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We demonstrated widely tunable mid-infrared (6.3–12 μm) optical vortex pulse generation from a ZGP difference frequency generator pumped by a 2 μm optical vortex laser with a cascaded KTP geometry. The mid-infrared vortex output carried the same topological charge as that of the 1 μm pump output without any destruction. A pulse energy of >135 μJ was obtained in the wavelength region of 6.3–7.0 μm.
© 2014 Optical Society of America
1. Introduction
Optical vortices [1–5], which exhibit an axial dark core and orbital angular momentum characterized by mħ (where m is an integer termed the topological charge) originating from a phase singularity, have been intensely studied in a variety of research fields, such as quantum information [6–8], space division multiplexing [9,10], optical manipulation [11–13], super-resolution microscopy [14–16], exciton spectroscopy [17,18], optical cloaking [19], and materials processing [20, 21]. Recently, optical vortex laser nano-fabrication, in which chiral structures on a nano-scale are formed, has also been demonstrated [22–24]. These applications require that optical vortices will be available with a wide range of frequencies, so as to match the absorption bands of target materials. Most studies of optical vortices have focused on the near-infrared [25–28] and visible [29] regions.
However, there have been no reports on optical vortices in the mid-infrared (5–20 μm) region, which includes the eigen-frequencies for numerous molecules. This is because conventional phase modulation devices, e.g. spiral phase plates and spatial light modulators, do not cover the mid-infrared. The study of moderate-energy mid-infrared vortex pulses promises to open up a new generation of molecular technologies, such as super-resolution molecular spectroscopy and chiral organic materials processing.
To date, we have successfully demonstrated millijoule level 2-μm vortex pulse generation from a 1-μm vortex pumped KTiOPO4 (KTP) optical parametric oscillator (termed a 2-μm vortex laser) [30, 31]. This system, in which the vortex signal and Gaussian idler pulses are produced in the frequency range of 1.9–2.2 μm, can readily be extended to generate tunable mid-infrared vortex pulses by a conventional difference frequency generation (DFG) technique.
In this paper, we propose a novel 2-μm vortex laser with a cascaded KTP geometry for generation of collinear vortex signal and Gaussian idler beams. Furthermore, to the best of our knowledge, we present the first demonstration of widely tunable mid-infrared (6.3–12 μm) vortex pulses by combining the 2-μm vortex laser with a nonlinear crystal zinc germanium phosphide (ZGP) by difference frequency generation. The mid-infrared vortex output carries the same topological charge as that of the signal output from the 2-μm vortex laser. Its pulse energy was measured to be >135 μJ within the wavelength region of 6.3–7.0 μm.
2. 2-μm optical vortex laser
As stated in our previous publications [31, 32], the idler output (extraordinary wave) is laterally displaced from the signal output by walk-off effects of the KTiOPO4 (KTP) crystal, resulting in non-collinear output coupling of the signal and idler. Thus, the signal and idler outputs must be weakly focused onto the nonlinear ZiGeP2 (ZGP) crystal, so as to yield non-collinear spatial overlap between the signal and idler outputs for the DFG as shown in Fig. 1(a). The difference frequency output can be written in Cartesian coordinates as the following formula,
where θ is the half angle between the signal and idler outputs, L is the length of the nonlinear crystal, EDFG, Es, and Ei are the electric fields of the difference frequency, the signal and idler outputs, respectively.
Fig. 1 (a) Non-collinear phase matching in difference frequency generator. (b), (c), (d) Simulated beam profiles of the DFG output at θ = 0, 4mrad, and 8mrad, respectively. 2ω0 and L were fixed to be 800 μm, and 20 mm, respectively.
Assuming that the signal and idler outputs exhibit the first-order vortex and Gaussian spatial profiles, Eq. (1) can be expressed as the following,
where ωs and ωi are the beam waists of the signal and idler outputs, respectively. The spatial intensity profile IDFG of the difference frequency output is then given bySuch non-collinear phase matching between the signal and idler outputs will break the cylindrical symmetry and degrade the purity of the vortex output. In fact, simulating intensity profile IDFG using 2ω0 = 800 μm, L = 20 mm, and θ = 4 mrad, as described in Figs. 1(c) and 1(d), exhibits lateral displacement of the phase singularity, indicating a mixed mode formed by the superposition of a Gaussian and first-order vortex modes. To generate high quality mid-infrared vortex output, the lateral displacement of the idler output arising from the walk-off effects of KTP should be cancelled out, so that collinear phase matching for the DFG is maintained.The conservation law of topological charges, ms, mi, and mDFG, of the signal, idler, and difference frequency photons, also requires the general relationship mDFG = ms-mi. The topological charge, mi, of the idler output without phase singularity was 0. Thus, the relationship, mDFG = ms, can be established.
Figure 2 shows a schematic diagram of the experimental setup. A 2-μm vortex laser was formed from a 1-μm vortex pumped KTP optical parametric oscillator with a stable cavity configuration. The cavity was composed of a concave input mirror (M1) with a curvature of 2000 mm and high transmissivity and high reflectivity for 1-μm and 2-μm wavelengths, respectively; a flat output mirror (M2) with a reflectivity of 50% for 2 μm and high transmissivity for 1 μm. The cavity length was ~80 mm. With this setup, the topological charge of the pump beam is expected to be selectively transferred to the signal output (ordinary wave) arising from the walk-off effects in the KTP crystal, as stated in our previous study [32].
Fig. 2 Experimental setup for tunable mid-infrared (6.3–12 μm) optical vortex generation using ZGP difference frequency generator pumped by a 2-μm optical vortex laser.
Two KTP crystals (12 × 9 × 27 mm, 53° cut to the z-axis for type II phase matching), mounted on computer controlled Galvano stages, were cascaded inside the cavity. To compensate for the lateral displacement of the idler output (extraordinary wave) arising from the walk-off effects [30], the second KTP crystal was rotated against the first KTP crystal. In the present setup, the effective lateral displacement of the idler output was estimated to be < 1/500 of that (~1.2 mm) obtained in our previous setup without the cascaded KTP geometry, thus allowing collinear phase matching to be achieved for the DFG.
This cavity geometry also enabled us to tune the wavelengths of the signal and idler outputs within wavelength ranges of 1.8–2.1 μm for the signal and 2.6–2.1 μm for the idler. The KTP crystal faces had antireflection coatings for 1–2.5 μm.
The pump laser used was a conventional Q-switched Nd:YAG laser (Lotis, LS-2136; pulse duration: 25 ns; wavelength: 1.064 μm; PRF: 50 Hz; nearly Gaussian spatial form). Its output was converted into a first-order optical vortex with a topological charge of m = 1 by a spiral phase plate azimuthally divided into 16 segments with nπ/8 phase shift (where n is an integer between 0 and 15) [33]. The spatial form of the pump beam is shown in the inset of Fig. 2. The pump beam was delivered onto the KTP crystal as a spot with a diameter of ~450 μm.
As shown in Fig. 3, the maximum energies of the signal (1949 nm) and idler (2339 nm) outputs were measured to be 3.5 mJ and 2.5 mJ at a pump energy of 31 mJ, respectively. The slope efficiencies of the signal and idler outputs were also estimated to be 14% and 8%, respectively.
The signal output had an annular intensity profile owing to the phase singularity. Its wavefront was further analyzed using a self-referenced interferometric technique [31] with a pyro-electric camera (spatial resolution of 100 μm). A pair of Y-shaped fringes, as shown in Fig. 4(b), demonstrated that the signal output was a first-order optical vortex. In contrast, the idler output exhibited a Gaussian profile without phase singularity. These results indicate that the topological charge of the pump beam was selectively transferred to the signal output.
Fig. 4 (a) Spatial profile and (b) wavefront of the signal (1.83 μm) output. (c) Spatial profile and (d) wavefront of the idler (2.54 μm) output.
Figure 5 indicates that the lasing wavelength of the signal and idler outputs ranged within 1820–1954 nm and 2561–2335 nm, respectively. The wavelength tunability was limited by the high reflection coating of the cavity mirrors.
Without the cascaded KTP geometry, the wavelength tunability of the signal and idler outputs was limited to 1923–1955 nm and 2376–2335 nm by the low parametric gain as well as the lateral displacement of the idler output arising from the walk-off effects. The experimental energies of the signal (1949 nm) and idler (2339 nm) outputs were also limited to 1.2 mJ and 1.0 mJ respectively at a pump energy of 31.4 mJ.
3. Difference frequency generation
The signal and idler outputs, propagating collinearly from the 2-μm vortex laser, were delivered as a 2-mm spot onto an un-coated ZGP crystal with dimensions of 10 × 10 × 7 mm for DFG [34].
The ZGP crystal allowed us to achieve collinear Type-I phase matching (o-e→e) [35], and careful adjustment of its orientation angle tuned the lasing wavelength of the difference frequency output in the range 6.3–12 μm. A Ge filter was used to remove the undesired 2- and 1-μm outputs, thereby selectively obtaining the difference frequency output. Spatial displacement of the phase singularity arising from walk-off effects in the ZGP crystal will degrade the beam quality of the difference frequency output. However, in this setup the expected spatial displacement (~130 μm) was much smaller than the beam size (2 mm) of the signal (or idler) output, resulting in almost negligible degradation due to spatial displacement effects.
The difference frequency output with an annular spatial profile in the near- and far-fields exhibited a topological charge of 1, which was the same as that of the signal output, as shown in Figs. 6(a) and 6(b). The signal and idler outputs had wavelengths of 1949 nm and 2339 nm, corresponding to a difference frequency of 11.7 μm. The pulse energy of the difference frequency output was measured to be 33.4 μJ.
Fig. 6 Spatial forms of the difference frequency output (11.7 μm) in the (a) near- and (b) far-fields and (c) wavefront of mid-infrared output. Spatial forms of the 11.7 μm output in the (d) near- and (e) far-fields from the previous 2 μm laser without a cascaded KTP geometry.
In contrast, the difference frequency output generated by using the previous 2-μm vortex laser without the cascaded KTP geometry shows the lateral displacement of phase singularity owing to the superposition of an undesired Gaussian and first-order vortex modes, as described in Figs. 6(d) and 6(e). The π/2 azimuthal rotation of the phase singularity between the near and far fields also results from Gouy phase shift dispersion between the Gaussian and the first-order vortex modes. The non-collinear phase matching further impacts the effective spatial overlap between the difference frequency, signal and idler outputs, limiting the difference frequency output energy to 3.5 μJ.
The above experimental results are well consistent with simulations. Thus, a 2 μm vortex laser with a cascaded KTP geometry enables collinear output coupling of the vortex signal and Gaussian idler outputs, thereby producing high-quality mid-infrared vortex output with high efficiency.
As shown in Fig. 7(a), the lasing wavelength of the mid-infrared vortex output was tuned in the range 6.3–12 μm without any degradation of beam quality. The tuning range was limited by the transmission window of the Ge filter and the wavelength tunability of the 2 μm vortex laser. The maximum pulse energy of the 6.5 μm output was measured to be 160 μJ at the pump energy of ~4.6 mJ, corresponding to a conversion efficiency from the 2 μm output to the 6.5 μm output of 3.5%. Figure 7(b) shows the pulse energy of the 6.5-μm output as a function of the total energy (2 μm pump energy) of the 2 μm signal and idler outputs. The 6.5 μm pulse energy was almost proportional to the square of the 2 μm pump energy, resulting from the second-order nonlinear frequency conversion. Finally, a vortex pulse with an energy of >135 μJ was also generated in the wavelength region of 6.3–7.0 μm. The pulse width of the vortex pulse was typically measured to be 11 ns.
Fig. 7 (a) Experimental energy plots of the mid-infrared vortex output normalized by the 6.5μm vortex output energy. (b) 6.5 µm vortex output energy versus 2 µm vortex energy. Insets show spatial profiles and lasing spectrum of the 6.5 μm vortex output.
4. Conclusion
We have demonstrated widely tunable mid-infrared (6.3–12 μm) optical vortex pulse generation from a 2 μm optical vortex laser in a cascaded KTP geometry pumped ZGP difference frequency generator. The topological charge of the 1 μm pump output was transferred to the mid-infrared vortex output without any destruction. The vortex output with a pulse energy of >135 μJ was generated in a wavelength region of 6.3–7.0 μm.
Further energy scaling of the system will be possible by optimizing the focusing optics for difference frequency generation including anti-reflection coating on the ZGP crystal surface for 2–12 μm.
Acknowledgments
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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