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.
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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
and focal length 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.
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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.more » « less
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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.
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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
at and at . 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
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. -
Abstract The goal of this letter is to introduce the concept of a non-resonant fractional random laser. This is achieved by extending the classical Letokhov model of photon diffusion through disordered gain media to fractional differential operators in space and time. Fractional transport equations effectively describe anomalous photon sub-diffusion phenomena in non-uniform random scattering media with memory and long-range spatial correlation effects. In particular, by analytically solving fractional transport equations in the one-dimensional slab geometry we obtain simple closed-form expressions for the critical amplification volumes required to initiate the laser action in both fractional-order (FO) and distributed-order (DO) space-time fractional reaction-diffusion equations. Our findings demonstrate the benefits of anomalous sub-diffusive photon transport in active media with correlated disorder and stimulate the engineering of novel non-resonant random lasers with significantly reduced footprint and amplification volumes beyond the limitations of uniform disorder and Markovian diffusion processes.
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Abstract In this work, reconfigurable metafilm absorbers based on indium silicon oxide (ISO) were investigated. The metafilm absorbers consist of nanoscale metallic resonator arrays on metal-insulator-metal (MIM) multilayer structures. The ISO was used as an active tunable layer embedded in the MIM cavities. The tunable metafilm absorbers with ISO were then fabricated and characterized. A maximum change in the reflectance of 57% and up to 620 nm shift in the resonance wavelength were measured.more » « less