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     

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     

Grating degeneration technique and sandwich structures forholographic N×N passive star couplers

Design for an efficient N×N passive integrated optical star coupler are proposed. The concepts of grating degeneration and sandwich structures are presented. The techniques and their combinations can significantly reduce the number of gratings required by the coupler and thus make it possible to build holographic N×N star couplers with recording materials of a moderate dynamic range     

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     

Power-efficient layout of a fiber-optic multistar that permits log2 N concurrent baseband transmissions among N stations

A passive, single-hop, fiber-optic interconnection among N stations, each with two transmitters and one receiver, and a round-robin transmission schedule for it, which jointly permit log ₂ N concurrent noninterfering transmissions on a single wavelength, has recently been described. This is a substantial improvement over the previously known limit of two concurrent transmissions, but the layout of this interconnection poses a challenge in terms of both wiring complexity and path loss. A power-efficient implementation of this interconnection using several stages of balanced fiber-optic star couplers is presented here. With lossless components, path loss is N, the same as that of a single-star interconnection that permits only a single transmission at a time. Consequently, the high degree of parallelism translates into higher capacity. The required number of (2×2) star couplers is also very similar to that required for implementing a single N×X star     

Optical switch matrix with simplified N×Ntree structure

Optical switch matrices with compact size and excellent crosstalk characteristics are discussed. Novel architectures for optical switch matrices are obtained by condensing the structure of N× N tree structure. 4×4 switches fabricated on LiNbO₃ substrates are discussed     

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%     

The number of digital straight lines on an N×N grid

The number of digital straight lines on an N×N grid is shown. A digital straight line is equivalent to a linear dichotomy of points on a square grid. The result is obtained by determining a way of counting the number of linearly separable dichotomies of points on the plane that are not necessarily in general position. The analysis is easily modified to provide a simple solution to a similar problem considered by C. Berenstein and D. Lavine (1988) on the number of digital straight lines from a fixed starting point     

A WDM cross-connected star topology for multihop lightwave networks

The authors propose a star topology for multihop lightwave networks in which the conventional N×N passive star coupler is replaced by fixed wavelength division multiplexed (WDM) cross connects. The proposed topology overcomes three major limitations of the conventional star topology. First, it reduces the number of wavelengths needed in a (p,k) ShuffleNet from kp ^k+1 wavelengths in the conventional topology to p wavelengths in the proposed one. Second, the signal power loss due to the 1/N power splitting at the star coupler no longer exists in the WDM cross connects and, therefore, the restriction on the supported number of users by the star network is alleviated. Third, it completely eliminates the need for wavelength filtering at the input to the receivers as is the case in the conventional star topology     

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=∞     

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     

A technique for real-time measurement of Nth-orderderivativesdNV/dIN

A technique for the measurement of device derivatives d ^NV/dI^N of arbitrary order N described. Measurement is accomplished by injecting a test current composed of the sum of N square waves into the rest device, and then multiplying the corresponding voltage change by the product of those same square waves, followed by low-pass filtering. The algorithm is implemented in real time using a mixture of analog and digital circuitry, and its application to semiconductor laser control in high-speed optical communications is described     

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     

An O(kn) algorithm for a circularconsecutive-k-out-of-n:F system

An O(k×n) algorithm is described for evaluating the reliability of a circular consecutive-k-out- n:F system     

Effect of binary modulation codes with rate R=1/Non equivalent discrete-time models for channels with intersymbolinterference

For a data transmission system with intersymbol interference and noise in which signaling occurs by means of nonoverlapping rectangular pulses, a relation between the equivalent discrete-time models for uncoded and coded transmission is derived. It applies to binary modulation codes with rate R=1/N, where N is a positive integer. Examples suggest that these models are often affected by coding in a manner that is incompatible with a commonly adopted definition of coding gain     

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     

N-shift cross-orthogonal sequences

N-shift cross-orthogonal sequences and a complete complementary code derived from them are defined and discussed. A general method for generating this code is also discussed. A synchronous multiple-user spread-spectrum multiple system is proposed that uses N-shift cross-orthogonal sequences     

M×N Booth encoded multiplier generatorusing optimized Wallace trees

The architecture of a design method for an M-bit by N -bit Booth encoded parallel multiplier generator are discussed. An algorithm for reducing the delay inside the branches of the Wallace tree section is explained. The final step of adding two N±M-1-bit numbers is done by an optimal carry select adder stage. The algorithm for optimal partitioning of the N ±M-1-bit adder is also presented     

Index-and-dimensional taper and its application to photonic devices

A mode-field-converting optical channel waveguide with tapered refractive index and cross-sectional dimensions is proposed. In this waveguide, both the refractive index and cross-sectional dimensions of a core are adiabatically varied along a propagation direction in such a way that the normalized frequency V of the waveguide may be kept constant. Since radiation loss caused by waveguide imperfections is strongly dependent on the V value, the waveguide has good mode-field-converting capability without causing high radiation loss. Layer thickness and index of a core of a silica waveguide were tapered by modulating a raw material gas flow in a flame hydrolysis deposition method, and a channel width taper was formed by a photolithographical technique. In order to confirm the usefulness, taper waveguides have been used (1) to achieve good field matching between a fiber and a guided-wave optical switch, and (2) to fabricate a fiber-compatible monolithic 32×32 star coupler in a small chip