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**Articles 1 to 20 of 31**
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## February

Experimental demonstration of a secondary source of partially polarized states

- received 11/10/2014; accepted 02/22/2015; posted 02/23/2015; Doc. ID 226689
- [full text: PDF (1284) KB)]
- Abstract: We present a simple device that works as a secondary source of light with prescribed polarization properties. The device has great versatility, allowing complete control over both the degree of polarization and the Stokes vector that belongs to the fully polarized component of partially polarized light beams. We report experimental results that illustrate the device's versatility by showing how polarized states can be moved within the Poincaré ball along spiraling paths.

**Keywords (OCIS):**

- (120.3180) Instrumentation, measurement, and metrology : Interferometry
- (120.5410) Instrumentation, measurement, and metrology : Polarimetry
- (230.5440) Optical devices : Polarization-selective devices

Statistical similarity and complete coherence of electromagnetic fields in time and frequency domains

- received 12/23/2014; accepted 02/22/2015; posted 02/23/2015; Doc. ID 231299
- [full text: PDF (523) KB)]
- Abstract: We investigate the statistical similarity of partially polarized, partially coherent electromagnetic fields in time and frequency domains, and the relationship between statistical similarity and complete coherence. We find that both in time domain and in frequency domain the complete coherence of two fields is equivalent to the fields being both fully polarized and statistically similar. Unlike in scalar coherence theory, statistical similarity alone is found not to constitute a sufficient condition for complete coherence. We derive the conditions under which spectrally completely coherent fields are also temporally fully coherent, and we point out that temporally completely coherent fields are necessarily fully spectrally coherent at all frequencies. Complete temporal and spectral coherence of electromagnetic fields are found to be related to the recently introduced concept of strict cross-spectral purity, but in contrast to the scalar case, strict cross-spectral purity is not a necessary condition for complete temporal coherence if the fields have different spectral polarization states.

**Keywords (OCIS):**

- (030.1640) Coherence and statistical optics : Coherence
- (030.6600) Coherence and statistical optics : Statistical optics
- (260.2110) Physical optics : Electromagnetic optics
- (260.5430) Physical optics : Polarization

Uniform asymptotics of paraxial boundary diffraction waves

- received 12/04/2014; accepted 02/19/2015; posted 02/19/2015; Doc. ID 229076
- [full text: PDF (1945) KB)]
- Abstract: Starting from the paraxial formulation of the boundary-diffracted-wave theory proposed by Hannay [J. Hannay, J. Mod. Opt. \textbf{47,} 121-124 (2000)] and on exploiting its intrinsic geometrical character, we re-discover some classical results of Fresnel diffraction theory, valid for ``large' hard-edge apertures, within a somewhat unorthodox perspective. In this way a geometrical interpretation of the Schwarzschild's uniform asymptotics of the paraxially diffracted wavefield by circular apertures [K. Schwarzschild, Sitzb. M\"unchen Akad. Wiss. Math.-Phys. Kl. \textbf{28,} 271 - 294 (1898)] is given and later generalized to deal with arbitrarily shaped apertures with smooth boundaries. A quantitative exploration is then carried out, with the language of catastrophe optics, about the diffraction patterns produced, within the geometrical shadow, by opaque elliptic disks under plane wave illumination. In particular, the role of the ellipse's evolute as geometrical caustic of the diffraction pattern is emphasized through an intuitive interpretation of the underlying saddle coalescing mechanism, obtained by suitably visualizing the saddle topology changes induced by letting the observation point to move along the ellipse's major axis.

**Keywords (OCIS):**

- (000.3870) General : Mathematics
- (070.2580) Fourier optics and signal processing : Paraxial wave optics
- (260.1960) Physical optics : Diffraction theory

Generic Propagation of Beams with Sharp Spatial Boundaries

- received 12/04/2014; accepted 02/19/2015; posted 02/20/2015; Doc. ID 228627
- [full text: PDF (594) KB)]
- Abstract: The propagation of spatial beams with initially sharp transverse boundaries is investigated theoretically with the paraxial wave equation (analytically and numerically) and experimentally. The sharp boundaries generate a universal pattern, which is a consequence of the Schrödinger-like nature of the paraxial dynamics. As a consequence, an approximate analytical expression can be derived for the longitudinal propagation dynamics of the beam. We show that the derived analytical expression is not only a good approximation for the solution of the paraxial approximation wave equation, but it is also a good approximation for the solution of the full electromagnetic wave equation as well. Good agreement between the analytical expression and experiment results is presented.

**Keywords (OCIS):**

- (070.2580) Fourier optics and signal processing : Paraxial wave optics
- (110.1220) Imaging systems : Apertures
- (200.0200) Optics in computing : Optics in computing
- (260.1960) Physical optics : Diffraction theory
- (070.7345) Fourier optics and signal processing : Wave propagation

Interpretation of azimuthal angle dependence of periodic gratings in Mueller Matrix Spectroscopic Ellipsometry

- received 12/12/2014; accepted 02/19/2015; posted 02/20/2015; Doc. ID 229470
- [full text: PDF (943) KB)]
- Abstract: Mueller matrix spectroscopic ellipsometry becomes increasingly important for determining structural parameters of periodic line gratings. Due to the anisotropic character of gratings, the measured Mueller matrix elements are highly azimuthal angle dependent. Measurement results are interpreted by basic principles of diffraction on gratings. The spectral and azimuthal angle dependent intensity changes are correlated to so called Rayleigh singularities, i.e. wavelengths, where the number of diffraction orders changes. The positions of the Rayleigh singularities are calculated analytically and overlapped with measured spectra of two different types of photomasks with transparent and reflecting substrates, respectively. For both types of gratings, the Rayleigh singularities reproduce the contours of the spectra. Increasing grating periods result in a shift of these contours to longer wavelengths. Characteristic differences between the two photomasks are explained by the influence of the transmission orders, which are determined by the substrate transparency.

**Keywords (OCIS):**

- (050.1950) Diffraction and gratings : Diffraction gratings
- (260.1960) Physical optics : Diffraction theory
- (260.2130) Physical optics : Ellipsometry and polarimetry
- (290.5870) Scattering : Scattering, Rayleigh
- (300.3700) Spectroscopy : Linewidth
- (300.6550) Spectroscopy : Spectroscopy, visible

A Method of Field Expansions for Vector Electromagnetic Scattering by Layered Periodic Crossed Gratings

- received 12/23/2014; accepted 02/19/2015; posted 02/20/2015; Doc. ID 231273
- [full text: PDF (1725) KB)]
- Abstract: In many applications of scientific and engineering interest the accurate modeling of scattering of linear waves by periodic layered media plays a crucial role. From geophysics and oceanography to materials science and imaging, the ability to simulate such configurations numerically in a rapid and robust fashion is of paramount importance. In this contribution we focus upon the specific problem of vector electromagnetic radiation interacting with a multiply layered periodic crossed diffraction grating. While all of the classical methods for the numerical simulation of partial differential equations have been brought to bear upon this problem, we argue here that in this particular context a High--Order Perturbation of Surfaces (HOPS) approach is superior. In particular, we describe how the Method of Field Expansions (FE) can be extended to the fully vectorial and three dimensional scattering problem in the presence of multiple layers. With specific numerical experiments we will show the remarkable efficiency, fidelity, and high--order accuracy one can achieve with an implementation of this algorithm.

**Keywords (OCIS):**

- (240.6680) Optics at surfaces : Surface plasmons
- (050.1755) Diffraction and gratings : Computational electromagnetic methods

Poynting vector profile of a tightly focused radially polarized beam in the presence of primary aberrations

- received 01/07/2015; accepted 02/19/2015; posted 02/20/2015; Doc. ID 231817
- [full text: PDF (5239) KB)]
- Abstract: The Poynting vector profile of a tightly focused radially polarized beam has some unique and interesting properties. For instance the light on the optical axis in the focal volume corresponds to a null Poynting vector indicating the light there to be non-propagating. However the beam here is considered to be an unaberrated one. Thus it will be important to know whether the commonly occurring monochromatic aberrations can have any effect on the ideal Poynting vector profile of a radially polarized beam. In this paper we make use of Fourier transform form of the vectorial diffraction theory to investigate the effect of primary aberrations on the Poynting vector profile of a radially polarized beam under tight focusing condition. We present here the results from our study on the behaviour of both the time averaged and time dependent Poynting vector profiles in the focal volume.

**Keywords (OCIS):**

- (140.7010) Lasers and laser optics : Laser trapping
- (220.1010) Optical design and fabrication : Aberrations (global)
- (260.1960) Physical optics : Diffraction theory
- (260.5430) Physical optics : Polarization

Perturbative analysis of partially coherent illumination for coma aberration measurements

- received 12/16/2014; accepted 02/18/2015; posted 02/20/2015; Doc. ID 229343
- [full text: PDF (388) KB)]
- Abstract: The theory of coma aberration measurement for aerial image sidelobe peaks is extended from coherent illumination to partial illumination. We prove that the coma aberration linearity of the intensity difference between the two peaks is satisfied even in the partially coherent case. Using weak diffraction approximation, we analytically reveal the coherence dependency of the aberration measurement sensitivity for a single line in a bright field. We confirm that our derived formulas are well matched with numerical lithography simulation results. These results provide guidelines for the measurement condition; higher aberration sensitivity is available under the higher coherence of the illumination pupil.

**Keywords (OCIS):**

- (110.2990) Imaging systems : Image formation theory
- (110.3960) Imaging systems : Microlithography
- (110.4980) Imaging systems : Partial coherence in imaging
- (260.1960) Physical optics : Diffraction theory
- (070.7345) Fourier optics and signal processing : Wave propagation

Derivatives of Optical Path Length: from Mathematical Formulation to Applications

- received 12/30/2014; accepted 02/17/2015; posted 02/18/2015; Doc. ID 231551
- [full text: PDF (1372) KB)]
- Abstract: The optical path length (OPL) of an optical system is a highly important parameter since it determines the phase of the light passing through the system and governs the interference and diffraction of the rays as they propagate. The Jacobian and Hessian matrices of the OPL are of fundamental importance in tuning the performance of a system. However, the OPL varies as a recursive function of the incoming ray and the boundary variable vector, and hence computing the Jacobian and Hessian matrices is extremely challenging. In an earlier study by the present group, this problem was addressed by deriving the Jacobian matrix of the OPL with respect to all of the independent system variables of a non-axially symmetrical system. In the present study, the proposed method is extended to the Hessian matrix of a non-axially symmetrical optical system. The proposed method facilitates the cross-sensitivity analysis of the OPL with respect to arbitrary system variables and provides an ideal basis for automatic optical system design applications in which the merit function is defined in terms of wavefront aberrations. An illustrative example is given. It is shown that the proposed method requires fewer iterations than that based on the Jacobian matrix and yields a more reliable and precise optimization performance.

**Keywords (OCIS):**

- (080.0080) Geometric optics : Geometric optics
- (080.2740) Geometric optics : Geometric optical design
- (080.3620) Geometric optics : Lens system design
- (080.1753) Geometric optics : Computation methods

An Analytical Expression for the Average Ensquared Energy

- received 11/20/2014; accepted 02/17/2015; posted 02/19/2015; Doc. ID 227227
- [full text: PDF (639) KB)]
- Abstract: We derive an expression for the average area of intersection between a blur spot of radius R and a square pixel where the center of the blur is uniformly chosen from the pixel interior. Implications of the result are then discussed in the context of a point source detection problem.

**Keywords (OCIS):**

- (110.2970) Imaging systems : Image detection systems
- (110.3080) Imaging systems : Infrared imaging
- (220.4830) Optical design and fabrication : Systems design

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

- received 12/10/2014; accepted 02/16/2015; posted 02/18/2015; Doc. ID 228994
- [full text: PDF (553) KB)]
- Abstract: The vertical mode expansion method (VMEM) (X. Lu et al., J. Opt. Soc. Am. A 31, 293-300, 2014) is a frequency-domain numerical method for solving Maxwell's equations in structures that are layered in a cylindrical region and its exterior. Based on expanding the electromagnetic field in one-dimensional vertical modes, VMEM reduces the original three-dimensional problem to a two-dimensional (2D) problem on the vertical boundary of the cylindrical region. However, VMEM has so-far only been implemented for structures with circular cylindrical regions. In this paper, we develop a VMEM for structures with an elliptic cylindrical region, based on separation of variables in the elliptic coordinates. A key step in VMEM is to calculate the so-called Dirichlet-to-Neumann (DtN) maps for 2D Helmholtz equations inside or outside the ellipse. For numerical stability reasons, we avoid the analytic solutions of the Helmholtz equations in terms of the angular and radial Mathieu functions, and construct the DtN maps by a fully numerical method. To illustrate the new VMEM, we analyze the transmission of light through an elliptic aperture in a metallic film, and the scattering of light by elliptic gold cylinders on a substrate.

**Keywords (OCIS):**

- (050.1755) Diffraction and gratings : Computational electromagnetic methods
- (290.5825) Scattering : Scattering theory
- (050.6624) Diffraction and gratings : Subwavelength structures

Intensity fluctuations of multimode laser beams in underwater medium

- received 11/17/2014; accepted 02/15/2015; posted 02/18/2015; Doc. ID 226959
- [full text: PDF (397) KB)]
- Abstract: In an oceanic optical communications link, the received intensity fluctuations, quantified by the scintillation index are formulated and evaluated when a multimode laser is used. The variations of the scintillation index versus the oceanic turbulence parameters are examined for different multimode laser structures. Oceanic turbulence parameters used are the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, the Kolmogorov inner scale and the parameter w that defines the ratio of temperature to salinity contributions to the refractive index spectrum. The results in this paper can be used to improve the performance in the design of oceanic optical communications links.

**Keywords (OCIS):**

- (010.3310) Atmospheric and oceanic optics : Laser beam transmission
- (010.4450) Atmospheric and oceanic optics : Oceanic optics
- (290.5930) Scattering : Scintillation

Diffraction of a focused wave by an aperture: a new perspective

- received 10/29/2014; accepted 02/13/2015; posted 02/20/2015; Doc. ID 225845
- [full text: PDF (580) KB)]
- Abstract: A new approach for calculating the field in the focal region along lines through the focal point of a lens is presented. In particular, the method is applied to a circular aperture. It is also applied to other shaped apertures, including circular sectors or segments, such as a semicircular aperture or Hilbert mask, and for polygonal shapes. The diffracted field is calculated by a one-dimensional Fourier transform, and can be used for accurate calculation at observation points distant from the focus. The approach gives new insight in appreciating the asymptotic behavior of the diffracted field, and the existence of intensity zeros, for different aperture shapes.

**Keywords (OCIS):**

- (050.1960) Diffraction and gratings : Diffraction theory
- (260.1960) Physical optics : Diffraction theory

Free Space Non-Perpendicular Electric-Magnetic Fields

- received 11/10/2014; accepted 02/13/2015; posted 02/18/2015; Doc. ID 226647
- [full text: PDF (7501) KB)]
- Abstract: The electric and magnetic components of an electromagnetic wave in free space are believed by many to be perpendicular to each other. We outline a procedure by which electromagnetic potentials are constructed, and we derive free-space non-perpendicular electric-magnetic fields from these potentials. We show, for example, that in free-space Bessel-related fields, at a small region near the origin, the angle between these components spans a range of 7.5⁰ to 172.5⁰, that is, they are far from being perpendicular. This can be contrasted with plane waves, where, following the same procedure, we verify that the electric field strength (E(x,y,z,t)) and the magnetic flux density (B(x,y,z,t)) are indeed perpendicular to each other and to the direction of propagation.

**Keywords (OCIS):**

- (260.2110) Physical optics : Electromagnetic optics
- (070.7345) Fourier optics and signal processing : Wave propagation

Effective degree of coherence: a second look

- received 12/10/2014; accepted 02/11/2015; posted 02/20/2015; Doc. ID 229397
- [full text: PDF (679) KB)]
- Abstract: In this paper we show that the most general set of transformations of electromagnetic fields for which overall coherence properties can reasonably be expected to remain unchanged is the set of scaled unitary transformations. Building on our earlier results concerning coherence functionals that are invariant to scaled unitary transformations, we prove that the effective degree of coherence is the only such functional that is `additive' in the sense that it can be computed for linear combinations of fields from its values for pairwise sums of the constituent fields. Additionally, we highlight the fact that the invariance of the effective degree of coherence to scaled unitary transformations means that it has the same value when computed from most of the important representations of electromagnetic fields. We then go on to use the effective degree of coherence to provide a generalization of the scalar two-point degree-of-coherence function to a system consisting of two orthogonal Hilbert spaces. Interestingly, several commonly used local measures of coherence and polarization turn out to be special cases of this generalization.

**Keywords (OCIS):**

- (030.1640) Coherence and statistical optics : Coherence
- (030.6600) Coherence and statistical optics : Statistical optics
- (260.2110) Physical optics : Electromagnetic optics
- (260.5430) Physical optics : Polarization

Modified reciprocity relation for the time dependent diffusion equation

- received 10/15/2014; accepted 02/09/2015; posted 02/09/2015; Doc. ID 225023
- [full text: PDF (451) KB)]
- Abstract: The classical reciprocity relation of radiative transfer fails for two points placed in regions having different indices of refraction. A modified reciprocity relation that involve the relative refractive index between the two points considered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (J. Opt. Soc. Am. A, 14, 486-490, 1997). In this paper we extend these findings to the time-dependent diffusion equation and we discuss some implications to diffuse optical tomography.

**Keywords (OCIS):**

- (170.3660) Medical optics and biotechnology : Light propagation in tissues
- (170.3880) Medical optics and biotechnology : Medical and biological imaging
- (170.5280) Medical optics and biotechnology : Photon migration
- (290.1990) Scattering : Diffusion

Range Resolved Mode Mixing in a Large Volume for the Mitigation of Speckle and Strategic Target Orientation Requirements in Active Millimeter-Wave Imaging

- received 12/23/2014; accepted 02/08/2015; posted 02/18/2015; Doc. ID 231336
- [full text: PDF (2587) KB)]
- Abstract: In spite of many reports of active millimeter-wave imaging in the literature, speckle and requirements for cooperative target orientation significantly reduce its practical usefulness. Here we report a new technique, range resolved mode mixing (RRMM), which significantly mitigates both of these issues. It also provides a three dimensional (3D) image. RRMM accomplishes this by combining multimode illumination (which eliminates the requirement for cooperative target orientation) with range resolution (which provides statistical independence of speckle patterns for averaging and the 3D image). The use of a 5W Extended Interaction Klystron Amplifier results in large signal margins in the 50 m scale atrium of the Physics Department at Ohio State University. It appears that there are a number of scenarios out to a range of 1 km for which his approach is useful to provide 3D images, with minimal speckle, and no requirement for cooperative target orientation.

**Keywords (OCIS):**

- (030.1670) Coherence and statistical optics : Coherent optical effects
- (030.6140) Coherence and statistical optics : Speckle
- (110.0110) Imaging systems : Imaging systems
- (110.6795) Imaging systems : Terahertz imaging

Understanding disability glare: light scatter and retinal illuminance as predictors of sensitivity to contrast

- received 10/07/2014; accepted 02/06/2015; posted 02/09/2015; Doc. ID 224550
- [full text: PDF (2150) KB)]
- Abstract: The presence of a bright light in the visual field has two main effects on the retinal image: reduced contrast and increased retinal illuminance due to scattered light; the latter can, under some conditions, lead to an improvement in retinal sensitivity. The combined effect remains poorly understood, particularly at low light levels. A psychophysical flicker-cancellation test was used to measure the amount and angular distribution of scattered light in the eye for 40 observers. Contrast thresholds were measured using a functional contrast sensitivity test. Pupil-plane glare-source illuminances (i.e. 0, 1.35, 19.21 lm/m2), eccentricities (5°, 10°, 15°), and background luminances (1, 2.6, 26 cd/m2) were investigated. Visual performance was better than predicted, based on loss of retinal image contrast caused by scattered light, particularly in the mesopic range. Prediction accuracy improved significantly when the expected increase in retinal sensitivity in the presence of scattered light was also incorporated in the model.

**Keywords (OCIS):**

- (290.0290) Scattering : Scattering
- (330.0330) Vision, color, and visual optics : Vision, color, and visual optics
- (330.1800) Vision, color, and visual optics : Vision - contrast sensitivity
- (330.5510) Vision, color, and visual optics : Psychophysics
- (330.7320) Vision, color, and visual optics : Vision adaptation
- (290.2648) Scattering : Stray light

Theory and Operational Rules for the Discrete Hankel Transform

- received 02/06/2015; accepted 02/06/2015; posted 02/11/2015; Doc. ID 234161
- [full text: PDF (1128) KB)]
- Abstract: Previous definitions of a Discrete Hankel Transform have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a Discrete Hankel Transform that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the Discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

**Keywords (OCIS):**

- (070.0070) Fourier optics and signal processing : Fourier optics and signal processing
- (070.2025) Fourier optics and signal processing : Discrete optical signal processing
- (070.2465) Fourier optics and signal processing : Finite analogs of Fourier transforms

Mirage is an image in a flat ground surface

- received 07/29/2014; accepted 02/04/2015; posted 02/06/2015; Doc. ID 219870
- [full text: PDF (711) KB)]
- Abstract: Mirage is a fascinating phenomenon that has attracted many scientists to report their observations and descriptions about it. There are two different approaches to mirage formation. The more popular one is attributed to the total internal reflection that occurs in near ground air layers on hot sunny days. According to the other approach, mirage is an image in a rough surface that is observed at grazing angles of incidence. Most of the existing descriptions are qualitative and some include calculations based on guessing temperature change with no concrete experiments. In this report, first we show the Fermat's principle also concerns the wave nature of light and constructive and destructive interference are essential for image formation. Then, we provide a brief review of the image formation theory in a rough plane and demonstrate by experiments in lab and deserts that the temperature gradient in near ground air layers does not lead to mirage formation.

**Keywords (OCIS):**

- (010.4030) Atmospheric and oceanic optics : Mirages and refraction
- (110.2990) Imaging systems : Image formation theory
- (290.5880) Scattering : Scattering, rough surfaces

**Articles 1 to 20 of 31**
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