Analysis of coplanar E-H planeT-junction using dissimilar rectangular waveguides

An analysis of a T-junction that differs from conventional H -plane T-junctions in that the T arm is rotated by 90° and coupling takes place through an inclined slot is presented. Since use of standard X-band waveguides results in such a T-junction operating above 11.7 GHz, nonstandard waveguide dimensions have been considered to bring down the operating frequency to 9.375 GHz. The effect of a change of the broad dimension of the primary feed waveguide on the resonant conductance is evaluated. The variations of resonant length with the angle of inclination of the slot, and coupling with frequency, are presented     

Studies on wide inclined slots in the narrow wall of rectangularwaveguide

Investigations of the resonant length and admittance of inclined slots in the narrow wall of a rectangular waveguide that are sufficiently wide for applications involving high power handling capacity are presented. For high accuracy, the integrals appearing in the expression for the self-reaction are evaluated numerically instead of attempting to derive closed-form expressions, which are applicable only to thin slots. Numerical data on the variation of resonant length with slot width and also on the variation of real and imaginary parts of the admittance with 2L/λ as well as frequency for wide slots are presented. Comparison between theory and experimental results is presented for a slot with a width of 1.6 mm and a depth of cut in both the broad walls of 2.23 mm     

Performance parameters of a wavelength-division demultiplexer madewith a single 3×3 coupler optical fiber ring or loopresonator

The performance parameters of a two-channel demultiplexer made with a single 3×3 coupler fiber ring or loop resonator are evaluated theoretically. These parameters include crosstalk, output intensity of the selected channel, and channel separation. Their dependence on the parameters of the coupler and the fiber such as the coupling length of the coupler, kd, the phase change of the fiber delay line, &thetas;, and the round-trip amplitude transmission coefficient of the fiber ring or loop G, which is the product of the amplitude transmission coefficients of the coupler and the fiber delay line and the amplitude gain of the degenerate two-wave mixing, is investigated. It is found that the best performance can be obtained at G=1     

Cladding layer thickness-controlled directional coupler opticalswitch

The AlGaAs/GaAs cladding layer thickness-controlled directional coupler optical switch (CTC-SW) is discussed. To increase the efficiency of coupling between two waveguides, the CTC-SW was designed with a thin i-AlGaAs cladding layer h between the two waveguides. The coupling length L_c can be reduced, without reduction of the extinction ratio and increase of the switching voltage. For instance, L_c of CTC-SW (h=0.07) can be reduced 40% more than that of a conventional directional coupler switch (h=0). The extinction ratio is near 20 dB, both for the crossover (applied voltage V=0 V) and straight-through (V =19 V) states. A technique for adjusting L_c to the device length was developed     

Analysis of N×N passive optical starcoupler based on the normal modes of N input waveguides

An integrated passive N×N optical star coupler on silicon wafer is described. Antiresonant reflecting optical waveguides (ARROWs) are analyzed and utilized as the input and output waveguides of the N×N coupler. Combining the exact solutions of the slab ARROW waveguide with the effective index method, a 5×5 coupler is analyzed. In the slab waveguide analysis, the input waveguides are coupled to their neighbors. The interaction of the waveguides is described in terms of the normal modes of propagation. The resultant field distribution is then diffracted into the free space region which separates the input and output sections. The radiation illuminates the receiving aperture from which the receiving N waveguides branch out, each output element obtaining equal power levels. Different types of loss such as spillover loss and mismatch loss were analyzed and estimated for N=5. A 5×5 star coupler with a transmission efficiency of 56% at a wavelength of 1.3 μm is achievable     

On the effect of gap width on the admittance of solid circularcylindrical dipoles

A center-fed, solid, circular cylindrical dipole of radius a with feed gap of width 2d radiating in a circular waveguide of radius b terminated in infinite ground planes is rigorously analyzed by applying both the conservation-of-complex-power technique and the multiple-reflections technique. The analysis begins by studying the dependence of the dipole admittance on its feed gap width and on its length, 2l, as well as on b, with ka (k=2π/λ is the number) as a parameter. From the decreasing amplitudes of the almost periodic oscillations of these input admittances as b/λ is increased, the input admittances of dipoles radiating in free space (b→∞) are estimated using a variable-bound approach. The effect of gap width (d/a⩽5) for different lengths of dipoles (0.2⩽2l/λ⩽1) in free space and for different thicknesses (ka⩽0.2) is then established. The feed gap dependence for a half-wave dipole is also examined in detail for d /a⩽10 and ka⩽0.14     

Directional coupler switch with reduced voltage-length product

The phase change×interaction length product needed to switch a directional coupler is shown to be reduced by decreasing the coupling coefficient at the middle of the interaction region. To implement the structure with parallel waveguides, an additional fabrication process to produce the low index region was needed. Instead of reducing the index, enlarging the waveguide gap can be used to decrease the coupling coefficient to gain the same effect. To reduce the coupling coefficient at the middle of the interaction region, the gap between waveguides was gradually enlarged from both ends to the center. To simplify the fabrication processes, the varied waveguide gap structure was used. The single-mode waveguides were fabricated on z cut LiNbO₃ by in-diffusing 7-μm-wide ti. The design, fabrication, and measurements are discussed     

Compound radiating slots in a broad wall of a rectangular waveguide

An analysis is presented of the characteristics of a broad wall radiating slot, offset from the center line and tilted with respect to the longitudinal axis of a rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness, and are solved for the slot aperture E-field using the method of moments. Compound slot characteristics are then deduced, including resonant length and dominant mode scattering. Numerical results for the scattering from resonant slots are presented over a range of offsets, tilt angles, frequencies and waveguide dimensions. For resonant compound slots, offset and tilt are shown to control the aperture electric-field amplitude with a phase variability of 360°. The results have significant applications in the design of compound slot arrays     

On the existence of optimum cyclic burst correcting codes over GF(q)

A cyclic b-burst correcting code over GF(q) of redundancy r and length n=(q^r-b+1-1)/(q-1) is said to be optimum. It is proved that a necessary condition for the existence of such a code is the existence of a square-free polynomial in GF(q)[x] of degree b-1 which is not divisible by x such that its period and the degrees of its irreducible factors are relatively prime to q-1. Moreover, if such a polynomial exists, then there are an infinite number of optimum cyclic b-burst correcting codes over GF(q)     

A 5 kW CW CO2 laser using a novel negative-branchunstable resonator with a phase-unifying output coupler

A 5 kW CW CO₂ laser using a negative-branch unstable resonator (M=-1.5) is proposed and characterized experimentally. The resonator consists of a stepwise variable reflecting output coupler, called the phase-unifying output coupler, and a total reflector. A 5 kW CW laser beam with diffraction limited quality (2&thetas;=0.45 mrad) is obtained and affected by the focal point in the resonator. The misalignment angle to reduce the laser power to 95% is improved by a factor of 19 compared with a positive-branch unstable resonator (M=1.5) with a phase-unifying output coupler at the same resonator length     

Queueing analyses of traffic access control strategies withpreemptive and nonpreemptive disciplines in wideband integrated networks

A multiserver queueing model of access control strategies for a wideband integrated services digital network (ISDN) is considered. There are two types of service requests (SRs): Type 1 SR requires b servers (basic bandwidth units, BBUs) of the c available servers, while Type 2 SR requires a single server. Both types of SRs are queuable in two separate infinite-size buffers. A Type 1 SR is allowed to seize d(⩽b) servers at first and then acquire additional servers as they become available to meet the original requirement of b servers. The arrival processes of both types of SRs are Poisson and the service times are exponentially distributed with mean b/dμ₁ and 1/μ₂ for Type 1 SR and Type 2 SR, respectively. Preemptive and nonpreemptive priority disciplines with movable boundary are analyzed using the Neuts' matrix-analytic approach. Numerical examples of the queue length distribution and the mean waiting time of the SRs are presented     

On the three-coefficient window family

The definition of the three-coefficient window family is extended to the form: w(t,b)=0.5(1-b)+0.5 cos(2πt/T)+0.5b cos(4πt/T ), |t|⩽T/2, -0.25⩽b⩽0.25, and its spectral behavior is investigated. It is found that with the parameter b adjusted to different values, this window family can attain a minimum main lobe width of 1.38, a maximum sidelobe attenuation of 64.19 dB, and a highest cutoff rate of 30 dB/oct     

Admittance of an isolated waveguide-fed slot radiating betweenbaffles using a spectrum of two-dimensional solutions

An efficient method of computing resonant length and admittance characteristics of an isolated broad-wall shunt slot radiating between baffles of finite height is presented. The outer three-dimensional (3D) field problem associated with this geometry is reduced to a two-dimensional (2D) one via a Fourier transformation with respect to the longitudinal z direction. For each value of the longitudinal wave number k_z an integral equation is solved for the E field in the mouth of the plates using the method of moments. This procedure is repeated for several discrete values of k_z, to obtain a spectrum of 2D solutions which are then inverse-transformed to construct the 3D solution in the spatial domain for the exterior baffle region and the half space. The slot aperture field is determined by the conventional moment method solution to the integral equation that enforces the continuity of the H field across the slot. Scattering properties of the slot are then deduced. Numerical results for the resonant length and resonant conductance are presented. Computer results are found to be in good agreement with experimentally measured data     

Full-wave analysis of broad wall slot's Characteristics in rectangular waveguides

A rigorous analysis of the resonant characteristics for a broad wall waveguide slot by using the finite-difference time-domain method is presented. Four types of slots including a radiating longitudinal shunt slot, a longitudinal/transverse coupling slot, a centered-inclined coupling slot and a compound coupling slot are analyzed. Lots of slot characteristics such as the resonant length, scattering parameters and normalized admittance in different offsets, tilt angles or slot sizes are obtained. Because the shape of slots is a rectangle with rounded ends in practical fabrication, an accurate modeling and computation for the slots with rounded ends is implemented, and the resonant lengths calculated coincide well with the Stegen's measured data and method of moments results. From these computed results, it is found that all the resonant characteristics of the slots with rounded ends are significantly different from those with normal rectangular ends.     

Roundoff error analysis of the discrete Wigner distribution usingfixed-point arithmetic

The issue of roundoff noise effects in the implementation of the discrete Wigner distribution using fixed-point arithmetic is addressed. The sign-magnitude number representation is assumed throughout the analysis. The measure of roundoff noise effects in an algorithm is the output noise-to-signal ratio. Using a statistical model, an analytical expression of the noise-to-signal ratio is derived as a function of the wordlength b and the transform length N. The noise-to-signal ratio is obtained by evaluating the signal and noise powers at different points in the algorithm, then reflecting to the output both signal and noise powers. Based on the derived noise-to-signal ratio is is noted that if the transform length is doubled, then) one additional bit is required in the wordlength to maintain a constant noise-to-signal ratio. It is demonstrated through the software simulations that the predicted noise-to-signal ratio is a good closed-form estimate of the `true' roundoff error. It is also found from the simulation that the wordlength b and the transform length N=2^v must satisfy the condition b- v⩾4     

An algorithm for determining if a rate (n-1)/npunctured convolutional encoder is catastrophic

The algorithm determines whether or not the punctured state diagram contains a zero-weight cycle. The punctured encoder is assumed to be obtained from a rate 1/b, b⩽n, antipodal encoder of a given constraint length. The algorithm is much simpler to implement in software than the previously known method of calculating the GCD of the determinants of the n distinct (n-1)×(n-1) submatrices of the generator matrix. The computational complexity of the algorithm is no worse than the computational complexity of the GCD method for relatively short constraint lengths, that is, the constraint lengths for which the Viterbi algorithm is implemented     

复合缝波导耦合器的全波分析

本文使用时域有限差分法 (FDTD法 )对由两根正交矩形波导构成的复合缝耦合器进行了严格分析 ,得出在不同偏置、倾斜角度和谐振频率下耦合缝隙的谐振长度和散射参量特性 ;并对带有短路器的复合缝波导耦合器系统进行了分析 ,得出短路片移动时该小系统的传输特性     

S matrix of slot-coupled H-plane tee junctionusing rectangular waveguides

Complex scattering matrix parameters of a slot-coupled, waveguide tee junction are determined using a moment method of analysis with entire orthogonal basis functions and a rigorous analysis of the effect of wall thickness. The variations of the equivalent network parameter, coupling, and return loss with frequency are evaluated, and the results are compared with experimental data. The unitary property of the S matrix is verified. The dependence of coupling on slot length, slot width, and thickness is presented     

What is the confocal parameter?

A novel derivation is presented of the Gaussian beam as a limit of the solution to the full wave equation. Usually, the functional form of the Gaussian beam is found by a two-step process. First, the Green's function of the paraxial wave equation is identified. Then, since the paraxial wave equation is invariant under translation, the z-axis variable is replaced by z+jb. It is shown that when starting with a solution of the full three-dimensional Helmholtz equation in spherical coordinates, performing the transformation z→z+jb corresponds physically to causing the phase fronts of the solution to become ellipsoids. The separation of the foci of the ellipsoids is 2b, where b is the confocal parameter of the beam. In the paraxial limit the ellipsoidal solution becomes a Gaussian beam. Adopting this approach to Gaussian beams allows a simple, geometrical interpretation of the optical resonator stability criterion     

Efficient N×N star coupler based on Fourieroptics

A technique for constructing an efficient N×N star coupler suitable for mass production in integrated form for large N at optical frequencies is discussed. The coupler can be realised using Si technology by means of two arrays of strip waveguides and a dielectric slab formed on a glass substrate. Power transfer between the two arrays is accomplished through radiation in the dielectric slab with theoretical efficiency exceeding 30% under optimised conditions