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The aim of this work is to determine the varying dielectric constant of a biological nanostructured system via electrostatic force microscopy (EFM) and to show how this method is useful to study natural photonic crystals. We mapped the dielectric constant of the cross section of the posterior wing of the damselfly Chalcopteryx rutilans with nanometric resolution. We obtained structural information on its constitutive nanolayers and the absolute values of their dielectric constant. By relating the measured profile of the static dielectric constant to the profile of the refractive index in the visible range, combined with optical reflectance measurements and simulation, we were able to describe the origin of the strongly iridescent wing colors of this Amazonian rainforest damselfly. The method we demonstrate here should be useful for the study of other biological nanostructured systems.

The interplay between order and disorder in photonic lattices opens up a wide range of novel optical scattering mechanisms, resonances, and applications that can be obscured by typical ordered design approaches to photonics. Striking examples include Anderson localization, random lasers, and visible light scattering in biophotonic structures such as butterfly wings. In this work, we present a profound example of light localization in photonic crystal waveguides by introducing long-range correlated disorder. Using a rigorous three-dimensional Bloch mode expansion technique, we demonstrate how inter-hole correlations have a negative contribution to the total out-of-plane radiative losses, leading to a pronounced enhancement of the quality factor, $Q$, and $Q/V$ cavity figures of merit in the long-range correlation regime. Subsequently, the intensity fluctuations of the system are shown to globally increase with the correlation length, highlighting the non-trivial role of long-range disorder on the underlying scattering mechanisms. We also explore the possibility of creating ultra-high quality cavity modes via inter-hole correlations, which have various functionalities in chip-based nonlinear optics and waveguide cavity-quantum electrodynamics.

Using a semi-analytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic band gap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line., 10 pages, 9 figures

Technological advances allow the control of light at the nanoscale and to strongly enhance the light–matter interaction in highly engineered devices. Enhancing the light–matter interaction is needed for applications in research areas such as quantum technology, energy harvesting, sensing, and biophotonics. Here, we show that a different approach, based on the use of disorder, rather than the precise engineering of the devices, and fabrication imperfections as a resource, can allow the efficient trapping of visible light on a chip. We demonstrate, for the first time to our knowledge, Anderson localization of light at visible wavelengths in a nanophotonic chip. Remarkably, we prove that disorder-induced localization is more efficient in confining visible light than highly engineered optical cavities, thus reversing the trend observed so far. We measure light-confinement quality factors approaching 10 000 that are significantly higher than values previously reported in two-dimensional photonic crystal cavities. These measurements are well explained using a three-dimensional Bloch mode expansion technique, where we also extract the mode quality factors and effective mode volume distributions of the localized modes. Furthermore, by implementing a sensitive imaging technique, we directly visualize the localized modes and measure their spatial extension. Even though the position where the cavities appear is not controlled, given the multiple scattering process at the basis of their formation, we are able to locate with nanometer-scale accuracy the position of the optical cavities. This is important for the deterministic coupling of emitters to the disorder-induced optical cavities and for assessing light localization. Our results show the potential of disorder as a novel resource for the efficient confinement of light and for the enhancement of the light–matter interaction in the visible range of wavelengths.

The iridescent wings of the Chalcopterix rutilans damselfly (Rambur) (Odonata, Polythoridae) are investigated with focused ion beam/scanning electron microscopy, transmission electron microscopy, and time-of-flight secondary ion mass spectrometry. The electron microscopy images reveal a natural photonic crystal as the source of the varying colors. The photonic crystal has a consistent number and thickness (∼195 nm) of the repeat units on the ventral side of the wing, which is consistent with the red color visible from the bottom side of the wing in all regions. The dorsal side of the wing shows strong color variations ranging from red to blue depending on the region. In the electron microscopy images, the dorsal side of the wing exhibits varied number and thicknesses of the repeat units. The repeat unit spacings for the red, yellow/green, and blue regions are approximately 195, 180, and 145 nm, respectively. Three-dimensional analysis of the natural photonic crystals by time-of-flight secondary ion mass spectrometry reveals that changes in the relative levels of Na, K, and eumelanin are responsible for the varying dielectric constant needed to generate the photonic crystal. The photonic crystal also appears to be assembled with a chemical tricomponent layer structure due to the enhancement of the CH6N3+ species at every other interface between the high/low dielectric constant layers.

We present a detailed theoretical study of the effects of structural disorder on LN photonic crystal slab cavities, ranging from short to long length scales, using a fully-3D Bloch mode expansion technique. We compute the optical density of states, quality factors and effective mode volumes of the cavity modes, with and without disorder, and compare with the localized modes of the corresponding disordered photonic crystal waveguide. We demonstrate how the quality factors and effective mode volumes saturate at a specific cavity length and become bounded by the corresponding values of the Anderson modes appearing in the disordered waveguide. By means of the intensity fluctuation criterion, we observe Anderson localization for cavity lengths larger than around L31, and show that the field confinement in the disordered LN cavities is mainly determined by the local characteristics of the structural disorder as long as the confinement region is far enough from the cavity mirrors and the effective mode localization length is much smaller than the cavity length; under this regime, the disordered cavity system becomes insensitive to changes in the cavity boundaries and a good agreement with the intensity fluctuation criterion is found for localization. Surprisingly, we find that the Anderson localized modes do not appear as new disorder-induced resonances in the main spectral region of the LN cavity modes, and, moreover, the disordered DOS enhancement is largest for the disordered waveguide system with the same length. These results are fundamentally interesting for applications such as lasing and cavity-QED, and provide new insights into the role of the boundary condition on finite-size slow-light waveguides. They also point out the clear failure of using models based on the cavity boundaries/mirrors and a single slow-light Bloch mode to describe cavity systems with large N.

We present a fully three-dimensional Bloch mode expansion technique and a photon Green function formalism to compute the quality factors, mode volumes, and Purcell enhancement distributions of a disordered W1 photonic crystal slab waveguide in the slow-light Anderson-localization regime. By considering fabrication (intrinsic) and intentional (extrinsic) disorder we find that the Purcell enhancement statistics are well described by log-normal distributions without any fitting parameters. We also compare directly the effects of hole size fluctuations as well as fluctuations in the hole position. The functional dependence of the mean and standard deviation of the quality factor and Purcell enhancement distributions is found to decrease exponentially with the square root of the extrinsic disorder parameter. The strong coupling probability between a single quantum dot and an Anderson-localized mode is numerically computed and found to exponentially decrease with the squared extrinsic disorder parameter, where low disordered systems give rise to larger probabilities when state-of-the-art quantum dots are considered. The optimal spatial regions to position quantum dots in the W1 waveguide are also discussed. These theoretical results are fundamentally interesting for disordered photonics and connect to recent experimental works on photonic crystal slab waveguides in the slow-light regime. Our three-dimensional slab results also contradict some previous findings that use simpler two-dimensional models to understand these complex planar systems.

We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady-state, thanks to their radiative coupling by mutual interaction through the normal modes of a photonic crystal dimer. We employ a quantum master equation formalism to quantify the steady-state entanglement by calculating the system {\it negativity}. Calculations are specified to consider realistic semiconductor nanostructure parameters for the photonic crystal dimer-quantum dots coupled system, determined by a guided mode expansion solution of Maxwell equations. Negativity values of the order of 0.1 ($20\%$ of the maximum value) are shown for interdot distances that are larger than the resonant wavelength of the system. It is shown that the amount of entanglement is almost independent of the interdot distance, as long as the normal mode splitting of the photonic dimer is larger than their linewidths, which becomes the only requirement to achieve a local and individual qubit addressing. Considering inhomogeneously broadened quantum dots, we find that the steady-state entanglement is preserved as long as the detuning between the two quantum dot resonances is small when compared to their decay rates. The steady-state entanglement is shown to be robust against the effects of pure dephasing of the quantum dot transitions. We finally study the entanglement dynamics for a configuration in which one of the two quantum dots is initially excited and find that the transient negativity can be enhanced by more than a factor of two with respect to the steady-state value. These results are promising for practical applications of entangled states at short time scales., 10 pages, 7 figures

We study the mutual interaction between two identical quantum dots coupled to the normal modes of two-site photonic crystal molecules in a planar waveguide geometry, i.e. photonic crystal dimers. We find that the radiative coupling between the two quantum emitters is maximized when they are in resonance with either the bonding or the antibonding modes of the coupled cavity system. Moreover, we find that such effective interdot coupling is sizable, in the meV range, and almost independent from the cavities distance, as long as a normal mode splitting exceeding the radiative linewidth can be established (strong cavity-cavity coupling condition). In realistic and high quality factor photonic crystal cavity devices, such distance can largely exceed the emission wavelength, which is promising for long distance entanglement generation between two qubits in an integrated nanophotonic platform. We show that these results are robust against position disorder of the two quantum emitters within their respective cavities., 10 pages, 6 figures

We study the reflectivity spectra of photonic crystal slab cavities using an extension of the scattering matrix method that allows treating finite sizes of the spot of the excitation beam. The details of the implementation of the method are presented and then we show that Fano resonances arise as a consequence of the electromagnetic interference between the discrete contribution of the fundamental cavity mode and the continuum contribution of the light scattered by the photonic crystal pattern. We control the asymmetry lineshape of the Fano resonance through the polarization of the incident field, which determines the relative phase between the two electromagnetic contributions to the interference. We analyse the electric field profile inside and outside of the crystal to help in the understanding of the dependence on polarization of the reflectivity lineshape. We also study with our implementation the dependence of the Fano resonances on the size of the incident radiation spot.

En este trabajo se estudian los modos electromagnéticos en cristales fotónicos uno-dimensionales y dos-dimensionales (1D y 2D) a través del método de diferencias finitas en el dominio de las frecuencias FDFD. Los diagramas de bandas son calculados para cristales 1D regulares y con defecto, al igual que sus perfiles de intensidad electromagnética. De igual manera se calculan los diagramas de bandas y perfiles de intensidad para cristales 2D regulares en redes hexagonal y cuadrada. Nuestros cálculos son comparados con los obtenidos en el software MPB proporcionado por el MIT y basado en el método de expansión de ondas planas.

Photonic resonators that allow an electromagnetic field to be confined in an ultrasmall volume with a long decay time are crucial to a number of applications requiring enhanced nonlinear effects. For applications to integrated photonic devices on chip, compactness and optimized in-plane transmission become relevant figures of merit as well. Here we optimize an encapsulated $\mathrm{Si}/{\mathrm{Si}\mathrm{O}}_{2}$ photonic-crystal nanobeam cavity at telecom wavelengths by means of a global optimization procedure, where only the first few holes surrounding the cavity are varied to decrease its radiative losses. This strategy allows us to theoretically achieve intrinsic quality factors close to 10 million, sub-diffraction-limited mode volumes, and in-plane transmission above 65%, in a structure with a very small footprint of about $8\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$. We address and quantitatively assess the dependence of the main figures of merit on the nanobeam length and on fabrication disorder. Finally, we study a system of two optimized and laterally coupled nanobeam cavities with the goal of demonstrating an unconventional photon blockade at room temperature in a monolithic passive device. We estimate the single-photon nonlinearity of this device and discuss the relevant figures of merit, which lead to sub-Poissonian photon statistics of the transmitted signal. Our results hold promise for prospective experiments in low-power nonlinear and quantum photonics.

We study Kerr frequency combs and dissipative Kerr solitons in silicon photonic crystal coupled-cavity waveguides (CCW) with globally optimized dispersion at telecom wavelengths. The corresponding threshold for comb generation is found to explicitly depend on the main CCW figures of merit, namely, mode volume, normal mode quality factor and slow-light group index. Our analysis is carried out by solving the non-linear dynamics of the CCW Bloch modes in presence of Kerr non-linearity and two-photon absorption. Our results open the way to CCW comb generation via dispersion engineering and slow-light enhancement., Comment: Updated version with DOI

We propose a system of coupled microring resonators for the generation frequency combs and dissipative Kerr solitons in silicon at telecommunication frequencies. By taking advantage of structural slow-light, the effective non-linearity of the material is enhanced, thus relaxing the requirement of ultra-high quality factors that currently poses a major obstacle to the realization of silicon comb devices. We demonstrate a variety of frequency comb solutions characterized by threshold power in the 10-milliwatt range and a small footprint of 0.1 mm(2), and study their robustness to structural disorder. The results open the way to the realization of low-power compact comb devices in silicon at the telecom band. (c) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement