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Photonic scattering materials, such as biological tissue and white paper, are made of randomly positioned nanoscale inhomogeneities in refractive index that lead to multiple scattering of light. Typically these materials, both naturally-occurring or man-made, are formed through self assembly of the scattering inhomogeneities, which imposes challenges in tailoring the disorder and hence the optical properties. Here, We report on the nanofabrication of photonic scattering media using direct laser writing with deterministic design. These deterministic scattering media consist of submicron thick polymer nanorods that are randomly oriented within a cubic volume. We study the total transmission of light as a function of the number density of rods and of the sample thickness to extract the scattering and transport mean free paths using radiative transfer theory. Such photonic scattering media with deterministic and controllable properties are model systems for fundamental light scattering in particular with strong anisotropy and offer new applications in solid-state lighting and photovoltaics., Comment: 18 pages, 9 figures

To investigate the performance of three-dimensional (3D) nanostructures, it is vital to study in situ their internal structure non-destructively. Hence, we perform synchrotron X-ray holographic tomography on exemplary 3D silicon photonic band gap crystals without irreversible preparation steps. Here, we obtain real space 3D density distributions of whole crystals buried on 2 mm^2 beams with 20 nanometer resolution. Our X-ray results identify why structures that look similar in scanning electron microscopy have vastly different nanophotonic functionality: One crystal with a broad photonic gap reveals 3D periodicity as designed ("Good"), a second structure without gap reveals a buried void ("Bad"), a third one without gap is shallow due to fabrication errors ("Ugly"). We conclude that X-ray tomography is a crucial tool to critically assess 3D functional nanostructures., Comment: 8 pages, 5 figures, includes supplementary material

We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In particular, we study the transport of light in the visible wavelength range between $420$ and $700$ nm through silicone plates filled with YAG:Ce$^{3+}$ phosphor particles, that even re-emit absorbed light at different wavelengths. We measure the total transmission, the total reflection, and the ballistic transmission of light through these plates. We obtain average single particle properties namely the scattering cross-section $\sigma_s$, the absorption cross-section $\sigma_a$, and the anisotropy factor $\mu$ using an analytical approach, namely the P3 approximation to the radiative transfer equation. We verify the extracted transport parameters using Monte-Carlo simulations of the light transport. Our approach fully describes the light propagation in phosphor diffuser plates that are used in white LEDs and that reveal a strong absorption ($L/\ell_{\mathrm{a}} > 1$) up to $L/\ell_{\mathrm{a}} = 4$, where $L$ is the slab thickness, $\ell_{\mathrm{a}}$ is the absorption mean free path. In contrast, the widely used diffusion theory fails to describe this parameter range. Our approach is a suitable analytical tool for industry, since it provides a fast yet accurate determination of key transport parameters, and since it introduces predictive power into the design process of white light emitting diodes.

We have performed an x-ray holotomography study of a three-dimensional (3D) photonic band gap crystal. The crystals was made from silicon by CMOS-compatible methods. We manage to obtain the 3D material density throughout the fabricated crystal. We observe that the structural design is for most aspects well-realized by the fabricated nanostructure. One peculiar feature is a slight shear-distortion of the cubic crystal structure. We conclude that 3D X-ray tomography has great potential to solve many future questions on optical metamaterials., Comment: 3 pages, 3 figures

We demonstrate that photonic crystals can be used to generate powerful and highly coherent laser radiation when injecting a beam of free electrons. Using theoretical investigations we present the startup dynamics and coherence properties of such laser, in which gain is provided by matching the optical phase velocity in the photonic crystal to the velocity of the electron beam., Comment: 6 pages, 5 figures

We have studied the transport of light through phosphor diffuser plates that are used in commercial solid-state lighting modules (Fortimo). These polymer plates contain $\mathrm{YAG:Ce}^{+3}$ phosphor particles that elastically scatter light and Stokes shifts it in the visible wavelength range (400-700 nm). We excite the phosphor with a narrowband light source, and measure spectra of the outgoing light. The Stokes shifted light is separated from the elastically scattered light in the measured spectra and using this technique we isolate the elastic transmission of the plates. This result allows us to extract the transport mean free path $l_{\mathrm{tr}}$ over the full wavelength range by employing diffusion theory. Simultaneously, we determine the absorption mean free path $l_{\mathrm{abs}}$ in the wavelength range 400 to 530 nm where $\mathrm{YAG:Ce}^{+3}$ absorbs. The diffuse absorption $\mu_{\mathrm{a}} =\frac{1}{l_{\mathrm{abs}}}$ spectrum is qualitative similar to the absorption coefficient of $\mathrm{YAG:Ce}^{+3}$ in powder, with the $\mu_{\mathrm{a}}$ spectrum being wider than the absorption coefficient. We propose a design rule for the solid-state lighting diffuser plates.

Current nanostructure fabrication by etching is usually limited to planar structures as they are defined by a planar mask. The realisation of three-dimensional (3D) nanostructures by etching requires technologies beyond planar masks. We present a method to fabricate a 3D mask that allows to etch three-dimensional monolithic nanostructures by using only CMOS-compatible processes. The mask is written in a hard-mask layer that is deposited on two adjacent inclined surfaces of a Si wafer. By projecting in single step two different 2D patterns within one 3D mask on the two inclined surfaces, the mutual alignment between the patterns is ensured. Thereby after the mask pattern is defined, the etching of deep pores in two oblique directions yields a three-dimensional structure in Si. As a proof of concept we demonstrate 3D mask fabrication for three-dimensional diamond-like photonic band gap crystals in silicon. The fabricated crystals reveal a broad stop gap in optical reflectivity measurements. We propose how 3D nanostructures with five different Bravais lattices can be realised, namely cubic, tetragonal, orthorhombic, monoclinic, and hexagonal, and demonstrate a mask for a 3D hexagonal crystal. We also demonstrate the mask for a diamond-structure crystal with a 3D array of cavities. In general, the 2D patterns for the different surfaces can be completely independent and still be in perfect mutual alignment. Indeed, we observe an alignment accuracy of better than 3.0 nm between the 2D mask patterns on the inclined surfaces, which permits one to etch well-defined monolithic 3D nanostructures., Comment: 18 pages, 10 figures

This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate all known photonic crystal structures with a demonstrated 3D band gap., Comment: 21 pages, 6 figures, 2 tables, Chapter 8 in "Light Localisation and Lasing: Random and Pseudorandom Photonic Structures", Eds. M. Ghulinyan and L. Pavesi (Cambridge University Press, Cambridge, 2015, ISBN 978-1-107-03877-6)

We study light transport in phosphor plates of white light-emitting diodes (LEDs). We measure the broadband diffuse transmission through phosphor plates of varying YAG:Ce$^{3+}$ density. We distinguish the spectral ranges where absorption, scattering, and re-emission dominate. Using diffusion theory, we derive the transport and absorption mean free paths from first principles. We find that both transport and absorption mean free paths are on the order of the plate thickness. This means that phosphors in commercial LEDs operate well within an intriguing albedo range around 0.7. We discuss how salient parameters that can be derived from first principles control the optical properties of a white LED., Comment: 14 pages, 9 figures

We present a method to map the absolute electromagnetic field strength inside photonic crystals. We apply the method to map the electric field component Ez of a two-dimensional photonic crystal slab at microwave frequencies. The slab is placed between two mirrors to select Bloch standing waves and a subwavelength spherical scatterer is scanned inside the resulting resonator. The resonant Bloch frequencies shift depending on the electric field at the position of the scatterer. To map the electric field component Ez we measure the frequency shift in the reflection and transmission spectrum of the slab versus the scatterer position. Very good agreement is found between measurements and calculations without any adjustable parameters., Comment: 12 pages, 7 figures

We have performed ultrafast pump-probe experiments on a GaAs-AlAs microcavity with a resonance near 1300 nm in the "original" telecom band. We concentrate on ultimate-fast optical switching of the cavity resonance that is measured as a function of pump-pulse energy. We observe that at low pump-pulse energies the switching of the cavity resonance is governed by the instantaneous electronic Kerr effect and is achieved within 300 fs. At high pump-pulse energies the index change induced by free carriers generated in the GaAs start to compete with the electronic Kerr effect and reduce the resonance frequency shift. We have developed an analytic model which predicts this competition in agreement with the experimental data. Our model includes a new term in the intensity-dependent refractive index that considers the effect of the probe pulse intensity, which is resonantly enhanced by the cavity. We calculate the effect of the resonantly enhanced probe light on the refractive index change induced by the electronic Kerr effect for cavities with different quality factors. By exploiting the linear regime where only the electronic Kerr effect is observed, we manage to retrieve the nondegenerate third order nonlinear susceptibility for GaAs from the cavity resonance shift as a function of pump-pulse energy., Comment: 31 pages, 8 figures

We measure localized and extended mode profiles at the band edge of slow-light photonic-crystal waveguides using phase-sensitive near-field microscopy. High-resolution band structures are obtained and interpreted, allowing the retrieval of the optical density of states (DOS). This constitutes a first observation of the DOS of a periodic system with weak disorder. The Van Hove singularity in the DOS expected at the band edge of an ideal 1D periodic structure is removed by the disorder. The Anderson-localized states form a "tail" in the density of states, as predicted by Lifshitz for solid-state systems.

We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconstruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends deeper in the surrounding photonic crystal when the band edge is approached.

We present time-resolved emission experiments of semiconductor quantum dots in silicon 3D inverse-woodpile photonic band gap crystals. A systematic study is made of crystals with a range of pore radii to tune the band gap relative to the emission frequency. The decay rates averaged over all dipole orientations are inhibited by a factor of 10 in the photonic band gap and enhanced up to 2? outside the gap, in agreement with theory. We discuss the effects of spatial inhomogeneity, nonradiative decay, and transition dipole orientations on the observed inhibition in the band gap., Comment: 5 figures, update author list

The smallest structures that conventional lenses are able to optically resolve are of the order of 200 nm. We introduce a new type of lens that exploits multiple scattering of light to generate a scanning nano-sized optical focus. With an experimental realization of this lens in gallium phosphide we have succeeded to image gold nanoparticles at 97 nm optical resolution. Our work is the first lens that provides a resolution in the nanometer regime at visible wavelengths., Comment: 4 pages, 3 figures

We experimentally study spatial fluctuations of the local density of states (LDOS) inside three-dimensional random photonic media. The LDOS is probed at many positions inside the random photonic media by measuring emission rates of a large number of individual fluorescent nanospheres. The emission rates are observed to fluctuate spatially. We analyze the variance of these fluctuations for samples with different scattering strengths. The measured variance of the emission rates agrees well with a model that takes into account the effect of the nearest scatterer only., Comment: 4 pages, 4 figures, we added a description about the depth of the single fluorescent spheres and a text about LDOS distribution because of dipole orientations as pointed out by a referee.

We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal photonic crystals. Strong deviations from the Lambertian emission profile are observed. An attenuation of 60 % is observed in the angle dependent radiant flux emitted from the samples due to photonic stop bands. At angles that correspond to the edges of the stop band the emitted flux is increased by up to 34 %. This increase is explained by the redistribution of Bragg-diffracted light over the available escape angles. The results are quantitatively explained by an expanded escape-function model. This model is based on diffusion theory and adapted to photonic crystals using band structure calculations. Our results are the first angular redistributions and escape functions measured at near-infrared, including telecom, wavelengths. In addition, this is the first time for this model to be applied to describe emission from samples that are optically thick for the excitation light and relatively thin for the photoluminesence light., Comment: 24 pages, 8 figures (current format = single column, double spaced)

We study experimentally time-resolved emission of CdSe quantum dots in an environment with a controlled local density of states (LDOS). The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS, allowing us to determine the size-dependent quantum efficiency and oscillator strength. We find that the quantum efficiency decreases with increasing emission energy mostly due to an increase in nonradiative decay. For the first time, we manage to obtain the oscillator strength of the important class of CdSe quantum dots. The oscillator strength varies weakly with frequency in agreement with behavior of quantum dots in the strong confinement limit. Surprisingly, the measured absolute values are a factor of 5 below theoretically calculated values. Our results are relevant for applications of CdSe quantum dots in spontaneous emission control and cavity quantum electrodynamics.

The radiative and non-radiative decay rates of InAs quantum dots are measured by controlling the local density of optical states near an interface. From time-resolved measurements we extract the oscillator strength and the quantum efficiency and their dependence on emission energy. From our results and a theoretical model we determine the striking dependence of the overlap of the electron and hole wavefunctions on the quantum dot size. We conclude that the optical quality is best for large quantum dots, which is important in order to optimally tailor quantum dot emitters for, e.g., quantum electrodynamics experiments., Comment: 5 pages, 3 figures

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim to interpret ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters and the intensity in an emission decay curve are not proportional, but the density is a time-integral of the intensity. The integral relation is crucial to correctly interpret non-single-exponential decay. We derive the proper normalization for both a discrete, and a continuous distribution of rates, where every decay component is multiplied with its radiative decay rate. A central result of our paper is the derivation of the emission decay curve in case that both radiative and non-radiative decays are independently distributed. In this case, the well-known emission quantum efficiency can not be expressed by a single number anymore, but it is also distributed. We derive a practical description of non-single-exponential emission decay curves in terms of a single distribution of decay rates; the resulting distribution is identified as the distribution of total decay rates weighted with the radiative rates. We apply our analysis to recent examples of colloidal quantum dot emission in suspensions and in photonic crystals, and we find that this important class of emitters is well described by a log-normal distribution of decay rates with a narrow and a broad distribution, respectively. Finally, we briefly discuss the Kohlrausch stretched-exponential model, and find that its normalization is ill-defined for emitters with a realistic quantum efficiency of less than 100 %., Comment: 18 pages, 5 figures; revised order of presentation

We studied the rate of spontaneous emission from colloidal CdSe and CdTe nanocrystals at room temperature. The decay rate, obtained from luminescence decay curves, increases with the emission frequency in a supra-linear way. This dependence is explained by the thermal occupation of dark exciton states at room temperature, giving rise to a strong attenuation of the rate of emission. The supra-linear dependence is in agreement with the results of tight-binding calculations., Comment: 11 pages

A detailed diamond anvil-cell study using synchrotron X-ray diffraction, Raman scattering, and optical microscopy has been conducted for the He-N system, with a view to the weakly-bound van der Waals molecule interactions that can be formed in the gas phase. High pressure is found to stabilize the formation of a stoichiometric, solid van der Waals compound of He(N2)11 composition which may exemplify a novel class of compounds found at high pressures in the interiors of the outer planets and their satellites.