Efficient method for accelerating line searches in adjoint optimization of photonic devices by combining Schur complement domain decomposition and Born series expansions.

A line search in a gradient-based optimization algorithm solves the problem of determining the optimal learning rate for a given gradient or search direction in a single iteration. For most problems, this is determined by evaluating different candidate learning rates to find the optimum, which can be expensive. Recent work has provided an efficient way to perform a line search with the use of the Shanks transformation of a Born series derived from the Lippman-Schwinger formalism. In this paper we show that the cost for performing such a line search can be further reduced with the use of the method of the Schur complement domain decomposition, which can lead to a 10-fold total speed-up resulting from the reduced number of iterations to convergence and reduced wall-clock time per iteration.

Miniature Optical Particle Counter and Analyzer Involving a Fluidic-Optronic CMOS Chip Coupled with a Millimeter-Sized Glass Optical System.

Our latest advances in the field of miniaturized optical PM sensors are presented. This sensor combines a hybrid fluidic-optronic CMOS (holed retina) that is able to record a specific irradiance pattern scattered by an illuminated particle (scattering signature), while enabling the circulation of particles toward the sensing area. The holed retina is optically coupled with a monolithic, millimeter-sized, refracto-reflective optical system. The latter notably performs an optical pre-processing of signatures, with a very wide field of view of scattering angles. This improves the sensitivity of the sensors, and simplifies image processing. We report the precise design methodology for such a sensor, as well as its fabrication and characterization using calibrated polystyrene beads. Finally, we discuss its ability to characterize particles and its potential for further miniaturization and integration.

Publisher Correction: Integrated photonic guided metalens based on a pseudo-graded index distribution.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Determining the optimal learning rate in gradient-based electromagnetic optimization using the Shanks transformation in the Lippmann-Schwinger formalism.

In gradient-based optimization of photonic devices, within the overall design parameter space, one iteratively performs a line search in a one-dimensional subspace as spanned by the search direction. While the search direction can be efficiently determined with the adjoint variable method, there has not been an efficient algorithm that determines the optimal learning rate that controls the distance one moves along the search direction. Here we introduce an efficient algorithm of determining the optimal learning rate, using the Shanks transformation in the Lippmann-Schwinger formalism. Our approach can determine very accurately the optimal learning rates at each epoch, with only a modest increase of computational cost. We show that this approach can significantly improve the figure of merits of the final structure, as compared to conventional methods for estimating the learning rate.

Integrated photonic guided metalens based on a pseudo-graded index distribution.

In this article, we report an integrated optical nanolens exhibiting a pseudo-graded index distribution in a guided configuration. This dielectric metalens relies on a permittivity distribution through dielectric strips of the core material, which is compatible with existing silicon photonic technology. We show in this paper that effective medium theory (EMT) inaccurately predicts the focal length of such devices, and we propose an efficient and accurate design approach based on 2D finite element method (FEM) mode calculations that are in good agreement with 3D FDTD simulations. The lens was fabricated on a 200 mm silicon on insulator pilot line, and fibre-to-fibre optical characterizations revealed an excellent transmission of 85% for TM polarization, in line with the simulated performance (90%). The proposed approach can be easily extended to width-variable strips, enabling the realization of all types of graded index devices, especially those derived from transformation optics.

Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition.

Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total computational domain. Here we show that the adjoint variable method can be combined with the Schur complement domain decomposition method. With this combination, in each optimization step, the simulation only involves the degrees of freedom that are inside the design region. Our approach should significantly improve the computational efficiency of adjoint variable method based optimization of photonic structures.

Effect of Metallic Nanoparticles on Improving the Detection Capacity of a Micro-SERS Sensor Created by the Hybrid Waveguide of Metallic Slots and Dielectric Strips.

The enhancement factor (EF) of surface-enhanced Raman scattering (SERS) mainly depends on the electrical field intensity of surface plasmons in the place of Raman-active molecules. Because of this dependence, the Raman detection sensitivity is much higher with molecules in a small metallic gap than near a single metallic surface because of the intense local electric field resulting from the interaction between metallic objects. In this study, we investigate the SERS detection capacity improved by metallic nanoparticles in a micro-SERS sensor made of a metallic slot and a dielectric strip using the three-dimensional finite-difference time domain method. We calculated the field and charge distributions in the metallic sphere-slot junction to discuss the electromagnetic interaction between the in-sphere localized surface plasmon and the in-slot surface plasmon polariton. After that, the EF dependence of the sensor on the in-slot particle's position, size, shape, and number is demonstrated and discussed to show the strategy of optimizing the SERS detection capacity. It follows the rule that a strong enhancement always appears in a small metallic gap due to the strong field confinement. We show that the averaging SERS enhancement factor around the particle can be increased by 105 times, compared to the averaging EF in the slot without metallic nanoparticles that is reported in our previous work, reaching 106 (all factors in this study are obtained by the fourth power of the division of the local plasmonic field E Loc to the maximum electric value of the incident light E Inc(max)) and at some single points, we have a factor as high as 1010, which is enough to detect a single molecule. With metallic nanoparticles, the micro-SERS sensor can be developed into a highly sensitive tool for the portable and stable Raman detection of molecules or markers in pharmacology, biology, etc.

Theoretical investigation of SERS nanosensors based on hybrid waveguides made of metallic slots and dielectric strips.

Surface-enhanced Raman spectroscopy (SERS) is widely used to sensitively detect molecules or markers in pharmacology, biology, etc. We study numerically the possibility to realize SERS detections directly on a photonic chip. It is presented that a SERS sensor created by combining a gold slot waveguide and a Si3N4 strip waveguide can be designed to excite enhanced Raman effects and extract their scattering signals on a chip. Using 3D finite-difference time-domain simulations, the SERS processes, excitation of surface plasmon in slots and radiation of induced Raman dipoles, are analyzed to simulate SERS detections in reality. It demonstrates the influence of the geometrical parameters on the electromagnetic fields in slots and therefore the local enhancements, based on the |E|4-approximation. The results show that a SERS nanosensor can be achieved based on the hybrid waveguide. The integration of this sensor with a micro-laser and a micro-demultiplexer, could achieve an on-a-chip and fully integrated system for portable and fast SERS detections.

Temporal coupled mode theory of standing wave resonant cavities for infrared photodetection.

Standing wave resonating cavities have been proposed in the past to increase the performance of infrared detectors by minimizing the volume of photogeneration, hence the noise, while maintaining the same quantum efficiency. We present an approach based on the temporal coupled mode theory to explain their behavior and limitations. If the ratio of the imaginary part of the absorber's dielectric function to the index of the incident medium ε″(d)/n0 is larger than 1.4, then the absorption cross section σ(a) can attain its maximum value, which for an isolated cavity is approximately 2λ/π. Besides, for σ(a) to exceed the cavity width, the incident medium refractive index must be close to unity. Metallic loss is negligible in the infrared, making those resonators suitable for integration in infrared photodetectors.

Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

Partially localized hybrid surface plasmon mode for thin-film semiconductor infrared photodetection.

We use numerical simulations to show that a suitably dimensioned periodic arrangement of vertical metallic metal-dielectric-metal nanocavities supports a hybrid plasmonic mode whose spatial electric field distribution is suitable for use in infrared photodetectors based on an unpatterned semiconductor thin-film absorbing layer. The partially localized nature of the hybrid mode offers reduced sensitivity to the angle of incoming light and smaller pixel sizes compared with surface plasmonic modes coupled by diffraction.

Angular and polarization properties of cross-holes nanostructured metallic filters.

It has been shown in literature that cross-shaped holes arrays can be made insensitive to polarization at normal incidence, and can even feature good stability for off-normal incidence. In this work we look for the optimal design rules to obtain high spectral stability conditions in the visible for those structures, through a complete review of all geometrical parameters using CMOS-compatible materials. Rigorous Coupled Wave Analysis (RCWA) simulations have been used to identify the most-impacting parameters and to determine typical ranges allowing for the realization of low-color errors image sensors whatever the light incidence. It appears that the two main parameters are the ratio of the arm width to the arm length of the crosses and the distance between crosses, which both have to be low to ensure stable responses of the filters. We demonstrate the results with CIE chromaticity diagrams reporting the responses of a RGB filter designed with the established rules under various illumination conditions.

Loss mechanisms of surface plasmon polaritons propagating on a smooth polycrystalline Cu surface.

We study the propagation properties of surface plasmon polaritons on a Cu surface by means of photoemission electron microscopy. Use of a CMOS process to fabricate the Cu thin film is shown to enable very high propagation distances (up to 65 µm at 750 nm wavelength), provided that the copper native oxide is removed. A critical review of the optical loss mechanisms is undertaken and shed light on the effect of single grain boundaries in increasing the propagation losses of the plasmon. A microscopic interpretation is provided, relying on groove induced electromagnetic hot spots.