This paper proposes three techniques to reduce the time required to calculate single diffraction efficiencies or a series of diffraction efficiencies obtained from rigorous coupled-wave analysis algorithms. These are a technique using the properties of the Toeplitz matrix, a technique for reducing the number of variables in a function of Fourier coefficients, and a technique for using parallel computing. On the example of tasks on plotting the dependences of the diffraction efficiency of two-layer two-relief sawtooth microstructures with antireflection coatings on the angle of incidence of radiation, it is shown that using the properties of Toeplitz matrices can significantly reduce the calculation time. Parallel computing also reduces the calculation time, but it uses more RAM.
The harmonic sawtooth microstructure allows the diffractive lens to operate with polychromatic radiation, in particular, with the radiation of RGB LEDs, but only with restrictions due to axial color and specific field curvature. Its reason is the jump in the working diffraction order with an increase of the wave angle of incidence. The permissible wave angles of incidence at the microstructure were estimated using the example of a harmonic diffractive lens made of crown-like plastic E48R.
Based on a complete system of boundary conditions for an electromagnetic field incident on a periodic structure, an algorithm is presented that allows you to convert such a system, leaving only the unknown amplitudes of the transmitted diffraction orders. The method underlying the algorithm belongs to the family of Fourier-space methods so devices and fields are represented as a sum of spatial harmonics. It is shown that the results of calculating the diffraction efficiency obtained using this approach completely coincide with the results obtained in the framework of the enhanced transmittance matrix approach and the scattering matrix approach. The dependences of diffraction efficiency on the wavelength and angle of incidence of the microstructure obtained by this method are presented. These results are consistent with the conclusions made in earlier studies, based on a different approach in the framework of a rigorous coupled-wave analysis.
Aberration properties and correction capabilities of objectives containing two or three cemented radial gradient- index lenses are analyzed. It is shown that the simplest radial gradient-index system, which can be corrected for all third-order monochromatic aberrations, is the cemented doublet with flat external and spherical cemented surfaces. Aberration properties of the cemented component made of two different inhomogeneous materials and having only four flat surfaces are analogous. It is also shown that the simplest radial gradient-index system, which can be simultaneously corrected for all third- and fifth-order monochromatic aberrations, is the cemented triplet made of three different inhomogeneous materials and having spherical surfaces. The methods and examples of aberrations-free objectives design are given.
Possibilities of all third- and fifth-order monochromatic aberrations elimination of the system consisting of three cemented lenses with the radial distribution of refractive index are shown. The design procedures for removal these aberrations are presented.
This book, originally published April 1st, 1997, has been republished as an eBook April 19th, 2022.
The use of diffractive and gradient-index (GRIN) lenses as components of imaging optical systems has been investigated for several decades. The elements have proved competitive in their unique focusing and aberration properties and in terms of their additional degrees of freedom for optical design. This book systematically examines the physical principles of diffractive and GRIN elements.
The possibilities of fabrication of high-resolution diffractive lenses having sufficiently large diameter for x ray applications by spatial-frequency multiplication method are shown. The ways of determining the optimal spatial-frequency of a parent zone plate are discussed.
Optical hybrid systems, i.e., systems containing the optical elements of different types (diffractive and gradient-index lenses), are considered. The correction possibilities of two- and three-element hybrid objectives are analyzed. It is shown that the two-element objective may be corrected for all monochromatic third-order aberrations. As a result the space frequency of diffractive lens structure and the magnitude of the refractive index change of gradient-index lens can be decreased. Various fifth-order aberrations can also be corrected. This objective forms a high resolution image and wide linear field in the image space. The three-element hybrid objective consists of one diffractive and two gradient-index lenses. This objective has a symmetric configuration and unit magnification. It is shown that in such an objective, which is free from all third-order aberrations, it is possible to eliminate simultaneously three out of four different fifth-order aberrations. In particular, this result remains valid if the optical power of the diffractive element is equal to zero. The design of a three-element hybrid objective is reported. The resulting designs are compared with homogeneous objectives.
The optical hybrid systems, i.e. systems, containing the optical elements of different types (diffractive and GRIN lenses) are considered. The corrective scope of two- and three-element hybrid objectives are investigated. It is shown that the two-element objective may be corrected for all monochromatic 3d-order aberrations. The three-element hybrid objective, which is inverstigated here, consists of one diffractive and two GRIN lenses. This objective has symmetric configuration and unit magnification. It is shown that in such objective, free of all 3d-order aberrations, it's possible to eliminate simultaneously the three out of the four different even 5th-order aberrations.
The diffractive optical elements in recent time have found sufficiently wide utilization and what is more the regions and volumes of their applications are constantly widened. In holographic optical elements ( HOE ) production processes ( production of diffraction gratings, mirrors, lenses, etc.) the important role is played by the light sensitive media, in which the interference pattern, created by the laser beams is directly registered. The demands that are applied to such media are rather rigid, especially under production of HOE with submicron sizes. The wide range of photo-induced phenomena exhibited by the chalcogenide vitreous semiconductors ( ChVS ),especially the photodoping 1 and photostimulated ChVS solubility changes 2 enable to use them in a quality of registering media suitable for HOE production.3'4
The optical hybrid systems, i.e., systems containing the optical elements of different types (diffractive and gradient-index lenses), are considered. The corrective scope of two- and three-element hybrid objectives are investigated. It is shown that the two-element objective may be corrected for all monochromatic third-order aberrations. It is possible in a wide range of relations between optical powers diffractive and gradient-index lenses. It allows us to reduce the space frequency of the structure of the diffractive lens and to decrease the magnitude of the refractive index change of gradient-index lens. In addition, the correction of various fifth-order aberrations may be achieved in this case too. As a result this objective forms the image with high resolution and a wide linear field in the image space. The three-element hybrid objective consists of one diffractive and two gradient-index lenses. This objective has symmetric configuration and unit magnification. It is shown that in such an objective, which is free from all third-order aberrations, it's possible to eliminate simultaneously three out of the four different even fifth-order aberrations. In particular, the validity of this result is conserved if the optical power of the diffractive element is equal to zero. The design of a three-element hybrid objective is given. The resulting designs are compared with homogeneous objectives.
Systems for reading data from optical disks are suggested. In these systems a diffractive lens simultaneously executes the functions of a focusing objective and the dispersive element of dynamical autofocusing device. The design of diffractive lens structure is given for two cases. In the first case the objective focusing semiconductor laser emission consists of a single diffractive lens. In the second case, it consists of a diffractive and homogeneous lens with spherical surfaces. When designing the diffractive lens structure, one must consider that semiconductor lasers have a heat instability of emission frequency and emission wavelength spread from one sample to another.
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