Precise and versatile formula for birefringent filters

In an investigation of extraordinary- (E-) ray behavior and the index of refraction for E waves in a uniaxial crystal, a precise and versatile formula for birefringent filters, based on the exact construction of the optical path difference, is set up with neither the approximation Δn = n(o) - n(e) ≤ (or n(e)), nor the ambiguity sin(θ)sin(r(ω)) = n(e). The exact construction gives the correct variation of the position and the dimension in each path, yielding the path difference while the filter is tuning. The formula is applicable not only to a filter with its optical axis parallel to the entrance surface (PAPS) but also to a filter with its axis inclined to the surface (PAIS). Also, the formula indicates that a FAIS allows laser wavelengths to be tuned over a wider range than does a FAPS. The origin of the wider range is interpreted to be the greater variation in the index for the FAIS while the filter is tuning. With the help of the formula we design a FAIS for tuning a cw Ti:sapphire laser.     

Synthesis and tuning of high-order Solc-type birefringent filters

Multiple optical wavelength passbands of Solc-type filters can be reselected within each fixed half-period by a scheduled rotation of each birefringent filter element. No additional wave plates are needed, and wavelength channels can be switched on or off while others continue unaffected. Designs for high-order transfer functions suitable for wavelength multiplexing are given along with experimental results for a set of fifth-order filters. This tuning concept is verified and its application in fiber-optic multiplexers is discussed.     

Low-loss birefringent spectral filters comprising three identical retarders

Basic fan or folded arrangements comprising three identical retarders in cascade between parallel or crossed polarizers are presented for constructing birefringent spectral filters without an internal polarizer. The retarders' axes are oriented with an angle increment of theta or -theta preferably with /theta/ 相似文献   

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications.     

高精度分光光度计测量光谱透过率

由安光所自行设计的高精度分光光度计目的是高精度测量滤光片透过率。该系统特点是基于双光栅单色仪的全自动单光束测量仪器。在出射光路中引入了积分球,用来消除光束的偏振性和不均匀性,而且在信号接收部分提出了将滤光片和探测器作为整体考虑,优点是接近滤光片的实际使用环境,减少了其实际测量误差。着重叙述了该仪器的设计过程和不确定度分析。测量的不确定度源包括光源的稳定性,双单色仪重复性、再现性,光束的均匀性,内反射,探测器线性、稳定性、偏振性、均匀性,系统杂散光。经本仪器测量的滤光片透过率合成不确定度为5.859×10-3,完全满足测量精度要求。     

Holodiagrams in birefringent media

The modifications to the holodiagram concept to describe free propagation (the extraordinary ray) inside birefringent materials are described. Holodiagrams are graphs showing the loci where the sum or the difference in the optical path from a generic point to two foci is the same. The holodiagrams obtained in this way give the shape of the surfaces that satisfy Fermat's principle, conjugate by reflection of one focus into the other, and represent the interference fringes obtained if both points are coherent sources. The reflection law in birefringent media is investigated in relation to this diagram. One direction for the optical axis is considered: parallel to the line joining the source and the observation point. Quartz-type and calcite-type crystals are studied.     

Synthesis of birefringent reflective gratings

The layer-peeling method for reconstruction of fiber and waveguide gratings is extended to the case of birefringent reflective gratings with polarization-dependent background index and polarization-dependent effective index contrast. Using a discrete grating model, we characterize the set of possible reflection and transmission Jones matrices and show that for a given wavelength, the total structure can be represented by a discrete reflector sandwiched between two retardation sections. In reflection the discrete reflector acts as a partial polarizer. A method for designing birefringent gratings is developed and tested numerically.     

Phase-shifting birefringent scatterplate interferometer

We realized what we believe is a new phase-shifting scatterplate interferometer by exploiting the polarization characteristics of a birefringent scatterplate. The common-path design of the interferometer reduces its sensitivity to environmental effects, and phase shifting allows quick and accurate quantitative measurements of the test surface. A major feature of the birefringent scatterplate approach for phase shifting is that no high-quality optical components are required in the test setup. The theory of the interferometer is presented, the procedure for the fabrication of the birefringent scatterplate is described, and experimental results are shown.     

Materials for birefringent coatings

We discuss recent developments in methods for monitoring the anisotropic growth and properties of tilted columnar films and present results for the perpendicular incidence birefringence of aluminum oxide, Merck Substance Hi, silicon oxide, tantalum oxide, titanium oxide, and zirconium oxide.     

Duty cycle dependence of a periodically poled LiNbO3-based electro-optic Solc filter

We demonstrate that the performance of a periodically poled LiNbO3- (PPLN-) based electro-optic Solc filter is dependent on the duty cycle of the crystal. This may limit the performance of the device for applications such as add-drop filtering and switching, owing to the deterioration of the extinction ratio. It is shown that by adding a retarder to the Solc filter it is possible to improve the extinction ratio; thus the dependence of the filter on the duty cycle can be reduced. Using Jones calculus, we analyzed the effect of a variable retarder that can also be rotated on the extinction ratio. We experimentally observed a 6 dB increase in the extinction ratio when we used a half-wavelength retarder.     

Paraxial theory for birefringent lenses

The generalized ray tracing for the extraordinary ray through uniaxial crystals developed by Avenda?o-Alejo and Stavroudis [J. Opt. Soc. Am. A 19, 1674 (2002)] has been applied to derive paraxial refracting equations. Paraxial equations are derived for three cases where the incident, ordinary, and extraordinary rays lie in the incident plane: (a) the crystal axis is parallel to the optical axis, (b) the crystal axis is orthogonal to the optical axis and lies in the plane of incidence, and (c) the crystal axis is orthogonal to both the optical axis and the incident plane. The paraxial ray-tracing equations for the extraordinary ray are represented by matrix operators. The elements of the matrix system give all the information of the focal points and of the principal points. Gaussian formulas are derived, and some examples are presented.     

Design considerations of form birefringent microstructures

Diffraction characteristics of high-spatial-frequency (HSF) gratings are evaluated for application to polarization-selective computer-generated holograms by the use of two different approaches: second-order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE- and TM-polarized waves are investigated in terms of various input parameters, and results obtained with second-order EMT and RCWA are compared. It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach. The design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer-generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between the largest form birefrin gence and the lowest reflectivities.     

Crystallinity enhances light transmissivity through low-density polyethylene sheets

The effect of the crystalline structure (crystallinity and crystallite size) on the light transmissivity in low-density polyethylene sheets has been studied. Wide-angle X-ray diffraction, DSC, and UV/visible spectroscopy techniques have been used. The increase in crystallinity enhanced the light transmissivity in the visible region, but no significant effect in the UV region was obtained. The crystallite size showed no clear relation to transmissivity.     

Mode-coupling analysis in axisymmetric birefringent waveguides

Axisymmetric periodic media such as annular layers have axi-symmetric birefringence. I report the theoretical analysis of mode coupling in axisymmetric birefringent waveguides. Any of the LP(11) modes in a perturbed system can couple with a corresponding LP(11) mode that is orthogonal to the original mode with respect to both the polarization direction and the node line of an electric field. The coupling beat length depends on the amount of birefringence, which can be as short as 5 mm for a practical structure.     

Depolarization and retardation of a birefringent slab

Mueller matrices for normal transmission of light through a birefringent slab are formulated to analyze retardation and depolarization. A finite wave band, wedge slab, and microroughness may cause a spread in retardance, which in turn produces depolarization. The spectra of depolarization, cross-polarized transmittance, and retardance by rotating-analyzer ellipsometry are simulated for the quasi-monochromatic effect with a finite bandwidth. These spectra agree excellently with the measured spectra for a sapphire slab. The depolarization spectrum simulated for the wedge effect fits the measured spectrum in the long-wave region but is too small in the short-wave region. The depolarization simulated for incoherent multiple reflections demonstrates the oscillating structure, which is small compared with the measured depolarization. The finite bandwidth effect contributes more than the other effects to the measured depolarization of a sapphire slab.     

Information-theoretic analyses of a birefringent blur filter

We present the results of an information-theoretic analysis of an undersampled imaging system that contains a birefringent blur filter. We vary the spacing between replicas of the nonblurred point-spread function produced by the birefringent blur filter to find the value that yields the maximum information density. Comparison is made between this value and that yielded by a conventional qualitative design. We then analyze the effects of defocus aberration on the design of the birefringent blur filter. A wide search of blur-defocus space yields local peaks in the information density surface. The information density at these peaks is shown to exceed the maximum information density associated with the optimized birefringent blur filter or defocus alone, particularly when the fill factor of the photodetector array is low.     

Flattening spectral transmittance of birefringent interleaver filter

Abstract

A new method to produce flattening spectral transmittance for a birefringent interleaver filter based on the interference of polarized light is presented. In previous publications, each birefringent crystal was required to be of equal thickness and only one group of crystal azimuth angles was obtained. In addition, the shape of the spectral transmittance was not sufficiently flat and the flatness width of the passband and stopband was not sufficiently wide. The proposed method has advantages over previously published methods. It is based on the Fourier transform, and the thickness of each crystal can be different. All numerical solutions can be obtained for crystal azimuth angles provided ripples are small in relation to the relatively wide passband and the stopband. Three birefringent crystals are used and all the azimuth angles of the crystals are obtained when ripples are limited to a uniform 0.1% in both the passband and stopband, with widths greater than 2/11 of the period. The influence of the change of azimuth angle and crystal thickness on the spectral transmittance of the system is discussed.