Using effective medium theories to design tailored nanocomposite materials for optical systems

Modern optical systems are subject to very restrictive performance, size and cost requirements. Especially in portable systems size often is the most important factor, which necessitates elaborate designs to achieve the desired specifications. However, current designs already operate very close to the physical limits and further progress is difficult to achieve by changing only the complexity of the design. Another way of improving the performance is to tailor the optical properties of materials specifically to the application at hand. A class of novel, customizable materials that enables the tailoring of the optical properties, and promises to overcome many of the intrinsic disadvantages of polymers, are nanocomposites. However, despite considerable past research efforts, these types of materials are largely underutilized in optical systems. To shed light into this issue we, in this paper, discuss how nanocomposites can be modeled using effective medium theories. In the second part, we then investigate the fundamental requirements that have to be fulfilled to make nanocomposites suitable for optical applications, and show that it is indeed possible to fabricate such a material using existing methods. Furthermore, we show how nanocomposites can be used to tailor the refractive index and dispersion properties towards specific applications

DIFFRACTION OF LIGHT BY SOUND WAVES

QC 351 A7 no. 83Diffraction of light by a sinusoidal sound wave is discussed in detail. Assuming that the sound column modulates only the phase of the incident light in both time and space, the frequencies, wavevectors, and intensities of the diffracted waves are obtained for normal incidence. A transition length (width of sound beam) is defined, above which all diffraction effects disappear due to destructive interference. Constructive interference is obtained, however, provided the light is incident at the Bragg angle, in which case the diffracted beam appears to be reflected from the acoustic wavefronts. The transition length thus separates the region of multiple -order (Raman -Nath) diffraction from the region of single -order (Bragg) diffraction. It is found to be directly proportional to the square of the acoustic wavelength and inversely proportional to the optical wavelength. In the case of Bragg diffraction, the energy is exchanged sinusoidally between the diffracted and undiffracted beams. Owing to the finite width of the sound beam, the Bragg condition is relaxed, and the effect can be used to control the direction and phase of the diffracted beam or to determine the angular distribution of the acoustic power. Next, a particle picture of diffraction in terms of photons and phonons is given. The diffraction process is described as a single as well as a multiple three -particle interaction. The effects of finite optical and acoustic beamwidths and variation of acoustic frequency are considered in terms of momentum conservation. Finally, an analysis based on Maxwell's equations for an arbitrarily polarized light beam propagating in an arbitrary direction is given using the partial -wave approach. A set of coupled difference- differential equations for the diffracted amplitudes is derived from the optical wave equation and analytic solutions are obtained in the Raman-Nath and Bragg regions of diffraction. The results for normal and Bragg incidence are obtained as special cases. Limits of the two regions are defined, thus giving a transition region in which numerical solutions can be obtained.This title from the Optical Sciences Technical Reports collection is made available by the College of Optical Sciences and the University Libraries, The University of Arizona. If you have questions about titles in this collection, please contact [email protected]

Wavefront analysis from its slope data

In the aberration analysis of a wavefront over a certain domain, the polynomials that are orthogonal over and represent balanced wave aberrations for this domain are used. For example, Zernike circle polynomials are used for the analysis of a circular wavefront. Similarly, the annular polynomials are used to analyze the annular wavefronts for systems with annular pupils, as in a rotationally symmetric two-mirror system, such as the Hubble space telescope. However, when the data available for analysis are the slopes of a wavefront, as, for example, in a Shack-Hartmann sensor, we can integrate the slope data to obtain the wavefront data, and then use the orthogonal polynomials to obtain the aberration coefficients. An alternative is to find vector functions that are orthogonal to the gradients of the wavefront polynomials, and obtain the aberration coefficients directly as the inner products of these functions with the slope data. In this paper, we show that an infinite number of vector functions can be obtained in this manner. We show further that the vector functions that are irrotational are unique and propagate minimum uncorrelated additive random noise from the slope data to the aberration coefficients.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Diffraction and geometrical optical transfer functions: calculation time comparison

In a recent paper, we compared the diffraction and geometrical optical transfer functions (OTFs) of an optical imaging system, and showed that the GOTF approximates the DOTF within 10% when a primary aberration is about two waves or larger [Appl. Opt., 55, 3241-3250 (2016)]. In this paper, we determine and compare the times to calculate the DOTF by autocorrelation or digital autocorrelation of the pupil function, and by a Fourier transform (FT) of the point-spread function (PSF); and the GOTF by a FT of the geometrical PSF and its approximation, the spot diagram. Our starting point for calculating the DOTF is the wave aberrations of the system in its pupil plane, and the ray aberrations in the image plane for the GOTF. The numerical results for primary aberrations and a typical imaging system show that the direct integrations are slow, but the calculation of the DOTF by a FT of the PSF is generally faster than the GOTF calculation by a FT of the spot diagram.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]