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In this paper, we investigate the localization properties of optical waves in disordered systems with multifractal scattering potentials. In particular, we apply the localization landscape theory to the classical Helmholtz operator and, without solving the associated eigenproblem, show accurate predictions of localized eigenmodes for one- and two-dimensional multifractal structures. Finally, we design and fabricate nanoperforated photonic membranes in silicon nitride (SiN) and image directly their multifractal modes using leaky-mode spectroscopy in the visible spectral range. The measured data demonstrate optical resonances with multiscale intensity fluctuations in good qualitative agreement with numerical simulations. The proposed approach provides a convenient strategy to design multifractal photonic membranes, enabling rapid exploration of extended scattering structures with tailored disorder for enhanced light-matter interactions.

 

We present compact integrated speckle spectrometers based on monofractal and multifractal scattering media in a silicon-on-insulator platform. Through both numerical and experimental studies we demonstrate enhanced optical throughput, and hence signal-to-noise ratio, for a number of random structures with tailored multifractal geometries without affecting the spectral decay of the speckle correlation functions. Moreover, we show that the developed multifractal media outperform traditional scattering spectrometers based on uniform random distributions of scattering centers. Our findings establish the potential of low-density random media with multifractal correlations for integrated on-chip applications beyond what is possible with uncorrelated random disorder.

 

We propose a rigorous approach for the inverse design of functional photonic structures by coupling the adjoint optimization method and the 2D generalized Mie theory (2D-GMT) for the multiple scattering problem of finite-sized arrays of dielectric nanocylinders optimized to display desired functions. We refer to these functional scattering structures as “photonic patches.” We briefly introduce the formalism of 2D-GMT and the critical steps necessary to implement the adjoint optimization algorithm to photonic patches with designed radiation properties. In particular, we showcase several examples of periodic and aperiodic photonic patches with optimal nanocylinder radii and arrangements for radiation shaping, wavefront focusing in the Fresnel zone, and for the enhancement of the local density of states (LDOS) at multiple wavelengths over micron-sized areas. Moreover, we systematically compare the performances of periodic and aperiodic patches with different sizes and find that optimized aperiodic Vogel spiral geometries feature significant advantages in achromatic focusing compared to their periodic counterparts. Our results show that adjoint optimization coupled to 2D-GMT is a robust methodology for the inverse design of compact photonic devices that operate in the multiple scattering regime with optimal desired functionalities. Without the need for spatial meshing, our approach provides efficient solutions at a strongly reduced computational burden compared to standard numerical optimization techniques and suggests compact device geometries for on-chip photonics and metamaterials technologies.

 

We propose the inverse design of ultracompact, broadband focusing spectrometers based on adaptive diffractive optical networks (a-DONs). Specifically, we introduce and characterize two-layer diffractive devices with engineered angular dispersion that focus and steer broadband incident radiation along predefined focal trajectories with the desired bandwidth and nanometer spectral resolution. Moreover, we systematically study the focusing efficiency of two-layer devices with side length$L=100\mathrm{\mu <\#comment/>}\mathrm{m}$and focal length$f=300\mathrm{\mu <\#comment/>}\mathrm{m}$across the visible spectrum and demonstrate accurate reconstruction of the emission spectrum from a commercial superluminescent diode. The proposed a-DONs design method extends the capabilities of efficient multi-focal diffractive optical devices to include single-shot focusing spectrometers with customized focal trajectories for applications to ultracompact spectroscopic imaging and lensless microscopy.

 

We propose an efficient inverse design approach for multifunctional optical elements based on adaptive deep diffractive neural networks (a-D²NNs). Specifically, we introduce a-D²NNs and design two-layer diffractive devices that can selectively focus incident radiation over two well-separated spectral bands at desired distances. We investigate focusing efficiencies at two wavelengths and achieve targeted spectral line shapes and spatial point-spread functions (PSFs) with optimal focusing efficiency. In particular, we demonstrate control of the spectral bandwidths at separate focal positions beyond the theoretical limit of single-lens devices with the same aperture size. Finally, we demonstrate devices that produce super-oscillatory focal spots at desired wavelengths. The proposed method is compatible with current diffractive optics and doublet metasurface technology for ultracompact multispectral imaging and lensless microscopy applications.

 

We present an erratum to our Letter [ Opt. Lett. 46 , 5360 ( 2021 ) 10.1364/OL.437936 ]. This erratum refers to Fig. 3, where a previous version was wrongly uploaded during the final resubmission of the paper. This correction has no influence on the text, the results, and the conclusions of the original Letter. 

We propose a novel framework for the systematic design of lensless imaging systems based on the hyperuniform random field solutions of nonlinear reaction-diffusion equations from pattern formation theory. Specifically, we introduce a new class of imaging point-spread functions (PSFs) with enhanced isotropic behavior and controllable sparsity. We investigate PSFs and modulated transfer functions for a number of nonlinear models and demonstrate that two-phase isotropic random fields with hyperuniform disorder are ideally suited to construct imaging PSFs with improved performances compared to PSFs based on Perlin noise. Additionally, we introduce a phase retrieval algorithm based on non-paraxial Rayleigh–Sommerfeld diffraction theory and introduce diffractive phase plates with PSFs designed from hyperuniform random fields, called hyperuniform phase plates (HPPs). Finally, using high-fidelity object reconstruction, we demonstrate improved image quality using engineered HPPs across the visible range. The proposed framework is suitable for high-performance lensless imaging systems for on-chip microscopy and spectroscopy applications.

 

We design and characterize a novel axilens-based diffractive optics platform that flexibly combines efficient point focusing and grating selectivity and is compatible with scalable top-down fabrication based on a four-level phase mask configuration. This is achieved using phase-modulated compact axilens devices that simultaneously focus incident radiation of selected wavelengths at predefined locations with larger focal depths compared with traditional Fresnel lenses. In addition, the proposed devices are polarization-insensitive and maintain a large focusing efficiency over a broad spectral band. Specifically, here we discuss and characterize modulated axilens configurations designed for long-wavelength infrared (LWIR) in the 6 µm–12 µm wavelength range and in the 4 µm–6 µm midwavelength infrared (MWIR) range. These devices are ideally suited for monolithic integration atop the substrate layers of infrared focal plane arrays and for use as compact microspectrometers. We systematically study their focusing efficiency, spectral response, and cross-talk ratio; further, we demonstrate linear control of multiwavelength focusing on a single plane. Our design method leverages Rayleigh–Sommerfeld diffraction theory and is validated numerically using the finite element method. Finally, we demonstrate the application of spatially modulated axilenses to the realization of a compact, single-lens spectrometer. By optimizing our devices, we achieve a minimum distinguishable wavelength interval of$\mathrm{\Delta <\#comment/>}\mathrm{\lambda <\#comment/>}=240\mathrm{n}\mathrm{m}$at${\mathrm{\lambda <\#comment/>}}_c=8\text{µ<\#comment/>}\mathrm{m}$and$\mathrm{\Delta <\#comment/>}\mathrm{\lambda <\#comment/>}=165\mathrm{n}\mathrm{m}$at${\mathrm{\lambda <\#comment/>}}_c=5\text{µ<\#comment/>}\mathrm{m}$. The proposed devices add fundamental spectroscopic capabilities to compact imaging devices for a number of applications ranging from spectral sorting to LWIR and MWIR phase contrast imaging and detection.

 

We design and characterize compact phase-modulated axilens devices that combine efficient point focusing and grating selectivity within four-level phase mask configurations. Specifically, we select and characterize in detail two device configurations designed for long-wavelength infrared (LWIR) operation in the$6\text{µ<\#comment/>}\mathrm{m}-<\#comment/>12\text{µ<\#comment/>}\mathrm{m}$wavelength range. These devices are ideally suited for monolithic integration atop the substrate layers of infrared focal plane arrays (IR-FPAs) for use in multiband LWIR photodetection. We systematically study their focusing efficiency, spectral response, and crosstalk ratio, and we demonstrate a single-component microspectrometer. Our design method leverages the Rayleigh–Sommerfeld (RS) diffraction theory that is validated numerically using the finite element method (FEM). The proposed devices are broadband and polarization insensitive and add fundamental spectroscopic capabilities to miniaturized optical components for a number of applications in LWIR detection and spectroscopy.