Photon statistics of semiconductor microcavity lasers

Room Temperature Lasing from Semiconducting Single-Walled Carbon Nanotubes

Miniaturized near-infrared semiconductor lasers that are able to generate coherent light with low energy consumption have widespread applications in fields such as optical interconnects, neuromorphic computing, and deep-tissue optogenetics. With optical transitions at near-infrared wavelengths, diameter-tunable electronic structures, and superlative optoelectronic properties, semiconducting single-walled carbon nanotubes (SWCNTs) are promising candidates for nanolaser applications. However, despite significant efforts in this direction and recent progress toward enhancing spontaneous emission from SWCNTs through Purcell effects, SWCNT-based excitonic lasers have not yet been demonstrated. Leveraging an optimized cavity-emitter integration scheme enabled by a self-assembly process, here we couple SWCNT emission to the whispering gallery modes supported by polymer microspheres, resulting in room temperature excitonic lasing with an average lasing threshold of 4.5 kW/cm². The high photostability of SWCNTs allows stable lasing for prolonged duration with minimal degradation. This experimental realization of excitonic lasing from SWCNTs, combined with their versatile electronic and optical properties that can be further controlled by chemical modification, offers far-reaching opportunities for tunable near-infrared nanolasers that are applicable for optical signal processing, in vivo biosensing, and optoelectronic devices.

Single- and Twin-Photons Emitted from Fiber-Coupled Quantum Dots in a Distributed Bragg Reflector Cavity

In this work, we develop single-mode fiber devices of an InAs/GaAs quantum dot (QD) by bonding a fiber array with large smooth facet, small core, and small numerical aperture to QDs in a distributed Bragg reflector planar cavity with vertical light extraction that prove mode overlap and efficient output for plug-and-play stable use and extensive study. Modulated Si doping as electron reservoir builds electric field and level tunnel coupling to reduce fine-structure splitting (FSS) and populate dominant XX and higher excitons XX⁺ and XXX. Epoxy package thermal stress induces light hole (lh) with various behaviors related to the donor field: lh h₁ confined with more anisotropy shows an additional X_Z line (its space to the traditional X lines reflects the field intensity) and larger FSS; lh h₂ delocalized to wetting layer shows a fast h₂-h₁ decay; lh h₂ confined shows D_3h symmetric higher excitons with slow h₂-h₁ decay and more confined h₁ to raise h₁-h₁ Coulomb interaction.

Wet-Etched Microlens Array for 200 nm Spatial Isolation of Epitaxial Single QDs and 80 nm Broadband Enhancement of Their Quantum Light Extraction

Uniform arrays of three shapes (gauss, hat, and peak) of GaAs microlenses (MLs) by wet-etching are demonstrated, ∼200 nm spatial isolation of epitaxial single QDs embedded (λ: 890–990 nm) and broadband (Δλ∼80 nm) enhancement of their quantum light extraction are obtained, which is also suitable for telecom-band epitaxial QDs. Combined with the bottom distributed Bragg reflector, the hat-shaped ML forms a cavity and achieves the best enhancement: extraction efficiency of 26%, Purcell factor of 2 and single-photon count rate of 7×106 counts per second at the first lens; while the gauss-shaped ML shows a broader band (e.g., longer λ) enhancement. In the MLs, single QDs with featured exciton emissions are observed, whose time correlations prove single-photon emission with multi-photon probability g(2)(0)=0.02; some QDs show both biexciton XX and exciton X emissions and exhibit a perfect cascade feature. This work could pave a step towards a scalable array of QD single-photon sources and the application of QD photon-pair emission for entanglement experiments.

Thermal, Quantum Antibunching and Lasing Thresholds from Single Emitters to Macroscopic Devices

Starting from a fully quantized Hamiltonian for an ensemble of identical emitters coupled to the modes of an optical cavity, we determine analytically regimes of thermal, collective anti-bunching and laser emission that depend explicitly on the number of emitters. The lasing regime is reached for a number of emitters above a critical number-which depends on the light-matter coupling, detuning, and the dissipation rates-via a universal transition from thermal emission to collective anti-bunching to lasing as the pump increases. Cases where the second order intensity correlation fails to predict laser action are also presented.

Distinguishing intrinsic photon correlations from external noise with frequency-resolved homodyne detection

In this work, we apply homodyne detection to investigate the frequency-resolved photon statistics of a cw light field emitted by a driven-dissipative semiconductor system in real time. We demonstrate that studying the frequency dependence of the photon number noise allows us to distinguish intrinsic noise properties of the emitter from external noise sources such as mechanical noise while maintaining a sub-picosecond temporal resolution. We further show that performing postselection on the recorded data opens up the possibility to study rare events in the dynamics of the emitter. By doing so, we demonstrate that in rare instances, additional external noise may actually result in reduced photon number noise in the emission.

Ten years of spasers and plasmonic nanolasers

Ten years ago, three teams experimentally demonstrated the first spasers, or plasmonic nanolasers, after the spaser concept was first proposed theoretically in 2003. An overview of the significant progress achieved over the last 10 years is presented here, together with the original context of and motivations for this research. After a general introduction, we first summarize the fundamental properties of spasers and discuss the major motivations that led to the first demonstrations of spasers and nanolasers. This is followed by an overview of crucial technological progress, including lasing threshold reduction, dynamic modulation, room-temperature operation, electrical injection, the control and improvement of spasers, the array operation of spasers, and selected applications of single-particle spasers. Research prospects are presented in relation to several directions of development, including further miniaturization, the relationship with Bose-Einstein condensation, novel spaser-based interconnects, and other features of spasers and plasmonic lasers that have yet to be realized or challenges that are still to be overcome.

Non-stationary statistics and formation jitter in transient photon condensation

While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes.

Description of non-equilibrium phase transitions is problematic, due to the absence of suitable free energy landscapes. Here, the authors experimentally show delayed photon condensation and timing jitter in a dye-filled microcavity, modelled by a non-equilibrium extension of the free-energy landscape.

Real time g(2) monitoring with 100 kHz sampling rate

We introduce a technique to determine photon correlations of optical light fields in real time. The method is based on ultrafast phase-randomized homodyne detection and allows us to follow the temporal evolution of the second-order correlation function g⁽²⁾(0) of a light field. We demonstrate the capabilities of our approach by applying it to a laser diode operated in the threshold region. In particular, we are able to monitor the emission dynamics of the diode switching back and forth between lasing and spontaneous emission with a g⁽²⁾(0)-sampling rate of 100 kHz.

Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback

Microlasers are ideal candidates to bring the fascinating variety of nonlinear complex dynamics found in delay-coupled systems to the realm of quantum optics. Particularly attractive is the possibility of tailoring the devices' emission properties via non-invasive delayed optical coupling. However, until now scarce research has been done in this direction. Here, we experimentally and theoretically investigate the effects of delayed optical feedback on the mode-switching dynamics of an electrically driven bimodal quantum-dot micropillar laser, characterizing its impact on the micropillar's output power, optical spectrum and photon statistics. Feedback is found to influence the switching dynamics and its characteristics time scales. In addition, stochastic switching is reduced with the subsequent impact on the microlaser photon statistics. Our results contribute to the comprehension of feedback-induced phenomena in micropillar lasers and pave the way towards the external control and tailoring of the properties of these key systems for the nanophotonics community.

Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source

Two-level emitters are the main building blocks of photonic quantum technologies and are model systems for the exploration of quantum optics in the solid state. Most interesting is the strict resonant excitation of such emitters to control their occupation coherently and to generate close to ideal quantum light, which is of utmost importance for applications in photonic quantum technology. To date, the approaches and experiments in this field have been performed exclusively using bulky lasers, which hinders the application of resonantly driven two-level emitters in compact photonic quantum systems. Here we address this issue and present a concept for a compact resonantly driven single-photon source by performing quantum-optical spectroscopy of a two-level system using a compact high-β microlaser as the excitation source. The two-level system is based on a semiconductor quantum dot (QD), which is excited resonantly by a fiber-coupled electrically driven micropillar laser. We dress the excitonic state of the QD under continuous wave excitation, and trigger the emission of single photons with strong multi-photon suppression (g ( 2 ) ( 0 ) = 0.02 ) and high photon indistinguishability (V = 57±9%) via pulsed resonant excitation at 156 MHz. These results clearly demonstrate the high potential of our resonant excitation scheme, which can pave the way for compact electrically driven quantum light sources with excellent quantum properties to enable the implementation of advanced quantum communication protocols.

A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities

Exploring the limits of spontaneous emission coupling is not only one of the central goals in the development of nanolasers, it is also highly relevant regarding future large-scale photonic integration requiring energy-efficient coherent light sources with a small footprint. Recent studies in this field have triggered a vivid debate on how to prove and interpret lasing in the high-β regime. We investigate close-to-ideal spontaneous emission coupling in GaN nanobeam lasers grown on silicon. Such nanobeam cavities allow for efficient funneling of spontaneous emission from the quantum well gain material into the laser mode. By performing a comprehensive optical and quantum-optical characterization, supported by microscopic modeling of the nanolasers, we identify high-β lasing at room temperature and show a lasing transition in the absence of a threshold nonlinearity at 156 K. This peculiar characteristic is explained in terms of a temperature and excitation power-dependent interplay between zero-dimensional and two-dimensional gain contributions.

Thresholdless quantum dot nanolaser

Thresholdless lasing is an outstanding challenge in laser science and is achievable only in devices having near unity quantum efficiency even when not lasing. Such lasers are expected to exhibit featureless linear light output curves. However, such thresholdless behavior hinders identification of the laser transition, triggering a long-lasting argument on how to identify the lasing. Here, we demonstrate thresholdless lasing in a semiconductor quantum dot nanolaser with a photonic crystal nanocavity. We employ cavity resonant excitation for enabling the thresholdless operation via focused carrier injection into high cavity field regions. Under conventional (above bandgap) excitation, the same nanolaser exhibits a typical thresholded lasing transition, thereby facilitating a systematic comparison between the thresholdless and thresholded laser transitions in the single device. Our approach enables a clear verification of the thresholdless lasing and reveals core elements for its realization using quantum dots, paving the way to the development of ultimately energy-efficient nanolasers.

A few-emitter solid-state multi-exciton laser

We report on non-conventional lasing in a photonic-crystal nanocavity that operates with only four solid-state quantum-dot emitters. In a comparison between microscopic theory and experiment, we demonstrate that irrespective of emitter detuning, lasing with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}^{\mathrm{(2)}}=1$$\end{document}g(2)=1 is facilitated by means of emission from dense-lying multi-exciton states. In the spontaneous-emission regime we find signatures for radiative coupling between the quantum dots. The realization of different multi-exciton states at different excitation powers and the presence of electronic inter-emitter correlations are reflected in a pump-rate dependence of the β-factor.

Emission from quantum-dot high-β microcavities: transition from spontaneous emission to lasing and the effects of superradiant emitter coupling

Measured and calculated results are presented for the emission properties of a new class of emitters operating in the cavity quantum electrodynamics regime. The structures are based on high-finesse GaAs/AlAs micropillar cavities, each with an active medium consisting of a layer of InGaAs quantum dots (QDs) and the distinguishing feature of having a substantial fraction of spontaneous emission channeled into one cavity mode (high β-factor). This paper demonstrates that the usual criterion for lasing with a conventional (low β-factor) cavity, that is, a sharp non-linearity in the input-output curve accompanied by noticeable linewidth narrowing, has to be reinforced by the equal-time second-order photon autocorrelation function to confirm lasing. The paper also shows that the equal-time second-order photon autocorrelation function is useful for recognizing superradiance, a manifestation of the correlations possible in high-β microcavities operating with QDs. In terms of consolidating the collected data and identifying the physics underlying laser action, both theory and experiment suggest a sole dependence on intracavity photon number. Evidence for this assertion comes from all our measured and calculated data on emission coherence and fluctuation, for devices ranging from light-emitting diodes (LEDs) and cavity-enhanced LEDs to lasers, lying on the same two curves: one for linewidth narrowing versus intracavity photon number and the other for g(2)(0) versus intracavity photon number.

Exciton-polariton trapping and potential landscape engineering

Exciton-polaritons in semiconductor microcavities have become a model system for the studies of dynamical Bose-Einstein condensation, macroscopic coherence, many-body effects, nonclassical states of light and matter, and possibly quantum phase transitions in a solid state. These low-mass bosonic quasiparticles can condense at comparatively high temperatures up to 300 K, and preserve the fundamental properties of the condensate, such as coherence in space and time domain, even when they are out of equilibrium with the environment. Although the presence of a confining potential is not strictly necessary in order to observe Bose-Einstein condensation, engineering of the polariton confinement is a key to controlling, shaping, and directing the flow of polaritons. Prototype polariton-based optoelectronic devices rely on ultrafast photon-like velocities and strong nonlinearities exhibited by polaritons, as well as on their tailored confinement. Nanotechnology provides several pathways to achieving polariton confinement, and the specific features and advantages of different methods are discussed in this review. Being hybrid exciton-photon quasiparticles, polaritons can be trapped via their excitonic as well as photonic component, which leads to a wide choice of highly complementary trapping techniques. Here, we highlight the almost free choice of the confinement strengths and trapping geometries that provide powerful means for control and manipulation of the polariton systems both in the semi-classical and quantum regimes. Furthermore, the possibilities to observe effects of the polariton blockade, Mott insulator physics, and population of higher-order energy bands in sophisticated lattice potentials are discussed. Observation of such effects could lead to realization of novel polaritonic non-classical light sources and quantum simulators.

Laser Particle Stimulated Emission Microscopy

We introduce an optical microscopy technique that utilizes micro- or nanolasers embedded in a sample as imaging probes. The narrow spectra and nonlinear power dependence of stimulated emission from the laser particles yield optical sectioning, subdiffraction resolution, and low out-of-focus background. A proof of concept is demonstrated using perovskite nanowires.

Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers

Light is often characterized only by its classical properties, like intensity or coherence. When looking at its quantum properties, described by photon correlations, new information about the state of the matter generating the radiation can be revealed. In particular the difference between independent and entangled emitters, which is at the heart of quantum mechanics, can be made visible in the photon statistics of the emitted light. The well-studied phenomenon of superradiance occurs when quantum–mechanical correlations between the emitters are present. Notwithstanding, superradiance was previously demonstrated only in terms of classical light properties. Here, we provide the missing link between quantum correlations of the active material and photon correlations in the emitted radiation. We use the superradiance of quantum dots in a cavity-quantum electrodynamics laser to show a direct connection between superradiant pulse emission and distinctive changes in the photon correlation function. This directly demonstrates the importance of quantum–mechanical correlations and their transfer between carriers and photons in novel optoelectronic devices.

Classical light sources are characterized by their intensity and coherence, whereas quantum light sources are described by photon correlations. Here, the authors provide a connection between the two for the case of superradiant emission from quantum dots in a nanolaser.

Systematic study of thresholdless oscillation in high-β buried multiple-quantum-well photonic crystal nanocavity lasers

Buried multiple-quantum-well (MQW) 2D photonic crystal cavities (PhC) achieve low non-radiative recombination and high carrier confinement thus making them highly efficient emitters. In this study, we have investigated the lasing characteristics of high-β(spontaneous emission coupling factor) buried MQW photonic crystal nanocavity lasers to clarify the theoretically-predicted thresholdless operation in high-β nanolasers. The strong light and carrier confinement and low non-radiative recombination in our nanolasers have enabled us to clearly demonstrate very smooth lasing transition in terms of the light-in vs light-out curve and cavity linewidth. To clarify the thresholdless lasing behavior, we carried out a lifetime measurement and a photon correlation measurement, which also confirmed the predicted behavior. In addition, we systematically investigated the dependence of β on the detuning frequency, which was in good agreement with a numerical simulation based on the finite-difference time-domain method. This is the first convincing systematic study of nanolasers based on an MQW close to the thresholdless regime.

Monolithically Integrated High-β Nanowire Lasers on Silicon

Reliable technologies for the monolithic integration of lasers onto silicon represent the holy grail for chip-level optical interconnects. In this context, nanowires (NWs) fabricated using III-V semiconductors are of strong interest since they can be grown site-selectively on silicon using conventional epitaxial approaches. Their unique one-dimensional structure and high refractive index naturally facilitate low loss optical waveguiding and optical recirculation in the active NW-core region. However, lasing from NWs on silicon has not been achieved to date, due to the poor modal reflectivity at the NW-silicon interface. We demonstrate how, by inserting a tailored dielectric interlayer at the NW-Si interface, low-threshold single mode lasing can be achieved in vertical-cavity GaAs-AlGaAs core-shell NW lasers on silicon as measured at low temperature. By exploring the output characteristics along a detection direction parallel to the NW-axis, we measure very high spontaneous emission factors comparable to nanocavity lasers (β = 0.2) and achieve ultralow threshold pump energies ≤11 pJ/pulse. Analysis of the input-output characteristics of the NW lasers and the power dependence of the lasing emission line width demonstrate the potential for high pulsation rates ≥250 GHz. Such highly efficient nanolasers grown monolithically on silicon are highly promising for the realization of chip-level optical interconnects.

Dynamical Buildup of Lasing in Mesoscale Devices

The classical description of laser field buildup, based on time-averaged photon statistics of Class A lasers, rests on a statistical mixture of coherent and incoherent photons. Here, applying multiple analysis techniques to temporal streams of data acquired in the threshold region of a Class B mesoscale laser, we conclusively show that new physics is involved in the transition: the lasing buildup is controlled by large dynamical spikes, whose number increases as the pump is raised, evolving into an average coherent field, modulated by population dynamics, and eventually relaxing to a steady state for sufficiently large photon numbers. These results explain inconsistencies observed in small scale devices. Implications for nanolaser coherence properties, threshold identification and regimes of operation, including new potential applications, are discussed.

Electro-optical switching between polariton and cavity lasing in an InGaAs quantum well microcavity

We report on the condensation of microcavity exciton polaritons under optical excitation in a microcavity with four embedded InGaAs quantum wells. The polariton laser is characterized by a distinct non-linearity in the input-output-characteristics, which is accompanied by a drop of the emission linewidth indicating temporal coherence and a characteristic persisting emission blueshift with increased particle density. The temporal coherence of the device at threshold is underlined by a characteristic drop of the second order coherence function to a value close to 1. Furthermore an external electric field is used to switch between polariton regime, polariton condensate and photon lasing.

Quantum-memory effects in the emission of quantum-dot microcavities

The experimentally measured input-output characteristics of optically pumped semiconductor microcavities exhibits unexpected oscillations modifying the fundamentally linear slope in the excitation power regime below lasing. A systematic microscopic analysis reproduces these oscillations, identifying them as a genuine quantum-memory effect, i.e., a photon-density correlation accumulated during the excitation. With the use of projected quantum measurements, it is shown that the input-output oscillations can be controlled and enhanced by an order of magnitude when the quantum fluctuations of the pump are adjusted.

A comparison between experiment and theory on few-quantum-dot nanolasing in a photonic-crystal cavity

We present an experimental and theoretical study on the gain mechanism in a photonic-crystal-cavity nanolaser with embedded quantum dots. From time-resolved measurements at low excitation power we find that four excitons are coupled to the cavity. At high excitation power we observe a smooth low-threshold transition from spontaneous emission to lasing. Before lasing emission sets in, however, the excitons are observed to saturate, and the gain required for lasing originates rather from multi-excitonic transitions, which give rise to a broad emission background. We compare the experiment to a model of quantum-dot microcavity lasers and find that the number of excitons that must be included to fit the data largely exceeds the measured number, which shows that transitions involving the wetting layer can provide a surprisingly large contribution to the gain.

Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements

We present a novel experimental technique that can differentiate unequivocally between chaotic light and coherent light with amplitude fluctuations, and thus permits us to characterize unambiguously the output of a laser. This technique consists of measuring the second-order intensity cross correlation at the outputs of an unbalanced Michelson interferometer. It is applied to a chaotic light source and to the output of a semiconductor nanolaser whose "standard" intensity correlation function above threshold displays values compatible with a mixture of coherent and chaotic light. Our experimental results demonstrate that the output of such lasers is not partially chaotic but is indeed a coherent state with amplitude fluctuations.

Coherence time measurements using a single detector with variable time resolution

We present a simple technique for measuring coherence times for stationary light fields using a single detector with tunable time resolution. By measuring the equal-time second-order correlation function at varying instrument response functions it is possible to determine the coherence time and also the shape of the temporal decay without the need to record time-resolved data. The technique is demonstrated for pseudothermal light. Possible applications for dynamic light scattering and photon statistics measurements are discussed.

The single quantum dot-laser: lasing and strong coupling in the high-excitation regime

The emission properties of a single quantum dot in a microcavity are studied on the basis of a semiconductor model. As a function of the pump rate of the system we investigate the onset of stimulated emission, the possibility to realize stimulated emission in the strong-coupling regime, as well as the excitation-dependent changes of the photon statistics and the emission spectrum. The role of possible excited charged and multi-exciton states, the different sources of dephasing for various quantum-dot transitions, and the influence of background emission into the cavity mode are analyzed in detail. In the strong coupling regime, the emission spectrum can contain a line at the cavity resonance in addition to the vacuum doublet caused by off-resonant transitions of the same quantum dot. If strong coupling persists in the regime of stimulated emission, the emission spectrum near the cavity resonance additionally grows due to broadened contributions from higher rungs of the Jaynes-Cummings ladder.

Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity

We couple localized plasmon modes in nanowire pairs with resonator modes of a microcavity. Depending on the position of the nanowire pair in the resonator, the electric (symmetric) or magnetic (antisymmetric) plasmon mode is coupled, manifested by a huge anticrossing in the dispersion diagram. We explain this behavior by taking the symmetry and spatial distribution of the electric fields in the resonator into account. Experimental spectra verify the predicted mode-splitting due to the resonant coupling and agree well with theory. Our work can serve as a model system for far-field plasmon-plasmon coupling and paves the way toward enhanced localized plasmon-plasmon interaction in photonically coupled three-dimensional Bragg structures.

Splitting and lasing of whispering gallery modes in quantum dot micropillars

We have studied the whispering gallery mode (WGM) resonances of GaAs/AlGaAs microcavity pillars containing InAs quantum dots. High quality factor WGMs are observed from a wide range of pillars with diameters from 1.2 to 50 μm. Multimode lasing with sub-milliwatt thresholds and high beta-factors approaching unity is observed under optical pumping in a 4 μm diameter pillar. Mode splitting is observed in WGMs from pillars with diameters of 5 μm, 20 μm and 50 μm.We develop a model in which the mode splitting in the larger pillars is caused by resonant scattering from the quantum dots themselves. The model explains why splittings are observed in all of the larger pillars and that the splitting decreases with increasing wavelength. Numerical simulations by COMSOL confirm that the model is plausible. This mechanism of splitting should be general for all circular resonant structures containing quantum dots such as microdisks, rings, toroids, and microspheres.

Interplay of Goos-Hänchen shift and boundary curvature in deformed microdisks

As the fabrication of wavelength-scale optical microcavities is becoming feasible, extended ray models which include first-order wave corrections have attracted considerable interest. By using such a model, we find an unexpected shift of phase-space structures in momentum direction which can be attributed to the Goos-Hänchen shift in position direction and the boundary curvature ("periodic orbit shift," POS); this shift is calculated analytically for a general cavity shape. By comparing it to wave calculations in the special case of a limaçon-shaped microcavity, it is shown that mode localization occurs on the shifted, rather than the original, phase-space structures. Comparing of our analytical result to literature data, we find good agreement, which suggests that the POS may be responsible for many cases of previously reported, but unexplained, mismatches between Husimi functions and the ray-dynamical phase space.

Emission properties and photon statistics of a single quantum dot laser

A theoretical description for a single quantum-dot emitter in a microcavity is developed.We analyze for increasing steady-state pump rate the transition from the strong-coupling regime with photon antibunching to the weak-coupling regime with coherent emission. It is demonstrated how Coulomb interaction of excited carriers and excitation-induced dephasing can strongly modify the emission properties. Our theoretical investigations are based on a direct solution of the Liouville-von Neumann equation for the coupled carrier-photon system. We include multiple carrier excitations in the quantum dot, their Coulomb interaction, as well as excitation-induced dephasing and screening. Similarities and differences to atomic systems are discussed and results in the regime of recent experiments are interpreted.

Demonstration of coherent emission from high-beta photonic crystal nanolasers at room temperature

We report on lasing at room temperature and at telecommunications wavelength from photonic crystal nanocavities based on InAsP/InP quantum dots. Such laser cavities with a small modal volume and high quality factor display a high spontaneous emission coupling factor (beta). Lasing is confirmed by measuring the second-order autocorrelation function. A smooth transition from chaotic to coherent emission is observed, and coherent emission is obtained at eight times the threshold power.

High-Q design of semiconductor-based ultrasmall photonic crystal nanocavity

We report a high-Q design for a semiconductor-based two-dimensional zero-cell photonic crystal (PhC) nanocavity with a small mode volume. The optimization of displacements of hexagonal-lattice air holes in the Gamma-M direction, in addition to the Gamma-K direction, resulted in a cavity quality factor Q of 2.8 x 10(5) sustaining the small modal volume of 0.23(lambda(0)/n)(3). The momentum space consideration of out-of-plane radiation loss showed that the optimization of air hole displacements in both the in-plane x and y directions reduced FT components in the leaky region along the k(x) and k(y) axes, respectively. This high-Q cavity design is applicable to Si and GaAs semiconductor materials.

Single-molecule photon emission statistics for systems with explicit time dependence: Generating function approach

Generating function calculations are extended to allow for laser pulse envelopes of arbitrary shape in numerical applications. We investigate photon emission statistics for two-level and V- and Lambda-type three-level systems under time-dependent excitation. Applications relevant to electromagnetically induced transparency and photon emission from single quantum dots are presented.

Direct observation of correlations between individual photon emission events of a microcavity laser

Lasers are recognized for coherent light emission, the onset of which is reflected in a change in the photon statistics. For many years, attempts have been made to directly measure correlations in the individual photon emission events of semiconductor lasers. Previously, the temporal decay of these correlations below or at the lasing threshold was considerably faster than could be measured with the time resolution provided by the Hanbury Brown/Twiss measurement set-up used. Here we demonstrate a measurement technique using a streak camera that overcomes this limitation and provides a record of the arrival times of individual photons. This allows us to investigate the dynamical evolution of correlations between the individual photon emission events. We apply our studies to micropillar lasers with semiconductor quantum dots as the active material, operating in the regime of cavity quantum electrodynamics. For laser resonators with a low cavity quality factor, Q, a smooth transition from photon bunching to uncorrelated emission with increasing pumping is observed; for high-Q resonators, we see a non-monotonic dependence around the threshold where quantum light emission can occur. We identify regimes of dynamical anti-bunching of photons in agreement with the predictions of a microscopic theory that includes semiconductor-specific effects.

Photonic crystal nanocavity laser with a single quantum dot gain

We demonstrate a photonic crystal nanocavity laser essentially driven by a self-assembled InAs/GaAs single quantum dot gain. The investigated nanocavities contain only 0.4 quantum dots on an average; an ultra-low density quantum dot sample (1.5 x 10(8) cm(-2)) is used so that a single quantum dot can be isolated from the surrounding quantum dots. Laser oscillation begins at a pump power of 42 nW under resonant condition, while the far-detuning conditions require ~145 nW for lasing. This spectral detuning dependence of laser threshold indicates substantial contribution of the single quantum dot to the total gain. Moreover, photon correlation measurements show a distinct transition from anti-bunching to Poissonian via bunching with the increase of the excitation power, which is also an evidence of laser oscillation using the single quantum dot gain.

Transient chirp in high-speed photonic-crystal quantum-dot lasers with controlled spontaneous emission

We report on a series of experiments on the dynamics of spontaneous emission controlled nanolasers. The laser cavity is a photonic-crystal slab cavity, embedding self-assembled quantum dots as gain material. The implementation of cavity electrodynamics effects increases the large signal modulation bandwidth significantly, with measured modulation speeds of the order of 10 GHz while keeping an extinction ratio of 19 dB. A linear transient wavelength shift is reported, corresponding to a chirp of less than 100 pm for a 35 ps laser pulse. We observe that the chirp characteristics are independent of the repetition rate of the laser up to 10 GHz.

Output characteristics of pulsed and continuous-wave-excited quantum-dot microcavity lasers

In the rapidly evolving field of quantum-dot-based microcavity lasers the device characterization is of great importance. In this Letter, we study how information can be obtained from the input/output curve by using a microscopic laser theory for the coupled cavity-quantum-dot system. Semiconductor effects such as a nonlinear source term of spontaneous emission, Pauli blocking, and the absence of complete carrier inversion lead to significant deviations from atomic systems. Especially for pulsed excitation, saturation effects have a tremendous impact on the input/output characteristics and render a simple determination of the spontaneous emission coupling beta impossible.

Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [Lu, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.

Combining directional light output and ultralow loss in deformed microdisks

A drawback of optical modes in microdisk cavities is their isotropic light emission. Here we report a novel, robust, and general mechanism that results in highly directional light emission from high-quality modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds) and applies even to microlasers operating in the common multimode regime. We demonstrate our novel mechanism for the limaçon cavity and find directional emission with narrow angular divergence for a significant range of geometries and material parameters.