Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit

Despite the enormous technological interest in micro and nanolasers, surprisingly, no class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In class-B lasers $-$applicable for most solid-state lasers at room temperature$-$, the macroscopic polarization decay rate is larger than the cavity damping rate which, in turn, exceeds the upper level population decay rate. Here we carry out a density-matrix theoretical approach for generic class-B lasers, and provide closed equations for the photonic and atomic reduced density matrix in the Fock basis of photons. Such a relatively simple model can be numerically integrated in a straightforward way, and exhibits all the expected phenomena, from one-atom photon antibunching, to the well-known S-shaped input-output laser emission and super-Poissonian autocorrelation for many atoms ($1\leq g^{(2)}(0)\leq 2$), and from few photons (large spontaneous emission factors, $\beta\sim1$) to the thermodynamic limit ($N\gg1$ and $\beta\sim 0$). Based on the analysis of $g^{(2)}(\tau)$, we conclude that super-Poissonian fluctuations are clearly related to relaxation oscillations in the photon number. We predict a strong damping of relaxation oscillations with an atom number as small as $N\sim 10$. This model enables the study of few-photon bifurcations and non-classical photon correlations in class-B laser devices, also leveraging quantum descriptions of coherently coupled nanolaser arrays.Comment: 23 pages, 6 figure

Binary image classification using collective optical modes of an array of nanolasers

Recent advancements in nanolaser design and manufacturing open up unprecedented perspectives in terms of high integration densities and ultra-low power consumption, making these devices ideal for high-performance optical computing systems. In this work, we exploit the symmetry properties of the collective modes of a nanolaser array for a simple binary classification task of small digit images. The implementation is based on a 8 × 8 nanolaser array and relies on the activation of a collective optical mode of the array—the so-called “zero-mode”—under spatially modulated pump patterns.This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay, Reference No. ANR-10-LABX-0035) and by Grant No. ANR UNIQ DS078. G.T. and C.M. are supported, in part, by Ministerio de Ciencia, Innovación y Universidades (Grant No. PID2021-123994NA-C22); C.M. also acknowledges funding from Institució Catalana de Recerca i Estudis Avançats (Academia). K.J. acknowledges support from the China Scholarship Council (Grant No. 202006970015).Peer ReviewedPostprint (published version

Improving image contrast in fluorescence microscopy with nanostructured substrates

Metallic and dielectric nanostructures can show sharp contrastedresonances, sensitive to the environment, and high field enhancement insub-wavelength volumes. For this reason, these structures are commonlyused as molecular sensors. Only few works have focused on theirapplication in optical microscopy, in particular in superresolution. In thiswork we have designed, fabricated and optically tested a nanostructuredTiO2 substrate, fabricated by direct embossing of TiO2 derived film, as asubstrate for fluorescence microscopy. Moreover, using numericalsimulations, we have compared the signal to background noise with respectto other metallo-dielectric structures. We show that the TiO2 structure is agood candidate for reducing the thickness of the fluorescence excitationdown to ~100 nm. Therefore, this substrate can be used to obtain TotalInternal Reflection (TIRF) axial resolution without a TIRF-Microscopysystem.Fil: Brunstein, Maia. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; FranciaFil: Cattoni, Andrea. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; FranciaFil: Estrada, Laura Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Yacomotti, Alejandro M.. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; Franci

Experimental study of speckle patterns generated by low-coherence semiconductor laser light

Speckle is a wave interference phenomenon that has been studied in various fields, including optics, hydrodynamics, and acoustics. Speckle patterns contain spectral information of the interfering waves and of the scattering medium that generates the pattern. Here, we study experimentally the speckle patterns generated by the light emitted by two types of semiconductor lasers: conventional laser diodes, where we induce low-coherence emission by optical feedback or by pump current modulation, and coupled nanolasers. In both cases, we analyze the intensity statistics of the respective speckle patterns to inspect the degree of coherence of the light. We show that the speckle analysis provides a non-spectral way to assess the coherence of semiconductor laser light.Postprint (published version

Angular emission properties of a layer of rare-earth based nanophosphors embedded in one-dimensional photonic crystal coatings

The angular properties of light emitted from rare-earth based nanophosphors embedded in optical resonators built in one-dimensional photonic crystal coatings are herein investigated. Strong directional dependence of the photoluminescence spectra is found. Abrupt angular variations of the enhancement caused by the photonic structure and the extraction power are observed, in good agreement with calculated polar emission patterns. Our results confirm that the optical cavity favors the extraction of different wavelengths at different angles and that integration of nanophosphors within photonic crystals provides control over the directional emission properties that could be put into practice in phosphorescent displays.Ministerio de Ciencia e Innovación MAT2008- 02166, CSD2007-00007Junta de Andalucía FQM3579, FQM524

Tracking exceptional points above laser threshold

Recent studies on non-Hermitian optical systems having exceptional points (EPs) have revealed a host of unique characteristics associated with these singularities, including unidirectional invisibility, chiral mode switching and laser self-termination, to mention just a few examples. The vast majority of these works focused either on passive systems or active structures where the EPs were accessed below the lasing threshold, i.e. when the system description is inherently linear. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed and tracked above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning will impede the formation of an EP, here we demonstrate that this same detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the nonlinear EP in the lasing regime. Furthermore, unlike linear non-Hermitian systems, we find that the spectral location of EPs above laser threshold varies as a function of total pump power and can therefore be continuously tracked. Our work is a first step towards the realization of lasing EPs in more complex laser geometries, and enabling the enhancement of photonic local density of states through non-Hermitian symmetries combined with nonlinear interactions in coupled laser arrays