ExplicitN-polynomials of 2-power degree over finite fields,I

For an odd prime powerq the infinite field GF(q ² )= _n0 GF (q ²ⁿ ) is explicitly presented by a sequence (f _n)₁ ofN-polynomials. This means that, for a suitably chosen initial polynomialf ₁, the defining polynomialsf _nGF(q)[x] of degrees2 ⁿ are constructed by iteration of the transformation of variablexx+1/x and have linearly independent roots over GF(q). In addition, the sequences are trace-compatible in the sense that the relative traces map the corresponding roots onto each other. In this first paper the caseq1 (mod 4) is considered and the caseq3 (mod 4) will be dealt with in a second paper. This specific construction solves a problem raised by A. Scheerhorn in [11].     

Tunable blue laser based on intracavity frequency doubling with a fan-structured periodically poled LiTaO(3) crystal

We introduce a new concept for a wavelength-tunable frequency-doubled laser diode with a single control parameter. The concept is based on intracavity frequency doubling in an external resonator geometry with spatial separation of the spectral components. The use of a fan-structured periodically poled LiTaO(3) crystal permits tuning of both the fundamental and the second harmonic simultaneously with one aperture. We demonstrate tunability over more than 10 nm in the blue (480.4 to 490.6 nm) with output powers of the order of 50 nW.     

Dynamic Safety-Stocks for Asymptotic Optimality in Stochastic Networks

This paper concerns control of stochastic networks using state-dependent safety-stocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the Dai-Wang re-entrant line. In each case, a single policy is proposed that is independent of network load ρ?. The following conclusions are obtained for the controlled network in each case, where the finite constant K ₀ is independent of load: The policy is fluid-scale asymptotically optimal, and satisfies the bound 2 $$ eta_ast \le \eta \le \eta_\ast + K_0 \log(\eta_\ast),\quad 0 \le \rho_\bullet \le 1, $$ where η_* is the optimal steady-state cost. These results are based on the construction of an approximate solution to the average-cost dynamic programming equations using a perturbation of the value function for an associated fluid model. Moreover, a new technique is introduced to obtain fluid-scale asymptotic optimality for general networks modeled in discrete time. The proposed policy is myopic with respect to a perturbation of the value function for the fluid model.     

Fabrication of periodically poled lithium tantalate for UV generation with diode lasers

Fabrication of periodically poled lithium tantalate (PPLT) with periods as short as 1.3 μm for second harmonic generation (SHG) in the UV range and for optical parametric oscillators pumped at 532 nm is reported. Both the maximum crystal size of up to 40 mm and the minimum poling period of 1.3 μm are improvements on earlier results, achieved by optimizing the poling conditions and by using a novel electrode design consisting of electrode structures on both surfaces of the crystal. Single-pass SHG of a master oscillator power amplifier (MOPA) diode laser with an output power of 1.36 mW at 336 nm using a 16-mm-long PPLT crystal with a 1.5 μm poling period is reported. Received: 11 June 2001 / Published online: 18 July 2001     

Singly resonant continuous-wave optical parametric oscillator pumped by a diode laser

We report on what is believed to be the first singly resonant cw optical parametric oscillator (SRO) that is directly pumped by a diode laser. The SRO consists of a 38-mm-long periodically poled LiNbO(3) crystal in a four-mirror signal-resonant ring cavity. Pumped by 2.5 W of 925-nm diode-laser radiation, the SRO generates 480 mW of single-frequency idler radiation at 2.1mum . The wavelengths of the signal and the idler output are tuned in the ranges of 1.55 to 1.70mum and 2.03 to 2.29mum, respectively, by tuning the wavelength of the diode laser from 924.0 to 925.4 nm.     

A 9.5-W 82-MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding

We report on an injection-seeded 9.5-W 82-MHz-repetition-rate picosecond optical parametric generator (OPG) based on a 55 mm long crystal of periodically poled lithium niobate (PPLN) with a quasi-phase-matching (QPM) grating period of 29.75 μm. The OPG is excited by a continuously diode pumped mode-locked picosecond Nd:YVO₄ oscillator-amplifier system. The laser system generates 7 ps pulses with a repetition rate of 82.3 MHz and an average power of 24 W. Without injection-seeding the total average output power of the OPG is 8.9 W, which corresponds to an internal conversion efficiency of 50%. The wavelengths of the signal and idler waves were tuned in the range 1.57–1.64 μm and 3.03–3.3 μm, respectively, by changing the crystal temperature from 150 °C to 250 °C. Injection seeding of the OPG at 1.58 μm with 4 mW of single frequency continuous-wave radiation of a distributed-feedback (DFB) diode laser increases the OPG output to 9.5 W (53% conversion efficiency). The injection seeding increases the pulse duration and reduces the spectral bandwidth. When pumped by 10 W of 1.06 μm laser radiation, the duration of the signal pulses increased from 3.6 ps to 5.5 ps while the spectral bandwidth is reduced from 4.5 nm to 0.85 nm. Seeding thus improved the time-bandwidth product from 1.98 to a value of 0.56, much closer to the Fourier limit. Received: 29 April 2002 / Published online: 8 August 2002     

Wide wavelength tuning of an optical parametric oscillator through electro-optic shaping of the gain spectrum

We present a novel technique for tuning an optical parametric oscillator (OPO) through electro-optically induced shape variations of the parametric gain spectrum in quasi-phase-matched lithium niobate (LN). The diode-pumped, triply resonant continuous-wave OPO is based on a 58-mm-long LN crystal that consists of three equally long sections, the outer sections being periodically poled with a 50% duty cycle. The center section is single-domain material and serves as a tunable phase shifter through the electro-optic effect. By application of a voltage of up to 1230 V, the OPO signal and idler wavelengths are tuned over 102 nm from 1560 to 1660 nm, in good agreement with theory.     

Generation of sub-6-fs blue pulses by frequency doubling with quasi-phase-matching gratings

We demonstrate the generation of sub-6-fs pulses centered at 405 nm by frequency doubling of 8.6-fs Ti:sapphire laser pulses. The frequency doubling is carried out in a nonlinearly chirped quasi-phase-matching grating fabricated in a lithium tantalate substrate. This device simultaneously provides frequency conversion and pulse compression of the positively prechirped fundamental pulses. The second-harmonic pulses are characterized in a cross-correlation setup, and their pulse shapes are retrieved by two iterative phase-reconstruction algorithms. The generated second-harmonic spectrum spans a bandwidth of 220 THz. To our knowledge, these are the shortest pulses ever generated in the blue spectral region.     

A 180 mW Nd:LaSc3(BO3)4 single-frequency TEM00 microchip laser pumped by an injection-locked diode-laser array

A TEM₀₀ single-frequency, diode-pumped microchip laser of Nd(25%):LaSc₃(BO₃)₄ is operated with an output power of 180 mW. For best performance the laser was pumped by the 450 mW diffraction-limited single-frequency radiation of an injection-locked AlGaAs diode-laser array and cooled to the temperature of liquid nitrogen. The active and passive losses of the microchip laser were investigated by measuring the relaxation oscillation frequency and by comparing the experimental results with values obtained from appropriate rate equations. The power-dependent far-field pattern is in good agreement with the intensity distribution calculated by assuming a thermally induced waveguide cavity.     

Tunable ultraviolet radiation by second-harmonic generation in periodically poled lithium tantalate

We describe electric-field poling of fine-pitch ferroelectric domain gratings in lithium tantalate and characterization of nonlinear-optical properties by single-pass quasi-phase-matched second-harmonic generation (QPM SHG). With a 7.5-microm-period grating, the observed effective nonlinear coefficient for first-order QPM SHG of 532-nm radiation is 9 pm/V, whereas for a grating with a 2.625-microm period, 2.6 pm/V was observed for second-order QPM SHG of 325-nm radiation. These values are 100% and 55% of the theoretically expected values, respectively. We derive a temperature-dependent Sellmeier equation for lithium tantalate that is valid deeper into the UV than currently available results, based on temperature-tuning experiments at different QPM grating periods combined with refractive-index data in the literature.