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     

An efficient N×N passive optical starcoupler

A novel method is presented for configuring an N× N passive star optical coupler and eliminating the excess loss problem associated with such couplers. A space-varying refractive index slab is introduced as a key design element for such a coupler. The wave mixing method is used to implement the coupler     

Efficient N×N star couplers using Fourier optics

A technique for constructing an efficient N×N star coupler with large N at optical frequencies is described. The coupler is realized in free space using two arrays, each connected to N single-mode fibers. The highest efficiencies are obtained using a planar arrangement of two linear arrays separated by a dielectric slab serving as free-space region. The coupler is suitable for mass production in integrated form, with efficiencies exceeding 35%     

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     

Theory of an efficient N×N passive opticalstar coupler

A method for configuring an efficient N×N optical passive star coupler is introduced. It makes the construction of a one-piece coupler possible and thus eliminates the excess loss problem associated with cascade couplers and reduces the structural complexity. The authors show that a 100% efficiency figure can be achieved through the entire array by using a properly designed space-varying refractive-index slab. The authors give a mathematical analysis of the space-varying refractive-index slab and examine spatial frequencies of the required refractive-index pattern. The authors demonstrate how the wave-mixing method can be utilized as one possible method of configuring such a slab, using a constant temporal optical frequency involving nonlinear media such as photorefractive crystals     

Electromagnetic scattering of finite strip array on a dielectricslab

A feast recursive algorithm is used to compute the scattering properties of a finite array of strip gratings on a dielectric slab. this algorithm has a computational complexity of O(N log² N) for one incident angle and O(N ² log N) for N incident angles. It uses plane wave basis for expanding the incident wave and the scattered wave. The scattered wave is expanded in terms of a Sommerfeld-type integral with spectral distribution along a vertical branch cut, rendering its expansion very efficient. To validate the scattering solution obtained using the recursive algorithm, comparisons with the method of moments are illustrated. The current distributions on the strips and scattering patterns are both presented. Since this algorithm has reduced computational complexity and is fast compared to other conventional methods, it can be used to analyze very large strip arrays. Scattering solution of a 50-wavelength wide strip is illustrated     

Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

Computation of mutual coupling between slot-coupled microstrippatches in a finite array

An analytical method is presented for the evaluation of mutual coupling between slot-coupled microstrip patches in a finite array. The approach is a combination of the equivalence principle and the reciprocity theorem and uses the spectral domain Green's functions for a dielectric slab in a moment method solution for the unknown patch and slot current distribution. The excitation mechanism of the patches is taken into account by introducing an N-port equivalent network, and the impedance matrix of an array of N-element slot-coupled patches is evaluated directly from its network voltage and current matrices of order N². As examples, the mutual impedances and scattering coefficients for two-, four-, and eight-element arrays are evaluated. Results are compared with measured data     

Roles of low field mobility and its carrier-concentrationdependences in high electron mobility transistors and other field effecttransistors

A model is proposed for high-electron-mobility transistors (HEMTs) and other heterostructure FETs in which the dependence of low field mobility μ on carrier concentration N_s is taken into account. On the basis of this model, the influence of μ and its N_s dependence on drain current and transconductance g_m are clarified, In particular, high mobility (>10⁵ cm²/V-s) is shown to be effective in achieving and maintaining the intrinsic limit of g_m(=ε₂ν_s/d*) irrespective of bias conditions, where ν_s is the saturation velocity and ε₂ and d* are the dielectric permittivity and the effective thickness of the gate insulator, respectively. The N_s dependence of mobility is found to greatly affect the gate-voltage dependence of g _m and leads, in some cases, to an appreciable increase of g_m above its intrinsic limit     

The sublinear relationship between index change and carrier densityin 1.5 and 1.3 μm semiconductor lasers

The carrier-induced index change was measured using a novel injection-reflection technique in combination with differential carrier lifetime data. The observed relation between index change and injected carrier density at bandgap wavelength is nonlinear and is approximately given by δn_act=-6.1×10^-14 ( N)^0.66 for a 1.5-μm laser and δn _act=-1.3×10^-14 (N)^0.68 for a 1.3-μm laser. The carrier-induced index change for a 1.3-μm laser at 1.53-μm wavelength is smaller and is given by δn _act=-9.2×10^-16 (N)^0.72      

On the Hamming distance properties of group codes

Under certain mild conditions, the minimum Hamming distance D of an (N, K, D) group code C over a non-abelian group G is bounded by D⩽N -2K+2 if K⩽N/2, and is equal to 1 if K>N/2. Consequently, there exists no (N, K, N-K+1) group code C over an non-abelian group G if 1<K<N. Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D=1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N, K, D) group code over an abelian group G that is not elementary abelian, then there exists an (N, K, D) group code over a smaller elementary abelian group G'. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G     

Measurement and analysis of photocurrent transient characteristicsfor hydrogenated amorphous-silicon photodiodes

The relations between the photocurrent transient after the end of steady-state illumination for hydrogenated amorphous silicon photodiodes and the related film properties for undoped hydrogenated amorphous silicon prepared by mercury-sensitized photochemical vapor deposition are investigated. The photocurrent transient characteristic indicates significant correlations with the film properties, such as electron drift mobility (μ_d), silicon dangling bond density (N _s), a minimum in the density of states near the Fermi level (N_min), and space-charge density (N _i). The photocurrent transient decay decreases with increasing μ_d and with decreasing N_s, M_min, and N_i. This result was confirmed by a model analysis     

Quadtree-structured recursive plane decomposition coding of images

The approximation of two-dimensional highly correlated grey value functions can be performed using a linear model of the type f( x, y)=a+bx+cy. The set of plane parameters (PPs) [a, b, c] can be determined in the least squares sense for a block of size N×N pixels, for example. Starting with a block size of 2×2 pixels, it is shown that the PPs obey a recursive law such that the PPs of a 2N×2N block can be computed recursively when only the PPs of the four adjacent subblocks of size N×N in the lower decomposition level are known. This concept of recursive plane decomposition (RPD) is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost. Extensive comparisons to other state-of-the-art image coding algorithms are reported     

Phase-locked laser array far-field normalization

The normalization of the far-field distribution from phase-locked linear arrays of evanescently coupled semiconductor diode lasers is evaluated. As the element number N→∞, the peak irradiance of the fundamental array mode tends to 81% of the peak irradiance of an array of in-phase equal-intensity diodes. It is also found that for N⩾10, the peak irradiance is proportional to 0.81 (1+1/N)N², and the diffraction-limited beamwidth is approximately 1.19 λ(N+1)S where λ is the vacuum wavelength and S is the array period. The far-field array factor is the same for an N-element array and an (N+1) S-wide cosine source as long as N⩾10     

The inductance matrix of a multiconductor transmission line inmultiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N_c conducting cylinders in inhomogeneous media consisting of N_d homogeneous regions with permeabilities μ_i and permittivities ϵ _i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of N_c conductors in N_d regions with permeabilities μ _i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of N_c conductors in N_d regions with permittivities ϵ _i. It is shown that [L]=μ₀ϵ₀[C^'] ^-1, where [C^'] is the capacitance matrix of an auxiliary electrostatic problem of N_c conductors in N_d regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ^' _i/ϵ₀=μ₀/μ_i     

Perfect N-phase sequences and arrays [spread spectrumcommunication]

Perfect sequences and arrays have periodic autocorrelation functions whose out-of-phase values are zero. Time-discrete N-phase sequences and arrays have complex elements of magnitude one, and one of (2π/N)n, 0⩽n<N , different phase values. Existence conditions and construction methods for perfect N-phase sequences and arrays with a small alphabet of possible phase values are introduced. Combining the existence conditions with, methods of advanced computer search, new perfect N-phase arrays have been found. The resulting lowest number N of perfect N-phase sequences and arrays up to 40 elements are given in a table, after having applied the construction methods     

On minimizing the peak-to-average power ratio for the sum of N sinusoids

A new derivation is presented of a previously known relationship for phasing N equal-amplitude, equally spaced (in frequency) sinusoids so that the peak-to-average power ratio of their sum is 2.6 dB. The method of derivation provides intuitive insight into why this result is possible, and shows that the 2.6 dB figure is obtained independently of N as long as N is large. Any phase or frequency modulation can be applied simultaneously to all N sinusoids without altering this result     

Systolic arrays for the discrete Hartley transform

Recently, R.N. Bracewell (1983) introduced the discrete Hartley transform (DHT) as an alternative to the discrete Fourier transform (DFT). Two linear systolic array models for the (DHT) are derived. One model requires O(2N-1) in the computational phase and O(N) in the preloading phase. The other model requires O(2N-1) in the computational phase and O(N) in the output phase. A square systolic array for two-dimensional DHT is also constructed by combining the individual advantages of each model. The CORDIC algorithm is proposed as an alternative to conventional multipliers. To speed up the systolic array, two-level pipelining with CORDIC is also possible     

Recursive algorithms for calculating the scattering from Nstrips or patches

Using the definition of recursive relations for the reflection operator for N strips or patches, two easily programmable recursive algorithms are developed to calculate the electromagnetic scattering by N strips or patches. One algorithm is for arbitrary excitation, and the other is for a fixed excitation. The recursive algorithms require the inversion of small matrices at each stage and hence are suitable for programming on smaller computers. If the N strips or patches are identical and equally spaced, symmetry can be exploited to speed up the algorithms. A program was developed to calculate scattering by N strips, and the result is shown to converge to scattering by a large strip when the N strips are contiguous     

A linear lightwave Benes network

The authors consider linear lightwave networks with a single waveband that have N inputs, each with a transmitter, and N outputs, each with a receiver, interconnected by optical links, broadcast stars, and wavelength-independent 2×2 switches. The transmitters and receivers can tune to C different wavelengths. The authors describe a rearrangeably nonblocking network that is a modification of the Benes network and uses transmitters that are fixed tuned and switches with two states. The network uses [1+o(1)] N/log₂(N/C) switches, which is shown to be nearly the minimum number. It is also shown that, if C =o(log N), then a rearrangeably nonblocking network requires [1+o(1)]Nlog₂N switches even if the switches have more than two states