We theoretically compute the coupling constant C between two emission modes of an extended cavity laser with a multiple quantum-well active layer. We use an optimized Monte Carlo model based on the Markov chain that describes the elementary events of carriers and photons over time. This model allows us to evaluate the influence on C of the transition from a class A laser to a class B laser and illustrates that the best stability of dual-mode lasers is obtained with the former. In addition, an extension of the model makes it possible to evaluate the influence of different mode profiles in the cavity as well as the spatial diffusion of the carriers and/or the inhomogeneity of the temperature. These results are in very good agreement with previous experimental results, showing the independence of C with respect to the beating frequency and its evolution versus the spatial mode splitting in the gain medium.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Tribute to Jean-Yves Jaffray July 22, 1939 February 26, 2009 Michèle Cohen, Alain Chateauneuf, Eric Danan, Thibault Gajdos, Raphaël Giraud, Meglena Jeleva, Fabrice Philippe, Jean-Marc Tallon, Jean-Christophe Vergnaud

Nous presentons un modele traitant du passage au seuil des nanolasers grâce a une chaˆinechaˆine de Markov simulee par Monte-Carlo. La quantification des variables traitees dans le modele permet de mettre enevidenceen´enevidence les allumages et extinctions autour du seuil laser. La coexistence d'un regime pulse avec un regime continu bruite lors du passage au seuil montre que celui-ci ne peut plusetreplusˆplusetre defini avec precision pour les nanolasers

A Markov model of semiconductor nanolaser is constructed in order to describe finely the effects of quantum fluctuations in the dynamics of the laser, in particular by considering the transition to lasing. Nanolasers are expected to contain only a small number of emitters, whose semiconductor bands are simulated using true carrier energy states. The model takes into account carrier-carrier interactions in the conduction and valence bands, but the result is a huge Markov chain that is often too demanding for direct Monte-Carlo simulation. We introduce here a technique to split the whole chain into two subchains, one referring to thermalization events within the bands and the other to laser photonic events of interest. The model is applied to the analysis of laser transition and enlightens the coexistence of a pulse regime triggered by the quantum nature of the photon with the birth of the known coherent cw regime. This conclusion is highlighted by calculated time traces. We show that on the ultrasmall scale of nanolasers, we are unable to define perfectly the threshold.

Monte Carlo markovian models of a dual-mode semiconductor laser with quantum well (QW) or quantum dot (QD) active regions are proposed. Accounting for carriers and photons as particles that may exchange energy in the course of time allows an ab initio description of laser dynamics such as the mode competition and intrinsic laser noise. We used these models to evaluate the stability of the dual-mode regime when laser characteristics are varied: mode gains and losses, non-radiative recombination rates, intraband relaxation time, capture time in QD, transfer of excitation between QD via the wetting layer... As a major result, a possible steady-sate dual-mode regime is predicted for specially designed QD semiconductor lasers thereby acting as a CW microwave or terahertz-beating source whereas it does not occur for QW lasers.

A $(p,q)$-ary chain is a special type of chain partition of integers with parts of the form $p^aq^b$ for some fixed integers $p$ and $q$. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound $m$. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of $m$, asymptotically independent of $\max(p,q)$, and we provide an efficient algorithm to compute it.

Monte Carlo markovian models of a dual-mode semiconductor laser with quantum well (QW) or quantum dot (QD) active regions are proposed. Accounting for carriers and photons as particles that may exchange energy in the course of time allows an ab initio description of laser dynamics such as the mode competition and intrinsic laser noise. We used these models to evaluate the stability of the dual-mode regime when laser characteristics are varied: mode gains and losses, non-radiative recombination rates, intraband relaxation time, capture time in QD, transfer of excitation between QD via the wetting layer... As a major result, a possible steady-state dual-mode regime is predicted for specially designed QD semiconductor lasers thereby acting as a CW microwave or terahertz-beating source whereas it does not occur for QW lasers.

We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion, aside from the law of energy conservation. Only a single corpuscle in contact with a heat bath submitted to a z and t-invariant force is considered. Most of the end results are known but the method appears to be novel. The mathematics being elementary, the present paper should facilitate the understanding of the ideal gas law and of classical thermodynamics even though not-usually-taught concepts are being introduced.

This paper describes the modeling of quantum-dot lasers with the aim of assessing the conditions for stable cw dual-mode operation when the mode separation lies in the THz range. Several possible models suited for InAs quantum dots in InP barriers are analytically evaluated, in particular quantum dots electrically coupled through a direct exchange of excitation by the wetting layer or quantum dots optically coupled through the homogeneous broadening of their optical gain. A stable dual-mode regime is shown possible in all cases when quantum dots are used as active layer whereas a gain medium of quantum well or bulk type inevitably leads to bistable behavior. The choice of a quantum-dot gain medium perfectly matched the production of dual-mode lasers devoted to THz generation by photomixing.

The ideal-gas barometric and pressure laws are derived from the Democritian concept of independent corpuscles moving in vacuum, plus a principle of simplicity, namely that these laws are independent of the kinetic part of the Hamiltonian. A single corpuscle in contact with a heat bath in a cylinder and submitted to a constant force (weight) is considered. The paper importantly supplements a previously published paper: First, the stability of ideal gases is established. Second, we show that when walls separate the cylinder into parts and are later removed, the entropy is unaffected. We obtain full agreement with Landsberg’s and others’ (1994) classical thermodynamic result for the entropy of a column of gas submitted to gravity.

The present work is a translation from french to english of our previous \g{D\'emocrite et la puissance motrice du feu}, amended on a number of respects. It is mainly of historical and pedagogical interest. We suggest that the concepts introduced in the ancien Greece by Anaximander (flat earth) and Democritus (corpuscles moving in vacuum) allow us to obtain through qualitative observations and plausible generalizations the maximum efficiency and work of heat engines, results that were firmly established around 1824 by Carnot. A prologue introduces the subject. We next present the concept of thermal equilibrium and consider a model consisting of two reservoirs located at different altitudes, each with $g$ sites. Each site may contain a specified number of corpuscles. One particular site plays the role of \g{working agent}. We subsequently consider an alternative model consisting of independent corpuscles submitted to gravity and in contact with heat baths. Only average quantities are considered, leaving out fluctuations and questions of stability.

We present the design and the fabrication of a dual-wavelength micro-photonic resonator combining a photonic crystal membrane (PCM) and a vertical Fabry Perot (FP) cavity where the former is embedded in the latter. A strong optical coupling between a PCM Gamma-point Bloch mode and a FP mode at the same frequency can be used to provide a dual-wavelength device with a frequency difference which is analysed in terms of modes overlapping. We propose and demonstrate a process flow that can be used to provide such a device. Optical reflectivity characterisation is presented for a monolithic device and photoluminescence dual-wavelength spontaneous emission is demonstrated in an extended vertical cavity. Finally the dual-mode laser emission stability is examined with numerical Monte Carlo simulation.

The air density on earth decays as a function of altitude $z$ approximately according to an $\exp(-w\,z/\theta)$-law, where $w$ denotes the weight of a nitrogen molecule and $\theta=\kB T$ where $k_B$ is a constant and $T$ the thermodynamic temperature. To derive this law one usually invokes the Boltzmann factor, itself derived from statistical considerations. We show that this (barometric) law may be derived solely from the democritian concept of corpuscles moving in vacuum. We employ a principle of simplicity, namely that this law is \emph{independent} of the law of corpuscle motion. This view-point puts aside restrictive assumptions that are source of confusion. Similar observations apply to the ideal-gas law. In the absence of gravity, when a cylinder terminated by a piston, containing a single corpuscle and with height $h$ has temperature $\theta$, the average force that the corpuscle exerts on the piston is: $\ave{F}=\theta/h$. This law is valid at any temperature, except at very low temperatures when quantum effects are significant and at very high temperatures because the corpuscle may then split into smaller parts. It is usually derived under the assumption that the temperature is proportional to the corpuscle kinetic energy, or else, from a form of the quantum theory. In contradistinction, we show that it follows solely from the postulate this it is independent of the law of corpuscle motion. On the physical side we employ only the concept of potential energy. A consistent picture is offered leading to the barometric law when $w\,h\gg\theta$, and to the usual ideal-gas law when $w\,h\ll\theta$. The mathematics is elementary. The present paper should accordingly facilitate the understanding of the physical meaning of the barometric and ideal-gas laws.

The present work is a translation from french to english of our previous Démocrite et la puissance motrice du feu, amended on a number of respects. It is mainly of historical and pedagogical interest. We suggest that the concepts introduced in the ancien Greece by Anaximander (flat earth) and Democritus (corpuscles moving in vacuum) allow us to obtain through qualitative observations and plausible generalizations the maximum efficiency and work of heat engines, results that were firmly established around 1824 by Carnot. A prologue introduces the subject. We next present the concept of thermal equilibrium and consider a model consisting of two reservoirs located at different altitudes, each with g sites. Each site may contain a specified number of corpuscles. One particular site plays the role of working agent. We subsequently consider an alternative model consisting of independent corpuscles submitted to gravity and in contact with heat baths. Only average quantities are considered, leaving out fluctuations and questions of stability.

It is very rare to find in a single person both the qualities of a remarkable scientific mind and of a wonderful human being. With this tribute to Jean-Yves Jaffray, we hope to convince the reader of his outstanding creativity and vision, of the coherence of his work, and of its relevance for some topics in decision theory that are currently under lively debate. As a scientist, Jean-Yves Jaffray can be characterized by one main insight and one main concern. His main insight is that a sound decision theory must explicitly use all the information available to the decision maker. This information about events must further be treated in a strictly objective manner. In the models he proposed as a result, objective information can be disentangled from subjective attitudes with respect to this information. For that purpose, before asking how to represent preferences, one must wonder how to treat and represent the given information. Jean-Yves’ main concern in designing his models is that they must be tractable, implementable and testable. This leads him to emphasize the simplicity of the models he puts forward, including the way the arrival of new information is modeled, and to develop experiments to test them. This adherence to objectivity together with his concern for implementable models fits well with Jean-Yves’ applied work in statistics and computer science that we will not review here. After some words on his early contributions, we will discuss the way he addressed different questions linked to Decision Theory : How to describe information (or lack of information) on events? How to model decisions in this framework? How to evaluate decisions? How to update in the presence of new

We consider a special type of integer partitions in which the parts of the form p^aq^b, for some relatively prime integers p and q, are restricted by divisibility conditions. We investigate the problems of generating and encoding those partitions and give some estimates for several partition functions.

We discuss a model consisting of two reservoirs, each with N possible ball locations, at heights E(h) and E(l)< E(h) in a gravitational field. The two reservoirs contain n(h) and n(l) weight 1 balls. Empty locations are treated as weight 0 balls. The reservoirs are shaken so that all possible ball configurations are equally likely to occur. A cycle consists of exchanging a ball randomly chosen from the higher reservoir and a ball randomly chosen from the lower reservoir. We relate this system to a heat engine and show that the efficiency, which is defined as the ratio of the average work produced to the average energy lost by the higher reservoir, is 1-E(l)/E(h). When n(l) is comparable to n(h), the efficiency is found to coincide with the maximum efficiency 1-T(l)/T(h), where the temperatures T(l) and T(h) are defined from a simple expression for the entropy. We also discuss the evaluation of fluctuations and the history of the Carnot discovery.