Diffraction gratings have often been used to direct light in a direction that is off axis of an incident light path. In general, these gratings produce a number of diffracted orders with different locations and intensities. Over time the desire to control the output from the grating has brought about different gratings and methods of controlling the output. However, these gratings have all been limited in several ways. Whether it be a lack of intensity control or order control, no grating has been able to control all of these properties at the same time. In this work we will explore a new technique that creates generalized gratings with intensity, order and phase control. To get an idea of where previous gratings fail we will look into their range of outputs to get an idea of the issues that must be overcome. Quickly we see that while a grating may have some control over which orders are present, it is not complete control. The same also holds true for the relative intensities of the orders of the gratings. From this we test a new generalized grating that has complete control over the number of orders, their relative intensities and even phase. It is from this range of control that numerous applications are possible ranging from interconnects to optical tweezers. Throughout this paper we will explore the tools provided by the grating and ways to implement them. However, this is just a road map to give an idea of what the grating can do. Ultimately using this set of techniques the user is able to create a grating that fits their order, intensity or phase needs.
