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We report on a millijoule level Er:YAG ceramic pulsed vortex laser resonantly pumped by an annular beam at 1532 nm. By means of an uncoated YAG crystal plate inserting into the cavity and a proper thermal gradient on the ceramic, 1.03 mJ LG0,-1 mode and 0.97 mJ LG0, + 1 mode were respectively produced, and no vortex mode instability problem was observed. We believe the directly generated millijoule level optical vortex with well–defined helicity will have potential applications in material modification and processing, high-field laser physics, and nonlinear optics, etc.
© 2016 Optical Society of America
1. Introduction
Vortex lasers characterized by helical phase front and donut-shaped intensity profile, carry orbital angular momentum (OAM) of lħ per photon [1], where l is the topological charge number, and have been widespread investigated in areas including optical trapping and manipulation of particles [2,3], improving channel capacity in classical [4] and quantum communications [5], etc. The Laguerre–Gaussian (LGpl) laser mode with zero radial order (p = 0) but nonzero azimuthal order (l≠0) is a typical optical vortex, and has spurred widespread interest in recent decades. Common methods used for creating this LG0l mode include “fork” grating [6], spiral phase plate [7], liquid-crystal spatial light modulators [8], and mode converter [9], etc., and generally suffer from drawbacks of power handling limitation, low damage threshold, and high production cost. Recently, direct generation of LG0l beam in a solid-state laser resonator with annular pump is in the spotlight of scientific interest due to its simple cavity structure, power scalability, and excellent beam quality [10–15]. For this method, its principle is the selection of transverse mode, since the laser mode which matches well with the annular pump beam will firstly oscillate in the resonator [10]. During the lasing process, we have found that topological charges of the generated optical vortex is changeable from l = 1 to l = 2, driven by thermal-induced lens at high pump level [11,13]. Most recently, people find that doughnut laser beam maybe not a real LG0l mode but an incoherent superposition of two petal beams [16], even if it is a real LG0l beam, it is the general superposition of LG0,+l mode and LG0,-l mode in an identical resonator [12], and so, it has zero average orbital angular momentum. Therefore, it is necessary to discriminate the LG0,+l and LG0,-l beams that characterized by opposite orbital angular momentum [12,17] but identical transverse intensity distribution in a solid–state resonator. Moreover, for now, the bulk of the work with direct generation of LG0l beams has been focused on the continuous wave (cw) operation and 1 µm lasers. Pulsed vortex lasers with high single pulse energy are relatively scarce, and which are considered to be potentially useful for material nanostructure processing [18], high-field laser physics [19], nonlinear frequency conversion [20], and supercontinuum generation [21].
In this letter, vortex pulses at 1645 nm are directly generated in an Er:YAG ceramic solid-state resonator resonantly pumped by an annular beam at 1532 nm. The pure LG0, + 1 and LG0,-1 modes optical vortex are successfully produced with the help of an uncoated YAG crystal plate and proper thermal gradient on the ceramic. The generated 1.03 mJ LG0,-1 mode laser and 0.97 mJ LG0, + 1 mode laser will have potential applications in material modification and processing. After further investigating the characteristics of the optical vortex, we found that the stable LG0, + 1 and LG0,-1 modes oscillated at different wavelengths and had different output laser intensities.
2. Experiment setup
The experimental setup used to directly generate pulsed vortex laser is shown in Fig. 1. The annular pump beam was obtained by reshaping the Gauss beam from a fiber-coupled laser diode (LD) with a central hollow (4 mm diameter) plane mirror M, and the transfer efficiency is about 70%. Then the 1532 nm annular beam was focused onto Er:YAG ceramic with the focal spot size of inner radius 123 µm and outer radius 300 µm. The confocal parameter of the annular pump beam was calculated to be 22.4 mm, which was long enough to cover the whole gain region. The dimension of the 1.0 at.% Er:YAG ceramic is 2 mm × 3 mm × 15 mm, and its end faces are anti-reflective coated at 1500–1700 nm. In order to obtain the LG0l mode but not TEM00 mode, a designed plane-concave cavity in which the LG0l mode matches well with the annular pump beam [22], was employed in this experiment. The input mirror M1 is high-transmission (HT, T>95%) coated at 1532 nm and high-reflective (HR, R>99.8%) coated at lasing wavelength. The output coupler M2 with R = 200 mm (or 100 mm) curvature radius has a transmission of 10% at 1500–1700 nm. An acousto–optic (A–O) Q–switch, used for pulsed operation, is high-transmission coated at 1500–1700 nm, and both Er:YAG ceramic and A–O Q–switch are water-cooled at 17 °C. An uncoated YAG crystal plate with dimensions of Φ25.4 mm × 1 mm is used as handedness selector. The generated vortex beam and its interferences pattern from the homemade Mach–Zehnder interferometer are recorded by a mid-infrared CCD (Xeva–1.7) camera.
Fig. 1 Experimental setup used to excite and characterize the pulsed vortex lasers, inset is the schematic diagram of the produced interferences patterns with different tilt angles of YAG plate.
3. Results and analysis
Without the A–O Q–switch, the laser preferentially operated in cw regime, and the resonator with 4 cm long and R = 200 mm output coupler was selected to generate the desired LG0l beam. Figure 2(a) shows the experimentally recorded transverse-mode pattern when the output power is optimized to its highest power level. The beam profile with an unclear center but bright outer ring indicates that LG0l mode has matched with annular pump beam, but is strongly affected by thermal lens effect [11,22]. Then we adjusted the focal position in the transverse section of the Er:YAG ceramic to increase thermal gradient, since proper thermal lens is helpful for LG0l mode generation [11,13]. As observed in Figs. 2(b)–2(e), the output transverse mode profiles are much different when moving the focus position in the transverse section of the ceramic, and a clear donut shaped intensity profile in Fig. 2(d) is indicative of a pure LG0l mode. When the pump was focused on the edge of the ceramic, as shown in Fig. 2(e), a higher-order mode was observed. The underlying mechanism is that overloaded thermal gradient gives rise to serious thermal lens, which reduces the sizes of oscillating modes and makes the higher-order mode match well with pump beam [13,23]. Thereafter, we fixed the focus position as shown in Fig. 2(d), and further checked the helical phase of the generated LG0l mode with a home-made Mach–Zehnder interferometer. The interference pattern of LG0l mode with spherical reference beam (obtained by an aperture and convex lens, as shown in Fig. 1) was unstable, which mainly included three intensity patterns: spiral pattern with left-handedness, disordered state, and spiral pattern with right-handedness. We may recognize that LG0l modes with l = + 1 and l = –1 are either simultaneously oscillating or randomly fluctuating between them, and so have zero average OAM.
Fig. 2 Relative focus transverse position of pump beam on the Er:YAG ceramic and the corresponding output mode profile.
Based on the propagation dynamics of Laguerre–Gaussian modes in the standing-wave cavity, the electric-field distribution for LG0, ± 1 mode can be written as [17]:
where A(r) is the complex function describing the distribution of the field amplitude, ω is angular frequency, k is wavenumber, and φ is azimuthal angle. One can expect that standing-wave of the LG0, + 1 and LG0,-1 modes are two-lobed transverse intensity distribution at a fixed position, and they rotate by 2π radians in the opposite directions, respectively, after spreading one wavelength. Therefore, we may recognize that the directions of Poynting vector for the linearly polarized two LG modes are different but spiral along z axis synchronously [1,17], which implies that different transmission loss can be induced by Fresnel reflection [12]. Thus, if the output LG beams are linear polarization, a tilted YAG crystal plate could be expected to distinguish two modes and produce remarkably pure and stable LG01 mode with well-determined handedness.
In order to produce pulsed vortex laser beam, the cavity was stretched to 9 cm and an A–O Q-switch was inserted, as shown in Fig. 1. An output coupler with 100 mm curve radius was used to satisfy the best mode-matching conditions between annular pump beam and LG01 mode. Then we adjusted the ceramic position to obtain a donut shaped laser beam, just like the intensity profile shown in Fig. 2(d). With a Glan–Taylor prism, we observed that the laser was elliptical polarization and the intensity ratio of long axes to short axes was 14.6:1, which was close to linear polarization and could be attributed to the thermal birefringence effect [24,25]. Thereafter, the expected pure LG0, + 1 (or LG0,-1) mode was successfully obtained when we tilted the YAG plate to 3.4° (or −3.2°). The experimentally recorded transverse intensity profile of two modes is shown in Figs. 3(a) and 3(b), respectively. When passing the beam through a home-made Mach–Zehnder interferometer, the interference patterns with clear spiral structure were observed and as shown by Figs. 3(c)–3(d). After about twenty minutes, the spiral structure was still stable and clear, which revealed that helicity control mechanism based on appropriate thermal gradient and Fresnel loss that introduced by the uncoated YAG plate was robust and effective. Hence, we may surmise that some underlying selection mechanism based on the intrinsic anisotropy of refraction index and stimulated emission cross-sections in low symmetry laser medium may be developed to control the wavefront handedness, just as in the case of the Nd:LYSO monoclinic crystal [11,26].
Fig. 3 (a) and (b) are the experimentally recorded transverse intensity profiles of the pulsed LG0, + 1 and LG0,-1 beam, respectively. (c) and (d) are the corresponding interference patterns.
When the output laser was fixed in a LG0,-1 mode, the mean output power was measured at pulse repetition frequency (PRF) of 1 kHz and 5 kHz. As described in the inset in Fig. 4 (left), the lasing efficiency at 5 kHz was as expected better than that at 1 kHz, a maximum mean output power of 1.21 W was obtained, corresponding to a slope efficiency of 17%. The relatively low efficiency (45% lower than that without the YAG plate) was attributed to the large insert loss introduced by the tilt of YAG plate and its uncoated surface. In the experiment, no vortex mode instability problem was observed even under the highest pump power level, which indicated that the thermal driven higher-order mode generation did not work in present experiment [13], since the high quantum efficiency of resonant pumping scheme. Even so, generation of higher-order LG beams is possible by reducing the laser waist, sucn as redesign of the laser cavity [22] or further increasing the theraml lens [11]. Figure 4 (left) shows the single pulse energy of the vortex laser at PRF of 1 kHz, the largest single pulse energy is 1.03 mJ for LG0,-1 mode, and 0.97 mJ for LG0, + 1 mode. We believe this directly generated millijoule level vortex laser with well-defined helicity will have potential applications in material modification and processing [18]. Thereafter, the temporal behaviors of the pulsed vortex laser were recorded by a high-speed photoelectric detector and a 1 GHz bandwidth digital oscilloscope (Tektronix Inc). Figure 4 (right) shows the typical pulse train at PRF of 1 kHz, for the LG0,-1 laser mode, the uniform time interval between adjacent pulses and the orderly queue on the train imply the stability of the oscillating laser mode. The pulse profile of the LG0,-1 laser mode is shown in the inset, 50 ns pulse width at the maximum mean output power producing 20 kW peak power.
Fig. 4 Left: single pulsed energy of LG0, + 1 and LG0,-1 mode at PRF of 1 kHz, inset is average output power of LG0,-1 mode versus pump power, at PRF of 1 kHz and 5 kHz, respectively. Right: typical pulse train of LG0,-1 mode at 1 kHz PRF, inset is the corresponding single pulse profile with 50 ns pulse duration.
To further investigate the characteristics of the generated pulse vortex lasers, we measured the output laser spectra using a high-resolution (0.02 nm) optical spectrum analyzers (OSA, AQ6370C, YOKOGAWA), and the results are shown in Fig. 5. Comparing to the situation that without YAG plate in the cavity, laser spectra of pure LG modes are dramatically narrowed, which indicates that the YAG plate serving as an etalon has worked. The full width at half maximum (FWHM) of both LG0, + 1 and LG0,-1 laser mode are 0.04 nm, i.e., three longitudinal modes in our laser cavity. Few oscillated longitudinal modes in standing-wave cavity are helpful for producing stable and pure vortex [12], that is why no mode instability problem was observed as previously described. As shown in Fig. 5, peak wavelengths of LG0, + 1 and LG0,-1 laser modes are 1645.26 nm and 1645.31 nm, respectively. The small discrepancy was caused by the different tilt angle of the YAG plate, and the different emission intensity of the two LG beams was attributed to the different stimulated emission cross-sections at these two wavelengths and the different tilt angle of the YAG plate.
4. Conclusions
In summary, millijoule level 1645 nm pulse vortex was directly generated in an Er:YAG ceramic solid stated laser, pumped by an annular beam at 1532 nm. Control of vortex helicity was successfully realized based on thermal birefringence effect and Fresnel loss, which were introduced by appropriate thermal gradients and an tilted YAG crystal plate, respectively. Finally, 1.03 mJ pulse vortex in LG0,-1 mode and 0.97 mJ in LG0, + 1 mode were respectively achieved at the PRF of 1 kHz. We believe this directly generated millijoule level vortex laser with well-defined helicity will have potential applications in material processing. After further investigating the spectrum characteristics, we found that stable propagation of LG0, + 1 and LG0,-1 modes were located at 1645.26 nm and 1645.31 nm, respectively.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (No. 61505072), Natural Science Foundation of Jiangsu Province, China (No. BK20150240), and Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 15KJB510009).
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