In modern nanophotonics, multipolar interference plays an indispensable role to realize novel optical devices represented by metasurfaces with unprecedented functionalities. Not only to engineer sub-wavelength structures that constitute such devices but also to realize and interpret unnatural phenomena in nanophotonics, a program that efficiently carries out multipole expansion is highly demanded. MENP is a MATLAB program for computation of multipole contributions to light scattering from current density distributions induced in nanophotonic resonators. The main purpose of MENP is to carry out post-processing of a rigid multipole expansion for full-field simulations that in principle provide the information of all near- and far-field interactions (e.g., as a total scattering cross section). MENP decomposes total scattering cross sections into partial ones due to electric and magnetic dipolar and quadrupolar terms based on recently developed exact multipole expansion formulas. We validate the program by comparing results for ideal and realistic nanospheres with those obtained with the Mie theory. We also demonstrate the potential of MENP for analysis of anapole states by calculating the multipole expansion under the long-wavelength approximation, which enables us to introduce toroidal dipole moments.

A spherical dielectric particle can sustain the so-called whispering-gallery modes (WGMs), which can be regarded as circulating electromagnetic waves, resulting in the spatial confinement of light inside the particle. Despite the wide adoption of optical WGMs as a major light confinement mechanism in salient practical applications, direct imaging of the mode fields is still lacking and only partially addressed by simple photography and simulation work. The present study comprehensively covers this research gap by demonstrating the nanoscale optical-field visualization of self-interference of light extracted from excited modes through experimentally obtained photon maps that directly portray the field distributions of the excited eigenmodes. To selectively choose the specific modes at a given light emission detection angle and resonance wavelength, we use cathodoluminescence-based scanning transmission electron microscopy supplemented with angle-, polarization-, and wavelength-resolved capabilities. Equipped with semi-analytical simulation tools, the internal field distributions of the whispering-gallery modes reveal that radiation emitted by a spherical resonator at a given resonance frequency is composed of the interference between multiple modes, with one or more of them being comparatively dominant, leading to a resulting distribution featuring complex patterns that explicitly depend on the detection angle and polarization. Direct visualization of the internal fields inside resonators enables a comprehensive understanding of WGMs that can shed light on the design of nanophotonic applications.