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Abstract
Different from the traditional ideal column symmetry cavities, we directly generated the cylindrical vector pulsed beams in the folded six-mirror cavity by employing a c-cut Tm:CaYAlO4 (Tm:CYA) crystal and SESAM. By adjusting the distance between the curved cavity mirror (M4) and the SESAM, both the radially polarized beam and azimuthally polarized beam are generated around 1962 nm and the two vectorial modes can be freely switched in the resonator. Further increased the pump power to 7 W, the stable radially polarized Q-switched mode-locked (QML) cylindrical vector beams were also obtained with an output power of 55 mW, the sub-pulse repetition rate of 120.42 MHz, pulse duration of ∼0.5 ns and the beam quality factor M2 of ∼2.9. To our knowledge, this is the first report of radially and azimuthally polarized beams in the 2 µm wavelength solid-state resonator.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cylindrical vector beams (CVB) with spatially non-uniform polarization distribution and the novel polarization singularity effect have aroused great interest. In particular, radially polarized beam and azimuthally polarized beam share the donut pattern and have been widely applied in optical trapping [1], laser processing [2], and micro and nano-fabrication [3]. In addition, the polarization states of radially polarized beam show rotational symmetry distribution in space, which can break through the traditional optical diffraction limit after deep focusing [4], and can be used for high-resolution imaging [5], and particle acceleration in ultrafast lasers [6,7]. Especially, due to the additional unique properties entitled of “eye-safe” laser and “strong water molecule absorption” from the 2 µm laser, the Tm (thulium)-doped bulk has become promising candidates for the high precision laser medical, ultra-high resolution LIDAR, and new attosecond laser driving pump source fields [8].
Compared with fiber laser [9,10], the cylindrical vector beam generated in solid state laser has the advantages of easy mode manipulation and high pulse energy, which has caused extensive research. Up to now, the active generation of cylindrical vector beams in the solid-cavity can be realized in the following ways: 1) by shaping the pump spot to a ring configuration in the microchip laser or using a grating waveguide structures [11–13]; 2) using high power pump source excites thermal birefringence of laser crystal [14–16]; 3) using the birefringence crystals of typical c-cut type in an idea cylindrical symmetrical cavity [17–20]. The first method above can directly produce pure cylindrical vector beams, but suffers a large pump loss; the thermal birefringence method always need a strong pumping and the obtained polarization pattern always accompany with a poor stability and purity due to the instable thermal effect. By the third method, one can adjust the cavity mirrors to distinguish the ordinary ray (o-ray) and extraordinary ray (e-ray) modes to select polarization states. Based on these methods, the cylindrical vector beams including radially polarized and azimuthally polarized at 1 µm and 1.6 µm have been successfully obtained [17–20]. Unfortunately, there are no reports on the direct generation of cylindrical vector beams in the 2 µm of solid state lasers.
In fact, crystal materials are the key to CVB generation in the 2 µm band. Recently, the Aluminate have been regarded as an ideal laser host for high power paser generation due to its high thermal stability and low cost [21]. The typical CaYAlO4 (CYA) crystal belongs to K2NiF4 structure and is a tetragonal ABCD4 compound [22]. The Ca2+ and Y3+ ions are randomly distributed between layers of the octahedron, and thus offered an excellent optical and mechanism. Especially for the Tm(Thulium) doped CYA crystal, due to the high gain emission cross-section and favorable broad emission spectrum originating from the disorder and multisite structure, it has been regarded as an ideal candidate for the high quality laser emission generation in around 2 µm water absorption band. Furthermore, a-cut CYA crystals can generate linearly polarized beam, while the anisotropic property of c-cut CYA crystals have the potential to generate CVB.
In this paper, by using the birefringence effect of c-cut Tm:CYA crystal, we demonstrated the radially polarized and azimuthally polarized beams at around 1962 nm. In the folded six-mirror cavity, we introduce column symmetry compensation through azimuthally folding. Controllable radially polarized and azimuthally polarized beams are realized by changing the distance between the M4 and the SESAM, operating in Q-switched mode-locking pulsed states. The radially polarized laser emission has a pulse repetition rate of 120.42 MHz and a pulse duration of 0.5 ns and an output average power of 55 mW, respectively.
2. Experiment setup and results
The experimental setup of the cylindrical vector beams of Tm:CYA laser is shown in Fig. 1. The pump source is a laser diode (LD) with 105 µm core diameter and 0.22 numerical aperture (NA) at 793 nm, which emitted laser is focused on the laser crystal through a telescope system consisting of two flat-convex mirrors of the identical focal length (f = 100 mm). The gain media is a c-cut slice-like Tm:CYA crystal with a dopant of 6 at% and the dimensions of 3 mm ×3 mm × 6.1 mm.The corresponding the refractive indices for ordinary and extraordinary rays are calculated to be no = 1.870 and ne = 1.892 around 2 µm [23]. We wrapped the laser crystal in a copper heat sink, conducting water cooling at 18°C to prevent thermal fracture of the crystal. The two faces of the crystal are coated with an anti-reflective (AR) coating in the range of 1900 ∼ 2100 nm. The lenses of L1 and L2 collimation focus on the pump beam with the same focal lengths of 100 mm. The curvature radius of the plane-concave mirrors M1, M2, and M3 are all 100 mm and are coated with high reflectance (R > 99.7%) to 1850 nm to 2100 nm band, the additional plano-concave mirror M4 has a curvature radius of 50 mm and same reflectance from 1850 nm to 2100 nm. A plane-concave mirror with a transmittance of 5% is used as the output coupler (OC). A semiconductor saturable absorption mirror (SESAMs) (BATOP. Inc, SAM-1960-5-10 ps) at 1960 nm was used to initialed the pulsed laser operation, with a modulation depth of 3%, and a saturation fluence of 30 µJ/cm2. We adjusted the distance of SESAM to M4 by applying it on a three-dimensional displacement platform with an accuracy of 10 µm in the direction parallel to the ray (z-direction in Fig. 1). Based on the ABCD law of the assumption of the fundamental mode, the laser beam radius at the center of the Tm:CYA crystal and on the surface of the SESAM were estimated to be 39×44 µm and 38×111 µm, respectively.
Fig. 1. Schematic of the cylindrical vector beams control c-cut Tm:CYA laser. L1, L2: convex lens; M1, M2, M3, and M4: plano-concave mirrors; OC: output coupler; HR: high reflectivity mirror. PBS: polarizing beam splitter; CCD: charge coupled device.
To characterize the different CVB modes, we added the polarizing beam splitter (PBS) which was applied on a rotatable device with a rotation accuracy of 1° outside the laser cavity, as shown in Fig. 1. After that, the laser beam profile was recorded by the mid-infrared charge coupled device (WinCamD-IR-BB, pixel size of 17 µm). A 1 GHz bandwidth oscilloscope (Keysight, DSO-104A,) and a 12.5 GHz bandwidth photodetector were used to record the waveform. An Optical Spectrum Analyzer (Yokogawa AQ6375 1.2∼2.4 µm) with a high resolution of 0.05 nm was used to monitor the output optical spectrum.
3. Results and discussion
When the laser passes through the c-cut crystal, the stable cavity length of the extraordinary laser is longer than that of the ordinary laser line due to the birefringence effect as shown in the Fig. 1 [17]. The laser mode of cavity resonance can be selected by changing the end mirror position and thus changing the cavity length.
The relationships between the output power and the incident pump power with HR mirror and SESAM as end-mirror are shown in Fig. 2. For the HR mirror, by adjusting the mirror, the output laser work at the typical fundamental transverse mode. The laser output pump threshold is 1.3 W, the maximum output average power was up to 734 mW at the incident pump power of 12 W, corresponding to a slope efficiency of 6.84%, an optical to optical conversion efficiency of 6.12%. Compared with the donut laser, it has a higher efficiency. For the SESAM mirror, by carefully adjusting the cavity parameters, the output laser work at the typical cylindrical vector beams mode. The output pump threshold of CVB is 4 W, increasing the pump power from 4 W to 12 W, the laser can maintain a stable cylindrical vector beams output of with donut shape, with the output power lineally creased from 5.5 mW to 129 mW. Corresponding to a slope efficiency of 1.54%, an optical to optical conversion efficiency of 1.08%.
Fig. 2. The average output power versus incident pump powers in CW (continuous wave, black) and Cylindrical vector beams (blue) of Tm:CYA c-cut laser.
By further carefully adjusting the distance L between the M4 and the SESAM, the radially polarized and azimuthally polarized beams are obtained in Fig. 3. Figure 3(a) shows the typical radially polarized beam, where the distance L between SESAM and M4 is 45.43 mm, Figs. (a1) - (a4) show the corresponding intensity distribution of laser beams after the PBS when the PBS was rotated at different orientations, and the white arrow represents the polarization direction of the transmitted laser of PBS. At the pump power of 6 W, the average output power was 44 mW, and the low-power pump is adopted to avoid the unstable thermally induced birefringence effect caused by high power. The standard deviation of output power in each polarization direction is 2.5 mW. At the same pump power, the obtained azimuthally polarized beam is as shown in Fig. 3(c) by adjusted the distance L to 45.14 mm, with an average output power of 52 mW. Figures 3(c1) - (c4) demonstrate the intensity distributions after passing through the rotatable PBS, the standard deviation of output power in each polarization direction is 4 mW.
Fig. 3. Experimental measurement and theoretical simulation of CVB. (a) The typical radially polarized beam intensity distribution at 6 W pump power; (a1) - (a4) is the intensity distribution after passing through the rotatable PBS; (b) The theoretical simulation result of a radially polarized beam; (b1) - (b4) are the theoretical simulation results of intensity distribution after passing through the PBS; (c) Typical azimuthally polarized beam intensity distribution at 6 W pump power ; (c1) - (c4) is the intensity distribution after passing through the PBS; (d) The theoretical simulation result of an azimuthally polarized beam; (d1) - (d4) are the theoretical simulation results of intensity distribution after passing through the rotatable PBS; (e) Spectrum of the (a) in linear coordinates; (f) Spectrum of the (c) in linear coordinates.
To further explore the relationship between polarization state and intensity distribution, we conduct the theoretical simulation based on Formula 1 [24]. The ideal radially or azimuthally polarized electric fields $\boldsymbol{E}_{BG}^{(\nu )}({r,\phi ,z} )$ can be written as:
$Q(z )$ defined as: $Q(z )= \textrm{exp}\{{i{\beta^2}z/[{2k({1 - i\textrm{z}/{z_0}} )} ]} \}$.
${\boldsymbol{T}_e}({r,\phi ,z} )$ is the electric field component of $\boldsymbol{\; T}({r,\phi ,z} )$:
To detect the polarization state distribution of the CVB, a linear polarizer is added to the simulation, which can be written as:
The simulation results of radially polarization laser intensity distribution are shown in Fig. 3(b), and the theoretical simulation results of intensity distribution after passing through the rotatable PBS are shown in (b1) - (b4). Figure 3(d) is the simulation results of azimuthally polarization laser intensity distribution, the theoretical simulation results of intensity distribution after passing through the rotatable PBS are shown in (d1) - (d4). We can see that Figs. 3(a1), (a2), (c1), and (c2) agree well with the simulation results, and Figs. 3(a3), (a4), (c3), and (c4) slightly deviate from the simulation results due to the mixing of CVB modes caused by cavity folding. Figures 3(e) and (f) are the optical spectrum in linear coordinates of Figs. 3(a) and (c) respectively. The central wavelength of the radially polarized beam is almost the same as the azimuthally beam.
By increasing the pump power to 7 W while keeping the distance L between M4 and SESAM at 45.43 mm, the stable Q-switched mode-locking pulsed radially polarized beam with an average output power of 55 mW was also obtained, with the pulse parameters shown in Fig. 4. The total intensity distribution of radially polarized laser as shown in Fig. 4(a), the cellular structure is the result of interference caused by reflection from the mirror. To detect whether it is a radially polarized laser, a PBS was placed in front of the beam profiling camera. It can select the polarization direction of the transmitted laser. The intensity distribution of the transmitted laser with different polarization directions is shown in Figs. 4(a1) - (a4), the white arrows indicate the direction of polarization.
Fig. 4. Laser intensity distribution and pulse trains from the Tm:CYA c-cut laser with the pump power of 7 W. (a) The radially polarized laser intensity distribution; (a1)-(a4) are the intensity distribution after passing through a PBS; (b) The pulse trains for 10 µs time scales; (c) The pulse trains for 100 ns time scales; (d) The waveform of the single pulse.
According to the Ref. [25], beam quality factor could be measured in the electronic control guide, CCD and lens (the focal length f = 100 mm) device as shown in Fig. 1. The corresponding beam quality factor in the x and y directions are $M_x^2$=3.17 and $M_y^2$=2.6, respectively (The average value in both directions was 2.9, which is close to the theoretical value of 2 [26]). We used the oscilloscope with the bandwidth of 1 GHz and the detector with the bandwidth of 12.5 GHz to measure pulse shape. Figure 4(b), (c), and (d) show the pulse trains at time scales of 10 µs, 100 ns, and 12 ns, respectively, with a pulse repetition rate of 120.42 MHz, a pulse duration of 0.5 ns, and the full width at half maximum of Q-switched envelope of 4.23 µs by the electronic oscilloscope. According to the formula in Ref. [27], ${\tau _{measure}} = \sqrt {\tau _{real}^2 + \tau _{probe}^2 + \tau _{oscilloscope}^2} $, the measured pulse width ${\tau _{measure}} = 500\; ps$, for the probe : ${\tau _{probe}} = \frac{{0.312}}{{{f_{probe}}}} = \frac{{0.312}}{{12.5\,\textrm{GHz}}} = 24.96\,ps$, for the oscilloscope : ${\tau _{oscilloscope}} = \frac{{0.312}}{{{f_{oscilloscope}}}} = \frac{{0.312}}{{1\,\textrm{GHz}}} = 312\,ps$. Therefore, the real pulse width of the QML was calculated to be ${\tau _{real}} \approx 390\,\textrm{ps}$.
To explore the formation mechanism of CVB in our cavity, we further studied the radially polarized beam evolution as the distance L between SESAM and M4. By precisely setting the distance L around 45 mm, the spot patterns can have evolved from the typical HG01 mode to radially polarized mode and then to HG10 modes (as shown in Fig. 5(a) and (c)) near the radially polarized beam (as shown in Fig. 5(b)), with the distance L are measured to be 45.41 mm, 45.43 mm, and 45.48 mm, respectively. The corresponding output average power at 4 W pump power are 11 mW, 8.2 mW, and 7 mW, respectively. The white arrow indicates the direction of the beam polarization. The radially polarized donut beam should be the coherent superposition of the HG01 and HG10 modes [28,29]. For the formation mechanism of CVB, the SESAM play the role that the unique defect mirror characteristic with low reflectivity suppresses the oscillation of lower-order transverse modes [24].
Fig. 5. Measured typical transverse mode and transmission with the changing distances of L between SESAM and M4.
4. Conclusions
In conclusion, we have experimentally demonstrated the cylindrical vector beams modulation in the c-cut Tm:CYA laser. By using the birefringence effect of crystal and small $\Delta \textrm{n}\,(\Delta \textrm{n} = $ne-no = 0.02), both radially polarized laser and azimuthally polarized laser are directly generated in the free space folded-cavity resonator, operating in Q-switched mode-locking pulsed states. By easily adjusting the distance between M4 and SESAM, the radially and azimuthally polarized modes can be well controlled and switched. In the future, we are expected to use c-cut Tm:CYA crystal to obtain continuous-wave stable mode-locked CVB in the current folded cavity.
Funding
National Natural Science Foundation of China (61805111); Jiangsu Normal University (2021XKT1246, 2022XKT1339); Xuzhou Science and Technology Program (KC21043); State Key Laboratory of Transient Optics and Photonics (SKLST201707); Priority Academic Program Development of Jiangsu Higher Education Institutions.
Disclosures
The authors declare there are no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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