Absolute and relative nonlinear optical coefficients of KDP, KD*P,BaB2O4, LiIO3, MgO:LiNbO3,and KTP measured by phase-matched second-harmonic generation

Both absolute and relative nonlinear optical coefficients of six nonlinear materials measured by second-harmonic generation are discussed. A single-mode, injection-seeded, Q-switched Nd:YAG laser with spatially filtered output was used to generate the 1.064-μm fundamental radiation. The following results were obtained: d₃₆(KD*P)=0.38 pm/V, d₃₆(KD*P)=0.37 pm/V, |d₂₂(BaB ₂O₄)|=2.2 pm/V, d₃₁(LiIO₃ )=-4.1 pm/V, d₃₁(5%MgO:MgO LiNbO₃)=-4.7 pm/V, and d_eff(KTP)=3.2 pm/V. The accuracy of these measurements is estimated to be better than 10%     

Temperature sensitivity of phase-matched second-harmonic generationin LiIO3

Measurements were made of the temperature dependence (between 23 and 65°C) of the phase-matching angle &thetas;_pm for type I frequency doubling of 1064-nm laser light in lithium iodate (LiIO₃). The measured value of d&thetas;_pm/dT is -14.7±1 μrad/°C, which corresponds to a thermal sensitivity β_T =0.24±0.02 cm^-1/°C for this process. Also calculated is a value of d&thetas;_pm/dT using experimentally determined thermooptic data available in the literature. The calculated value of d&thetas;_pm/dT is -31±18 μrad/°C using literature values of n and dn/dT for LiIO₃. The extreme sensitivity of the calculated value of d&thetas;_pm/dT to small errors in the thermooptic coefficients may be the reason for this discrepancy     

Optimum codes of dimension 3 and 4 over GF(4)

n_q(k,d), the length of a q-ary optimum code for given k and d, for q=4 and k=3, 4 is discussed. The problem is completely solved for k=3, and the exact value of n₄(4,d) is determined for all but 52 values of d     

A strengthening of the Assmus-Mattson theorem

Let w₁=d,w₂,…,w _s be the weights of the nonzero codewords in a binary linear [n,k,d] code C, and let w' ₁, w'₂, …, w'₃, be the nonzero weights in the dual code C1. Let t be an integer in the range 0<t<d such that there are at most d-t weights w'_i with 0<w'_i ⩽n-t E. F. Assmus and H. F. Mattson, Jr. (1969) proved that the words of any weight w_i in C form a t-design. The authors show that if w₂⩾d+4 then either the words of any nonzero weight w_i form a (t+1)-design or else the codewords of minimal weight d form a {1,2,…,t,t+2}-design. If in addition C is self-dual with all weights divisible by 4 then the codewords of any given weight w_i form either a (t +1)-design or a {1,2,…,t,t+2}-design. The proof avoids the use of modular forms     

Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm

The author reports the stable generation of 0.2-W average power IR pulses around 3.2 μm from the KTP parametric oscillator pumped by the Nd:YAG laser at 1.064 μm. In addition, improved Sellmeier's equations, which correctly predict almost all of the nonlinear experiments thus far reported, are presented, together with the absolute values of d₃₁ and d₃₂     

Elastic constants and thermal fracture of AgGaSe2 andd-LAP

The elastic constants and thermoelastic coefficients of silver gallium selenide and deuterated l-arginine phosphate (d-LAP) are reported. Their fracture strength as measured by indentation tests is also reported. These data are used to calculate their thermal fracture resistance, a parameter which is important in high-average-power laser systems. Their thermal fracture resistance is then compared to that of other nonlinear crystals. To the extent that the damage threshold increases with fracture temperature, the data on AgGaSe₂ and d-LAP are favorable indicators of a higher damage threshold. In particular, the data suggest that d-LAP should compare favorably with other solution-grown materials such as lithium iodate and KDP. Preliminary data on the damage threshold of d-LAP appear to confirm that it is indeed more damage resistant than comparably prepared samples of these other solution-grown materials     

Second harmonic generation and sum frequency mixing of dualwavelength Nd:YAlO3 laser in flux grown KTiOPO4crystal

On the basis of accurately measured refractive indexes, the authors have obtained the Sellmeier's equations for flux grown KTiOPO ₄ (KTP) crystal and used them to calculate the phase matched angles (&thetas;_m, φ_m) and effective nonlinear coefficients (d_eff) for type I and III second harmonic generation (SHG) and sum frequency mixing (SFM) of radiations at 1.0795 and 1.3414 μm. The optimum phase matching conditions for 1.0795 and 1.3414 μm SHG are that &thetas;_m=86.88 and 58.88°, respectively, in an XZ plane (φ=0) and for SMF of 1.0795 and 1.3414 μm in the same plane 76.02°. The corresponding d_eff values calculated from &thetas; _ms are 18.07×10^-9 and 17.42×10^-9 esu     

Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b ⩾1 length 2n+2r(d-1) for d⩽3 and length 2n+2r(d-1)(2d -1) for d>3, where r is the least integer ⩾log₂ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2²¹ codewords. A construction is presented for which from a given code C ₁ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C₂, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed     

Measurement of nonlinear coefficient and phase matchingcharacteristics of AgGaS2

The nonlinear optical characteristics of AgGaS₂ were investigated by measuring visible parametric fluorescence with a pump wavelength of 600 nm. A value of d₃₆ [AgGaS₂ ]=31±5×10^-12 m/V for the nonlinear coefficient was determined. The temperature dependence of phase matching up to 100°C was studied. A significant temperature effect, although much smaller than for LiNbO₃, was found and results in a change in the infrared difference frequency generated of ~0.6 cm^-1 -°C^-1     

The (d,k) subcode of a linear block code

A simple technique employing linear block codes to construct (d,k) error-correcting block codes is considered. This scheme allows asymptotically reliable transmission at rate R over a BSC channel with capacity C_BSC provided R ⩽C_d,k-(1+C_BSC), where C_d,k is the maximum entropy of a (d,k ) source. For the same error-correcting capability, the loss in code rate incurred by a multiple-error correcting (d,k) code resulting from this scheme is no greater than that incurred by the parent linear block code. The single-error correcting code is asymptotically optimal. A modification allows the correction of single bit-shaft errors as well. Decoding can be accomplished using off-the-shelf decoders. A systematic (but suboptimal) encoding scheme and detailed case studies are provided     

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     

Minimum distance of logarithmic and fractional partialm-sequences

Two results are presented concerning the partial periods (p-p's) of an m-sequence of period 2ⁿ-1. The first proves the existence of an m-sequence whose p-p's of length approximately (n+d log₂ n) have minimum distance between d and 2d for small d. The second result is of an asymptotic nature and proves that the normalized minimum distance of p-p's whose length is any fraction of the period of the m-sequence, approaches 1/2 as the period of m-sequence tends to infinity     

Proton-exchanged LiNbO3 waveguides: the effects ofpost-exchange annealing and buffered melts as determined by infraredspectroscopy, optical waveguide measurements, and hydrogen isotopicexchange reactions

Infrared spectroscopy in the OH stretching region has been used to determine the extent of proton exchange in x- and z-cut lithium niobate as a function of temperature and time. The behavior observed is consistent with the occurrence of a diffusion-limited process within LiNbO₃. Apparent activation energies for the process determined from infrared spectroscopic measurements are consistent with the existence of a minimum exchange temperature and show that a relationship exists between waveguide depth and absorption band area. The measurements are also shown that hydrogen-bonded OH is substantially removed by annealing and that the extent of its formation is reduced by using buffered (lithium benzoate/benzoic acid) melts. It is suggested that hydrogen-bonded OH groups are responsible for many of the problems associated with proton-exchanged waveguides. Therefore, implementation of either annealing or buffered melts as part of the fabrication process is required to realize good-quality proton-exchanged waveguides     

Identities and approximations for the weight distribution of q-ary codes

An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k , d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q ^-(n-k) as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance     

Evidence for continuous visible chemical lasing from the fast nearresonant energy transfer pumping of atomic sodium

Energy transfer from selectively formed metastable states of SiO is used to pump sodium-atom laser amplifiers at λ≈569 nm (4d²D-3p²P), λ≈616 nm (5s²S-3p² P), and λ≈819 nm (3d²D -3p²P). The a³Σ⁺ and b³Π states of SiO are generated in high yield from the Si+N₂O→SiO+N₂ reaction. The energy stored in the triplet states is transferred in a highly efficient collisional process to pump sodium atoms to their lowest excited 3d² D, 4d²D, and 5s²S states. Adopting a sequence in which high concentrations of silicon and sodium atoms are mixed and oxidized, a continuous amplification (gain condition) is monitored which suggests the creation of a population inversion among the receptor sodium-atom energy levels and forms the basis for full cavity oscillation on the Na4 d²D-3p²P transition at 569 nm     

On the influence of coding on the mean time to failure fordegrading memories with defects

The application of a combined test-error-correcting procedure is studied to improve the mean time to failure (MTTF) for degrading memory systems with defects. The degradation is characterized by the probability p that within a unit of time a memory cell changes from the operational state to the permanent defect state. Bounds are given on the MTTF and it is shown that, for memories with N words of k information bits, coding gives an improvement in MTTF proportional to (k/n) N(d_min^-2)/(d_min ^-1), where d_min and (k/n) are the minimum distance and the efficiency of the code used, respectively. Thus the time gain for a simple minimum-distance-3 is proportional to N^-1. A memory word test is combined with a simple defect-matching code. This yields reliable operation with one defect in a word of length k+2 at a code efficiency k/(k+2)     

Generalized Hamming weights of linear codes

The generalized Hamming weight, d_r(C), of a binary linear code C is the size of the smallest support of any r-dimensional subcode of C. The parameter d_r(C) determines the code's performance on the wire-tap channel of Type II. Bounds on d_r(C), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d_r(C) is presented and examples are given of codes meeting this bound with equality     

Self-switching in hollow waveguides with a Kerrlike nonlinearpermittivity

The dispersion relations, stability, and excitation of the stationary nonlinear transverse electric (TE) waves guided by a nonlinear hollow waveguide are examined numerically. This waveguide consists of a self-focusing nonlinear film bounded by two identical linear claddings of the higher refractive index. Since a minimum power for guidance of the stationary waves always exists, the nonlinear hollow waveguide acts as a lower threshold device. A stability analysis using the beam propagation method shows that all the stationary TE_n modes, including the asymmetric TE₀ mode, are stable on the positively sloped branch (dP/dβ>0) of the nonlinear dispersion curve. The lower threshold device using the nonlinear hollow waveguide exhibits very sharp power-switching characteristics, and the required device length is fairly short     

On the decoding of algebraic-geometric codes over Fq forq⩾16

It is proved that for algebraic-geometric codes on a curve over F _q for q⩾37 or on a curve of sufficiently large genus over F_q for q⩾16 there exists a polynomial decoding algorithm up to (d*-1)/2 errors, d* being the designed minimum distance     

Queueing analyses of traffic access control strategies withpreemptive and nonpreemptive disciplines in wideband integrated networks

A multiserver queueing model of access control strategies for a wideband integrated services digital network (ISDN) is considered. There are two types of service requests (SRs): Type 1 SR requires b servers (basic bandwidth units, BBUs) of the c available servers, while Type 2 SR requires a single server. Both types of SRs are queuable in two separate infinite-size buffers. A Type 1 SR is allowed to seize d(⩽b) servers at first and then acquire additional servers as they become available to meet the original requirement of b servers. The arrival processes of both types of SRs are Poisson and the service times are exponentially distributed with mean b/dμ₁ and 1/μ₂ for Type 1 SR and Type 2 SR, respectively. Preemptive and nonpreemptive priority disciplines with movable boundary are analyzed using the Neuts' matrix-analytic approach. Numerical examples of the queue length distribution and the mean waiting time of the SRs are presented