We investigate use of the anisotropic radial basis functions expansion as a means to represent surface errors on aspheric and freeform surfaces. We show how the optimal choice of the shape parameter and the placement of radial basis function (RBF) nodes can increase accuracy of the surface approximation. We show an example of the adaptive grid refinement. In our approach, complex surfaces are modeled with general arbitrary representation while the anisotropic RBFs expansion models perturbation of the base surface. We show how both the global and the localized surface errors can be modeled across a wide spatial frequency range. With our method, the impact of the structured surface errors on the arbitrary surfaces when applied on the standardized image quality metrics can be assessed for the purpose of optical tolerancing.
We investigate use of the anisotropic radial basis functions expansion as a means to represent aspheric and freeform surfaces. We apply this method to represent surface perturbations for the purpose of optical tolerancing. In our approach both global and localized surface errors can be modeled across wide spatial frequency range. With our method impact of structured surface errors on arbitrary surfaces and applied on standardized image quality metrics can be assessed for the purpose of optical tolerancing.
We present a theoretical design study concerning compact freeform lens array for laser beam splitting. In our approach beam splitting optical element is designed as a compact element combining both functions of collimation and beam splitting into one component. Main emphasis of our paper is on the design methodology and subsequent theoretical analysis of design approach for such elements using examples of regular and irregular beam splitting elements. We use multi-parameter optimization method in conjunction with custom merit function implemented in ray-tracing software to implement our designs. In our design approach, we introduce a novel pupil sampling method based on Fibonacci grid. First, we deal with examples using regular lens arrays designed independently. Next, we evaluate some of standard and readily available freefrom surface representations that can replace usual description of lens array by compact continuous freeform surface. As a final example, we consider example design of irregular beam splitter with potential for control of power distribution between spots in focal plane. Some of designed structures are initially produced by optimization with some discontinuities that need to be removed to enforce smoothness of final design. We demonstrate application of local filtering techniques to produce smoothed versions of surfaces with discontinuities. Possible applications of similar designs are in laser fiber coupling and off-axis multi-spot generation where power splitting ratio can be arbitrarily predefined.
High-contrast gratings (HCG) are the ultra-thin elements set to operate in near-wavelength regime with the period of the
grating smaller then wavelength and with the high-index grating fully surrounded by low-index material. We
concentrate on topics scarcely explored in the literature such as the spectral response phenomenology of HCGs with the complex unit cells. We show that the spectral response is robust under the symmetric unit cell perturbations, while
asymmetric unit cell perturbations may introduce completely new spectral response. Further, we show examples of
highly fragmented spectra present in the case of HCGs with the aperiodic topology in the unit cell. Our results can serve as guidance for the design of the complex HCGs and help with the choice of the efficient initial grating topology prior to global optimization procedure.
We analyze wave propagation, bandgap structure, resonances and Gaussian beam propagation in superlattices containing
Negative Index Metamaterials. We focus to resonances within non-Bragg banndgaps emerging when average refractive
index is zero. We analyze influence of absorption in NIMs on the resonances inside frequency regions predicted to belong
to non-Bragg bandgaps of periodic and non-periodic structures. Further, we study resonances in finite, single defect and
double defect structures where defects are introduced by structural parameter change. We compare different examples of
spectral transmission resonances and field profiles under oblique incidence, for different polarizations and study influence
of impendence matching and defect mode coupling. Finally, we consider examples of Gaussian beam propagation in these
structures.
We analyze coupled optical defect cavities realized in finite one-dimensional photonic crystals (PC). Viewing these as open systems, where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and quasi-normal modes (QNM) (eigenfunctions). Single-defect structures (PC atoms) can be viewed as elementary building blocks for multiple-defect structures (PC molecules) with more complex functionality. The QNM description links the resonant behavior of individual PC atoms to the properties of the PC molecules via eigenfrequency splitting. A variational principle for QNMs permits one to predict the eigenfield and the complex eigenvalues in PC molecules, starting with a field template incorporating the relevant QNMs of the PC atoms. Furthermore both the field representation and the resonant spectral transmission close to these resonances are obtained from a variational formulation of the transmittance problem using a template with the most relevant QNMs. The method applies to both symmetric and nonsymmetric single and multiple-cavity structures with weak or strong coupling between the defects.
We investigate the thermal antenna behavior of emissive/absorptive substrates coated by passive optical multilayer systems
that contain negative refractive index metamaterials (NIM). Spectral and angular distributions of the thermal radiation
emittance for periodic defect-containing multilayer with NIM is addressed. We analyze realistic finite structures and took
into account dispersion and losses in the NIM part. The application of NIM-containing 1D structures offers new degrees
of freedom for the design, thus opening a path to obtain spectrally and spatially selective thermal emitters that could lead
to improvements in the existing systems for thermal radiation control.
We analyze coupled optical defect cavities realized in finite one-dimensional Photonic Crystals. Viewing these as
open systems where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies
(eigenvalues) and Quasi-Normal-Modes (eigenfunctions). Single defect structures (photonic crystal atoms) can be viewed
as elementary building blocks for multiple-defect structures (photonic crystal molecules) with more complex functionality.
The QNM description links the resonant behavior of individual PC atoms to the properties of the PC molecules via
eigenfrequency splitting. A variational principle for QNMs permits to predict the eigenfield and the complex eigenvalues
in PC molecules starting with a field template incorporating the relevant QNMs of the PC atoms. Further, both the field
representation and the resonant spectral transmission close to these resonances are obtained from a variational formulation
of the transmittance problem using a template with the most relevant QNMs. The method applies to both symmetric and
nonsymmetric single and multiple cavity structures with weak or strong coupling between the defects.
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