Design of Diffractive Optical Elements: Optimality, Scale and Near-field Diffraction Considerations

In this research, two related research topics were investigated. The first one is the use of scalar diffraction theory for the purpose of simulating and implementing diffractive optical elements (DOEs). The main focus was on the optimal design of computer-generated holograms (CGHs). Two existing methods were combined to improve the reconstructed image of a CGH. The new method combines the Optimal Decimation-in-Frequency Iterative Interlacing Technique (ODIFIIT) with the Lohmann coding scheme. Simulations indicate that the reconstructed image produced with this method has less error than reconstructions with either method alone. Physical reconstructions were performed and compared to the simulated results. Near field diffraction from DOEs with feature sizes on the order of a wavelength were also simulated and analyzed. Both the small feature size and the close observation distance make scalar diffraction theory inaccurate. For this situation, a complete electromagnetic theory is necessary to achieve accurate results. XFDTD software made by Remcom was used to simulate these elements and their diffracted fields. XFDTD calculates the diffracted fields by using a leapfrog finite difference time domain algorithm to solve Maxwell’s curl equations directly. Fresnel zone plates and reflection and amplitude gratings were simulated. An amplitude grating was also combined with a Fresnel zone plate to imitate a Fourier lens system like that used for reconstructing the image from a computer-generated hologram. The angular spectrum of plane waves was also used to study these systems, and results were compared. Results showed that XFDTD can accurately simulate small-scale DOEs. Precise knowledge of the diffracted field from small-scale DOEs will play an important and useful role in future optical systems as feature sizes reach the nano-scale level.