Highly conducting metal-film subwavelength hole arrays, lithographically fabricated on highresistivity silicon wafers in optical contact with thick silicon plates, have been characterized by terahertz time-domain spectroscopy with subpicosecond resolution and over a frequency range from 0.5 to 3 THz with 5 GHz resolution. Awell-defined ringing structure extending to more than 250 psec is observed on the trailing edge of the transmitted THz pulse. In the frequency domain this ringing structure

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... rresponds to a new type of extremely sharp resonant line structure between the fundamental surface plasmon modes of the hole array. A simple theoretical model is presented and shows good agreement with the experimental data. Although the microwave and terahertz transmission through thin-metal films or metal foils perforated periodically with apertures has been studied since 1967 [1-6], unusual high-transmission resonances through subwavelength hole arrays were only recently discovered [7, 8] at optical frequencies. These resonances occurred at wavelengths different from those predicted by the classic diffraction theory [2] . Since this discovery much work has been done to experimentally characterize the transmission of thin subwavelength hole arrays in the optical [9-21], infrared [22] , and THz [23-28] regions. The enhanced transmission is now understood to be due to the excitation of surface plasmon (SP) resonances [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] 24, 25, [27] [28] [29] [30] [31] [32] [33] . The SP enhancement can be affected by the refractive index of the adjacent medium [9,12], the shape and orientation of the holes [10, 20, 27] , and the thickness of the metal film [16] . In all these measurements, SP enhanced transmission has been observed only at the frequencies determined by the integral order SP modes coupled to the array [7, 8] . Here, we present observations of a new type of high-transmission, extremely narrow resonances at frequencies between those of the integral order SP modes. These resonances correspond to SP propagation in directions different than those allowed by the integral order modes. We call these resonances fractional order surface plasmons (FSP), which are made possible by the high conductivity of metal films at THz frequencies. In this Letter, we present a time-domain and frequency-domain study of the amplitude and phase transmission properties of a thin-metal-film subwavelength hole array, lithographically fabricated on a silicon wafer. The utilized THz time-domain spectroscopy (THz-TDS) technique measures the complete THz electric field pulse with subpicosecond time resolution [34] . For this characterization a subpicosecond THz pulse is incident on the hole array. The transmitted THz pulse consisted of an attenuated subpicosecond pulse due to the classical electromagnetic transmission of the array, followed by a dramatic ringing structure, extending to approximately 250 psec and due to the SPs excited by the incident pulse. The observed ringing provides a measure of the time dependence and lifetime of the generated, frequency-dependent, standing waves spatially coherent with the array and composed of counterpropagating, SPs. The complex numerical Fourier transforms of the measured THz pulses give both spectral amplitude and phase. The long temporal scans of the pulse measurement yields a frequency resolution of 5 GHz. We observe a complex spectral structure for the output pulses compared to the smooth featureless spectrum of the input pulses. The transmission of the array is strongly enhanced by the lowest order SP with a peak power transmission 4 times greater than the geometrical transmission. In the frequency domain, the extensive ringing on the trailing edge of the transmitted pulses corresponds to amplitude and phase resonances in the region between the lowest order SP modes of the hole array. In the THz-TDS measurement, the input THz pulse, polarized along the x axis, is incident on the metal face of the sample at the beam waist. To a good approximation, the incoming THz beam has a linearly wavelengthdependent Gaussian profile with an 9.2 mm diameter beam waist (1=e point in amplitude) at 1 THz. The metal hole array is a lithographically fabricated 280-nm-thick Al layer deposited onto a doubleside polished 0.32-mmthick, high-resistivity Si wafer. The 60 m period of the hole array has submicron precision with the rectangular hole dimensions of 15 m (x axis) 30 m (y axis). The ratio of hole area to the total area is 1=8, equal to the geometric power transmission. A 10-mm-thick highresistivity Si plate was placed in optical contact with the backside of the wafer to eliminate the backside reflection, thereby enabling clean observations of plasmon dynamics to an unprecedented 250 psec.