Performance of Multilevel Diffractive Lenses as a Function of f-Number

New design model for high efficiency cylindrical diffractive microlenses

A new model, i.e., the decreasing thickness model (DTM) is proposed and employed for designing the cylindrical diffractive microlenses (CDMs). Focal performances of the designed CDMs are theoretically investigated by solving Maxwell’s equations with the boundary element method. For comparison, the CDMs designed by the traditional equal thickness model (ETM) are also studied. Theoretical simulations demonstrate that focal performances of the designed CDMs are improved a lot via replacing the traditional ETM with the proposed DTM. Concretely, the focal efficiency is heightened and the focal spot size is shrunk. Experimental measurements verify the theoretical simulations well. Especially, the above-mentioned improvements become more prominent for the CDM with a higher numerical aperture.

Simulated propagation of ultrashort pulses modulated by low-Fresnel-number lenses using truncated series expansions

Numerical simulation of the paraxial propagation of pulses modulated by lenses is demonstrated using the Laguerre-Gaussian (LG) series expansion method. This technique allows for relatively swift evaluation of the structures of several individual monochromatic fields transformed by arbitrary amplitude and phase modulating pupil functions, which can be superimposed via the inverse Fourier transform to determine the structure of a modulated pulse. The transformation of ultrashort pulses by spherical, diffractive, and conical lenses is simulated using this method, which is particularly effective with the use of vector and matrix techniques available in many popular numerical software packages. A description of the convergence of the LG series to the results of the conventional integral techniques is presented for a conical lens under illumination by a continuous wave from which a simple but robust criterion for axial accuracy in problems of circular symmetry is suggested.

Evaluation of the shadow effect in terahertz kinoform gratings

The experimental and numerical evaluation of the shadow effect in kinoform diffractive gratings for the terahertz (THz) range is given. This effect limits the diffractive efficiency of dense gratings, which are the base of the elements suited for convenient beam focusing and imaging in THz. The observed effect of redirecting most of the incident energy into stray -1st diffractive order is observed and discussed. The presented results show the great significance of the shadow effect in selected kinoform gratings and prove the utility of the used methodology of numerical simulations.

Rigorous coupled wave analysis applied to transmission efficiency of diffractive beam array relays for free-space optical interconnects

Parallel high-density free-space optical interconnects typically relay multiple channels in an array configuration; thus, they require good uniformity across their aperture for optimum performance. Rigorous coupled wave analysis is used to determine the throughput off-axis diffraction efficiency for Fresnel lenses within a diffractive imaging relay. The rigorous results are compared with scalar theory and show a significant nonuniformity not predicted by scalar theory. However, the polarization sensitivity is found to be negligible for the f-numbers considered (f/2.9 to f/10.2). These results are supported by experiment.

Electromagnetic design of an all-diffractive millimeter-wave imaging system

We present the design and electromagnetic analysis of an all-diffractive millimeter-wave imaging system having a field of view of +/- 15 degrees. This system consists of two 16-level diffractive lenses, with the stop in contact with the first lens. By considering the Seidel aberrations for a diffractive lens and applying the corresponding stop shift formula, we established the expressions of third-order wave aberrations for this system. By setting all primary Seidel aberrations to zero and solving the corresponding system of equations, we obtained two sets of solutions for this two-element all-diffractive system, which totally compensate for all Seidel aberrations. To assess image system performance, we apply the finite-difference time-domain technique and a vector plane-wave spectrum method, in combination, to validate the performance of the system. To reduce the computational cost and thereby enable the complete electromagnetic analysis of the system, a four-step analysis procedure has been developed and applied as an electromagnetic system model.

Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm

We propose a rigorous electromagnetic design of two-dimensional and finite-aperture diffractive optical elements (DOEs) that employs an effective iterative optimization algorithm in conjunction with a rigorous electromagnetic computational model: the finite-difference time-domain method. The iterative optimization process, the finite-difference time-domain method, and the angular spectrum propagation method are discussed in detail. Without any approximation based on the scalar theory, the algorithm can produce rigorous design results, both numerical and graphical, with fast convergence, reasonable computational cost, and good design quality. Using our iterative algorithm, we designed a diffractive cylindrical lens and a 1-to-2-beam fanner for normal-incidence TE-mode illumination, thus showing that the optimization algorithm is valid and competent for rigorously designing diffractive optical elements. Concerning the problem of fabrication, we also evaluated the performance of the DOE when the DOE profile is discrete.