This PDF file contains the front matter associated with SPIE Proceedings Volume 8171, including the Title Page, Copyright Information, Table of Contents, Introduction, and the Conference Committee listing.

The degree of polarization is a central quantity in the characterization of random electromagnetic beams and it has been introduced both in the time and the frequency domains. Physically, the spectral degree of polarization corresponds to that of a field obtained by filtering a generally broad-band light by a narrow-band filter. It is known that the two degrees of polarization can generally assume different values and no simple relationship exists between them. For example, a stationary field can have an arbitrary degree of polarization in the frequency domain although the field is fully unpolarized in the time domain. Moreover, the field can be fully polarized at every frequency, but in the time domain the field may be anything between unpolarized and polarized. In this work, we study the connections between the time and frequency domain degrees of polarization. We introduce a mean spectral degree of polarization and show that it provides an upper limit for the value of the time-domain degree of polarization that can be obtained if arbitrary unitary transformations are performed in the frequency domain. A mean spectral degree of polarization equal to one indicates that the field is fully polarized in the frequency domain and thus can be made fully polarized also in the time domain by unitary transformations in the frequency domain, i.e., without absorption of energy.

It is shown how scattering media may allow to confer high polarization degree (DOP ≈ 0.75) to an incident depolarized beam (DOP ≈ 0). The statistics of the polarization degree versus scattering directions or space location are investigated with a CCD camera at a speckle resolution. Numerical calculation and experimental data are compared and show high agreement for a sample highly inhomogeneous in the bulk. The probability density function of the DOP follows a 3u² variation.

We break down the equilibrium state and the diffraction invariant property of a non-diffracting speckle field by removing its continuous part of the phase while leaving all vortices behind. During the propagation of such a phase corrected non-diffracting speckle field, the vortex density drops down to a minimum value and then comes back to an equilibrium value which is even higher than the initial one. Before the phase corrected field returns back to its new equilibrium state, another least-squares phase removal will be applied, at the position where there is a minimum vortex density, to further remove vortices from the speckle field. Such a process of removing least-squares phase and propagating the phase corrected field over a distance can be repeated to eliminate most of optical vortices. Statistical results show that most of optical vortices can be removed from a non-diffracting speckle field. Finally, a semi-plane wave without optical vortices can be obtained from an initial non-diffracting speckle field with multiple steps of least-square phase correction.

We analyze the classic Hanbury Brown-Twiss effect for thermal electromagnetic fields in space-frequency domain. We compare two different approaches and show that the normalized correlation of intensity fluctuations is fully characterized by the spectral electromagnetic degree of coherence, a result analogous to scalar analysis of the effect. Differences between the two approaches are discussed.

Huygens-Fresnel principle is well used in analyzing wavefront propagation in vacuum. However, we should clear if this principle is available in the space including absorptive objection, such as a grating. In this paper we analyze if a grating can diffract a beam when the grating set on the focus point and the grating pitch is larger than the Airy disc, especially the phenomenon in a special interferometer [1]. The special interferometer shown in reference [1] has an extended incoherent light source modulated by a binary grating. The light source is imaged onto a sinusoidal transmission grating by the tested lens. The pitch of the binary grating is half of the period of the sinusoidal grating. Light coming from an arbitrary point of the light source is focused onto the sinusoidal grating. Two kinds of analysis method are considered. One is using Huygens-Fresnel principle as described in reference [1]: the concave beam can be resolved to a pair of waves. Each wave is diffracted by the sinusoidal grating. By using the modulated extended light source, only one color interferogram interfered by -1^st and +1^st order beams can be observed. By shifting the sinusoidal grating; the phase of the interferogram can be modulated; therefore, the intensity after the grating will change. The intensity variation is the contrast of the interferogram. The other analysis method is to calculate the intensity after the sinusoidal grating as in a normal Ronchi test. If two points on the light source separated by distance of the binary grating's pitch is picked up, the intensity of each point after the grating changes sinusoidally when the sinusoidal grating is shifted. Because the period of the modulation grating is half of the sinusoidal grating's pitch, the intensities of the two points change with "pi" phase difference. The total intensity after the sinusoidal grating does not change even if the sinusoidal grating is shifted. We found that the confusion in reference of complex transmission and amplitude transmission is one reason of the difference. We also reviewed the developing of Huygens-Fresnel principle from Maxwell equations. To get Huygens-Fresnel principle, condition of non absorptive elements is needed. Because transmission grating is an absorptive element, wavelet should be integrated before the grating. We also found that the substrate influences the phase of complex transmission when NA of the test is large. We performed an experiment to show that the contrast is almost zero, not 21% as calculated by the theory shown in the paper of refer.

Butterfly's wing has paid great attention due to its unique properties, such as attractive iridescence, super-hydrophobic characteristics, and quick heat dissipation ability. These characteristics are closely related to its structure. The multilayer thin-film structures that make up a butterfly's wing produce a bright iridescence from reflected daylight. In this study, we will introduce the optical effect of viewing angle, structural characterizations and color-producing mechanism. Since the reflectance patterns are extended in angle, we have to use a spectrophotometer equipped with an integrating sphere. According to the result, the peak reflectrance decreasing, blue-shifts and the difference between spectra of p-polarization and the s-polarization was enlarged when the incident angle increasing. In addition, the directional and strongly angle-dependent reflection of the ventral wings suggests the question whether or not the wing reflections may play a role in visual signaling by the butterflies during flight. Furthermore, we determined the shape and surface texture of the scales by scanning electron microscope (SEM). From SEM images, the scales cover the wing membrane and appear to overlap like roof tiles. These nanometer structures of the cover scales will decide the attractive iridescence of the wing.

The nature of electromagnetic (EM) phenomena, including light, is not fully clear. Postulated rejection of EM ether as a hypothetical habitat and distribution of EM waves, holds in the uncertainty and the problem of understanding the existence of most of these waves, because the notion of "wave" inseparable from the concept of "environment". EM ether, as a hypothetical environment of origin and propagation of EM waves, was declined by postulate. This keeps the uncertainty in the problem of understanding the existence of these waves actually, since the definition of "wave" is an part of the definition of "environment". The input in physics of the concept of wave "coherence", which was necessary to explain the phenomenon of interference of light, also requires a transparent physical interpretation. Today use of the idea of the several-meters - length wave zugs, which are emitted by individual atoms, is at least unconvincing, thus there is technical ability to generate powerful light pulses of 10^-15 s. A quantum model of the structure of the optical packet stream, which provides a transparent physical interpretation of all parameters of coherent light, is offered. In this model parameters of coherence are organically linked with the geometry parameters of the quantum packets. Developments of classical wave optics will not be discarded. To coordinate with the quantum-packet model and modern views about the nature of light, we either give them a new interpretation or adjust, or develop these developments. In particular, a new interpretation of the experimental fact increase the radius of coherence of light coming from distant sources (stars) is offered. Modern conception of light corpuscles-photons is formulated. The estimations of the size of the spatial localization of the photon is received. "Diffraction of photons" is considered.

A polarization model for calculating the ellipticities of the clockwise and counterclockwise output beams in square ring resonators is established in this article. The model takes into account the following parameters such as Ar, g, ξ and Φ simultaneously, where Ar is the distortion angle, g is the phase shift of all four mirrors, ξ is the angle between the S-polarization and the substrate "fast" axis of the output mirror, Φ is the birefringence angle of the output mirror. With the consideration of the output mirror's stress effect, the parameters such as ξ and Φ have unsymmetrical influences on the ellipticities of clockwise and counterclockwise beams, and the distortion angle is unequal to zero when the ellipticities of clockwise and counterclockwise output beams are equivalent. Based on those novel results, A novel method to controll the distortion angle during the alignment process with the eliminatation of the output mirror's stress effect simultaneously has been proposed in this article and this method can decrease the magnetic bias of square ring resonators effectively. These interesting findings are important to the research of high precision and super high precision ring laser gyros.

The optical speckle field generated by the scattering of a laser beam on a rough surface contains useful information about the surface properties especially in the case of the incident beam illuminates only a few correlation cells of the surface roughness. The study of the transition from the non Gaussian to the Gaussian regime of the speckle field can increase the amount of accessible information concerning the surface roughness. The probability density function of intensity is helpful to characterize an optical speckle field, but we do not obtain information about the qualification of spatial distribution of the field. To qualify this spatial intensity distribution, we propose to use the Minimum Spanning Tree methodology. From the tree constructed from the set of points of the local maxima of the intensity distributions in an observation plane, we determine the mean and the standard deviation of the edges length of the tree and we qualify the distributions of this points (ordered, cluster, random...). Using high resolution images, we will present the first results concerning the study of a Gaussian transition of a speckle field by the Minimum Spanning Tree method and some preliminary results about the study of the spatial distribution of phase singularities in this transition. At the end, we will highlight that this new approach appears to be a very robust way to characterize the correlation length of a surface roughness and its illumination conditions, and offers a new criterion to study the optical speckle field.

Electromagnetism theory is used to calculate the effect of aperture receiver on the polarization of scattered light. The result is a spatial average (several speckle grains within the aperture) responsible for a depolarization process similar to that of temporal situation. The associated DOP is calculated versus surface parameters (roughness, slope...) and reveals new signatures for identification of samples. The DOP is also calculated in a multi-scale manner, that is, versus the receiver aperture. Examples are given to separate surface and bulk scattering.

Given a beam propagation algorithm, whether it is a commercial implementation or some other in-house or research implementation, it is not trivial to determine whether it is suitable either for a wide range of applications or even for a specific application. In this paper, we describe a range of tests with "known" results; these can be used to exercise beam propagation algorithms and assess their robustness and accuracy. Three different categories of such tests are discussed. One category is tests of self-consistency. Such tests often rely on symmetry to make guarantees about some aspect of the resulting field. While passing such tests does not guarantee correct results in detail, they can nonetheless point towards problems with an algorithm when they fail, and build confidence when they pass. Another category of tests compares the complex field to values that have been experimentally measured. While the experimental data is not always known in precisely, and the experimental setup might not always be accessible, these tests can provide reasonable quantitative comparisons that can also point towards problems with the algorithm. The final category of tests discussed is those for which the propagated complex field can be computed independently. The test systems for this category tend to be relatively simple, such as diffraction through apertures in free space or in the pupil of an ideal imaging system. Despite their relative simplicity, there are a number of advantages to these tests. For example, they can provide quantitative measures of accuracy. These tests also allow one to develop an understanding of how the execution time (or similarly, memory usage) scales as the region-of-interest over which one desires the field is changed.

We discuss how the rigorous grating theory can be extended to cover also partially coherent illumination such that the method stays computationally reasonable. We first discuss the S-matrix formalism if the input field is not a simple plane wave, and then continue the approach to the case of partial coherence. We illustrate the approach by investigating the imaging of a grating in a classical bright-field imaging setup.

The application of the Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) series expansions in the paraxial simulation of optical pulses is described and presented through examples of pulse modulation by diffractive Fresnel lenses and axicons. Using the FDTD technique we exhibit the physical propagation of a Hermite-Gaussian mode outside of the paraxial regime, with a width parameter of the same order of magnitude as the wavelength. In higher order modes this causes evanescence at the source of such modes, and we describe the loss of energy caused by this phenomenon. Using recently derived expressions for the non-paraxial propagation of Hermite-Gaussian modes, we discuss the use of modal techniques outside of the usual paraxial restriction, which allows for an efficient modal synthesis of Rayleigh-Sommerfeld diffraction effects in the far-field.

Although proximity printing is the oldest and, in view of the basic optical setup, simplest photolithographic technique, it still remains in heavy use in the semiconductor manufacturing industry. The fact that this technique exists for a long time does not mean that there is no more room for improvements or new applications. Lending concepts developed for modern projection scanners and steppers and adapting them for our purposes, we demonstrate how numerical simulation and optimization can help to make the proximity printing process more stable against process variations and to increase the resolution for critical features. For this purpose, we numerically optimize the angular spectrum of the illumination and the mask layout. Furthermore, we couple the optimization of the optical degrees of freedom to the simulation of photoresist development to assess the effects of changes to the illumination and mask on the final photoresist profile.

Source Mask Optimization (SMO) is one of the most important techniques available for extending ArF immersion lithography. The combination of freeform source shape and complex mask pattern, determined by SMO, can extend the practical resolution of a lithography system. However, imaging with a small k1 factor (~0.3 or smaller) is very sensitive to many imaging parameters, such as illumination source shape error, lens aberration, process property, etc. As a result, care must be taken to insure that the source solution from SMO can be produced by the real illuminator, which is subject to its own imaging constraints. One approach is to include an illuminator simulator in the SMO loop so that only realizable illumination pupils are considered during optimization. Furthermore, the real source shape must be re-adjusted to realize expected imaging performance as may be seen, for example, in an Optical Proximity Effect (OPE) curve. In this paper we present and describe both the illuminator simulator, which can predict the real pupilgram on the exposure tool quickly, and an illumination pupilgram re-adjustment method that can effectively control the various illumination parameters to get optimum imaging performance, which is required for the lithography process design. The adjusting method uses pupilgram modulation functions, which are similar to Zernike polynomials used in wavefront aberration analysis for lithographic projection lens, to describe the optimal pupilgram adjustment, and the resulting modulation can then be realized by the illuminator system.

Extreme ultraviolet (EUV) - lithography at a wavelength around 13.5 nm is considered as the most promising successor of optical projection lithography. This paper reviews simulation models for EUV lithography. Resist model parameters are calibrated with experimental data. The models are applied for the investigation of the impact of mask multilayer defects on the lithographic process.

This paper proposes an analytical model to describe the mask diffraction in EUV lithography. The model is used to improve the understanding of the EUV mask performance and to analyze relevant mask topography effects. The multilayer and absorber constituting the EUV mask are simulated separately in this model. The light incident on the mask is first diffracted by the absorber, and then reflected by the multilayer and propagated upwards through the absorber again. The multilayer reflection is calculated by a mirror approximation, and the absorber transmission is calculated by a modified Kirchhoff model, where the absorber is considered to be thin and located in a certain plane. Moreover, an analytical expression of the diffraction spectrum of masks with arbitrary pattern orientation is derived. Comparisons with rigorous simulation are used to validate the accuracy of the developed model. It predicts mask diffraction of 16nm wide line and space features. For 0.35 NA EUV systems with an incidence angle of 6° the simulated CD errors are below 0.5 nm, with a pattern pitch ranging from 32nm to 250nm.

The internal electric field enhancement is critical for the laser induced damage properties of pulse compression gratings (PCG) in high-energy laser systems. Due to complex fabrication processes of PCG such as coating, interference lithography and etching, different kinds of defects, like nodular defects in multilayers and non-uniformities of the grating profiles on PCG surface, can't be practically avoided. From simulation results, we can know that some of these defects have little effect on the spectral response of optical elements, but they may produce huge changes of internal electric fields and thus decrease the damage threshold of PCG. To obtain a better understanding of the dependence of the internal electric field enhancement on these defects and their dimensions, this work is focused on the near field distributions of defective PCGs using rigorous electric magnetic field (EMF) solvers.

Visibility, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) are quantities that characterize the quality of the image in ghost (or correlation) imaging. The visibility in quantum and classical ghost imaging with scalar light is known to improve as the order of imaging increases. Recently also electromagnetic ghost imaging has started to attract attention. In this work we analyze the effects of both the order of imaging and the degree of polarization (P) of the illumination on the image quality parameters. The source is a classical, partially polarized, random electromagnetic field obeying Gaussian statistics. The beam is split into several (N) parts which are directed either into the object or reference arms and the associated intensity correlations are calculated. When N > 2, more than one reference arm may exist which contributes to the background. We consider two different definitions for the visibility, as well as the SNR and CNR, and examine their attainable limiting values in second- and higher-order ghost imaging as a function of the degree of polarization. Both expressions of the visibility behave in a similar manner; they increase with the order of imaging and the degree of polarization. In second-order imaging the SNR decreases, due to increased noise, as P increases, while the CNR remains essentially constant. We emphasize that the exact numerical values depend on the definitions used and on the number of object arms in the setup.

In this work we present an analysis of non-slanted reflection gratings by using a corrected Coupled Wave Theory which takes into account boundary conditions. It is well known that Kogelnik's Coupled Wave Theory predicts with great accuracy the response of the efficiency of the zero and first order for volume phase gratings, for both reflection and transmission gratings. Nonetheless, since this theory disregard the second derivatives in the coupled wave equations derived from Maxwell equations, it doesn't account for boundary conditions. Moreover only two orders are supposed, so when either the thickness is low or when high refractive index high are recorded in the element Kogelnik's Theory deviates from the expected results. In Addition, for non-slanted reflection gratings, the natural reflected wave superimpose the reflection order predicted by Coupled Wave theories, so the reflectance cannot be obtained by the classical expression of Kogelnik's Theory for reflection gratings. In this work we correct Kogelnik's Coupled Wave Theory to take into account these issues, the results are compared to those obtained by a Matrix Method, showing good agreement between both theories.

The results of the observation of process of the photo-induced frequency doubling of light in germanium-silicate patterns are presented. During the investigation a big anomalous growth of the light absorption has been detected in the region of the high induced electric field. The absorption blocks the process of the writing of the grating of the nonlinear second-order susceptibility and leads to the self-disappearance of the frequency doubling. Some properties of the observed phenomenon have been studied in experiments and the possible mechanisms of the dynamics of the observed processes are discussed.