Relaxation (physics) | EPFL Graph Search

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(−t/τ) (exponential decay). In simple linear systems Mechanics: Damped unforced oscillator Let the homogeneous differential equation: :m\frac{d^2 y}{d t^2}+\gamma\frac{d y}{d t}+ky=0 model damped unforced oscillations of a weight on a spring. The displacement will then be of the form y(t) = A e^{-t/T} \cos(\mu t - \delta). The constant T (=2m/\gamma) is called the relaxation time of the system and the constant μ is the quasi-frequency. Electronics: RC circuit In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially: : V(t)=V_0 e^{-\frac{t}{RC}} \ , The constant \tau = RC\ is cal

Dynamics of quantum dot lasers

Pablo Moreno

The exceptional performance of self-assembled Quantum Dot (QD) materials renders them extremely appealing for their use as optical communications devices. As lasers, they feature reduced and temperature independent threshold current and proper emission wavelength at the fiber telecommunication windows. These characteristics, together with the low linewidth enhancement factor and broad spectrum, make QD materials extremely attractive for application as light emitters or amplifiers. There exist, nevertheless, several unclear issues which prevent QDs from conquering the new generation of optoelectronic devices. Their differential efficiency is lower than expected. The output power of QD lasers is lower than that of their quantum well counterpart. Still, it is their dynamics which has incited the majority of studies. The modulation bandwidth of these devices seems to be limited by the relaxation of carriers from the upper energetic layers to the low levels within the dot. Besides, the electron-hole interaction is widely unknown, the extent of the electron-hole Coulombic attraction is not yet established. Throughout this thesis I present a theoretical and experimental study of the gain and phase dynamics of quantum dot lasers. I explain the appearance of different decay times observed in pump and probe experiments in QD amplifiers as a result of the different electron and hole relaxation times, by means of an electron-hole rate-equation model. The ultrafast hole relaxation first leads to an ultrafast recovery of the gain, which is then followed by electron relaxation and, on the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. Our results corroborate with spectral measurements of the dephasing and gain in QD amplifiers. Additionally, our work is compared with existing pump and probe results. Exploiting the capacity of QD lasers to emit at two different wavelengths corresponding to the ground state (GS) and excited state (ES), I present a theoretical study of the QD dynamics, based on a linearization of the QD rate-equations. The results predict the existence of single oscillation frequency of GS and ES, meaning that both states are highly coupled. In order to verify our theory, we perform two kinds of experiments. By modulating these lasers at high frequency, we measure separately the dynamics of GS and ES. However, in contradiction to our theory, two different modulation frequencies are found. Additional temporally-resolved measurements of the laser dynamics reveal a surprising effect. By injecting a sub-bandgap pump in an InAs/InGaAs QD laser, the emitted photons are depleted. Through additional transmission and photocurrent measurements, we relate this observation with carrier photoexcitation, which was so far only theoretically addressed. The role of carrier photoexcitation in our experimental laser dynamics is further supported by a rate-equation model. Impelled by this finding, we study the effect of carrier photoexcitation in the static and dynamic characteristics. We find that carrier photoexcitation reduces the efficiency of QD lasers, which is one of the major QD handicaps, and depletes the GS lasing after the ES threshold, as observed experimentally. Moreover, by adding carrier photoexcitation to our linearization of the rate-equations, we find that the theory predicts the appearance of two lasing resonance frequencies, in agreement with our previous experimental results. Additionally, we deal with the improvement of carrier relaxation. In tunnel injection devices, carriers are given an additional path towards the ground state of the dot by growing a quantum well layer close to the QD active plane. Through the quantum-mechanical tunneling effect, carriers relax from the nearby quantum well layer to the QDs, which speeds up relaxation. We aim at the increase of the modulation bandwidth while keeping the good performances quantum dot lasers have exhibited, such as low and temperature insensitive threshold current and proper emission wavelength. In the final part of this work, we present dynamical measurements of 1.5 µm InAs/InP tunnel injection and non-tunnel injection QD lasers, which display remarkable static characteristics. After proving with static measurements that tunnel injection is actually taking place in these structures, we show several dynamic measurements. Pump and probe measurements on QD devices show that the tunnel injection samples exhibit a slightly faster relaxation time than the non-tunnel injection samples used as reference, meaning that relaxation time is improved with tunnel injection. However, by probing the device with an ultrafast pump no improvement of the dynamic characteristics is observed. These results confirm that the laser dynamic properties of InP QD lasers, both standard and tunnel-injection designs, are actually not limited by relaxation of carriers. We point towards the size distribution of these quantum dash-like structures as the limiting factor of the modulation frequency.

EPFL2008

Magnetization Reversal Dynamics in Ferromagnetic Semiconductors

Liza Herrera Diez

This thesis is dedicated to the study of the magnetization reversal dynamics in compressively strained (Ga,Mn)As and differently functionalized (Ga,Mn)As materials. In the first part the domain wall dynamics of pure (Ga,Mn)As/GaAs materials is in the focus. The changes in the magnetic anisotropy energy landscape occurring as a function of temperature are monitored in detail by different experimental techniques. These measurements provide the necessary information for the identification of the temperature ranges corresponding to different magnetic anisotropy regimes. Knowing the biaxial anisotropy and uniaxial anisotropy dominated regimes the dependence of the domain wall dynamics on the magnetic anisotropy landscape is studied. Critical changes in domain wall alignment observed by Kerr microscopy are found upon changing from biaxial to uniaxial anisotropy. These changes could be partially attributed to the tendency of the system to minimize magnetic free poles at the domain boundaries. To complement the space resolved studies of the magnetization reversal, magnetic time relaxation effects are addressed. In particular the magnetic aftereffect in (Ga,Mn)As/GaAs is studied in detail. The irreversible aftereffect is evidenced as a critical reduction of the domain wall velocity with time under a constant applied magnetic field below coercivity. This time relaxation is tracked as a function of both time and magnetic field. The measurements show that the overall relaxation is composed of two relaxation processes acting in parallel at short and long time scales. By fitting these experimental results the values of the relaxation times of both relaxation processes were obtained. By this modeling also the values of the activation volumes for two independent (Ga,Mn)As materials are estimated. In the second part of this thesis the possibilities of tuning the electrical and magnetic properties of (Ga,Mn)As by volume and surface treatments are explored. As for the volume modification, oxygen species were incorporated into the (Ga,Mn)As films by means of exposure to an oxygen plasma. The incorporation of oxygen was evidenced by depth profile X-ray photoelectron spectroscopy. This treatment is found to weaken the ferromagnetism, visible as a reduction in the Curie temperature, and to hinder the electrical transport evidenced as an increase in the electrical resistance. In agreement with theories accounting for the hole mediated ferromagnetism in (Ga,Mn)As this behaviour was related to a hole compensation mechanism arising from the presence of oxygen impurities sitting in interstitial positions of the (Ga,Mn)As Zinc blende structure. In the last part, the modulation of the electrical and magnetic properties via surface functionalization is presented. The effects produced by the adsorption of molecular species on (Ga,Mn)As are similar to those found after oxygenation, namely a strong weakening of the magnetic properties and an increase in the values of the electrical resistance. However, in this case the distinctive feature is provided by the possibility of regulating the hole quenching effect by exploiting the additional degree of freedom provided by the chemical properties of the adsorbates. The adsorbate chosen for these experiments are dye molecules that absorb light in the visible range, in this way allowing for a light modulated interaction with the substrate. Using this concept is was possible to observe a modulation of the ferromagnetic transition temperature, the coercive field and the electrical resistance upon illumination. These observations provide a proof of principle for the realization of photo-sensitized (Ga,Mn)As devices where the magnetic properties can be regulated by light.

EPFL2011

A magnetic tunnel to shelter hyperpolarized fluids

Geoffrey Bodenhausen, Aurélien Bornet, Sami Jannin, Pascal Miéville, Jonas Milani, Roger Mottier, Basile Vuichoud

To shield solutions carrying hyperpolarized nuclear magnetization from rapid relaxation during transfer through low fields, the transfer duct can be threaded through an array of permanent magnets. The advantages are illustrated for solutions containing hyperpolarized H-1 and C-13 nuclei in a variety of molecules. (C) 2015 Author(s).

American Institute of Physics2015