Microwave transmission modes in compound metallic gratings Y. G. Ma, 1, * X. S. Rao, 2 G. F. Zhang, 1 and C. K. Ong 1 1 Centre for Superconducting and Magnetic Materials, Department of Physics, National University of Singapore, Singapore 117542, Singapore 2 Temasek Laboratories, National University of Singapore, Singapore 119260, Singapore Received 4 April 2007; revised manuscript received 10 May 2007; published 10 August 2007 Microwave transmission through one-dimensional metallic compound grating is studied up to 18 GHz. The metallic compound grating consists of a basic unit of one slit a type, two slits ab type, and three slits abc type of different widths. Greatly enhanced transmission is observed at the frequencies near the first and second order waveguide harmonics. The splitting of transmission peak is found for the ab- and abc-type grating. This effect is explained by the multiphase patterns of the E-field distributions inside the slits, predicted by the numerical calculations. These resonance modes are further physically understood in terms of their photonic band structures. The theoretical bands for the a-type grating are calculated using a quasianalytic model and those for the ab- and abc-type gratings with superlattice periodicities are plotted according to Brillouin zone folding effect, which show good agreement with the measured results. DOI: 10.1103/PhysRevB.76.085413 PACS numbers: 73.20.Mf, 78.70.Gq, 42.25.Bs, 42.79.Dj I. INTRODUCTION In the last few years after the discovery of extraordinary light transmission through two-dimensional metallic hole arrays, 1 a great deal of effort has been done to understand the electromagnetic EM diffraction through subwavelength metallic apertures triggered by both scientific interests and potential important applications. 2–4 So far, the excitation of surface plasmon polaritons SPPs in the dielectric/metal interface 5–8 has been generally believed to play a crucial role in this effect. In one-dimensional metallic grating, the local- ized cavity and/or slit field resonance, regarded as waveguide mode, can also give rise to enhanced electromagnetic trans- mission or absorption. 9 Other than the SPPs and waveguide mode, there is a third kind of resonance, known as phase resonance, 10,11 reported in metallic gratings with period of several cavities and/or slits contributed to the enhancement of the transmission mode. For such compound gratings, when illuminated at p-polarized radiation there are charac- teristic frequencies at which the adjacent slits can resonate at out-of-phase configurations accompanied by strong field in- tensification effect inside the cavity and/or slit. 12,13 The in- crease of the cavity and/or slit numbers in compound grat- ings will give rise to new degrees of freedom for the near- field distribution. The multiple patterns for phase resonance can be produced as a result of redistribution of electromag- netic energies when reaching the characteristic frequencies at different diffraction orders. A resultant maximization of the specular efficiency or splitting of transmission peak has been predicted in compound gratings of finite arrays of cavities and/or slits in period. 13–15 In this work, we study the microwave transmissions on compound metallic gratings. Their structures are changed by periodically increasing the slit widths in the Al slat arrays. Different from the previously reported gratings, 14,15 our com- pound gratings are of no structural symmetry in their basic units. Thus, they can be regarded as the general cases for electromagnetic diffractions on metallic gratings and can ex- cite all the possible resonance modes at normal incidence without degeneracy. Complex transmission features peak and dip associated with these resonance modes are ob- served, which are numerically understood 16 by multiphase distributions of the resonant fields inside the slits. The physi- cal origin for these phase patterns is explored in terms of their photonic band structures from both experimental mea- surement and theoretical calculations where a quasianalytic model and Brillouin zone folding effect are employed. II. SAMPLES AND MEASUREMENT In Fig. 1, we schematically show the samples constructed by stacking together 30 aluminum slats of width w = 4.5 mm, height h = 18.5 mm, and length 30 cm. Figure 1a shows the structure of a uniform grating with air-filled slit of width a = 0.5 mm, thereby corresponding to a period d = 5 mm. Figures 1b and 1c show two compound grat- ings with unit cells consisting of two slits of widths a =0.25 mm and b =0.5 mm and three slits of widths a E  y x z (a) a-type a=0.5mm d=5mm w=4.5mm h=18.5mm (c) abc-type a=0.25mm c=1mm d=15.25mm b=0.5mm a=0.25mm d=9.75mm b=0.5mm (b) ab-type FIG. 1. Schematic illustrations of the sample gratings of a a type, b ab type, and c abc type together with their parameters. The incidence plane is in the yz plane with the E-field directions perpendicular to the grating slits. PHYSICAL REVIEW B 76, 085413 2007 1098-0121/2007/768/0854135 ©2007 The American Physical Society 085413-1