Equilibrium and eigenfunctions estimates in the semi-classical regime

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.Comment: 13 pages, 1 figure, perhaps to be revise

Three-dimensional carrier-dynamics simulation of terahertz emission from photoconductive switches

A semi-classical Monte Carlo model for studying three-dimensional carrier dynamics in photoconductive switches is presented. The model was used to simulate the process of photoexcitation in GaAs-based photoconductive antennas illuminated with pulses typical of mode-locked Ti:Sapphire lasers. We analyzed the power and frequency bandwidth of THz radiation emitted from these devices as a function of bias voltage, pump pulse duration and pump pulse location. We show that the mechanisms limiting the THz power emitted from photoconductive switches fall into two regimes: when illuminated with short duration (<40 fs) laser pulses the energy distribution of the Gaussian pulses constrains the emitted power, while for long (>40 fs) pulses, screening is the primary power-limiting mechanism. A discussion of the dynamics of bias field screening in the gap region is presented. The emitted terahertz power was found to be enhanced when the exciting laser pulse was in close proximity to the anode of the photoconductive emitter, in agreement with experimental results. We show that this enhancement arises from the electric field distribution within the emitter combined with a difference in the mobilities of electrons and holes.Comment: 7 pages, 7 figure

Spectral fluctuations of Schr\"odinger operators generated by critical points of the potential

Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.\medskip keywords : Semi-classical analysis; Schr\"odinger operators; Equilibriums in classical mechanics.Comment: 18 pages, Final versio

Carrier dynamics in ion-implanted GaAs studied by simulation and observation of terahertz emission

We have studied terahertz (THz) emission from arsenic-ion implanted GaAs both experimentally and using a three-dimensional carrier dynamics simulation. A uniform density of vacancies was formed over the optical absorption depth of bulk GaAs samples by performing multi-energy implantations of arsenic ions (1 and 2.4MeV) and subsequent thermal annealing. In a series of THz emission experiments the frequency of peak THz power was found to increase significantly from 1.4 to 2.2THz when the ion implantation dose was increased from 10^13 to 10^16 cm-3. We used a semi-classical Monte-Carlo simulation of ultra-fast carrier dynamics to reproduce and explain these results. The effect of the ion-induced damage was included in the simulation by considering carrier scattering at neutral and charged impurities, as well as carrier trapping at defect sites. Higher vacancy concentrations and shorter carrier trapping times both contributed to shorter simulated THz pulses, the latter being more important over experimentally realistic parameter ranges.Comment: 6 pages, 7 figure

Simulation and optimisation of terahertz emission from InGaAs and InP photoconductive switches

We simulate the terahertz emission from laterally-biased InGaAs and InP using a three-dimensional carrier dynamics model in order to optimise the semiconductor material. Incident pump-pulse parameters of current Ti:Sapphire and Er:fibre lasers are chosen, and the simulation models the semiconductor's bandstructure using parabolic Gamma, L and X valleys, and heavy holes. The emitted terahertz radiation is propagated within the semiconductor and into free space using a model based on the Drude-Lorentz dielectric function. As the InGaAs alloy approaches InAs an increase in the emitted power is observed, and this is attributed to a greater electron mobility. Additionally, low-temperature grown and ion-implanted InGaAs are modelled using a finite carrier trapping time. At sub-picosecond trapping times the terahertz bandwidth is found to increase significantly at the cost of a reduced emission power.Comment: 9 pages, 7 figure

Charge trapping in polymer transistors probed by terahertz spectroscopy and scanning probe potentiometry

Terahertz time-domain spectroscopy and scanning probe potentiometry were used to investigate charge trapping in polymer field-effect transistors fabricated on a silicon gate. The hole density in the transistor channel was determined from the reduction in the transmitted terahertz radiation under an applied gate voltage. Prolonged device operation creates an exponential decay in the differential terahertz transmission, compatible with an increase in the density of trapped holes in the polymer channel. Taken in combination with scanning probe potentionmetry measurements, these results indicate that device degradation is largely a consequence of hole trapping, rather than of changes to the mobility of free holes in the polymer.Comment: 4 pages, 3 figure

Local Swift-BAT active galactic nuclei prefer circumnuclear star formation

We use Herschel data to analyze the size of the far-infrared 70micron emission for z<0.06 local samples of 277 hosts of Swift-BAT selected active galactic nuclei (AGN), and 515 comparison galaxies that are not detected by BAT. For modest far-infrared luminosities 8.5<log(LFIR)<10.5, we find large scatter of half light radii Re70 for both populations, but a typical Re70 <~ 1 kpc for the BAT hosts that is only half that of comparison galaxies of same far-infrared luminosity. The result mostly reflects a more compact distribution of star formation (and hence gas) in the AGN hosts, but compact AGN heated dust may contribute in some extremely AGN-dominated systems. Our findings are in support of an AGN-host coevolution where accretion onto the central black hole and star formation are fed from the same gas reservoir, with more efficient black hole feeding if that reservoir is more concentrated. The significant scatter in the far-infrared sizes emphasizes that we are mostly probing spatial scales much larger than those of actual accretion, and that rapid accretion variations can smear the distinction between the AGN and comparison categories. Large samples are hence needed to detect structural differences that favour feeding of the black hole. No size difference AGN host vs. comparison galaxies is observed at higher far-infrared luminosities log(LFIR)>10.5 (star formation rates >~ 6 Msun/yr), possibly because these are typically reached in more compact regions in the first place.Comment: 7 pages, 3 figures, accepted for publication in Astronomy & Astrophysic

Polarisation-sensitive terahertz detection by multicontact photoconductive receivers

We have developed a terahertz radiation detector that measures both the amplitude and polarization of the electric field as a function of time. The device is a three-contact photoconductive receiver designed so that two orthogonal electric-field components of an arbitrary polarized electromagnetic wave may be detected simultaneously. The detector was fabricated on Fe+ ion-implanted InP. Polarization-sensitive detection is demonstrated with an extinction ratio better than 100:1. This type of device will have immediate application in studies of birefringent and optically active materials in the far-infrared region of the spectrum.Comment: 3 pages, 3 figure