We generated tunable 2-μm optical vortex pulses with a topological charge of 1 or 2 in the wavelength range 1.953–2.158 μm by realizing anisotropic transfer of the topological charge from the pump beam to the signal output in a vortex-pumped half-symmetric optical parametric oscillator. A maximum vortex output energy of 2.1 mJ was obtained at a pump energy of 22.8 mJ, which corresponds to a slope efficiency of 15%. The topological charges of the signal and idler output were investigated using a shearing interferometric technique employing a low-spatial-frequency transmission grating.
© 2012 OSA
Optical vortices [1–5] exhibit unique characteristics including doughnut-shaped spatial profiles, helical wavefronts, and orbital angular momentum due to a phase singularity characterized by mη (where m is an integer known as the topological charge). They have been widely investigated and have been used in many applications including optical tweezers [6–8], super-resolution microscopes , quantum communication, information processing [10, 11], and spectroscopy [12, 13]. Optical vortex pulses with a non-zero total angular momentum (defined as the vector sum of the orbital and spin angular momenta) can also be used to inexpensively and rapidly fabricate chiral metal nanoneedles [14, 15], which have the potential to be used in applications such as nanoscale imaging systems, metamaterials, energy-saving field emission displays, plasmonic probes, and biomedical nanoelectromechanical systems. However, the optical vortices used in the above-mentioned studies generally have wavelengths in the near-infrared and visible regions [16–21]. Optical vortices in the mid-infrared region, in which many molecules have eigenfrequencies due to vibrational modes, have the potential to be used to investigate new aspects of molecular spectroscopy [22, 23] and organic material processing. In particular, tunable mid-infrared optical vortex sources are strongly desired for these applications.
We have successfully demonstrated 2-μm optical vortex output from a 1.064 μm optical vortex pumped optical parametric oscillator (OPO) . Orbital angular momentum sharing between signal and idler outputs then occurred.
However, the lasing wavelength of the output was fixed at 2.128 μm. There has been no report about tunable optical vortex sources in the mid-infrared region.
In this study, we present the first demonstration, to the best of our knowledge, of tunable, milli-joule-level 2-μm optical vortex output with a topological charge m of 1 or 2 in the wavelength range 1.953–2.158 μm. In this wavelength region, anisotropic topological charge transfer from the pump beam to the signal output due to mode dispersion of the Gouy phase shift and the walk-off effect of the KTP crystal occurs in a half-symmetric cavity.
2. Experimental setup
Figure 1(a) shows a schematic diagram of a KTiOPO4 optical parametric oscillator (KTP-OPO)  pumped by a 1-μm optical vortex. The OPO was pumped by a conventional Q-switched Nd:YAG laser (Lotis, LS-2136; pulse duration: 25 ns; wavelength: 1.064 μm; PRF: 50 Hz). The pump laser output had a nearly Gaussian spatial profile. It was converted into a first- or second-order optical vortex with a topological charge m of 1 or 2 by a spiral phase plate that was azimuthally divided into 16 segments with a nπ/8 phase shift (where n is an integer between 0 and 15) . Figures 2(a) and 2(b) show the spatial profiles of the optical vortex pump beam for m = 1 and 2, respectively. The loosely focused optical vortex was injected into the OPO, which contains a 5 × 5 × 30 mm KTP crystal cut at an angle of 51.4° relative to the z-axis for type II (ordinary wave (o-wave) → ordinary wave (o-wave) + extraordinary wave (e-wave)) phase matching . In degenerate down-conversion, the pump beam is down converted from 1.064 to 2.128 μm. The wavelength of the signal (or idler) beam output can be tuned by carefully controlling the phase-matching angle. The focused first (second)-order optical vortex beam produced a 520 μm (760 μm) spot on the KTP crystal. The KTP crystal faces are antireflection coated for 1.064 and 2.128 μm.
A resonator was formed from input and output mirrors with radii of curvature of 2000 and 100 mm, respectively. The input mirror (M1) has a high transmissivity and a high reflectivity at wavelengths of 1 and 2 μm respectively, while the output mirror (M2) has a reflectivity of 80% for 2 μm and a high transmissivity for 1 μm. The ~60-mm-long cavity was nearly half-symmetric and had a finite confocal length LR, which imparts a non-zero Gouy phase shift to laser modes during a round trip in the cavity.
Conservation of orbital angular momentum in second-order nonlinear processes  provides us a dilemma in an optical parametric down-conversion process, i.e., how does the orbital angular momentum of pump beam divide between signal and idler outputs?
As noted in previous studies [24, 29], we expected that the topological charge of the pump beam would be anisotropically transferred to the signal (or idler) output in this setup. The signal (o-wave) and idler (e-wave) outputs were separated by a polarizing beam splitter (PBS) and their spatial forms were imaged using a pyroelectric camera (Spiricon Pyrocam III; spatial resolution: 100 μm). To avoid undesired factors (walk-off, phase-matching acceptance etc..) in the up-conversion interferometric technique as related in our previous paper, we also investigated directly the wavefronts of the output beams by employing an amplitude transmission grating (multiple slit grating) with a low spatial frequency (10 lines/mm). As shown in Fig. 1(b), the signal (or idler) beam was diffracted by the multiple slit grating. The zeroth(0th)- and first(1st)-order diffracted beams were selectively filtered by a slit, and they were collected by a lens on the pyroelectric camera, thereby forming a self-reference interferogram. With this system, a pair of forked fringes with 2 (or 3) legs are observed at an observation plane when the signal (or idler) output has a topological charge of 1 (or 2) .
Figure 3(a) shows the output energy as a function of the pump energy when pumping using the optical vortex. When pumping with a first-order optical vortex, the maximum signal output energy was 2.1 mJ at the maximum pump level. The slope efficiency was 15% and the lasing threshold was 8.3 mJ. The energy of the idler output was approximately half (1.0 mJ) that of the signal output due to poor spatial mode overlap as a result of the walk-off effect , as discussed below.
When pumping with a second-order optical vortex, the maximum signal output energy was 0.58 mJ at the maximum pump level. This lower output energy is due to the second-order optical vortex having a larger focused spot on the KTP crystal than the first-order optical vortex. The slope efficiency was limited to 7.0% and the lasing threshold was 13.7 mJ.
Figure 4 shows the spatial profiles of the signal and idler outputs observed with a pyroelectric camera. The calculated self-interference patterns are also shown in Fig. 4 for comparison. The signal output exhibited an annular intensity profile due to a phase singularity (Fig. 4(a)), while the idler output had a Gaussian profile without a phase singularity (Fig. 4(d)).
The signal output exhibited a topological charge of 1, as evidenced by a pair of forked fringes with 2 legs (Fig. 4(b)). In contrast, the idler output had no phase singularity (Fig. 4(e)), indicating that the topological charge of the idler output was zero. The simulated patterns shown in Figs. 4(c) and 4(f) are of the self-interference patterns for topological charges of 1 and zero (i.e., no phase singularity). The simulated patterns coincide well with the experimental results, which confirms the topological charges of the outputs in the experiment.
These results demonstrate that the orbital angular momentum of the pump beam was selectively transferred to the signal output. The pulse energy of the first-order optical vortexoutput in this experiment was approximately four times higher than that (0.5 mJ) obtained in our previous experiment .
To confirm anisotropic topological charge transfer in which the topological charge of the pump beam is selectively transferred to the signal output from the pump beam, we also pumped the KTP-OPO by a second-order optical vortex. Figures 4(g)–4(l) show spatial profiles of the signal, idler outputs, and simulated patterns. The signal output exhibits an annular profile due to a phase singularity, whereas the idler output has a Gaussian profile without any phase singularity. The interferogram of the signal output also exhibits a pair of forked fringes with 3 legs, indicating that the signal output has a topological charge of 2. These results demonstrate that anisotropic topological charge transfer occurred from the pump beam to the signal output.
We also investigated the wavelength tunability of the 2-μm optical vortex output realized by controlling the orientation angle of the KTP crystal. The KTP-OPO was pumped by a first-order (or second-order) 1-μm optical vortex. Figure 5 shows the signal output power normalized by the signal output power at a lasing wavelength of 2.128 μm (degenerate case) as a function of the signal wavelength. Figure 6 shows the spatial forms and self-interference patterns of signal output from the first-order 1-μm optical-vortex-pumped OPO. A signal output with a topological charge of 1 was generated in the wavelength range 1.953–2.158 μm, as evidenced by the annular profile and the pair of forked fringes with 2 legs. These results demonstrate that anisotropic topological charge of the pump beam to the output permit tunable 2-μm optical vortex output to be generated without destroying the phase singularity. In the present experiments, the wavelength tuning range was limited by the bandwidth of the high reflection coating of the cavity mirrors and the antireflection coating of the KTP crystal.
Mode-order-dependent Gouy phase shift in the half-symmetric cavity will prevent topological charge sharing between the signal and idler outputs. The Gouy phase shift ϕm is given by, where Lc is the propagation length, LR is the confocal length of the cavity, and m is the mode order corresponding to the topological charge . The Gouy phase shift difference between the first-order optical vortex (m = 1) and Gaussian modes (m = 0) is estimated to be 2.3 rad for the signal output (o-wave); it prevents coherent coupling between the first-order optical vortex (m = 1) and Gaussian modes (m = 0), as found in our previous experiments based on a plane-parallel resonator . The pump and signal outputs have ordinary polarization. Therefore, we then neglected birefringence-induced astigmatism as related in Ref .
Furthermore, the walk-off effect due to the birefringence of the KTP crystal also induces a lateral displacement of the idler output in a half-symmetric cavity. As shown in Fig. 7(a) , the idler output ejected from the KTP crystal is directed toward the concave output coupler. The reflected idler output deviates slightly so that it is laterally displaced onto the KTP crystal. The spatial overlap η between the original and laterally displaced idler outputs is given byEqs. (1)–(3), η was plotted as function of Δd (Fig. 8 ). At any Δd, the spatial overlap for the optical vortex is significantly lower than that for the Gaussian output. When Δd = 200 μm estimated by the experimental parameters listed in Table 1 , the spatial overlap (0.27) for the optical vortex output was less than half that (0.55) for the Gaussian output The spatial overlap for the optical vortex output at an input face of the crystal (Δd’ = 440 μm) was also estimated to be ~1% (Fig. 7(b)), thereby preventing the idler output lasing at the vortex mode. In fact, many round trips in the cavity induce a further displacement so that any transverse modes are not permitted to be reproduced after one round-trip as shown in Fig. 7(b). And thus, efficient lasing of the idler output even in the Gaussian mode was prevented.
When pumping with the optical vortex with m>2, we believe that the orbital angular momentum will be also transferred selectively to the signal output.
We have demonstrated tunable (1.953–2.158 μm), milli-joule-level 2-μm optical vortex output generation from an optical-vortex-pumped OPO with a half-symmetric cavity configuration for the first time. The topological charge of the pump beam is transferred to the signal output. Signal outputs with topological charges of m = 1 and 2 had pulse energies of 2.1 and 0.58 mJ at maximum pump energies of 22.8 and 21.8 mJ, corresponding to slope efficiencies of 15 and 7%, respectively. The idler output had no phase singularity and its pulse energy was limited to less than half that of the signal output due to the poor spatial mode overlap due to the walk-off effect. This anisotropic topological charge transfer from the pump beam to the signal output is due to a mode-order-dependent Gouy phase shift.
The authors acknowledge support from a Grant-in-Aid for Scientific Research (No. 24360022) from the Japan Society for the Promotion of Science.
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