Single-polarization single-mode photonic crystal fibers

A new structure of single-polarization single-mode (SPSM) photonic crystal fiber (PCF) is proposed and analyzed by using a full-vector finite element method with anisotropic perfectly matched layers. From the numerical results it is confirmed that the proposed fiber is low-loss SPSM-PCF within the wavelengths ranging from 1.48 to 1.6 /spl mu/m, where only the slow-axis mode exists and the confinement loss is less than 0.1 dB/km.     

Finite element beam propagation method for three-dimensionaloptical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide     

Modeling of two-dimensional photonic crystal resonant cavities incorporating elliptically shaped dielectric cylinders

Modeling of photonic crystal structures is an ongoing challenge. This letter is devoted to the theoretical modeling of photonic crystal resonant cavities, composed of elliptically shaped dielectric pillars. Through this rigorous study, we can examine the impact of the elliptical-shape deformations to important quantities related to the photonic crystal cavity performance, such as the quality factor and the resonance frequency.     

Formation of uniform GaAs multi-atomic steps with 20–30 nm periodicity and related structures on vicinal (111)B planes by MBE

We studied morphology of GaAs surfaces and the transport properties of two-dimensional electron gas (2DEG) on vicinal (111)B planes. Multi-atomic steps (MASs) are found on the vicinal (111)B facet grown by molecular beam epitaxy, which will affect electron transport on the facet. We also studied how the morphology of GaAs epilayers on vicinal (111)B substrates depends on growth conditions, especially on the As₄ flux. The uniformity of MASs on the substrates have been improved and smooth surfaces were obtained when the GaAs was grown with high As₄ flux, providing step periodicity of 20 nm. The channel resistance of the 2DEG perpendicular to the MASs is reduced drastically with this smooth morphology. These findings are valuable not only for fabricating quantum devices on the (111)B facets but also those on the vicinal (111)B substrates.     

Analysis of shielded microstrip lines with arbitrary metallizationcross section using a vector finite element method

The finite element method (FEM) with the high-order mixed-interpolation-type triangular element is used to solve the problem of practical microstrip lines with arbitrary metallization cross section. Analyses are carried out to produce the frequency characteristics of propagation constant, characteristic impedance, and attenuation constant of shielded microstrip lines with rectangular, trapezoidal, and semi-trapezoidal strip cross sections. A comparison of the numerical results with those of the existing results shows good agreement and thus verifies the versatility of the FEM. Also, the numerical results show the effects of the metallization cross sections on the transmission properties and thus emphasize the importance of considering the practical microstrip configurations in the design of miniaturized MMICs     

Photonic bandgap fibers with high birefringence

A highly birefringent air-guiding photonic crystal fiber which provides guidance by a full two-dimensional photonic bandgap (PBG) effect is proposed. The fiber core is formed by introducing a large air hole that has an area of four unit cells of the cladding materials. It is shown from computed results by a full-vector finite element method that the proposed PBG fiber has birefringence of the order of 10/sup -3/.     

Approximate scalar finite-element analysis of anisotropic optical waveguides

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides with a diagonal permittivity tensor is described. The accuracy of the method has been checked by calculating the eigenmodes of two-dimensional, anisotropic asymmetric slab waveguides. The results obtained for a channel waveguide embedded in LiNbO3 agree well with the results of the earlier vectorial finite-element method.     

Extraction of all coefficients of coupled-mode equations for natural, single-phase, unidirectional SAW transducers from dispersion characteristics computed by hybrid finite element method

A numerical method is presented for determining all of the coefficients of coupled-mode equations for natural, single-phase, unidirectional SAW transducers (NSP-UDTs). Substituting numerical results computed by the hybrid finite element method for infinite NSPUDTs with shorted and open electric ports into several relations derived from the coupled-mode theory, we can determine all of the coefficients. Specifically, the edge frequencies of a stop-band and the static capacitances yield the self-coupling coefficients and the amplitudes of mutual-coupling and transduction coefficients, and the electric potential standing wave on the substrate surface, which can be derived from the projection of the standing wave distributions of particle displacements and electric potential in the whole substrate onto the set of those predicted by the coupled-mode theory, yields the phases of mutual-coupling and transduction coefficients. NSPUDTs on ST-25°X quartz, Y-51.25°Z LiTaO₃, and 50°Y-25°XLa₃Ga₅SiO₁₄ substrates are investigated. Our results agree well with the earlier experimental ones     

More on Security of Public-Key Cryptosystems Based on Chebyshev Polynomials

Recently, a public-key cryptosystem based on Chebyshev polynomials has been proposed, but it has been later analyzed and shown insecure. This paper addresses some unanswered questions about the cryptosystem. We deal with the issue of computational precision. This is important for two reasons. Firstly, the cryptosystem is defined on real numbers, but any practical data communication channel can only transmit a limited number of digits. Any real number can only be specified to some precision level, and we study the effect of that. Secondly, we show that the precision issue is related to its security. In particular, the algorithm previously proposed to break the cryptosystem may not work in some situations. Moreover, we introduce another method to break the cryptosystem with general precision settings. We extend the method to show that a certain class of cryptosystems is insecure. Our method is based on the known techniques on the shortest vector problem in lattice and linear congruences.