Second- and higher order resonant gratings with gain or loss-PartII: designing complex-coupled DFB lasers with second-order gratings

For part I see, ibid., p. 1421, (2000). This paper deals with the investigation of second-order DFB lasers with a gain grating. It is shown that by proper choice of the duty cycle, one may take advantage of the different radiation losses between the mode with the lowest threshold gain and the second mode to increase the single-mode yield and also obtain a strong complex-coupling with high external efficiency. The impact of the random phase of high-reflection (HR)-coated facet on modal properties in an anti-reflection and HR combination is also investigated     

Green's functional approach to resonant cavity analysis

A new method for obtaining the propagation characteristics of resonant laser cavities is presented. Resonance wavelengths and threshold gains can be obtained for structures containing an arbitrary complex index of refraction profile. The method is based on determining the poles of the Green's function of the system, which is computed using an exact integral formalism     

A unified Green's function analysis of complicated DFB lasers

An efficient full-wave analysis technique for one-dimensional optical domains, known as the recursive Green's function method (RGFM), is presented for evaluation of distributed feedback (DFB) laser cavities with arbitrary material profiles. The method first constructs the Green's function of an inhomogeneous domain and subsequently uses Green's theorem to determine the laser optical field, lasing wavelength, and threshold gain. The technique is applied to investigate the performance of three DFB laser structures: a chirped-grating configuration, a modulated stripe width design, and a reduced duty cycle complex-coupled device. These structures are evaluated in terms of their single-mode lasing behavior and the uniformity of the optical field within the cavity     

Instabilities and nonlinear L-I characteristics in complex-coupledDFB lasers with antiphase gain and index gratings

Complex-coupled DFB lasers can be designed to provide large bandwidths and low chirp by adjusting the strength and phase of their index and gain gratings. In this paper we develop a self-consistent method of calculating the coupling coefficient of complex-coupled DFB lasers with a corrugated active region. Basic geometrical and structural parameters are used as inputs to the model. We show that antiphase coupling implies lasing on the short-wavelength side of the Bragg wavelength which in turn leads to instabilities and/or nonlinearities in the light-current characteristic. The critical output power for onset of instabilities is typically in the order of a few milliwatts. Time-domain simulations are used to assess the potential effects of these instabilities on optical communication systems. We find that transitions from a state of equal output powers from the facets to a state of dramatically different output powers occur within a few nanoseconds of turn-on. The origin of these instabilities is explained using a simple physical model and possible ways of increasing the critical power for instabilities are discussed. For example, we clearly show that the critical power for instability increases when the carrier lifetime is decreased     

Two-dimensional Green's function for a wedge with impedance faces

The solution for the two-dimensional (2-D) Green's function for a wedge with impedance faces is presented. The important feature of this Green's function is that there are no restrictions on the locations for the source and observation points-they can be anywhere. Its development proceeds along two separate lines: one for when the source or observation point is far from the wedge vertex and another one for when it is close. Much of the effort that has been expended in these formulations has been in obtaining forms for the Green's function which are efficient to evaluate numerically. This involved deforming the various contours of integration so that they are rapidly convergent and separating the contributions from the numerous singularities that occur in the integrands and evaluating them in closed form. The formulations that are employed here allow for the individual field components such as the diffracted, geometrical optics, and surface wave components to be identified and studied individually so that a physical understanding for the various scattering mechanisms for the impedance wedge can be appreciated     

The circular homogeneous-ferrite microwave circulator - an asymptotic Green's function and impedance analysis

A detailed analysis of the circular, homogeneous ferrite microwave circulator is provided. Particular emphasis is on the circulator's Green's function and the impact of the asymptotic term within the Green's function on convergence, data quality, and design methodology. The asymptotic term is shown to be logarithmic, which suggests that the Green's function is weakly singular when the source and observation points occupy the same location. With the Green's function properly understood, two techniques - one analytical and one numerical - are then offered to integrate that function in order to obtain Z-parameter data and, subsequently, S-parameter data. Data are provided to show rapid convergence of all parameters of interest. A small coupling angle approximation is then given for the Z-parameters and, from that approximation, a first-order design equation is obtained that relates the coupling angle to circulator radius. A circulator design example is presented and compared to a design associated with the Wu and Rosenbaum method; the comparison substantiates the small coupling angle approximation and design formula.     

Green's function analysis of single and stacked rectangularmicrostrip patch antennas enclosed in a cavity

A rigorous Green's function analysis of rectangular microstrip patch antennas enclosed in a rectangular cavity is described. The formulation makes use of a frequency-independent preprocessing (image extraction) on the spectral domain representation of the Green's function. Measured and simulated results are shown for both single and stacked-patch antennas enclosed in a cavity     

Microstructured fibre Bragg gratings: analysis and fabrication

A microstructured fibre Bragg grating that relies on a partial and localised etching of the cladding layer along the grating region is proposed. The main effect is the formation of defect states inside the bandgap depending on surrounding refractive index. This leads to the possibility of realising novel optoelectronic devices for sensing and telecommunication applications.     

Sub-threshold analysis and drain current modeling of polysilicon thin-film transistor using Green's function approach

An analytical analysis for a poly-crystalline silicon thin-film transistor is presented. The Green's function approach is adopted to solve the two-dimensional Poisson's equation using Neumann's boundary conditions at the silicon-silicon di-oxide interface. The developed model gives an insight of device behavior due to the effect of traps and also grain-boundary effect. The analysis of threshold voltage depicts short-channel effects and drain-induced barrier lowering. The model is extended to analyze the transfer characteristics and obtain the transconductance of the device. The results obtained show good agreement with the numerical model and with simulated results, thus proving the validity of our model.     

Singularity in Green's function and its numerical evaluation

The free-space scalar Green's functionghas anR^{-1}singularity, whereRis the distance between the source and observation points. The second derivatives ofghaveR^{-3}singularities, which are not generally integrable over a volume. The derivatives ofgare treated as generalized functions in the manner described by Gel'fand and Shilov, and a new formula is derived that regularizes a divergent convolution integral involving the second derivatives ofg. When the formula is used in the dyadic Green's function formulation for calculating theEfield, all previous results are recovered as special cases. Furthermore, it is demonstrated that the formula is particularly suitable for the numerical evaluation of the field at a source point, because it allows the exclusion of an arbitrary finite region around the singular point from the integration volume. This feature is not shared by any of the previous results on the dyadic Green's function.     

Exterior moment method analysis of conducting scatterers by using the interior Green's function

A new method using a Green's function in the interior region of a conducting scatterer is proposed to obtain a mutual admittance matrix in an exterior moment method analysis. A numerical example of a two-dimensional magnetic strip source located on an exterior surface of a perfectly conducting rectangular cylinder shows the validity of the method.<>     

Effect of grating phase difference on single-mode yield incomplex-coupled DFB lasers with gain and index gratings

In complex-coupled DFB lasers with both index and gain gratings, I have studied the effect of the phase difference between index and gain gratings on the single-mode yield considering the threshold gain difference (side-mode suppression ratio) and the optical field uniformity (spatial hole burning). I have obtained the optimum values of: (1) the phase difference ΔΩ between index and gain gratings, (2) the coupling strength (ℵL)_i of gain grating, and (3) the coupling strength (ℵL)_r of index grating, in order to obtain a high single-mode yield regardless of the relative positions of both facets, The used theory is based on the coupled-mode theory and includes the spatial hole burning correction and the standing wave effect. ΔΩ=π/4 (and 3π/4) DFB lasers with HR-AR facets have the highest single-mode yield and should have ~0.6⩽(ℵL)_i⩽~1.5 and (ℵL)_r<~1.25 in order to obtain above 50% yields. Even above 90% yields can be obtained with the range of ~1.1⩽(ℵL)_i⩽~1.4 and ~0.5⩽(ℵL)_r ⩽~0.85. The superior yield characteristics of ΔΩ=π/4 (and 3π/4) DFB lasers, which is above 2.4 times higher than that of ΔΩ=0 (and π) DFB lasers, comes from their better field intensity uniformity. The results presented in this paper provide insight into the variation of the threshold gain difference and the optical field uniformity with ΔΩ, (ℵL)_r, (ℵL)_i, and (ρ_l, ρ_r)     

Thermal analysis of layered electronic circuits with Green's functions

This paper presents a method for thermal simulation of electronic circuits using an analytical solution of the three-dimensional heat equation resulting from an appropriate circuit thermal model. The temperature fields in multilayered structures are computed analytically employing the Green's functions solution method. The entire solution methodology is illustrated in detail on the particular examples of electronic circuits containing multiple heat sources. Compared to the previous papers published by the authors, the method has been extended by including the possibility of simulating imperfect layer contacts. The simulation results are validated with infra-red measurements and results obtained using other methods. Additionally, the discussion of simulation errors caused mainly by different non-linear phenomena is included.     

High-efficiency CW operation of MOCVD-grown GaAs/AlGaAs vertical-cavity lasers with resonant periodic gain

A GaAs/AlGaAs vertical-cavity surface-emitting laser with resonant periodic gain has been grown by metal-organic chemical vapour deposition. The as-grown structure exhibits an optically pumped CW threshold below 15 mW at 300 K and a single-ended power efficiency up to 45%. Fundamental Gaussian and higher-order modes are observed with spectral widths (FWHM) as low as 0.27 AA.<>     

Optimization and fabrication of stitched long-period gratings for gain flattening of ultrawide-band EDFAs

We present the optimization and fabrication of the stitched long-period fiber gratings (SLPGs) for gain flattening of an ultrawide-band erbium-doped fiber amplifier (EDFA). With an improved genetic algorithm, the gain spectrum of a practical EDFA with bandwidth of 80 nm is flattened within /spl plusmn/0.69 dB by an optimized SLPG. Furthermore, the SLPG is designed specially for a point-by-point grating writing technique. A superior control of the fabrication procedure of the designed SLPG has been demonstrated in the experiment.     

Dyadic Green's function of multilayer cylindrical closed and sector-structures for waveguide, microstrip-antenna, and network analysis

A clear and systematic method to derive the spectral- and space-domain dyadic Green's function of arbitrary cylindrical multilayer and multiconductor structures is proposed. The derivation is either done for a circumferentially closed or a cylindrical sector structure, which is bounded by electric or magnetic walls in an azimuthal direction. The solution for the dyadic Green's function in the spectral domain is obtained via an equivalent circuit. Relations between the spectral and space domains for the dyadic Green's functions are derived using eigensolution expansions. Finally, the dyadic Green's function is applied to the problem of finding the propagation constants of the two-layer dielectric rod.     

Series resonant converter with auxiliary winding turns: analysis,design and implementation

Conventional series resonant converters have researched and applied for high-efficiency power units due to the benefit of its low switching losses. The main problems of series resonant converters are wide frequency variation and high circulating current. Thus, resonant converter is limited at narrow input voltage range and large input capacitor is normally adopted in commercial power units to provide the minimum hold-up time requirement when AC power is off. To overcome these problems, the resonant converter with auxiliary secondary windings are presented in this paper to achieve high voltage gain at low input voltage case such as hold-up time duration when utility power is off. Since the high voltage gain is used at low input voltage cased, the frequency variation of the proposed converter compared to the conventional resonant converter is reduced. Compared to conventional resonant converter, the hold-up time in the proposed converter is more than 40ms. The larger magnetising inductance of transformer is used to reduce the circulating current losses. Finally, a laboratory prototype is constructed and experiments are provided to verify the converter performance.     

Green's function technique for near-zone scattering by cylindrical wires with finite conductivity

With a technique not requiring matrix inversion, the current distribution induced on a straight thin wire by an incident plane wave or a nearby sinusoidal dipole is determined. The wire may have any length exceeding0.05lambdaand any finite conductivity such that the radius is equal to or greater than the skin depth.     

The time domain Green's function and propagator for Maxwell's equations

The free space time domain propagator and corresponding dyadic Green's function for Maxwell's differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Green's function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygen's principle cannot be satisfied. To illustrate the value of this Green's function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.