## 2 Materials and Methods
### Experimental Setup  
The experimental setup for generating white-light vortices consists of a femtosecond oscillator, a microstructured photonic crystal fiber, a two-dimensional SLM and various detectors, as depicted in Figure 5. These devices are arranged in a Fourier lens system with the SLM in the Fourier plane to generate optical vortices in the image plane. The laser oscillator is a Nd:YAG pumped Ti:Sapphire oscillator emitting at a center wavelength of 800 nm. This laser generates ultrashort pulses when mode-locked with a 20 fs duration. Immediately after the oscillator, the beam passes through a pulse-shaping compressor, essential for optimizing the super-continuum output by pre-chirping the input pulse. Before the beam is coupled into the microstructured fiber, steering mirrors and a waveplate are used to ensure a level and horizontally polarized beam. A 20X microscope objective lens is mounted onto an XYZ translation stage to couple the beam into the nonlinear photonic crystal fiber (NKT Photonics FemtoWhite 800), mounted on a similar stage. The fiber consists of a honeycomb structure with a central core surrounded by air gaps. The core of the fiber is \(1.8\pm 0.3\)\(\upmu\)m, allowing a single transverse mode and a nonlinear interaction through the length of the fiber, which produces a broad spectral bandwidth from 500 nm to over 1000 nm. The Femtowhite 800 fiber is designed to work optimally with a Ti:Sapphire oscillator. The coherent supercontinuum beam exiting the fiber then travels through a 4f Fourier lens system. The output light expanding from the fiber is collimated with a 70 cm focal length lens, and is incident  
Figure 4: Simulated supercontinuum vortex generated from the superposition of individual vortices with wavelengths \(\lambda=520\) nm, 570 nm, 600 nm and 650 nm. Figure 5: Experimental setup for generation of white-light vortices from a femtosecond source, with a spatial light modulator. onto a Hamamatsu X8267-14 DB two-dimensional SLM, located at 70 cm from the lens. This SLM has a pixel array of \(768\times 768\) active pixels, with a pixel size of 26 \(\upmu\)m\({}^{2}\) and a diffraction efficiency above 70% for a blazed grating conformed by a four-pixel sawtooth phase lattice. Its 2\(\upmu\) phase modulation depends upon the wavelength, it requires a gray level scale from 0 to 97 for 540 nm, increasing to 228 levels for 900 nm [28]. Since the SLM has a large aperture (2 cm \(\times\) 2 cm), various colored filters can be placed in front of it to segment the SLM by color, or the entire supercontinuum spectrum can be used to generate white light vortices. The modulated light is reflected back through the f = 70 cm lens and onto a pick-off mirror that reflects the light to the CCD detector in the imaging plane. This well-known technique creates a far-field pattern at the CCD that is a Fourier transform of the field at the SLM, as presented in Figure 6.  
Various detectors are used to collect the white light vortex data. The supercontinuum spectrum is collected using an Ocean Optics spectrum analyzer (USB2000 + XR), the vortex intensity image (in false color) is captured using a DataRay WinCamD-UHR and the colored optical vortices are recorded with a 24.7 \(\times\) 15.6 mm CCD sensor in a Nikon D70s DSLR camera. The optimized supercontinuum spectrum ranges from 500 nm to over 1000 nm in the near IR. Various experiments call for the use of filters to narrow down the spectrum incident on the SLM. A variable wavelength filter placed directly after the fiber may be used to select a narrow bandwidth, approximately 20 nm wide, that can be centered anywhere over the entire range of the supercontinuum. Red and green filters (Edmund Optics NT46-139 and NT30-634) that transmit a larger region of the spectrum are employed as well. These filters can be placed side-by-side directly in front of the SLM to generate independently controllable vortices of different color. The supercontinuum spectrum can be altered by changing the power or pulse shape of the input beam into the fiber.