Fig. 3. Correlations in the CL into a dielectric waveguide produced by modulated electrons.

(A) Conceptual scheme of the experimental setting on the basis of photonic circuitry. A laser field structures a pulsed electron beam, which excites coherent radiation in a parallel-aligned waveguide. Mixing a replica of the driving laser field, E_R, with the CL field, E_CL, results in a difference between the signals recorded in the detectors at the output ports of the interferometer, I₁ and I₂. (B) Properties of CL emitted into the waveguide for an interaction length of 30 μm positioned at a distance z = 6.43 mm away from the electron modulation region. The coherent CL amplitude (blue) is the product of the spectral coupling amplitude, ∣g_ω∣ (red), and $\sqrt{\text{DOC}}(\mathrm{\omega })$ (gray), where phase matching between the electron and the guided modes limits the CL emission to a single harmonic peak. (C) to (H) show CL properties as a function of the propagation length near the fiber, L_prop: (C) to (E) show the spectral distribution of ∣g_ω∣ and $\langle {\widehat{a}}_{\mathrm{\omega }}\rangle$, whereas (F) to (H) show the emitted CL-field pulse in the time domain, E(t). The different columns show the CL properties for an electron propagation length L_prop = 10 μm (C and F), 100 μm (D and G), and 1 mm (E and H) along the waveguide. The effect of L_prop on the peak probability of emission is reflected in the vertical scale. When the coupling bandwidth is narrower than the width of the DOC [e.g., in (E)], the CL pulse is temporally distorted (H). Details of the coupling into a cylindrical waveguide are presented elsewhere (36).