By means of the Keldysh-Green-function method, the electrochemicalpotential variations across a constriction are analyzed. We discuss specifically the case of a one-dimensional chain joining two Bethe lattices of coordination four. Our results show that the total conductance of the system and its local chemical potential variations depend dramatically on the interference between the chain transmittivity and the reflectivity at the reservoir-chain contact. We show a case in which, with a transmittivity less than one, a zero chemical-potential drop is found along the inner linear chain.With the advent of mesoscopic physics, ' a lot of in-

In this work, continuous-wave broadly tunable simultaneous generation of red ͑650-690 nm͒, green ͑520-575 nm͒, and blue ͑425-495 nm͒ light in aperiodically poled Zn-diffused LiNbO 3 :Er 3ϩ /Yb 3ϩ channel waveguides is reported after Ti:sapphire excitation in the 850-990 nm range. The red and green emissions arise from energy transfer and upconversion mechanisms between Yb 3ϩ and Er 3ϩ ions, while the blue light with a maximum efficiency of 0.04% W Ϫ1 cm Ϫ1 is produced by quasi-phase matching processes. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1617367͔ Lithium niobate (LiNbO 3 ) compares favorably with other ferroelectric crystals for nonlinear optical applications not only because of its large nonlinear coefficients but also because of the possibility of modulating them, offering the option of nonlinear frequency conversion via quasi-phase matching ͑QPM͒ processes. Several nonlinear devices based on periodic ͑PPLN͒ or aperiodically ͑APPLN͒ poled LiNbO 3 have been reported, including the additional advantage of using waveguiding structures, where high power densities are easily available. [1][2][3][4][5][6][7][8] In this work, nonlinear channel waveguides fabricated by Zn diffusion in Er 3ϩ /Yb 3ϩ codoped APPLN are used to generate simultaneous red, green, and blue ͑RGB͒ light. AP-PLN crystals were grown by the off-centered Czochralski method, along the a axis, with automatic diameter control by a crucible-weighting technique. The initial melts containing congruent LiNbO 3 (͓Li͔/͓Nb͔ϭ0.945) were doped with Er 2 O 3 and Yb 2 O 3 with a purity grade of 99.99%.The growth conditions, pulling and rotation rates and the seed crystal shift, were adjusted appropriately to favor the formation of modulated ferroelectric domain distributions 9 in order to achieve red, green, and blue light under excitation in the 880-1040 nm spectral range (Yb 3ϩ absorption band͒. Using this procedure chirped-period-poled domain structures are obtained. The domain pattern from a y-cut wafer was revealed by etching in a diluted solution of HF:HNO 3 ͑1:2 by volume͒ for 1 h and then checked by conventional optical microscopy. As illustrated in Fig. 1, the wafer exhibits several chirped-period-poled domain structures with periods ranging from 5 to 16 m, being the averaged period of ϳ7 m.The wafer was then polished to optical grade in order to fabricate the channel waveguides by Zn diffusion. 7,10,11 In the present work, the metal diffusion was performed following a two-step procedure ͑exchange and diffusion͒ [12][13][14] which preserves the initial wafer ferroelectric pattern. 15 The exchange process at 550°C for 2 h was performed followed by annealing in open atmosphere at 850°C for 4 h. These conditions produce a 4 m depth Gaussian index profile, with a maximum index change of 0.15% and 0.20% in the extraordinary and ordinary refractive indices, respectively. These waveguides support two modes in the visible range and are single mode at the IR pump wavelengths used in the experiments.The experimental configuration used in the mea...

In this work, laser operation at 1.76 m in Tm 3+ : LiNbO 3 Zn-diffused channel waveguides is reported. The laser emission is single polarized with the electric field parallel to the optic axis ͑ -polarization͒ and operates in continuous-wave regime, at room temperature. The threshold of laser oscillation is in the range of 40 mW, the slope efficiency is around 1%, and both magnitudes are dependent on the channel width, in accordance with the mode overlap between the pump and signal modes within the waveguides. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1887813͔ Tm 3+ -activated materials have been extensively investigated in the last years due to their broad infrared luminescence emissions, from 1400 nm up to 2100 nm ͑associated with 3 H 4 → 3 F 4 and 3 F 4 → 3 H 6 transitions͒, with potential interest in fields, such as S-band optical amplification, surgery, and remote sensing. 1-9 When rare-earth ions are incorporated into LiNbO 3 , it is possible to combine the optical characteristics of the rare-earth ions with the electro-optic, acoustooptic, and nonlinear properties of LiNbO 3 , together with the availability of well-developed techniques to fabricate lowloss channel waveguides. [10][11][12][13][14] Laser action of thulium-doped lithium niobate was first demonstrated in bulk material 1 and then in a guiding configuration using Ti-indiffused channel waveguides. 2 The observed stimulated emission was associated with the 3 F 4 → 3 H 6 transition of Tm 3+ ions, occurring at 1 = 1.85 m in bulk, and simultaneously at 1 = 1.85 m and 2 = 1.81 m in the waveguide configuration. These two emissions correspond to Tm 3+ transitions which are predominantly -polarized. 1,15 In this work, we report -polarized laser oscillation of Tm 3+ ions, in Zn-diffused channel waveguides, operating in a slightly shorter-wavelength region, 1.76 m, also corresponding to the 3 F 4 → 3 H 6 Tm 3+ transition. Laser oscillation is sustained in continuous-wave regime, at room temperature, without signs of photorefractive damage even in this -polarized laser emission ͑electric field parallel to the optic axis͒, in accordance with previous reports of the high resistance to optical damage of Zn-diffused waveguides. 12,13 Tm 3+ -doped LiNbO 3 crystal has been grown by the Czochralski method. The content of Tm 3+ in the initial melt was 2.0 mol %. The boule was oriented by Laue x-ray diffraction and then, slices perpendicularly to the c axis ͑z-cut samples͒ were cut and polished to optical quality. Zn diffusion has been used to fabricate the optical waveguides. Using this method, channel waveguides-having optical losses in the range of 0.3 dB/ cm ͑at = 1.55 m͒-are fabricated. 16,17 In the present work, the ion exchange was carried out at 550°C for 2 h, and then the sample was annealed at 850°C for 4 h. During the ion exchange step, both sample surfaces are immersed in the Zn atmosphere and, therefore, a planar waveguide is simultaneously formed at the wafer surface opposite to the channel waveguides. M-line spectroscopic measurements per...

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The electronic transport properties of a linear chain have k e n analysed. m e chain conductance, the electrochemical potential variations along the chain, and a m e defect scattering effects have been discussed using the non-equilibrium Keldysh formalism. For the elastic regime we show that there is a deep link between the chain mnductance and the elemchemical potential drop along the chain. For the inelastic regime we discuss how the quantum interference associated with the electronic transpon is damped by the inelastic scattering.