We present a theoretical study of the optical angular momentum transfer from a circularly polarized plane wave to thin metal nanoparticles of different rotational symmetries. While absorption has been regarded as the predominant mechanism of torque g
eneration on the nanoscale, we demonstrate numerically how the contribution from scattering can be enhanced by using multipolar plasmon resonance. The multipolar modes in non-circular particles can convert the angular momentum carried by the scattered field, thereby producing scattering-dominant optical torque, while a circularly symmetric particle cannot. Our results show that the optical torque induced by resonant scattering can contribute to 80% of the total optical torque in gold particles. This scattering-dominant torque generation is extremely mode-specific, and deserves to be distinguished from the absorption-dominant mechanism. Our findings might have applications in optical manipulation on the nanoscale as well as new designs in plasmonics and metamaterials.
Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these techniques,
supersaturating models by augmenting the natural covariates in the problem with an additional indicator for each case in the data set. We attach a penalty term for these case-specific indicators which is designed to produce a desired effect. For regression methods with squared error loss, an $ell_1$ penalty produces a regression which is robust to outliers and high leverage cases; for quantile regression methods, an $ell_2$ penalty decreases the variance of the fit enough to overcome an increase in bias. The paradigm thus allows us to robustify procedures which lack robustness and to increase the efficiency of procedures which are robust. We provide a general framework for the inclusion of case-specific parameters in regularization problems, describing the impact on the effective loss for a variety of regression and classification problems. We outline a computational strategy by which existing software can be modified to solve the augmented regularization problem, providing conditions under which such modification will converge to the optimum solution. We illustrate the benefits of including case-specific parameters in the context of mean regression and quantile regression through analysis of NHANES and linguistic data sets.
