Fig. 1. (a) Structural diagram of the optical funnel. PEC (colored pink) and PMC (colored blue) are used as the top/bottom and side boundaries of the whole funnel, respectively. To show the internal structure of the funnel more clearly, the PEC and PMC on part 2 (colored red) and the neck (colored green) are not drawn. (b) Refractive index distribution of the whole structure. (c) An implementable structure of the designed optical funnel by filling ceramic blocks with different permittivity (indicated by different colors and numbers) or air inside the waveguide, where w1=2λ0/3, w2=0.01w1, w3=0.001w1, h=0.01w1, Δh=0.01h, and the working wavelength λ0=3  m.

Fig. 2. Simulated results. (a) Amplitudes of electric fields and magnetic fields distributions inside the funnel when a TEM wave of unit amplitude is illuminated onto the inlet of the designed optical funnel. (b) Electric fields (red) and magnetic fields (blue) enhancement factor along the axis of the optical funnel (x=0), where w1=2/3λ0, w2=0.01w1, w3=0.1w2, h=0.01w1, and Δh=0.01h. (1), (2), and (3) represent the corresponding regions in (a).

Fig. 3. Average value (dots; left y axis), standard deviations (error bars; left y axis), and uniformity (blue squares and red diamonds; right y axis) of the (a) electric fields and (b) magnetic fields with varied funnel width in the funnel’s neck (at 0.1 GHz). Average value (dots; left y axis), standard deviations (error bars; left y axis), and uniformity (red diamonds; right y axis) of the (c) electric fields and (d) magnetic fields in the funnel’s neck with varied frequency (with funnel-width ratios w1/w2=100 and w1/w3=1000).

Fig. 4. (a), (b) Numerical simulation and (c), (d) theoretical calculation results for the electric and magnetic fields enhancement factors in the funnel’s air neck, respectively, when the funnel-width ratios (w1/w2 and w2/w3) of the designed optical funnel vary.

Fig. 5. Simulated results: the relation between the working frequency and the electric/magnetic fields enhancement factors AE (red) and AH (blue) in the air neck of the designed funnel with fixed funnel-width ratios w1/w2=100 and w1/w3=1000.

Fig. 6. (a) In the reference space, 2D structural correspondence between the rectangular waveguides and (b) the optical funnel in the real space, respectively, based on the coordinate transformation in Eq. (4).

Fig. 7. Funnel 2D view (x−y plane) from Fig. 1(a). Different y coordinates indicate different locations in the funnel: y=y1 represents the end of part 1; y=y2 represents the end of the thin layer; y=y3 represents the end of part 2 (the upper part); and y=y4 represents the end of part 3.

Table 1. Permittivity of the Ceramic Blocks^a