## 2 Materials and Methods
### Experimental Setup
By lowering the power of the input beam, a simple method is provided to switch between a broadband supercontinuum light source from the fiber and the narrowband (\(\sim\)40 nm) femtosecond source. In the low-power case, the fiber acts merely as a spatial filter for the mode locked laser. This is used as a quick reference to view the difference between SCG vortex interference and narrowband interference, and it is also possible to un-modelock the laser to compare with the CW case. When the SCG vortices are not filtered to a narrow bandwidth, the various colors will diffract at different angles, giving the vortex image a spatial chirp. With a CW beam, there is no spatial chirp. Optical vortices are generated by encoded phase patterns onto the SLM resulting in phase modulation of the SCG beam. To generate a single vortex, a forked grating pattern is displayed on the \(768\times 768\) pixel active region of the SLM, generated by a LabView VI that allows for real time control of  
Figure 6: Spatial modulation in the far field from phase modulation in the near field with a 2f system. the blazed grating and spiral phase (vortex charge). Multiple vortices can also be displayed on the SLM, allowing for independent control of different vortices. Figure 7 shows the VI with a sample vortex pattern that is displayed onto the SLM. The LabView VI generates a vortex pattern through the combination of a blazed grating with a spiral phase. The blazed grating is set from 0 to \(2\pi\) through the grayscale of the SLM, and this allows for the vortex to be diffracted away from the zeroth order. The SLM has been calibrated for various wavelengths in order to display the correct gray level scale for the wavelength incident on the vortex pattern. The size of the blazed grating in both the x and y-direction, the charge of the spiral phase plate, the gray level scale, the quantity of vortex patterns displayed onto the SLM and their location can all be controlled through the LabView VI. This provides ultimate flexibility in generating multiple vortices of arbitrary size, charge and location. The broad spectrum of the supercontinuum light allows for the use of optical filters for selecting the color of the vortex. Multiple filters can be used, each covering a small section of the SLM that matches a specific vortex pattern. Since the Hamamatsu SLM has a large active area and high-resolution, it is possible to separate different regions of the SLM as effectively independent modulators. This is used to demonstrate vortex interference, whereby two vortices are created on each half of the SLM, then made to interfere in the image plane. Since the two sections of the SLM are independently controllable by the LabView code, vortex generation of equal or unequal charge is possible. Additionally, arbitrary blazed gratings can be added to each vortex controlling their location in the image plane. This setup can produce multiple vortices, each at different wavelengths with the use of only a single light source. With this experimental setup we have been able to produce up to six independent vortices with full control. For clarity, we present results here for only a pair of independent vortices.