Field Enhancement and Helicity Maximization of Structured Light for Chirality Detection and SERS Applications
This dissertation is devoted to understanding the characteristics of an electromagnetic field associated to its interaction with matter and devising structured lights to innovate a platform for nanoscale circular dichroism and to extend the applications of surface enhanced Raman spectroscopy. Circular dichroism is a spectroscopy technique used in characterization of the average of chirality in a sample by using circularly polarized plane waves. Here, we present a circular dichroism framework for characterization of chirality in nanoparticles instead of bulk of matter. To that end, similar to some previous studies, we employ Poynting theorem to analyze the interaction of electromagnetic fields with chiral matter and illustrate the significance of helicity density of the field in interaction with chital matter. We then proceed by introducing a universal upper bound for helicity density of electromagnetic fields which is linearly proportional to the energy density of the field divided to its angular frequency. We call electromagnetic fields reaching this upper bound optimally chiral and prove rigorously that an optimally chiral field possesses a pure spin angular momentum which is collinear with its linear momentum. We also present some practical optimally chiral structured lights including optical laser beams and the nearfield of a designed nanoantenna. The proposed optical laser beams include Gaussian beams with circular polarization and also a beam composed of a radially and an azimuthally polarized beam with specific phase shift and relative amplitudes. We also discuss in detail how to obtain an optimally chiral nearfield in the proximity of a nanoantenna which enables chirality characterization at nanoscale and below the diffraction limit. Indeed, we show that a nanoantenna with balanced electric and magnetic dipole moments generates optimally chiral scattered field which in combination with an optimally chiral incident field forms an optimally chiral total nearfield. Our investigations prove the importance of optimally chiral illumination when the nearfield of a nanoantenna is used in chirality characterization at the nanoscale. In particular, we explore helicity and energy densities in the nearfield of a spherical dielectric nanoantenna illuminated by an optimally chiral combination of azimuthally and radially polarized beams. This beam combination generates parallel induced electric and magnetic dipole moments in the nanoantenna that in turn generate optimally chiral scattered field with the same helicity sign of the incident field. The application of helicity maximization to nearfields results in helicity enhancement at nanoscale which is of great advantage in the detection of nanoscale chiral samples, microscopy, and optical manipulation of chiral nanoparticles. Based upon the concept of helicity maximization, we devise a platform for chirality characterization of nanoparticles. The platform consists of measuring the extinction powers of a chiral nanoparticle in its interaction with two optimally chiral excitation in two separate experiments and employ the measured powers in dissymmetry factor g defined as the difference between the extinction powers divided to their arithmetic average. When the excitations possess equal electric and magnetic energy densities at the location of the chiral nanoparticle and helicity densities equal in magnitude and opposite signs, dissymmetry factor g is proportional to the chirality of the nanoparticle normalized to its electric polarizability. We further validate the feasibility of our proposed platform and showed that chiral nanoparticles made of PGA as small as 20 nm are detectable when utilizing the instruments available in the market. We further demonstrate that using optimally chiral lights for determining the chirality of a nanoparticle using the dissymmetry factor g, eliminates the need of the specific knowledge of the values of field’s energy and helicity densities. The helicity maximization concept generalizes the use of the dissymmetry factor for nanoparticle chirality detection to any chiral structured light illumination. We also showed that the helicity maximization upgrades the conventional circular dichroism technique to chirality detection at the surface level instead of the bulk when the chiral sample is deposited on a substrate composed of an array of nanoantenna. We derived the required condition for an array of Silicon nanospheres to generates a planar distribution of optimally chiral nearfield, in terms of array effective electric and magnetic polarizabilities that satisfy the effective Kerker condition. Importantly the array would not contribute to the generated CD signal when used as a substrate for detecting chirality of a thin layer of chiral molecules. This eliminates the need to separate the CD signal generated by the array from that of the chiral sample. Finally, we investigate the field enhancement in the hot spots of a chain of gold nanoparticles deposited on a substrate composed of an array of plasmonic rods on a glass slab. The proposed structure is fabricated by taking advantage of dielectrophoresis where the plasmonic rods on a glass substrate are used to apply an electric field to gold nanoparticles in a suspension to align them along a line perpendicular to the rods. We show that Rayleigh anomaly in the array of rods adds an extra factor to the field enhancement in the hot spot of the gold nanoparticles which in return enhances the Raman signal and improves the detection.