Tuning Fabry-Perot resonances via diffraction evanescent waves

By studying acoustic and electromagnetic wave transmission through a periodic array of subwavelength holes or slits with various channel lengths, we demonstrate both experimentally and theoretically that diffraction evanescent waves can play an important role in tuning the Fabry-Perot (FP) resonances. In particular, there can be total transmission peaks at wavelengths much below that of the Rayleigh-Wood limit, and FP resonances can occur for channel length $\sim 16\%$ thinner than the half wavelength. In addition, the FP resonance condition can be tuned via both the periodicity and area fraction of holes. As a function of the ratio between the periodicity and plate thickness, the FP resonance is smoothly linked to the surface-wave-like mode induced by the periodic structure factor.

Figure 1

(Color online) (a) Transmittance of an ultrasonic wave at normal incidence through the structured brass plate with $a=2.0\mathrm{mm}$, $r=0.6\mathrm{mm}$, and $t=2.0\mathrm{mm}$. (b) Transmittance of microwave at normal incidence through the metallic grating of one-dimensional slits with periodicity $a=28\mathrm{mm}$, slit width $d=9\mathrm{mm}$, and thickness $t=38\mathrm{mm}$. The transmission peak being $>100\%$ is due to the finite size effect of the sample. The arrow indicates the Rayleigh-Wood frequency. Insets: Schematic pictures of the unit cells for the acoustic and electromagnetic samples.

Figure 2

(Color online) Intensity distributions of pressure field at the rear surface of the sample for two selected distances, $z=0.02$ and $0.17\mathrm{mm}$, at the resonance frequency of $0.598\mathrm{MHz}$. The sample has the same parameter values as those in Fig. 1. (a) and (b) are the measured and calculated field pattern at $z=0.02\mathrm{mm}$, respectively; (c) and (d) are the same for $z=0.17\mathrm{mm}$, respectively. The holes are delineated by dashed lines.

Figure 3

(Color online) Calculated acoustic and EM transmission frequencies for a square lattice of holes and metallic grating, respectively, plotted as a function of inverse channel length. Black solid lines are for normal incidence, whereas the green and red lines are for incident angle $\theta =30°$ along the [1,1] and [0,1] directions, respectively. Green ($30°\Gamma \mathrm{M}$) and red ($30°\Gamma \mathrm{X}$) dashed lines indicate the Rayleigh-Wood frequencies along these two directions. Black dashed lines delineate the Fabry-Perot condition, $t=n\lambda ∕2$, with the order $n$ denoted. The magenta dashed line represents the EM wave transmission peaks at normal incidence for a metallic grating with $d∕a=0.32$. The blue line is determined by Eq. (5), with a slope of $\sim 0.42$ (i.e., $t\cong 0.42\lambda$). Inset: Calculated resonant transmission frequencies for a plate with a square lattice of holes, in which $a=2.0\mathrm{mm}$, $t=1.0\mathrm{mm}$, and $r$ is varied from $0.1\text{to}1\mathrm{mm}$. A minimum occurs at $r=0.3a$.

Figure 4

(Color online) Solid symbols and solid lines are the measured and calculated resonant transmission frequencies of a normally incident acoustic wave on a square lattice of holes with $r=0.3a$, respectively. The solid lines are the same as the black solid lines in Fig. 3. Star symbols (measurement) and dashed lines (calculation) denote the case of an acoustic wave at 20° incidence angle along the [0,1] direction. Open symbols represent the measured transmission peaks of a normally incident microwave on a metallic grating with $d∕a=0.32$. The inset shows the measured acoustic transmittances at normal incidence for various plate thicknesses, with $a=2.0\mathrm{mm}$ and $r=0.6\mathrm{mm}$. The thickness (in mm) of each plate is given to the right of the spectrum.