Controlled generation of mode-switchable nanosecond pulsed vector vortex beams from a Q-switched fiber laser

Youyou Hu; Youyou Hu; Youyou Hu; Youyou Hu; Zhiyuan Ma; Zhiyuan Ma; Weiqian Zhao; Jiang Zhao; Jun Liu; Qingli Jing; Jiantai Dou; Bo Li

doi:10.1364/OE.469245

1. Introduction

In recent years, it can be seen vector vortex beams [1–5] have received increasing interest due to their unique polarization or phase distribution. The complex polarization states and angular momentums of VVBs can be described by the high-order Poincaré sphere (HOPS), so VVBs are also called HOPS beams, including cylindrical vector beam and vortex beam, which are located at the equator and the poles of the HOPS, respectively [6]. Wherein CVB possesses axis-symmetric distribution of polarization, and there is a polarization singularity in the beam center. So, the CVB presents a hollow light intensity distribution. In addition, the CVBs with radial polarization component can be tightly focused by a high numerical aperture (NA) focusing lens to generate subwavelength longitudinal electric fields and break through the diffraction limit of traditional beams. Therefore, CVBs are widely applied in super-resolution optical microscopy [7], super resolution imaging [8], laser micro processing [9], optical tweezers [10], optical needles [11], etc. While the vortex beam contains phase singularity in the beam center duo to the helical phase wavefront of exp(ilθ), where l is topological charges (TCs) and each photon possesses an orbital angular momentum (OAM) of lћ. The vortex beams with different TCs are mutually orthogonal, which makes them have enormous application potential in optical communication [12] and quantum entanglement [13]. The beams between the equator and the poles are the elliptically polarized cylindrical vector beams and their additional degrees of freedom allow one to control the polarization, to manipulating optical forces and torques on a dielectric Rayleigh particle [14]. Besides, the EPCVBs have been confirmed to be of great significance for the visualization of quantum emitters near the interface [15].

Although there are many applications of VVBs at present, it is undeniable that increasing the order of VVB is an important factor to improve application performance [16]. For example, high-order VVBs have a significant effect on improving the precision and sensitivity of optical microscopy measurements [17] and in remote sensing [18]. Moreover, the entanglement of very high OAM can increase the sensitivity of angular resolution [19].

So far, various methods have been proposed to generate controllable higher-order VVBs. In general, these methods can be classified into passive method and active method. Among them, the passive method refers to modulate the phase, amplitude, polarization and other characteristics of scalar Gaussian beam by using light field manipulation elements outside the laser cavity to generate high-order VVBs, including Q-plates [20–23], metasurface [24–26], polarization-selective Gouy phase shifter [27], spatial light modulator (SLM) [28], and vortex retarder [29]. Conversely, the active method means to generate VVBs directly in the laser cavity. Commonly, it uses some special optical elements insert the laser cavity to generate the VVBs such as crystal birefringence [30–32], and Brewster angle characteristics [33], or the special cavity configuration design [34]. But in these methods, they cannot generate other VVBs except radially polarized beam or azimuthally polarized beam. To generate more different modes of VVBs in the laser cavity, mode selective couplers (MSC) [35], long-period fiber grating (LPFG) [36] and Q-plate [1,2,37] have been inserted into the cavity. Among them, the fabrication process of Q-plate is more mature than that of MSC and LPFG. And the Q-plate can cooperate with other polarizing elements to control Pancharatnam-Berry phase [38] in the cavity, thereby generating VVBs of various modes easily. In addition, integrated on-chip lasers [39,40] have been shown to generate a fraction of the modes of VVBs. Compared with passive methods, active methods have the advantages of compact, efficient, and high quality [41]. However, due to the low flexibility [42], they have not been widely used to generate VVBs of different orders. To the best of our knowledge, there is no report that a laser can generate mode-switchable VVBs on the arbitrary position of the HOPS between two different orders in the cavity.

In this letter, we demonstrated a ring Q-switched Yb-doped fiber laser that can generate mode-switchable nanosecond pulsed VVBs between two different orders. In the spatial optical path of the fiber laser, several cascaded Q-plates, divided into two Q-plate groups, are applied for intracavity mode conversion between LP₀₁ mode and vector vortex beams. In one Q-plate group, two quarter wave plates are inserted into two cascaded Q-plates to achieve the addition and subtraction of the order of Q-plates. By tuning the polarization state in the cavity, mode-switchable vector vortex beams, including CVBs, EPCVBs and vortex beams, of two different orders can be generated on demand. As far as we know, this is the first time to realize the direct generation of mode-switchable VVBs on the arbitrary position of the HOPS between two different orders from a fiber laser.

2. Theory

Q-plates, also called vortex wave plate (VWP) [43], are a kind of polarized optics devices and made of birefringent liquid crystal polymers, which are commonly used to control the amplitude, phase or polarization of light, especially for the generation of VVBs.

To explain the working principle of Q-plate, Jones matrix and Jones vector are used to describe the effect of polarization device on the polarized state of light, respectively. According to Jones vector theory, the Jones matrix of Q-plate can be represented by [21,29],

(1)$$J_{\mathrm{m,\ \delta }}^ -{=} \left( {\begin{array}{{cc}} {\cos 2\alpha (\phi )}&{\sin 2\alpha (\phi )}\\ {\sin 2\alpha (\phi )}&{ - \cos 2\alpha (\phi )} \end{array}} \right),$$

or

(2)$$J_{\mathrm{m,\ \delta }}^ +{=} \left( {\begin{array}{{cc}} {\cos 2\alpha (\phi )}&{ - \sin 2\alpha (\phi )}\\ {\sin 2\alpha (\phi )}&{\cos 2\alpha (\phi )} \end{array}} \right),$$

where α(ϕ) is direction angle of the fast-axis, and can be characterized by,

(3)$$\alpha (\phi )= \frac{m}{2}\phi + \delta .$$

Where m is the order of Q-plate, ϕ is the angle between the fast-axis of local positions and ${0^ \circ }$ fast-axis, δ is a parameter related to the order of Q-plate and can be written as,

(4)$$\delta = \frac{{\sigma (m - 2)}}{2},$$

and σ is the angle between the ${0^ \circ }$ fast-axis and the x-axis. For convenience, in the following calculations, assume that σ is equal to 0. Equation (1) and Eq. (2) can be converted by a half-wave plate (HWP), of which the fast-axis direction is horizontal.

Here, the conversion of light in two Q-plates can be analyzed with the example of arbitrary linearly polarized beam passing through two identical Q-plates. When the beam passes through the Q-plate, it can be expressed by,

(5)$$J_1^ -{=} \left( {\begin{array}{{cc}} {\cos 2\alpha (\phi )}&{\sin 2\alpha (\phi )}\\ {\sin 2\alpha (\phi )}&{ - \cos 2\alpha (\phi )} \end{array}} \right)\left[ {\begin{array}{{c}} {\cos \theta }\\ {\sin \theta } \end{array}} \right] = \left[ {\begin{array}{{c}} {\cos [2(\frac{m}{2}\phi + \delta ) - \theta ]}\\ {\sin [2(\frac{m}{2}\phi + \delta ) - \theta ]} \end{array}} \right],$$

where θ is the direction angle of linearly polarized beam. It can be seen from Eq. (5) that the output beam has vector polarization characteristics. After passing through another Q-plate, it can be expressed by the following formula,

(6)$$J_2^ -{=} J_{\mathrm{m,\ \delta }}^ -{\cdot} J_1^ -{=} \left[ {\begin{array}{{c}} {\cos \theta }\\ {\sin \theta } \end{array}} \right].$$

It can be seen from Eq. (6) that no matter what the order of the Q-plate is, after passing through two cascaded identical Q-plates, the beam is still linearly polarized with the same direction angle of polarization as the incident beam. The same method can also be used to analyze the situation when the incident beam is circularly or elliptically polarized.

When the expression of the Q-plate is ${J^ - }$, the Jones matrix after the combination of two identical Q-plates can be represented by the identity matrix,

(7)$$J_{\mathrm{m,\ \delta }}^ -{\cdot} J_{\mathrm{m,\ \delta }}^ -{=} \left[ {\begin{array}{{cc}} 1&0\\ 0&1 \end{array}} \right].$$

On the contrary, when the expression of the Q-plate is ${J^ + }$, the Jones matrix after the combination of two Q-plates of opposite order is also the identity matrix,

(8)$$J_{\mathrm{m,\ \delta }}^ +{\cdot} J_{\mathrm{\ -\ m,\ \delta }}^ +{=} \left[ {\begin{array}{{cc}} 1&0\\ 0&1 \end{array}} \right].$$

Besides, when the cascaded Q-plates have different orders, the Jones matrix can be expressed as,

(9)$$J_{{m_2}}^ - J_{{m_1}}^ -{=} \left[ {\begin{array}{{cc}} {\cos [{({{m_2} - {m_1}} )\phi } ]}&{ - \sin [{({{m_2} - {m_1}} )\phi } ]}\\ {\sin [{({{m_2} - {m_1}} )\phi } ]}&{\cos [{({{m_2} - {m_1}} )\phi } ]} \end{array}} \right] = J_{{m_2} - {m_1}}^ + .$$

It can be found that for the two cascaded Q-plates with different orders of m₁ and m₂, the total order is m₂-m₁. Combining Eq. (8) and Eq. (9), we can obtain,

(10)$$J_{{m_2}}^ - J_{{m_1}}^ -{\cdot} J_{{m_1}}^ - J_{{m_2}}^ -{=} J_{{m_2} - {m_1}}^ +{\cdot} J_{{m_1} - {m_2}}^ +{=} \left[ {\begin{array}{{cc}} 1&0\\ 0&1 \end{array}} \right].$$

Furthermore, Ref. [29] proves that when the expression of Q-plate is ${J^ - }$, the order of m₁+ m₂ can be achieved by inserting the HWP between two Q-plates. It can be expressed by,

(11)$$J_{{m_2}}^ - {H_x}J_{{m_1}}^ -{=} \left[ {\begin{array}{{cc}} {\cos [{({{m_2} + {m_1}} )\phi } ]}&{\sin [{({{m_2} + {m_1}} )\phi } ]}\\ {\sin [{({{m_2} + {m_1}} )\phi } ]}&{ - \cos [{({{m_2} + {m_1}} )\phi } ]} \end{array}} \right] = J_{{m_2} + {m_1}}^ -,$$

where H_x is the Jones matrix of the HWP with the fast-axis angle in the x-axis.

Likewise, by placing two quarter-wave plates (QWPs) between the two Q-plates, the addition and subtraction of the orders of two Q-plates can be flexibly controlled. It can be written as,

(12)$$\left\{ {\begin{array}{{cc}} {J_{{m_2} - {m_1}}^ +{=} J_{{m_2}}^ - {Q_x}{Q_y}J_{{m_1}}^ -{=} J_{{m_2}}^ - \left[ {\begin{array}{{cc}} 1&0\\ 0&i \end{array}} \right]\left[ {\begin{array}{{cc}} 1&0\\ 0&{ - i} \end{array}} \right]J_{{m_1}}^ -{=} J_{{m_2}}^ - J_{{m_1}}^ - }\\ {J_{{m_2} + {m_1}}^ -{=} J_{{m_2}}^ - {Q_x}{Q_x}J_{{m_1}}^ -{=} J_{{m_2}}^ - \left[ {\begin{array}{{cc}} 1&0\\ 0&i \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&i \end{array}} \right]J_{{m_1}}^ -{=} J_{{m_2}}^ - {H_x}J_{{m_1}}^ - } \end{array}}, \right.$$

where Q_x and Q_y are the Jones matrix of QWPs with the fast-axis angles in the x- and y-axes, respectively.

In summary, in the case that the beam divergence and phase shift are not considered, the mutual conversion between the VVBs and the LP₀₁ mode can be obtained by using two cascaded Q-plates groups. Further, in one Q-plates group, two QWPs are inserted between the Q-plates, and the addition or subtraction of the orders of Q-plates can be achieved. This provides a theoretical basis for designing fiber lasers for the intracavity generation of order-tunable VVBs.

3. Experimental setup

Firstly, according to the Eq. (7), a Q-switched ring fiber laser with cascaded Q-plates in the resonator is proposed, and its ability to generate nanosecond pulsed high-order VVBs is confirmed. The system structure is shown in Fig. 1. Here, the structure of the laser cavity is built up with fiber and free space part, and this structure is often used in all-normal-dispersion femtosecond fiber lasers [44].

Fig. 1. The system structure diagram of the fiber laser that generate nanosecond pulsed high-order VVBs. LD: laser diodes; Yb: ytterbium-doped gain fiber; WDM: wavelength division multiplexer; PC: polarization controller; Col1: 1030 nm collimator; Q-plate1 & Q-plate2: vortex retarder; BS: non-polarizing beam splitter cube; Cr⁴⁺: YAG: Q-Switched crystal; Col2: aspheric lenses; ISO: polarization-independent isolator. BQP: beam quality profiler.

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In the laser, the total cavity length is about 6.7 meters, of which the spatial optical path is 25.4cm. A 976nm laser diode (LD, DKPhotonics, LC97Z600-76) is applied to pump a 1-meter-long Yb-doped gain fiber (LIEKKI, Yb1200-4/125) through a 980/1030nm wavelength division multiplexer (WDM, DK photonics, WDM-980/1030).

A fiber polarization controller (THORLABS, CPC250) is used to adjust the polarization state in the cavity. It can be replaced with a linear polarizer and a quarter wave plate placed behind the Q-switched crystal without affecting the Q-switched operation. In order to meet the collimation of the space optical path, a 1030nm collimator (DK Photonics, MCCOL-1030) is used to collimate the beam to the free space with the working distance of 50cm, the working wavelength of 1030 ± 15nm, and the output beam size of 0.4mm. The Q-switched crystal (DHC, Φ7 × 1 × 1mm, Cr⁴⁺: YAG) is employed in the spatial optical path to adjust the Q factor in the cavity, thereby generating optical pulses.

Then, two Q-plates (LBTEK, VR3-1030) are inserted into the spatial optical path of the fiber laser to achieve highly efficient conversion of the transverse mode in the cavity. It is worth noting that in order to ensure that the beam does not diverge when incident on the second Q-plates, the distance between the Q-plates is set within the Rayleigh range of the expanded beam and in the above theoretical analysis, both zero-degree fast-axis angle of Q-plates are set to ${0^ \circ }$. So, in the experiment, it will also be set like this.

The output mirror adopts a non-polarizing beam splitter cube (THORLABS, BS017), which can output the beam while ensuring the polarization state in the cavity. Its transmission / reflection ratio of is 50:50. To minimize the influence of the nonpolarized beam splitter cube on the polarization of the transmitted/reflected beam and obtain the optimal mode output, the incident beam shall be perpendicular to the incident plane of the nonpolarized beam splitter cube with an error of no more than ${2^ \circ }$.

An aspherical mirror (THORLABS, C397TMD-C) is used to recouple the beam from the spatial optical path to the fiber path with an effective focal length of 11 mm and a working distance of 9.346 mm, with a coupling efficiency of approximately 72.41%. A polarization independent isolator (DK photonics, MCHI-1030) keeps ring light path unidirectional.

Secondly, according to Eq. (12), two pieces of Q-plates and four pieces of QWP were added to the spatial optical path based on the original scheme, and the ability of mode switchable between two different orders is confirmed. The system structure is given in Fig. 2.

Fig. 2. The spatial optical path structure diagram of the fiber laser that generate nanosecond pulsed and switchable order VV beam. Q-P1 & Q-P2: Q-plate of order 3; Q-P3 & Q-P4: Q-plate of order 1; BS: non-polarizing beamsplitter cube; QC: Q-Switched crystal; Col1: 1030 nm collimator; Col2: aspheric lenses. QWP1-4: quarter-wave plates.

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In Fig. 2, the two Q-plates with the order of 1 is inserted (LBTEK, VR1-1030) to the spatial optical path of the cavity. Then the fast-axis direction of QWP2 and QWP4 in the system is fixed on the x-axis, and the order of the output VVB can be controlled by rotating QWP1 and QWP3 at the same time. When the fast-axis of QWP1 and QWP3 is also on the x-axis, the addition of the order of Q-plate can be realized, and when the directions of QWP1 and QWP3 are on the y-axis, the subtraction of the order of Q-plates can be realized. Taking the combination of Q-plates of order 1 and 3 as an example, Fig. 2 shows the simulation diagram of the distribution of the transverse mode with two kinds QWP state in the spatial optical path of the cavity.

In the actual operation process, the light beam should first pass through the Q-plate with a smaller order. This is because when the order is too large, the beam diverges faster, which is not conducive to mode conversion. The distance between the cascaded Q-plates should be within the Rayleigh distance of the VVBs.

4. Results and discussion

The generated CVBs and vortex beams were captured by a beam quality profiler (THORLABS, BC106N-VIS/M) and the output polarization state is measured by a polarization analyzer (THORLABS, PAX1000IR1/M). As shown in Figs. 3(a1)-(d1), the output vortex beam spot shape with TCs of 3 and the 3rd order CVB are given. They are located on the poles and the equator of the 3rd Poincaré sphere (PS) respectively. The arrows marked in the figure are the polarization states of each point on the cross section of the spot. Using a polarization controller to adjust the polarization state in the cavity and observing it with a polarization analyzer, the switching between the two modes can be easily completed. Figures 3(a2),(b2) shows the beam characteristics of the output vortex beam with TCs of -3 and 3 after passing through the double-slit plate, which also proves that the output beam has a helical wavefront. Beam characteristics of the output third-order CVB after passing through a linear polarizer with an angle of ${0^ \circ }$ are given in Figs. 3(c2),(d2), and according to it, the polarization state distribution of the beam spot in Figs. 3(c1),(d1) can be drawn.

Fig. 3. Output vortex beam spot shape with TCs of (a1) −3 and (b1) 3; and the spot shape of (c1),(d1) the 3rd order CVB. The double slit interference pattern of the vortex beam with TCs of (a2) +3 and (b2) −3; and (c2),(d2) the output 3rd order CVB pass through a linear polarizer with polarizer angle of 0°. Where “m” represents the orders of the CVBs or EPCV beams, and “l” represents the TCs of the vortex beams.

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Multiple Q-plates are cascaded to output the spot shape, as shown in Fig. 4. Adjust the PC so that the polarization state of the beam incident on the first Q-plate is a linearly polarized beam in the y-axis direction, and ensure that the fast axes of QWP2 and QWP4 in Fig. 2 are in the x-axis direction, and the fast axes of QWP1 and QWP3 are in the y-axis direction. The spot shape of the output CVB of order m = 3-1 is shown in Fig. 4(a1). It located on the equator of the 2nd PS. When it passes through the linear polarizer in the x-axis direction, the beam spot shape is shown in Fig. 4(b1). Then adjust the QWP1 and QWP3 to ensure the fast-axes of theirs are in the x-axis. The spot shape of the output CVB of order m = 3 + 1 (located on the equator of the 4th PS) is shown in Fig. 4(c1) and it passes through the linear polarizer in the x-axis direction, the beam spot shape is shown in Fig. 4(b1).

Fig. 4. Multiple Q-plates cascaded output spot shape, high-order VV beam outputs with orders of (a1)-(a4) 3-1, (c1)-(c4) 3 + 1. The initial polarization state of incident light to cascaded Q-plates is (a1)-(d1) y-axis direction linear polarized beam; (a2)-(d2) left-circularly polarized beam; (a3)-(d3) x-axis direction linear polarized beam; (a4)-(d4) left-circularly polarized beam. (b1), (d1), (b3), (d3) CVB spot shapes after passing the linear polarizer with the fast-axis in the x-axis; (b2), (d2), (b4), (d4) the double-slit interference pattern of the output vortex beam. Where “l” represents the TCs of the vortex beams.

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The reflection from the non-polarizing beamsplitter cube will change the direction of the circularly polarized beam and the sign of the TCs. Therefore, when the polarization state of the beam incident on the first Q-plate is right-handed circularly polarized beam, a vortex beam with negative TCs will be obtained when the order of the Q-plates is subtracted, and a vortex beam with positive TCs will be obtained when the orders of the Q-plate is added. This result can be seen from the double slit interference pattern of Fig. 4(b2) and Fig. 4(d2). The beam spot shape is shown in Fig. 4(a2) and Fig. 4(c2). The same conclusion can be extended to the condition that the polarization state of the beam incident on the first Q-plate is right-circularly polarized beam. The results are shown in Figs. 4(a4)-(d4). Further, Figs. 4(a3)-(d3) shows the results when the incident beam is a linearly polarized beam in the x-axis direction.

The output EPCV beams are shown in the Fig. 5. Comparing Fig. 3 and Fig. 4, the spot shape after the beam passes through the linear polarizer, it can be found that the breakpoint of the spot after the EPCV beams passes through the linear polarizer is no longer obvious. This is because the principal axes of the elliptically polarized components in each direction in the EPCV beam contain components in the x- and y-directions with different weights. Besides, it can be found in the comparison of Fig. 4(b3) and Fig. 5(a2) that the main axis (long axis) of the elliptical polarization component of EPCV beam is still consistent with the CVB distribution on the equator of the same longitude on the same order Poincaré sphere.

Fig. 5. The output EPCV beams with (a) m = 2, (b) m = 3, and (c) m = 4. The EPCV beams with the orders are (a2)-(a4) m = 2, (b2)-(b4) m = 3, and (c2)-(c4) m = 4 pass through the different direction linear polarizer.

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It is difficult to characterize the position of EPCV beams on the HOPS by simply analyzing the intensity distribution of the linearly polarized component with a linear polarizer. Therefore, the Stokes vector of the output beams were measured and the result is shown in Fig. 6. Where the ɛ is the ratio of the minor axis to the major axis of elliptical polarization, ϑ is the angle between major axis and x-axis. The polarization azimuth (PA) and the polarization ellipticity (PE), are given by $\psi = {\tan ^{ - 1}}({{S_2}/{S_1}} )$ and $\chi = {\sin ^{ - 1}}({{S_3}/{S_0}} )$ respectively, where S₀, S₁, S₂, and S₃ are the Stokes vector [40]. In Fig. 6, it can be found that values of PE are different when the right-handed elliptically polarized or circularly polarized beam incident the order of the Q-plates is m = 3-1 and m = 3 + 1. This can be explained by the difference in the Jones matrices of theirs. When the LP₀₁ mode is incident on the Q-plates with the expression $J_m^ -$ with any polarization state on the 0th-order Poincaré sphere, it can be expressed as,

(13)$$\begin{aligned} J_{m,0}^ - {P_{\varepsilon ,\vartheta }} &= \left( {\begin{array}{{cc}} {\cos m\phi }&{\sin m\phi }\\ {\sin m\phi }&{ - \cos m\phi } \end{array}} \right)\left( {\begin{array}{{cc}} {a({\cos \vartheta + i\varepsilon \sin \vartheta } )}\\ { - a(\sin \vartheta - i\varepsilon \cos \vartheta )} \end{array}} \right)\\ &= \frac{{a({1 + \varepsilon } )}}{2}{e^{i({m\phi + \vartheta } )}}\left( {\begin{array}{{c}} 1\\ { - i} \end{array}} \right) + \frac{{a({1 - \varepsilon } )}}{2}{e^{ - i({m\phi + \vartheta } )}}\left( {\begin{array}{{c}} 1\\ i \end{array}} \right)\\ &= \frac{{a({1 + \varepsilon } )}}{2}|{m,R} \rangle + \frac{{a({1 - \varepsilon } )}}{2}|{ - m,L} \rangle . \end{aligned}$$

Where a is the major axis of the elliptically polarized. When the beam incident on the Q-plates with the expression $J_m^ +$, the expression of the outgoing beam can be written by,

(14)$$J_{m,0}^ + {P_{\varepsilon ,\vartheta }} = \frac{{a({1 - \varepsilon } )}}{2}|{m,R} \rangle + \frac{{a({1 + \varepsilon } )}}{2}|{ - m,L} \rangle .$$

Fig. 6. The Stokes vector of the output beams. Where “m” represents the orders of the CVBs or EPCV beams, and “l” represents the TCs of the vortex beams.

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From Eq. (13) and Eq. (14), it is easy to see that the weights of the left- and right-handed circularly polarized component of the outgoing beams are interchanged, when pass through Q-plates with the different expression. Therefore, the value of S₃ and the position on the HOPS is change in the space. According the values of PE and PA in Fig. 6, the order and specific position of the output VVBs on the Poincaré sphere can be determined. It also proves that we directly generate arbitrary HOPS beams with two different orders in the fiber laser cavity.

Before measuring the laser output pulse and power characteristics. Firstly, the influence of different modes on the output power was studied by using a beam quality profiler. The results are shown in the inset of Fig. 7(a). In the legend, “C” represents circularly polarized light incident on the first Q-plate (the output mode is vortex beam), and “L” represents the line Polarized light incident (the output mode is CVB). The results show that the output mode has a negligible effect on the laser output power, which is due to the low insertion loss of the QWPs and Q-plates. Besides, the control of polarization by the PC, produces neither internal losses nor back reflections; because it simply rotates the polarization state of the light in the fiber through a stress-induced birefringence mechanism. Therefore, the following research on the output power and pulse characteristics of the laser is carried out under the condition of the outputting a vortex beam with TC of 3.

Fig. 7. The output of (a) slope efficiency, different areas indicate different working states in the figure, CW: continuous wave regime; QS: Q-switched regime; the inset is the power measured by the beam profiler in different modes of output, C represents the incidence of circularly polarized beam, L represents the incidence of linearly polarized beam. (b) Optical spectrum of the fiber laser.

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The output power is shown in Fig. 7(a), measured by an optical power meter (THORLABS, PM16-425), the continuous wave (CW) threshold and slope efficiency are 37.4 mW and 33.4%, respectively. When the pump power is lower than 425 mW, the laser works in the CW regime, and when the pump power is higher than 425 mW, the laser operates in the Q-switched (QS) regime. Moreover, the performance of the laser with more optical elements was studied, of which the CW threshold increases from 37.4 mW to 38.9 mW, and the QS threshold increases from 425 mW to 427.6 mW. Thus, the insertion loss of these optical elements, as well as the influences on the laser threshold, is negligible. The output spectrum measured by a spectrum analyzer (Yokogawa AQ6370C) is shown in Fig. 7(b). The central wavelengths were 1029.43 nm when the output was continuous wave, and 1029 nm when the output was pulsed light. The reason for this spectral wavelength shifted may be caused by the absorption loss of the Q-switched crystal. According to Fig. 7(b), it is measured that when working in the passive Q-switched regime, the bandwidth is broadened by 0.41nm at 3dB. It also illustrates the generation of pulses from another aspect.

Figure 8(a) depicts the effect of the pump power range from 450mW to 600mW on the pulse width and pulse repetition rate of the resulting pulse train in Q-switched operation. When the pump power in the laser cavity was increased from 450mW to 600mW, the pulse width decreased from 1.41µs to 360ns, and the pulse repetition rate increased from 40kHz to 241kHz. The inset of Fig. 8(a) shows the shape of the pulse. With the increase of pump power, the discharge and charge time in the cavity decrease, and the nonlinear effect increases, so that the pulse repetition rate shows an increasing trend and the pulse width shows a decreasing trend. Figure 8(b) shows the evolution of the 3-D pulse sequence when the pump power is 450mW to 600mW. It can be seen that the pulse duration of the Q-switched pulse decreases and the repetition frequency increases with the pump power. This is consistent with the above-mentioned changes in intracavity pulse width and repetition frequency. In addition, when the pump power is in the range of 450mW to 600mW, the single pulse energy decreases from 2.3uJ to 0.6uJ.

Fig. 8. When working in the passive Q-switched regime, (a) the relationship between pulse width and repetition frequency and absorbed pump power; inset shows a single pulse when the pump power is 600 mW. (b) Evolution of 3-D pulses for pump power ranging from 450 mW to 600 mW.

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5. Summary

In conclusion, in this work, starting from the theory, we introduced and demonstrated the ring Ytterbium-doped fiber laser with cascade Q-plates, and verified its ability to generate mode-switchable nanosecond pulsed VVBs between two different orders through experiments. The experimental results show that the laser slope efficiency is 33.4% and the central wavelengths of the CW and pulse beam output spectra are 1029.43 nm and 1029 nm, respectively. The bandwidth broadens 0.41 nm at 3-dB. When the pump power of the laser is increased to 425 mW, the working state of the laser will change from CW regime to Q-switched regime. Further, when the pump power is ranged from 450W to 600 mW, the pulse width decreases from 1.41µs to 360 ns, the pulse repetition frequency increases from 40kHz to 241kHz, and the single pulse energy decreases from 2.3uJ to 0.6uJ. The measured Stokes vector and the Jones vector theory confirm the correctness and validity of the method. This work lays the foundation for the flexible generation of VVBs on the arbitrary position of the HOPS with multiple different orders in the laser cavity. Besides, it has potential to generate VVBs of more orders by applying more higher-order Q-plates and ultrashort pulsed VVBs based on mode-locked technology.

Funding

National Natural Science Foundation of China (11947110, 12104190); Jiangsu Provincial Key Research and Development Program (BE2022143); Natural Science Foundation of Jiangsu Province (BK20190953, BK20210874).

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.

References

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Controlled generation of mode-switchable nanosecond pulsed vector vortex beams from a Q-switched fiber laser

Abstract

1. Introduction

2. Theory

3. Experimental setup

4. Results and discussion

5. Summary

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (14)

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