Selective transverse mode operation of a fiber laser based on few-mode FBG for rotation sensing

Xiao Liang; Xiao Liang; Yang Li; Yang Li; Zhaoxin Geng; Zhingming Liu

doi:10.1364/OE.27.037964

1. Introduction

Fiber lasers with selective transverse mode operation are of great interest with the development of mode-division multiplying (MDM) techniques to increase transmission capacity limit set by standard SMF in the modern communication system [1–3]. Few-mode components, such as few-mode fiber and few-mode FBG, have drawn considerable attention due to their inherently distinctive characteristics of high-order modes [4–13]. Conventional single-mode fiber lasers operate in the fundamental transverse mode for achieving near-diffraction-limit beam quality [14]. The mode-selective fiber lasers exploit the spatial degree of freedom in fibers [15–19]. The few-mode components are the key of a mode selective fiber laser, which tunes the gain and loss to discriminate modes for selective transverse mode operation. The few-mode FBG was introduced into the switchable transverse mode fiber laser, and three wavelengths could be switched freely by adjusting the polarization controller (PC) to tune the loss of resonance peaks [10]. In their previous work, a Mach-Zehnder interferometer (MZI) filter constructed from the few-mode fiber was used to achieve wavelength-switchable fiber laser [11]. A dual-transverse-mode microsquare laser with a tunable wavelength interval using a square-ring-patterned contact window was designed and demonstrated by H. Long et al. [7]. The microsquare resonator with a vertex output waveguide and a square-ring injection window is used to realize a tunable transverse mode wavelength interval. In [8], a pair of few-mode FBGs as an efficient transverse mode selector was employed, and lasing in a specific transverse mode is enabled. J. M. O. Daniel et al. proposed a technique for the electronically-controllable generation and switching of transverse modes within a multi-mode fiber laser oscillator [20]. The switching between LP₀₁ and LP₁₁ modes is up to 20 kHz. J. Dong et al. demonstrated a passively mode-locked fiber laser incorporating a two-mode FBG for transverse-mode selection [21]. The proposed laser can provide a continuous-wave output at the LP₀₁ mode, the LP₁₁ mode, or their mix.

In this paper, a fiber laser with selective transverse mode operation based on few-mode FBG was demonstrated. The few-mode FBG is fabricated from the EMCF, which is particularly designed supporting only two mode groups [22,23]. The LP₁₁^odd modes in the fast axis of the EMCF are cutoff in the 1550 nm wavelength region. The spectrum of the few-mode FBG has two distinct resonance peaks corresponding to the LP₀₁ mode self-coupling and LP₀₁ and LP₁₁^even cross-coupling. The intensity of the resonance could be tuned by the offset between the incident SMF and few-mode FBG. The detailed characterization of the EMCF and few-mode FBG were firstly analyzed. The mode selective laser was configured and experimentally demonstrated, and the stability of the proposed mode selective laser was also discussed in the following. Besides, a temperature-insensitive rotation sensing system employing the mode selective laser and EMCF was preliminarily demonstrated in section 3. The working principle of the proposed rotation sensing system was presented, which is quite similar to a polarized beam passing through a polarizer. And experimental results were discussed.

2. Few-mode fiber laser

2.1 Few-mode FBG

The EMCF was particularly designed to support only two mode groups, which is characterized by the elliptical core areas. Such a design could discriminate against the high-order degenerate modes, leaving strict two modes in the target wavelength region. The EMCF is fabricated by the conventional modified chemical vapor deposition (MCVD) and solution-doping techniques. The micro-image of the cross-section is shown in Fig. 1(a), and the relative refractive index profiles in both fast and slow axes, measured by optical fiber analyzer (EXFO NR9200), are given in Fig. 1(b) with the reference index of 1.444. Besides, the geometry could be read from the measured index profiles in Fig. 1(b). The diameters each layer along the elliptical slow-axis are as follows: 4.628 µm, 9.056 µm, 15.848 µm, and 22.64 µm. To show which modes can be supported by the designed few-mode fiber, we used the finite element method (FEM) to calculate the dispersion curves of the guided modes. In calculations, the incident field is the fundamental mode from the communication SMF, and the two fibers are coaxial. The calculated results are given in Fig. 1(c). As depicted in Fig. 1(c) the LP₁₁^odd modes have the cutoff wavelength at about 1425 nm so that the EMCF could support only LP₀₁ and LP₁₁^even mode groups around 1550 nm. This is due to the fact that the circular symmetry of the fiber has been eliminated, the second-order modes LP₁₁^even and LP₁₁^odd have different cutoff properties, and LP₁₁^odd mode is suppressed by elliptical fast-axis [22]. The corresponding field distribution is shown in the insets of Fig. 1(b). Since the two mode groups also have polarization components due to the asymmetry, the dispersion curve in both x and y directions are given. It can be seen from the dispersion curves that the birefringence is less than 5×10⁻⁶, which corresponds to the ellipticity as small as 0.203. The excitation coefficients of the guided modes are also given in Fig. 1(d). The excitation coefficients were calculated from the overlap integral between the incident field and the guided mode fields [24]. It’s found that the excitation coefficients for the two mode groups are NOT equal in the coaxial excitation with incident Gaussian field, the ratio is 60:40.

Fig. 1. Schematics of (a) the micro-image of the cross-section; (b) index profile of the homemade EMCF, the insets show the mode groups supported by the EMCF; (c) the dispersion curves of the supported modes; and (d) excitation coefficients for different modes.

Download Full Size | PDF

The light coupling takes place between counterpropagating core modes when a normal FBG is inscribed in a few-mode fiber. The slowly varying amplitude and of the jth mode traveling in the + z and –z directions evolve according to the coupled-mode equations [25]:

(1)$$\left\{ {\begin{array}{l} {\frac{{d{A_j}}}{{dz}} = i\sum\limits_k {{A_k}({K_{kj}^t + K_{kj}^z} ){{\exp }^{i({{\beta_k} - {\beta_j}} )z}}} }\\ \qquad+ i\sum\limits_k {{B_k}({K_{kj}^t - K_{kj}^z} ){{\exp }^{ - i({{\beta_k} + {\beta_j}} )z}}} \\ {\frac{{d{B_j}}}{{dz}} ={-} i\sum\limits_k {{A_k}({K_{kj}^t - K_{kj}^z} ){{\exp }^{i({{\beta_k} + {\beta_j}} )z}}} }\\ \qquad- i\sum\limits_k {{B_k}({K_{kj}^t + K_{kj}^z} ){{\exp }^{ - i({{\beta_k} - {\beta_j}} )z}}} \end{array}} \right.$$

The Bragg reflection resonances are determined by the following phase match condition [25]:

(2)$$\beta _k^ +{+} \beta _j^ -{=} \frac{{2\pi }}{\Lambda }$$

(3)$${\lambda _{k \to j}} = ({n_{eff, k}^ +{+} n_{eff, j}^ - } )\Lambda $$

where $\beta _k^ + $, $\beta _k^{-}$ and $\Lambda $ are the kth forward-propagating, jth backward-propagating, and the grating period, respectively. The spectra could be characterized by solving the coupled-mode equations with the initial conditions [25]. For FBG inscribed in SMF, it involves only the fundamental modes propagating in opposite directions. While for the FBG inscribed in the EMCF, we should consider the self-coupling in the two modes and the cross-coupling between LP₀₁ and LP₁₁^even [26–30], due to the asymmetric index profile in grating over the fiber core by the UV laser side illumination. In that case, the coupled-mode equation could be simplified as:

(4)$$\left\{ {\begin{array}{l} \frac{{d{A_1}}}{{dz}} = i{A_1}K_{11}^t + i{A_2}K_{21}^t{\exp^{i({{\beta_2} - {\beta_1}} )z}}\\ \quad+ i{B_1}K_{11}^t{\exp^{ - i2{\beta_1}z}} + i{B_2}K_{21}^t{\exp^{ - i({{\beta_2} + {\beta_1}} )z}}\\ \frac{{d{B_1}}}{{dz}} ={-} i{A_1}K_{11}^t{\exp^{i2{\beta_1}z}} - i{A_2}K_{21}^t{\exp^{i({{\beta_2} + {\beta_1}} )z}}\\ \quad- i{B_1}K_{11}^t - i{B_2}K_{21}^t{\exp^{ - i({{\beta_2} - {\beta_1}} )z}}\\ \frac{{d{A_2}}}{{dz}} = i{A_1}K_{12}^t{\exp^{i({{\beta_1} - {\beta_2}} )z}} + i{A_2}K_{21}^t\\ \quad+ i{B_1}K_{12}^t{\exp^{ - i({{\beta_1} + {\beta_2}} )z}} + i{B_2}K_{22}^t{\exp^{ - i2{\beta_2}z}}\\ \frac{{d{B_2}}}{{dz}} ={-} i{A_1}K_{11}^t{\exp^{i({{\beta_2} + {\beta_1}} )z}} - i{A_2}K_{22}^t{\exp^{i2{\beta_2}z}}\\ \quad- i{B_1}K_{12}^t{\exp^{ - i({{\beta_1} - {\beta_2}} )z}} - i{B_2}K_{22}^t \end{array}} \right.$$

The subscripts 1 and 2 correspond to LP₀₁ and LP₁₁^even mode, and $K_{kj}^t(k, j = 1, 2)$ is the transverse coupling coefficient between kth and jth modes. The initial condition is usually given by ${B_1}(0 )= {B_2}(0 )= 0,$ and the ratio between ${A_1}(0 )$ and ${A_2}(0 )$ is related to the excitation coefficients, which could be acquired from the power coupling coefficient determined by the overlap integral between the incident filed and guided modes [4,24].

The calculated transmission spectra of the dual-mode FBG with different mode power ratio by solving the Eq. (4) with conventional transfer matrix method are shown in Fig. 2(a). The refractive indices for LP₀₁ and LP₁₁^even are 1.44490 and 1.44435 in 1550 nm, respectively. The uniform grating length and period are 3 cm and 537.5 nm. We get two pronounced peaks on the transmission spectra locating at 1553.04 nm and 1553.45 nm, which agrees with the calculated value from Eq. (3). In experiments, we applied the conventional phase-mask combined with UV exposure technique and hydrogen-loaded EMCF to fabricate the few-mode FBG. The grating period is 537.5 nm, and the grating length is determined by the uniform phase-mask. The measured transmission and reflection spectra are shown in Fig. 2(b). As we can see on the transmission spectrum, three dips correspond to the LP₀₁ self-coupling, cross-coupling of two mode groups, and LP₁₁^even self-coupling. It is demonstrated experimentally that the EMCF can support only two modes, LP₀₁ and LP₁₁^even. The resonant wavelength for LP₀₁ self-coupling is 1553.14 nm in Fig. 2(b), while the calculated value from Eq. (3) is 1553.04 nm. And the resonant wavelength for cross-coupling is 1553.57 nm, while the calculated value is 1553.45 nm. There is somewhat different between the simulation and experiment, which is caused by calculation and measurement errors. The refractive indices are theoretically calculated by FEM. The pronounced peaks in simulation, which is calculated by them, is provided with calculation errors. And, the fabrication and measurement of this few-mode FBG would lead to error propagation, which causes that the experiment results would be not error-free. Therefore, the existence of errors would be reasonable.

Fig. 2. (a) Calculated reflectance spectra under different mode power ratio, the inset is the schematic diagram of the few-mode FBG resonance; (b) transmission and reflection spectra of the few-mode FBG inscribed in the EMCF.

Download Full Size | PDF

2.2 Mode-selective fiber laser

The transverse mode selection could be realized by adjusting the power ratio between the two guided modes [4]. That is to say, we can tune the excitation coefficients of the two guided modes, and then utilizing the mode competition to achieve mode selection. The offset coupling was introduced to adjust the excitation coefficients and the schematic diagram is shown in Fig. 3(a). Since the LP₁₁^odd components are cutoff around 1550 nm, we only show the relationship between excitation coefficients and offset in the x-direction (slow axis). Suppose the incident beam is a Gaussian beam, the excitation coefficient could be expressed as:

(5)$$\eta _v^{offstet} = \frac{1}{\omega }\sqrt {\frac{2}{\pi }} \frac{{\int\!\!\!\int_s {\exp ( - \frac{{{{(x + \Delta x)}^2} + {y^2}}}{{{\omega ^2}}}){\psi _v}(x, y)dxdy} }}{{\int\!\!\!\int_s {{\psi _v}(x, y)\psi _v^\ast (x, y)dxdy} }}$$

where $\omega $ denotes the Gaussian beam waist, ${\psi _v}({x, y} )$ represents the field distribution of the guided modes. The calculated results are presented in Fig. 3(b). The zero offset corresponds to the coaxial case, and the excitation coefficients are equal to 0.2 when the offset is 3.52 µm. In that case, the transmission peaks of the few-mode FBG have equal intensity. Further increasing the offset, the LP₁₁^even mode has a higher excitation coefficient, then the transmission peak of the cross-coupling has a higher intensity and endure lower loss in the lasing process. While the offset is smaller than 3.52 µm, the LP₀₁ mode has a higher excitation coefficient and the wavelength switches to the self-coupling peak in lasing. The experiments of the few-mode FBG at different offsets are presented, and the corresponding spectra are shown in Fig. 4.

Fig. 3. (a) Schematic of the offset between the SMF and few-mode FBG;(b) relationship between the offset and excitation coefficients of transverse modes.

Download Full Size | PDF

Fig. 4. Spectra of few-mode FBG at different offsets (a) 0 µm; (b) 3.5 µm; (c) 7 µm.

Download Full Size | PDF

In experiments, a fiber laser with selective mode operation is configurated, as shown in Fig. 5(a). The laser consists of 7 m long EDF as the gain medium, 980 nm pump laser, 980/1550 wavelength division multiplexing (WDM), reflector with 99.5% reflectivity, and the few-mode FBG as the wavelength selector. The SMF and the few-mode FBG are axially aligned and the two facets are parallelly close to each other using a commercial fusion splicer (FSM-100P+, FujikuraTM) with 0.1 µm step. There is no splicing between the SMF and this few-mode FBG, which would easily adjust the excitation coefficients of transverse modes. The output of the laser is measured by an optical spectrum analyzer (OSA, AQ6375) with 0.05 nm resolution. The output power and the laser spot were measured by the power meter and CCD camera, respectively. As discussed above, the zero offset makes the excitation coefficient of LP₀₁ higher than that of LP₁₁^even. In that case, the loss of the resonance peak corresponding to LP₀₁ self-coupling is smaller then the wavelength of 1553.57 nm lases, as shown in Fig. 5(c). The side mode suppression ratio (SMSR) is as high as 41 dB, and the laser spot confirms the LP₀₁ mode operation. In the following, the offset was set to 7 µm, the excitation coefficient of LP₀₁ and LP₁₁^even are about 0.16 and 0.25, respectively. The lasing wavelength switched to the cross-coupling peak, which corresponds to 1553.14 nm, as given in Fig. 5(c). The SMSR is as high as 49 dB, and the laser spot presents LP₀₁ and LP₁₁^even hybrid mode operation. It should be mentioned that the pump laser is at full power of 100 mW in both cases. The input-output dependence curves of the two wavelengths are shown in Fig. 5(d). The linear fittings demonstrate a good linearity of the output curves. The slope efficiency of LP₀₁ mode and hybrid mode operation are 20.8% and 14.5%, respectively.

Fig. 5. (a) Laser setup; (b) LP₀₁ laser operation; (c) LP₀₁ and LP₁₁^even laser operation; (d) the input-output characteristic curves in different working regions.

Download Full Size | PDF

To evaluate the stability of the proposed mode selective laser, we continuously monitored the output spectra and corresponding power in two different regions for 50 minutes. The results are summarized in Fig. 6. The spectra in Figs. 6(a) and 6(b) are recorded every 5 minutes during the 50 minutes long operation. The fluctuation of the central wavelength and intensity are summarized in Figs. 6(c) and 6(d). In LP₀₁ mode operation, the central wavelength variation is smaller than 0.006 nm and the intensity variation is within 0.411 dBm. While for the hybrid mode operation, the central wavelength variation is smaller than 0.008 nm and the intensity variation is within 1.5 dBm. These results reveal that the proposed mode selective laser has a good performance on stability.

Fig. 6. Stabilization of laser (a) LP₀₁ laser operation, (b) LP₀₁ and LP₁₁^even laser operation; central wavelength and intensity variation of (c) LP₀₁ laser operation, (d) LP₀₁ and LP₁₁^even laser operation.

Download Full Size | PDF

3. Few-mode laser for rotation sensing

The mode selective laser has an asymmetric output spot, and the EMCF also has asymmetric elliptical core area. The LP₁₁^odd modes are successfully suppressed around 1550 nm due to such a fiber design. The cross-coupling laser spot is circular and axis asymmetric. Therefore, it is possible to implement the mode selective laser and EMCF in rotation sensing instead of the intensity-modulated scheme [31]. The rotation sensing setup is schematically shown in Fig. 7, it consists of the mode selective laser, EMCF, rotation stage, and monitoring system. The EMCF was clamped by the high precision fiber rotator. And the spread beam was split and detected by the power meter and CCD camera. The laser spot was imaged by a micro-objective before detected by the CCD. In experiments, the output of the mode selective laser was axially aligned with the clamped EMCF. The power and laser spot were detected simultaneously as the high precision fiber rotator rotating the EMCF with a small angle.

Fig. 7. Rotation sensing system based on mode selective laser and EMCF.

Download Full Size | PDF

The mode selective laser works in the hybrid mode region. The offset between the SMF and the few-mode FBG is 7 µm. According to Figs. 2 and 3 we can conclude that the LP₁₁^even mode occupies most of the energy even though the output is hybrid mode operation. Besides, the LP₁₁^odd is suppressed in the 1550 nm wavelength region, so the EMCF will stop incident mode patterns that similar to LP₁₁^odd in the fast axis. That is to say, the excitation coefficient of LP₁₁^odd in EMCF is zero when the incident beam has the pattern of LP₁₁^odd in the fast axis. The principle diagram of the rotation sensing system is shown in Fig. 8(a). Rotating the EMCF is equivalent to rotating the few-mode FBG. In the 0° case, the incident beam patterns match the supported mode by the EMCF, and we get the maximal transmission. However, the 90°-rotated incident mode pattern is similar to LP₁₁^odd, which will be blocked by the EMCF. In that case, we get minimal transmission. Such transmission variation appears alternately as the rotation angle varying from 0° to 360°. The principle is quite similar to a polarized beam passing through a polarizer, as shown in Fig. 8(d). We used the hybrid mode as the incident beam and calculated the extinction ratio of the transmitted beam through EMCF with different rotating angles. The result is presented in Fig. 8(b). In the 180° case, the extinction ratio is 0.62 rather than 1.0. That is because of the asymmetric lob of LP₁₁^even. On the other hand, the axial symmetry of hybrid mode would be broken down as the laser spot shown in Fig. 5(c), and the lowest excitation coefficient would not ideally appear at 90° and 270°. In experiments, we detected the transmitted power when rotating the EMCF, and the curve is shown in Fig. 8(c). The calculated dips locate at 104° and 255.7°, while the measured values are 99.5° and 259.4°. Such discrimination may arise from the finite experiment measurements. It should be noted that the minimal detected power is almost zero does not mean the energy is all blocked by the EMCF at 90° and 270° cases. There is still a small amount of energy that couples to LP₀₁ mode and be detected by the power meter. It is just too small to be distinguished. For rotation sensing, we approximately found four linear regions, as indicated in Fig. 8(c). The sensitivity is 0.079 mW/°, 0.064 mW/°, 0.064 mW/° and 0.089 mW/°, therefore, the average sensitivity is 0.074 mW/° from experiments. A rotation sensing system based on mode selective laser and EMCF was preliminarily demonstrated.

Fig. 8. (a) The principle diagram of the rotation sensing system; (b) calculation results of the extinction ratio in EMCF with different rotating angles; (c) the experiment results of the transmitted power in EMCF with different rotating angle ; (d) the extinction ratio by a polarized beam passing through a polarizer with different angles.

Download Full Size | PDF

The variation of the measured angle as a function of the environmental temperature is experimentally examined. The few-mode FBG filter and the EMCF are located in a heating furnace, as indicated in Fig. 7(b). We chose 5 angles, 0°, 40°, 90°, 130°, and 180° to test the influence of temperature. As the temperature increasing from 10°C to 90°C, the variation of the measured angle is within ± 2°, as shown in Fig. 9. The test results indicate that the sensor head is temperature insensitive and could be used in a wide temperature range.

Fig. 9. The variation of the measured angle as a function of the environmental temperature.

Download Full Size | PDF

4. Summary

A mode selective fiber laser based on particularly designed few-mode FBG inscribed in EMCF was successfully demonstrated. The few-mode FBG has two distinct resonance peaks corresponding to LP₀₁ self-coupling and hybrid mode cross-coupling. The output mode is switchable by excitation coefficients adjustment of the two modes through offset incidence. The proposed mode selective laser shows good stability in 50 minutes operation, and the wavelength variation within 0.006 nm and 0.008 nm and intensity variation within 0.411 dBm and 1.5 dBm are demonstrated for two regions, respectively. The mode selective laser, together with the EMCF, could be used in rotation sensing, and sensitivity of 0.074 mW/° was preliminarily demonstrated. And the rotation sensing system is insensitive to temperature, and the measured angle is within ± 2° in the temperature range of 10-90°C.

Funding

National Natural Science Foundation of China (61905293, 61774175); Natural Science Foundation of Beijing Municipality (4181001); Leading Project of Youth Academic Team @ Minzu University of China (317201929); National Basic Research Program of China (973 Program) (2017YFB0405400).

Disclosures

The authors declare no conflicts of interest.

References

1. B. Nenad, Y. Yang, R. Yongxiong, T. Moshe, K. Poul, H. Hao, A. E. Willner, and R. Siddharth, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013). [CrossRef]

2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]

3. R. G. H. van Uden, C. M. Okonkwo, C. Haoshuo, D. W. Hugo, and A. M. J. Koonen, “Time domain multiplexed spatial division multiplexing receiver,” Opt. Express 22(10), 12668–12677 (2014). [CrossRef]

4. M. M. Ali, Y. Jung, K. S. Lim, M. R. Islam, S. U. Alam, D. J. Richardson, and H. Ahmad, “Characterization of Mode Coupling in Few-Mode FBG With Selective Mode Excitation,” IEEE Photonics Technol. Lett. 27(16), 1713–1716 (2015). [CrossRef]

5. L. Di and W and A. Clarkson, “Polarization-dependent transverse mode selection in an Yb-doped fiber laser,” Opt. Lett. 40(4), 498–501 (2015). [CrossRef]

6. Z. Hong, S. Fu, D. Yu, T. Ming, and D. Liu, “All-fiber tunable LP11 mode rotator with 360° range,” IEEE Photonics J. 8(5), 1–7 (2016). [CrossRef]

7. L. Heng, H. Yong-Zhen, M. Xiu-Wen, Y. Yue-De, X. Jin-Long, Z. Ling-Xiu, and L. Bo-Wen, “Dual-transverse-mode microsquare lasers with tunable wavelength interval,” Opt. Lett. 40(15), 3548–3551 (2015). [CrossRef]

8. T. Liu, S. P. Chen, and J. Hou, “Selective transverse mode operation of an all-fiber laser with a mode-selective fiber Bragg grating pair,” Opt. Lett. 41(24), 5692–5695 (2016). [CrossRef]

9. Q. Mo, Z. Hong, D. Yu, S. Fu, L. Wang, K. Oh, M. Tang, and D. Liu, “All-fiber spatial rotation manipulation for radially asymmetric modes,” Sci. Rep. 7(1), 2539 (2017). [CrossRef]

10. Y. Qi, S. Jiang, Z. Kang, M. Lin, W. Jin, and S. Jian, “Low-threshold wavelength-switchable fiber laser based on few-mode fiber Bragg grating,” Opt. Fiber Technol. 29, 70–73 (2016). [CrossRef]

11. Y. Qi, Z. Kang, S. Jiang, M. Lin, W. Jin, Y. Lian, and S. Jian, “Wavelength-switchable fiber laser based on few-mode fiber filter with core-offset structure,” Opt. Laser Technol. 81, 26–32 (2016). [CrossRef]

12. G. Yin, C. Wang, Y. Zhao, B. Jiang, T. Zhu, Y. Wang, and L. Zhang, “Multi-channel mode converter based on a modal interferometer in a two-mode fiber,” Opt. Lett. 42(19), 3757–3760 (2017). [CrossRef]

13. A. Li, Y. Wang, Q. Hu, and W. Shieh, “Few-mode fiber based optical sensors,” Opt. Express 23(2), 1139–1150 (2015). [CrossRef]

14. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23(21), 1683–1685 (1998). [CrossRef]

15. D. S. Moon, U. C. Paek, Y. Chung, X. Dong, and P. Shum, “Multi-wavelength linear-cavity tunable fiber laser using a chirped fiber Bragg grating and a few-mode fiber Bragg grating,” Opt. Express 13(15), 5614–5620 (2005). [CrossRef]

16. D. S. Moon, B. L. Sang, Y. G. Han, and Y. Chung, “Investigation of a multiwavelength Raman fiber laser based on few-mode fiber Bragg gratings,” Opt. Lett. 30(17), 2200–2202 (2005). [CrossRef]

17. G. Sun, Y. Zhou, L. Cui, and Y. Chung, “Polarization controlled multiwavelength switchable erbium-doped fiber laser based on high birefringence few-mode fiber loop mirror,” Laser Phys. 21(11), 1914–1918 (2011). [CrossRef]

18. T. Wang, F. Shi, Y. Huang, J. Wen, Z. Luo, F. Pang, and X. Zeng, “High-order mode direct oscillation of few-mode fiber laser for high-quality cylindrical vector beams,” Opt. Express 26(9), 11850–11858 (2018). [CrossRef]

19. D. Yang, P. Jiang, Y. Wang, W. Bo, and Y. Shen, “Dual-wavelength high-power Yb-doped double-clad fiber laser based on a few-mode fiber Bragg grating,” Opt. Laser Technol. 42(4), 575–579 (2010). [CrossRef]

20. J. M. Daniel and W. A. Clarkson, “Rapid, electronically controllable transverse mode selection in a multimode fiber laser,” Opt. Express 21(24), 29442–29448 (2013). [CrossRef]

21. J. Dong and K. S. Chiang, “Mode-Locked Fiber Laser With Transverse-Mode Selection Based on a Two-Mode FBG,” IEEE Photonics Technol. Lett. 26(17), 1766–1769 (2014). [CrossRef]

22. L. Xiao, S. Liu, L. Yang, Z. Liu, and S. Jian, “Characteristics of a high extinction ratio comb-filter based on LP 01 –LP 11 even mode elliptical multilayer-core fibers,” Opt. Fiber Technol. 21, 103–109 (2015). [CrossRef]

23. L. Xiao, L. Yang, Y. Bai, B. Yin, Z. Liu, and S. Jian, “Stable dual-wavelength laser combined with gain flattening ML-FMF Bragg grating filter,” Opt. Commun. 358, 1–5 (2016). [CrossRef]

24. W. S. Mohammed, A. Mehta, and E. G. Johnson, “Wavelength Tunable Fiber Lens Based on Multimode Interference,” J. Lightwave Technol. 22(2), 469–477 (2004). [CrossRef]

25. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

26. C. Lu and Y. Cui, “Fiber Bragg grating spectra in multimode optical fibers,” J. Lightwave Technol. 24(1), 598–604 (2006). [CrossRef]

27. R. Gao, J. Ye, and X. Xin, “Directional acoustic signal measurement based on the asymmetrical temperature distribution of the parallel microfiber array,” Opt. Express 27(23), 34113–34125 (2019). [CrossRef]

28. R. Gao and D. Lu, “Temperature compensated fiber optic anemometer based on graphene-coated elliptical core micro-fiber Bragg grating,” Opt. Express 27(23), 34011–34021 (2019). [CrossRef]

29. R. Gao, M. Zhang, and Z.-m. Qi, “Miniature all-fibre microflown directional acoustic sensor based on crossed self-heated micro-Co2+-doped optical fibre Bragg gratings,” Appl. Phys. Lett. 113(13), 134102 (2018). [CrossRef]

30. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014). [CrossRef]

31. Q. Fu, J. Zhang, C. Liang, I. P. Ikechukwu, G. Yin, L. Lu, Y. Shao, L. Liu, D. Liu, and T. Zhu, “Intensity-modulated directional torsion sensor based on in-line optical fiber Mach-Zehnder interferometer,” Opt. Lett. 43(10), 2414–2417 (2018). [CrossRef]

Selective transverse mode operation of a fiber laser based on few-mode FBG for rotation sensing

Abstract

1. Introduction

2. Few-mode fiber laser

2.1 Few-mode FBG

2.2 Mode-selective fiber laser

3. Few-mode laser for rotation sensing

4. Summary

Funding

Disclosures

References

Cited By

Figures (9)

Equations (5)

Optics Express