Phase-locked arrays of antiguides: analytical theory

By employing a variational technique on the eigenvalue equation for finite arrays of antiguides we obtain accurate analytical expressions for key parameters characterizing the resonant array modes: the radiation loss at resonance, α_RR, and the propagation constant at resonance. The previously empirical finding that α_RR is equal to the radiation loss of a single antiguide divided by the number of array elements is found to be a good approximation only for large element/interelement width ratios (⩾3) and for, high-index-step (Δn⩾0.05) devices. By using an expansion, the radiation loss versus index-step curve is well approximated near resonance by a parabola, which gives curve halfwidths at half intensity only 10 to 15% less than numerically calculated values. An extremely accurate approximation formula is obtained for the resonant-mode propagation constant over large ranges in index-step variation around the resonance point. The obtained formulae are discussed in light of device design     

Resonant leaky-wave coupling in linear arrays of antiguides

In a uniform array of antiguides, when codirectional leaky waves from adjacent elements add in phase, each element equally couples to all others, causing the fundamental-mode near field to become uniform. The resonance condition is derived. When codirectional leaky waves are out of phase, coupling is only nearest-neighbour, causing the fundamental-mode near-field intensity envelope to be cosine-like. The consequences are discussed     

Phase-locked laser arrays revisited

Over the past decade major breakthroughs have occurred, both in theory and experiment, that have allowed phase-locked arrays of semiconductor laser diodes to meet their promise of reliable, high-continuous-wave (CW) power (≅0.5 W) operation in diffraction-limited beams as well as multiwatt (5-10 W) near-diffraction-limited peak-pulsed-power operation. In this review the authors describe a corrected picture for the array modes, arrays of antiguides and the concept of resonant leaky-wave coupling, and relevant recent results     

Phase-locked injection laser arrays with nonuniform stripe spacing

A new type of phase-locked injection laser array which utilises nonuniform spacing between the lasing stripes has been studied. The variation in spacing alters the stripe-to-stripe coupling which modifies the array mode selection. Arrays that operate with a single far-field lobe have been fabricated.     

Phase-locked injection laser arrays with variable stripe spacing

A phase-locked injection laser array is described which utilizes variations in spacing of identical lasing elements to vary the coupling between them. In general, phase-locked arrays have been fabricated as periodic structures with uniform coupling, although arrays with different element sizes have been described. An important advantage of the variable spacing array (VSA) structure over those designs is that the fundamental array mode can be readily matched to a uniform pumping profile across the entire array aperture. This allows the variable spacing arrays to be optimized for high-power operation. A coupled-mode analysis indicates that excellent matching of fundamental array mode to a uniform gain distribution can be obtained. However, for some array geometries the operation of array modes other than conventional 0 and 180° phase shift modes is enhanced. Variable spacing arrays have exhibited phase-locked behavior to CW outputs as high as 80 mW (7 elements) and single longitudinal mode operation to powers > 50 mW. Observation of the array emission patterns confirms the results of the coupled-mode analysis.     

Phase-locked arrays of buried-ridge InP/InGaAsP diode lasers

Phased-locked arrays of buried-ridge InP/InGaAsP diode lasers, emitting at 1.3 μm, were investigated both theoretically and experimentally. These arrays consist of index-guided buried-ridge lasers which are coupled via their evanescent optical fields. The field patterns and the modal gains of the array supermodes were calculated by using a simple waveguide model. The theoretical results show that buried-ridge arrays can be designed such that only the fundamental supermode is excited. In that case, the array lasers are coupled in-phase, which yields single-lobed, diffraction limited far-field patterns. The buried-ridge InP/InGaAsP arrays were grown by liquid phase epitaxy. These arrays exhibited single-lobed beams less than 4° in width up to more than twice the threshold current. Comparison of the measured field patterns and the calculated ones indicated that these arrays oscillated mainly in the fundamental supermode.     

PHASE－LOCKED 2－D JOSEPHSON JUNCTION ARRAYS AS SUBMILLIMETER OSCILLATORS

This letter presents the results of numerical simulations for phase-locked 2-D Josephson junction array oscillator.The simulation result shows that the junctioons of 2-D array can mutually phase-locked in a considerable area if the parameters can be carefully selected.The oscillators are formed with up to 33 identical Nb/AlOx/Nb junctions,and the junctions are connected with Nb microstrip resonators.Optimum structure parameters for ocsillator circuit design can be obtained with these simulation results.     

The theory of endfire arrays

The general King-Sandler array theory has been examined in detail for the case of endfire arrays. Since it is not necessary to assume identical current distributions, a distinction is made between specification of the base voltages and currents. The driving-point impedances for specified base voltages and currents are presented for arrays of up to 25 elements. The effect of interaction between the element currents in distorting the radiation pattern is shown for the 15-element endfire array. The results indicate that the unequal current distributions have a pronounced effect in determining the driving-point impedances, sidelobe levels and back-to-front ratios of endfire arrays.     

The theory of broadside arrays

The general King-Sandler array theory has been examined in detail for the case of broadside arrays. Since it is not necessary to assume identical current distributions on every element in the array, a distinction is made between specified base currents and voltages. The driving-point impedances for specified base currents and voltages are presented for arrays of up to 25 elements. The effect of interaction between the element currents in the base impedances and radiation patterns is clearly shown for the broadside array. The results indicate that the major effect of unequal current distributions in the broadside array is to cause important variations in the driving-point impedances and little effect in the radiation patterns.     

Single-mode birefringent fibers: An analytical theory

We investigate whether, in a linearly birefringent step-index single-mode fiber, Maxwell's equations can be solved rigorously by separation of variables. If the initial assumptions are the same as in an isotropic fiber, then, although many more steps are needed, the final equations are simple and easy to compare with the isotropic case. It is shown that their solutions are never exactly self-consistent. Consequently, the states of polarization of the transverse fields are sensitive to anisotropy, as it had already been proved experimentally. Furthermore, an isotropic fiber "equivalent" to the anisotropic one for what concerns one individual polarization state can be defined only within an uncertainty range comparable to the birefringence.     

Phased arrays - part 1: theory and architectures

An overview of electronically scanned array technology with a brief introduction of the basic theory and array architectures are presented. Implementations, current state-of-the-art, and future trends are briefly reviewed in Part II of this paper     

Sampling theory for neuromagnetic detector arrays

The sampling theorem for wave-number-limited multivariable functions is applied to the problem of neuromagnetic field mapping. The wave-number spectrum and other relevant properties of these fields are estimated. A theory is derived for reconstructing neuromagnetic fields from measurements using sensor arrays which sample either the field component B_z perpendicular to the planar grid of measurement points, or the two components partial B_z/partial x and partial B_z /partial y of its gradient in the xy plane. The maximum sensor spacing consistent with a unique reconstruction is determined for both cases. It is shown that, when two orthogonal components of the gradient are measured at every site of the measurement grid, the density of these sensor-pair units can be reduced, without risk of aliasing, to half of what is necessary for single-channel sensors in an array sampling B_z alone. Thus the planar and axial gradiometer arrays are equivalent in the sampling sense provided that the number of independent measurements per unit area is equal     

A theory of two-dimensional linear recurring arrays

In this paper, two-dimensional arrays of elements of an arbitrary finite field are examined, especially arrays having maximum-area matrices. We first define two-dimensional linear recurring arrays. In order to study the characteristics of two-dimensional linear recurring arrays, we also define two-dimensional linear cyclic codes. A systematic method of constructing two-dimensional linear recurring arrays having maximum-area matrices is given using the theory of two-dimensional cyclic codes. These arrays, here calledgamma beta-arrays, may be said to be two-dimensional analogs ofM-sequences. Agamma beta-array of areaN_x times N_yexists overGF(q)if and only ifN_x N_yis equal toq^N _ 1for some positive integerN. Many interesting characteristics of thegamma beta-array, such as the properties of its autocorrelation function and the properties of the characteristic arrays, are deduced and explained.     

Fractal antenna engineering: the theory and design of fractalantenna arrays

A fractal is a recursively generated object having a fractional dimension. Many objects, including antennas, can be designed using the recursive nature of a fractal. In this article, we provide a comprehensive overview of recent developments in the field of fractal antenna engineering, with particular emphasis placed on the theory and design of fractal arrays. We introduce some important properties of fractal arrays, including the frequency-independent multi-band characteristics, schemes for realizing low-sidelobe designs, systematic approaches to thinning, and the ability to develop rapid beam-forming algorithms by exploiting the recursive nature of fractals. These arrays have fractional dimensions that are found from the generating subarray used to recursively create the fractal array. Our research is in its infancy, but the results so far are intriguing, and may have future practical applications     

Three-dimensional analytical simulation of self- and cross-responsivities of photovoltaic detector arrays

Decreasing dimensions, along with an increasing number of elements in imaging photodiode arrays, result in the degradation of spatial resolution and sensitivity due to lateral transport. This effect is modeled using a novel 3-D analytical solution of the continuity equation. The model enables the full 3-D analysis of lateral transport as manifested in excess carrier distribution, photocurrent, and self- and cross-responsivities. Three detector structures are investigated: the semi-infinite substrate, the perfectly collecting, and the perfectly reflecting backside. The front and rear illuminations are treated. The calculated results for the 3-D case deviate fundamentally from those predicted by the 1-D model. The 3-D model succeeds in explaining the reduced quantum efficiency of small-area detectors. It also predicts the limited effect diffusion length has on self-responsivity and cut-off wavelength. The calculated spectral responses fit extremely well data measured on InSb and HgCdTe test arrays. As a powerful design tool, the model enables optimizing responsivity and crosstalk by varying element geometry and spacing, optical aperture, lifetime, and spectral range. The model can be applied to any semiconductor photodiode array provided the relevant physical and geometrical parameters are known.     

Features of vectorial modes in phase-coupled VCSEL arrays: experiments and theory

We present a detailed study of oxide-confined, vertical-cavity surface-emitting lasers (VCSELs) where the reflectivity of the top mirror has been patterned by means of a metal grid, which at the same time acts also as an electrode. Owing to their features, these kind of devices are commonly referred to as phase-coupled VCSEL arrays. The analysis is based on a joint experimental and theoretical effort: the former is devoted to a complete characterization of the emission properties, while the latter is based on a comprehensive fully vectorial model for the structure eigenmodes with the details of their complex structure. The detected characteristics make them quite attractive for various applications and the comparison of their modal properties with the model is proved to be essential for a deep understanding of these lasers. In particular, we observed and explain, for the first time, a characteristic behavior of the lasing array, which displays spatially inhomogeneous polarization characteristics with symmetry properties with respect to the array diagonals. The good matching between theory and experiment opens new perspectives for an optimized device, where the typical four lobe far-field emission is converted in a narrow central lobe: two different proposals will be discussed.     

Highly coherent, in-phase-mode operation of 20-element resonantarrays of antiguides

Twenty-element resonant-optical-waveguide (ROW) arrays are discussed. Fringe-visibility measurements, performed on in-phase-operating devices, reveal high coherent (γ>0.86) across the whole array structure. The devices maintain diffraction-limited beams to 2.8×threshold. Uniform near-field intensity profiles confirm that the arrays are operating close to the resonant coupling condition and thus are fully coupled