Tunable 3 µm optical vortex parametric oscillator

We propose a tunable millijoule-level 3-µm vortex laser formed with a 1-µm ns vortex pulse-pumped quasi-phase matching MgO-doped periodically poled lithium niobate (MgO:PPLN) optical parametric oscillator with a singly resonant plane-parallel cavity configuration. The wavelength of the vortex output is tuned within the range of 3.360–3.677 µm merely by controlling the temperature of the MgO:PPLN crystal. The maximum vortex output energy of 2.14 mJ is obtained at the maximum pump energy of 21 mJ, and corresponds to an optical to optical conversion efficiency of 10.2% and a photon conversion efficiency of 33.5%. The handedness of the vortex output is controlled just by inverting the handedness of the pump vortex beam.


Introduction
Optical vortices carry a ring-shaped spatial form and an orbital angular momentum (OAM) of lħ per photon arising from a phase singularity and characterized by an azimuthal phase profile of e i'' (where φ is the azimuthal angle on a plane orthogonal to the direction of propagation of light and ' is the topological charge). [1][2][3][4][5][6] They have been widely investigated in many applications, such as optical trapping 7) and manipulation, 8,9) quantum information, 10) "super-resolution" microscopes with a high spatial resolution beyond the diffraction limit, 11,12) spatially multiplexing optical telecommunications with high data capacity, [13][14][15] and nonlinear spectroscopy. 16,17) In recent years, it has been further discovered that optical vortices twist materials, such as metal, silicon, and azo-polymer, to create chiral nano=micro structured materials. [18][19][20][21] The wavelength versatility of optical vortex sources is highly desired for the above-mentioned applications because this facilitates matching of the lasing frequency to the absorption bands of the materials being studied.
To generate optical vortices, a mode conversion technique from a conventional Gaussian beam to an optical vortex is mostly used by employing phase elements such as an azimuthally segmented spiral phase plate (SPP), 22) a q-plate, 23) or a spatial light modulator (SLM). 24) Such phase elements are typically designed for a specific laser wavelength, and hence, they inherently constrain the wavelength versatility of the optical vortex sources. Direct generation of optical vortex modes from a laser cavity by employing an annular beam pumping for the laser medium, a centrally damaged cavity, 25) a bounce laser with non-parabolic thermal lensing of the laser medium, 26) and a computer-designed laser with an SLM as a back cavity reflector, 27) is possible. In addition, it is capable of efficiently producing high power and high beam quality optical vortices; however, in this case, the optical vortex output lacks the wavelength versatility.
We and our co-workers have successfully developed a tunable, visible or near-infrared, vortex laser source based on an optical vortex pumped, LiB 3 O 5 (LBO) or KTiOPO 4 (KTP) optical parametric oscillator (OPO), [28][29][30][31][32] and a widely tunable 5-18 µm vortex laser source formed of the KTP-OPO in combination with a ZnGeP 2 or an AgGaSe 2 difference frequency generator. 33,34) Optical vortex sources in the wavelength region of 3 µm, in which water exhibits strong absorption owing to OHbonding, will find potential applications in various fields such as environmental optics, medical therapy, and organic materials processing. In fact, an optical parametric oscillator in a singly resonant folding ring cavity, in which the large astigmatism breaks the cylindrical symmetry of the cavity to prevent the vortex mode oscillation of the signal output, 35) has been demonstrated to generate continuous-wave (CW) 3-µm optical vortex. In addition, a femtosecond 3-µm optical parametric amplifier 36) has been reported.
However, nanosecond, 3-µm optical vortex sources with moderate (millijoule-level) pulse energy, which allow us to fabricate chiral structures of polymeric materials and develop "super-resolution" molecular spectroscopes, have not yet been established.
We report, for the first time, a nanosecond, millijoulelevel 3-µm optical vortex source formed from a 1-µm vortex pumped quasi-phase matching MgO-doped periodically poled lithium niobate (PPLN) OPO with a compact linear cavity. The lasing wavelength of the system was tuned within a wavelength range of 3.360-3.677 µm. The maximum vortex output energy was measured to be 2.14 mJ at the maximum pump energy of 21 mJ, which corresponds to an optical conversion efficiency of 10.2% and a photon conversion efficiency of 33.5%. The handedness control of the vortex output was further achieved just by inverting the handedness of the 1 µm pump vortex. Such a plane-parallel cavity configuration allows the development of a compact 3-µm vortex source by utilizing minimal cavity elements, i.e., two flat mirrors. Figure 1 shows a schematic diagram of our laser system. A conventional flash-lamped Q-switched Nd:YAG laser (Gaussian spatial form, pulse duration 25 ns, wavelength 1.064 µm, pulse repetition frequency 50 Hz) was used as the pump source. Its output was shaped to be a first-order optical vortex with a topological charge, l, of 1 by using a spiral phase plate azimuthally segmented into 16 segments with a nπ=8 phase shift (where n is an integer between 0 and 15). To invert the sign (handedness) of the topological charge, l, of the pump beam, the spiral phase plate was then reversed. The optical vortex pump beam was focused to be an annular spot with a diameter of 900 µm using a lens with a focal length of 750 mm, and the beam was directed toward the OPO. A 5 mol % MgO-doped PPLN crystal (MgO:PPLN) with dimensions 40 × 4 × 2 mm 3 and a grating period of 30 µm was used as a nonlinear crystal to avoid photorefractive damage and ensure a type-0 (e → e + e) phase-matching for 1.064 µm pumping. Its end facets were anti-reflection coated for 1.064, 1.53, and 3.5 µm wavelengths. The crystal was mounted in an oven to control its temperature within 30-200°C with an accuracy of 0.1°C.
The astigmatism in our system formed due to two flat mirrors might be negligible once the cavity is well aligned to lase. However, such the plane-parallel cavity with features of stable and unstable resonators will yield the higherorder mode (i.e., the vortex mode) with an infinite mode field size and provide significant diffraction loss in the vortex mode compared to the fundamental Gaussian mode, thereby preventing the signal from lasing at the vortex mode.
In fact, the parametric gain of the vortex mode is determined by the spatial amplitude overlap efficiency, η, of the hollow pump and signal vortex modes in the nonlinear crystal as given by the following formula where l (= 1) is the topological charge of the signal output, and ω p (∼ 0.5 mm) and ω s are the mode field sizes of the pump and signal beams, respectively. 34) Thus, the spatial overlap of the pump and signal vortex modes, which is inversely proportional to ! 2 s , will be significantly limited to nearly zero with an increase of the signal mode field size ω s . In contrast, the spatial overlap of the pump vortex and signal Gaussian modes ( ÀÀÀÀÀ! ! s )! p ffiffiffiffiffi ffi 2 p =! s ) decrease gradually and inversely with ω s , thereby yielding non-zero parametric gain of the Gaussian mode with l = 0. Thus, the plane-parallel cavity allows the topological charge of the pump beam to be transferred to the idler output. The resulting idler output should operate at the vortex mode. Sharma et al. demonstrated the selective control of OAM transfer from the pump to the resonant-signal or non-resonant idler by adjusting the spatial overlap between the resonant cavity mode and the pump beam by varying the physical separation of the cavity focusing mirrors. 37) This linear cavity configuration, enabling the unidirectional OAM transfer to the non-resonant idler, should allow the development of ultra-compact 3 µm vortex source by utilizing minimal cavity elements, i.e., only two flat mirrors.
The undesired signal beam was removed by employing an AR-coated filter with a high transmission of >95% for 3.5 µm. The spatial profile and wavefront of the idler output were observed using a pyroelectric camera (Spiricon Pyrocam III; spatial resolution: 75 µm).

Results and discussion
Figures 2(a)-2(f) show the spatial profiles and wavefronts of the pump, signal, and idler outputs at a crystal temperature of 125°C. The idler output (3.5 µm) then exhibited an annular spatial profile originated due to phase singularity, while the signal output (1.53 µm) had a Gaussian spatial profile without any phase singularities. As evidenced with a pair of downward and upward Y-shaped fringes with two legs obtained by self-referenced interferometer, the handedness of idler output was fully identical with that of the pump beam. 30) These above results indicate that the topological charge of the pump beam was selectively transferred to the idler output. The generated vortex beam exhibited a slightly asymmetric intensity profile arising from the spatial intensity profile of the pump beam (the flash-pumped laser exhibited spatial intensity fluctuation). Replacing the pump source with a diodepumped laser with high beam quality will improve the quality of the generated vortex beam further. Figure 3 shows the output energy of the OPO as a function of pump energy at a crystal temperature of 125°C. The wavelengths of the signal and idler outputs were 1.53 and 3.5 µm, respectively. The maximum vortex output energy of 2.14 mJ was obtained at maximum pump energy of 21 mJ, and it corresponds to the optical-optical conversion effi-   Moreover, note that the signal output energy was rather low (<0.21 mJ) even at the maximum pump level owing to very low out-coupling from the high-Q cavity for the signal output.
The wavelength of vortex output was tuned within the region of 3.360-3.677 µm by only controlling the PPLN crystal temperature as shown in Figs. 4(a) and 4(b). The measured tuning curve was well fitted with the one simulated employing Sellmeier equations. 38) Further, the spectrum bandwidths of the pump and idler outputs were estimated to be ∼10 GHz (∼0.03 nm) and >80 GHz (∼2.4 nm), respectively, by measuring the temporal coherence functions [ Fig. 4(c)]. Such a broadband vortex idler output was originated by relatively wide phase matching bandwidth of the PPLN.
The vortex output energy was then measured to be ∼2 mJ. The vortex output with a topological charge of 1 was generated within a wavelength region of 3.360-3.677 µm, as evidenced by the annular spatial form and pair of Y-shaped forked fringes (Fig. 5). These indicate that the singly resonant plane-parallel cavity configuration transfers the topological charge of the pump beam to the idler output selectively, thereby ensuring the tunable 3-µm optical vortex generation.
The wavelength tuning range was limited by the temperature dispersion and the grating period of the PPLN crystal and it will be further expanded by utilizing a PPLN crystal with multiple gratings 39) or fan-out grating. 40) When the SPP was reversed (the pump beam was lefthanded), the idler output was also left-handed, as evidenced by a pair of upward and downward Y-shaped fringes [ Fig. 6(d)].

Conclusions
In this study, we have developed, for the first time, a tunable millijoule-level 3-µm vortex source based on a 1-µm vortex pumped MgO-doped periodically poled lithium niobate (MgO:PPLN) optical parametric oscillator with a singly resonant linear plane-parallel cavity configuration, in which the topological charge of the pump beam was selectively transferred to the idler output. The maximum vortex output energy of 2.14 mJ was obtained at the maximum pump energy of 21 mJ and it corresponds to the optical-optical conversion efficiency of 10.2%. The handedness of vortex output was completely identical to that of the pump vortex beam. Further power scaling of the 3-µm vortex laser system with a simple linear cavity will be possible only by the improvement of the pumping system. Note that the wavelength tuning range of the system will be further expanded by utilizing a PPLN crystal with multiple gratings 38) or a fan-out grating. 39) A higher-order vortex output generation will also be possible by employing the SLM for modulating the pump wavefront.  The commercial SPP and SLM in the mid-infrared region have not been established well, hence, such tunable moderate energy 3-µm optical vortex sources will open the door to new generation technologies such as chiral organic materials processing, super-resolution molecular spectroscopy and environmental optics.