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Abstract: We present the first handedness control of an optical vortex output from a vortex-pumped optical parametric oscillator. The handedness of the optical vortex was identical to that of the pump vortex beam. Over 2 mJ, 2-μm optical vortex with a topological charge of ± 1 was achieved. We found that the handedness of a fractional vortex with a half integer topological charge can also be selectively controlled.
© 2013 Optical Society of America
1. Introduction
Optical vortices, which exhibit unique features such as helical wavefronts characterized by the azimuthal phase exp(imφ) (m is an integer termed the topological charge) and annular intensity profiles due to on-axial phase singularity, have orbital angular momentum, mħ, per photon [1–5]. They have been widely investigated for various applications including optical manipulation [6], optical trapping [7], super-resolution microscopy [8], ultra-fast closed-loop spectroscopy [9, 10], and material processing [11, 12]. We and our associates have found that the helical wavefront of an optical vortex can be transferred to a metal through a laser ablation process to form chiral nanostructures [13]. Furthermore, we also found that the chirality of the nano-structures was directly determined by the handedness (clockwise or counter-clockwise direction) of the helical wavefront of the optical vortices [14].
Such chiral nano-structures will enable us to determine the chirality and optical activity of molecules and chemical composites on the nanoscale. They may also allow us to fabricate plasmonic structures and planar metamaterials with chiral selectivity. For instance, a sub-micron scale chiral structure called a gammadion array [15, 16] exhibits optical activity in the terahertz region (chiral metamaterial).
A key issue in fabricating such optical devices based on chiral nanostructures formed by optical vortices is the frequency extension of optical vortices to meet the absorption bands of materials. A further concern is the selective control of the handedness of the optical vortex output.
Several preliminary studies concerning the nonlinear frequency extension of optical vortices, i.e., second harmonic generation [17, 18], sum frequency generation, stimulated Raman scattering [19], optical parametric amplification, and optical parametric oscillators [20, 21] have been conducted. To date, we have successfully demonstrated a milli-joule level, tunable 2-μm optical vortex output from a 1-μm optical vortex pumped KTiOPO4 (KTP) optical parametric oscillator with a half-symmetric cavity configuration [22]. We have also addressed orbital angular momentum sharing between signal and idler outputs in a 1-μm optical vortex pumped optical parametric oscillator with a plane-parallel cavity configuration, resulting in a 2-μm fractional optical vortex generation [23]. However, these previous works focused only on the magnitude of the topological charge of the vortex output, and paid little attention to the handedness.
The direct generation of optical vortex outputs from solid-state lasers in combination with annular beam pumping [24–26], spatial filtering based on thermal lensing [27, 28], an intracavity spiral phase plate [29], and a defected cavity mirror [30] has also been investigated thoroughly. However, in most cases, the handedness of the vortex output in these lasers was determined randomly.
Selective control of the handedness of 2-μm vortex or fractional vortex lasers will enable the creation of chiral nanostructures of polymers. In particular, the fractional optical vortex output with the radial opening intensity distribution will provide us with a means to create split-ring resonator arrays for metamaterials.
In this paper, we demonstrate the first handedness control of a 2-μm optical vortex or fractional vortex output from a 1-μm optical vortex pumped optical parametric oscillator merely by inverting the handedness of the optical vortex pump beam.
2. Experimental setup
Figure 1 shows a schematic diagram of a 1-μm optical vortex pumped KTP optical parametric oscillator [31]. A conventional Q-switched Nd:YAG laser (pulse duration: 20 ns, wavelength: 1.064 μm, PRF: 50 Hz, maximum pulse energy: 21 mJ, spatial form: Gaussian profile) was used as the pump source of the optical parametric oscillator, and its output was converted into an optical vortex with a topological charge, m, of 1, by using a spiral phase plate, azimuthally divided into 16 segments with an nπ/8 phase shift (where n is an integer between 0 and 15) [32]. To invert the sign (handedness) of the topological charge, m, of the pump beam, the spiral phase plate was reversed. The pump beam was focused to be a ϕ 670 μm spot on the KTP crystal by a lens with a focal length of 500 mm. The resonator comprised 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; and a concave output mirror (M2) with a curvature of 100 mm, a reflectivity of 80% for 2-μm and a high transmissivity for 1-μm. A KTP crystal with dimensions of 5 × 5 × 30 mm was cut at θ = 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 wavelength of the signal (o-wave) and idler (e-wave) outputs was 2.128 μm).
Fig. 1 Experimental setups for an optical parametric oscillator pumped by a 1-μm optical vortex beam and the wavefront measurement using a transmission grating with low spatial frequency.
As described in our previous work, in this system (with stable cavity configuration), the topological charge of the pump beam is anisotropically transferred to the signal output, resulting in a signal output (vortex output) with a topological charge of 1. To confirm the handedness of the signal output, interferometric measurements were also performed using a transmission grating with low spatial frequency (20 /mm). As shown in Fig. 1, the 0th and 1st order diffracted beams were selectively filtered by a slit, and collected by a lens on a pyroelectric camera, thereby forming a self-referenced interferogram. The existence of a phase singularity is evidenced by a pair of fork-like dislocations [33]. The charge of the phase singularity, determined by the direction of the fork-like dislocations, is also defined as + 1 (right-handed) when the upward fork-like fringes appear on the left side.
3. Results & Discussions
When the pump beam was right-handed (Figs. 2(a) and 2(b)), the signal output exhibited an annular intensity profile and a pair of upward fork-like fringes, indicating that the signal output was a right-handed optical vortex with a charge, m, of + 1 (Figs. 2(c) and 2(d)). The simulated self-interference fringes of the right-handed optical vortex are presented in Fig. 2(e).
Fig. 2 (a) Spatial form, and (b) self-interference fringes of the right-handed pump beam. (c) Spatial form, (d) self-interference fringes, and (e) simulated fringes of the signal output obtained with right-handed pumping. (f) Spatial form, and (g) self-interference fringes of the left-handed pump beam. (h) Spatial form, (i) self-interference fringes, and (j) simulated fringes of the signal output with left-handed pumping.
When the spiral phase plate for the pump beam was reversed (the pump beam was left-handed as shown in Figs. 2(f) and 2(g)), the resulting handedness of signal output was also inverted, evidenced by the inverted fork-like fringes as shown Fig. 2(i). The simulated self-interference fringes of the optical vortex with charge m, of −1, are shown in Fig. 2(j). The experimental results are in good agreement with the simulations.
We further investigated the handedness control of the optical vortex output from the optical parametric oscillator with the nearly plane-parallel cavity configuration. The concave output mirror was replaced by a flat output mirror. With this setup, topological charge sharing of the pump beam between the signal and idler outputs occurs, resulting in a fractional vortex signal output with a half-integer topological charge, m, of 0.5.
When the pump vortex beam was right-handed, the signal output had a half-integer topological charge of + 0.5, as evidenced by an upward radial opening intensity profile shown in Fig. 3(a) and a pair of upward fork-like fringes as shown in Fig. 3(b). The simulated spatial form and self-interference fringes of the fractional vortex having a topological charge, m, of + 0.5 (Figs. 3(e) and 3(f)) are consistent with those of the signal output.
Fig. 3 Spatial forms of the signal output in a nearly plane-parallel cavity configuration. (a) Spatial form and (b) interferometric fringes of the signal output with right-handed pumping. (c) Spatial form and (d) interferometric fringes of the signal output with left-handed pumping. (e)-(h) Simulated spatial forms and self-interference fringes of the signal output.
When the pump vortex beam was left-handed, the signal output still exhibited an upward radial opening (Fig. 3(c)). However, a pair of fork-like fringes were flipped upside down (Fig. 3(d)), indicating that the signal output had a half integer topological charge, m, of −0.5. We also simulated the spatial form (Fig. 3(g)) and self-interference fringes (Fig. 3(h)) of a fractional vortex having a topological charge of −0.5. There was good agreement between the simulations and experiments.
These results indicate that the handedness of the signal output with an integer or non-integer topological charge is determined only by the handedness of the pump beam.
Figure 4 shows the output energy as a function of the pump energy. The right-handed (left-handed) optical vortex output energy of 2.0 mJ (2.2 mJ) with a topological charge of + 1 (−1) was obtained at the maximum pump energy of 21 mJ, corresponding to an optical-optical efficiency of 10.5% in the stable cavity configuration. With the nearly plane-parallel cavity configuration, the maximum energy of the signal output (fractional vortex output) with a half-integer topological charge, m, of + 0.5 was measured to be 0.9 mJ, corresponding to an optical-optical efficiency of 4.3%. The left-handed signal output energies were almost identical to those of the right-handed signal outputs.
With this present system, the reflectivity of the output coupler was not optimized yet. Also, the beam propagation factor of the pump beam (the vortex output shows M2 of ~2) impacted the intracavity parametric gain. Further improvement of the optical-optical efficiency of the system up to 20-30% will be possible by optimizing the outcoupling of the cavity as well as the focusing optics for the pump beam [34].
In the optical parametric oscillator, the nonlinear interaction between a signal (or an idler) and pump electric fields (not intensity profiles) encourages the oscillation of the signal (or idler) output. Thus, the gain can be determined from the spatial overlap efficiency η between the signal and pump fields (not intensity profiles), given by
where Epm and Esn are the electric fields of the pump beam and signal output, respectively, m and n are the indices for the handedness ( ± 1), and ωp is the beam waist of the pump beam. When the signal output is an optical vortex (a beam waist ωs) given by, a general relationship η given by,is established. If the signal output is the fractional vortex formed by the Gaussian and vortex outputs given by, the relationshipη becomesThese relationships indicate that the handedness of the signal output must be the same as that of the pump beam and the slope efficiency (10-11%) of the signal output in the nearly plane-parallel cavity configuration must be less than that (16-18%) in the stable cavity configuration. These results support the findings of our experiments.
4. Conclusion
We have demonstrated the handedness control of a 2-μm optical vortex output with an integer or non-integer topological charge from a 1-μm vortex pumped optical parametric oscillator, for the first time. The handedness of the 2-μm vortex output was fully determined by the handedness of the 1-μm pump vortex beam. The maximum 2-μm vortex output energy achieved was 2.2 mJ, corresponding to an optical-optical efficiency of 10.5%.
As stated in our previous work [22,23], the walk-off effect forces the phase singularity of the idler output (extra-ordinary ray) to displace spatially toward the margin of the spatial form of the idler output, resulting in that the idler output looked a Gaussian beam. To investigate the handedness of the idler output, the walk-off compensation, e.g. using an intracaivity double KTP crystal [34], will be needed.
Selective control of the handedness of the 2-μm vortex output opens up a new generation of material processing, such as chiral polymeric nano-structures.
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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