Total Spontaneous Emission Rate Research Articles

Spontaneous emission enhancement and directional emission by an optical nanonatenna array on a metallic mirror

Optical nanoantennas support surface plasmon polariton (SPP) with a confinement of light breaking through the diffraction limit, and thereby achieving an enhancement and regulation of electromagnetic field on a deep-subwavelength scale. In this paper, a periodic array of optical nanoantennas on a metallic mirror is proposed, where the antennas are gold nanocubes forming a two-dimensional periodic array, and a single point emission source is located in the nanogap between the antenna of gold nanocube and the gold mirror. The nanogap between the antenna and mirror can support gap surface plasmon, which results in an enhanced spontaneous emission rate. Meanwhile, the periodic array of nanoantennas can support the surface lattice resonance (SLR), which can achieve directional far-field radiation perpendicular to the substrate or in a specified direction by properly designing the array period. To design the antenna that can simultaneously achieve an enhancement of spontaneous emission rate and a directional radiation of far field, the calculation of the radiation field of a single point source in a periodic structure is transformed into the calculation of the radiation fields of a set of pseudoperiodic point-source arrays by combining the array scanning method (ASM) and full-wave rigorous numerical method, thus giving the spontaneous emission rate of the emitter and the near-field distribution of the antenna. Concerning the calculation of the angular distribution of far-field radiation intensity, we start from the Maxwell’s equations and provide a rigorous formulation and proof of the reciprocity-theorem method. This proof is different from those reported in existing literature and has a more rigorous applicability for infinite-extent periodic structures or has a lower amount of computational work. Based on the reciprocity-theorem method, the antenna parameters are designed so that the enhancement factor of far-field radiation intensity reaches a maximum value of 2756 in the direction perpendicular to the substrate, and simultaneously, the enhancement factors of total spontaneous emission rate and far-field spontaneous emission rate of the point source reach 1097 and 55.50, respectively. The proposed antenna has a simple structure that is easy to design and fabricate, and the proposed design method is intuitive and easy to implement, which can be used to guide the design of high-speed, high-brightness and directional-radiation light sources.

Broadband Enhancement of the Spontaneous Emission by an Optical Dipole Nanoantenna on Metallic Substrate: an Intuitive Model of Surface Plasmon Polariton

Optical nanoantennas can achieve electromagnetic-field enhancement under far-field excitation or spontaneous-emission enhancement under excitation by radiating emitters. Among them, nanoantennas on a metallic substrate (i.e., the so-called nanoparticle-on-mirror antennas) have drawn great research interests due to their ease in forming metallic gaps of sizes down to a few nanometers or even subnanometer. Here we propose an optical dipole nanoantenna on a metallic substrate with a broadband enhancement of spontaneous emission. Its total and radiative emission-rate enhancement factors can be up to 5454 and 1041, respectively. In the near-infrared band, the wavelength range of spontaneous-emission enhancement (Purcell factor over 1000) can reach 260nm. By changing the width of the slit between the two antenna arms and changing the length of the antenna arms, the spontaneous-emission enhancement bandwidth and enhancement factors can be adjusted, respectively, which brings great freedom and simplicity to the design process. The antenna can achieve a strong far-field radiation within a central anglular zone (polar angle <i>θ</i>≤60°) corresponding to a certain numerical aperture of objective lens, and therefore can increase the intensity of the fluorescence collected by the objective lens. Based on the above performances, the antenna can provide a broadband enhancement of spontaneous emission for fluorescent molecules or quantum dots (whose fluorescence spectrum usually covers a certain wavelength range), which is of great significance for applications such as high-speed and super-bright nanoscale light sources and high-sensitivity fluorescent-molecule sensing.<br>To clarify the underlying physical mechanisms, we build up a semi-analytical model by considering an intuitive excitation and multiple-scattering process of surface plasmon polaritons (SPPs) that propagate along the antenna arms. All the parameters used in the model (such as the SPP scattering coefficients) are obtained via rigorous calculations based on the first principle of Maxwell’s equations without any fitting process, which ensures that the model has a solid electromagnetic foundation and can provide quantitative predictions. The SPP model can comprehensively reproduce all the radiation properties of the antenna, such as the total and radiative emission rates and the far-field radiation pattern. Two phase-matching conditions are derived from the model for predicting the antenna resonance, and show that under these conditions, the SPPs on the antenna arms form a pair of Fabry-Perot resonance and therefore are enhanced, and the enhanced SPPs propagate to the emitter in the nanogap (or scattered into the free space), so as to enhance the total spontaneous emission rate (or the far-field radiative emission rate). Besides, this pair of Fabry-Perot resonance result in a pair of resonance peaks close to each other, which then forms the broadband enhancement of spontaneous emission.

Broadband enhancement of spontaneous emission by optical dipole nanoantenna on metallic substrate: An intuitive model of surface plasmon polariton

<sec>Optical nanoantennas can achieve electromagnetic-field enhancement under far-field excitation or spontaneous-emission enhancement under excitation by radiating emitters. Among them, nanoantennas on a metallic substrate (i.e. the so-called nanoparticle-on-mirror antennas) have aroused great research interest due to their ease in forming metallic gaps of sizes down to a few nanometers or even subnanometer. Here we propose an optical dipole nanoantenna on a metallic substrate with a broadband enhancement of spontaneous emission. Its total and radiative emission-rate enhancement factors can reach up to 5454 and 1041, respectively. In the near-infrared band, the wavelength range of spontaneous-emission enhancement (Purcell factor over 1000) can reach 260nm. By changing the width of the slit between the two antenna arms and also the length of the antenna arms, the spontaneous-emission enhancement bandwidth and enhancement factors can be adjusted, respectively, which brings great freedom and simplicity to the design process. The antenna can achieve a strong far-field radiation within a central anglular zone (polar angle <i>θ</i>≤60°) corresponding to a certain numerical aperture of objective lens, and therefore can increase the intensity of the fluorescence collected by the objective lens. Based on the above performances, the antenna can provide a broadband enhancement of spontaneous emission for fluorescent molecules or quantum dots (whose fluorescence spectrum usually covers a certain wavelength range), which is of great significance for the applications such as in high-speed and super-bright nanoscale light sources and high-sensitivity fluorescent-molecule sensing.</sec><sec>To clarify the underlying physical mechanisms, we build up a semi-analytical model by considering an intuitive excitation and multiple-scattering process of surface plasmon polaritons (SPPs) that propagate along the antenna arms. All the parameters used in the model (such as the SPP scattering coefficients) are obtained via rigorous calculations based on the first principle of Maxwell's equations without any fitting process, which ensures that the model has a solid electromagnetic foundation and can provide quantitative predictions. The SPP model can comprehensively reproduce all the radiation properties of the antenna, such as the total radiative emission rate and the far-field radiation pattern. Two phase-matching conditions are derived from the model for predicting the antenna resonance, and show that under these conditions, the SPPs on the antenna arms form a pair of Fabry-Perot resonance and therefore are enhanced, and the enhanced SPPs propagate to the emitter in the nanogap (or scattered into the free space), so as to enhance the total spontaneous emission rate (or the far-field radiative emission rate). Besides, this pair of Fabry-Perot resonance results in a pair of resonance peaks close to each other, then enhancing the spontaneous emission with a broadband.</sec>

Spontaneous Emission Enhancement by a Rectangular-Aperture Optical Nanoantenna: An Intuitive Semi-Analytical Model of Surface Plasmon Polaritons

The spontaneous-emission enhancement effect of a single metallic rectangular-aperture optical nanoantenna on a SiO2 substrate was investigated theoretically. By considering the excitation and multiple scattering of surface plasmon polaritons (SPPs) in the aperture, an intuitive and comprehensive SPP model was established. The model can comprehensively predict the total spontaneous emission rate, the radiative emission rate and the angular distribution of the far-field emission of a point source in the aperture. Two phase-matching conditions are derived from the model for predicting the resonance and show that the spontaneous-emission enhancement by the antenna comes from the Fabry–Perot resonance of the SPP in the aperture. In addition, when scanning the position of the point source and the aperture length, the SPP model does not need to repeatedly solve the Maxwell’s equations, which shows a superior computational efficiency compared to the full-wave numerical method.

Time delay concealment and unpredictability enhancement of nanolasers under external cavity regulation

As an important optical element of the optical integration in the future, nanolasers has been a research hotspot in recent years, and the corresponding structural engineering and output characteristics have been widely investigated. However, the nonlinear dynamical performances of nanolasers are rarely reported. Only some preliminary analyses of the dynamic behavior under the optical feedback, optical injection and mutual injection can be found. Some researches pointed out the future prospect of nanolasers, however, some chaos-based applications have not been explored. Therefore, we numerically investigate chaos dynamics in a nanolaser subjected to optical feedback and in another nanolaser subjected to chaotic injection from the former structure by using single mode rate equation, which includes the Purcell cavity-enhanced spontaneous emission factor <i>F</i> and spontaneous emission coupling factor <i>β</i>. The <i>F</i> denotes the ratio of the spontaneous emission rate into the cavity mode to the total spontaneous emission rate in the bulk medium in the absence of a cavity and <i>β</i> represents the fraction of spontaneous emitted photons which are coupled into cavity mode. Specifically, chaos time delay signature (TDS) and unpredictability are evaluated by the peak size of autocorrelation function (ACF) and permutation entropy (PE) respectively. Such kinds of calculations have the advantage of fast operation speed and anti-noise robustness. The results show that the increasing of bias current and the decreasing of gain saturation factor <i>ε</i>, <i>F</i> and <i>β</i> are beneficial to improving the unpredictability and suppressing TDS because the weak damping of the relaxation oscillation leads to strong oscillation. Large linewidth enhancement factor <i>α</i> will increase the number of laser oscillating modes, sideband modes, the spectral components, and enhance the dispersion effect, which will also weaken the information about outer cavity and improve the complexity of chaos. In addition, the above-mentioned chaos properties can be enhanced by injecting the chaos output from a nanolaser subjected to optical feedback into another (slave) nanolaser, which is due to the nonlinear interaction between the driving chaotic signal and the internal electric field of the slave nanolaser. Finally, two-dimensional maps depicting high unpredictability and TDS concealment in the parameter space of the frequency detuning and the injection strength are obtained. It can be found that unpredictability degree can be enhanced by choosing high detuning frequency and intermediate injection strength in the non-injection locking area. The numerical results pave the way for generating the high-quality chaotic sources on a chip or the photonic integrated circuits based on novel semiconductor nanolaser and its related applications.

Optical polarization characteristics for AlGaN-based light-emitting diodes with AlGaN multilayer structure as well layer* *Project supported by the National Natural Science Foundation of China (Grant No. 61874168), the Jiangsu Province I-U-R Cooperation Project, China (Grant No. BY2019114), and the Nantong Science and Technology Project, China (Grant No. JC2019006).

The optical properties of AlGaN-based quantum well (QW) structure with two coupled thin well layers are investigated by the six-by-six K – P method. Compared with the conventional structure, the new structure, especially the one with lower Al-content in the barrier layer, can enhance the TE-/TM-polarized total spontaneous emission rate due to the strong quantum confinement and wide recombination region. For the conventional QW structure, the reduction of well thickness can lead the degree of polarization (DOP) to decrease and the internal quantum efficiency (IQE) to increase. By using the coupled thin well layers, the DOP for the structure with high Al-content in the barrier layer can be improved, while the DOP will further decrease with low Al-content in the barrier layer. It can be attributed to the band adjustment induced by the combination of barrier height and well layer coupling. The IQE can also be further enhanced to 14.8%–20.5% for various Al-content of barrier layer at J = 100 A/cm2. In addition, the efficiency droop effect can be expected to be suppressed compared with the conventional structure.

Enhanced TE-polarized emission of AlGaN-based deep-ultraviolet light emitting diodes by using an InAlN insertion layer

The optical properties of Al0.44Ga0.56N/Al0.59Ga0.41N multiple quantum well structures with an InxAl1-xN insertion layer between the barrier layer and the well layer are investigated by using the effective mass theory. The numerical results show the TE-dominated emission can be realized by using the InxAl1-xN insertion layer, which can be mainly attributed to the larger separation of the electron-hole wave-function for the TM-dominated transition. Note that the rearrangement of valence subbands is also an important factor to enhance the TE polarization emission for the InxAl1-xN insertion layer with the lower In-content. The ratios of TE-polarized total spontaneous emission rate between the InxAl1-xN insertion layer structures (x = 0.11, 0.13, 0.15) and the conventional structure can reach 1.76–2.05 in the current density range of 2–300 A cm−2 due to the larger product of Fermi–Dirac distribution functions of electron and hole. Furthermore, the InxAl1-xN insertion layer structures with x = 0.15–0.17 show the largest TE polarization emission.

Near-field relaxation of a quantum emitter to two-dimensional semiconductors: Surface dissipation and exciton polaritons

The total spontaneous emission rate of a quantum emitter in the presence of an infinite MoS\textsubscript{2} monolayer is enhanced by several orders of magnitude, compared to its free-space value, due to the excitation of surface exciton polariton modes and lossy modes. The spectral and distance dependence of the spontaneous emission rate are analyzed and the lossy-surface-wave, surface exciton polariton mode and radiative contributions are identified. The transverse magnetic and transverse electric exciton polariton modes can be excited for different emission frequencies of the quantum emitter, and their contributions to the total spontaneous emission rate are different. To calculate these different decay rates, we use the non-Hermitian description of light-matter interactions, employing a Green's tensor formalism. The distance dependence follows different trends depending on the emission energy of quantum emitter. For the case of the lossy surface waves, the distance dependence follows a $z^{-n}$, $n=2,3,4$, trend. When transverse magnetic exciton polariton modes are excited, they dominate and characterize the distance dependence of the spontaneous emission rate of a quantum emitter in the presence of the MoS\textsubscript{2} layers. The interaction between a quantum emitter and a MoS\textsubscript{2} superlattice is investigated and we observe a splitting of the modes supported by the superlattice. Moreover, a blue shift of the peak values of the spontaneous emission rate of a quantum emitter is observed as the number of layers is increased. The field distribution profiles, created by a quantum emitter, are used to explain this behavior.

Lamb shift of a lossy two-level emitter inside a leaky cavity: A universal description based on an equivalent dissipative model

We present an universal description for Lamb shift of a lossy two-level-emitter (TLE) inside a leaky cavity by combining the quantum dissipation theory and the perturbative treatment developed in cavity QED. The total spectrum function of bath associated with the TLE is deduced by the standard method developed for a quantum dissipation model, from which the total spontaneous emission rate and Lamb shift are calculated. The developed calculation scheme is able to reproduce the known Purcell enhancement factor and is shown to be in agreement with the analysis made for a confocal resonator. It is found that the Lamb shift due to a leaky cavity mode has a sharp drop when sweeping across the resonance point. The physics behind this unusual behavior and the related experimental observations made on both atom-cavity and quantum-dot cavity systems are also analyzed.

Modified spontaneous emissions of europium complex in weak PMMA opals

Engineering spontaneous emission by means of photonic crystals (PHC) is under extensive study. However PHC modification of line emissions of rare earth (RE) ions has not been thoroughly understood, especially in cases of weak opal PHCs and while emitters are well dispersed into dielectric media. In this study, poly-methyl methacrylate (PMMA) opal PHCs containing uniformly dispersed europium chelate were fabricated with finely controlled photonic stop band (PSB) positions. Measurements of luminescent dynamics and angle resolved/integrated emission spectra as well as numerical calculations of total densities of states (DOS) were performed. We determined that in weak opals, the total spontaneous emission rate (SER) of Σ(5)D(0)-(7)F(J) for Eu(3+) was independent of PSB positions but was higher than that of the disordered powder sample, which was attributed to higher effective refractive indices in the PHC rather than PSB effect. Branch SER of (5)D(0)-(7)F(2) for Eu(3+) in the PHCs, on the other hand, was spatially redistributed, suppressed or enhanced in directions of elevated or reduced optical modes, keeping the angle-integrated total unchanged. All the results are in agreement with total DOS approximation. Our paper addressed two unstudied issues regarding modified narrow line emission in weak opal PHCs: firstly whether PSB could change the SER of emitters and whether there exist, apart from PSB, other reasons to change SERs; secondly, while directional enhancement and suppression by PSB has been confirmed, whether the angle-integrated overall effect is enhancing or suppressing.

A coupled gain calculation and output characteristics of the two Ne-like 2s and 2p hole X-ray laser lines

In most collisionally pumped X-ray lasers the lasing transitions considered are a result of collisional excitation of a Ne-like ground state 2p electron into a 3p excited level. However, there are suggestions of producing plasma conditions for collisional pumping of the inner-shell 2s electrons into highly excited 3s levels, with lasing arising as a 2p electron fills the 2s hole. Simulations on various Ne-like ions such as germanium, krypton, and yttrium, using collisional pumping, to get gain on the inner-shell transitions at 62, 50.2, and 42 Å , respectively, have shown gains on the inner-shell transitions up to 30 cm - 1 . It has been suggested that the large Doppler linewidth associated with shorter wavelengths is responsible for the smallness of the small-signal gain in the inner-shell transitions relative to than that predicted for the more usual 2p-hole transitions. However, experimental investigations of this 2s-hole inner-shell laser line, using collisional pumping technique, were unable to register any output. In this paper we report the result of calculations of the gain and the total spontaneous emission rate for the 2s-hole and the 2p-hole X-ray laser lines using a coupled four level model. It is shown that the small-signal gain of the 2s-hole inner-shell transition decreases with increasing pumping rates of the 2p-hole upper and lower levels. The output characteristics of the Ne-like inner-shell transition is simulated using this four-level model and the effects of saturation of the 2p-hole line on the 2s-hole transition is studied showing that the saturation of the former may have a severe effect on the output of the later.

Semiconductor photonic dots: Visible wavelength-sized optical resonators

Here we describe a strategy toward constructing semiconductor photonic dots in the ultraviolet to blue region. An array of ZnS dots was grown on a GaAs substrate with a selective growth method. The ZnS dots have a pyramidal structure with the base plane of 800 nm square and the height of 300 nm. The {034} crystallographic planes form the sidewalls of the pyramids. Therefore, the size of the pyramidal dots is uniquely determined by the mask patterning. The optical reflection spectra showed clear resonance peaks which are reasonably assigned by the calculation of the resonance modes. Each resonance showed the Q values on the order of 160–300, a reasonable value to observe the modification of the total spontaneous emission rate in this kind of photonic dots.

Spontaneous emission from two two-level entangled atoms

The properties of spontaneous emission from two identical two-level entangled atoms interacting with a multimode-vacuum field are reexamined from the view point of the degree of entanglement and the relative phase. We find that the total spontaneous emission rate depends on the degree of entanglement and the relative phase in general, and that in different cases, the positive correlation or the negative correlation exists in the two entangled atoms which leads to the well-known superradiation or subradiation. Moreover, in some cases, the superradiation or subradiation is very dependent on the degree of entanglement and the relative phase. In addition, the decoherence for the four Bell basis states, caused by interaction with the environment, is discussed. Finally, the properties of the spontaneous emission spectra for the triplet states are presented.

Spontaneous-emission coupling from multiemitters to the quasimode of a Fabry-Pérot microcavity.

Using a continuous basis set of optical modes, the spontaneous emission into the lowest-order resonant quasimode of a planar cavity is analyzed for the case of a laterally distributed multiemitter system. We show that for a spatially distributed, randomly phased multiemitter system, the spontaneous rate into the lowest-order cavity quasimode contains a Purcell effect, increases with increasing mode quality factor Q, and saturates when the mode loss becomes less than the dipole dephasing rate. Cooperative effects leading to superradiance for a properly phased multiemitter system are also considered, for which the change in the cavity-confined total spontaneous emission rate can be sizable. \textcopyright{} 1996 The American Physical Society.

On the rate equations of semiconductor lasers for measuring spontaneous emission factor

The rate equations used for measuring spontaneous emission factor /spl beta/ is examined through the comparison of numerical results. The results show that /spl beta/ obtained by using total spontaneous emission rate R/sub sp/=N//spl tau//sub sp/ is about double of that using R/sub sp/=BN/sup 2/. The magnitude difference between the measured /spl beta/ and that predicted by classical theory [8] will disappear by using more reasonable R/sub sp/=BN/sup 2/. The results also show that the magnitude of /spl beta/ may be underestimated by ignoring the nonradiative recombination rates. >

Spectral linewidth in microcavity surface-emitting lasers

The Schawlow–Townes expression for the laser linewidth predicts a substantial cw linewidth enhancement in microcavity lasers, in which a large fraction of spontaneous emission is directed into the lasing mode, in contrast with conventional semiconductor lasers, in which the lasing mode accepts only a tiny fraction of spontaneously emitted photons. By performing a theoretical analysis of rigorous solutions of the wave equation in the surface-emitting cavity and of the band structure in the active region, it is shown that the increase in the linewidth is much slower than the increase in the spontaneous-emission factor β because of reductions in the total spontaneous emission rate, the threshold carrier density, and the linewidth enhancement factor and an increased slope of the light-current characteristic obtained for the microcavity laser in steady state. Also much smaller driving currents in a microcavity laser are required to achieve the same power output compared with conventional semiconductor lasers, resulting in a linewidth of the order of several hundred MHz at moderate driving currents for the former. We also discuss the various factors influencing the linewidth in microcavity and strained quantum well lasers and the relation between lasing threshold and spectral linewidth in both macroscopic and microscopic cavity lasers.

Properties of monolithic integration of a resonant tunneling diode and a quantum well laser

An investigation of the electrical and optical characteristics of a resonant tunneling diode monolithically integrated with a quantum well laser is carried out. An analytic expression for the propagating model current is given in terms of the total spontaneous emission rate. The laser is pumped by the current emitted by the resonant tunneling diode. When the current in the laser exceeds the threshold current, laser light is produced. Since the current in the laser exhibits negative differential resistance similar in behavior to the current of a resonant tunneling diode, a bistable light output can be obtained from this new device.

Approximate dependence of the spontaneous emission rate on electron and hole concentrations

The total spontaneous emission rate (R/sub sp/) is an important quantity, which is widely used in the particle rate equation of light-emitting diodes and semiconductor lasers. It is important to find the explicit dependence of R/sub sp/ on electron and hole concentrations. Such an approximate analytical expression is proposed both for two- and three-dimensional systems. Accuracy of the approximation is within 15% for undoped and 25% for doped semiconductors. Dependence of the relative error on the electron-hole concentrations and a quantitative comparison of the approximate, and exact expressions are illustrated. >

Microcavity semiconductor laser with enhanced spontaneous emission.

A metal-clad optical waveguide with a semiconductor microcavity structure is proposed to increase the coupling efficiency of spontaneous emission into a lasing mode (spontaneous emission coefficient \ensuremath{\beta}) and to increase a total spontaneous emission rate simultaneously. Such a microcavity semiconductor laser with enhanced spontaneous emission has novel characteristics, including high quantum efficiency, low threshold pump rate, broad modulation bandwidth, and intensity noise reduced to below the shot-noise limit (amplitude squeezing).

Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator.

We report the alteration of visible spontaneous emission by atoms coupled to the degenerate modes of a confocal resonator. The partial emission rate into the resonator modes is enhanced by a factor of 19 when the resonator is tuned to the atomic transition frequency and inhibited by a factor of 42 when it is detuned. This results in a fractional increase of 1.6% and decrease of 0.5%, respectively, in the total spontaneous emission rate, which we verify by monitoring changes in the intensity of light emitted out the sides of the resonator as it is tuned.