Optical system design for orthosymplectic transformations in phase space

On the basis of a matrix formalism, we analyze the paraxial optical systems composed by generalized lenses and fixed free-space intervals, suitable for orthosymplectic transformations in phase space. Flexible configurations to perform the attractive operations for optical information processing such as image rotation, separable fractional Fourier transformation, and twisting for different parameters are proposed.     

确定相空间重构参数的一种新方法

用相点的惯量矩来描述相轨迹在相空间中展开的程度,用相点的惯量矩的相对变化来描述相轨迹展开的快慢。导出了相点关于主对角线的、与重构参数有关的惯量矩公式。用该公式计算了相点的惯量矩的相对变化,选出了不同维数的延迟时间。从非零延迟时间中选出的最小维数就是嵌入维数,该非零延迟时间就是最终确定的延迟量。用此方法获得的参数重构出的相轨迹质量较好,且具有抗噪能力强。     

Parametric down and up conversion in the Wigner representation of quantum optics

Abstract

We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.     

Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space

New representations are defined for describing electromagnetic wave fields in free space exactly in terms of rays for any wavelength, level of coherence or polarization, and numerical aperture, as long as there are no evanescent components. These representations correspond to tensors assigned to each ray such that the electric and magnetic energy densities, the Poynting vector, and the polarization properties of the field correspond to simple integrals involving these tensors for the rays that go through the specified point. For partially coherent fields, the ray-based approach provided by the new representations can reduce dramatically the computation times for the physical properties mentioned earlier.     

Complex signal representation, Mandel's theorem, and spiral phase quadrature transform

Complex (or analytic) signal representation as introduced by Gabor plays an important role in optical signal processing and in coherence theory of optical fields. Several definitions for extending the notion of complex signal representation to two dimensions have appeared in the literature. These definitions differ in their choice of the quadrature transform for a two-dimensional signal. We study the problem of determining the complex representation for two-dimensional real signals (or images) using a least-square minimization framework first used by Mandel [J. Opt. Soc. Am.57, 613 (1967)JOSAAH0030-3941]. In particular, we seek a suitable quadrature transform such that the resultant complex image has the least fluctuating envelope in an ensemble-averaged sense. It is observed that the spiral phase quadrature transform for two-dimensional signals is a solution of this analysis.     

水下目标辐射噪声相空间重构参数选取方法

利用自相关函数法和平均互信息法求取相空间重构的延迟参数,对实测数据计算结果进行了分析比较,确定了相空间重构时间延迟参数的选择方法。在用伪最近邻法进行相空间重构嵌入维数的选取时,使用时空曲线法计算TheilerWindow的窗口值W,并以此为依据剔除由于时间上的邻近而造成的空间上的邻近的最近邻点,改进了伪最近邻计算嵌入维数的方法。实测数据计算结果表明,该方法能够获取合理、有效的嵌入维参数。     

Ocean optics estimation for absorption,backscattering, and phase function parameters

We propose and test an inverse ocean optics procedure with numerically simulated data for the determination of inherent optical properties using in-water radiance measurements. If data are available at only one depth within a deep homogeneous water layer, then the single-scattering albedo and the single parameter that characterizes the Henyey-Greenstein phase function can be estimated. If data are available at two depths, then these two parameters can be determined along with the optical thickness so that the absorption and scattering coefficients, and also the backscattering coefficient, can be estimated. With a knowledge of these parameters, the albedo and Lambertian fraction of reflected radiance of the bottom can be determined if measurements are made close to the bottom. A simplified method for determining the optical properties of the water also is developed for only three irradiance-type measurements if the radiance is approximately in the asymptotic regime.     

Amplitude and phase representation of monochromatic fields in physical optics

The conservation equation for a monochromatic field with arbitrary polarization propagating in an inhomogeneous transparent medium is expressed in terms of amplitude and phase variables. The expressions obtained for linearly polarized fields are compared with the results obtained in the eikonal approximation. The electric field wave equation is written in terms of intensity and phase variables. The transport equations for the irradiance and the phase are shown to be particular cases of these derivations. The conservation equation arising from the second-order differential wave equation is shown to be equivalent to that obtained from Poynting's theorem.     

Generalized Wigner distributions,moments and conditional correspondence rules

Methods are presented to generate conditional moments for all quasi-probability distributions, and explicit expressions for all conditional moments are given. In analogy to the generalized characteristic function operator, which generates all joint quasi-distribution functions, the conditional characteristic function operator which generates all conditional quasi-distributions is defined. This allows one to introduce the concept of conditional correspondence rules; formulations are given for all such rules.     

New relation between input and output fields based on Collins diffraction formula and the Wigner function in entangled state representation

Based on the correspondence between the Collins diffraction formula (optical Fresnel transform) and the transform matrix element of a three-parameter two-mode squeezing operator in the entangled state representation 1 Fan, H-Y and Lu, H-L. 2006. Opt. Lett., 31: 2622–2624.  [Google Scholar] we further explore the relationship between output field intensity determined by the Collins formula and the input field's probability distribution along an infinitely thin phase space strip, both in the spatial domain and the frequency domain. The entangled Wigner function is introduced for recapitulating the result.     

Realistic eight-port homodyne detection and covariant phase space observables

We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.     

Optical, thermal and phase transition studies in Sn1-x Ge x Te

The optical and thermal properties of the mixed semiconducting alloy, Sn_1-xGe_xTe, is studied by photo acoustics, for various Ge concentrations and phase transition for a particular concentration is also studied by the same method. The results are compared with the available literature values and discussed.     

Optical properties of highly scattering media determined from changes in attenuation, phase, and modulation depth

The optical properties of scattering media determine the attenuation (A) and the transit time (?t?) of light reflected from the medium as well as the phase (?) and modulation depth (M) of an intensity-modulated lightwave. Our primary finding is that the ratio of changes in A, ?, and M is approximately independent of the scattering properties and gives a good estimate of the absorption coefficient. These changes can be induced either by small changes in the absorption coefficient of the medium, by the tuning of the wavelength, or by changes in the light source-detector distance. The application for the in vivo monitoring of hemoglobin and oxyhemoglobin concentrations in human tissue is discussed.     

Optical Bistability,Instability and Optical Computing

The formation of a cone-type light beam structure in an amplifying medium exhibiting the Kerr-type non-linearity and two-photon absorption is considered. The dependences of the relative diameter, contrast, and the position of the origin of a filamentary light region (that formed on the beam axis) on the active medium parameters are investigated. The effects of additional factors, such as a dielectric tube covering the active medium cylinder, the inhomogeneity of the medium amplification in the cross-section, and a saturable absorber mixed with the active medium on the light propagation pattern, are also discussed. Here, it is shown that a cone-type light beam structure is highly stable under the influence of such factors. It is noted that picosecond and sub-picosecond spectroscopy, including the study of multiphoton transitions and the measurement of the Kerr-type non-linearity constant in a medium on observation of a cone-type light beam structure, are possible.     

Expert representation of design repository space: A comparison to and validation of algorithmic output

Development of design-by-analogy tools is a promising design innovation research avenue. Previously, a method for computationally structuring patent databases as a basis for an automated design-by-analogy tool was introduced. To demonstrate its strengths and weaknesses, a computationally-generated structure is compared to four expert designers' mental models of the domain. Results indicate that, compared to experts, the computationally-generated structure is sensible in clustering of patents and organization of clusters. The computationally-generated structure represents a space in which experts can find common ground/consensus – making it promising to be intuitive/accessible to broad cohorts of designers. The computational method offers a resource-efficient way of usefully conceptualizing the space that is sensible to expert designers, while maintaining an element of unexpected representation of the space.