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Abstract
Double-end polarized pumping scheme combined with off-axis pumping technique has been first introduced to generate vortex beams in a z-type cavity. By employing double-end pumping, two different transverse modes can be excited simultaneously. The phase delay between these two modes can be finely tuned by manipulating the cavity structure. Direct emission of a chirality controllable Laguerre Gaussian LG01 vortex beam with slope efficiency of more than 40% has been realized by a double-end polarized pumped Yb:KYW laser. Other modes, such as dual-LG01 mode, cross-shaped mode, and LG10 mode, have also been demonstrated from our laser setup.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical vortex has phase singularities in the wavefront and exhibits a donut-shaped intensity profile. It has been widely used in optical communications [1,2], optical tweezers [3], super-resolution microscopy [4], fluorescence microscopy [5], atom guiding [6] and micro-machining [7,8]. Especially, significant development in laser micromachining has been seen since the past two decades. Structured laser beams have the potential to direct fabricate complex structures. As it has already been reported that the vortex beam [7–9] can be used to engrave sub-wavelength ring structures on materials. This kind of annular structures can be potentially used in micro-ring filters, modulators [10,11] and lasers [12]. Except the ring structures, other complex beam profile such as cross-shaped beam may have possible applications in fabricating cross-shaped structure based microfluidic devices [13] and sensors [14].
Generation methods of vortex beam including passive and active ways, which depend on whether the amplifying media is involved [15], have been reported. In general, passive methods convert beams with spatially homogeneous phase into vortex beams by using spiral phase plate [16], spatial light modulators [17], computer generated holographic converters [18], specially designed metasurfaces [19], optical wedges [20] and astigmatic lenses [21]. However, these passive methods normally require extra optical components, which may introduce the beam distortion [22], make the system complicated, difficult in alignment and expensive [23]. Active methods, also called direct generation, involve the use of laser cavity design to force the laser oscillating in Laguerre Gaussian (LG) modes. It draws rising attention in the past few years, due to the advantage of good beam quality. Active methods include transverse mode selection using thermal lensing effect of laser gain media [24], ring shape pumping technique by tailoring the pump beam into a doughnut shape by a hollow-core fiber [25] or a specially fabricated reflective mirror [26], inserting circular absorber [27] or spiral phase plate [28] or a defect-spot cavity mirror [22,29] in the laser cavity, mode conversion by polarization maintaining fiber [30]. However, exploiting thermal lens effect normally requires high pump power and other methods require specially designed components, which makes these active methods less attractive, low efficiency and complicated.
Recently, directly realization of LG modes inside laser resonator without any extra components has been reported. For example, in [23] and [31], the authors rotate the gain medium both in xz and yz planes to convert laser mode from diagonal HG01 mode to chirality controllable LG01 mode. Using this laser crystal rotating induced off-axis pumping technique, the laser slope efficiency dependent on the absorbed pump power is reported as high as 41.1%. However, the output doughnut beam is distorted and the intensity distribution is asymmetric in x and y directions. In [32], the authors use asymmetric pumping distribution and pumping width control to generate LG0, ± 1 mode with pump-to-laser efficiency of ~0.03%. We also employ off-axis pumping technique and intra-cavity astigmatism manipulation to generate chirality controllable LG01 mode from a z-type cavity with slope efficiency of only ~7.3% [33]. In order to achieve nice vortex beam with high efficiency, a new method by employing double-end polarized pumping scheme combined with off-axis pumping technique to generate chirality controlled LG01 and dual-LG01 vortex beams has been proposed. Double-end polarized pump scheme is a common method used to increase the laser efficiency and reduce the pump polarization sensitivity [34,35]. The random polarized output pump laser is split into two parts with orthogonal polarizations, rotating the polarization of one pump, and then double end pumping the Yb:KYW crystal along the Nm-axis with high absorption cross section. Off-axis pumping technique is employed for both pumping ends to generate two controlled high order Hermit-Gaussian (HG) modes simultaneously. Intra-cavity astigmatism caused by tilted curved mirrors in the z-type cavity and laser crystal with different thermo-optic coefficients is utilized to control the Gouy phase delay between different HG modes in order to achieve vortex emission. In our experiments, handedness controllable LG01 vortex beam with slope efficiency of more than 40% can be obtained from our double end pumped Yb:KYW laser. Besides, we find that other complex laser beam profiles, such as cross-shaped beam or LG10 mode can also be achieved with high efficiency.
2. Experimental setup and analysis
The experimental setup is shown in Fig. 1(a). The random polarized output laser from a single mode fiber coupled 1.2 W LD is split to two parts by a cube polarizer after the collimation lens L1. The P-polarized pump is directly coupled into a 5% doped 5 × 5 × 3 mm3 Yb:KYW crystal from Lens L2. The Nm axis of Yb:KYW is parallel to the P-polarization of pump laser. The S-polarized laser is reflected by the cube polarizer, rotated by a half waveplate 90° to P-polarization and then coupled back into the laser crystal by three tuning mirrors M6, M7, M8 and Lens L3. M1 and M2 are dichroic mirrors of 100 mm radius with anti-reflection (AR) coating at pump wavelength, and high-reflection (HR) coating at lasing wavelength. Output coupler (OC) has a reflectivity of 98.5%. M3, M4 and M5 are tuning mirrors with HR coating. All the cavity mirrors are 12.7 mm diameter round mirrors. The distance between M1 and M2 is around 102 mm, between M2 and M3 is around 255 mm, between M3 and OC is around 270 mm, between M1 and M4 is around 226 mm, between M4 and M5 is around 350 mm. The total cavity length is about 1203 mm. Pumping point at the laser crystal can be controlled by tilting collimation lens L1 for the left end, and tilting tuning mirror M8 for the right end. After emission, the laser output is injected into a Mach-Zehnder interferometer, which consists of two non-polarized beam splitter (NPBS), a convex lenses L4 combined with a pinhole to create a plane wave as reference beam and a filter to decrease the intensity of the signal beam. A CCD camera is used to detect the interference pattern.
Fig. 1 Sketch of (a) experimental setup; (b) double-end pumping scheme combined with off-axis pumping technique.
Off-axis pumping method is a common technique to achieve high order HG mode [36]. By situating the pump beam position at one of the brightest spots, desired HG mode can be obtained. Double end pumping scheme combined with off-axis pumping technique offers the opportunity that two pump beam positions at the laser crystal can be selected to excite two transverse mode simultaneously, as shown in Fig. 1(b). Coherent superposition of these two transverse modes will result in generation of laser modes with new beam profiles. Taking HG10 mode for example, coherent superposition of HG10 mode and HG01 mode will result in a diagonal HG10 mode. Orientation of the diagonal HG10 mode to the x and y axes is −45° for the case of (HG10 + HG01) and 45° for the case of (HG10-HG01). The orientation can be controlled by pointing one of the pump position horizontally from left to right while keeping the other one still, as shown in Fig. 1(b). Once the diagonal HG10 mode is achieved, LG0, ± 1 mode can be achieved by introducing π/2 phase difference between HG10 and HG01 modes [32], as shown in Figs. 2(a) and 2(b). The phase difference of different HGnm modes is caused by different Gouy phase φ, which can be calculated by the cavity roundtrip ABCD matrix, expressed as [33]
Fig. 2 Simulation results of (a) coherent superposition of HG10 and HG01 modes with π/2 phase difference to form LG0, + 1 mode. The simulated interference pattern with plane wave has been shown to indicate the positive spiral phase; (b) coherent superposition of HG10 and HG01 modes with -π/2 phase difference to form LG0,-1 mode. The simulated interference pattern with plane wave has been shown to indicate the negative spiral phase; (c) coherent superposition of HG10 and HG02 modes with π/2 phase difference to form dual-LG0,1 mode; The simulated interference pattern with plane wave contains two forks with opposite fork directions in each of the LG01 mode. (d) Gouy Phase difference between HG10 mode and HG01 mode dependent on arm length between M2 and Yb:KYW.
Normally HG10 mode and HG01 mode are degenerated modes with equal Gouy phase. However, in the z-type cavity, non-normal angle of incidence on the concave mirrors results in different focal length fT = Rcos(α)/2 and fS = R/2cos(α) in the tangential and sagittal plane respectively, where R is the concave mirrors radius of curvature and α is the angle of incidence of the beam onto the concave mirrors [33]. Another point is that differences of focal lengths in tangential and sagittal planes due to different thermo-optic coefficients in the laser crystal will also result in astigmatism, i.e. Gouy phase difference. Figure 2(d) shows the calculated Gouy phase difference Δφ = |φT−φS| between HG10 and HG01 modes considering both the curved mirrors and thermal lensing effect of the laser crystal. It is clear from Fig. 2(d), by translating curved mirror M2, phase difference of π/2 can be obtained between HG10 and HG01 modes due to the cavity astigmatism, i.e. LG01 vortex beam could be generated. The chirality of the LG01 mode can be controlled by manipulating the pumping point laterally at one pump end, as shown in Fig. 1(b). Other than LG01 mode, simultaneous dual vortex can also be obtained from the double-end pumping cavity by the combination of HG10 mode and HG02 mode with π/2 phase delay, as shown in Fig. 2(c). The simulated interference pattern of the single vortex modes and dual vortex mode with plane wave have been shown in Fig. 2. The interference pattern of single vortex modes shows a single downward fork for LG0, + 1 and upward fork for LG0,-1, while the interference pattern of the dual vortices contains two forks with opposite fork directions in each of the LG01 mode.
Coherent superposition of other HG modes can generate other complex transverse modes. For example, cross-shaped beam can be generated by combination of fundamental Gaussian mode and HG11 mode with π/2 phase difference, as shown in Fig. 3(a). This kind of cross-shaped beam, has great potential in complex profile micromachining, is not a normal transverse mode inside the laser cavity and has never been reported before as far as we know. It also shows in Fig. 3(b), that LG10 mode can be achieved by combination of HG02 mode and HG20 mode.
Fig. 3 Simulation results of (a) coherent superposition of fundamental Gaussian mode and HG11 modes with π/2 phase delay to form cross-shaped mode; (b) coherent superposition of HG02 mode and HG20 modes to form LG10 mode.
3. Experimental results
3.1 Vortex beam generation
Firstly HG10 and HG01 modes are achieved by off-axis pumping from only the left end or right end respectively, as shown in Figs. 4(a) and 4(b). Then a nice doughnut mode with ring-to-center intensity contrast of around 15.5 dB from CCD camera can be achieved once pumped from both ends and fine tune the position of M2, as shown in Fig. 4(c). The output doughnut beam is injected into the interferometer, and the interferograms are shown in Figs. 4(d) and 4(e). By laterally moving the right end pumping point at the laser crystal by adjusting tuning mirror M8, interference patterns with left-downward fork-shape stripes (defined as LG0, + 1) and right-upward fork-shape stripes (defined as LG0,-1) with one fork can be clearly observed, which is similar to the simulation results shown in Figs. 2(a) and 2(b).
Fig. 4 Experimental results of (a) HG10 mode emission by left-end pumping; (b) HG01 mode emission by right-end pumping; (c) Doughnut mode emission by double-end pumping; (d) Interferograms measured for LG0, + 1 mode; (e) Interferograms measured for LG0,-1 mode.
The absorbed pump power dependent output power function of both LG0, ± 1 modes are shown in Fig. 5. Maximum output power of 216 mW for LG0, + 1 and 227 mW for LG0,-1 have been realized. The slope efficiency is fitted as 40.9% for LG0, + 1 mode and 40.2% for LG0,-1 mode. From Fig. 5, we also see the beam profile evolution with increasing absorbed pump power. When the pump power is low, a diagonal HG mode is observed. When the absorbed pump power is in the range of 444 mW to 571 mW, the beam starts to be like a circle with inhomogeneous distribution in x and y distributions. Once the absorbed pump power increases above 571 mW, a nice doughnut mode beam can be achieved. This beam profile evolution indicates that although the thermal lens effect is weak due to the 1 W pumping, the differences of focal lengths in tangential and sagittal planes due to different thermo-optic coefficients in the laser crystal also play an important role in LG01 vortex beam emission. So if a high pump power is employed to increase the output power, a constant temperature device such as a cooling system for the laser crystal should be required to ensure the constant phase shift and stable laser running.
Simultaneous dual vortex laser generation can also be realized from our laser setup, as shown in Fig. 6(a). Similar to the above description, firstly a HG2,0 mode is achieved by left end off-axis pumping. Then the pumping point from right end is finely tuned until the laser output with two vortices is attained, still in LG01 mode for each one. Similar to the simulation result in Fig. 2(c), Fig. 6(b) shows the interference pattern of the dual vortices with plane wave, which contains two forks with opposite fork directions in each of the LG01 mode. The maximum output power of dual vortex emission reduces to 114.5 mW at absorbed pump power of ~761 mW.
Fig. 6 Experimental results of (a) Dual-LG01 mode emission obtained by double-end pumping; (b) Interferograms measured for dual-LG01 mode.
3.2 Complex mode generation
Besides vortex beam generation, other complex modes as discussed before, like cross-shaped mode and LG10 mode have also been realized in the experiments. Figure 7(a) shows a beam profile of cross-shaped mode, whose slope efficiency is fitted as 41.9%, as shown in Fig. 7(c). LG10 mode with high slope efficiency of 39.1% is also achieved, as shown in Figs. 7(b) and 7(c). During the experiments, we also see the beam profile evolution of complex beam dependent on the absorbed pump power. For cross-shaped mode, when the absorbed pump power is low, an elliptical beam profile is firstly observed. When the absorbed pump power is in the range of 380 mW to 539 mW, the beam has a rectangle-like shape. Once the absorbed pump power increases above 570 mW, the cross-shaped beam profile can be observed. For LG10 mode, the beam profile evolution is relatively simple. At the low absorbed pump power, the beam looks like a rhombus 2 × 2 four dark spots array inside and a bright dot in the center. When the absorbed pump power increases to 507 mW, LG10 mode can be formed.
Fig. 7 Experimental results of (a) Cross-shaped mode emission obtained by double-end pumping; (b) LG10 mode emission obtained by double-end pumping; (c) The absorbed pump power dependent output power function of cross-shaped mode and LG10 mode.
4. Conclusion
In summary, we use a double-end polarized pumping scheme combined with off-axis pumping technique to directly generate vortex beams, cross-shaped mode and LG10 mode from a Yb:KYW laser with high slope efficiency. Double end pumping scheme offers the possibility to excite two transverse mode simultaneously inside the cavity. By utilizing the astigmatism caused by the tilted curved mirrors in the z-typed cavity and the thermal lensing effect of the laser crystal, Gouy phase difference between different HGn,m modes can be manipulated to obtain output lasers with various beam profiles. Experimentally, we have achieved chirality controlled LG01 mode emission, dual-vortex emission, crossed-shaped beam and LG10 mode. In our opinion, this technique can be extended to multiple pumping scheme with more than one laser crystal in order to generate higher order vortices and even more complex beam profiles. Moreover, a saturable absorber such as SESAM can be easily added into such a z-type cavity to obtain the ultrafast vortex generation.
Funding
National Natural Science Foundation of China (NSFC) (61605133); Sichuan Province International Cooperation Research Program, China (2016HH0033); Chengdu Science and Technology Program, China (2015-GH02-00021-HZ).
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