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)     

Double series representation of bounded signals

Series representations of the form f(t)~Σ_n=-∞^∞Σ _k=-∞^∞a_n,kν(t-n)_e ^2πkts/ for bounded signals f(t) are studied, as are conditions on the unit function ν(t), such that coefficients a_n,k reveal the energy content of f(t) in the time interval n-(1/2)⩽t⩽n+(1/2) and frequency interval 2π(k-(1/2))⩽ω⩽2π(k+(1/2)). These conditions turn out to be orthogonality and integrability. Based on these conditions a number of properties of the expansion are derived, including summability of the double series and energy and power estimations. Some examples of the expansion are presented     

Emission cross sections and spectroscopy of Ho3+ laserchannels in KGd(WO4)2 single crystal

The spectroscopic properties of Ho³⁺ laser channels in KGd(WO₄)₂ crystals have been investigated using optical absorption, photoluminescence, and lifetime measurements. The radiative lifetimes of Ho³⁺ have been calculated through a Judd-Ofelt (JO) formalism using 300-K optical absorption results. The JO parameters obtained were Ω₂=15.35×10^-20 cm², Ω ₄=3.79×10^-20 cm², Ω₆ =1.69×10^-20 cm². The 7-300-K lifetimes obtained in diluted (8·10¹⁸ cm^-3) KGW:0.1% Ho samples are: τ(⁵F₃)≈0.9 μs, τ( ⁵S₂)=19-3.6 μs, and τ(⁵F₅ )≈1.1 μs. For Ho concentrations below 1.5×10²⁰ cm^-3, multiphonon emission is the main source of non radiative losses, and the temperature independent multiphonon probability in KGW is found to follow the energy gap law τ_ph ^-1(0)=βexp(-αΔE), where β=1.4×10^-7 s^-1, and α=1.4×10³ cm. Above this holmium concentration, energy transfer between Ho impurities also contributes to the losses. The spectral distributions of the Ho³⁺ emission cross section σ_EM for several laser channels are calculated in σ- and π-polarized configurations. The peak a σ_EM values achieved for transitions to the ⁵I₈ level are ≈2×10^-20 cm² in the σ-polarized configuration, and three main lasing peaks at 2.02, 2.05, and 2.07 μm are envisaged inside the ⁵I₇→⁵I₈ channel     

A non-Shannon-type conditional inequality of information quantities

Given n discrete random variables Ω={X₁,…,X_n}, associated with any subset α of {1,2,…,n}, there is a joint entropy H(X_α) where X_α={X_i: i∈α}. This can be viewed as a function defined on 2^{1,2,…,n} taking values in [0, +∞). We call this function the entropy function of Ω. The nonnegativity of the joint entropies implies that this function is nonnegative; the nonnegativity of the conditional joint entropies implies that this function is nondecreasing; and the nonnegativity of the conditional mutual information implies that this function is two-alternative. These properties are the so-called basic information inequalities of Shannon's information measures. An entropy function can be viewed as a 2ⁿ -1-dimensional vector where the coordinates are indexed by the subsets of the ground set {1,2,…,n}. As introduced by Yeng (see ibid., vol.43, no.6, p.1923-34, 1997) Γ_n stands for the cone in IR(2ⁿ-1) consisting of all vectors which have all these properties. Let Γ_n* be the set of all 2ⁿ -1-dimensional vectors which correspond to the entropy functions of some sets of n discrete random variables. A fundamental information-theoretic problem is whether or not Γ¯_n*=Γ_n. Here Γ¯_n * stands for the closure of the set Γ_n*. We show that Γ¯_n* is a convex cone, Γ₂*=Γ₂, Γ₃*≠Γ₃, but Γ¯₃ *=Γ₃. For four random variables, we have discovered a conditional inequality which is not implied by the basic information inequalities of the same set of random variables. This lends an evidence to the plausible conjecture that Γ¯_n*≠Γ_n for n>3     

In-circuit hot-carrier model and its application to inverter chainoptimization

An analytical in-circuit device lifetime model and design methodology for minimizing hot-carrier effects in an inverter chain are presented. Based on the model, in-circuit device lifetime, τ_AC , for hot-carrier induced degradation is given by τ_AC =τ_DC/R, R≡√π/2√Vcc/b√(T _rise.T_fall)/T_c where τ_DC is the device lifetime under a DC test, T_rise and T_fall are the rise time for input and fall time for output, T_C is cycle time and b is a constant. The model also shows that minimizing circuit delay in the inverter chain maximizes hot-carrier reliability     

On estimating the spectral exponent of fractional Brownian motion

Three estimators of the exponent α in the power spectral density g(λ)=c_g|λ|^-α of fractional Brownian motion are evaluated. These are (i) the periodogram-based estimator αˆ_PG (ii) the maximum likelihood estimator αˆ_ML; and (iii) the Allan (1966) variance-based estimator αˆ_AV. Large-sample properties of the mean-square error (MSE) and the associated sampling distribution are examined, αˆ_PG emphasis on the case α∈(1, 2). The MSE performance of αˆ_PG is judged to be inferior to that of both αˆ_ML and αˆ_AV. The rate of decrease of MSE is the same for αˆ_ML and αˆ_AV; the former estimator has smaller MSE, while the latter is less sensitive to departures from the power-law model and is considerably easier to compute     

Characterization of polynomial functions and application totime-frequency analysis

We propose necessary and sufficient conditions for a function φ(t) to be a polynomial and establish a formula that allows us to compute the value of the derivative φ'(t) of a polynomial at any point in terms of the values of this polynomial. For this purpose, we establish that any polynomial φ(t) of degree ⩽Q can be represented as a linear combination of φ(t-t₁), …, Q(t-t_Q), where t₁, …, t_Q denote arbitrary parameters. A similar property is established for the derivative φ'(t). Some signal processing applications of these results are discussed,     

A statistical method for obtaining the factors inelectronic-component reliability-prediction models

According to US Mil-Hdbk-217, the failure rate of most electronic components can be predicted as λ_p=λ_b×π₁ ×π₂···π_n. A statistical method of obtaining these parameters is presented. The method is based on large quantities of field data, and the more current the data are, the more accurate the values of each level of λ_b and π_i. Using these values, the models in US Mil-Hdbk-217 can be applied to predict the life of electronic products. The method can also be used to verify the present values of each level of λ_b and π_i, and to provide the basis of further amendment     

Effects of pad and interconnection parasitics on forward transittime in HBTs

A new analytical expression using Y-parameters is derived from the full heterojunction bipolar transistor (HBT) equivalent circuit including probe-pattern parasitics, in order to extract the forward transit time accurately without a conventional de-embedding procedure. The correction procedure of this Y-parameter method does not require the measurement of extra test patterns such as “open” or “short” structures, thus being free of the possible de-embedding errors attributed to the inaccuracy of test structures. To compare the de-embedding effect on τ_F in the Y-parameter method with that in the previous f_T method, C_π/g_mo versus 1/I_c curves are plotted with 1/2πf_T versus 1/I_c in the cases of de-embedding and no de-embedding. This comparison clearly exhibits that the contribution of the probe-pattern parasitics to τ_F in the Y-parameter method is much smaller than that in the conventional f _T method. The smaller contribution to τ_F may result in the enhancement of the de-embedding accuracy in the Y-parameter method     

Reduction of the current gain of the n-p-n transistor component ofa thyristor due to the doping concentration of the p-base

The reduction of the current amplification factor of a wide-base transistor, with growing doping concentration in the base region, is investigated. A method for the determination of the minority-carrier lifetime τ_n in the base region and the emitter Gummel number G_e is developed. The method is based on transistor structures differing only in the base width. It was found that the lifetime τ_n decreases according to the power law τ_n~N^-0.45_A. This result is analyzed for different recombination processes. Good agreement is obtained if shallow impurities acting as recombination centers are assumed. The injection-limited current gain β_γ decreases significantly with an increase in the total number of the doping concentration of the base, reaches a broad maximum, and then falls slowly. The maximum value of G_e is found to be 1.1×10¹⁴ cm^-4-s in good agreement with theoretical results. Finally, the contribution of the injection efficiency γ and the transport factor α_T to the current gain α are determined. It is found that α is limited mainly by the injection efficiency γ     

Delayed-self-heterodyne measurement of laser frequency fluctuations

The two-sample (or Allan) variance of frequency fluctuations was used for laser frequency-noise characterization at Fourier frequencies below 1 MHz. The delayed self-heterodyne technique was used for the variance measurement. Analytical calculations ensure that just twice the variance values were observed at τ<0.3τ_d, where τ is the averaging time for the frequency measurement and τ_d is the delay time. The variance measurements of 1.5-μm distributed Bragg reflector and distributed feedback laser diodes were demonstrated at 6.0×10^-7⩽τ⩽1.0×10^-4 [s] by using an 81.5-km fiber delay line. Observed flicker fluctuations (or 1/ f noise) are discussed     

Combinatorial bounds for list decoding

Informally, an error-correcting code has "nice" list-decodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. We report linear codes with nontrivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H^-1(1-R-1/c)·n. This answers the main open question from the work of Elias (1957). This result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors, improving previous results of Guruswami and Sudan (see IEEE Trans. Inform. Theory, vol.45, p.1757-67, Sept. 1999, and Proc. 32nd ACM Symp. Theory of Computing (STOC), Portland, OR, p. 181-190, May 2000) in this vein. Specifically, for every ε > 0, we present a polynomial time constructible asymptotically good family of binary codes of rate Ω(ε⁴) that can be list-decoded in polynomial time from up to a fraction (1/2-ε) of errors, using lists of size O(ε^-2). On the negative side, we show that for every δ and c, there exists τ < δ, c₁ > 0, and an infinite family of linear codes {C_i}_i such that if n_i denotes the block length of C_i, then C _i has minimum distance at least δ · n_i and contains more than c₁ · n_i^c codewords in some Hamming ball of radius τ · n_i. While this result is still far from known bounds on the list-decodability of linear codes, it is the first to bound the "radius for list-decodability by a polynomial-sized list" away from the minimum distance of the code     

Rejection of an FH signal in a DS spread-spectrum system usingcomplex adaptive filters

The performance of a direct sequence QPSK spread-spectrum receiver using adaptive filters in the presence of frequency hopped interference is analyzed. The analysis includes both the adaptive prediction error filters and the adaptive transversal filters with two-sided taps. If the product of the instantaneous frequency offset Ω_l, between the jamming signal and the carrier of the spread-spectrum signal, and the sampling period Δ is 360° (Ω_l·Δ=360°), the filter gain is reduced to zero. The filter gain G highly depends on the filter adaptation rate μ. Depending on μ, G can vary from zero to more than 20 dB for a jammer/signal power ratio (J/S) of 20 dB. If Ω _l·Δ is small enough (⩽10°), the performance of the transversal filter is better than that of the prediction error filter, in the case when μ is small. For larger values of μ or Ω_l·Δ, these performances are approximately the same. Numerical results for the hopping sequence of the jamming signal are also presented. Besides the filter gain the analysis of the adaptation rate (time constant) filter misadjustment and the system bit error probability is also included     

Upper bounds on trellis complexity of lattices

Unlike block codes, n-dimensional lattices can have minimal trellis diagrams with an arbitrarily large number of states, branches, and paths. In particular, we show by a counterexample that there is no f(n), a function of n, such that all rational lattices of dimension n have a trellis with less than f(n) states. Nevertheless, using a theorem due to Hermite, we prove that every integral lattice Λ of dimension n has a trellis T, such that the total number of paths in T is upper-bounded by P(T)⩽n!(2/√3)^n2(n-1/2)V(Λ) ^n-1 where V(n) is the volume of Λ. Furthermore, the number of states at time i in T is upper-bounded by |S_i|⩽(2/√3)^i2(n-1)V(Λ)²ⁱ² n/. Although these bounds are seldom tight, these are the first known general upper bounds on trellis complexity of lattices     

Multivariate regression estimation of continuous-time processesfrom sampled data: local polynomial fitting approach

Let (Y,X)={Y(t),X(t),-∞j) be a renewal point processes on (0,∞), with a finite mean rate, independent of (Y,X). We consider the estimation of regression function r(x₀, x₁,...,x_m-1; τ₁,...,τ_m) of ψ(Y(τ_m)) given (X(0)=x₀, X(τ₁)=x₁,...,X(τ_m-1)=_x-1 ) for arbitrary lags 0<τ₁<...< τ_m on the basis of the discrete-time observations {Y(t_j),X(t_j),t_j)_j=1ⁿ . We estimate the regression function and all its partial derivatives up to a total order p⩾1 using high-order local polynomial fitting. We establish the weak consistency of such estimates along with rates of convergence. We also establish the joint asymptotic normality of the estimates for the regression function and all its partial derivatives up to a total order p⩾1 and provide explicit expressions for the bias and covariance matrix (of the asymptotically normal distribution)     

Optimal covering polynomial sets correcting three errors for binarycyclic codes

The covering polynomial method is a generalization of error-trapping decoding and is a simple and effective way to decode cyclic codes. For cyclic codes of rate R<2/τ, covering polynomials of a single term suffice to correct up to τ errors, and minimal sets of covering polynomials are known for various such codes. In this article, the case of τ=3 and of binary cyclic codes of rate R⩾2/3 is investigated. Specifically, a closed-form specification is given for minimal covering polynomial sets for codes of rate 2/3⩽R<11/15 for all sufficiently large code length n; the resulting number of covering polynomials is, if R=2/3+ρ with ρ>0, equal to nρ+2V√nρ+(1/2) log_φ(n/ρ)+O(1), where φ=(1+√5)/2. For all codes correcting up to three errors, the number of covering polynomials is at least nρ+2√nρ+O(log n); covering polynomial sets achieving this bound (and thus within O(log n) of the minimum) are presented in closed-form specifications for rates in the range 11/15⩽R<3/4     

On the testing of the magnetic field integral equation with RWGbasis functions in method of moments

For electromagnetic analysis using method of moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor Ω₀ equal to the solid angle external to the surface at the testing points, which is 2π everywhere on the surface of the object, except at the edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with Ω₀=2π leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the Ω₀ factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference     

Iterative Channel Estimation Based on B-splines for Fast Flat Fading Channels

We propose novel low-complexity iterative channel estimators based on B-splines. Local splines are adopted for computational simplicity. Minimum mean square error (MMSE) local splines with integral sampling are derived. The MSE of the proposed estimators depends on signal-to-noise ratio, fading rate, sampling interval, spline order and the number of weighting coefficients; these dependencies are investigated. The linear and cubic local splines with as few as seven weighting coefficients are capable of achieving MSE and BER performance comparable to those of the Wiener filter and the spheroidal basis expansion. However, a significantly lower complexity is achieved using B-splines     

Improved redundancy of a version of the Lempel-Ziv algorithm

The Lempel-Ziv data compression algorithm has the property that for finite-memory sources the redundancy ρ_n (defined as the difference between the average code rate and the entropy when the memory size is n) is O (log log n/log n). We suggest a new version of the algorithm with redundancy ρ_n=O (1/log n)     

A binary analog to the entropy-power inequality

Let {X_n}, {Y_n} be independent stationary binary random sequences with entropy H( X), H(Y), respectively. Let h(ζ)=-ζlogζ-(1-ζ)log(1-ζ), 0⩽ζ⩽1/2, be the binary entropy function and let σ(X)=h^-1 (H(X)), σ(Y)=h^-1 (H(Y)). Let z_n=X_n⊕Y_n , where ⊕ denotes modulo-2 addition. The following analog of the entropy-power inequality provides a lower bound on H(Z ), the entropy of {Z_n}: σ(Z)⩾σ(X)*σ(Y), where σ(Z)=h^-1 (H(Z)), and α*β=α(1-β)+β(1-α). When {Y _n} are independent identically distributed, this reduces to Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973)