We have developed a scattering-matrix approach for numerical calculation of resonant states and Q-values of a nonideal optical disk cavity of an arbitrary shape and of an arbitrary varying refraction index. The developed method has been applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q-values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface combined with the examination of Poincare surfaces of section and Husimi distributions.
We propose a coupled microdisk laser as a compact and tunable laser source for the generation of a coherent continuous wave THz radiation by photomixing. Using the Schrödinger-Bloch model including the nonlinear effect of active medium, we find single mode and two mode lasings depending on the pumping strength. We explain the transitions of lasing modes in terms of resonant modes which are the solutions of the Schrödinger-Bloch model without active medium and nonlinear interaction. In particular, a two mode lasing is shown to generate THz oscillating frequency originating from the light beatin…
We demonstrate lasing mode selection in nearly circular semiconductor microdisks by shaping the spatial profile of optical pump. Despite of strong mode overlap, adaptive pumping suppresses all lasing modes except the targeted one. Due to slight deformation of the cavity shape and boundary roughness, each lasing mode has distinct emission pattern. By selecting different mode to be the dominant lasing mode, we can switch both the lasing frequency and the output direction. Such tunability by external pump after the laser is fabricated enhances the functionality of semiconductor microcavity lasers…
We demonstrate an effective control of nonlinear interactions of lasing modes in a semiconductor microdisk cavity by shaping the pump profile. A target mode is selected at the expense of its competing modes either by increasing their lasing thresholds or suppressing their power slopes above the lasing threshold. Despite of strong spatial overlap of the lasing modes at the disk boundary, adaptive pumping enables an efficient selection of any lasing mode to be the dominant one, leading to a switch of lasing frequency. The theoretical analysis illustrates both linear and nonlinear effects of sele…
We perform numerical studies of the effect of sidewall imperfections on the resonant state broadening of the optical microdisk cavities for lasing applications. We demonstrate that even small edge roughness causes a drastic degradation of high-Q whispering gallery (WG) mode resonances reducing their Q-values by many orders of magnitude. At the same time, low-Q WG resonances are rather insensitive to the surface roughness. The results of numerical simulation obtained using the scattering matrix technique, are analyzed and explained in terms of wave reflection at a curved dielectric interface co…
A long existing issue for microdisk lasers is the small spontaneous emission coupling rate (β) in microdisk,. We found that it is due to the coupling of emitter spontaneous emission into competing Fabry-Perot (FP) modes in the microdisk cavity. Based on this analysis, we propose a new type of photonic crystal microdisk (PCM) laser to drastically suppress the photonic density of states in the vertical FP modes. As a result, we obtained a three fold increase of β than previously reported highest β of 0.15 at room temperature. The spontaneous emission control in truncated photonic crystals become…
We report single-mode lasing in subwavelength GaAs disks under optical pumping. The disks are fabricated by standard photolithography and two steps of wet chemical etching. The simple fabrication method can produce submicron disks with good circularity, smooth boundary and vertical sidewalls. The smallest lasing disks have a diameter of 627 nm and thickness of 265 nm. The ratio of the disk diameter to the vacuum lasing wavelength is about 0.7. Our numerical simulations confirm that the lasing modes are whispering-gallery modes with the azimuthal number as small as 4 and very small mode volume.
Formation, emission and lasing properties of strain-free InP(As)/AlInAs quantum dots (QDs) embedded in AlInAs microdisk (MD) cavity were investigated using transmission electron microscopy and photoluminescence (PL) techniques. In MD structures, the QDs having nano-pan-cake shape have height of ~2 nm, lateral size of 20-50 nm and density of ~5x109 cm-2. Their emission observed at ~940 nm revealed strong temperature quenching, which points to exciton decomposition. It also showed unexpected type-I character indicating In-As intermixing, as confirmed by band structure calculations. We observed l…
Whispering gallery mode microdisk cavities fabricated by direct laser writing are studied using dark-field imaging and spectroscopy in the visible spectral range. {Dark-field imaging allows us to directly visualize the spatial intensity distribution of whispering gallery modes. We extract their azimuthal and radial mode indices from dark-field images, and find the axial mode number from the dispersion relation. The scattering spectrum obtained in the confocal arrangement provides information on the density of optical states in the resonator. The proposed technique is a simple non-invasive way …
Low threshold lasers realized within compact, high quality optical cavities enable a variety of nanophotonics applications. Gallium nitride (GaN) materials containing indium gallium nitride (InGaN) quantum dots and quantum wells offer an outstanding platform to study light matter interactions and realize practical devices such as efficient light emitting diodes and nanolasers. Despite progress in the growth and characterization of InGaN quantum dots, their advantages as the gain medium in low threshold lasers have not been clearly demonstrated. This work seeks to better understand the reasons …
Optical characterization of AlGaAs microdisk resonant cavities with a quantum dot active region is presented. Direct passive measurement of the optical loss within AlGaAs microdisk resonant structures embedded with InAs/InGaAs dots-in-a-well (DWELL) is performed using an optical-fiber-based probing technique at a wavelength (lambda~1400 nm) that is red-detuned from the dot emission wavelength (lambda~1200 nm). Measurements in the 1400 nm wavelength band on microdisks of diameter D = 4.5 microns show that these structures support modes with cold-cavity quality factors as high as 360,000. DWELL-…
Fast and highly accurate method based on the Muller contour integral equations and a trigonometric-trigonometric Galerkin discretization technique is presented for spectral design and fine-tuning of clusters of whispering-gallery (WG) mode microdisk resonators and photonic crystal (PC) defect cavities. It is shown that degeneracy and near-degeneracy of natural modes as well as modes optical confinement in coupled resonator clusters are significantly influenced by the symmetry of the structure. Photonic molecules with greatly enhanced quality factors are designed by exploiting the symmetry of t…
We demonstrate uni-directional evanescent coupling of lasing emission from a wavelength-scale deformed microdisk to a waveguide. This is attributed to the Goos-Hänchen shift and Fresnel filtering effect that result in a spatial separation of the clockwise (CW) and counter-clockwise (CCW) propagating ray orbits. By placing the waveguide tangentially at different locations to the cavity boundary, we may selectively couple the CW (CCW) wave out, leaving the CCW (CW) wave inside the cavity, which also reduces the spatial hole burning effect. The device geometry is optimized with a full-wave simula…
Metastable wurtzite crystal phases of semiconductors comprise enormous potential for high-performance electro-optical devices, owed to their extended tunable direct band gap range. However, synthesizing these materials in good quality and beyond nanowire size constraints has remained elusive. In this work, the epitaxy of wurtzite InP microdisks and related geometries on insulator for optical applications is explored. This is achieved by an elaborate combination of selective area growth of fins and a zipper-induced epitaxial lateral overgrowth, which enables co-integration of diversely shaped c…
The quality factor (Q), mode volume (Veff), and room-temperature lasing threshold of microdisk cavities with embedded quantum dots (QDs) are investigated. Finite element method simulations of standing wave modes within the microdisk reveal that Veff can be as small as 2(lambda/n)^3 while maintaining radiation-limited Qs in excess of 10^5. Microdisks of diameter D=2 microns are fabricated in an AlGaAs material containing a single layer of InAs QDs with peak emission at lambda = 1317 nm. For devices with Veff ~2 (lambda/n)^3, Qs as high as 1.2 x 10^5 are measured passively in the 1.4 micron band…
GeSn alloys are nowadays considered as the most promising materials to build Group IV laser sources on silicon (Si) in a full complementary metal oxide semiconductor-compatible approach. Recent GeSn laser developments rely on increasing the band structure directness, by increasing the Sn content in thick GeSn layers grown on germanium (Ge) virtual substrates (VS) on Si. These lasers nonetheless suffer from a lack of defect management and from high threshold densities. In this work we examine the lasing characteristics of GeSn alloys with Sn contents ranging from 7 \% to 10.5 \%. The GeSn layer…
InGaN-based active layers within microcavity resonators offer the potential of low threshold lasers in the blue spectral range. Here we demonstrate optically pumped, room temperature lasing in high quality factor GaN microdisk cavities containing InGaN quantum dots (QDs) with thresholds as low as 0.28 mJ/cm2. This work, the first demonstration of lasing action from GaN microdisk cavities with QDs in the active layer, provides a critical step for the nitrides in realizing low threshold photonic devices with efficient coupling between QDs and an optical cavity.
A system for studying microcavity resonators at cryogenic temperatures (~10 K) through evanescent coupling via optical fiber taper waveguides is reported, and efficient fiber coupling to AlGaAs microdisk cavities with embedded quantum dots is demonstrated. As an immediate application of this tool, we study high-resolution tuning of microdisk cavities through nitrogen gas adsorption, as first discussed by Mosor, et al. By proper regulation of the nitrogen gas flow and delivery of the gas to the sample surface, continuous tuning can be achieved with modest gas flows, and overall wavelength shift…
Hybridization of surface-plasmon and dielectric waveguide whispering-gallery modes are demonstrated in a semiconductor microdisk laser cavity of sub-wavelength proportions. A metal layer is deposited on top of the semiconductor microdisk, the radius of which is systematically varied to enable mode hybridization between surface-plasmon and dielectric modes. The anti-crossing behavior of the two cavity mode types is experimentally observed via photoluminescence spectroscopy and optically pumped lasing action at a wavelength of 1.3 micron is achieved at room temperature.
Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes …
The smaller the size of a light-emitting microcavity, the more important it becomes to understand the effects of the cavity boundary on the optical mode profile. Conventional methods of laser physics, such as the paraxial approximation, become inapplicable in many of the more exotic cavity designs to be discussed here. Cavities in the shape of microdisks, pillars and rings can yield low lasing thresholds in a wide variety of gain media: quantum wells, wires and even dots, as well as quantum cascade superlattices and GaN. An overview of the experimental and theoretical status is provided, with …
We introduce a class of unidirectional lasing modes associated with the frozen mode regime of non-reciprocal slow-wave structures. Such asymmetric modes can only exist in cavities with broken time-reversal and space inversion symmetries. Their lasing frequency coincides with a spectral stationary inflection point of the underlying passive structure and is virtually independent of its size. These unidirectional lasers can be indispensable components of photonic integrated circuitry.
We report on the radiative interaction of two single quantum dots (QDs) each in a separate InP/GaInP-based microdisk cavity via resonant whispering gallery modes. The investigations are based on ab initio coupled disk modes. We apply optical spectroscopy involving a $4f$-setup, as well as mode-selective real space imaging and photoluminescence mapping to discern single QDs coupled to a resonant microdisk mode. Excitation of one disk of the double cavity structure and detecting photoluminescene from the other yields proof of single photon emission of a QD excited by incoherent energy transfer f…
Limaçon-shaped microdisk lasers are promising on-chip light sources with low lasing threshold and unidirectional output. We conduct an experimental study on the lasing dynamics of Limaçon-shaped semiconductor microcavities. The edge emission exhibits intensity fluctuations over a wide range of spatial and temporal scales. They result from multiple dynamic processes with different origins and occurring on different spatiotemporal scales. The dominant process is an alternate oscillation between two output beams with a period as short as a few nanoseconds.
In single microdisks, embedded active emitters intrinsically affect the cavity mode of microdisks, which results in a trivial symmetric backscattering and a low controllability. Here we propose a macroscopical control of the backscattering direction by optimizing the cavity size. The signature of positive and negative backscattering directions in each single microdisk is confirmed with two strongly coupled microdisks. Furthermore, the diabolical points are achieved at the resonance of two microdisks, which agrees well with the theoretical calculations considering backscattering directions. The…
We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and grey cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by the discrete diffraction and are stable when the bistability of homogenous states is absent.
GeSn alloys offer a promising route towards a CMOS compatible light source and the realization of electronic-photonic integrated circuits. One tactic to improve the lasing performance of GeSn lasers is to use a high Sn content, which improves the directness. Another popular approach is to use a low to moderate Sn content with either compressive strain relaxation or tensile strain engineering, but these strain engineering techniques generally require optical cavities to be suspended in air, which leads to poor thermal management. In this work, we develop a novel dual insulator GeSn-on-insulator…
We study a re-configurable nonreciprocal fiber ring cavity setup to generate tunable optical frequency combs. Coherent combs can be obtained by finely exploiting bi-chromatic Brillouin lasing and cascaded four-wave mixing in the nonlinear fiber cavity. We introduce a numerical model of the cavity system, which is validated by comparisons with experiments. Our work shows the importance of the mode pulling effect, controlled by the pump laser detuning, in setting the dynamics of the comb. This effect along with the impact of multimode lasing had been overlooked in previous fiber experiments. We …
Effective, permanent tuning of the whispering gallery modes (WGMs) of p-i-n doped GaN microdisk cavity with embedded InGaN quantum dots over one free spectral range is successfully demonstrated by irradiating the microdisks with a ultraviolet laser (380nm) in DI water. For incident laser powers between 150 and 960 nW, the tuning rate varies linearly. Etching of the top surface of the cavity is proposed as the driving force for the observed shift in WGMs, and is supported by experiments. The tuning for GaN/InGaN microdisk cavities is an important step for deterministically realizing novel nanop…
Lasers differ from other light sources in that they are coherent, and their coherence makes them indispensable to both fundamental research and practical application. In optomechanical cavities, phonon and photon lasing is facilitated by the ability of photons and phonons to interact intensively and excite one another coherently. The lasing linewidths of both phonons and photons are critical for practical application. However, thus far, these linewidths have not been explored in detail in cavity optomechanical systems. This study investigates the underlying dynamics of lasing in optomechanical…
A formula for the laser linewidth of arbitrary cavities in the multimode non-linear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the non-linear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant d…
We investigate the nonlinear optical features of a graphene sheet embedded in an active cavity and we show that, when tuned near its lasing threshold, the cavity is able to isolate the spatially localized graphene nonlinearity thus producing a very strong nonlinear device response with multi-valued features. As opposed to standard situations where the small thickness of the graphene sheet hampers its remarkable nonlinear optical properties to be exploited, in our scheme the strong nonlinear optical regime is mainly triggered by the very intrinsic planar localization of graphene nonlinearity. T…
Cuboid-shaped organic microcavities containing a pyrromethene laser dye and supported upon a photonic crystal have been investigated as an approach to reducing the lasing threshold of the cavities. Multiphoton lithography facilitated fabrication of the cuboid cavities directly on the substrate or on the decoupling structure, while similar structures were fabricated on the substrate by UV lithography for comparison. Significant reduction of the lasing threshold by a factor of ~30 has been observed for cavities supported by the photonic crystal relative to those fabricated on the substrate. The …
The authors show clear experimental evidence of lasing of exciton polaritons confined in L3 photonic crystal cavities. The samples are based on an InP membrane in air containing five InAsP quantum wells. Polariton lasing is observed with thresholds as low as 120 nW, below the Mott transition, while conventional photon lasing is observed for a pumping power one to three orders of magnitude higher.
Intersubband polariton -- LO phonon interaction in mid-infrared non-dispersive cavities: experimental demonstration of spontaneous scattering and perspectives towards polariton lasing
Erbium-doped lithium niobate high-Q microdisk cavities were fabricated in batches by UV exposure, inductively coupled plasma reactive ion etching and chemo-mechanical polishing. The stimulated emission at 1531.6 nm was observed under the pump of a narrow-band laser working at 974 nm in erbium-doped lithium niobate microdisk cavity with threshold down to 400 μW and a conversion efficiency of 3.1{\times}10^{-4} %, laying the foundation for the LNOI integrated light source research.
Here we report lasing action in limaçon-shaped GaAs microdisks with quantum dots (QDs) embedded. Although the intracavity ray dynamics is predominantly chaotic, high-$Q$ modes are concentrated in the region $χ> χ_c$ as a result of wave localization. Strong optical confinement by total internal reflection leads to very low lasing threshold. Our measurements show that all the lasing modes have output in the same direction, regardless of their wavelengths and intracavity mode structures. This universal emission direction is determined by directed phase space flow of optical rays in the open chaot…
We study, theoretically and experimentally, disorder-induced resonances in randomly-layered samples,and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigen-frequencies and pinpoint the locations of the resonant cavities that appear in individual realizations of random samples, for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigen-frequency is independent of the location i…
We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g. a bad-cavity correction to the Henry $α$ factor and a multimode Schawlow--Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell--Bloch equations, we handle quantum and …
The 4-bar crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient frequency conversion without poling, twinning or other engineered domain inversions. 4-bar symmetry means that a 90 degree rotation is equivalent to a crystallographic inversion. Therefore, propagation geometries where light circulates about the 4-bar axis produce effective domain inversions, useful for quasi-phasematching. Microdisk optical cavities also offer resonance field-enhancement and excellent spatial overlap, resulting in highly efficient frequency conversion in micrometer-scale volumes.…
We demonstrate gallium phosphide (GaP) microdisk optical cavities with intrinsic quality factors $ > 2.8\times10^{5}$ and mode volumes $< 10 (λ/n)^3$, and study their nonlinear and optomechanical properties. For optical intensities up to $8.0\times10^4$ intracavity photons, we observe optical loss in the microcavity to decrease with increasing intensity, indicating that saturable absorption sites are present in the GaP material, and that two-photon absorption is not significant. We observe optomechanical coupling between optical modes of the microdisk around 1.5 $μ$m and several mechanical res…
Using a pair of coupled LRC cavities we experimentally demonstrate that instabilities and amplification action can be tamed by a spatially inhomogenous gain. Specifically we observe the counter-intuitive phenomenon of stabilization of the system even when the overall gain provided is increased. This behavior is directly related to lasing death via asymmetric pumping, recently proposed in [M. Liertzer {\it et al}., Phys. Rev. Lett. {\bf 108}, 173901 (2012)]. The stability analysis of other simple systems reveals the universal nature of the lasing death phenomenon.
PT-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to a host of novel optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realizations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robu…
We present a generic classical light condensation (LC) phenomenon in linear photonic mode systems, such as cw laser cavities, in a noisy environment (spontaneous emission, etc.), based on weighting the modes in a loss-gain scale rather than in photon energy. It is characterized by a sharp transition from multi- to single-mode oscillation. The study uses a linear multivariate Langevin formulation which gives a mode occupation hierarchy that functions like Bose-Einstein statistics. We find that condensation occurs when the spectral filtering has near the lowest loss mode a power law dependence w…
Zinc Oxide thin films were grown on c-sapphire substrates using pulsed laser deposition. Pump power dependence of surface emission spectra, acquired using a quadrupled 266 nm laser, revealed room temperature stimulated emission (threshold of 900 kW/cm2). Time dependent spectral analysis plus gain measurements of single-shot, side-emission, spectra pumped with a nitrogen laser revealed random lasing indicative of the presence of self-forming laser cavities. It is suggested that random lasing in an epitaxial system rather than a 3-dimensional configuration of disordered scattering elements, was …
Half-wave plasmonic nanolasers near the localization limit
Harvard Medical School（哈佛医学院）；Massachusetts General Hospital（麻省总医院）；Rice University（莱斯大学）；Harvard-MIT Health Sciences and Technology（哈佛-麻省理工学院健康科学与技术）；Massachusetts Institute of Technology（麻省理工学院）
Microcavity polaritons are bosonic light-matter particles that can emit coherent radiation without electronic population inversion via bosonic scattering. This phenomenon, known as polariton lasing, strongly depends on the polaritons' confinement. Shrinking the polaritons' mode volume increases the interactions mediated by their excitonic part, and thereby the density-dependent blueshift of the polariton to a higher energy is enhanced. Previously, polariton lasing has been demonstrated in micropillars with diameters larger than three microns, in grating based cavities, fiber cavities and photo…
We propose and analyze a new type of a resonant high-Q cavity for lasing, sensing or filtering applications, which is based on a surface states of a finite photonic crystal. We demonstrate that such the cavity can have a Q factor comparable with that one of conventional photonic band-gap defect mode cavities. At the same time, the distinguished feature of the surface mode cavity is that it is situated directly at the surface of the photonic crystal. This might open up new possibilities for design of novel photonic devices and integration of photonic circuits.
The lasing behavior of one dimensional GaAs nanobeam cavities with embedded InAs quantum dots is studied at room temperature. Lasing is observed throughout the quantum dot PL spectrum, and the wavelength dependence of the threshold is calculated. We study the cavity lasers under both 780 nm and 980 nm pump, finding thresholds as low as 0.3 uW and 19 uW for the two pump wavelengths, respectively. Finally, the nanobeam cavity laser wavelengths are tuned by up to 7 nm by employing a fiber taper in near proximity to the cavities. The fiber taper is used both to efficiently pump the cavity and coll…
The distribution of spacings between the lasing frequencies for an ensemble of random lasers in the two-mode regime was computed. The random lasers are implemented as open chaotic cavities filled with an active medium. The spectral properties of the passive cavities are modeled with non-Hermitian random matrices. The spacing distribution is found to depend on the relation between the gain-profile width and the mean spacing of the passive-cavity modes. The distribution displays mode repulsion and, under certain conditions, agrees with the Wigner surmise. The role of mode competition is discusse…
We discuss a class of lasing modes created by a spatially inhomogeneous gain profile. These lasing modes are "extra modes", in addition to, and very different from, conventional lasing modes, which arise from the passive cavity resonances. These new modes do not have high intensity across the entire gain region, but instead are localized at the gain boundary and throughout the gain-free region. They are surface modes, originating from the transmission resonances of the gain-free region. Using an S-matrix description we connect these surface modes to the lasing modes in PT-symmetric (balanced g…
Spatio-temporal instabilities are widespread phenomena resulting from complexity and nonlinearity. In broad-area edge-emitting semiconductor lasers, the nonlinear interactions of multiple spatial modes with the active medium can result in filamentation and spatio-temporal chaos. These instabilities degrade the laser performance and are extremely challenging to control. We demonstrate a powerful approach to suppress spatio-temporal instabilities using wave-chaotic or disordered cavities. The interference of many propagating waves with random phases in such cavities disrupts the formation of sel…
Topological photonics provides a fundamental framework for robust manipulation of light, including directional transport and localization with built-in immunity to disorder. Combined with an optical gain, active topological cavities hold special promise for a design of light-emitting devices. Most studies to date have focused on lasing at topological edges of finite systems or domain walls. Recently discovered higher-order topological phases enable strong high-quality confinement of light at the corners. Here we demonstrate lasing action of corner states in a nanophotonic topological cavity. W…
