Fig. 1. Main plot. A 2D high-ε disk of radius r (shown in yellow) surrounded by air, along with the electric field (with polarization pointing out of the page) of its resonant whispering-gallery mode superimposed (shown in red/white/blue in regions of positive/zero/negative field respectively). Side plot. Radial plot of the electric field of the mode shown in the main plot (basically a cross-section of the main plot). Note that in air (radius/r > 1) the field follows a Hankel-function form, with an initial exponential-like regime (with long tails compared to the small disk size), followed by the oscillatory/radiation regime (whose presence means that energy is slowly leaking out of the disk). Table. Numerical FDFD (and in parentheses analytical SV) results for the wavelength and absorption, radiation and total loss rates, for two different cases of subwavelength-disk resonant modes. Note that disk-material loss-tangent Im{ε}/Re{ε}=10⁻⁴ was used. (The specific parameters of the plot are highlighted with bold in the table.) Finally, note that for the 3D case the computational complexity would be immensely increased, while the physics would not be significantly different. For example, a spherical object of ε = 147.7 has a whispering gallery mode with m = 2, Q_rad = 13,962, and λ/r = 17. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 2. Plot. System of two same 2D high-ε disks of radius r (yellow) for medium-distance D coupling between them, along with the electric field of the normal mode, which is an even superposition of the single-disk modes of Fig. 1, superimposed (red/white/blue). Note that there is also a normal mode, which is an odd superposition of the single-disk modes of Fig. 1 (not shown). Table. Numerical FDFD (and in parentheses analytical CMT) results for the average of the wavelength and loss rates of the two normal modes (individual values not shown), and also the coupling rate and “strong/weak-coupling” figure-of-merit as a function of the coupling distance D, for the two cases of disk modes presented in Fig. 1. Only distances for non-radiative (D < 2r_C) coupling are considered. Note that the average Γ^rad (and thus total Γ) shown are slightly different from the single-disk value of Fig. 1, due to far-field interference effects present for the two normal modes, for which CMT cannot make predictions and this is why analytical results for Γ^rad are not shown but the single-disk value is used. (The specific parameters of the plot are highlighted with bold in the table.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 3. Plot. A wire loop of radius r connected to a pair of d-spaced parallel plates (shown in yellow) surrounded by air, along with a slice of the magnetic field (component parallel to the axis of the circular loop) of their resonant mode superimposed (shown in red/white/blue in regions of positive/zero/negative field respectively). Table. Numerical FEFD (and in parentheses analytical) results for the wavelength and absorption, radiation and total loss rates, for two different cases of subwavelength-loop resonant modes. Note that for conducting material copper (σ = 5.998 × 10⁷ S/m) was used. (The specific parameters of the plot are highlighted with bold in the table.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 4. Plot. System of two same wire loops connected to parallel plates (yellow) for medium-distance D coupling between them, along with a slice of the magnetic field of the even normal mode superimposed (red/white/blue). Note that there is also an odd normal mode (not shown). Table. Numerical FEFD (and in parentheses analytical) results for the average wavelength and loss rates of the two normal modes (individual values not shown), and also the coupling rate and “strong/weak-coupling” figure-of-merit as a function of the coupling distance D, for the two cases of modes presented in Fig. 3. Note that the average Γ^rad shown are again slightly different from the single-loop value of Fig. 3, due to far-field interference effects present for the two normal modes, which again the analytical model cannot predict and thus analytical results for Γ^rad are not shown but the single-loop value is used. (The specific parameters of the plot are highlighted with bold in the table.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 5. Plots. A disk (yellow) in the proximity at distance D_h/w of an extraneous object (yellow): (a) a high ε = 49 + 16i (which is large but actually appropriate for human muscles in the GHz regime [16]) square object of same size (area) with the disk, and (b) a large roughened surface of ε = 2.5 + 0.05i (appropriate for ordinary materials such as concrete, glass, plastic, wood [16]), along with the electric field of the disk’s perturbed resonant mode superimposed (red/white/blue). Tables. Numerical FDFD results for the parameters of the disk’s perturbed resonance, including absorption rate inside the extraneous object and total (including scattering from the extraneous object) radiation-loss rate, for the two cases of disk modes presented in previous figures. Note that again disk-material loss-tangent Im{ε}/Re{ε}=10⁻⁴ was used, and that is again different (decreased or even increased) from the single-disk of Fig. 1, due to (respectively constructive or destructive) interference effects this time between the radiated and strongly scattered far-fields. (The specific parameters of the plots are highlighted with bold in the tables.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 6. Plot. System of two same disks (yellow) for medium-distance D coupling between them in the proximity at equal distance D of two extraneous objects (yellow): both a high ε = 49 + 16i square object of same size (area) with the disks and a large roughened surface of ε = 2.5 + 0.05i, along with the electric field of the system’s perturbed even normal mode superimposed (red/white/blue). Table. Numerical FDFD results for the average wavelength and loss rates of the system’s perturbed two normal modes (individual values not shown), and also the perturbed coupling rate and “strong/weak-coupling” figure-of-merit as a function of the distance D, for the two cases of disk modes presented in previous Figures. Only distances for non-radiative (D < 2r_C) coupling are considered. Note once more that the average Γ^rad takes into account interference effects between all radiated and scattered far-fields. (The specific parameters of the plot are highlighted with bold in the table.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 7. Black line. Efficiency of converting the supplied power into useful work (η_work) as a function of the perturbed coupling-to-loss figure-of-merit, optimized with respect to the power-extracting rate Γ_work (related to the load impedance), for all values of the various quality factors that are present in the system. Blue and red lines. Ratios of power conversion respectively into radiation (including scattering from nearby extraneous objects) and dissipation inside an extraneous object as a function of the figure-of-merit for dielectric disks of and , and for three values of . Green line. Ratio of power conversion into radiation for conducting-wire loops of and , and assuming . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)