| dc.description.abstract | With light being manipulated at subwavelength scales, photonic design has been explored for various applications. In this dissertation, we investigate potential application of photonic design to chemical analysis, with a focus on spectrometry and chemical sensing.
First, we demonstrate inverse design of single-layer metasurfaces with shape optimization. Each of the designed metasurfaces simultaneously focuses light and shapes the spectra of focused light without using any filters. Thus, both spatial and spectral properties of the meta-optics are engineered. We chose the color matching functions of the CIE 1931 XYZ color space as the target spectral shapes and a distant region with a finite size as the focal area.
We then present an inverse-design approach for computational spectrometers, in which the scattering media are topology-optimized to achieve higher robustness in inference, without the need of a training set of spectra and noise. Our approach also allows the selection of the inference algorithm to be decoupled from that of the scatterer. For smooth spectra, we devise a regularized reconstruction algorithm based on Chebyshev interpolation, which yields higher accuracy compared with conventional treatment in which the spectra are sampled at equally spaced frequencies or wavelengths with equal weights. Our approaches are numerically demonstrated via inverse design of integrated computational spectrometers and reconstruction of example spectra. The inverse-designed spectrometer exhibits significantly better performance in the presence of noise than its counterparts with random scatterers.
Furthermore, we discuss chemical detection using optical resonances, which can increase the sensitivity of measurements to material perturbations and also accelerate photochemical reactions. We show that these two effects can be combined multiplicatively, to enhance the detection via weak/low-concentration photochemical reactions far beyond what could previously be attained. For an optical resonance with a quality factor Q, the sensitivity of our detection scheme is enhanced by ~ Q² (where ~ denotes approximate proportionality), as demonstrated by both theoretical arguments and numerical simulations of a simple optical grating resonance coupled with reaction-diffusion equations. Such an approach opens a door to further improvements by careful design of the resonance: even a 3-parameter optimization of the grating resonance yields an additional ≈ 7 × improvement.
Finally, regarding linear electromagnetic systems possessing time-reversal symmetry, we present an approach to bound ratios of internal fields excited from different ports, using only the scattering matrix, improving upon previous related bounds by Sounas and Alù (2017). By reciprocity, emitted-wave amplitudes from internal dipole sources are bounded in a similar way. When applied to coupled-resonant systems, our method constrains ratios of resonant coupling/decay coefficients. We also obtain a relation for the relative phase of fields excited from the two ports and the ratio of field intensities in a two-port system. In addition, although lossy systems do not have time-reversal symmetry, we can still approximately bound loss-induced non-unitarity of the S matrix using only the lossless S matrix. We show numerical validations of the near-tightness of our bounds in various scattering systems. | |
