Use of steel substrates in diffractive optics: Near field of high surface quality steel tape gratings

Steel tape is used in optical applications due to its mechanical properties. However, roughness of steel surfaces affects to wave propagation. The effect can be observed using diffraction gratings with low periods. In such a case, self-images of the grating appear at certain periodic distances from the grating (Talbot planes). When standard steel is used, the contrast of Talbot self-images strongly decreases with the distance from the grating. In this work, we prove that controlling the surface quality of steel, it is possible to improve its optical behavior and, as a consequence, high quality surface steel represents a good choice for diffractive optics when the use of chrome-on-glass masks is not indicated. As an example, we have manufactured a diffraction grating over a high quality steel surface by means of an ablation process with a nanosecond pulsed laser. The contrast of the self-images for these gratings decreases very slowly with the distance, in comparison with the self-images obtained with standard steel tape gratings.     

The role of diffraction in dispersive optical bistability

A finite difference method is applied to the study of diffractive effects in dispersive optical bistability. Although quite elementary, the method produces extensive results in an efficient way. A detailed comparison is made with previous quasi-fast Hankel transform results, and the approach to the diffractionless limit is discussed.     

Multidot recording of rainbow and multicolor holographic stereograms

A new method for rainbow and multicolor holographic stereograms is described using the technique of multidot recording, which was originally developed for the syntheses of full-parallax holographic stereograms. Instead of recording vertical parallax, an image of horizontal slit is synthesized for rainbow holography. It becomes possible to obtain large images by a compact optical system, since the hologram is composed of many small elementary holograms. Multicolor image is also produced by the same system introducing a simple image processing. Experimental results of three-dimensional and color imagery are demonstrated.     

Talbot effect with Cantor transmittances

We show the Talbot effect for Cantor transmittances, which are obtained as a product superposition of periodic components. The self-images for each periodic component can be superimposed with the self-images or the optical noise corresponding to the remaining components. Due to the integer scaling factor among periodic components, there are also self-images positions for the complete fractal structure.     

Robust 2 × 2 Multimode Interference Optical Switch

A robust 2 × 2 photonic switch based on multimode interference (MMI) effects is proposed. We demonstrate that the device is very tolerant to material modifications and typical fabrication errors. This is a result of the MMI design and the high symmetry of the switch. The key parameter for the operation of the device is that the input light forms a pair of well defined self-images exactly in the middle of the switch. The index modulated regions precisely overlap the positions where these two self-images are formed. By creating identical contact features at these locations, any refractive index change induced in the material as a result of electrical isolation will be replicated in both self-images, and therefore the off-state output will not be altered. In the same way, offset and dimension errors are reflected symmetrically on both self-images and do not seriously affect the imaging. The characteristics of the switch under different scenarios are investigated using the finite difference beam propagation method. By employing this configuration, crosstalk levels better than −20 dB are achievable over a wavelength range of 100 nm while maintaining polarization independence.     

Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics

Classical theory of crystals states that a medium to be considered homogeneous must satisfy the following requirements (a) the dimension of the elementary cell must be much smaller than the incident wavelength; (b) the sample must contain a large number of elementary cells, i.e. it must be macroscopic with respect to wavelength. Under these conditions, macroscopic quantities can be introduced in order to describe the optical response of the medium. We analytically demonstrate that for a symmetric elementary cell those requirements can be relaxed, and it is possible to assign a permittivity and a permeability to a composite structure, even if the metamaterial cannot be considered homogeneous under the requirements stated above. However, the effective permittivity and permeability in some cases may give rise to unphysical, effective behaviors inside the medium, notwithstanding the fact that they satisfy requirements like being Kramers-Kronig pairs, for example, and are consistent with all the linear properties outside the structure (i.e. reflection, transmission, and absorption at all frequencies). In some situations the medium is assigned a magnetic response even though the medium is not magnetically active. In particular, we demonstrate that the homogenization procedure can lead to a medium that locally violates the second principle of thermodynamics. We also show that, in the non-homogeneous regime, it is not possible to describe the nonlinear behavior of the structure using an effective parameters approach, despite the possibility to assign an effective linear refractive index.     

Theory of speckle displacement and decorrelation and its application in mechanics

The paper deals with the determination of tensor of the so-called small deformation of an elementary area of an object surface by means of an optical experimental method, which makes use of properties of the speckle field in an optically free space or in an image field. The term “small deformation tensor” is introduced and a relationship between a small deformation tensor of surface and a speckle field in free space or image field is analyzed.     

First-order aberration of a misfocused self-imaging system

We analyze the characteristics of a self-imaging system that appear across a misfocused image plane. We approach this problem from the point of view of aberration theory. First, we derive the aberration functions (corresponding to several self-imaging rays of different orders) which are linear in a small shift of focus, and then we examine their roles in the amplitude spectra of misfocused self-images. We show that the aberration of the mth-order self-imaging ray is responsible for a lateral shift of the image amplitude component of frequency m/Mp, where M is the magnification of the system and p is the fundamental period of an object grating. We also analyze the role of wavefront aberrations in the image irradiance as an observable quantity. We then show that the theoretical estimation of irradiance of the aberrated image is in good agreement with the experiment and the focus-shift aberration can exert a severe effect on the irradiance spectrum of image in a complicated way.     

Approximate optical cloaking in an axisymmetric silicon photonic crystal structure.

Axisymmetric photonic crystal structures may be designed to possess interesting optical properties, particularly when the photonic band structure of the material is highly anisotropic. We use finite element calculations to demonstrate an approximate electromagnetic cloaking effect imparted by a structure consisting of concentric silicon photonic crystal layers. The results show that it is possible to bend light around an object by simply using anisotropy. The calculations show that the cloaking mechanism is fundamentally different from Pendry's approach. This design may work as a practical solution for optical cloaking.     

Zernike-basis expansion of the fractional and radial Hilbert phase masks

The linear Hilbert phase mask or transform has found applications in image processing and spectroscopy. An optical version of the fractional Hilbert mask is considered here, comprising an imaging system with a circular, unobscured pupil in which a variable phase delay is introduced into one half of the pupil, split bilaterally.The radial Hilbert phase mask is also used in image processing and to produce optical vortices which have applications in optical tweezers and the detection of exoplanets.We subjected the fractional and radial Hilbert phase masks to Zernike function expansion in order to compute the image plane electromagnetic field distribution using Nijboer-Zernike theory. The Zernike functions form an orthogonal basis on the unit circle. The complex-valued Zernike expansion coefficients for these two phase masks were derived for use in the context of the Extended Nijboer-Zernike (ENZ) theory of image formation. The ENZ approach is of interest in that it allows a greater range of defocus to be dealt with, provides a simple means of taking a finite source size into account and has been adapted to high Numerical Aperture (NA) imaging applications.Our image plane results for the fractional Hilbert mask were verified against a numerical model implemented in the commercial optical design and analysis code, Zemax^®. It was found that the Nijboer-Zernike result converged to the Zemax^® result from below as the number of Zernike terms in the expansion was increased.     

Nonreciprocal frequency doubling of electromagnetic waves through double resonance and Bragg reflection in photonic crystals

A computational study of the uni-directional second-harmonic generation in a one-dimensional dual photonic crystal structure made of GaAs, AlAs and SiO₂ with quadratic optical nonlinearity and material dispersion is presented. The computational approach uses a shooting method to solve nonlinear wave equations for coupled fundamental and second-harmonic fields and the invariant imbedding method to obtain the linear transmittance and group index spectra. The dual structure consists of two substructures, the conversion structure creating a strongly enhanced second-harmonic signal and the filter structure blocking the fundamental frequency field by Bragg reflection while permitting the passage of the second-harmonic field. The conversion structure is built with an elementary cell consisting of four sublayers whose thicknesses are systematically varied. Doubly resonant second-harmonic generation with very high conversion efficiency is achieved for light incident from the conversion structure side by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure. A new mechanism to enhance second-harmonic generation by controlling the energy flow between the fundamental frequency and second-harmonic fields has also been found.     

基于ANSYS的红外光学系统的有限元分析

红外光学系统作为空-空导弹的重要有机组成部分,要经历复杂的动力学环境。采用有限元分析方法对红外光学系统结构在工作状态下的变形、应力及固有频率进行了全面分析。验证了光学系统的结构是否满足光学像质要求和刚度要求,确定了面形变化的显著区域,并专门对其中的关键结构进行了详细分析,进而提出结构优化的途径。该方法对光学系统结构设计和分析具有现实意义,有助于进一步分析研究光学系统结构动力学。     

Dynamic behaviour of structures in large frequency range by continuous element methods

The continuous element method is presented in the context of the harmonic response of beam assemblies. A general formulation is described from the displacement solution of the elementary problem. A direct computation of elementary dynamic stiffness matrices is presented. In the present formulation, distributed loadings are taken into account. In the case of more complex geometries for which many coupling phenomena occur, an explicit formulation is no more conceivable. In this case, a numerical approach is presented. This approach allows an algorithmic computation of exact dynamic stiffness matrices. This method, called “Numerical Continuous Element”, allows one to consider the coupled vibrations of curved beams and those of helical beams. The validation of this numerical method is achieved by comparisons with the harmonic response of various beams obtained by a finite element approach. Finally, a comparison between eigenfrequencies obtained experimentally and numerically for a straight beam and a helical beam has been made to evaluate the performances of the method.     

ZEMAX与ANSYS动态数据交换的实现及其在光学设计中的应用研究

通过对Zemax动态数据交换技术DDE(Dynamic Data Exchange)通信接口进行研究,实现了ANSYS-中继软件-Zemax的DDE闭环通信,并应用到了望远镜光学系统受环境温度场影响的光学像质评估中,实现了有限元分析和光学像质评价的动态联合。用ANSYS建立有限元模型,分析由温度场引起的光学镜面形变。通过Zernike多项式拟合,将拟合系数通过ANSYS-Zemax的DDE通信链路传递给Zemax进行光学系统的像质分析。反之,像质分析的结果也可以动态地传递给ANSYS,以便进一步指导机械结构的优化设计。此有限元系统-光学系统通信链路的实现可大大提高数据的可靠性和设计效率。     

Wavelet-modified binary phase-only morphological correlation for color pattern recognition

This paper reports a morphological phase-only correlation technique based on bit-map representation for recognition of color as well as grey images in a hybrid digital-optical correlation architecture. The color image is decomposed into its R, G and B components, and each component is further decomposed into eight disjoint elementary images depending upon the bit-map representation of the color value at each pixel. Bit-map representation of the pixel values of an image reduces the required computational time. A set of twenty-four disjoint wavelet-modified binary phase-only filters (WBPOFs) are generated from these bit-map decomposed images. The target image is similarly decomposed into eight disjoint images each of R, G and B and their digital Fourier transforms multiplied with the corresponding WBPOFs. The product functions thus obtained are added up to form a single resultant product function, whose optical Fourier transformation gives the correlation peaks for the presence of R, G and B components in the image. The single product function overcomes the necessity of obtaining the final optical Fourier transformation of the R, G and B components separately. The novelty of this approach lies in the fact that the WBPOFs synthesized by this procedure are thus able to identify both colored as well as gray images and can tolerate salt-and-pepper noise to a considerable extent.     

High reflectivity phase conjugation in magnetized diffusion driven semiconductors

Optical phase conjugation via stimulated Brillouin scattering (OPC-SBS) in magnetized diffusion driven semiconductors under the off-resonant transition regime has been investigated theoretically. The model is based upon the coupled-mode approach and incorporates the effect of pump absorption through the first-order induced polarization. The linear dispersion is found not to affect the reflectivity of the phase conjugate Stokes shifted Brillouin mode. The reflectivity of the image radiation is dependent upon the Brillouin susceptibility and can be significantly enhanced through n-type doping of the crystal and the simultaneous application of magnetic field. Moreover, the threshold of the pump intensity required for the occurrence of SBS in the crystal with finite optical attenuation can be considerably diminished through a suitable choice of the excess carrier concentration and the magnetic field. Consequently, OPC-SBS becomes a possible tool in phase-conjugate optics even under not-too-high power laser excitation by using moderately doped n-type semiconductors kept under the influence of magnetic field. Numerical estimates made for n-InSb crystal at 77 K duly irradiated by nanosecond pulsed 10.6 μm CO₂ laser show that high OPC-SBS reflectivity (70%) can be achieved at pump intensities below the optical damage threshold if the crystal is used as an optical waveguide with relatively large interaction length (L ∼5 mm) which proves its potential in practical applications such as fabrication of phase conjugate mirrors.     

On the eigenvalue problem associated with Feynman path integration

When the lagrangian is not explicit function of time, the Nth approximation to the propagator may be viewed as the Nth power of anitary operator — the infinitesimal time propagator. We solve the eigenvalue problem associated with the operator for some special cases. In the limit of large N the eigenfunctions are shown to be identical to those of the finite time propagator. We also present an elementary method to evaluate the propagator corresponding to an action function encountered in the study of electron gas in a random potential. The evaluation of this propagator within Feynman's polygonal approach was not possible until recently.     

Double radiooptical resonance in <Superscript>87</Superscript>Rb atomic vapor in cells with antirelaxation wall coating

The object of investigation is double radiooptic resonance in ⁸⁷Rb atomic vapor contained in a cell covered by an antirelaxation coating. The Dicke narrowing is studied in terms of the quantum-kinetic approach. It is found that optical pumping using a laser with a “wide” radiation spectrum makes it possible to improve the short-term stability of the frequency standard by an order of magnitude compared with a narrow-spectrum laser.