Theoretical Analysis of a Volume Holographic Lens Using Matlab

Volume holographic lenses have great potential for different types of applications requiring light redirection and beam shaping such as solar light collection and LED light management. For lighting applications using LEDs, it is essential to make a highly efficient optical element to be placed in front of the LED in order to decrease energy losses. For that reason, a careful theoretical analysis of the properties and operation regime of the lens must be carried out at the design stage. The characteristics of focusing Holographic Optical Elements (HOE) depend on many factors including their thickness, spatial frequency, the angular range of incidence of the incoming light, recording wavelength and replay wavelength. Simulation of lens performance that takes into account the above parameters is critical for designing experimentally efficient HOEs, including for LED applications. In this paper, the parameters of a volume cylindrical holographic lens have been analyzed by using Kogelnik Coupled Wave Theory and Bragg's Law. Simulations have been carried out in Matlab to define the regime of operation of a model unslanted grating and cylindrical holographic lens and discussed in the context of possible limitations imposed by recording the optical element in a photosensitve material. This theoretical analysis is very useful in designing lenses to avoid production of multiple beams and lowered efficiency. The analysis can also help in devising strategies to overcome these limitations and in achieving diffraction efficiency approaching 100%.