Near-field resonances in photon emission via interaction of electrons with coupled nanoparticles

Abstract

In this work we construct the first-principles theory for the near-field resonances arising in the system of two different coupled nanoparticles excited by the external field. The obtained expressions are valid for an arbitrary external field; the detailed analysis is performed for the case of a fast electron passing by. The energy of electron is arbitrary, so the results are valid both for relativistic and nonrelativistic electrons. We have obtained rigorous analytical solution for the radiation field and for distribution of radiation over angles and frequencies.The effect of interaction between the single particles manifests itself very distinctly in conditions of resonance, resulting in a spectral shift of the radiation maximum, significant increase of its altitude, and, interestingly, in clear oscillations in radiation intensity not only when the particles are very close to each other, but even when the distance between the particles exceeds considerably their sizes. It attests to the strong influence of interaction on the radiation processes in a system of coupling particles.

Theory of Smith-Purcell radiation from a 2D array of small noninteracting particles

“…Note that all the theory developed here does suppose that the single particles composing the array do not interact. This approximation holds true when the distance between them significantly exceeds their sizes; see [24].…”

On the Polarizability of a Cluster of Interacting Particles in Polarization Radiation

“…where E act is the total field acting on a microparticle. Following the approach outlined in [14], we obtain the i-th component of the field at long distances in form (4) where δ is is the Kronecker symbol, k is the wave-vector, is the Fourier image of the s-component of the field of the electron at point : (5) , and (6) and we used the notations:…”

“…In recent years, a series of studies appeared in which the authors investigated SPR from singleperiod gratings with simultaneous excitation of surface plasmons, which significantly enhance the radiation [12,13]. In [14], on an example of a cluster of two particles, it was shown that radiation enhancement is possible not only due to the excitation of plasmons on the surface of such structures, but also due to the interaction between elements. The interaction effect manifests itself in the shift in radiation frequencies, splitting of maxima, and the appearance of new intensity maxima.…”

On the reducing the number of equations in the problem of radiation of a cluster of interacting particles

“…В случае отсутствия взаимодействия между частицами (элементами) мишени решение задачи об излучении кластера сводится к решению одночастичной задачи, с учетом лишь набега фаз для волн от соседних частиц. Однако, как показано ранее [8], в процессе поляризационного излучения учет взаимодействия между частицами может быть весьма существен, вести к новым эффектам в картине излучения, в том числе к резонансному усилению, изменению положения пиков наибольшей интенсивности. В этом случае эффект взаимодействия между элементами кластера приводит к необходимости решать систему взаимосвязанных уравнений, что резко усложняет поиск решения даже для достаточно небольшого числа частиц в кластере.…”

“…Вычислим поле излучения с учетом взаимодействия всех частиц. В системе двух частиц учет взаимодействия был выполнен в работе [8]. Неравенство R 0 << λ позволяет воспользоваться для расчета дипольным приближением.…”