We report on the terahertz transmission properties through a single slit in a thin metallic film. The properties are studied by comparing the transmissions of TE- and TM-polarized electromagnetic waves over a broad spectral range from the geometrical regime to the subwavelength limit. In the geometrical regime, the remarkable terahertz transmission due to guided modes is observed even without the contribution of surface waves. Whereas in the subwavelength limit, the surface charge oscillations associated with the TM-polarized guided mode give rise to strong transmission enhancement. The nature of the mechanisms for the terahertz transmission is elucidated using theoretical simulations of the near-field distributions and electromagnetic energy flow.
©2009 Optical Society of America
Resonant properties of plasmonic structures have been of considerable interest owing to their fundamental importance and applications in various fields [1,2]. In particular, the enhanced transmission through periodic arrays of slits or individual structures have been extensively studied both theoretically and experimentally for understanding the underlying mechanisms of the phenomenon [3–5]. The excitations of guided modes supported by the geometry and surface plasmon resonances have been suggested to play an important role in the enhanced transmission [3–6]. However, the relative contribution of these two dominant mechanisms to the transmission through an individual slit in a thin metallic film has not been directly compared over the broad spectral range from the subwavelength limit to the geometrical regime, despite its routine appearance in theoretical calculations . Terahertz (THz) time-domain spectroscopy, which has been widely used to improve the understanding of the optical properties of these structures [8–17], is a powerful technique in that it permits broad dynamic range measurements over a sufficiently wide frequency range to span the subwavelength limit to the limit of geometrical optics [18–20].
In this work, we therefore present the THz transmission through a single slit in a thin metallic film. The transmission spectra of TE- and TM-polarized THz waves are measured on the samples with different slit widths and compared over a broad spectral range from the geometrical regime to the subwavelength limit. In the geometrical regime, the resonant THz transmission due to the wave-guided modes determined by the slit width is even observed for TE polarization where there is no contribution of surface plasmonic effects . On the contrary, in the subwavelength limit, the TM-polarized transmission spectra experimentally show the strong enhancement. Theoretical simulations of the electric near-field distributions reveal that the phenomenon is due to the guided mode associated with the surface charge oscillations on the sharp edges of the single slit. We believe that the systematic understanding for the single slit as one of the most basic systems of the plasmonic structures provides opportunities for designing surface plasmon-based devices and circuits.
2. Experiments and Simulations
We use a standard THz time-domain spectroscopy system which provides broadband single-cycle pulses with the spectral range of f = 0.05 to 2 THz. All measurements are performed at normal incidence, as illustrated in Fig. 1(a) . For the measurements of the transmission spectra for a given slit width, the sample is rotated between the angles of 0° and 90° so that the electric fields are aligned parallel (TE polarization) and perpendicular (TM) to the slits, respectively. One major difference between TE and TM polarizations is that surface plasmonic effects are not expected for TE polarization configuration, since the TE waves are not likely to induce electric charge oscillation (i.e. ) [22,23].
The metallic slits are made from two 10 μm thick stainless steel films. To make the samples having continuously adjustable slit widths, two plates are bound on two mechanical stages, respectively, in which position resolution less than several microns can be easily achieved. The slits have the line edge roughness 3σ of less than 5 μm, two orders of magnitudes less than the incident THz wavelengths of interest. In the experiments, the slit width a is varied from 100 μm to 800 μm, in steps of 100 μm, which covers the broad spectral range from 0.016λ (subwavelength limit) to 5.3λ (geometrical regime) in the measurable THz frequency range. Shown in Fig. 1(b) are time traces of the incident THz wave (black line) and the TE- (blue line) and TM- (red line) polarized transmission amplitudes, for a slit width of 400 μm. Fourier transforming the time traces results in the amplitude spectra as shown in Fig. 1(c).
Figure 2(a) shows the measured TE-polarized transmission amplitude spectra normalized by the corresponding TM-polarized transmission. This normalization method is reasonable due to the fact that the TM-polarized wave propagates through the single slit with a negligible dispersion since the lowest TM mode (i.e. the TEM mode) becomes dominant, which means that it has an effective refractive index essentially equal to 1 and the transmission coefficient is almost independent of frequency . This normalization method removes any effects that may arise due to the frequency-dependent spot size of the THz wave incident on the slit due to diffraction-limited focusing of the input beam.
We first note that in the long-wavelength limit, the transmission amplitudes in all spectra are rapidly decreasing with decreasing frequency, since only evanescent waves are allowed inside the slits in the spectral regime below the lowest TE-mode cutoff frequency. For a perfect conductor, the first waveguide mode is determined by a cutoff width of , which means that, with increasing slit width a, the guided-mode resonance peaks shifts toward longer wavelength. The measured transmission amplitudes shown in Fig. 2(a) not only show the remarkable transmission peaks due to the first waveguide mode but also clearly distinguishable resonance peaks due to the higher-order modes.
The observed peak positions [dots in Fig. 2(b)] and the predicted values from the TE mode cutoffs [lines in Fig. 2(b)] are plotted versus the half wavelength cutoff frequency c/2a, where c is the speed of light. The theoretical peak values are predicted by the guided modes which are determined by the condition that the incident electric field must be equal to zero at boundaries. In the spectral range of our spectrometer, the first three guided modes are visible. Figure 2(c) shows the electric field waveforms of the three guided modes: (black trace), (red trace), and (blue trace). In the THz region, the skin depth for most common metals including stainless steel is much smaller than the wavelength. This makes that our experimental results are quite consistent with theoretical predictions as shown in Fig. 2(b).
Simulation results shown in Fig. 3 show the electric near-field distributions and Poynting vectors of two guided modes. COMSOL Multiphysics, a commercially available software based on the finite element method, are used to obtain the simulated results. To clearly show the transmitted electric field patterns and the energy flow, the simulations are performed at the wavelength of 800 and 160 μm which are the spectral positions of the first and third guided modes of the 400 μm width single slit, respectively. The spatial profiles at the entrance of the slit due to the guided modes are clearly shown in Fig. 3(a) and 3(c), having minimal points at the edges of the slit. The field lines of the Poynting vectors shown in Fig. 3(b) and 3(d) reveal the funnel-like energy flows inside the slit. The resonant transmission induced by the guided modes, especially the enhanced transmission larger than one found at the cutoff frequency, is explained by a combination of waveguiding effects and the funnel-like distributions of the electromagnetic power flow. The surface currents along the x-axis are induced by the TE-polarized incident light at the metal surface. Subsequently, the surface currents near the slit edges induce magnetic fields along z-axis, which results in the funnel-like distributions of the electromagnetic power into the slit.
Now we focus on the extreme subwavelength limit, i.e. when the incident wavelength is much larger than the cutoff wavelength. Here, the transmission amplitudes for the TM-polarized THz wave are much greater than those for the TE-polarized case. This is shown in Fig. 4(a) in which the measured TM-polarized transmission amplitude spectra are normalized by the corresponding TE-polarized transmission. To characterize the slit width dependence better, the transmitted amplitude ratio between two modes are compared at four different frequencies (0.15, 0.2, 0.25, and 0.3 THz) in Fig. 4(b). These experimental results provide us an interesting feature. We first note that the transmitted amplitude ratio becomes very rapidly larger as the frequency decreases or as the slit width becomes narrower. Even though part of the rapid increase of the ratio comes from the attenuation of the incident TE-polarized light in a subwavelength slit, comparing the ratio between the transmission amplitudes of TE- and TM-polarized waves provides us a better understanding to design devices based on polarization control, such as subwavelength slot waveguides for optical manipulation .
However, we would also expect to realize the strong enhancement in the extreme subwavelength limit . In our measurements, obtaining a quantitative measurement of the enhancement factor is challenging, because one must consider factors such as the angular distribution pattern of transmitted light in relation to the acceptance angle of the far-field detection. Also, a large variation of the incident spot size due to the broad spectral range in the THz region makes it difficult to define the illumination conditions experimentally, because it is difficult to measure the ratio between the electromagnetic radiations impinging on the area of the slit and on the metal surfaces surrounding the slit. By using a simple theoretical prediction of the spot size of the incident THz wave based on Gaussian beam optics, we obtain area-normalized enhancement factors as shown in Fig. 5 , which shows that the enhancement factor becomes larger as the slit becomes subwavelength in scale. Therefore, we can say that, in the subwavelength limit, the transmitted amount of power through the slit is larger than the total amount of electromagnetic power incident only on the area of the slit. This phenomenon is expected due to the electric charges accumulated at the edges of the slit deliver energy from the electromagnetic radiation impinging on the surfaces surrounding the slit. Although not a quantitative measurement, this is clear evidence of the increasing field enhancement with decreasing frequency for TM-polarized incident waves.
In order to understand the origin of the transmission enhancement in the subwavelength regime, the electric near-field distributions are calculated for TM and TE polarizations as shown in Fig. 6 , respectively. To obtain spatial field profiles in the subwavelength regime, the simulations are performed under the specific condition of , where the slit width and the wavelength are 400 and 6000 μm, respectively. For TE polarization, only a surface current along the slit edges is created by the propagating electric field, which causes very little transmission through the slit when the frequency of the incident light is much smaller than the cutoff frequency. On the contrary, for TM polarization where the impinging electric field is perpendicular to the slit a surface current is induced along the metal surface. The surface current induced on the perfectly conducting plate having a slit formed with two Sommerfeld half planes gives rise to accumulated charges at the sharp edges of the slit as shown in Fig. 6(a). The accumulated surface charges which are proportional to the TM-polarized local electric field feel the opposite charges at the edge of opposite side each other, which can generate strong electric field across the slit. The generated strong electric field induces the strong funneling of the electromagnetic power into the slit, subsequently leading to the enhanced transmission.
To provide a more intuitive discussion of the surface-wave-assisted waveguiding in thin metallic films, the classical Fabry-Perot theory can be applied to predict the resonant frequencies of the guided mode by a single slit . In the subwavelength limit, the spectral peak positions of the resonant transmission is given by the condition of , where h and m are the slit thickness and the Fabry-Perot mode number, respectively. The first Fabry-Perot-like mode, , is known as a fundamental mode of the slit structures. Here, the electric fields on the opposite sides of the slit are in antiphase with each other. As a result, symmetry considerations dictate that it is difficult to excite the first and higher Fabry-Perot-like modes in the thin metallic film. Therefore, the only guided mode assisted by the surface charge oscillations is given by the condition of , which can be called as quasi-zero-order Fabry-Perot mode in which strong in-phase coupling is achieved [27,28]. For the mode, the resonant wavelength tends to infinite as the width of the slit approaches zero. Therefore, although there are no transmission maxima, the TM transmission efficiency is larger than the TE transmission
In conclusion, we have investigated the terahertz transmission properties of an individual slit in a metallic film of thickness much smaller than the wavelength, over a broad spectral range from the geometrical regime to the subwavelength limit. In the geometrical regime, the resonant transmission of TE-polarized incident wave becomes predominant, which is due to the wave-guided modes determined by the slit width. In contrast, in the subwavelength limit, the TM-polarized transmission spectra show the strong relative enhancement resulting from the quasi-zero-order Fabry-Perot mode assisted by the accumulated surface charges on the sharp edges of the slit. We would expect that the systematic understanding for the single slit can improve the quality of designing polarization-dependent devices and its overall efficiencies.
This research has been supported in part by the Korea Research Foundation Grant No. KRF-2007-357-C00035, the National Science Foundation, and Peter M. and Ruth L. Nicholas Post-Doctoral Fellowship Program.
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