge of ensuring the pure LP01 enter in the PLMA-LPFG [35]. The reflected spectrum of FBG1 and FBG2 in Fig. 3. can be measured with hybrid spatial modes injection by adjusting the lateral offset. The test light source is a broadband amplified spontaneous emission (ASE) at around 1064nm [37,43]. The right reflector is FBG2 with the reflection spectrum in Fig. 3(b) and the reflectivity is about 99.6%. The two peaks in the left represent reflections of LP11 modes at 1063nm and the right two peaks represent reflections of LP01 mode group at around 1063.8nm. The coupled peaks of LP01 and LP11 is weak which is impossible to detect because of the fabricating technique. FBG2 works as a mode selective filter by reflecting LP01 modes and passing through LP11 modes at around 1064nm [22,23]. The ISO protects the oscillator from the possible damage from reflected beams. The part of mode superposition setup mainly contains: a 50:50 high-power PM coupler (PLMA-OC), a fiber stretcher to adjust phase difference and a high-power polarization beam splitter (PLMA-PBS). The fiber in the entire experimental setup is PLMA fiber (red lines) except the multi-mode fiber as the pigtail fiber (blue lines) of the multi-mode pump source.
Fig. 2. The schematic for high-power CVBs PM fiber laser. LD, laser diode; (2 + 1)×1COM, pump beam combiner; FBG, fiber bragg grating; PLMA-DC-YDF, double-cladding pumped large-mode area PM Ytterbium-doped fiber; CPS, cladding pump stripper; MS, mode stripper; LPFG, long period fiber grating; ISO, isolator; PLMA-OC, 50:50 high-power PM coupler; PLMA-PBS, high-power polarization beam splitter; TDL, time delay line; COL, collimator.
4. Results and discussion
When the pump power reach the threshold value of 2.7W, the oscillator start to emit continuous wave LPy 11a laser mode. The output properties of LPy 11a mode from the oscillator are measured at the T point in Fig. 2. Then Fig. 4(a) shows the power characteristic of the oscillator, the output power increases linearly with the pump power, the corresponding slope efficiency is 24.4%. When the pump power arrives at 50W we get the maximum output power at 11.9W of LPy 11a. In general, the double-cladding pumped oscillator makes sure the high-power HOM generation with the help of PLMA-LPFG and FBG. Operation mechanism can be explained as followed. If the coupling efficiency of PLMA-LPFG is less than 50%, the laser resonates at the LP01 reflection peak of FBG2 due to mode competition effects. The mode coupling efficiency of the PLMA-LPFG is estimated to be about 40% by measuring the power ratio of the HOM and the fundamental mode with the help of bend loss method [22]. FBG2 can reflect almost all LP01 and transmit LP11 mode. As a result, LP01 oscillates in the cavity and vector LP11 is output from the cavity. As depicted in Fig. 4(b), the output spectrum of the oscillator is measured and the charge-coupled device (CCD) camera records the mode field distribution. The slight difference in the area of the two lobes (LPy 11a) is caused by the unilateral exposure of the CO2 laser when the LPFG was inscribed. The degree of polarization and beam quality of LPy 11a could be further optimized by adjusting the polarization state of fundamental mode before PLMA-LPFG and tailoring the inscription direction of PM fiber precisely.
After the beam is separated by PLMA-OC, the nether fiber passes through the fiber stretcher, which can be adjusted slightly to change the phase difference between the two LPy 11a. Our fiber stretcher consists of two cylinders for fixing the optical fiber and a micrometer function as the TDL [37,43]. In the PLMA-PBS in Fig. 3, when the beam enters port1 and exits in port3, the polarization direction keeps unchanged in parallel with the fast axis. When the beam from port2 to port3, the polarization direction changes from the fast axis into the slow axis. As a result, the mode field distribution and the polarization direction of the beam at port 2 will rotate 90 degrees at the same time equivalent to the process: LPy 11a→LPx 11b. The PLMA-PBS obtain the targeted LP11 modes. Finally, under the circumstance of satisfying Eq. (3), mode of TE01 is generated stably. Then the laser pass through FBG3 which filters out latent LP01 to ensure the high mode purity output of the TE01 laser. The CVBs laser is monitored by a CCD camera again after an optical attenuator. The doughnut-shaped beam is checked by a linear polarizer to examine the polarization property as shown in Fig. 5. Due to the laser beam is collimated, the divergence angle of the far field is small. And the intensity distribution of CVBs will almost keep the same over several meters, which is validated by the measurement of the intensity distribution at several different position along its propagation. With the rapid growth of interest in researching vector beams (CVBs), several methods were demonstrated for mode component analysis and mode purity calculation. Such as fiber bending loss method [26], space light modulator [44], polarization purity analysis [16,17], one-dimensional intensity distribution detection method [33,38], machine learning [45]. We use the third and fourth method by collecting field intensity data from the CCD. In Fig. 6(a), the green line refers to the one-dimensional intensity distribution curve of TE01 in the vertical direction; the red line refers to the intensity distribution of LP01 mode by Gaussian-fitting. By calculating the area enclosed by the above-mentioned two curves, the power ratio of LP01 to TE01 mode approximately is 13:1, corresponding to mode distribution proportion of 92.3%. To be more accurate, three more one-dimensional light intensity distribution along the white dashed line are analyzed. The measurement and calculation results across the whole beam cross section reveal the average mode purity is about 91.2%. Accroding to the light intensity pattern collected by CCD and based on the method proposed in [17], we also analyzed the polarization purity of the CVBs. As depicted in Fig. 6(b), we use a aperture diaphragm to capture the local light field at eight different points in the doughnut-shaped beam, and then their degree of polarization (DOP) are measured through a linear polarizer. DOP is calculated by the equation: DOP = (Pazimuthal - Pradial) / (Pazimuthal + Pradial), Pazimuthal and Pradial refer to the optical power measured when the polarizing direction (orientation of transmission axis) of the linear polarizer is along the azimuthal and radial direction of the CVBs respectively. As a result, the polarization purity of the CVBs is about 92.24% in average. The variance, and standard deviation of DOP are 0.15% and 3.88% respectively. The purity of the output mode of vector beam will be further improved with the development of fiber grating manufacturing technology based on large mode area PM fiber [46,47].
Fig. 5. (a) The mode field distribution of TE01 CVB laser (b)-(e) after passing through a linear polarizer with four transmission axis orientations. (The white arrow refers to the direction of linear polarizer)
Fig. 6. (a) Mode purity analysis of TE01 mode. Inset: data sampling along the white dashed line. (b) Polarization purity analysis of TE01 mode. Inset: local light field are collected by a aperture diaphragm in the location of different white points respectively.
Finally, to test the stability of CVBs, the spectral characteristics of high-power CVBs lasers are measured at 10W interval of increment. In Fig. 7, when the pump power increased from 10W to 50W, the central wavelength stabilized around 1063.9 nm, and the 3 dB bandwidth spectrum (FWHM) gradually increased from 0.064 nm to 0.23 nm. The laser stability is observed when the pump power is 50W, as shown in Fig. 8. The spectrum shapes are almost the same, quantitatively; the fluctuations of center wavelength and FWHM are 0.23 nm and 0.26 nm respectively. The all-PM fiber architecture is insensitive to mechanical or thermal perturbations and the laser yields 3.1W of output power at 1063.6 nm for more than 4 hours continuously and stably. The compact high power CVBs can emit TE01 mode beam without any adjustment of spatial light path. Low transmission loss optical fiber component integrated in the laser cavity will be helpful for the enhancement of slope efficiency and output power. The mode profile and spectrum verify the all-PM fiber laser is a good technical route for high power CVBs laser.
Fig. 7. (a) Spectrum change with the pump power from 10 W to 50 W (b) Center wavelength and FWHM characteristic with pump power increased.
Fig. 8. (a) Spectrum characteristic during 80 min (b) Center wavelength and FWHM in max pump power of 50 W
5. Conclusion
Through theoretical analysis and experiments, we proposed and demonstrated an all-PM high-power CVBs fiber laser. By inscription FBG and LPFG on PLMA15-130, the high-power HOM is obtained from the oscillator, then after appropriate adjustment of fiber stretcher for mode superposition, stable high-power TE01 is achieved. FBGs play a role in constituting oscillator cavity and mode selection, which optimize the output efficiency and mode purity of LPy 11a. The method of mode superposition based on all-PM fiber is also suitable for the generation of other vector beams, we can also obtain high-power TM01 or orbital angular momentum beam with different PLMA-LPFG. It is believed that all-PM high-power CVBs fiber lasers will provide a new way for the power scaling of CVBs. Our laser can be applied to various scene in materials processing, laser cleaning and optical communication system.
Funding
Open Project of Advanced Laser Tenchnology Laboratory of Anhui Province (AHL2021ZR02); National Key Research and Development Program of China (2021YFF0307804).
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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