Strongly Inhibited Spontaneous Emission of PbS Quantum Dots Covalently Bound to 3D Silicon Photonic Band Gap Crystals.

We present an optical study of the spontaneous emission of lead sulfide (PbS) nanocrystal quantum dots in 3D photonic band gap crystals made from silicon. The nanocrystals emit in the near-infrared range to be compatible with 3D silicon nanophotonics. The nanocrystals are covalently bound to polymer brush layers that are grafted from the Si-air interfaces inside the nanostructure by using surface-initiated atom transfer radical polymerization. The presence and position of the quantum dots were previously characterized by synchrotron X-ray fluorescence tomography. We report both continuous wave emission spectra and time-resolved, time-correlated single photon counting. In time-resolved measurements, we observe that the total emission rate greatly increases when the quantum dots are transferred from suspension to the silicon nanostructures, likely due to quenching (or increased nonradiative decay) that is tentatively attributed to the presence of Cu catalysts during the synthesis. In this regime, continuous wave emission spectra are known to be proportional to the radiative rate and thus to the local density of states. In spectra normalized to those taken on flat silicon outside the crystals, we observe a broad and deep stop band that we attribute to a 3D photonic band gap with a relative bandwidth of up to 26%. The shapes of the relative emission spectra match well with the theoretical density of states spectra calculated with plane-wave expansion. The observed inhibition is 4-30 times, similar to previously reported record inhibitions, yet for coincidental reasons. Our results are relevant to applications in photochemistry, sensing, photovoltaics, and efficient miniature light sources.

Unsupervised machine learning to classify the confinement of waves in periodic superstructures.

We propose a rigorous method to classify the dimensionality of wave confinement by utilizing unsupervised machine learning to enhance the accuracy of our recently presented scaling method [Phys. Rev. Lett.129, 176401 (2022)10.1103/PhysRevLett.129.176401]. We apply the standard k-means++ algorithm as well as our own model-based algorithm to 3D superlattices of resonant cavities embedded in a 3D inverse woodpile photonic band gap crystal with a range of design parameters. We compare their results against each other and against the direct usage of the scaling method without clustering. Since the clustering algorithms require the set of confinement dimensionalities present in the system as an input, we investigate cluster validity indices (CVIs) as a means to find these values. We conclude that the most accurate outcome is obtained by first applying direct scaling to find the correct set of confinement dimensionalities, and subsequently utilizing our model-based clustering algorithm to refine the results.

Enhanced secrecy in optical communication using speckle from multiple scattering layers.

We study the secrecy of an optical communication system with two scattering layers, to hide both the sender and receiver, by measuring the correlation of the intermediate speckle generated between the two layers. The binary message is modulated as spatially shaped wavefronts, and the high number of transmission modes of the scattering layers allows for many uncorrelated incident wavefronts to send the same message, making it difficult for an attacker to intercept or decode the message and thus increasing secrecy. We collect 50,000 intermediate speckle patterns and analyze their correlation distribution using the Kolmogorov-Smirnov (K-S) test. We search for further correlations using the K-Means and Hierarchical unsupervised classification algorithms. We find no correlation between the intermediate speckle and the message, suggesting a person-in-the-middle attack is not possible. This method is compatible with any digital encryption method and is applicable for codifications in optical wireless communication (OWC).

Sensing the position of a single scatterer in an opaque medium by mutual scattering.

We investigate the potential of mutual scattering, i.e., light scattering with multiple properly phased incident beams, as a method to extract structural information from inside an opaque object. In particular, we study how sensitively the displacement of a single scatterer is detected in an optically dense sample of many (up to N = 1000) similar scatterers. By performing exact calculations on ensembles of many point scatterers, we compare the mutual scattering (from two beams) and the well-known differential cross-section (from one beam) in response to the change of location of a single dipole inside a configuration of randomly distributed similar dipoles. Our numerical examples show that mutual scattering provides speckle patterns with an angular sensitivity at least 10 times higher than the traditional one-beam techniques. By studying the "sensitivity" of mutual scattering, we demonstrate the possibility to determine the original depth relative to the incident surface of the displaced dipole in an opaque sample. Furthermore, we show that mutual scattering offers a new approach to determine the complex scattering amplitude.

Deep reactive ion etching of cylindrical nanopores in silicon for photonic crystals.

Periodic arrays of deep nanopores etched in silicon by deep reactive ion etching are desirable structures for photonic crystals and other nanostructures for silicon nanophotonics. Previous studies focused on realizing as deep as possible nanopores with as high as possible aspect ratios. The resulting nanopores suffered from structural imperfections of the nanopores, such as mask undercut, uneven and large scallops, depth dependent pore radii and tapering. Therefore, our present focus is to realize nanopores that have as cylindrical as possible shapes, in order to obtain a better comparison of nanophotonic observations with theory and simulations. To this end in our 2-step Bosch process we have improved the mask undercut, the uneven scallops, pore widening and positive tapering by optimizing a plethora of parameters such as the etch step time, capacitively coupled plasma (ion energy) and pressure. To add further degrees of control, we implemented a 3-step DREM (deposit, remove, etch, multistep) process. Optimization of the etching process results in cylindrical nanopores with a diameter in the range between 280 and 500 nm and a depth around 7µm, corresponding to high depth-to-diameter aspect ratios between 14 and 25, that are very well suited for the realization of silicon nanophotonic structures.

Wavefront shaping through a free-form scattering object.

Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are studied are slabs or wave-guides. In this paper, we study how macroscopic changes in the sample shape affect light scattering using the wavefront shaping technique. Using a flexible scattering material, we optimize the intensity of light in a focusing spot using wavefront shaping and record the optimized pattern, comparing the enhancement for different curvatures and beam radii. We validate our hypothesis that wavefront shaping has a similar enhancement regardless of the free-form shape of the sample and thus offers relevant potential for industrial applications. We propose a new figure of merit to evaluate the performance of wavefront shaping for different shapes. Surprisingly, based on this figure of merit, we observe that for this particular sample, wavefront shaping has a slightly better performance for a free-form shape than for a slab shape.

Scaling Theory of Wave Confinement in Classical and Quantum Periodic Systems.

Functional defects in periodic media confine waves-acoustic, electromagnetic, electronic, spin, etc.-in various dimensions, depending on the structure of the defect. While defects are usually modeled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly nontrivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of wave confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities raised to certain powers yield the confinement dimensionality of each band. Our classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave, both quantum and classical, and in any dimension. In the quantum regime, we illustrate our method on electronic confinement in 2D hexagonal boron nitride (BN) with a nitrogen vacancy, in agreement with previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptorlike behavior. We briefly discuss the generalization to quasiperiodic lattices.

Targeted Positioning of Quantum Dots Inside 3D Silicon Photonic Crystals Revealed by Synchrotron X-ray Fluorescence Tomography.

It is a major outstanding goal in nanotechnology to precisely position functional nanoparticles, such as quantum dots, inside a three-dimensional (3D) nanostructure in order to realize innovative functions. Once the 3D positioning is performed, the challenge arises how to nondestructively verify where the nanoparticles reside in the 3D nanostructure. Here, we study 3D photonic band gap crystals made of Si that are infiltrated with PbS nanocrystal quantum dots. The nanocrystals are covalently bonded to polymer brush layers that are grafted to the Si-air interfaces inside the 3D nanostructure using surface-initiated atom transfer radical polymerization (SI-ATRP). The functionalized 3D nanostructures are probed by synchrotron X-ray fluorescence (SXRF) tomography that is performed at 17 keV photon energy to obtain large penetration depths and efficient excitation of the elements of interest. Spatial projection maps were obtained followed by tomographic reconstruction to obtain the 3D atom density distribution with 50 nm voxel size for all chemical elements probed: Cl, Cr, Cu, Ga, Br, and Pb. The quantum dots are found to be positioned inside the 3D nanostructure, and their positions correlate with the positions of elements characteristic of the polymer brush layer and the ATRP initiator. We conclude that X-ray fluorescence tomography is very well suited to nondestructively characterize 3D nanomaterials with photonic and other functionalities.

Tailoring the properties of quantum dot-micropillars by ultrafast optical injection of free charge carriers.

We review recent studies of cavity switching induced by the optical injection of free carriers in micropillar cavities containing quantum dots. Using the quantum dots as a broadband internal light source and a streak camera as detector, we track the resonance frequencies for a large set of modes with picosecond time resolution. We report a record-fast switch-on time constant (1.5 ps) and observe major transient modifications of the modal structure of the micropillar on the 10 ps time scale: mode crossings are induced by a focused symmetric injection of free carriers, while a lifting of several mode degeneracies is observed when off-axis injection breaks the rotational symmetry of the micropillar. We show theoretically and experimentally that cavity switching can be used to tailor the dynamic properties of the coupled QD-cavity system. We report the generation of ultrashort spontaneous emission pulses (as short as 6 ps duration) by a collection of frequency-selected QDs in a switched pillar microcavity. These pulses display a very small coherence length, attractive for ultrafast speckle-free imaging. Moreover, the control of QD-mode coupling on the 10 ps time scale establishes cavity switching as an appealing resource for quantum photonics.

Spatially Shaping Waves to Penetrate Deep inside a Forbidden Gap.

It is well known that waves with frequencies within the forbidden gap inside a crystal are transported only over a limited distance-the Bragg length-before being reflected by Bragg interference. Here, we demonstrate how to send waves much deeper into crystals in an exemplary study of light in two-dimensional silicon photonic crystals. By spatially shaping the wave fronts, the internal energy density-probed via the laterally scattered intensity-is enhanced at a tunable distance away from the front surface. The intensity is up to 100× enhanced compared to random wave fronts, and extends as far as 8× the Bragg length, which agrees with an extended mesoscopic model. We thus report a novel control knob for mesoscopic wave transport that pertains to any kind of waves.

Experimental probe of a complete 3D photonic band gap.

The identification of a complete three-dimensional (3D) photonic band gap in real crystals typically employs theoretical or numerical models that invoke idealized crystal structures. Such an approach is prone to false positives (gap wrongly assigned) or false negatives (gap missed). Therefore, we propose a purely experimental probe of the 3D photonic band gap that pertains to any class of photonic crystals. We collect reflectivity spectra with a large aperture on exemplary 3D inverse woodpile structures that consist of two perpendicular nanopore arrays etched in silicon. We observe intense reflectivity peaks (R>90%) typical of high-quality crystals with broad stopbands. A resulting parametric plot of s-polarized versus p-polarized stopband width is linear ("y=x"), a characteristic of a 3D photonic band gap, as confirmed by simulations. By scanning the focus across the crystal, we track the polarization-resolved stopbands versus the volume fraction of high-index material and obtain many more parametric data to confirm that the high-NA stopband corresponds to the photonic band gap. This practical probe is model-free and provides fast feedback on the advanced nanofabrication needed for 3D photonic crystals and stimulates practical applications of band gaps in 3D silicon nanophotonics and photonic integrated circuits, photovoltaics, cavity QED, and quantum information processing.

Quantitative Determination of Dark Chromophore Population Explains the Apparent Low Quantum Yield of Red Fluorescent Proteins.

The fluorescence quantum yield of four representative red fluorescent proteins mCherry, mKate2, mRuby2, and the recently introduced mScarlet was investigated. The excited state lifetimes were measured as a function of the distance to a gold mirror in order to control the local density of optical states (LDOS). By analyzing the total emission rates as a function of the LDOS, we obtain separately the emission rate and the nonradiative rate of the bright states. We thus obtain for the first time the bright state quantum yield of the proteins without interference from dark, nonemitting states. The bright state quantum yields are considerably higher than previously reported quantum yields that average over both bright and dark states. We determine that mCherry, mKate2, and mRuby2 have a considerable fraction of dark chromophores up to 45%, which explains both the low measured quantum yields of red emitting proteins reported in the literature and the difficulties in developing high quantum yield variants of such proteins. For the recently developed bright mScarlet, we find a much smaller dark fraction of 14%, accompanied by a very high quantum yield of the bright state of 81%. The presence of a considerable fraction of dark chromophores has implications for numerous applications of fluorescent proteins, ranging from quantitative fluorescence microscopy to FRET studies to monitoring protein expression levels. We recommend that future optimization of red fluorescent proteins should pay more attention to minimizing the fraction of dark proteins.

X-ray Imaging of Functional Three-Dimensional Nanostructures on Massive Substrates.

To investigate the performance of three-dimensional (3D) nanostructures, it is vital to study their internal structure with a methodology that keeps the device fully functional and ready for further integration. To this aim, we introduce here traceless X-ray tomography (TXT) that combines synchrotron X-ray holographic tomography with high X-ray photon energies (17 keV) in order to study nanostructures "as is" on massive silicon substrates. The combined strengths of TXT are a large total sample size to field-of-view ratio and a large penetration depth. We study exemplary 3D photonic band gap crystals made by CMOS-compatible means and obtain real space 3D density distributions with 55 nm spatial resolution. TXT identifies why nanostructures that look similar in electron microscopy have vastly different nanophotonic functionality: one "good" crystal with a broad photonic gap reveals 3D periodicity as designed; a second "bad" structure without a gap reveals a buried void, and a third "ugly" one without gap is shallow due to fabrication errors. Thus, TXT serves to nondestructively differentiate between the possible reasons of not finding the designed and expected performance and is therefore a powerful tool to critically assess 3D functional nanostructures.

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals.

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size L of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a 1/L scale dependence for crystals in one, two and three dimensions.

Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes.

We study the energy density of shaped waves inside a quasi-1D disordered waveguide. We find that the spatial energy density of optimally shaped waves, when expanded in the complete set of eigenfunctions of the diffusion equation, is well described by considering only a few of the lowest eigenfunctions. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtain the energy density of transmission eigenchannels inside the sample by numerical simulation of the scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results of our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

Optimal all-optical switching of a microcavity resonance in the telecom range using the electronic Kerr effect.

We have switched GaAs/AlAs and AlGaAs/AlAs planar microcavities that operate in the "Original" (O) telecom band by exploiting the instantaneous electronic Kerr effect. We observe that the resonance frequency reversibly shifts within one picosecond when the nanostructure is pumped with low-energy photons. We investigate experimentally and theoretically the role of several parameters: the material backbone and its electronic bandgap, the quality factor, and the duration of the switch pulse. The magnitude of the frequency shift is reduced when the backbone of the central λ-layer has a greater electronic bandgap compared to the cavity resonance frequency and the frequency of the pump. This observation is caused by the fact that pumping with photon energies near the bandgap resonantly enhances the switched magnitude. We thus find that cavities operating in the telecom O-band are more amenable to ultrafast Kerr switching than those operating at lower frequencies, such as the C-band. Our results indicate that the large bandgap of AlGaAs/AlAs cavity allows to tune both the pump and the probe to the telecom range to perform Kerr switching without detrimental two-photon absorption. We observe that the magnitude of the resonance frequency shift decreases with increasing quality factor of the cavity. Our model shows that the magnitude of the resonance frequency shift depends on the pump pulse duration and is maximized when the duration matches the cavity storage time to within a factor two. In our experiments, we obtain a maximum shift of the cavity resonance relative to the cavity linewidth of 20%. We project that the shift of the cavity resonance can be increased twofold with a pump pulse duration that better matches the cavity storage time. We provide the essential parameter settings for different materials so that the frequency shift of the cavity resonance can be maximized using the electronic Kerr effect.

Observation of intensity statistics of light transmitted through 3D random media.

We experimentally observe the spatial intensity statistics of light transmitted through three-dimensional (3D) isotropic scattering media. The intensity distributions measured through layers consisting of zinc oxide nanoparticles differ significantly from the usual Rayleigh statistics associated with speckle and instead are in agreement with the predictions of mesoscopic transport theory, taking into account the known material parameters of the samples. Consistent with the measured spatial intensity fluctuations, the total transmission fluctuates. The magnitude of the fluctuations in the total transmission is smaller than expected on the basis of quasi-one-dimensional (1D) transport theory, which indicates that quasi-1D theories cannot fully describe these open 3D media.

Non-exponential spontaneous emission dynamics for emitters in a time-dependent optical cavity.

We have theoretically studied the effect of deterministic temporal control of spontaneous emission in a dynamic optical microcavity. We propose a new paradigm in light emission: we envision an ensemble of two-level emitters in an environment where the local density of optical states is modified on a time scale shorter than the decay time. A rate equation model is developed for the excited state population of two-level emitters in a time-dependent environment in the weak coupling regime in quantum electrodynamics. As a realistic experimental system, we consider emitters in a semiconductor microcavity that is switched by free-carrier excitation. We demonstrate that a short temporal increase of the radiative decay rate depletes the excited state and drastically increases the emission intensity during the switch time. The resulting time-dependent spontaneous emission shows a distribution of photon arrival times that strongly deviates from the usual exponential decay: A deterministic burst of photons is spontaneously emitted during the switch event.

Optimal control of light propagation through multiple-scattering media in the presence of noise.

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting.

We study the diffuse transport of light through polymer slabs containing TiO(2) scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470-840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 µm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 µm) consist of clusters of small particles (R<0.13 µm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.