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Abstract
We have demonstrated the first direct femtosecond vortex beam generation from a semiconductor saturable absorber mirror (SESAM) mode locked Yb:KYW oscillator, featuring a homemade defect-spot mirror. Experimentally, a Laguerre Gaussian LG01 vortex beam with a repetition rate of ∼103.5 MHz and a pulse duration of 298 fs has been obtained. Both the defect mirror induced spatial loss modulation and intra-cavity astigmatism are responsible for the doughnut mode generation. Further, the chirality of the vortex beam is controlled by slightly tilting the angle of the Yb:KYW crystal, which hence breaks the azimuthal symmetry inside the laser cavity and leads to differential losses for LG0,+1 and LG0,-1 modes. The potential of the vortex beam’s amplification by a 2-m long Yb-doped double cladding fiber (DCF) amplifier has also been demonstrated.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Vortex beams, well-known for their phase singularity and doughnut-shaped intensity profile, have found wide applications in optical communication [1], microscopy [2], optical tweezers [3], and material ablation [4]. Femtosecond vortex beams reform the traditional femtosecond laser technology. It can be used to engrave sub-wavelength ring structures on materials, which makes further extension to fabricate complex and unconventional surface structures possible [5–7]. Plus, vortex laser ablation can be used to fabricate chiral nano-needles [8,9]. Besides material processing, femtosecond vortex beams also show the potential applications in nanoparticle trapping [10,11], frequency doubling [12], and robust long-distance propagating in atmosphere [13,14].
However, femtosecond vortices generations are usually not easy due to the intrinsic wide spectral bandwidth [15]. Correcting elements are thus required to compensate for the topological charge dispersion caused by the broad spectral bandwidth in order to generate ultrafast optical vortices with conventional spiral phase plate and holograms [16–18]. Moreover, various kinds of mode converters, including cylindrical lenses mode converter [19,20], optical fiber based mode converter [21], and birefringent crystals based mode converter [22], have also been employed to achieve ultrafast optical vortices. Yet, these extra-cavity methods are accompanied by beam degradation, so it is not easy to get high beam quality [23,24].
Another possibility is to directly generate vortex beam from a laser cavity, which is advantageous in terms of system simplicity and beam quality [23]. Methods such as ring shape pumping technique [25], transverse mode selection using thermal lensing effect of laser gain media [26], inserting circular absorber [27] or spiral phase plate [28] in the laser cavity, employing a defect-spot cavity mirror [23,29], and mode conversion by polarization maintaining fiber [30] have been used to generate vortex beam directly from a laser cavity. Among them, inserting a defect-spot mirror inside the laser cavity is technically simple and attractive [29]. However, the direct generation of ultrafast vortex beams is seldom reported. Recently, we reported the first direct generation of ultrafast vortex beam by manipulating the cavity structure and employing the off-axis pumping technique [31]. However, the generated pulse train shows obvious modulation and may indicate two transverse laser modes oscillating inside the laser cavity, which limits its further applications.
In this paper, we demonstrate, to the best of our knowledge, the first direct generation of femtosecond vortex beam from a SESAM mode locked Yb:KYW oscillator by employing a defect-spot mirror inside the cavity. The chirality of the output beam can be controlled by slightly tuning the laser crystal angle. Furthermore, amplification of the vortex beam has been carried out with a 2-m long Yb-doped DCF amplifier (Yb1200-25/250DC). A maximum average power of 500 mW has been achieved during the experiment.
2. Experimental setup
The experimental setup is shown in Fig. 1. A single mode polarization-maintained fiber coupled laser diode (LD) at 980 nm, from 3SP Technologies, is used as pump source. The pump beam from the single mode fiber is collimated and focused into an anti-reflective coated Yb:KYW crystal (Ng-cut, 5×5×2 mm3 in size and 5% doping) by two aspherical lenses L1 and L2 with focal lengths of 18.53 mm and 70 mm respectively. The pump diameter is roughly calculated as 23 μm. A half-wave plate (HWP) is used to adjust the pump polarization parallel to the Np-axis of the Yb:KYW crystal for maximizing the laser crystal absorption. The output coupler (OC) has a transmission ratio of 0.3%. M1, M2 and M3 are all concave dichroic mirrors with radii of curvature of 100 mm, which are anti-reflective coated for pump wavelength and high-reflective coated for signal wavelength. A total roundtrip group delay dispersion (GDD) of approximately −3500 fs2 are offered by two pieces of chirped mirrors (M4 of −550 fs2 GDD, M5 of −1200 fs2 GDD). A BatopTM SESAM (SAM-1040-1-10ps), which a modulation depth of 0.6% and saturation fluence of 70μJ/cm2, has been used in the experiments. A defect-spot mirror is used as an end mirror. Because the OC is used as a cavity mirror instead of end mirror, there are two laser output beams. One of them is guided to a common path radial shear interferometer (CPRSI), which is used to check the phase singularity [31]. The other one is coupled into an Yb-doped DCF amplifier (Yb1200-25/250DC) with the help of two lenses L3 and L4. Both end surfaces of the fiber are cut at an angle of 8° to avoid parasitic oscillation. A multimode fiber coupled laser diode (LD2) with an output power of 5 W is used as the pump source. The output pump power is collimated and focused into the DCF by two aspherical lenses L5 and L6 with focal lengths of 11 mm and 18 mm. The DCF is coiled with a diameter of roughly 460 mm to maintain the high order mode running.
Fig. 1. Experimental setup of a Semiconductor Saturable Absorber Mirror (SESAM) mode locked Yb:KYW oscillator using a defect-spot mirror and its double-clad fiber (DCF) amplifier. LD, laser diode. DM: dichroic mirror. OC: output coupler. DCF: double cladding fiber. HWP: half wave plate. L: lens. M: mirror. NPBS: non-polarization beamsplitter. CCD: Charge-Coupled Device camera. The curved arrow above the laser gain medium shows the possibility of Yb:KYW crystal rotation. The laser crystal is mounted on a rotation stage, which can be rotated about the axis perpendicular to the optical table.
3. Experimental results and discussions
Defect spots, with diameters ranging from 150 μm to 300 μm (with a step of 50 μm), have been processed on a cavity mirror by a pulsed 266 nm laser (pulse repetition rate: 10 kHz, pulse energy: 17 μJ, pulse duration: 10 ns), as shown in Fig. 2(a). Experimentally, the defect spot with 150 μm diameter, the circled one in Fig. 2(a), has been tested to be the best one for vortex beam generation. During the experiments, smaller defect with diameter of 100 μm has also been fabricated on another mirror. By employing the 100 μm defect spot, doughnut mode can be obtained while chirality-controlled vortex beam cannot be clearly observed. This may be due to the fact that the cavity loss introduced into the laser resonator by the 100 μm defect spot is small. Therefore, the induced differential transmittance loss for incident beams with different angles doesn’t go to the extent that allows the vortex beam generation. Figure 2(b) shows its optical microscope image with a good circular shape. With the laser cavity well aligned, a linear polarized doughnut mode with a ring-to-center intensity contrast of approximately 15.9 dB has been achieved, as shown in Fig. 2(c) and (d). So far, we could not tell whether or not the doughnut mode carries optical orbital angular momentum (OAM), which has to be verified by interference measurement.
Fig. 2. (a) Picture of the defect-spot mirror with defect spots, with diameters ranging from 150 μm to 300 μm (50 μm step). The circled one is the defect spot of 150 μm we used in the experiments, (b) Optical microscope image of the circular spot defect with a diameter of 150 μm on the mirror; (c) Recorded beam profile of the doughnut beam by a CCD camera; (d) Intensity profile of the doughnut beam corresponding to Fig. 2(c). Dotted lines and red solid lines are experimental and fitted results.
The interference patterns are measured by a CPRSI. The input laser beam is divided to two by a non-polarization beamsplitter (NPBS), which then traverse the path of the interferometer in opposite directions and are combined again at the NPBS. Different from the well-known Michelson interferometer, both the reference and the sample beam share a common path in CPRSI, which is demanded for femtosecond pulses with short coherent length. The interference patterns are formed by overlapping the wavefront with an expanded duplicate of itself. The expanded wavefront can be roughly treated as a plane wave. The interference measurement confirms the vortex beam generation, and its chirality can be controlled by slightly rotating the laser crystal, as shown in Fig. 3. When the laser crystal is perpendicular to the cavity optical axis, the generated doughnut mode is actually an incoherent superposition of two opposite handed modes LG0,+1 and LG0,-1. So, the average OAM is close to zero [32]. The interference pattern is shown in Fig. 3(b), where no fork-shape stripes can be observed. With the laser crystal tilted by approximatively 1.5° (or −1.5°), chirality well-defined LG0,+1 or LG0,-1 mode can be obtained. The interference patterns are measured and recorded, as shown in Fig. 3(a) and (c). Typical downward fork-shape stripes with one fork, as shown in Fig. 3(a), indicates that the generated femtosecond vortex beam have a positive spiral phase with topological charge of 1. While an inverted upward fork structure, as shown in Fig. 3(c), indicates the generation of LG0,-1 vortex beam with a negative topological charge of −1. In our opinion, the crystal tilted angle dependent vortex generation is due to the angle dependent loss introduced to the laser cavity. When the laser crystal is perpendicular to the cavity optical axis, chirality-determined vortex beam cannot be generated due to the degeneracy of LG modes with opposite handedness [33]. In order to obtain vortex beam with well-determined handedness, methods such as tilting angle of output coupler [34], inserting mode-selecting components such as etalon [25], nanoscale stripes [35], quarter waveplate [36], YAG plate [37] and black phosphorus plate [33] were used to introduce differential loss for LG beams with opposite handedness. In our case, with the crystal tilted, chirality-determined vortex beam can also be realized. Once the laser crystal is tilted, the azimuthal symmetry is broken and the vortex beam generated. The chirality control principle is similar to that in [25] and [34]: the Poynting vector of LG mode follows the spiral path along the propagation direction, and its rotating direction is determined by the sign of the azimuthal order l [25]. From the Fresnel equations, it is known that the transmittance loss for the angled incident beam is higher than that for the normal incident one [25,34]. Hence one LG mode with determined chirality is selected.
Fig. 3. Interference patterns of (a) LG0,+1 mode; (b) incoherent superposition of LG0,+1 mode and LG0,-1 mode; (c) LG0,-1 mode.
The characteristics of the generated doughnut mode is measured. The output power as a function of pump power is shown in Fig. 4. Initially, the output laser beam shows a Hermite Gaussian HG01-like shape. LG0,+1 mode beam is obtained when the pump power is increased to ∼412 mW. From the experiment, we notice that both the spatial loss introduced by the defect spot and the astigmatism of thermal lens are important for the doughnut mode generation. Although the thermal lensing effect is weak at pump power lower than 1 W, the astigmatism due to different thermo-optic coefficients in the laser crystal will result in Gouy phase difference, which is helpful for the doughnut mode generation. Additionally, the tilted curved mirrors also bring in astigmatism inside the laser cavity, which may contribute to the generation of doughnut mode at low pump power range compared with the previously reported results [26,29]. At a pump power of ∼443 mW, continuous wave (CW) mode locking is achieved; while multi-pulse mode locking is observed when the pump power is higher than ∼515 mW.
Fig. 4. Laser output power as a function of the pump power. Yellow part: output laser beam with HG01-like shape; pink part: output laser beam with LG0,+1 mode; two dashed line indicates the mode locking and multi-pulse mode locking range respectively.
The temporal pulse trains of the soliton mode locked output laser at a pump power of 510 mW in a short period of 160 ns and long period of 200 μs are recorded and shown in Fig. 5(a) and (b). The pulse repetition rate is measured to be around 103.5 MHz. Figure 5(b), without any modulation, indicates a perfect CW mode locking condition without Q-switching. The laser spectrum is also recorded and shown in Fig. 5(c), which shows a bandwidth of 6 nm in FWHM (full-width at half-maximum). The autocorrelation trace is measured as around 460 fs and shown in Fig. 5(d), which corresponds to a pulse duration of 298 fs in FWHM if a sech2 shape pulse is assumed. The slightly larger time bandwidth product of ∼ 0.493 is due to the non-optimized GDD inside the laser cavity. Optimization of the intra-cavity GDD is not carried out further.
Fig. 5. Measured (a) oscilloscope trace of the mode locked pulses in a short period of 160 ns; (b) oscilloscope trace of the mode locked pulses in a long period of 200 μs; (c) laser emission spectrum; (d) measured autocorrelation trace.
Experimentally, we also try to amplify the LG0,+1 vortex beam by a 2 m long Yb-doped DCF amplifier (Yb1200-25/250DC), whose V-number at ∼1040 nm is ∼5.28 and which can support the propagation of doughnut shape LP11 mode. The fiber is loosely coiled with a diameter of roughly 460 mm to maintain high order transmission. Figure 6 (a) shows the intensity distribution of the amplified output beam, while Fig. 6(b) shows the intensity profile across the beam center. The distorted beam shape may come from the angle-cut fiber end. From Fig. 6(a) and (b), it is estimated that the measured profile corresponds to a superposition of approximately 75% LP11 mode and 25% LP01 mode. The unexpected excitation of fundamental LP01 mode may originate from the spatial distortion induced by the 8° angle of the input end facet of the fiber, when the doughnut-shaped beam is coupled into the fiber core [38]. The singularity of the amplified beam has also been checked by the CPRSI. A downward fork-shape stripe with one fork has been clearly observed, which confirms the feasibility of using few-mode fiber amplifier as power amplifier for OAM vortex beam. However the amplification of the LG0,-1 mode has not been realized in the experiment with unclear reason.
Fig. 6. Measured (a) intensity distribution of the amplified output beam; (b) the intensity profile across the beam center: -○- experimental results, — fitting curve; (c) interference pattern of the amplified output beam.
Figure 7(a) shows the output power as a function of the pump power. A 4 mW input seed beam is amplified to ∼500 mW at pump power of ∼5.26 W. Figure 7 (b) shows the spectrum of the amplified vortex beam when the pump power is 5.26 W, on which the modulation may come from the modes interference between LP01 mode and LP11 mode. No power saturation is observed in our experiments, which indicates further power scaling should be possible by using LD with higher power.
Fig. 7. Measured (a) Output power as a function of launched pump power; (b) Output spectrum after amplification at pump power of 5.26 W.
4. Conclusion
Direct generation of ultrafast vortex beam by employing a defect-spot mirror inside a SESAM mode locked Yb:KYW oscillator is simple and robust. The chirality of the output beam can be controlled by slightly tuning the laser crystal angle. Femtosecond vortex beam with a pulse duration of 298 fs at a repetition rate of 103.5 MHz has been realized. During the experiments, we have also shown the feasibility of power scaling of the generated vortex beam by using few-mode fiber amplifier. A maximum average power of ∼500 mW has been realized. This work may provide a simple and effective method to generate ultrafast vortex beam with controlled chirality. Next step, we plan to achieve direct generation of ultrafast vortex beam with higher OAM by optimizing the laser cavity configuration and the defect spot size.
Funding
National Natural Science Foundation of China (NSFC) (61605133); Sichuan Province International Cooperation Research Program, China (2016HH0033); Chengdu Science and Technology Program (2015-GH02-00021-HZ).
Acknowledgments
We would like to thank Mr. Toshio Otsu, Mr. Shota Kimura, and Dr. Dai Yoshitomi for their kind help in the experiments. We also would like to thank Dr. Shuntaro Tani for his helpful discussion.
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