The inverse design of optical devices that exhibit desired functionalities as well as the solution of complex inverse problems are becoming essential research directions in modern optical engineering. Recent advancements in computation algorithms, machine learning architectures and optimization methods offer efficient means to deal with complex photonics problems with a large number of degrees of freedom. In this thesis, I present our work on developing an integrated framework for the inverse design of diffractive optical elements and nanophotonic media with tailored optical responses. In the first part of our work, we introduce the design of single-layer diffractive optical devices that extend conventional imaging functions to include dual-band multi-focal microlenses for multi-band imaging, modulated axilenses for ultracompact spectrometers, and hyperuniform phase plates for lensless imaging systems. We design these diffractive elements based on Rayleigh-Sommerfeld scalar diffraction simulations. We also fabricate them using scalable lithography and experimentally characterize their predicted diffraction and imaging performances. While we successfully validated our designs, we also identified the fundamental limitations and challenges of single-layer diffractive devices. In order to address these problems, in the second part of the work we introduce a novel and flexible approach for the inverse design of diffractive optical elements based on adaptive deep diffractive neural networks (a-D2NNs). In particular, we demonstrate two-layer dual-band multi-focal devices that exceed the efficiency limit of traditional single-layer devices and we leverage the powerful a-D2NN inverse design platform to engineer systems with targeted spectral lineshapes and focusing point-spread functions. Moreover, we apply a-D2NNs to the inverse design of ultracompact spectrometers and demonstrate nanometer-range spectral resolution for 100 micron-size devices that can be fabricated using conventional lithographic procedures. Finally, we apply the a-D2NNs approach to the design of hyperuniform scalar random fields that we have introduced as novel lensless imaging systems with modulated transfer functions that produce enhanced image quality compared to state-of-the-art phase plates based on the Perlin noise. We additionally show that a-D2NNs can be used to efficiently design different classes of hyperuniform random media that are currently being explored for a number of optical applications. In the third part of my thesis, we propose and develop a deep learning framework for solving inverse photonics problems by employing physics-informed neural networks (PINNs). We solve the non-local effective medium problem for finite-size metamaterials and address losses and radiation effects. Furthermore, we apply PINNs to solve the invisible cloaking inverse problem beyond the quasi-static limit. Finally, we develop a general PINN framework for inverse retrieval of optical parameters based on near-field data information. Based on our approach, we show the successful retrieval of the electric and magnetic optical parameters (i.e., non-local permittivity and permeability functions) of two-dimensional and three-dimensional scatterers in the presence of absorption losses. Additionally, we demonstrate the application of the inverse PINN design to the scanning near-field microscopy technique under localized excitation and in the presence of noise. In the last part of our work, we couple adjoint optimization methods with the rigorous multiple scattering theory of cylinder arrays (i.e., two-dimensional generalized Mie theory) for the inverse design of small-size, photonic structures, called “photonic patches”, that achieve different functionalities with optimal efficiencies. Specifically, we present the inverse design of photonic patches that angularly shape incoming radiation and that focus light intensity over Fresnel-zone distances (~ 10μm) with engineered spectral lineshapes, enhanced local density of states and resonance quality factors.

Plasmonics can achieve the tight optical confinement and localization in the subwavelength domain. Surface plasmon polaritons (SPPs) are closely related to coupling to emitters in excitation and emission, waveguiding, and active modulating on the nanoscale. Due to these phenomenon, plasmonic nanostructures can be used for applications, such as light emission, photodetection, optical sensing, and spectroscopy. Conventional plasmonic nanostructures can support plasmonic modes, and it is typically optimized for a single wavelength window with planar plasmonic structures. Recent studies have reported some in-plane composite nanostructures and core-shell geometries can induce multiple plasmonic responses. However, it is challenging to achieve the control of individual plasmonic response due to the interdependent spectral tunability with changes in their in-plane geometries. In this dissertation, the concept of out-of-plane engineered nanoantenna structures is introduced, numerically calculated, and experimentally demonstrated. The nanolaminated MIM plasmonic structures show multiresonant plasmonic responses in the same antenna and each wavelength band can be tunable individually with different thicknesses of dielectric layers. The nanolaminated plasmonic structures has been reported for a scalable Surface-enhanced Raman spectroscopy (SERS) substrate for single-molecule sensitive and label-free chemical analysis. Due to the strong optical field confinement, the nanolaminated SERS substrates achieve increased SERS enhancement factor (EF) up to 1.6 x 108 with proper partial etching of dielectric layers. Furthermore, the nanolaminated MIM plasmonic structures have been successfully integrated with micro-scale pillar arrays to control the surface wettability for ultrasensitive SERS measurements. The hierarchical micro/nano plasmonic surface has densely packed intrinsic SERS-active hot spots that give rise to SERS EFs exceeding 107. This platform can take full advantage of low surface energy to control and measure the analyte in water droplets. Leidenfrost evaporation-assisted SERS sensing on the hierarchical substrates provides the way for ultrafast and ultrasensitive biochemical detections without a need for additional surface modifications and chemical treatments. / Doctor of Philosophy / The life in the 21th century has benefited from the technical revolutions of computational power that is based on the manipulation/storage of electrons. As predicted in Moore's law, the size of electronic microchip would go down, and the computational power has been enhanced due to the increase of transistor integration density. However, the two major factors, such as energy dissipation of electrons and signal delay of electronic circuit, limit the communication speed of electronics. These barriers have caused slowdown in the performance of computational power. Photonic solutions have been offered to solve the limitations based on the larger bandwidth and a rare energy dissipation, compared to electronic counterparts. Moreover, optical communications typically demand much lighter channel to deliver similar power/information than practical electrical cables do. Thus, light manipulation/enhancement techniques are envisioned to overcome the limitations and guide to the methodology of interconnections between the electronic circuits and optical platforms. Plasmonics can achieve the nanoscale light confinement and localization in the subwavelength domain. This strong confinement is originated from the coupling between the photons and the electron gas on the metal that results in surface plasmon polariton (SPP). SPPs are closely related to coupling to emitters in excitation and emission, waveguiding, and active modulating on the nanoscale. Due to these phenomenon, plasmonic nanostructures can be used for applications, such as light emission, photodetection, optical sensing, and spectroscopy. In this dissertation, the concept of out-of-plane engineered nanoantenna structures is introduced, numerically calculated, and experimentally demonstrated. This vertically stacked nanoantenna structure is composed of metal-insulator-metal (MIM) laminates fabricated by physical vapor deposition techniques. Although conventional plasmonic nanostructures can support plasmonic modes, it is typically optimized for a single wavelength window. The nanolaminated MIM nanostructures, by contrast, can induce multiresonant plasmonic response in the same antenna with several advantages: (1) reduced individual footprint size and volume of nanoantenna, (2) accurate control of layer thicknesses by thin film deposition technique for resonance tuning, (3) easier integration with other functional materials as gap layers, and (4) efficient transport of charge carriers or heat in nanolaminated layers. As a result of the tight optical field confinement, the nanolaminated plasmonic structures can be used for sensing application called Surface-enhanced Raman spectroscopy (SERS), which is a promising sensing platform for label-free biochemical analysis at the single-molecule level. Partial oxide etching process enables the analyte molecules to accommodate in strong enhancement region of the nanolaminated structures, resulting in amplified unique Raman features of molecular compounds as a finger print. The SERS enhancement factor is increased by one order of magnitude achieving 1.6x108. Furthermore, the nanolaminated plasmonic structures have been integrated with micro-scale pillar arrays to control the surface wettability for ultrasensitive SERS measurements.

Metasurfaces, introduced as a compact 2D alternative of metamaterials, have developed into a vast field in recent times for light manipulation at an ultra-compact scale. Metasurface applications have found a place in the literature for compact alternatives to lens, holograms, polarizers, color filters. Plasmonic metasurfaces consisting of noble metals such as gold and silver provide light confinement on an unprecedented scale. Gold and silver grown conventionally on transparent substrates are polycrystalline, and exhibit losses and limit performance of the device. Moreover, these materials have a lower damage threshold and melting point. To circumvent the lower melting point and damage thresholds, new materials, and material growing techniques need to be researched. <br>In the first part of this work, a metasurface for color holography with an epitaxially grown silver thin film on a transparent substrate is shown. The demonstrated metasurface has been the first ever epitaxial silver metasurface that operated in the transmission mode. This plasmonic hologram has also been the thinnest metasurface hologram operating in transmission mode at the time of its reporting. The holographic image of all three basic color components of red, green, and blue has been demonstrated in the transmission mode. The control of color has been achieved by resonant sub-wavelength slits and the phase can be manipulated through altering slit orientation. This amplitude and phase control pave the way to applications of ultra-compact polychromatic plasmonic metasurfaces for advanced light manipulation. In the second part, we explore temperature rise due to the optical absorption in plasmonic structures. Titanium Nitride based metasurfaces structures are fabricated, that work in harsh environmental conditions and high temperature. A time domain thermo reflectance technique for rapid measurement of temperature is explored. Finally, a practical design prototype for thermo-photovoltaic (TPV) emitters using plasmonic metasurfaces is fabricated and characterized.<br><br>

In the last few decades, the nanoscale fabrication of metallic structures has demonstrated promising applications in security (e.g. cryptography), photochemistry (e.g. plasmonassisted photo-chemistry), decoration (e.g. colouring), biocompatibility of implants and more. To fabricate such subwavelength nanostructures, we typically resort to the use of several nanolithography techniques that are lengthy and incompatible with large-scale production on complex substrates. For this purpose, we invented an innovative technique for the fast fabrication of nanostructures via the use of a picosecond laser. We used this technique to produce colourful coins for the Royal Canadian Mint which were presented at the World Money Fair in Germany in 2015 as a world rst. To ensure the long-term survival of these plasmonic colours, a new dual-layer passivation technique was conceived based on a atomic deposition process, to meet the commercialisation requirements of our industrial partner. A new burst colouring technology was also invented that allows for the creation of more visually appealing colours. These laser burst colours were also shown to have a high sensing potential and an overall better visual response to the application of the passivation layer.

<pre>The degree of freedom brought about by breaking the directional symmetry of space through the use of anisotropic media finds applications in numerous photonic systems. Almost all these systems are based on physical principles that are generalized extensions of their isotropic counterparts, much in the same way an ellipse is related to a circle. However, as we show, there are examples where, in the presence of loss, disorder or even coupling to the measurement apparatus, emerges a completely new behavior which is qualitatively different from the isotropic case. In this work we study these emergent phenomena found in open anisotropic photonic systems.</pre> <pre><br></pre> <pre>We demonstrate that open systems based on biaxial anisotropic medium can support exceptional points which are singularities in the parameter space of the system where the mode frequencies as well as the modes themselves coalesce. We also show that topological insulators, which are novel materials that behave as dielectric in the bulk but metallic in the surface and exhibit bianisotropy through the coupling of their electric and magnetic response, can emit thermal radiation that carries nonzero spin angular momentum. Next, after describing how the strong anisotropy of hyperbolic metamaterial can support electromagnetic fields propagating with high wavenumbers unbounded by the frequency, we show that a super-resolution imaging scheme based on such material is quite robust against substantial loss and disorder. Finally, we consider an example of an incoherent perfect absorber and show that loss and anisotropy in this case can work together to recover the ideal lossless limit for the absorbing performance. In addition to making new conceptual connections between photonics and other branches of science such as condensed matter physics, biotechnology and quantum mechanics, these new emergent phenomena are shown to have thermal, imaging and sensing applications.</pre>

Thesis advisor: Krzysztof Kempa / In my work presented in this dissertation, I have focused on simulation studies of light interaction with nanostructures made of metals and dielectrics. Of particular interest have been plasmonic effects. The structures included the wire and coaxial nanowaveguides, as well as periodic arrays of planar quasi-triangles, and periodic arrays of nanoholes in thin metallic films. In the nanowaveguides I focused on plasmon polariton modes which resemble the TEM modes propagating in the corresponding conventional radio transmission lines. This collaborative research, involving an experimental effort, showed how the nanoscopic plasmon polariton modes reduce in the retarded limit to the TEM modes, and in the non-retarded limit to the corresponding surface plasmon modes. My simulations explained details of recent experimental results involving plasmonic waveguiding in metallic nanowires. Similar results have been obtained for nanocoaxial waveguides. My simulations of the optical absorption in the arrays of nano quasi-triangles, recently observed experimentally, helped identify those as due to Mie plasmonic resonances in these nanoparticles. They also explained the peak shifts in terms of the 2D surface plasmon dispersion, and the plasmon momentum quantization. In the study of the arrays evolution from holes to quasi-triangles, my simulations provided the clue to the critical behavior of the peak position for structures approaching the percolation threshold (the transitional structure in the series, for which film resistance diverges), and allowed to identify the series of structures as an analog of the percolation threshold problem. Finally, I have simulated optical performance of nanorod arrays (or multi-core nanocoax), which have been employed as platform for novel solar cells. My simulations have been employed to predict and optimize these cells. My work resulted in 5 publications and 2 manuscripts in preparation. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Predicting and verifying the tunable optical properties of metal nanostructures is central to designing materials optimized for specific applications. Chemically- deposited nanostructures have been well-studied near the percolation threshold, but at lower surface coverages they exhibit sample-to-sample variations in the optical response. We identify how these variations are driven by the high variability in the particle size distribution in a particular surface coverage range. We then explore film- coupled nanoparticle systems consisting of a silver nanoparticle, thin dielectric spacer layer, and flat silver film, to enable tuning toward the blue and green parts of the spectrum. We use the boundary element method to visualize charge distributions of various resonances. We fabricate samples using thermal evaporation and spin coating methods, and use polarized reflectance spectroscopy to measure their optical response at an ensemble level. We achieve a 532nm resonance for 80nm silver nanoparticles on 13nm PMMA spacers and 100nm silver thin films. The resulting design is a candidate for enhancing fluorescence in a new spectral range. This dissertation includes previously unpublished co-authored material.

The design procedure for ultrafast silicon electro-optic switches using photonic crystals in order optimize the operation of the electro-optic switch is presented. The material medium selected for propagation of the optical signal through the switch is silicon nanocrystals in silica. A patterned slot waveguide with one-dimensional photonic crystals is proposed as the preferred slow light waveguide to be used in the design of the electro-optic switch. The ultrafast quadratic electro-optic Kerr effect is the physical effect utilized, and its analysis for slot waveguides is discussed. The optical structure analysis of the electro-optic switch using a ring resonator is presented and it is shown that the use of a slow light waveguide in the ring resonator can reduce the required externally applied electric field and the radius of the ring resonator.

This thesis deals with electrical and optical characterization  of p+i–n+ nanowire-based photodetectors/solar  cells. I have investigated their I-V performance and found that all of them exhibit a clear rectifying behavior with an ideality factor around 2.2 at 300K.  used Fourier transform infrared spectroscopy to extract their optical properties. From the spectrally resolved photocurrent data, I conclude that the main photocurrent is generated in the i-segment of the nanowire (NW) p-i-n junctions, with negligible  contribution from the substrate.   I also used a C-V technique to investigate the impurity/doping profiles of the NW p+-i-n+ junction.  The technique has been widely used for investigations of doping profiles in planar p-n junctions, in particular with one terminal (n or p) highly doped. To verify the accuracy of the technique, I also used a planar Schottky  sample with an already known doping profile for a test  experiment. The result is very similar to the actual data. When we used the technique to investigate the doping level in the NWs photodetectors grown on InP substrates, the results show a very high capacitance above 800pF which most likely is due to the influence of the parasitic capacitance from the insulating layer of SiO2. Thus,  a new sample design is required to investigate the  doping profiles of NWs.

As the developments in nanoscale fabrication and characterization technology, the investigation and applications of light in metal nanostructures have been becoming one of the most focused research areas. Metal materials allow to couple the incident light energy into electromagnetic waves propagating on the metal surface under certain configurations, which is called surface plasmon (SP). This feature tremendously expanded the application possibility of metals in optical regime, such as extraordinary transmission (EOT), near-field optics and surface enhanced spectroscopies. In this talk, various metal structures will be demonstrated which could control SP’s propagation, resonance andlocal field enhancement. A number of SP applications are benefited – the plasmonic bragg reflector (PBR), the frequency sensitive plasmonic microcavity, the subwavelength metallic taper, the long range surface plasmon (LRSP) waveguide and surface enhanced Raman spectroscopy (SERS). Especially for SERS, long-term effort was devoted into it to achieve the single molecule detection limit. / Graduate