Exotic radiation from a photonic crystal excited by an ultrarelativistic electron beam

We report the observation of an exotic radiation (unconventional Smith-Purcell radiation) from a one-dimensional photonic crystal. The physical origin of the exotic radiation is direct excitation of the photonic bands by an ultrarelativistic electron beam. The spectrum of the exotic radiation follows photonic bands of a certain parity, in striking contrast to the conventional Smith-Purcell radiation, which shows solely a linear dispersion. Key ingredients for the observation are the facts that the electron beam is in an ultrarelativistic region and that the photonic crystal is finite. The origin of the radiation was identified by comparison of experimental and theoretical results.

Figure 1

Experimental geometry. The electron beam is in the $x$ direction $10\mathrm{mm}$ above the photonic crystal. Cylinders for which data are given in Table are arrayed with axes in the $z$ direction. The intensity of millimeter-wave radiation is measured as a function of $(\theta ,\omega )$ at the far-field observation point in the $xy$ plane.

Figure 2

(Color) Intensity maps of radiation observed in the $xy$ plane for sample 2 (a) and sample 3 (b). The ratio of signal to noise was 5%. Thick solid lines with slopes $\pm c$ are the light lines forming the boundary of the light cone. Two $v_n$ lines, marked as $v_1$ and $v_2$, are drawn parallel to the light line. Dotted lines $u_1–u_5$ indicate the lines on which unconventional SPR appears.

Figure 3

(Color) Bird’s eye views of calculated intensity maps of radiation observed in the $xy$ plane for sample 2(a) and sample 3(b). The boundaries of the map are the light lines of slope $\pm c$. The quasiguided PBs of even (odd) parity with respect to the mirror plane $y=0$ are also shown by red (blue) lines in (a). In (b) only the even-parity modes are shown.