Optical antenna enhanced spontaneous emission

Atoms and molecules are too small to act as efficient antennas for their own emission wavelengths. By providing an external optical antenna, the balance can be shifted; spontaneous emission could become faster than stimulated emission, which is handicapped by practically achievable pump intensities. In our experiments, InGaAsP nanorods emitting at ∼200 THz optical frequency show a spontaneous emission intensity enhancement of 35× corresponding to a spontaneous emission rate speedup ∼115×, for antenna gap spacing, d = 40 nm. Classical antenna theory predicts ∼2,500× spontaneous emission speedup at d ∼ 10 nm, proportional to 1/d². Unfortunately, at d < 10 nm, antenna efficiency drops below 50%, owing to optical spreading resistance, exacerbated by the anomalous skin effect (electron surface collisions). Quantum dipole oscillations in the emitter excited state produce an optical ac equivalent circuit current, I_o = qω|x_o|/d, feeding the antenna-enhanced spontaneous emission, where q|x_o| is the dipole matrix element. Despite the quantum-mechanical origin of the drive current, antenna theory makes no reference to the Purcell effect nor to local density of states models. Moreover, plasmonic effects are minor at 200 THz, producing only a small shift of antenna resonance frequency.Antennas emerged at the dawn of radio, concentrating electromagnetic energy within a small volume <<λ³, enabling nonlinear radio detection. Such coherent detection is essential for radio receivers and has been used since the time of Hertz (1). Conversely, an antenna can efficiently extract radiation from a subwavelength source, such as a small cellphone. Despite the importance of radio antennas, 100 y went by before optical antennas began to be used to help extract optical frequency radiation from very small sources such as dye molecules (2–10) and quantum dots (11–14).In optics, spontaneous emission is caused by dipole oscillations in the excited state of atoms, molecules, or quantum dots. The main problem is that a molecule is far too small to act as an efficient antenna for its own electromagnetic radiation. Antenna length, l, makes a huge difference in radiation rate. An ideal antenna would preferably be λ/2, a half-wavelength in size. To the degree that an atomic dipole of length l is smaller than λ/2, the antenna radiation rate Δω is proportional to ω(l/λ)³, as given by the Wheeler limit (15). Spontaneous emission from molecular-sized radiators is thus slowed by many orders of magnitude, because radiation wavelengths are much larger than the atoms themselves. Therefore, the key to speeding up spontaneous emission is to couple the radiating molecule to a proper antenna of sufficient size.Since the emergence of lasers in 1960, stimulated emission has been faster than spontaneous emission. Now the opposite is possible. In the right circumstances, antenna-enhanced spontaneous emission could become faster than stimulated emission. Theoretically, very large bandwidth >100 GHz or >1 THz is possible when the light emitter is coupled to a proper optical antenna (16).Metal optics have been able to shrink lasers to the nanoscale (17–20), but high losses in metal-based cavities make it increasingly difficult to achieve desirable performance. Metal structures have also been used to enhance the spontaneous emission rate, such as by coupling excited material to flat surface plasmon waves (21–28). Flat metal surfaces are far from ideal antennas, resulting in low radiation efficiencies and large ohmic losses. Semiconductor emitters have been further limited by large surface recombination losses and by processing difficulties at the extremely small dimensions. Semiconductor experiments (29, 30) show weak antenna–emitter coupling, with the antenna enhancement sometimes masked by metal-induced elastic scattering that enhances light extraction from the semiconductor substrate. Light extraction alone can increase optical emission by 4n², as often used in commercial light-emitting diodes (LEDs), without necessarily modifying the spontaneous emission rate (31, 32).In this article, we elucidate the physics of antenna-enhanced spontaneous emission, using a traditional antenna circuit model, not the Purcell effect (33) nor a local density-of-states model (34). We use the circuit approach to analyze for the maximum possible spontaneous emission enhancement in the presence of spreading resistance losses (35) and the nonlocal anomalous skin effect (36) in the metal.We experimentally tested an optical dipole antenna, coupled to a “free-standing” 40-nm nanorod of semiconductor material. Thus far, optical emission measurements show a >115× antenna spontaneous emission rate enhancement factor compared with no antenna at all. At smaller dimensions, circuit theory predicts a spontaneous emission rate enhancement >10⁴×, but at the penalty of decreased antenna efficiency. Nonetheless, we will derive that >2,500× rate enhancement should be possible, while still maintaining antenna efficiency >50%.     

Plasmonic photonic crystals realized through DNA-programmable assembly

Three-dimensional dielectric photonic crystals have well-established enhanced light–matter interactions via high Q factors. Their plasmonic counterparts based on arrays of nanoparticles, however, have not been experimentally well explored owing to a lack of available synthetic routes for preparing them. However, such structures should facilitate these interactions based on the small mode volumes associated with plasmonic polarization. Herein we report strong light-plasmon interactions within 3D plasmonic photonic crystals that have lattice constants and nanoparticle diameters that can be independently controlled in the deep subwavelength size regime by using a DNA-programmable assembly technique. The strong coupling within such crystals is probed with backscattering spectra, and the mode splitting (0.10 and 0.24 eV) is defined based on dispersion diagrams. Numerical simulations predict that the crystal photonic modes (Fabry–Perot modes) can be enhanced by coating the crystals with a silver layer, achieving moderate Q factors (∼10²) over the visible and near-infrared spectrum.Enhancing light–matter interactions is essential in photonics, including areas such as nonlinear optics (1), quantum optics (2, 3), and high-Q lasing (4). In general, there are two ways of achieving this in optical cavities: (i) with long cavity lifetimes (high Q factors) and (ii) with strong photonic confinement (small mode volume, V) (2, 3). In particular, 3D dielectric photonic crystals, with symmetry-induced photonic band gaps (Bragg gaps), enhance light–matter interactions via high Q factors (4–6). However, the coupling strength between photons and electronic transitions within such systems is intrinsically weak owing to diffraction-limited photonic confinement (3, 7). Recently, it was suggested that a plasmonic counterpart of photonic crystals can prohibit light propagation and open a photonic band gap by strong coupling between surface plasmons and photonic modes (a polariton gap) if the crystal is in deep subwavelength size regime (8); these crystals have been referred to as polaritonic photonic crystals (PPCs) (9–12). This opens up the exciting possibility of combining plasmonics with 3D photonics in the strong coupling regime and optimizing the photonic crystals as small-mode-volume devices owing to the strong plasmonic mode confinement (13). However, such systems require control over the positioning of the plasmonic elements in the crystal on the nano- or deep subwavelength scale (8), and owing to this synthetic challenge such 3D PPCs have largely remained unexplored in the visible wavelength range.The recent discovery that DNA can be used to program the assembly of high-quality single crystals with well-defined crystal habits consisting of nanoparticles occupying sites in a preconceived lattice (14) opens up possibilities for fine tuning the interaction between light and highly organized collections of particles as a function of lattice constant and particle size. Here, we report that 3D plasmonic photonic crystals made by DNA-programmable assembly can be used to establish strong light–plasmon coupling with tunability based upon the DNA interconnects and the corresponding volume fraction of the plasmonic elements. The strong coupling is manifested in crystal backscattering spectra and mode splitting (0.10 and 0.24 eV) in dispersion diagrams. Simulation results that we also include show that, by coating the crystals with a silver layer, Fabry–Perot photonic modes of crystals can be enhanced, with moderate cavity Q factors (∼10²) over the visible and near-infrared (NIR) spectrum. In addition to being the first devices made by DNA-programmable colloidal crystallization, they illustrate the potential of the technique for making novel 3D crystals for photonic studies and applications.The plasmonic PPCs are synthesized from two batches of gold nanoparticles, each functionalized with oligonucleotide sequences that are hybridized to complementary linker sequences that induce the assembly of the particles into rhombic dodecahedra single crystals with a body-centered-cubic (BCC) arrangement of the particles (14) (Supporting Information, sections S1 and S2, Fig. S1, and Tables S1 and S2). The lattice constants and gold nanoparticle diameters of the three PPCs that we present (denoted PPC1, PPC2, and PPC3) are 27.2 and 5.6 nm, 32.2 and 9.0 nm, and 44.0 and 20.0 nm, respectively, resulting in substantially different gold volume fractions (PPC1 ∼0.91, PPC2 ∼2.3, and PPC3 ∼9.8%).PPCs can exhibit Fabry–Perot cavity modes (FPMs) owing to light interference induced by two parallel facets (15) in the microcavity geometry (Fig. 1 A and B) as long as the size of the PPCs is much larger than the wavelength of light (Supporting Information, section S3 and Fig. S2). FPMs can be detected via backscattering spectra (16) (Fig. 1 A and B) and allow one to probe the optical response of the PPCs. Importantly, within the PPCs the propagating photonic modes are expected to strongly couple to the gold nanoparticle surface plasmons (Fig. 1 B and C), forming a polariton band gap (8, 17). This is probed by optical experiments and theoretical calculations (Fig. 2, Supporting Information, sections S4–S6, and Figs. S3–S6). The backscattering spectra from the PPC center spots (Fig. 2 A, C, and E, Bottom) show Fabry–Perot interference patterns in the visible region (Fig. 2 B, D, and F, red lines). The agreement between a finite-difference time-domain (FDTD) simulation with a rhombic dodecahedron shape and an infinite slab model (Supporting Information, section S5 and Fig. S5) reveals the Fabry–Perot nature of these backscattering spectra, because FPMs are the only existing modes in the infinite slab geometry. Significantly, the Fabry–Perot oscillations are suppressed only around the surface plasmon resonance energy (∼530 nm; ∼2.3 eV) for PPC1 and PPC2, indicating the suppression of light propagation owing to coupling to surface plasmons. This behavior provides direct evidence for polariton band gap formation that is consistent with the theoretical predictions (8, 9, 18). These experimental results are in remarkably good agreement with two different infinite slab models, one with BCC crystal geometry and the other an effective medium theory (EMT) approximation that is based simply on the gold volume fraction without the effect of interparticle coupling (Fig. 2 B, D, and F; blue solid and dashed lines). For PPC3, FPMs are not observed below 500 nm (Fig. 2F) because of the strong absorption caused by the gold interband transition at relatively higher gold volume fraction. The discrepancy between the two models in FPM cutoff location (Fig. 2F, denoted by the two vertical lines) indicates that a considerable amount of interparticle coupling exists close to the surface plasmon resonance because EMT does not include interparticle coupling.Open in a separate windowFig. 1.A polaritonic photonic crystal made by DNA-programmable assembly. (A) Three-dimensional illustration of a plasmonic PPC, in the shape of a rhombic dodecahedron, assembled from DNA-modified gold nanoparticles. Red arrows indicate light rays normal to the underlying substrate, impinging on and backscattering through a top facet of the crystal (FPMs). The blue ones represent light rays entering through the slanted side facets and leaving the PPC through the opposite side, not contributing to the FPMs (Fig. S2). The top right inset shows the top view of the crystal with two sets of arrows defining two polarization bases at the top and side facets. The bottom right inset shows an SEM image of a representative single crystal corresponding to the orientation of the top right inset. (Scale bar, 1 µm.) (B) A 2D scheme showing the geometric optics approximation of backscattering consistent with the explanation in A. The hexagon outline is a vertical cross-section through the gray area in the top right inset of A parallel to its long edge. The box enclosed by a dashed line depicts the interaction between localized surface plasmons and photonic modes (red arrows; FPMs) with a typical near-field profile around gold nanoparticles. The contribution of backscattering through the side facets (blue arrows) to FPMs is negligible. (C) Scheme of plasmon polariton formation. The localized surface plasmons (yellow bar) strongly couple to the photonic modes (red bars; FPMs).Open in a separate windowFig. 2.Experimental and theoretical backscattering spectra of PPC1–3. (A) SEM image (Top) and optical bright field reflection mode image (Bottom) of PPC1 on a silicon substrate. (Scale bar, 1 µm.) (B) Measured backscattering spectrum (red solid line) of PPC1 from the center red spot in A, Bottom. Calculated backscattering spectra based on two infinite slab models with BCC crystal geometry (blue solid line) and EMT approximation (blue dashed line). FPMs are indicated by markers. (C–F) The same datasets for PPC2 and PPC3 as in A and B. PPC2 and PPC3 are on indium tin oxide (ITO)-coated glass slides. The optical images show bright spots at the center owing to backscattering from the top and bottom facets. Two vertical lines in F indicate spectral positions where FPMs are suppressed. (Scale bars, 1 µm.)Based on the spectral results, we examine the strong coupling behavior between the surface plasmons and FPMs in the PPCs with dispersion diagrams generated by FDTD photonic crystal analyses, including changes in the light–matter interactions by tailoring the lattice constant and gold nanoparticle size (Fig. 3 and Supporting Information, section S5). When the mode energies of PPC1 and PPC2 grow close to that of the localized surface plasmon resonance (LSPR), ?ω₀ (∼2.3 eV), the dispersion curves of the propagating modes form band gaps (Fig. 3 A and B). This is clearer in the absence of interband transition (insets of Fig. 3 A–C and Fig. S7 A–F). The origin of these band gaps is not the BCC translational symmetry of the crystals (Bragg gap) as in conventional dielectric photonic crystals (6). For Bragg gap formation in the visible, photonic crystals require a lattice constant an order of magnitude larger than those in this work (∼λ/2). Instead, the origin of the gaps is strong coupling between the surface plasmons and photonic modes owing to deep subwavelength lattice constants that define the separation of the polarizable particle components (high-density localized surface plasmons) (8, 9). In each crystal type (Fig. 3 A and B), coupling of this kind creates plasmon polaritons with anticrossing upper and lower branches in the dispersion diagrams forming a polariton band gap between the two branches, where propagating photonic modes are prohibited (8, 9, 17). The strength of the coupling is quantified by the mode splitting, ?Ω_R, (Supporting Information, section S7 and Fig. S7), which is the energy gap between the two branches at the resonant coupling point (17) (?Ω_R∼0.10 and 0.24 eV for PPC1 and PPC2, which are about ∼5 and ∼10% of ?ω₀; Fig. 3D). These mode splittings are comparable to a recently reported value based on 1D nanowire arrays on waveguide substrates (17). The EMT-generated curve without the effect of the interband transition (9) predicts a monotonically increasing mode splitting with the increase in gold volume fraction (1–10%; Fig. 3D), which agrees well with the FDTD photonic crystal analyses (Supporting Information, sections S6 and S7 and Fig. S7). This suggests the possibility of using metal volume fraction as a parameter to control coupling strength based on fine geometric tuning afforded by the DNA-programmable assembly technique (19). For PPC3, owing to the strong gold interband transition the upper branch in the dispersion diagram (Fig. 3C; <500 nm in Fig. 2F) is not clearly observable in the experiment, and therefore the mode splitting is not measurable. Based on a photonic crystal analysis without the presence of interband transitions, the upper branch of PPC3 is observed (Fig. 3C, Inset), and the mode splitting is ∼30% of ?ω₀ (Supporting Information, section S7 and Fig. S7). This large value arises due to the capability of the PPCs to coherently couple a large number of oscillators within a single microcavity.Open in a separate windowFig. 3.Calculated photonic mode dispersion, mode splitting, and effective mode index of PPC1–3. (A) The spectral density in the ΓN direction is presented for PPC1 (red is high, blue is low). Log10 scale is used. Red triangular markers are the FPMs in Fig. 2B (red markers). They are assigned to peak positions of the spectral densities and the mode number (N) is assigned on one FPM. (Inset) The same spectral density calculated based on the Drude model for gold (where there is no interband transition). (B and C) The same information as in A for PPC2 and PPC3. (D) The mode splitting to plasmonic mode energy ratio, ?Ω_R/?ω₀, is shown in terms of gold volume fraction. Blue dots are calculated based on EMT with the Drude model for gold. Squares are generated by a FDTD photonic crystal analysis with the Drude model for gold (red, green, and black: nanoparticle diameters 5.6, 9.0, and 20 nm; volume fraction of PPC3 indicated for 20 nm), and circles with experimentally measured gold permittivity (red and green: nanoparticle diameters 5.6 and 9.0 nm; PPC1 and PPC2). (E) EMT-based effective indices, Re[n_eff], for PPC1 (dotted line), PPC2 (dash-dot line), and PPC3 (dashed line). The index of the silica host medium (black solid line) is added as a reference. Red markers are Re[n_eff] based on the FPMs in A–C.Significantly, the strong coupling that we observe is further evidenced by quantifying the effective mode indices, Re[n_eff] (Fig. 3E). As the gold volume fraction increases to that of PPC3, the effective mode index drastically increases (Re[n_eff] ∼2) close to the LSPR frequency, indicating strong light coupling to surface plasmons and a large mode momentum gain (18, 20, 21). This is also apparent in the spectral profile, which shows an abrupt suppression of FPMs (two vertical lines in Fig. 2F) and a sharp increase in reflectance from 650 to 550 nm. This transition from Fabry–Perot to mirror-like behavior is due to an increase in both Re[n_eff] and Im[n_eff] close to the LSPR frequency (Fig. S6) that causes strong facet reflection and damping of the FPMs (18).The PPCs with lattice constants in the deep subwavelength regime can also behave as plasmonic cavity devices for studies such as cavity quantum electrodynamics (QED) (3, 22, 23). The plasmonic PPCs have, within a single structure, optical elements working on two different length scales: the plasmonic nanoparticles and the Fabry–Perot microcavity. Owing to localized surface plasmons, the gold nanoparticles exhibit extremely tight light confinement [a small mode volume, V <10⁻⁴(λ/n) (3), in the visible and NIR] around their metallic surfaces that augments light–matter interactions such as exciton–photon coupling (13, 24). These highly confined modes can be further enhanced (23, 25) if Q factors of Fabry–Perot modes are increased by coating the crystals with a silver layer (10–30 nm) (see Fig. S8 for the calculation approach and Figs. S9 and S10 for the experimental process). By simplifying the 3D shape of PPCs to a slab we can use the infinite slab model with a BCC crystal geometry to predict moderate Q factors (∼10²) of FPMs with varying silver layer thickness in the visible and NIR for PPC1–3 (Fig. 4). At ∼30-nm silver layer thickness, the Q factor saturates, and PPC1 exhibits the highest Q values owing to the lowest gold volume fraction. These numbers (∼10²; Fig. 4) are comparable to those of other plasmonic cavities in the literature (20, 23). This shows the possibility of tuning not just plasmonic modes by controlling BCC crystals but also enhancing the properties of photonic modes (FPMs) for further applications with excitonic materials such as dyes and quantum dots (26).Open in a separate windowFig. 4.Prediction of backscattering spectra and Q factor of silver-coated PPC1–3. (A) Backscattering spectra of PPC1–3 (from bottom to top: PPC1, PPC2, and PPC3) based on the infinite slab model with BCC crystal geometry. The thickness of the slabs is ∼1.3 µm, and that of silver coating layer is varied from 10 to 30 nm. As the coating thickness increases the line shape becomes sharper. The spectra of PPC1 and 2 are translated for comparison. (B) Q factors of each silver-coated slab are shown at FPMs (PPC1, red; PPC2, green; and PPC3, blue). The coating thickness is 30 nm.This work has shown how bioprogrammable colloidal crystallization can be used to access a new class of PPCs and related optical devices. Although the ability to create well-formed crystals via this technique is essential, it is the ability to tune light–plasmon coupling and plasmonic particle volume fraction that makes this approach so powerful from both fundamental science and potential device application standpoints. We anticipate that the studies herein and the single crystals realizable through the methodology will open the door to studying exciton–photon coupling in novel PPC plasmonic cavities and lead to new directions in cavity QED (22, 27), quantum optics (28–30), and quantum many-body dynamics (31, 32).     

Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers

High harmonic generation driven by femtosecond lasers makes it possible to capture the fastest dynamics in molecules and materials. However, to date the shortest subfemtosecond (attosecond, 10⁻¹⁸ s) pulses have been produced only in the extreme UV region of the spectrum below 100 eV, which limits the range of materials and molecular systems that can be explored. Here we experimentally demonstrate a remarkable convergence of physics: when midinfrared lasers are used to drive high harmonic generation, the conditions for optimal bright, soft X-ray generation naturally coincide with the generation of isolated attosecond pulses. The temporal window over which phase matching occurs shrinks rapidly with increasing driving laser wavelength, to the extent that bright isolated attosecond pulses are the norm for 2-µm driving lasers. Harnessing this realization, we experimentally demonstrate the generation of isolated soft X-ray attosecond pulses at photon energies up to 180 eV for the first time, to our knowledge, with a transform limit of 35 attoseconds (as), and a predicted linear chirp of 300 as. Most surprisingly, advanced theory shows that in contrast with as pulse generation in the extreme UV, long-duration, 10-cycle, driving laser pulses are required to generate isolated soft X-ray bursts efficiently, to mitigate group velocity walk-off between the laser and the X-ray fields that otherwise limit the conversion efficiency. Our work demonstrates a clear and straightforward approach for robustly generating bright isolated attosecond pulses of electromagnetic radiation throughout the soft X-ray region of the spectrum.High-order harmonic generation (HHG) is the most extreme nonlinear optical process in nature, making it possible to coherently upconvert intense femtosecond laser light to much shorter wavelengths (1, 2). High harmonics are radiated as a result of a coherent electron recollision process that occurs each half-cycle of the driving laser field while an atom is undergoing strong-field ionization. The short pulse duration of HHG (which must be shorter than the driving laser pulse) has made it possible to directly access the fastest timescales relevant to electron dynamics in atoms, molecules, and materials. The unique properties of attosecond HHG in the extreme UV (EUV) have uncovered new understanding of fundamental processes in atoms, molecules, plasmas, and materials, including the timescales on which electrons are emitted from atoms (3), the timescale for spin–spin and electron–electron interactions (4, 5), the timescale that determines molecular dissociation and electron localization (6–9), the timescale and mechanisms for spin and energy transport in nanosystems (10–12), as well as new capabilities to implement EUV microscopes with wavelength-limited spatial resolution (13).The temporal structure of HHG is related to the number of times a high-energy electron undergoes a coherent recollision process, as well as the time window over which bright harmonics emerge. Using multicycle 0.8-µm driving lasers, HHG generally emerges as a train of attosecond (as) pulses (14, 15) corresponding to a series of harmonic peaks in frequency space. This emission can narrow to a single isolated as burst when the driving laser field is a few optical cycles (∼5 fs) in duration (16, 17), with an associated broad continuous spectrum. Other techniques can isolate a single burst using a combination of multicolor fields and polarization control (18–26) or spatial lighthouse gating of the driving laser pulses (27, 28). Phase matching can also result in bright isolated as pulse generation for short driving laser pulses (29, 30). To obtain bright, phase-matched, high harmonic beams, the laser and HHG fields must both propagate at the speed of light c so that emission from many atoms interferes constructively. Above a critical ionization level, the phase velocity of the laser exceeds c, which terminates the HHG temporal emission. The chirp present on attosecond bursts can be compensated by using thin materials, gases, or chirped mirrors (31–33). To date, however, most schemes for creating isolated attosecond pulses require either very short-duration few-cycle 0.8-µm driving laser pulses that are difficult to reliably generate, or complex polarization modulation schemes. In addition, the carrier envelope phase (CEP) of the driving laser pulse must be stabilized.A more general understanding of how to efficiently sculpt the temporal, spatial, and spectral characteristics of HHG emission over an extremely broad photon energy range (from the EUV to the keV and higher) has emerged in recent years (34–39). This understanding is critical both for a fundamental understanding of strong-field quantum physics, as well as for applications which have fundamentally different needs in terms of the HHG pulse duration, spectral bandwidth, and flux. By considering both the microscopic single-atom response as well as the macroscopic coherent buildup of HHG, efficient phase-matched HHG can now be implemented from the EUV to >keV photon energies, simply by driving HHG with midinfrared (mid-IR) femtosecond driving lasers. This advance represents, to our knowledge, the first general-purpose, tabletop, coherent soft X-ray light source (39). Furthermore, theory suggested that bright isolated attosecond X-ray bursts would be achievable using multicycle mid-IR driving lasers in a phase-matched geometry (35). However, the low repetition rate of the driving lasers precluded experimental testing of these predictions. Moreover, formidable computation requirements meant that advanced simulations could not be fully extended into the mid-IR region at 2–4 µm.In this paper, we experimentally demonstrate a beautiful convergence of physics for mid-IR (2-µm) driving lasers by showing that the conditions for optimal bright, soft X-ray generation naturally coincide with the generation of bright isolated attosecond soft X-ray bursts. We combine advanced theory with a novel experimental method equivalent to high-resolution Fourier transform spectroscopy to measure bright, attosecond soft X-ray pulses for the first time, to our knowledge. Specifically, we measure a field autocorrelation pulse width of 70 as, corresponding to a transform-limited 35-as pulse, that is supported by a coherent supercontinuum spectrum extending to photon energies around 180 eV. We also validate experimentally, for the first time, to our knowledge, the most intuitive dynamic picture of phase matching of HHG in the time domain by clearly demonstrating that the temporal window during which phase matching occurs shrinks rapidly with increasing driving laser wavelength. Finally, we show through advanced theory that the isolated attosecond pulse is chirped to 300 as. Most surprisingly, we find that bright attosecond pulse generation in the soft X-ray region requires the use of longer-duration, multicycle, mid-IR driving lasers to mitigate group velocity walk-off issues that would otherwise reduce the conversion efficiency. By harnessing the beautiful physics of phase matching, this work represents the simplest and most robust scheme for attosecond soft X-ray pulse generation, and will make attosecond science and technology accessible to a broader community.     

Visible Light Trapping against Charge Recombination in FeOx–TiO2 Photonic Crystal Photocatalysts

Tailoring metal oxide photocatalysts in the form of heterostructured photonic crystals has spurred particular interest as an advanced route to simultaneously improve harnessing of solar light and charge separation relying on the combined effect of light trapping by macroporous periodic structures and compositional materials’ modifications. In this work, surface deposition of FeO_x nanoclusters on TiO₂ photonic crystals is investigated to explore the interplay of slow-photon amplification, visible light absorption, and charge separation in FeO_x–TiO₂ photocatalytic films. Photonic bandgap engineered TiO₂ inverse opals deposited by the convective evaporation-induced co-assembly method were surface modified by successive chemisorption-calcination cycles using Fe(III) acetylacetonate, which allowed the controlled variation of FeO_x loading on the photonic films. Low amounts of FeO_x nanoclusters on the TiO₂ inverse opals resulted in diameter-selective improvements of photocatalytic performance on salicylic acid degradation and photocurrent density under visible light, surpassing similarly modified P25 films. The observed enhancement was related to the combination of optimal light trapping and charge separation induced by the FeO_x–TiO₂ interfacial coupling. However, an increase of the FeO_x loading resulted in severe performance deterioration, particularly prominent under UV-Vis light, attributed to persistent surface recombination via diverse defect d-states.     

Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum

We show how bright, tabletop, fully coherent hard X-ray beams can be generated through nonlinear upconversion of femtosecond laser light. By driving the high-order harmonic generation process using longer-wavelength midinfrared light, we show that, in theory, fully phase-matched frequency upconversion can extend into the hard X-ray region of the spectrum. We verify our scaling predictions experimentally by demonstrating phase matching in the soft X-ray region of the spectrum around 330 eV, using ultrafast driving laser pulses at 1.3-μm wavelength, in an extended, high-pressure, weakly ionized gas medium. We also show through calculations that scaling of the overall conversion efficiency is surprisingly favorable as the wavelength of the driving laser is increased, making tabletop, fully coherent, multi-keV X-ray sources feasible. The rapidly decreasing microscopic single-atom yield, predicted for harmonics driven by longer-wavelength lasers, is compensated macroscopically by an increased optimal pressure for phase matching and a rapidly decreasing reabsorption of the generated X-rays.     

From the Cover: The liquid-liquid phase transition in silicon revealed by snapshots of valence electrons

The basis for the anomalies of water is still mysterious. Quite generally tetrahedrally coordinated systems, also silicon, show similar thermodynamic behavior but lack—like water—a thorough explanation. Proposed models—controversially discussed—explain the anomalies as a remainder of a first-order phase transition between high and low density liquid phases, buried deeply in the “no man’s land”—a part of the supercooled liquid region where rapid crystallization prohibits any experimental access. Other explanations doubt the existence of the phase transition and its first-order nature. Here, we provide experimental evidence for the first-order-phase transition in silicon. With ultrashort optical pulses of femtosecond duration we instantaneously heat the electronic system of silicon while the atomic structure as defined by the much heavier nuclear system remains initially unchanged. Only on a picosecond time scale the energy is transferred into the atomic lattice providing the energy to drive the phase transitions. With femtosecond X-ray pulses from FLASH, the free-electron laser at Hamburg, we follow the evolution of the valence electronic structure during this process. As the relevant phases are easily distinguishable in their electronic structure, we track how silicon melts into the low-density-liquid phase while a second phase transition into the high-density-liquid phase only occurs after the latent heat for the first-order phase transition has been transferred to the atomic structure. Proving the existence of the liquid-liquid phase transition in silicon, the hypothesized liquid-liquid scenario for water is strongly supported.     

Ab initio study of hot electrons in GaAs

Hot carrier dynamics critically impacts the performance of electronic, optoelectronic, photovoltaic, and plasmonic devices. Hot carriers lose energy over nanometer lengths and picosecond timescales and thus are challenging to study experimentally, whereas calculations of hot carrier dynamics are cumbersome and dominated by empirical approaches. In this work, we present ab initio calculations of hot electrons in gallium arsenide (GaAs) using density functional theory and many-body perturbation theory. Our computed electron–phonon relaxation times at the onset of the Γ, L, and X valleys are in excellent agreement with ultrafast optical experiments and show that the ultrafast (tens of femtoseconds) hot electron decay times observed experimentally arise from electron–phonon scattering. This result is an important advance to resolve a controversy on hot electron cooling in GaAs. We further find that, contrary to common notions, all optical and acoustic modes contribute substantially to electron–phonon scattering, with a dominant contribution from transverse acoustic modes. This work provides definitive microscopic insight into hot electrons in GaAs and enables accurate ab initio computation of hot carriers in advanced materials.Hot carriers (HCs) generated by the absorption of light or injection at a contact are commonly found in many advanced technologies (1–9). In electronics, the operation of high-speed devices is controlled by HC dynamics, and HC injection is a key degradation mechanism in transistors (10, 11). In solar cells and plasmonics, recent work has focused on extracting the kinetic energy of HCs before cooling (7, 9), a process defined here as the energy loss of HCs, ultimately leading to thermal equilibrium with phonons. HC dynamics is also crucial to interpret time-resolved spectroscopy experiments used to study excited states in condensed matter (12). This situation has sparked a renewed interest in HCs in a broad range of materials of technological relevance.Experimental characterization of HCs is challenging because of the subpicosecond timescale associated with the electron–phonon (e-ph) and electron–electron (e-e) scattering processes regulating HC dynamics. For example, HCs can be studied using ultrafast spectroscopy, but microscopic interpretation of time-resolved spectra requires accurate theoretical models. However, modeling of HCs thus far has been dominated by empirical approaches, which do not provide atomistic details and use ad hoc parameters to fit experiments (13, 14). Notwithstanding the pioneering role of these early studies, the availability of accurate ab initio computational methods based on density functional theory (DFT) (15) and many-body perturbation theory (16) enables studies of HCs with superior accuracy, broad applicability, and no need for fitting parameters.Hot electrons in gallium arsenide (GaAs) are of particular interest because of the high electron mobility and multivalley character of the conduction band. Electrons excited at energies greater than ∼0.5 eV above the conduction band minimum (CBM) can transfer from the Γ to the L and X valleys, with energy minima at ∼0.25 and ∼0.45 eV above the CBM, respectively (17). Such intervalley scattering processes play a crucial role in hot electron cooling and transport at high electric fields.Ample experimental data exist on hot electron transport and cooling in GaAs (12, 18–21). The interpretation of these experiments relies on Monte Carlo simulations using multiple parameters fit to experimental results. For example, Fischetti and Laux (13) used two empirical deformation potentials to model electron scattering induced by optical and acoustic phonons. Additionally, Fischetti and Laux (13) used simplified band structure and phonon dispersions. We note that, because multiple parameter sets can fit experimental results, the HC scattering rates due to different physical processes obtained empirically are not uniquely determined (13, 14).Although heuristic approaches can provide some insight into HC dynamics of well-characterized materials (e.g., GaAs), there is a lack of generally applicable, predictive, and parameter-free approaches to study HCs.Here, we carry out ab initio calculations of hot electrons in GaAs with energies up to 5 eV above the CBM. Our ability to use extremely fine grids in the Brillouin zone (BZ) allows us to resolve hot electron scattering in the conduction band with unprecedented accuracy. We focus here on three main findings. First, our overall computed e-ph scattering rates are in excellent agreement with those in previous semiempirical calculations in ref. 13 that combine multiple empirical parameters. The advantage of our approach is the ability to compute the electronic band and momentum dependence of the e-ph scattering rates without fitting parameters. Second, we show that both optical and acoustic modes contribute substantially to e-ph scattering, with a dominant scattering from transverse acoustic (TA) modes. This result challenges the tenet that HCs lose energy mainly through longitudinal optical (LO) phonon emission. Third, our calculations provide valuable means for quantitative interpretation of experiments of hot electron cooling in GaAs. In particular, the ultrafast (∼50 fs) e-ph relaxation times that we compute at the onset of the X valley are in excellent agreement with the fastest decay time observed in ultrafast optical experiments (18, 19, 21). This signal was attributed by some (18) to e-e scattering and by others (21) to e-ph scattering. The excellent agreement with time decay signals in time-resolved experiments shows the dominant role of e-ph scattering for hot electron cooling at low carrier density.Our approach combines electronic band structures computed ab initio using the GW (where G is the Green function, W is the screened Coulomb potential, and GW is the diagram employed for the electron exchange-correlation interactions) method (16) with phonon dispersions from density functional perturbation theory (DFPT) (22), and it is entirely free of empirical parameters. We compute the e-ph matrix elements using a Wannier function formalism (23) on very fine BZ grids and are able to resolve e-ph scattering for the different conduction band valleys. The e-e rates for hot electrons—also known as impact ionization (II) rates—are computed using the GW method (16, 24), and thus include dynamical screening effects. Additional details of our calculations are discussed in Methods.     

RE-Based Inorganic-Crystal Nanofibers Produced by Electrospinning for Photonic Applications

Electrospinning is an effective and inexpensive technique to grow polymer materials in nanofiber shape with exceptionally high surface-area-to-volume ratio. Although it has been known for about a century, it has gained much interest in the new millennium thanks to its low cost and versatility, which has permitted to obtain a large variety of multifunctional compositions with a rich collection of new possible applications. Rare-earth doped materials possess many remarkable features that have been exploited, for example, for diode pumped bulk solid-state lasers in the visible and near infrared regions, or for biomedical applications when grown in nanometric form. In the last few decades, electrospinning preparation of rare-earth-doped crystal nanofibers has been developed and many different materials have been successfully grown. Crystal host, crystal quality and nanosized shape can deeply influence the optical properties of embedded rare earth ions; therefore, a large number of papers has recently been devoted to the growth and characterization of rare earth doped nanofibers with the electrospinning technique and an up-to-date review of this rapidly developing topic is missing; This review paper is devoted to the presentation of the main results obtained in this field up to now with particular insight into the optical characterization of the various materials grown with this technique.     

Optical vector field rotation and switching with near-unity transmission by fully developed chiral photonic crystals

State-of-the-art nanostructured chiral photonic crystals (CPCs), metamaterials, and metasurfaces have shown giant optical rotatory power but are generally passive and beset with large optical losses and with inadequate performance due to limited size/interaction length and narrow operation bandwidth. In this work, we demonstrate by detailed theoretical modeling and experiments that a fully developed CPC, one for which the number of unit cells N is high enough that it acquires the full potentials of an ideal (N → ∞) crystal, will overcome the aforementioned limitations, leading to a new generation of versatile high-performance polarization manipulation optics. Such high-N CPCs are realized by field-assisted self-assembly of cholesteric liquid crystals to unprecedented thicknesses not possible with any other means. Characterization studies show that high-N CPCs exhibit broad transmission maxima accompanied by giant rotatory power, thereby enabling large (>π) polarization rotation with near-unity transmission over a large operation bandwidth. Polarization rotation is demonstrated to be independent of input polarization orientation and applies equally well on continuous-wave or ultrafast (picosecond to femtosecond) pulsed lasers of simple or complex (radial, azimuthal) vector fields. Liquid crystal–based CPCs also allow very wide tuning of the operation spectral range and dynamic polarization switching and control possibilities by virtue of several stimuli-induced index or birefringence changing mechanisms.

Optical vector field (more commonly called polarization) rotators and switches are essential components of all modern optical and photonic systems for communications, ellipsometry, metrology, biological/chemical detection, and quantum processing/computing (1–10). There are, however, some inherent limitations. Wave plates made with birefringent crystals, for example, require strict alignment of the optic axis with respect to the polarization orientation of incident light and generally do not work with laser vector beams of complex polarization fields; Faraday rotators that do not have this requirement are generally too cumbersome and bulky due to their weak optical rotatory powers. One promising approach to circumvent these limitations is to employ chiral optical materials such as chiral photonic crystals and metasurfaces. Nevertheless, structural chirality, such as chiral metamaterials, metasurfaces, and photonic crystals that are capable of very large optical rotatory power (up to ∼100,000°/mm), are inevitably accompanied by large absorption losses (11–15). In metamaterials/surfaces, the intrinsic noncircular absorption and nanofabrication difficulty also add to the limitation of their practical scalability in the interaction length, resulting in small (<π) net polarization rotation angle, very small aperture, and narrow operating spectral bandwidth (11–13). Similar issues confront most chiral photonic crystals (CPCs) due to the limitations of molecular self-assembly or nanofabrication/processing technique and high transmission loss associated with operation near the Bragg reflection band (14, 15).Here, we show by theory and experimental corroborations that a fully developed liquid crystal–based CPC, one for which the number of unit cells N approaches that (N → ∞) of an ideal crystal, can circumvent all the aforementioned limitations and possess several advantageous characteristics impossible with conventional low-N thin counterparts. Such high-period–number chiral photonic crystals (HN-CPCs) are achieved by fabricating cholesteric liquid crystals (CLCs) to thicknesses several hundred times that of conventional ones using a refined field-assisted self-assembly (FASA) technique (16, 17; see SI Appendix, Note 1, for more details). Optical properties of CLCs as CPCs arise from complex “collective” responses from many unit cells. While thicker crystals obviously give rise to larger effects, the resulting properties as the crystal thickness or period number N evolves from low values to a very high value do not lend themselves to such simple linear extrapolation; as a function of N, pleasant surprises and new insights and possibilities abound. Our studies show that for N > 500, these CLCs exhibit simultaneously broad transmission maxima and large polarization rotation power in the off-Bragg-resonance spectral regime. Polarization rotation is independent of input polarization orientation and acts equally well on simple or complex vector fields (18–22) of continuous-wave (CW) or ultrafast pulsed laser beams. Liquid crystal–based CPCs also allow dynamic polarization switching and control by virtue of field–induced index/birefringence changing mechanisms at modest or ultrafast (picosecond to femtosecond) speeds (23–34).     

Coupling of light and mechanics in a photonic crystal waveguide

Observations of thermally driven transverse vibration of a photonic crystal waveguide (PCW) are reported. The PCW consists of two parallel nanobeams whose width is modulated symmetrically with a spatial period of 370 nm about a 240-nm vacuum gap between the beams. The resulting dielectric structure has a band gap (i.e., a photonic crystal stop band) with band edges in the near infrared that provide a regime for transduction of nanobeam motion to phase and amplitude modulation of an optical guided mode. This regime is in contrast to more conventional optomechanical coupling by way of moving end mirrors in resonant optical cavities. Models are developed and validated for this optomechanical mechanism in a PCW for probe frequencies far from and near to the dielectric band edge (i.e., stop band edge). The large optomechanical coupling strength predicted should make possible measurements with an imprecision below that at the standard quantum limit and well into the backaction-dominated regime. Since our PCW has been designed for near-field atom trapping, this research provides a foundation for evaluating possible deleterious effects of thermal motion on optical atomic traps near the surfaces of PCWs. Longer-term goals are to achieve strong atom-mediated links between individual phonons of vibration and single photons propagating in the guided modes (GMs) of the PCW, thereby enabling optomechanics at the quantum level with atoms, photons, and phonons. The experiments and models reported here provide a basis for assessing such goals.

Recent decades have seen tremendous advances in the ability to prepare and control the quantum states of atoms, atom-like systems in the solid state, and optical fields in cavities and free space. However, the integration of these diverse elements to achieve efficient quantum information processing still faces diverse challenges, including the wide range of highly dissimilar physical systems (e.g., atoms, ions, solid-state defects, quantum dots) that could be utilized to realize heterogeneous systems for quantum logic, memory, and long-range coupling. Each of these systems has unique advantages, but they are disparate in their frequencies, their spatial modes, and the fields to which they couple. For example, the electronic degrees of freedom in atoms and atom-like defects typically respond at optical frequencies, while their spin degrees of freedom, which are suitable for long-term storage of quantum states, respond to microwave or radio frequencies. On the other hand, the transmission of quantum information over long distances at room temperature requires the use of telecom-band photons in single-mode optical fibers.Beginning with the pioneering work in refs. 1 and 2, mechanical systems have now been recognized as broadly applicable means for overcoming these disparities and transferring quantum states between different quantum degrees of freedom (3–6). This is because mechanical systems (7) can be engineered to couple efficiently and coherently to many different systems and can possess very low damping, particularly when operated at cryogenic temperatures. To date, quantum effects have been observed in mechanical systems coupled to superconducting qubits (via piezoelectric coupling) (8), optical photons (9–14), and microwave photons (15, 16). Efficient coupling has also been demonstrated between mechanical oscillators and spins in various solid-state systems, although to date the mechanical components of these devices have operated in the classical regime (17–23).In this article we describe nascent efforts to utilize strong coupling of atoms, photons, and phonons in nanophotonic photonic crystal waveguides (PCWs) to create a different generation of capabilities for quantum science and technology. Our long-term goal is to use optomechanical systems operating in the quantum regime to realize controllable, coherent coupling between isolated, few-state quantum systems. In our case, the system will consist of atoms trapped along a PCW that interact strongly with photons propagating in the guided modes (GMs) of the PCW (24). The mechanical structure of the PCW in turn supports phonons in its various eigenmodes of motion. While much has been achieved in theory and experiment for strong coupling of atoms and photons in nanophotonics, much less has been achieved (or even investigated) for the optical coupling of motion and light in the quantum regime for devices such as described in refs. 24 and 25.A longstanding challenge for this work is to achieve the integration of ultracold atoms with nanophotonic devices. If this challenge were overcome, quantum motion could be harnessed to investigate enhanced nonlinear atom–light interactions with single and multiple atoms. Additional quantum phases (31), different mechanisms for controlling atoms near dielectric objects (32), and strong atom–photon–phonon coupling (6) could be realized in the laboratory. Although difficult, this approach potentially benefits from several advantages when compared to conventional optomechanics, including 1) the extreme region of parameter space that atomic systems occupy (such as low mass and high mechanical Q factors), 2) the exquisite level of control and configurability of atomic systems, and 3) the preexisting quantum functionality of atoms, including internal states with very long coherence times.Of course, many spectacular advances of atomic physics already build upon these features (33–35). On one hand, experiments with linear arrays of trapped ions achieve coherent control over phonons interacting with the ions’ internal states as pseudospins. Goals that are very challenging for quantum optomechanics with nano- and microscopic masses, such as phonon-mediated entanglement of remote oscillators and single-phonon strong coupling, are routinely implemented with trapped ions. On the other hand, cavity quantum electrodynamics (QED) with neutral atoms produces strong interactions between single photons and the internal states of single atoms or ensembles, leading to demonstrations of state mapping and atom–photon entanglement (36).What is missing thus far, and what motivates the initial steps described here, is a strong atom-mediated link between individual photons and phonons, to enable optomechanics at the quantum level. Initial steps described here include 1) observation and characterization of the low-frequency, mechanical eigenmodes of an alligator photonic crystal waveguide (APCW) (26–29) and 2) the development of theoretical models that are validated in the nontraditional regime in which our system works (37, 38), namely, well-localized mechanical modes, but nonlocalized propagating photons both far from and near to the band edges of PCWs.     

Molding of Plasmonic Resonances in Metallic Nanostructures: Dependence of the Non-Linear Electric Permittivity on System Size and Temperature

In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients. Electronic scattering processes are described and included in the dielectric function, showing their role in determining plasmon lifetime at resonance. Relationships among permittivity, electric conductivity and refractive index are examined. Finally, a temperature dependent permittivity model is presented and is employed to predict temperature and non-linear field intensity dependence on commonly used plasmonic geometries, such as nanospheres.     

Strengthened Spin Hall Effect of Circularly Polarized Light Enabled by a Single-Layered Dielectric Metasurface

The spin Hall effect of light, referring to the spin-dependent and transverse splitting of light at an optical interface, is an interface-dependent phenomenon. In contrast to this commonly accepted statement, it has been recently reported that the spin Hall effect under circularly polarized light is interface-independent. Despite this interface-independence, however, the reflection of the spin Hall shifted beam is mostly suppressed under near-normal incidence, where the spin Hall shift is large because of the handedness reversal that occurs during the reflection. Here we present a single-layered dielectric metasurface to realize the interface-independent and strengthened spin Hall effect of light. Numerical simulation results confirmed that the anisotropic geometry of the metasurface induced phase-reversed reflection for one linear polarization and phase-preserved reflection for the other, thereby strongly strengthening the reflection of the spin-Hall-shifted beam. Our work will pave a route toward the precise displacement of the beam at the nanoscale without perturbing its polarization state.     

An Experimental and Theoretical Determination of Oscillatory Shear-Induced Crystallization Processes in Viscoelastic Photonic Crystal Media

A study is presented of the oscillatory shear-ordering dynamics of viscoelastic photonic crystal media, using an optical shear cell. The hard-sphere/“sticky”-shell design of these polymeric composite particles produces athermal, quasi-solid rubbery media, with a characteristic viscoelastic ensemble response to applied shear. Monotonic crystallization processes, as directly measured by the photonic stopband transmission, are tracked as a function of strain amplitude, oscillation frequency, and temperature. A complementary generic spatio-temporal model is developed of crystallization due to shear-dependent interlayer viscosity, giving propagating crystalline fronts with increasing applied strain, and a gradual transition from interparticle disorder to order. The introduction of a competing shear-induced flow degradation process, dependent on the global shear rate, gives solutions with both amplitude and frequency dependence. The extracted crystallization timescales show parametric trends which are in good qualitative agreement with experimental observations.     

Layer-Inversion Zones in Angular Distributions of Luminescence and Absorption Properties in Biaxial Crystals

We numerically depict the complete angular distributions of luminescence and absorption properties in biaxial media, by calculating the imaginary part of the optical index for all directions of propagation. Our simulations show a double-layer surface with specific topology and symmetry properties that greatly differ from those of the refractive index surface. Our calculations show that the two layers intersect and inverse themselves along continuous loci related to polarization-independent luminescence or absorption properties. Specificities related to the orthorhombic, monoclinic and triclinic biaxial crystal systems are discussed. Such theoretical developments should be considered to fully exploit innovating luminescent materials.     

Increasing the Efficiency of a Spintronic THz Emitter Based on WSe2/FeCo

We report an increase in terahertz (THz) radiation efficiency due to FeCo/WSe₂ structures in the reflection geometry. This can be attributed to an absorption increase in the alloy FeCo layer at the input FeCo/WSe₂ interface due to constructive interference, as well as to the backward transport of hot carriers from FeCo to WSe₂. In contrast to the transmission geometry, the THz generation efficiency in the reflection is much less dependent on the magnetic layer thickness. Our results suggest a cheap and efficient way to improve the characteristics of THz spintronic emitters with the conservation of a full set of their important properties.     

Light Green Crystals in May-Grünwald and Giemsa-Stained Bone Marrow Macrophages in Patients with Myeloid Leukaemia

A patient in a terminal stage of myelomocytic leukaemia had a number of elongated crystals in many bone marrow macrophages. The crystals were up to 20 micron long, showed a characteristic light green colour with May-Grünwald & Giemsa, but did not stain with Sudan Black B or PAS. Electron microscopy showed that many of the crystals had a rhomboid form, but failed to show periodicity with the magnification used. A search was made for similar light green crystalline inclusions in patients with different types of leukaemia. Identical inclusions were found in 2 out of 5 other cases of myelomonocytic leukaemia, and in 3 out of 5 cases of chronic myeloid leukaemia. In contrast, such inclusions were not found in any of 6 patients with acute lymphoblastic leukaemia, nor in 4 patients with chronic lymphocytic leukaemia.     

Impact of Liquid Crystals in Active and Adaptive Optics

Active and dynamic modulation of light has been one of major contributions of liquid crystals to Optics. The spectrum of application range from signposting panels to high resolution imaging. The development of new materials is the key to continued progress in this field. To promote this we will present in this paper recent uses of liquid crystals as active or adaptive modulators of light. Besides, we will reflect on their current limitations. We expect with this to contribute to the progress in the field of liquid crystals and thus the development of new useful tools for Active and Adaptive Optics.     

Plasmon-Induced Enhanced Light Emission and Ultrafast Carrier Dynamics in a Tunable Molybdenum Disulfide-Gallium Nitride Heterostructure

The effect of localized plasmon on the photoemission and absorption in hybrid molybdenum disulfide-Gallium nitride (MoS₂-GaN) heterostructure has been studied. Localized plasmon induced by platinum nanoparticles was resonantly coupled to the bandedge states of GaN to enhance the UV emission from the hybrid semiconductor system. The presence of the platinum nanoparticles also increases the effective absorption and the transient gain of the excitonic absorption in MoS₂. Localized plasmons were also resonantly coupled to the defect states of GaN and the exciton states using gold nanoparticles. The transfer of hot carriers from Au plasmons to the conduction band of MoS₂ and the trapping of excited carriers in MoS₂ within GaN defects results in transient plasmon-induced transparency at ~1.28 ps. Selective optical excitation of the specific resonances in the presence of the localized plasmons can be used to tune the absorption or emission properties of this layered 2D-3D semiconductor material system.     

Accounting for inhomogeneous broadening in nano-optics by electromagnetic modeling based on Monte Carlo methods

Many experimental systems consist of large ensembles of uncoupled or weakly interacting elements operating as a single whole; this is particularly the case for applications in nano-optics and plasmonics, including colloidal solutions, plasmonic or dielectric nanoparticles on a substrate, antenna arrays, and others. In such experiments, measurements of the optical spectra of ensembles will differ from measurements of the independent elements as a result of small variations from element to element (also known as polydispersity) even if these elements are designed to be identical. In particular, sharp spectral features arising from narrow-band resonances will tend to appear broader and can even be washed out completely. Here, we explore this effect of inhomogeneous broadening as it occurs in colloidal nanopolymers comprising self-assembled nanorod chains in solution. Using a technique combining finite-difference time-domain simulations and Monte Carlo sampling, we predict the inhomogeneously broadened optical spectra of these colloidal nanopolymers and observe significant qualitative differences compared with the unbroadened spectra. The approach combining an electromagnetic simulation technique with Monte Carlo sampling is widely applicable for quantifying the effects of inhomogeneous broadening in a variety of physical systems, including those with many degrees of freedom that are otherwise computationally intractable.In photonics experiments and applications, frequent use is made of ensembles of individual structures operating as a single whole; these include, for example, lithographically defined arrays of metallic nanostructures that form frequency-selective surfaces (1), metasurfaces (2–4) or sensor arrays (5), colloidal solutions or suspensions (6, 7), randomly dispersed nanoshells, quantum dots or nanocrystals on a substrate (8), and many others.Assuming that the elements in the ensembles are independent (i.e., they do not experience significant near- or far-field coupling), an assumption that can often be made in sparse, disordered systems, the optical response of these ensembles is simply the sum of the response of all of their constituents. In the case that such an ensemble is composed of many identical elements, its spectral response should be the same as that of each individual element. In real systems, however, the constituent elements are never precisely identical: Any fabrication or synthesis technique including top–down lithography and bottom–up self-assembly will introduce a distribution of geometrical parameters (also known as polydispersity) that leads to inhomogeneous broadening in the spectral features of the total ensemble (e.g., refs. 9–16). To avoid inhomogeneous broadening effects in experiments, complex techniques are sometimes used to measure the optical response of individual elements (17). Other times inhomogeneous broadening can be helpful, for example in situations where a broadband optical response is desired such as in photovoltaic applications (18).Although full-wave electromagnetic simulations are often used to model and understand optical systems that cannot be described analytically (e.g., ref. 19), these methods cannot easily account for polydispersity that leads to inhomogeneous broadening. This issue is sometimes addressed by artificially increasing the damping constant of materials (15), but this approach yields only nonspecific, qualitative information, does not provide a way to distinguish between the various sources of polydispersity (geometrical or material), and is in general not physical.In the present work, we demonstrate that a complex polydisperse ensemble of noninteracting elements can be fully modeled using a Monte Carlo approach (20, 21), using finite-difference time-domain (FDTD) simulations for the intermediate steps. Monte Carlo methods combined with electromagnetic calculations have previously been applied to problems in electromagnetics such as scattering from random rough surfaces (21–24) and light transport through tissues (25). Here we predict the extinction spectra of self-assembled gold nanorod chains (“nanopolymers”) suspended in a solution. This physical system has a large number of degrees of freedom (e.g., the lengths and widths of the individual nanorods comprising the chains, the total number of rods composing each chain, the gaps between the rods, and their orientation, etc.) and is therefore a particularly challenging model system.