Inverse design of optical pulse shapes for time-varying photonics.

Recent advancements in materials and metamaterials with strong, time-varying, nonlinear optical responses have spurred a surge of interest in time-varying photonics. This opens the door to novel optical phenomena including reciprocity breaking, frequency translation, and amplification that can be further optimized by improving the light-matter interaction. Although there has been recent interest in applying topology-based inverse design to this problem, we propose a novel approach in this article. We introduce a method for the inverse design of optical pulse shapes to enhance their interaction with time-varying media. We validate our objective-first approach by maximizing the transmittance of optical pulses of equal intensity through time-varying media. Through this approach, we achieve large, broadband enhancements in pulse energy transmission, including gain, without altering the incident pulse energy. As a final test, we maximize pulse transmission through thin films of indium tin oxide, a time-varying medium when strongly pumped in its ENZ band. Our work presents a new degree of freedom for the exploration, application, and design of time-varying systems and we hope it inspires further research in this direction.

Tunable plasmonics on epsilon-near-zero materials: the case for a quantum carrier model.

The carrier density profile in metal-oxide-semiconductor (MOS) capacitors is computed under gating using two classical models - conventional drift-diffusion (CDD) and density-gradient (DG) - and a self-consistent Schrödinger-Poisson (SP) quantum model. Once calibrated the DG model approximates well the SP model while being computationally more efficient. The carrier profiles are used in optical mode computations to determine the gated optical response of surface plasmons supported by waveguides incorporating MOS structures. Indium tin oxide (ITO) is used as the semiconductor in the MOS structures, as the real part of its optical permittivity can be driven through zero to become negative under accumulation, enabling epsilon-near-zero (ENZ) effects. Under accumulation the predictions made by the CDD and SP models differ considerably, in that the former predicts one ENZ point but the latter predicts two. Consequently, the CDD model significantly underestimates perturbations in n e f f of surface plasmons (by ∼4×) and yields incorrect details in surface plasmon fields near ENZ points. The discrepancy is large enough to invalidate the CDD model in MOS structures on ENZ materials under accumulation, strongly motivating a quantum carrier model in this regime.

Hyperpolarizability of Plasmonic Meta-Atoms in Metasurfaces.

Plasmonic metasurfaces are promising as enablers of nanoscale nonlinear optics and flat nonlinear optical components. Nonlinear optical responses of such metasurfaces are determined by the nonlinear optical properties of individual plasmonic meta-atoms. Unfortunately, no simple methods exist to determine the nonlinear optical properties (hyperpolarizabilities) of the meta-atoms hindering the design of nonlinear metasurfaces. Here, we develop the equivalent RLC circuit (resistor, inductor, capacitor) model of such meta-atoms to estimate their second-order nonlinear optical properties, that is, the first-order hyperpolarizability in the optical spectral range. In parallel, we extract from second-harmonic generation experiments the first-order hyperpolarizabilities of individual meta-atoms consisting of asymmetrically shaped (elongated) plasmonic nanoprisms, verified with detailed calculations using both nonlinear hydrodynamic-FDTD and nonlinear scattering theory. All three approaches, analytical, experimental, and computational, yield results that agree very well. Our empirical RLC model can thus be used as a simple tool to enable an efficient design of nonlinear plasmonic metasurfaces.

On the performance of optical phased array technology for beam steering: effect of pixel limitations.

Optical phased arrays are of strong interest for beam steering in telecom and LIDAR applications. A phased array ideally requires that the field produced by each element in the array (a pixel) is fully controllable in phase and amplitude (ideally constant). This is needed to realize a phase gradient along a direction in the array, and thus beam steering in that direction. In practice, grating lobes appear if the pixel size is not sub-wavelength, which is an issue for many optical technologies. Furthermore, the phase performance of an optical pixel may not span the required 2π phase range or may not produce a constant amplitude over its phase range. These limitations result in imperfections in the phase gradient, which in turn introduce undesirable secondary lobes. We discuss the effects of non-ideal pixels on beam formation, in a general and technology-agnostic manner. By examining the strength of secondary lobes with respect to the main lobe, we quantify beam steering quality and make recommendations on the pixel performance required for beam steering within prescribed specifications. By applying appropriate compensation strategies, we show that it is possible to realize high-quality beam steering even when the pixel performance is non-ideal, with intensity of the secondary lobes two orders of magnitude smaller than the main lobe.

Elimination of imaging artifacts in second harmonic generation microscopy using interferometry.

Conventional second harmonic generation (SHG) microscopy might not clearly reveal the structure of complex samples if the interference between all scatterers in the focal volume results in artefactual patterns. We report here the use of interferometric second harmonic generation (I-SHG) microscopy to efficiently remove these artifacts from SHG images. Interfaces between two regions of opposite polarity are considered because they are known to produce imaging artifacts in muscle for instance. As a model system, such interfaces are first studied in periodically-poled lithium niobate (PPLN), where an artefactual incoherent SH signal is obtained because of irregularities at the interfaces, that overshadow the sought-after coherent contribution. Using I-SHG allows to remove the incoherent part completely without any spatial filtering. Second, I-SHG is also proven to resolve the double-band pattern expected in muscle where standard SHG exhibits in some regions artefactual single-band patterns. In addition to removing the artifacts at the interfaces between antiparallel domains in both structures (PPLN and muscle), I-SHG also increases their visibility by up to a factor of 5. This demonstrates that I-SHG is a powerful technique to image biological samples at enhanced contrast while suppressing artifacts.

Plasmonic colours predicted by deep learning.

Picosecond laser pulses have been used as a surface colouring technique for noble metals, where the colours result from plasmonic resonances in the metallic nanoparticles created and redeposited on the surface by ablation and deposition processes. This technology provides two datasets which we use to train artificial neural networks, data from the experiment itself (laser parameters vs. colours) and data from the corresponding numerical simulations (geometric parameters vs. colours). We apply deep learning to predict the colour in both cases. We also propose a method for the solution of the inverse problem - wherein the geometric parameters and the laser parameters are predicted from colour - using an iterative multivariable inverse design method.

Investigating the Optical Properties of a Laser Induced 3D Self-Assembled Carbon-Metal Hybrid Structure.

Carbon-based and carbon-metal hybrid materials hold great potential for applications in optics and electronics. Here, a novel material made of carbon and gold-silver nanoparticles is discussed, fabricated using a laser-induced self-assembly process. This self-assembled metamaterial manifests itself in the form of cuboids with lateral dimensions on the order of several micrometers and a height of tens to hundreds of nanometers. The carbon atoms are arranged following an orthorhombic unit cell, with alloy nanoparticles intercalated in the crystalline carbon matrix. The optical properties of this metamaterial are analyzed experimentally using a microscopic Müller matrix measurement approach and reveal a high linear birefringence across the visible spectral range. Theoretical modeling based on local-field theory applied to the carbon matrix links the birefringence to the orthorhombic unit cell, while finite-difference time-domain simulations of the metamaterial relates the observed optical response to the distribution of the alloy nanoparticles and the optical density of the carbon matrix.

Effect of refractive index mismatch on forward-to-backward ratios in SHG imaging.

Nonlinear optical imaging in the epi-direction is used to image subresolution features. We find that a refractive index mismatch between the object to be imaged and the background medium can change the far-field intensity image. As an example, we study second harmonic generation (SHG) microscopy where the forward-to-backward (F/B) ratio is used to quantify subresolution features. We show both theoretically and experimentally that the inhomogeneous refractive index in collagen tendon tissue creates near-field effects, which can change the F/B ratio by ∼20%-25%, even though the effect is negligible for most of the individual fibrils in the tissue. This is caused by the sensitivity of the backward signal on phase matching conditions.

Gouy phase shift measurement using interferometric second-harmonic generation.

We report on a simple way to directly measure the Gouy phase shift of a strongly focused laser beam. This is accomplished by using a recent technique, namely, interferometric second-harmonic generation. We expect that this method will be of interest in a wide range of research fields, from high-harmonic and attosecond pulse generation to femtochemistry and nonlinear microscopy.

Laser-induced plasmonic colours on metals.

Plasmonic resonances in metallic nanoparticles have been used since antiquity to colour glasses. The use of metal nanostructures for surface colourization has attracted considerable interest following recent developments in plasmonics. However, current top-down colourization methods are not ideally suited to large-scale industrial applications. Here we use a bottom-up approach where picosecond laser pulses can produce a full palette of non-iridescent colours on silver, gold, copper and aluminium. We demonstrate the process on silver coins weighing up to 5 kg and bearing large topographic variations (∼1.5 cm). We find that colours are related to a single parameter, the total accumulated fluence, making the process suitable for high-throughput industrial applications. Statistical image analyses of laser-irradiated surfaces reveal various nanoparticle size distributions. Large-scale finite-difference time-domain computations based on these nanoparticle distributions reproduce trends seen in reflectance measurements, and demonstrate the key role of plasmonic resonances in colour formation.

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

Effects of refractive index mismatch on SRS and CARS microscopy.

An inhomogeneous linear refractive index profile, such as that occurring in biological tissues, is shown to significantly alter stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS) microscopy images. Our finite-difference time-domain simulations show that near-field enhancement and microlensing can lead to an increase of an object's perceived molecular density by a factor of nine and changes in its perceived position by 0.4 µm up to 1.0 µm. Thus the assumption that SRS scales linearly and CARS quadratically with density does not always hold. Furthermore, the inhomogeneous linear index can cause false CARS and AM-SRS signals, even for a homogeneous nonlinear susceptibility.

The Impact of Collagen Fibril Polarity on Second Harmonic Generation Microscopy.

In this work, we report the implementation of interferometric second harmonic generation (SHG) microscopy with femtosecond pulses. As a proof of concept, we imaged the phase distribution of SHG signal from the complex collagen architecture of juvenile equine growth cartilage. The results are analyzed in respect to numerical simulations to extract the relative orientation of collagen fibrils within the tissue. Our results reveal large domains of constant phase together with regions of quasi-random phase, which are correlated to respectively high- and low-intensity regions in the standard SHG images. A comparison with polarization-resolved SHG highlights the crucial role of relative fibril polarity in determining the SHG signal intensity. Indeed, it appears that even a well-organized noncentrosymmetric structure emits low SHG signal intensity if it has no predominant local polarity. This work illustrates how the complex architecture of noncentrosymmetric scatterers at the nanoscale governs the coherent building of SHG signal within the focal volume and is a key advance toward a complete understanding of the structural origin of SHG signals from tissues.

Analysis of forward and backward Second Harmonic Generation images to probe the nanoscale structure of collagen within bone and cartilage.

Collagen ultrastructure plays a central role in the function of a wide range of connective tissues. Studying collagen structure at the microscopic scale is therefore of considerable interest to understand the mechanisms of tissue pathologies. Here, we use second harmonic generation microscopy to characterize collagen structure within bone and articular cartilage in human knees. We analyze the intensity dependence on polarization and discuss the differences between Forward and Backward images in both tissues. Focusing on articular cartilage, we observe an increase in Forward/Backward ratio from the cartilage surface to the bone. Coupling these results to numerical simulations reveals the evolution of collagen fibril diameter and spatial organization as a function of depth within cartilage.

Dual-polarization plasmonic metasurface for nonlinear optics.

A plasmonic metasurface for the enhancement of nonlinear optical effects is proposed. The metasurface can simultaneously enhance perpendicularly polarized electric fields in the same volume. We illustrate application of the metasurface to the production of Terahertz radiation via the parametric process of difference frequency generation in 4¯3m non-centro symmetric materials, e.g., GaAs, which has a large second-order nonlinear susceptibility. An enhancement over bulk of almost two orders of magnitude near the surface supports the use of the proposed structure for thin-film, surface-based, or chip-based nonlinear optical applications for several crystal classes.

On the convergence and accuracy of the FDTD method for nanoplasmonics.

Use of the Finite-Difference Time-Domain (FDTD) method to model nanoplasmonic structures continues to rise - more than 2700 papers have been published in 2014 on FDTD simulations of surface plasmons. However, a comprehensive study on the convergence and accuracy of the method for nanoplasmonic structures has yet to be reported. Although the method may be well-established in other areas of electromagnetics, the peculiarities of nanoplasmonic problems are such that a targeted study on convergence and accuracy is required. The availability of a high-performance computing system (a massively parallel IBM Blue Gene/Q) allows us to do this for the first time. We consider gold and silver at optical wavelengths along with three "standard" nanoplasmonic structures: a metal sphere, a metal dipole antenna and a metal bowtie antenna - for the first structure comparisons with the analytical extinction, scattering, and absorption coefficients based on Mie theory are possible. We consider different ways to set-up the simulation domain, we vary the mesh size to very small dimensions, we compare the simple Drude model with the Drude model augmented with two critical points correction, we compare single-precision to double-precision arithmetic, and we compare two staircase meshing techniques, per-component and uniform. We find that the Drude model with two critical points correction (at least) must be used in general. Double-precision arithmetic is needed to avoid round-off errors if highly converged results are sought. Per-component meshing increases the accuracy when complex geometries are modeled, but the uniform mesh works better for structures completely fillable by the Yee cell (e.g., rectangular structures). Generally, a mesh size of 0.25 nm is required to achieve convergence of results to ∼ 1%. We determine how to optimally setup the simulation domain, and in so doing we find that performing scattering calculations within the near-field does not necessarily produces large errors but reduces the computational resources required.

Light-opals interaction modeling by direct numerical solution of Maxwell's equations.

This work describes a 3-D Finite-Difference Time-Domain (FDTD) computational approach for the optical characterization of an opal photonic crystal. To fully validate the approach we compare the computed transmittance of a crystal model with the transmittance of an actual crystal sample, as measured over the 400 ÷ 750 nm wavelength range. The opal photonic crystal considered has a face-centered cubic (FCC) lattice structure of spherical particles made of polystyrene (a non-absorptive material with constant relative dielectric permittivity). Light-matter interaction is described by numerically solving Maxwell's equations via a parallelized FDTD code. Periodic boundary conditions (PBCs) at the outer edges of the crystal are used to effectively enforce an infinite lateral extension of the sample. A method to study the propagating Bloch modes inside the crystal bulk is also proposed, which allows the reconstruction of the ω-k dispersion curve for k sweeping discretely the Brillouin zone of the crystal.

Imaging the noncentrosymmetric structural organization of tendon with Interferometric Second Harmonic Generation microscopy.

We report the imaging of tendon with Interferometric Second Harmonic Generation microscopy. We observe that the noncentrosymmetric structural organization can be maintained along the fibrillar axis over more than 150 µm, while in the transverse direction it is ∼1-15 µm. Those results are explained by modeling tendon as a heterogeneous distribution of noncentrosymmetric nano-cylinders (collagen fibrils) oriented along the fibrillar axis. The preservation of the noncentrosymmetric structural organization over multiple tens of microns reveals that tendon is made of domains in which the ratio between fibrils with positive and negative polarity is unbalanced.

Spatial-spectral coupling in coherent anti-Stokes Raman scattering microscopy.

Coherent anti-Stokes Raman scattering (CARS) microscopy is a third-order nonlinear optical technique which permits label-free, molecule-specific hyperspectral imaging. The interference between coherent resonant and non-resonant terms leads to well known distortions in the vibrational spectrum, requiring the use of retrieval algorithms. It also leads to spatial imaging distortions, largely due to the Gouy phase, when objects are smaller than the Rayleigh range. Here we consider that the focal position and spectral contributions to the nonlinear image formation are intrinsically coupled and cannot be corrected by conventional retrieval methods.

Femtosecond laser induced surface swelling in poly-methyl methacrylate.

We show that surface swelling is the first step in the interaction of a single femtosecond laser pulse with PMMA. This is followed by perforation of the swollen structure and material ejection. The size of the swelling and the perforated hole increases with pulse energy. After certain energy the swelling disappears and the interaction is dominated by the ablated hole. This behaviour is independent of laser polarization. The threshold energy at which the hole size coincides with size of swelling is 1.5 times that of the threshold for surface swelling. 2D molecular dynamics simulations show surface swelling at low pulse energies along with void formation below the surface within the interaction region. Simulations show that at higher energies, the voids coalesce and grow, and the interaction is dominated by material ejection.