Optical vortices are optical fields with helical wavefronts which have well-defined orbital angular momentum (OAM)^[1,2]. The OAM of optical vortices with a phase distribution of exp(ilφ) is lℏ/photon, where φ is the azimuthal angle, ℏ is the reduced Planck constant, l is the topological charge (TC) of the optical vortices; l is usually an integer. In 2004, Bezuhanov et al.^[3] experimentally generated optical vortices in the output beam of a 20 fs Ti:sapphire laser by aligning a computer-generated hologram (CGH) in a dispersionless 4f setup. After that, ultrashort fs optical vortices have attracted increasing attention. Many methods have been proposed to produce fs optical vortices, such as using a pair of gratings^[4,5]; a single refractive spiral phase plate (SPP)^[6]; a dispersion-compensating beam shaper composed of a prism pair and a CGH^[7]; a beam converter composed of achromatic wave plates, a uniaxial crystal, and a couple of lens^[8]; molecular modulation in a Raman-active crystal PBWO4^[9], a q-plate^[10], and so on. Some researchers have already produced an ultrashort optical vortex pulse of 6–7 fs by use of a high-quality fs laser with an ultrabroadband spectrum^[11–14]. Such fs optical vortices have been applied for material processing^[10,15–18], manipulation of microscopic particles, and so on. Such fs optical vortices in air, water, and other media have also been studied^[19–21].

A continuous SPP can be used to conveniently produce an optical vortex with high efficiency and high purity; it can always be used in image edge-enhancement in optical microscopy^[22–24]. In our work, by use of a fs laser passing through a continuous SPP, a high-quality broadband fs optical vortex was experimentally obtained.

The schematic of the experiment setup is shown in Fig. 1(a). The fs laser was expanded and collimated by passing through a 40× microscope objective, pinhole, and Fourier lens L1 with a focal length of 200 mm, successively. After passing through the aperture with a diameter of 20 mm, the fs laser transmitted the continuous SPP and transformed into fs optical vortex. Lens L2 with a focal length of 109 cm was set behind the SPP and a charge-coupled device (CCD) was set on the back focal plane of L2 for recording the intensity distribution of the optical field. The attenuator set before the CCD was used for protecting the CCD. In our work, we used the oscillator of a 20 TW fs Ti:sapphire laser. The oscillator has the power of 200 mW, with a repetition rate of 75 MHz and a center wavelength of 790 nm. It had a broad spectrum bandwidth of more than 100 nm and a pulse duration of less than 20 fs. The continuous SPP is made of fused quartz glass. It has a thickness of 3 mm and a diameter of 25.4 mm. The SPP, fabricated by use of the technology of gray exposure and reactive ion etching (RIE)^[25], was designed specifically for 800 nm. The largest etching depth was 1.77 μm for a SPP with the TC=1. Figure 1(b) shows the three-dimensional (3D) structure of the etched surface of the SPP, measured by a 3D profiler. Evidently the etching depth changes continuously around the singular point. Because the SPP is somewhat tilted on the profiler, the difference between the maximum and minimum depth is not equal to 1.77 μm. The maximum etching depth is measured to be about 1.7 μm, which has an error of 4% compared with the ideal value.

Figure 2 shows the spectrum of the laser pulse from the fs laser oscillator and the main amplifier laser before compression. The black solid line is the fs laser from the oscillator with a broad spectrum bandwidth of more than 100 nm, and the red dashed line is the spectrum of the main amplifier laser before compression with a spectrum bandwidth of about 70 nm. The 20 TW fs laser in our lab has a shortest pulse width of 24–25 fs.

Figure 3 shows the intensity distribution of the fs optical vortex with TC=1 in our work. The size of images is 0.5mm×0.5mm. From Fig. 3, it can be seen that the fs optical vortex is of high quality and demonstrates that the continuous SPP has a good quality. This indicates that the continuous SPP can be used for production of a fs optical vortex.

In our work, one cylindrical lens with a focal length of 400 mm was set before the CCD for measuring the TC of the optical vortices^[2,26]. The distance between the cylindrical lens and the CCD is 120 mm. Figure 4 shows the intensity distribution of the fs optical field after setting the cylindrical lens. The images has the size of 1mm×1mm. The intensity distribution demonstrates that the TC of the optical vortices is +1.

Then we analyzed the purity of the fundamental component of the optical vortex generated by the symmetrical beam transmitted through an ideal SPP made of fused quartz glass. Here we assumed the central wavelength of the fs laser is λ0=800nm. Because the material has the different refraction index for different wavelengths, the relation between the TC and wavelength can be expressed as m(λ)=n(λ)−1n(λ0)−1m(λ0),(1)where m(λ0)=m0 is the TC at 800 nm, and n(λ) is the refraction index of fused quartz glass. The relationship between the purity of the optical vortex and wavelength can be deduced as^[27,28]P(λ)=Cm2=sinc2[n(λ)−1n(λ0)−1−1].(2)where sinc represents sinc function and Cm represents the complex amplitude of the component exp(imφ).

Figure 5 shows the purity of the optical vortex generated by fused quartz glass as a function of the wavelength. The black dashed line represents the refraction index curve. The red dotted line and solid line represent the curves of the relative TC and purity, respectively. From Fig. 5, we can see that the purity of the optical vortex generated by a symmetrical beam transmitted through an ideal SPP made of fused quartz glass is greater than 97% at the wavelength in the range of 750–850 nm. For improving the purity of the optical vortex, we compared more than 100 kinds of glass and found that the SPP made of N-SF66 glass has the highest purity of greater than 98% over the wavelength range of 750–850 nm. We also can increase the ideal purity to greater than 99% by use of an achromatic SPP^[29].

From the spectrum of the main amplifier of the fs laser, we can see that the SPP made of fused quartz glass or N-SF66 glass is sufficient. The beam quality is the key factor affect the purity of the optical vortex. It is very difficult to improve the beam quality for high-power fs lasers. Consequently, advancing the beam quality is the main task.

In conclusion, a high-quality broadband fs optical vortex with TC=1 is obtained by use of a continuous SPP to modulate a broadband fs laser. The experimental results indicate that our continuous SPP is of good quality; it can be conveniently used for production of a high-power ultrashort fs optical vortex, which can be applied in high-energy-density physics.

We are grateful to Professor Qi-Ling Deng and Dr. Li-Fang Shi from Institute of Optics and Electronics, Chinese Academy of Sciences (CAS), for fabricating the SPP; and Dr. Cheng-Chun Tang from Institute of Physics, CAS, for operating the 3D optical profiler.