We demonstrate that conically tapered cylindrical apertures can be used to efficiently concentrate broadband terahertz (THz) radiation. Keeping the aperture diameter on the input plane fixed, we show that as the diameter of the aperture on the exit plane is decreased, we obtain an increase in the magnitude of the transmitted electric field that varies inversely with the output aperture diameter. Correspondingly, the transmitted THz intensity concentration increases inversely with the square of the output aperture diameter. For the smallest aperture that we fabricated, we obtain a ~50 fold increase in the transmitted THz intensity. We expect further increases in the intensity concentration with smaller output apertures. As the output aperture diameter is decreased with a corresponding increase in the concentration factor, we directly measure an increase in the propagation time delay of a narrowband pulse through the structure. Finally, we demonstrate that further increase in the concentration factor can be achieved by engraving circular grooves around the input aperture.
©2010 Optical Society of America
The ability to concentrate optical radiation has found broad utility in applications including imaging, nonlinear optics and development of compact optical and optoelectronic devices. The most common approach for achieving radiation concentration is through the use of a dielectric lens. However, the minimum lateral confinement is determined by diffraction, and thus is of the order of λo/n, where λo is the optical wavelength in free space and n is the medium refractive index. Recently, there has been great interest in the use of surface plasmons, namely electromagnetic waves bound to a metal-dielectric interface, to achieve subwavelength confinement [1,2]. Among the various approaches that have been examined, there have been a number of theoretical and numerical studies suggesting the possibility for subwavelength concentration of radiation using tapered metal wires and plates, as well as tapered holes and slits [3–12]. Associated with this increase in the transmission efficiency, a reduction in the group velocity of the transmitted radiation is also expected .
The topic of radiation concentration has been explored previously within the field of microscopy . In such cases, field enhancement near nanoscale metal structures originates from a combination of the geometrical properties of sharply tapered structures and localized surface plasmon resonances. This latter phenomenon typically depends sensitively on the wavelength in the visible and near-infrared region of the electromagnetic spectrum. In contrast to plasmonic applications in the visible, where Ag and Au are the metals of choice because of their low associated propagation losses, a broad range of metals (including Pb and many exotic metals ) exhibit sufficiently high conductivities in the terahertz (THz) spectral region , so that propagation losses over the appropriate examined length scale is minimal. One consequence of using such highly conducting materials in the THz range is that the geometrical parameters of the tapered structure can have significant influence on its effective dielectric properties [16,17].
We report here the experimental realization of concentrating THz radiation through a conically tapered circular aperture. As the diameter of the exit aperture is decreased, we obtain a corresponding increase in the concentration magnitude. For the smallest aperture that we fabricated, we obtain a ~50 fold increase in the transmitted THz intensity; additional increases in the intensity concentration are expected with smaller output apertures. By engraving circular grooves around the input aperture, we are able to further enhance the concentration, albeit over a narrow frequency range. The ability to concentrate radiation not only creates new opportunities in THz near-field spectroscopy and imaging, but also has significant implications in optical applications including photolithography and displays.
2. Experimental details
We used conventional THz time-domain spectroscopy (THz-TDS), as shown in Fig. 1(a) , to measure the properties of the tapered apertures (TAs). A unique aspect of THz-TDS is that the THz electric field is measured. Thus, both the amplitude and phase spectra are obtained, without the need to resort to Kramers-Kronig transformations. We measured the time-varying electric field of the radiated THz pulse and obtained the spectral amplitude and phase directly by performing Fourier analysis. We used photoconductive devices for both emission and coherent detection. An off-axis paraboloidal mirror was used to collect and collimate the THz radiation from the emitter, with the resulting 15 mm diameter THz beam normally incident on the TA. Reference transmission spectra were taken using apertures fabricated in 25 µm thick stainless steel foils. The detected transient photocurrent is then Fourier transformed and normalized to the reference transmission, yielding the electric field transmission spectrum in the range from ~0.05 - ~0.8 THz. We also used homemade bandpass filters to obtain narrowband frequency signals of 40 GHz full-width at half-maximum. The peak frequency of the narrowband radiation was chosen to be above the cutoff frequency of the TA.
We fabricated the TA structures using a Pb-Ti alloy that was melted and poured into a cylindrical mold. A tapered stainless steel wire was then placed in the mold perpendicular to the molten metal surface. A conically TA was formed when the wire is pulled out of the blend. We fabricated five different TA structures using 4-6 mm thick slabs of a lead-titanium blend with a circular input aperture diameter of 1.9 mm, a taper half-angle of 7.5°, and a circular output aperture diameter that varied between 200 µm and 800 µm, as shown in Fig. 1(a). An optical micrograph of one such conically TA is shown in Fig. 1(b). Reference cylindrical apertures were fabricated in 25 µm thick stainless steel foils by laser ablation. The TA with the annular grooves was fabricated by heating up the lead-titanium blend of the TA and pressing a bullseye structure fabricated in stainless steel. Upon cooling, the bullseye structure was removed, leaving engraved annular grooves centered about the input aperture TA.
It is apparent from the picture shown in Fig. 1(b) that imperfections exist not only within the TA, but also on the input and output planes of the structure. However, these defects are smaller than the relevant THz wavelengths. As we show in the simulations below using identical geometrical parameters, these blemishes do not appear to adversely affect the results. For reference purposes, we also fabricated a number of circular apertures in a 25 µm thick free-standing film of stainless steel. These apertures had diameters of 1.9 mm (D1), as well as values that correspond to D2 in each of the fabricated TAs.
3. Experimental results, simulation and discussion
Figure 2 summarizes our basic THz transmission results for the reference and tapered holes. Figure 2(a) shows representative THz transmission amplitude spectra, t(ν), up to ~0.9 THz for the 1.9 mm diameter and 440 µm diameter reference apertures in 25 µm thick metal films, as well as a TA structure with D1 = 1.9 mm and D2 = 440 µm. It is apparent that t(ν) for the two reference apertures is broadband, while that of the TA exhibits strong suppression below ~0.3 THz. For a circular aperture we would expect increasingly suppressed transmission below the cut-off frequency, νc ( = 1.841c/(πD2) , where c is the speed of light in vacuum). In the case of the 440 µm reference aperture, the film thickness (25 µm) is sufficiently small that frequencies below νc (~0.4 THz) exhibit only modest transmission suppression; whereas in the TA structure, the waveguide cutoff phenomenon is more evident. In all three cases, the high frequency roll-off arises from the frequency response associated with the photoconductive emitter-detector pair in the THz TDS system.
Figure 2(b) shows amplitude transmission efficiency, , where x corresponds to the appropriate reference (440 µm, in this case) or the TA. This quantity yields the relative spectral transmission efficiency of any aperture relative to a reference aperture of diameter D1. It is clear that even though the TA is nearly two orders of magnitude thicker than the reference 440 µm aperture, it exhibits greater transmission efficiency. Figure 2(b) (inset) shows the spectrum of the field amplitude concentration factor, fE(ν), where . Here, x corresponds to the output aperture diameter D2. In Fig. 2(c) we plot the field amplitude concentration factor, fE, which corresponds to the numerical value of fE(ν) at ~0.1 THz beyond the cutoff frequency of the output aperture, as a function of D2. We note that fE varies inversely with D2, so that the intensity scales with (D2)−2. In addition, the minimum frequency for which transmission concentration can be obtained corresponds to the cutoff frequency associated with D2 for each TA structure [Fig. 2(c) inset].
In order to improve our understanding and confirm the experimental observations, we performed 3D finite-difference time-domain (FDTD) calculations using parameters matching those used in our experiments; the results of these transmission concentration simulations are summarized in Fig. 3 . We assumed that the metal regions could be modeled as perfect electrical conductors, since the conductivities of conventional metals are very high at THz frequencies. Figure 3(a) shows a snapshot of the electric field pattern for a cross-section of a TA structure with D1 = 1.9 mm and D2 = 440 μm. A broadband vertically polarized THz plane wave is incident on the TA from the right; and on the left we show the vertically polarized THz pulse radiated from the aperture. It is apparent that a fraction of the incident pulse is reflected from the TA, resulting in a complex electric field distribution to the right of the TA input aperture. Within the TA structure itself, however the magnitude of the THz electric field clearly increases as it propagates through the TA. As expected, the pulse is radiated from the aperture in the form of a spherical wave.
In Fig. 3(b), we show fE(ν) for several TA structures with x ( = D2) = 200 µm, 300 µm, and 440 µm. We note that the simulated fE(ν) for the TA with D2 = 440 µm closely matches the experimentally derived fE(ν) response for the TA with D2 = 440 µm from Fig. 2(b). A low frequency concentration factor of less than 1 arises from the fact that for each TA structure, the long wavelength transmission is more sharply suppressed than with the corresponding reference aperture below the cutoff frequency. In Fig. 3(c) we show the fE value at ν > νc for TA structures with D2 ranging from 100 µm to 1100 µm. The amplitude concentration factor varies inversely with D2 over a wide range of output aperture diameters, suggesting the ability to obtain dramatically increased concentration factors by further decreasing D2. We also compare the calculated fE values with the fE values obtained experimentally; the excellent agreement obtained validates the simulation approach. The minimum frequency at which transmission concentration can be obtained corresponds to the cutoff frequency associated with D2 for each TA [Fig. 3(c) inset]; again in excellent agreement with experimental observations.
It has been suggested that with concentration of electromagnetic radiation through a tapered structure there should be a corresponding reduction in the group velocity of the transmitted radiation . This results in a group delay that is in excess to the simple transit time through the length of the TA (i.e. it results from a true reduction of the group velocity within the TA). From our time domain measurements, we can directly obtain the group velocity delay using two separate approaches: (i) based on the broadband transmission measurements discussed in Fig. 2; and (ii) by measuring delay times using narrowband THz pulses. In Fig. 4(a) we show the difference in the measured phase spectrum, Δφ(ν) between a TA structure having D1 = 1.9 mm and D2 = 440 µm, and a reference aperture with diameter of 440 µm. The spectral phase difference can be used to directly determine the excess group delay, τ(ν), as a function of frequency, ν, where
In Fig. 4(a) we show the obtained group velocity delay between a reference 440 µm diameter aperture and a TA structure with D2 = 440 µm, which is derived from the observed phase difference [Fig. 4(a) (inset)]. From this plot, we expect a value of τ = 3.5 ps at 0.38 THz. As a check of the observed group delay, we generated narrowband THz radiation at selected frequencies that lie just above the cutoff frequencies for several of the TA structures. In each case, the bandwidth of the incident radiation was less than 50 GHz. In Fig. 4(b), we show the measured delay time between a narrowband temporal THz pulse at 0.38 THz [Fig. 4(c)] propagating through a reference aperture of diameter 440 µm and a TA with the same output aperture diameter. The observed group velocity delay of 3.6 ps is in excellent agreement with the group velocity delay obtained from Fig. 4(a) at 0.38 THz. For the 5.55 mm thick TA structure, this group delay corresponds to a THz group velocity of 0.8c, where c is the speed of light in vacuum. As a necessary check, we show in Fig. 4(c) that the spectrum of the transmitted narrowband pulse through both apertures and the incident pulse are identical, demonstrating that no pulse distortion has occurred, which would complicate the extraction of a group velocity delay. In Fig. 4(d) we show the measured and simulated values of the group velocity delay as a function of D2; the black line is a linear fit to the experimental data that corresponds to a THz group velocity of 0.66c, which fits both the experiment and simulation τ-values. For cylindrical waveguides, it is well known that the group velocity varies with the cylinder diameter. Thus, for the TA, this value may be considered an effective group velocity, since the aperture diameter varies along the propagation axis . For comparison, we also plot the expected group velocity delay if the wave propagated along the 7.5° half angle conically tapered wall of the aperture with a group velocity of c. The effective measured group velocity in this case corresponds to 0.99c.
Finally, we demonstrate the ability to further enhance the THz transmission through the TA structure using fabrication external to the structure itself. In our measurements so far, the throughput is fundamentally limited by the amount of radiation incident on the input aperture. Structuring the surface around the input aperture can be used to direct more radiation into the TA . We have previously shown that when periodically spaced annular grooves surround an aperture, then the transmitted THz waveform consists of a superposition of oscillations arising from the coupling of the incident THz pulse to a surface wave pulse from the annular grooves . These oscillations are temporally shifted from one another in accordance with the spatial distance between the grooves. In Fig. 5 we show that the measured transmission enhancement is ~35% enhancement at ~0.3 THz relative to an identical bare TA structure (one with no surrounding grooves). Figure 5 (inset) shows an optical micrograph top view of a TA structure engraved with several annular grooves. The center-to-center spacing between these grooves is 1 mm, which corresponds to a THz frequency of 0.3 THz. We expect that optimization of the groove cross-section and number of grooves can further increase this enhancement .
In summary, our results clearly demonstrate the ability to obtain significant concentration of THz radiation through conically TA structures. Experimentally, we demonstrated a 7-fold increase in the electric field concentration of THz radiation, which corresponds to ~50-fold increase in the transmitted THz intensity. By adding a surface corrugation around the input aperture, an additional increase in the THz throughput was achieved. We also obtained a corresponding increase in the group velocity delay through the TA structure that is due from a reduction in the group velocity, in qualitative agreement with predictions. Simulations suggest that greater increase in the radiation concentration along with increase in the group delay can be obtained using smaller output apertures. By placing a thin wire down the center of the TA, the aperture would be transformed into a tapered coaxial waveguide . Such a structure would support a TEM mode, which does not have a corresponding cutoff frequency. Finally, in our present contribution we only examined conically TA apertures; we may obtain greater enhancement using other taper shapes. Our investigation is expected to lead to improved near-field imaging capabilities, as well as to new optoelectronic device embodiments that may be particularly important in the THz spectral range, which is largely devoid of usable optoelectronic devices.
This work was supported in part by the National Science Foundation under Grant # ECCS-0801965.
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