Calculation of the effective index for nonguiding regions: comment

In computer simulations the effective-index method is often used to reduce three-dimensional waveguide structures to two dimensions by definition of an effective index. For nonguiding regions, however, an effective index cannot be calculated. Jaeger and Lai [Appl. Opt. 31, 7183-7190 (1992)] present a method in which the choice of an effective index for nonguiding regions is based on a linear extrapolation formula. We show, however, that this linear relationship does not hold in the vicinity of cutoff and therefore yields an arbitrary effective index for the waveguide under cutoff. Furthermore it is shown that errors in simulations based on the effective-index method can actually be increased by the Jaeger and Lai method because of a further overestimation of the lateral contrast.     

Comment on "Low-loss terahertz ribbon waveguides"

We point out an important fundamental limitation associated with the dielectric ribbon waveguide described by Yeh [Appl. Opt.44, 5937 (2005)], which would restrict its practical use in ultrahigh- or terahertz-speed guided-wave applications, contrary to their underlying prediction, and we additionally point out a noteworthy inaccuracy in their introductory discussion.     

Feasibility of potassium-exchanged waveguides in BK7 glass for telecommunication devices

Based on recent results for potassium-exchanged optical waveguides in BK7 glass [Appl. Opt. 34, 455-458 (1995)], the feasibility of fiber-compatible waveguide fabrication for telecommunication wavelengths is studied. Modeling of waveguides gives the result that such waveguides with good properties cannot be achieved with this fabrication technique because of the observed saturation of diffusion depth.     

Two-wavelength lidar inversion algorithm

Potter [Appl. Opt. 26, 1250 (1987)] has presented a method to determine profiles of the atmospheric aerosol extinction coefficients by use of a two-wavelength lidar with the assumptions of a constant value for the extinction-to-backscatter ratio for each wavelength and a constant value for the ratio between the two extinction coefficients at the two wavelengths. Triggered by this idea, Ackermann [Appl. Opt. 36, 5134 (1997)] expanded this method to consider lidar returns that are a composition of scattering by atmospheric aerosols and molecules, assuming that the molecular scattering is known. In both papers the method is based on the well-known solutions of Bernoulli's differential equation in an iterative scheme with an unknown boundary transmission condition. This boundary condition is less sensitive to noise than boundary extinction conditions. My main purpose is to critically consider the principle behind Potter's method, because it seems that there are several reasons why the number of solutions is not limited to one, as suggested by his original work.     

Analysis of the birefringence of a silicon-on-insulator rib waveguide

A detailed analysis of the polarization characteristics (birefringence) of a silicon-on-insulator (SOI) rib waveguide is given. The fundamental TE- and TM-polarized modes of the SOI rib waveguide are calculated by a semivectorial finite-difference method. The rib width and the slab height of the SOI rib waveguide are normalized with respect to the total height of the silicon layer. A general relation between the two normalized parameters for a nonbirefringent SOI rib waveguide is obtained. According to this relation a nonbirefringent SOI rib waveguide can easily be designed. The fabrication tolerance for a nonbirefringent SOI rib waveguide is also analyzed, revealing that the tolerance can be increased by use of a larger total height of the silicon layer.     

Zero fringe visibility in the classical localization plane of a two-beam interferometer

In 1987 we published "Fringe localization depth" [Appl. Opt. 26, 5125 (1987)], where, with first principles, we generalized the van Cittert-Zernike theorem for two-beam amplitude-division interferometers illuminated by extended sources. In this generalization the complex degree of coherence between the interfering beams is equivalent to the Fraunhofer diffraction pattern of an aberrated optical system. In 1989 Hariharan and Steel [Appl. Opt. 28, 29 (1989)] commented on this paper and pointed out that the fringe visibility can be zero in the localization plane determined by the conventional pair-of-rays method. Now, we numerically and experimentally show a situation where the equivalent aberrations are such that this finding is verified and that the localization region splits in two, one ahead of and the other behind the classical localization plane.     

Loose abrasive line-contact machining of aspherical optical surfaces of revolution

A new fabrication technique for the generation of optical aspherical surfaces of revolution is presented. This fabrication technique combines the characteristics of conventional loose abrasive machining with features of high-precision machining tools. A prototype of the machine tool based on this fabrication technique is currently being developed. We describe the characteristics of this method. Fabrication of aspherical ultraprecise surfaces using a tube is a line-contact method for the generation of both on- and off-axis, convex and concave, aspherical surfaces of revolution. It employs a self-correcting process and enables the use of loose-abrasive ductile grinding [Appl. Opt. 30, 2761-2777 (1991)] and subsequent bowl-feed polishing [Appl. Opt. 26, 696-703 (1987); Opt. Eng. 31, 1086-1092 (1992); Appl. Opt. 33, 89-95 (1994)] for the generation of aspherical surfaces.     

Analysis of an optically controlled photonic switch

The principle that the coupling of light between two fiber waveguides can be controlled by the resonant interference of a third waveguide has been developed [Attard, Appl. Opt. 37, 2296-2302 (1998)]. Here significant details concerning the operation of a photonic switch are obtained, and a more complete analysis is presented. Multiple-resonant conditions are identified for slab and fiber control waveguides at large indices of refraction. Thus a selection of materials with an appropriate refractive index and a Kerr coefficient is rendered more easily. Furthermore it is shown that the light used to control the index of refraction in the control waveguide does not enter the output of the photonic switch but remains confined to the control waveguide, for either a slab or a multimode fiber control waveguide. Spatial fluctuations of the control light beam in the control waveguide do not affect the operation of the photonic switch. Tolerances have been determined for the spacing between the control waveguide and the photonic coupler and also for the index of refraction of the control waveguide.     

Analytical solution of the two-frequency lidar inversion technique

A two-frequency lidar inversion on the assumptions of a range-independent relationship between the extinction coefficients of the two considered lidar wavelengths and of constant extinction-to-backscatter ratios was originally developed by Potter [Appl. Opt. 26, 1250 (1987)]. It is an iterative procedure to retrieve the boundary value for solution of the single-scatter lidar equation. This boundary value is expressed by the aerosol transmission along the evaluated lidar path. Recently, Kunz [Appl. Opt. 38, 1015 (1999)] stated that there is not enough information in the lidar signals of two wavelengths to obtain a unique solution for the boundary value and hence for the aerosol extinction profile. It is shown that a unique solution of the two-frequency lidar inversion exists, for which an analytical expression of the boundary value and, hence, the aerosol extinction profile, is given.     

Comment on "Eigenfields and output beams of an unstable Bessel-Gauss resonator"

We comment on a recent paper by D. Ling et al. [Appl. Opt. 45, 4102 (2006)]. In that paper, the authors adopted the entire matrix formalism that we established in a previous work [J. Opt. Soc. Am. A 22, 1909 (2005)] for finding the eigenmodes of an unstable Bessel resonator. Nevertheless, the results are inaccurate mainly because (a) it was overlooked that light crosses through the axicon twice in a complete round trip and (b) the numerical method used to evaluate the diffraction integral equations cannot resolve the eigenvalues and eigenfields for the given resonator configuration.     

Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis

We report a sensitivity analysis for the algorithm presented by Gordon and Zhang [Appl. Opt. 34, 5552 (1995)] for inverting the radiance exiting the top and bottom of the atmosphere to yield the aerosol-scattering phase function [P(?)] and single-scattering albedo (omega(0)). The study of the algorithm's sensitivity to radiometric calibration errors, mean-zero instrument noise, sea-surface roughness, the curvature of the Earth's atmosphere, the polarization of the light field, and incorrect assumptions regarding the vertical structure of the atmosphere, indicates that the retrieved omega(0) has excellent stability even for very large values (~2) of the aerosol optical thickness; however, the error in the retrieved P(?) strongly depends on the measurement error and on the assumptions made in the retrieval algorithm. The retrieved phase functions in the blue are usually poor compared with those in the near infrared.     

Comment: Influence of illuminating beyond the object support on Zernike-type phase contrast filtering

In this comment, we clarify some serious misinterpretations that can arise from an uncritical use of the results presented in [Appl. Opt. 41, 2607, (2002)]. In particular, we point out that their suggestion of using "illumination beyond the object support" for measuring phase disturbances can result in distorted or strongly inaccurate interference patterns. We also point out that Llave and Castillo have misinterpreted our previous work describing the effect of phase object fill factor on the output interference patterns, which is in fact one of the key factors considered in the generalized phase contrast (GPC) method. Unlike the Zernike method, the GPC method results in an optimized visualization of the phase disturbance by the achievement of a matching condition between the applied filter and the spatial average of a given phase disturbance, thereby implying the optimal use of fill factor information.     

Use of grating theories in integrated optics.

Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.     

Optical bandwidth in coupling: the multicore photonic switch

In the present study, the bandwidth of a photonic switch described previously [Appl. Opt. 37,2296 (1998); 38, 3239 (1999)] is evaluated. First the optical bandwidth is evaluated for coupling between two fiber-core waveguides, in which the cores are embedded within the same cladding. Then the coupling bandwidth is determined for a fiber-core-to-slab-core waveguide, in which the cores are embedded within the same cladding. These bandwidths are then compared and contrasted with the bandwidths of the photonic switch, which consists of two fiber cores and a control waveguide. Two configurations of the photonic switch are considered: one in which the control waveguide is a fiber core and one in which the control waveguide is a slab core. For the photonic switch, the bandwidth characteristics are more complicated than for the coupled pairs, and these characteristics are discussed in detail.     

Comments on "Design and characterization of thin multiple aperture infrared cameras"

Recent analysis of a spatially multiplexed flat camera concept [Appl. Opt.48, 2115 (2009)] contains factual errors. Specifically, a performance metric and related signal-to-noise ratio analysis from an earlier work [Appl. Opt.45, 2901 (2006)] are inappropriately altered and incorrectly applied, and then associated with analytical and experimental results that cannot be properly interpreted. This comment corrects the misrepresentations.     

Analysis of characteristics of bent rib waveguides

With a perfectly matched layer boundary treatment, a semivectorial finite-difference method is used to calculate the eigenmodes of a single-mode (SM) or multimode (MM) bent rib waveguide. A detailed analysis is given for the dependence of the bending losses (including the pure bending loss and the transition loss) on geometrical parameters of the bent rib waveguide such as the rib width, the rib height, and the bending radius. The characteristics of the higher-order modes are analyzed. It is shown that the bending loss of the fundamental mode can be reduced effectively by increasing the width and height of the rib. For an integrated device, undesired effects due to the higher-order modes of a MM bent waveguide can be removed by appropriate choice of the geometrical parameters. An appropriately designed MM bent waveguide is used to reduce effectively the bending loss of the fundamental mode, and a low-loss SM propagation in a MM bent waveguide is realized when the bending losses of the higher-order modes are large enough.     

Development of a differential, optical, reflective displacement sensor by use of a multilayered waveguide

A noncontact and compact optical displacement sensor is proposed and demonstrated. The principle of this system is based on the differential optical-fiber displacement sensor [Appl. Opt. 38, 1103 (1999)]. The waveguide of the sensor consists of three thin plate glasses. This approach can miniaturize and lighten the system. The performance of the sensor is geometrically analyzed. The linearity and working range of the sensor are significantly improved compared with those of the optical fiber.     

Modified engagement method for matrix operation

We describe a modified engagement method for matrix operation based on a two-dimensional crossed-ring interconnection network. Our method incorporates fewer steps than that reported by Bocker et al. [Appl. Opt. 22, 804 (1983)], and its performance is found to be the most efficient (minimum steps) in comparison with other systolic and/or engagement methods for matrix operation. Thus, it may be helpful for other optical and electronic implementations of matrix operations. One compact optoelectronic integrity approach for implementing the modified engagement method is briefly described.     

Comment on "Redundancy of phase-space distribution functions in complex field recovery problems"

In a recent publication [Appl. Opt. 42, 1932 (2003)], redundancies of phase-space representations were studied. In particular, signal recovery from a single section of the ambiguity function was explored. It is shown that this signal-recovery method can be associated with interferometry.     

Complex encoding of rotation-invariant filters onto a single phase-only spatial light modulator

The accuracy and flexibility of the technique proposed by Davis et al. [Appl. Opt. 35, 2488 (1996)] for the encoding of the amplitude and the phase of a filter onto a single liquid-crystal spatial light modulator operating in a phase-only regime has been exploited to implement several filter designs in a convergent optical correlator. We have selected some filters, that given their mathematical structure showing some degree of rotational invariance, or having a parameter to regulate their behavior, require amore precise encoding. We present correlation results of outstanding quality for various rotationally invariant filter designs that have never been previously implemented with a real-time optical correlator.