Operation of a Raman laser in bulk silicon

A Raman laser based on a bulk silicon single crystal with 1.127 μm emission wavelength is demonstrated. The Si crystal with 30 mm length was placed into an external cavity and pumped by a Q-switched Nd:YAG master oscillator power amplifier system. Strong defocusing of the pump and Raman laser beam by free carriers was compensated by an intracavity lens. Raman laser operation with a pulse duration of 2.5 ns was identified by a Raman laser threshold significantly lower than the single-pass stimulated Raman-scattering threshold. Linear absorption losses of the 1.06415 μm pump radiation are strongly reduced by cooling the Si crystal to a temperature of 10 K.     

Identity-based learning and segregation in social networks under different institutional environments

To study the evolution of segregation in social networks across systems embedded in different institutional environments, we develop an identity-based learning model where segregation is stochastically conditioned by the initial distribution of the actor’s attention to identity and the updating of this distribution over time. The updating process, which we call the process of mutual learning multiplier, is based on an actor’s success and failure experiences in tying with the same-subgroup and cross-subgroup actors. Results from a Monte Carlo simulation of the model show that the mutual learning multiplier produces disproportional relationships between the initial distribution of identity attention and the level of segregation in social networks. We also find that those relationships are affected by the actors’ attention to structural holes, rate of learning from experience, system size, and the identity heterogeneity of the system. Overall, the model provides insights into various dynamics of network structuration across time and space.     

Channel coordination using product returns for a supply chain with stochastic salvage capacity

We examine returns policy in a Newsboy framework. Unlike the prior literature, however, we assume that both supplier and retailer have limited and stochastic salvage capacities. We first analyze the case of integrated supply chain in which the agents’ decisions are fully coordinated for the joint profits. The result prescribes a partial returns policy, in which the retailer returns a part of the leftovers to the supplier and liquidates the remainder through its clearance sale. In a decentralized system, the supplier should motivate the retailer to duplicate the outcome of the integrated system in choosing order and returns quantities. We propose three coordination contracts, of which each uses two benefit transfer schemes as an incentive to the retailer, instead of using a single benefit scheme as in the prior literature. All three effectively coordinate the supply chain. The supplier, as a Stakelberg leader, chooses the most profitable one since each contract yields the different shares of the agents’ profits.     

Stimulated Raman scattering in natural crystals of fluorapatite,Ca5(PO4)3F

Hexagonal Ca₅(PO₄)₃F, known as natural crystal fluorapatite and oldest host‐crystal for Ln³⁺‐lasant ions, is presented as a Raman‐active material. High‐order Raman‐induced χ⁽³⁾‐nonlinear processes are discovered in natural crystals of fluorapatite under picosecond pumping at 1.064 μm and 0.532 μm wavelength. A multitude of Stokes and anti‐Stokes components is generated in the ultraviolet, visible and near‐infrared spectral region by stimulated Raman scattering (SRS) and Raman four‐wave mixing (FWHM), resulting in a frequency comb with a width of 520 THz. The spectral lines are identified and attributed to the ν₁(A_g) vibration mode of the tetrahedral [PO₄] units which is related to a Raman shift of ω_SRS ≈ 965 cm⁻¹. The first Stokes steady‐state Raman gain coefficient in the near‐infrared spectral range is estimated to be >0.38 cm·GW⁻¹. Finally, a short review of SRS‐promoting vibration modes and observed χ⁽³⁾‐ nonlinear interactions in all known SRS‐active natural crystals (minerals) is given.

     

Eigenvalue inequalities and equalities

We consider cases of equality in three basic inequalities for eigenvalues of Hermitian matrices: Cauchy's interlacing inequalities for principal submatrices, Weyl's inequalities for sums, and the residual theorem. Several applications generalize and sharpen known results for eigenvalues of irreducible tridiagonal Hermitian matrices.     

Fuzzy rule generation methods for high-level computer vision

In many decision making systems involving multiple sources, the decisions made may be considered as the result of a rule-based system in which the decision rules are usually enumerated by experts or generated by a learning process. In this paper, we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high-level computer vision. Features are treated as linguistic variables that appear in the antecedent clauses of the rules. We present methods to generate the corresponding linguistic labels (values) and their membership functions. Rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods. Several examples are given.     

Miscibility of Solution Blends of Unsaturated Polyester Resin with Polystyrene and Polycarbonate

Miscibility studies of unsaturated polyester resin (UPR) blends with two different thermoplastics—polystyrene (PS) and polycarbonate (PC), in a common solvent, chloroform, were carried out by viscosity, ultrasonic velocity, density, and refractive index methods. Two interaction parameters, μ and α were calculated using viscosity data for these blends. The positive interaction parameter values (μ and α > 0) obtained for the UPR/PS blend and the negative interaction parameter values (μ and α < 0) obtained for the UPR/PC blend indicate that the former is a miscible blend and the latter is an immiscible blend. These results were further confirmed by the ultrasonic velocity, density, and refractive index measurements.     

Collinear broadband optical parametric generation in periodically poled lithium niobate crystals by group velocity matching

Collinear broadband optical parametric generation (OPG) using periodically poled lithium niobate (PPLN) crystals were designed and experimentally demonstrated with the quasi-phase matching (QPM) periods of 21.5, 24.0, and 27.0 μm. The broad gain bandwidth was accomplished by choosing a specific set of the period and the pump wavelength that allows the group velocities of the signal and the idler to match close to the degeneracy point. OPG gain bandwidth and also the spectral region could be controlled by proper design of QPM period and pump wavelength. The total OPG gain bandwidth of 600, 900, and 1200 nm was observed for the PPLN devices with QPM periods of 21.5, 24.0, and 27.0 μm, respectively. We have also observed multiple color visible generation whenever the OPG spectrum was significantly broad. From the visible peaks of the three PPLN samples, it is found that broad gain bandwidth is crucial in the temperature-insensitive collinear simultaneous RGB generation from a single crystal.