Condensed vortex ground states of rotating Bose-Einstein condensate in harmonic atomic trap

We study a system of $N$ Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular momentum and its collective component, we develop an algebraic approach to derive exact wave functions and energies of these ground states. We describe a broad class of the interactions for which these results are valid. This universality class is defined by simple integral condition on the potential. Most of the potentials of practical interest which have pronounced repulsive component belong to this universality class.Comment: 34 pages, 10 ps figures, minor revisions, to be publ. in Ann. Phy

Deposition and characterization of PECVD phosphorus doped silicon oxynitride layers for integrated optics applications

Phosphorus-doped silicon oxynitride layers have been deposited by a Plasma Enhanced Chemical Vapor Deposition process from $N_20$, 2% $SiH_4/N_2$ and 5% $PH_3/Ar$ gaseous mixtures. The $PH_3/Ar$ flow rate was varied to investigate the effect of the dopant to the layer properties. As deposited and annealed (600, 800, 900 and 1000 °C) layers were characterized by Fourier transform infrared spectroscopy, Rutherford backscattering spectroscopy and spectroscopic ellipsometry. In this way the refractive index could be determined as well as the amount of hydrogen that is responsible for enhanced absorption in the 3rd telecommunication window around 1550 nm. The N-H bonds concentration was found to decrease with the phosphorus concentration. Furthermore the bonded hydrogen in the entire P-doped layers have been eliminated after annealing at 1000 °C, while undoped SiON layers require annealing at 1150 °C

Reduction of hydrogen-induced optical losses of plasma-enhanced chemical vapor deposition silicon oxynitride by phosphorus doping and heat treatment

Plasma enhanced chemical vapor deposition phosphoros-doped silicon oxynitride (SiON) layers with a refractive index of 1.505 were deposited from $N_{2}O$, 2% $SiH_{4}/N_{2}$, and 5% $PH_{3}/Ar$ gaseous mixtures. The $PH_{3}/Ar$ flow rate was varied to investigate the effect of the dopant to the layer properties. We studied the compositions and the chemical environment of phosphorus, silicon, oxygen, nitrogen and hydrogen in these layers by using x-ray photoelectron spectroscopy and Fourier transform infrared spectroscopy. The number of N-H and O-H bonds, which are responsible for optical losses around 1.55 and 1.3 μm, decreases in the as-deposited layers with increasing phosphorus concentration. Furthermore, the bonded hyrogen in all P-doped layers has been eliminated after annealing at a temperature significantly lower than required for undoped silicon oxynitride layers, that is so to say 1000°C instead of 1150°C. The resulting optical loss in the entire third telecommunication window was well below 0.2dB/cm, making P-doped SiON an attractive material for demanding integrated optics applications

Influence of phosphorus doping on hydrogen content and optical losses in PECVD silicon oxynitride

PECVD Phosphorus-doped silicon oxynitride layers (n=1.5) were deposited from N2O, 2%SiH4/N2, NH3 and 5%PH3/Ar gaseous mixtures. Chemical bonds were determined by Fourier transform infrared spectroscopy. N–H bond concentration of the layers decreased from 3.29×10-21 to 0.45×10-21 cm−3, as the 5%PH3/Ar flow rate increased from 0 to 60 sccm. A simultaneous decrease of O–H related bonds was also observed within the same phosphine flow range. The optical loss of slab-type waveguides at λ=1505 nm was found to decrease from 14.1 to 6.2 dB/cm as the 5%PH3/Ar flow rate increased from 0 to 30 sccm, respectively. Moreover, the optical loss values around λ=1400 and 1550 nm were found to decrease from 4.7 to below 0.2 dB/cm and from 1.8 to 1.0 dB/cm respectively. These preliminary results are very promising for applications in low-loss integrated optical devices

Silicon oxynitride based photonics

Silicon oxynitride is a very attractive material for integrated optics. Besides possessing excellent optical properties it can be deposited with refractive indices varying over a wide range by tuning the material composition. In this contribution we will summarize the key properties of this material class and discuss several application examples. Preliminary results on novel processes, which will lead to largely reduced hydrogen incorporation and enable reflow of SiON material, are being presented