1. Introduction

Optical vortices [1–4], which have intriguing features such as a doughnut-shaped spatial profile, a helical (twisted) wavefront, and orbital angular momentum characterized by $L\hslash$ (where L is an integer called the topological charge) due to a phase singularity, have been actively investigated for many applications such as optical tweezers [5–7], super-resolution microscopes [8–10], and spectroscopy [11]. In particular, we have demonstrated laser ablation [12] and micro-needle fabrication using optical vortices having specific values of the total angular momentum (sum of the orbital and spin angular momenta) [13].

To date, the conservation of orbital angular momentum of an optical vortex has been demonstrated in nonlinear frequency conversion processes such as second harmonic generation (SHG) [14-15] and sum-frequency generation [16-17]. Anisotropic transfer of orbital angular momentum to the idler (or signal) output has been reported in a continuous-wave optical parametric oscillator in the visible region [18]. Smith et.al. have reported the direct production of optical vortex from the rotated image singly-resonant twisted-rectangle cavity [19]. However, those experiments only investigated the existence of a conservation law of orbital angular momentum or mode conversion of Gaussian pump beam to the vortex signal (or idler) output, in nonlinear frequency conversion processes. They did not explore the generation of a fractional vortex output having half-integer topological charge, nor measure quantitatively the output energy and power of the frequency-converted vortices.

Furthermore, they did not generate mid-infrared optical vortices, which can potentially lead to new generations of molecular spectroscopy and organic material processing.

In this study, 0.5-mJ 2-μm fractional vortex pulses of half-integer topological charge are produced for the first time from a mid-infrared optical parametric oscillator pumped by 1-μm optical vortices. The generation of 0.24-mJ mid-infrared vortex pulses with a topological charge of 1 is also demonstrated.

2. Experimental results

2.1 Setup

The experimental setup of the mid-infrared optical parametric oscillator pumped by 1-μm optical vortex pulses is sketched in Fig. 1 . The pump laser is a conventional flashlamp Q-switched Nd:YAG laser (Lotis LS-2136) with a wavelength of 1.064 µm and a pulse duration of 45 ns at a repetition rate of 50 Hz. Its collimated output has a Gaussian profile and is delivered to a spiral phase plate (SPP) azimuthally divided into 16 parts with an nπ/8 phase shifter (where n is an integer between 0 and 15) [20]. It is converted into an optical vortex (OV₁) with a topological charge L of 1. Next the output is converted into a second optical vortex (OV₂) having a topological charge L of 2 by using two overlaid SPPs. The optical vortices, exhibiting the annular spatial form shown in Fig. 2 , are used to pump an optical parametric oscillator [21] consisting of a KTiOPO₄ (KTP) crystal into which they are focused. The crystal has dimensions of 5 × 5 × 30 mm, cut at θ = 51.4° relative to the z-axis normal for type II (o-wave → o-wave + e-wave) phase matching in degenerate downconversion from 1.064 to 2.128 µm. The crystal faces are anti-reflection coated at 1.064 and 2.128 µm. The oscillator consists of a flat input mirror M₁ with high reflection (R = 98%) at 2.128 µm and high transmission (T = 90%) at 1.064 µm, and a flat output mirror M₂ with 80% reflection at 2.128 µm and high transmission at 1.064 µm.

 

Fig. 1 Experimental setup for a mid-infrared KTP OPO pumped by a 1-μm vortex beam.

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Fig. 2 Spatial profiles of the 1.064-μm vortex output for (a) OV₁, and (b) OV₂.

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2.2 Laser performance

Figure 3 panels (a) and (b) plot the output energy measured from the optical parametric oscillator as a function of the pump energy. For OV₁ pumping, the lasing threshold is found to be 11 mJ, and a maximum signal energy of 0.5 mJ is obtained for maximum pumping. The temporal width of the signal output is typically 31 ns, as shown in panel (c). The lasing spectrum of signal output is also shown in panel (d). The idler energy of 0.41 mJ is nearly identical with the signal energy because of the frequency degeneracy. On the other hand, OV₂ pumping results in a higher lasing threshold (13 mJ) and smaller output energy (0.24 mJ) compared to OV₁ pumping, because OV₂ has a larger beam propagation factor (M ²≈3) than does OV₁ (M ²≈2). Spatial forms of the signal and idler outputs observed with a pyroelectric CCD camera (Spiricon PyrocamIII) are shown in Fig. 4 .

 

Fig. 3 Characteristics of the output vortices: energies per pulse pumped by (a) OV₁ and (b) OV₂; (c) temporal evolution of the signal output, and (d) lasing spectrum of the signal output.

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Fig. 4 Spatial profiles of (a) the signal output pumped by OV₁, (b) the signal output pumped by OV₂, (c) the idler output pumped by OV₁, and (d) the idler output pumped by OV₂.

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To investigate the wavefront of the signal output, the interferometric fringes formed by a frequency-doubled signal beam and its plane reference beam are analyzed. The 2-μm pyroelectric CCD camera has poor spatial resolution (~100 μm) which limits the accuracy of the interferometric measurements. To overcome this limitation, the signal output is frequency-doubled using another KTP crystal (for type-II phase-matching) with dimensions of 10 × 10 × 20 mm, cut at θ = 53° and φ = 0° relative to the z-axis normal. A conventional silicon CCD camera can then be used. The spatial forms and wavefronts of the doubled signal output are shown in Fig. 5 .

 

Fig. 5 Spatial profiles and wavefronts of the frequency-doubled signal output: SHG profiles pumped by (a) OV₁ and (b) OV₂; panels (c) and (d) show the interference patterns corresponding to panels (a) and (b), respectively.

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For OV₁ pumping, the signal output for ordinary polarization shows a radial opening in its profile in Fig. 4(a), while its second harmonic exhibits a complete doughnut shape with a topological charge of 1 in Fig. 5(a) and forked fringes in Fig. 5(c). The signal output is thus a fractional optical vortex [22–24] with half-integer topological charge. For OV₂ pumping, the signal output for ordinary polarization has a doughnut-shaped profile in Fig. 4(b) due to a phase singularity. The frequency-doubled signal output has a doubled topological charge in Fig. 5(b), as evidenced by the two forked fringes in Fig. 5(d), although a slight spatial separation of the vortices due to walk-off is seen.

In contrast, the idler output for extraordinary polarization looks a slightly distorted Gaussian profile without a phase singularity, as depicted in Figs. 4(c) and 4(d). We also measured the wavefronts of the frequency-doubled idler output. Owing to walk-off effects [25], the phase singularity displaces spatially toward the margin of the spatial intensity profile of the idler output, resulting in that the topological charge of the idler output looked to disappear. The idler outputs for OV₁ and OV₂ pumpings have also topological charges of 0.5 and 1, respectively, as evidenced by a forked fringe and two forked fringes (Fig. 6(c) and 6(d)).

 

Fig. 6 Spatial profiles and wavefronts of the frequency-doubled idler output: SHG profiles pumped by (a) OV₁ and (b) OV₂; panels (c) and (d) show the interference patterns corresponding to panels (a) and (b), respectively.

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These results indicate that the topological charge of the pump laser is shared by the signal and idler outputs, and that half of the orbital angular momentum of the pump beam is transferred to the signal and idler outputs. The topological charge sharing between the signal and idler outputs stems from the cavity configuration. The (unstable) plane-parallel resonator makes the Rayleigh length x_R inside the cavity infinite because x_R ² = L ² ‖2R_m−L|/4, resulting in a zero Gouy phase shift of the beam accumulated over a round trip inside the cavity. Here L is the cavity length and R_m is the curvature of the cavity mirror. Therefore, anisotropic transfer of orbital angular momentum is prevented and topological charge sharing occurs. Further investigation is needed to fully understand the mechanism of the fractional vortex generation with half-integer topological charge.

3. Conclusion

A mid-infrared optical parametric oscillator pumped by a 1-μm optical vortex has been demonstrated for the first time. Mid-infrared fractional vortex pulses having half-integer topological charge have been created. The fractional vortex pulse has an energy of 0.5 mJ and a width of 31 ns. Generation of 0.24-mJ mid-infrared vortices with a topological charge of 1 were also achieved. Disappearance of the topological charge in the idler output, owing to walk-off effects in the KTP, has been observed. Further power scaling of the mid-infrared vortex output with half-integer (or integer) topological charge should be possible by optimizing the outcoupling of the resonator. The system can potentially be extended to terahertz vortex pulses by difference frequency generation.