Transition radiation in helical metamaterials with strong spatial dispersion

TL;DR

The paper addresses transition radiation from relativistic charges in helical metamaterials with strong spatial dispersion, a regime where a plasmon degree of freedom qualitatively alters emission. It develops an effective field theory that couples the electromagnetic field to a plasmon field, enabling a local Maxwell–plasmon description and linking Bragg maxima to the plasmon-polariton dispersion. A $(2N+1)$-wave approximation is employed to compute the dispersion and radiation spectra, and numerical simulations for representative optical metamaterials reveal distinct forward radiation and polarization signatures tied to plasmon-polariton branches. The approach also enables inverse spectroscopy: by measuring radiative maxima, one can reconstruct the plasmon dispersion, providing a practical tool for characterizing and exploiting metamaterials with strong spatial dispersion.

Abstract

The theory of transition radiation in helical metamaterials with strong spatial dispersion is developed in the framework of an effective field theory approach. The average number of photons radiated by a charged particle passing through a plate made of this metamaterial is obtained. Given the positions of the transition radiation maxima in momentum space for different velocities of a charged particle, the method for reconstruction of the dispersion law of plasmon-polaritons in metamaterials is proposed. Applying this method conversely, one can predict the radiation spectrum and polarization properties of transition radiation by means of the dispersion law of plasmon-polaritons in the metamaterial known, for example, from the effective model. It is shown that the strong spatial dispersion alters qualitatively the properties of transition radiation from a charged particle traversing normally a plate made of the helical metamaterial along its symmetry axis in the paraxial regime, viz., there is a nonzero forward radiation in contrast to transition radiation in media without strong spatial dispersion. Vavilov-Cherenkov radiation and the anomalous Doppler effect in helical metamaterials with strong spatial dispersion are described.

Figures (7)

• Figure 1: The dispersion law in the $(2N+1)$-wave approximation with $N=2$ taking into account the root selection procedure. The size of the point corresponds to the root weight lying between $0$ and $1$. The pink bands show the chiral and complete band gaps. On the left panel: The dispersion law in the paraxial limit $n_\perp=0$. On the middle panel: $n_\perp=0.2$. On the right panel: The dispersion law in the nonparaxial regime, $n_\perp=0.5$. The other parameters are chosen as $\alpha=\pi/4$, $\varepsilon=\varepsilon_h=1$ , $v=1$, and $\omega_p=0.5q$.
• Figure 2: The intensity of radiation of photons per volume of the cell in the momentum space from a relativistic electron with $\gamma=10$ moving along the symmetry axis of the helical medium with strong spatial dispersion as a function of the photon energy $k_0/q$ and the parameter $n_\perp=k_\perp/k_0$. The parameters of the medium are chosen as $\alpha=\pi/4$, $v=1$, $\varepsilon=\varepsilon_h=1$, and $\omega_p=0.5q$. On the left panel: the sample thickness is $L=40\pi/q$ corresponding to $20$ complete spiral periods. On the right panel: The sample thickness is $L=160\pi/q$ corresponding to $80$ complete spiral periods. The insets: The sections of the intensity plot with respect to $k_0/q$ and $n_\perp$ for the specimen width $L=160\pi/q$. The green line in the insets depicts the intensity of radiation of right-handed photons, whereas the red line indicates the intensity of radiation of left-handed photons.
• Figure 3: On the left panel: The dispersion law with $n_\perp=0.2$ where the root selection procedure is applied. Only the real-valued roots are depicted. The red dashed lines indicate $k_0=\beta_3(k_3+ql)$, $l\in\mathbb{Z}$. The points of intersection of these lines with the dispersion law are the solutions to the equation $x_i^l=0$ and specify the positions of maxima of the radiation intensity. On the right panel: $|\sum_{i}\delta_L(x_i^l)|^2$ as a function of the photon energy $k_0/q$ and the parameter $n_\perp=k_\perp/k_0$. The electron Lorentz factor is $\gamma=10$. These plots determine the maxima of radiation with different $l$ produced by the electron moving along the symmetry axis of the helical medium. The parameters of the medium are chosen as $\alpha=\pi/4$, $v=1$, $\varepsilon=\varepsilon_h=1$, $\omega_p=0.5q$, and the specimen thickness is $L=160\pi/q$, i.e., $80$ complete spiral periods. It is seen that the red dashed line with $l=-1$ almost completely coincides with one of the branches of the dispersion law. This degenerate case corresponds to a wide maximum of radiation with $l=-1$ on the right panel and to a wide maximum of radiation visible in Fig. \ref{['A_DensIntensity']} for the radiation intensity. This contribution becomes prominent for sufficiently thick specimens.
• Figure 4: The dispersion law in the $(2N+1)$-wave approximation with $N=2$ taking into account the root selection procedure. The size of the point corresponds to the root weight lying between $0$ and $1$. The pink bands show the chiral and complete band gaps. On the left panel: The dispersion law in the paraxial limit $n_\perp=0$ is shown. On the middle panel: $n_\perp=0.2$. On the right panel: The dispersion law in the nonparaxial regime, $n_\perp=0.5$, is presented. The other parameters are chosen as $\alpha=\pi/4$, $\varepsilon=\varepsilon_h=1$ , $v=1$, and $\omega_p=1.3q$.
• Figure 5: The intensity of radiation of photons per volume of the cell in the momentum space from a relativistic electron with $\gamma=10$ moving along the symmetry axis of the helical medium with strong spatial dispersion as a function of the photon energy $k_0/q$ and the parameter $n_\perp=k_\perp/k_0$. The parameters of the medium are chosen as $\alpha=\pi/4$, $v=1$, $\varepsilon=\varepsilon_h=1$, and $\omega_p=1.3q$. On the left panel: The sample thickness is $L=40\pi/q$ corresponding to $20$ complete spiral periods. On the right panel: The sample thickness is $L=160\pi/q$ corresponding to $80$ complete spiral periods. The insets: The sections of the intensity plot with respect to $k_0/q$ and $n_\perp$ for the specimen width $L=160\pi/q$. The green line in the insets depicts the intensity of radiation of right-handed photons, whereas the red line indicates the intensity of radiation of left-handed photons.