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We present a new class of plasmonic photoconductive THz emitters based on a complementary Sierpinski gasket fractal geometry. Due to the presence of sub-wavelength perforations on the surface of the antenna, these antennae operate in the plasmonic regime. By utilizing the unique self-similar and space filling of the tailored fractal surface and the plasmonic surface current spatial distribution, photoconductive THz emitters exhibiting superior performance (~80% increase in the emitted THz radiation power) to conventional bow-tie and Sierpinski gasket THz emitters are demonstrated. It is shown that the self-similarity of the surface plasmon current present on the antenna surface is responsible for this emission enhancement.
©2010 Optical Society of America
1. Introduction
There has been an increasing interest in utilizing terahertz (THz) radiation for imaging, spectroscopy, and sensing [1–3]. Properties such as low attenuation through common dielectrics; being of shorter wavelengths compared to microwaves, which results in higher resolution imaging; and, the non ionizing nature of the radiation at these frequencies (3 meV at 1 THz) makes THz radiation a suitable candidate for the above mentioned novel applications among others. With such attractive characteristics research for optimized THz emitters, in particular photoconductive (PC) switch emitters, has gained considerable attention in the THz community. To date, investigation of producing high-field THz radiation via PC emitters involved the implementation of various THz PC configurations, such as bowtie, strip line, log-periodic, as well as dipole antenna emitters, all utilizing photoconductively-driven excitation schemes [4–6]. Nonetheless, the common theme of such designs is the excitation of free carriers in a semiconductor gap and then coupling the THz radiation to free space by means of the surrounding metallic electrodes, which act as an emitting antenna. The emission properties of these THz sources have been explored both in terms of radiation spectrum bandwidth and the total radiation power emitted [4, 5]. In this regard, there have been reports on increasing the intensity of the THz radiation by optimizing the photoconductive antenna’s design [8,9]. In parallel, by utilizing complex photoconductive antenna designs, there have been investigations for obtaining better directivity [10] and multiband emission of THz radiation [11]. While much progress has been made in this area, to date there has not been any investigations on antenna surface engineering to improve the emission characteristics of the photoconductive antennae by means of sub-wavelength control of THz surface plasmon currents.
The magnitude and orientation of transient surface currents on a PC THz antenna govern the amount of the emitted THz power and the polarization purity of the emitted radiation. By modifying the surface current flow pattern on the radiating element (antenna arms or transmission line), the radiation characteristics of the emitter can be configured to provide a particular resonance frequency, bandwidth, gain, efficiency, and polarization selectivity. In the microwave regime, this task is often achieved by utilizing spatial patterning of the antenna patch surface in the form of a fractal arrangement.
Fractal-shaped antennae are becoming very attractive in designing innovative antennae for communication systems. This stems from their self-similar and space filling geometrical arrangement that map into unique electromagnetic radiation properties. Due to these unique properties, advanced antennae with capabilities of being miniature, operating at multi-frequencies and possessing high directivity have been realized [12–14]. In this paper, we present a new class of plasmonic PC THz emitters based on a Sierpinski gasket fractal geometry. Comprehensive investigation of the radiation characteristics of the complementary Sierpinski fractal PC THz emitters is introduced and explored for various fractal orders. By utilizing the unique aforementioned self-similar and space filling of the tailored fractal surface and the plasmonic surface current spatial distribution, PC THz emitters exhibiting superior performance to conventional bow-tie and Sierpinski gasket THz emitters are demonstrated .
Interestingly, the radiation power of the emitted THz shows an enhancement as the order of the complementary fractal was increased up to third order. To compare the radiation power of such antennae, Siepinski’s fractal antennae were also tested. It was found that the complimentary of the second-order Sierpinski triangle gave the best radiation power compared to all other fractal and bow-tie antennae. To quantify this, an ~80% increase in the radiated power of this antenna was observed when compared to the bow-tie antenna. To the best of our knowledge this is the first time that Sierpinski’s fractal antennae and their complimentary geometry have been used as emitters for the generation of THz radiation.
2. Experimental methods
The PC THz antenna architecture follows that of the common Sierpinski fractal. Here, one starts with a simple 60° equilateral triangle as basic bow-tie antenna. For the first iteration the middle of each sides are connected and that surface is cut out of the solid bow-tie antenna surface. The iteration process is repeated for different orders, i, such that any triangular portion is an exact replica of the whole gasket, or the gasket is perfectly self-similar. As the number of iterations increases, self-similar smaller triangular apertures are formed on the surface of the antenna. The dimension of the Sierpinski gasket is log (3/2) = 1.5849 and the total solid area of the antenna surface, Ai, at each iteration is given by:
The basic design of the PC THz emitter antenna structure is a complementary bow-tie Sierpinski gasket fractal. These emitter antennae were fabricated using an inverted pattern of a regular Sierpinski gasket fractal pattern, where the total solid area of the antenna surface, ACi = 1-Ai, at each iteration. However, in order to maintain a constant photoconductive area (optically-excited antenna feed point) for the complementary Sierpinski gasket fractal antennae, a 2 µm wide strip frame circumscribed the inverted Sierpinski gasket fractal units. Notably, with such reconfiguration, the electric field applied to the photocurrents is kept the same for all types of fractal antennae understudy. The PC THz emitters were fabricated by means of photolithography on a 500 µm thick semi-insulating (100) GaAs substrate having a resistivity of 2.5 × 107 Ω cm. Following a photolithography patterning step, thin layers (20nm/100nm) of Cr/Au were sputtered and the metallic fractal pattern is transferred to the substrate using a lift-off process. In order to apply a bias voltage to the antenna arms, two 10 µm wide transmission lines were attached to the fractal antenna elements. The emitters have a length of 95 µm and are flared at 60°, thus, by considering the GaAs permittivity, the bow-tie antennae are designed for a peak frequency of 0.5 THz. It should be noted that throughout the investigation the antennas’ shape and length are kept fixed and only the sub-wavelength features within the antenna are altered in a self-similar manner to form the Sierpinski gasket fractal. This ensures that at the optically-excited antenna feed point the biasing electric field is the same for all of the THz emitters.
Figure 1(a-d) illustrates scanning electron microscope (SEM) images of the fabricated complementary bow-tie PC THz emitter and the complementary Sierpinski PC THz emitters for the first three orders (i = 1, 2 and 3). Overall, it can be stated that the PC THz emitters encompass triangles of lengths ~52 µm for the complementary bow-tie emitter down to ~1.5 µm for the complementary third-order Sierpinski PC THz emitter.
Fig. 1 Complementary of (a) bow-tie, (b) first order, (c) second order, and (d) third order Sierpinski PC THz emitters
These sub-wavelength features of the antenna are vital to the operation of the PC THz emitters as they enable the emitters to access the THz plasmonic regime. For comparison, a traditional bow-tie antenna was fabricated along with three (i = 1, 2 and 3) Sierpinski PC THz emitters. SEM images of these emitters are shown in Fig. 2 .
Fig. 2 PC emitters of (a) the bow-tie, (b) first order, (c) second order, and (d) third order PC THz emitters.
The fabricated fractal PC THz emitters were illuminated by a 60 mW Ti:sapphire laser pulse having a duration of 10 fs, a central wavelength of 800 nm, and a repetition rate of 80 MHz. The laser pulse was focused onto the 5 µm gap between the two antenna arms that is biased at 12 Vpp. The emitted THz radiation was collected and collimated using a system of four off-axis gold-coated parabolic mirrors. The radiated THz and optical probe pulses were focused collinearly onto a 500 µm thick <111> ZnSe electro-optic crystal where complete information of the time-domain THz electric field was obtained. The resulting THz radiation was a single-cycle, linearly polarized, ~1 ps wide pulse.
3. Results and discussion
The effect of the sub-wavelength fractal openings present in the complementary Sierpinski PC THz emitters on the radiation properties of such emitters is investigated using time-domain THz spectroscopy. To isolate this effect, the electric field across the PC junctions was kept fixed for all fractal emitter having various orders. The spectral powers of the emitted radiation for complimentary Sierpinski PC THz emitter are illustrated in Fig. 3 along with the spectral power of a conventional bow-tie PC THz emitter.
Fig. 3 Spectral power for the complementary bow-tie and Sierpinski PC THz emitters orders one to three and the bow-tie PC THz emitters.
Interestingly, the THz radiated power of the complementary Sierpinski PC THz emitters increases as the fractal order is increased up to the second-order, after which it starts to decrease. It is worth noting that one finds a 20% increase in the radiation power when using the first order complimentary Sierpinski PC THz emitter compared to the bow-tie emitter. The highest emitted THz radiation enhancement was observed from the second-order complementary Sierpinski PC THz emitter; which, when compared to a bow-tie emitter of the same dimension, exhibits an ~80% increase in the emitted THz radiation power. Furthermore, it should be noted that this enhanced THz emission does not come at the expense of loss in the radiated THz bandwidth, as the detected bandwidth is almost identical (within 10%) to that of the bow-tie PC emitter of similar dimensions. Furthermore, this power enhancement cannot be attributed to the biasing electric field distribution since the optically-injected electrons and holes in the GaAs substrate in all of the emitters experience the same electric field of 2.4 × 108 V/cm at the 5 µm gap.
To shed light into the origin of the enhanced THz emission from the complementary Sierpinski PC THz emitters, radiation from Sierpinski PC THz emitters, which includes the bow-tie antenna, have been studied. The spectral powers of the emitted radiation from the Sierpinski PC THz emitter are illustrated in Fig. 4 along with the spectral power of a bow-tie PC THz emitter having the same dimensions.
Fig. 4 Spectral power for the bow-tie and Sierpinski PC THz emitters orders one to three. Note that the scale is normalized to the complementary THZ PC emitters
A similar trend is observed for the different orders of the Sierpinski PC THz emitters. All the Sierpinski PC THz emitters of different orders emit higher THz radiation compared to the bow-tie emitter, albeit lower than the complementary ones. The radiated power of the Sierpinski PC THz emitters increases as the fractal order is increased up to the second-order, after which it starts to decrease similar to the complementary ones. It should be mentioned that the presence of multi-resonances are expected for fractal surfaces when illuminated by a broadband electromagnetic radiation. For the second order Sierpinski antenna when illuminated by a broadband source (4 THz BW), the 3D-FDTD simulations show the presence of two resonance frequencies at ~0.6 and ~2.1 THz. Not surprisingly, the first resonance frequency of the second order Sierpinski PC THz emitter was ~0.6 THz when the emitted radiation was acquired by the THz-TDS system. However, since the maximum frequency emission of the GaAs-PC switch is 1.5 THz, the second resonance at 2.1 THz is not excited by the PC switch.
While both complementary Sierpinski and Sierpinski PC THz emitters exhibit higher THz emission characteristics with the former being of higher THz emission, it is imperative to pay close attention to their spectral peak. Figure 5(a,b) depicts a plot of the normalized spectral power of both complementary Sierpinski and Sierpinski PC THz emitters along with their corresponding bow-tie emitters.
Fig. 5 Normalized power plots of the (a) complimentary Sierpinski PC THz emitter and (b) Sierpinski PC THz emitter. The amount of frequency shift (Δf) is shown on the top right corner of the figures.
It is evident that the central frequency of the emitted radiation from the higher order complementary Sierpinski PC THz emitters are blue shifted by 20 GHz compared to the complementary of the bow-tie PC THz emitter (Fig. 5(a)). In contrast, the Sierpinski PC THz emitters have undergone a red shift by 26 GHz compared to the bow-tie emitter (Fig. 5(b)). The observed frequency shifting is attributed to the slight change of the impedance of the higher order antennae relative to their bow-tie counterparts. A similar effect has been observed at the microwave frequencies, where higher order Sierpinski's fractal antennae show a red frequency shift [12]. It should be noted that this increase in THz emitted radiation power is not due to change in the antennae directivity. Electromagnetic simulations indicated that there is no directivity change associated with the different orders of fractals as well as the complementary bow-tie PC emitter.
Since the surface’s sub-wavelength restructuring is responsible for this enhanced THz emission, it is only natural to examine what is occurring on the surface of the fractal emitters. A key lead is to examine the spatial distribution of the surface plasmon current density. Finite difference time domain (FDTD) numerical simulation was performed to obtain the plasmonic surface current densities on all the fractal PC THz emitters. The emitters’ dimensions and parameters are chosen to match the experimental ones including the antenna material (Au), transmission line, and the antenna substrate (GaAs). Figure 6 illustrates the spatial distribution of the surface plasmon current density, Jx(x,y), along the axis of the Sierpinski emitters acquired at an intermediate peak emission frequency of 0.55 THz.
Fig. 6 The spatial distribution of the surface plasmon current density, Jx(x,y), in logarithmic scale along the axis of the Sierpinski PC THz emitters of (a) the bow-tie, (b) first order, (c) second order, and (d) third order, acquired at an intermediate peak emission frequency of 0.55 THz.
It is well-known that the incorporation of antenna architecture into a PC THz emitter improves the coupling efficiency of the THz radiation from the semiconductor substrate to free-space. However, this coupling efficiency can be further enhanced by introducing an antenna operating in the plasmonic regime. Unlike the interaction with a smooth antenna surface, the THz electric field residing inside the semiconductor can interact with the antenna’s overall surface via coupling through collective electronic excitations at the antenna’s metallic surface (surface plasmons) provided that this surface satisfies the conservation of energy E and momentum k of the incident THz field. By engineering the antenna surface to have perforations of dimensions that are much less than the wavelength of the excited radiation, the THz generated from the PC gap is coupled to the sub-wavelength structures by means of inducing surface charges. The charge depolarization at these metallic features is assigned to the induced THz surface plasmon currents.
As shown in Fig. 6(a), the bow-tie PC THz emitter, the surface plasmon current is distributed in such a way that the current density increases along the sides of the structure. However, in the Sierpinski PC THz emitters i = 1, 2 and 3, the sub-wavelength perforations present on the fractal antennae redistribute these currents more towards the nodes on the side of the antenna (Fig. 6(b-d)). Furthermore, in Fig. 6(b-d) one clearly observes the self-similar current pattern on the sub-units of the fractal antenna. In these structures, the antenna surface behaves as a collection of individual sub-wavelength radiators that are coherently coupled to each other. It is the radiation resulting from these coherent and self-similarly-distributed currents that in the far-field augment the THz radiation emission.
It should be noted that an exact complementary Sierpinski PC THz emitter also produces a self-similar current pattern; however, in the present complementary Sierpinski PC THz emitters, the 2 µm wide circumscribing strip acts to steer Jx(x,y)towards the outer edges of the antenna, specifically near the antenna gap (Fig. 7 ).
Fig. 7 The spatial distribution of the surface plasmon current density, Jx(x,y), in logarithmic scale along the axis of the complementary Sierpinski PC THz emitters of (a) the bow-tie, (b) first order, (c) second order, and (d) third order, acquired at an intermediate peak emission frequency of 0.55 THz.
This modification in the surface plasmon currents within the triangular fractal units is responsible for improving the emission properties of the complimentary antenna compared to the bow-tie (Fig. 6(a)), its complementary (Fig. 7(a)), and Sierpinski PC THz emitters (Fig. 6(b-d)). As the complementary Sierpinski PC THz emitters order is increased, the perforations’ dimension present on the antenna surface shrinks as ~λ/10, λ/22, and λ/200 for the first, second, and third fractal orders, respectively. For i = 3 (Fig. 7(d)), the dimensions of the apertures become much smaller than the wavelength (λ/200) and the characteristics of the antenna plasmon surface current distribution resembles that of the solid surface bow tie antenna (Fig.6(a)). Here, the small fractal perforations do not participate in coupling of the surface plasmon to the antenna and thus, the THz emission power decreases.
It is evident that the THz radiation power for both the Sierpinski PC THz emitters and their complementary geometries increases from the first-order up to the second-order. This has been attributed to the self-similarity of the fractal architecture. To investigate the role of the fractal’s self-similarity on the enhanced THz emission, two THz PC emitters having fractal-like geometries were introduced as shown in Fig. 8 . In these geometries, the fractal iteration was introduced to only one side of the triangle of the first order Sierpinski PC THz emitter. These THz PC emitters do not possess the self-similar characteristics inherent to the Sierpinski gasket fractals. However, their metallic filled areas relative to the bow-tie shown in Fig. 6(a) are 69% and 67% for the structures shown in Fig. 8(a) and Fig. 8(b), respectively. This falls between that for the first-order (75%) and second-order (56%) Sierpinski PC THz emitters.
Fig. 8 SEM images of the fractal-like geometries iteration orders (a) two, and (b) three applied only to one side of the antenna. The spatial distribution of the surface plasmon current density of the, Jx(x,y), in logarithmic scale along the axis of the fractal-like geometries iteration orders (a) two, and (b) three applied only to one side of the antenna, acquired at an intermediate peak emission frequency of 0.55 THz.
The Sierpinski fractals PC emitters have been chosen for this investigation since the complementary fractal PC emitters used in this experiment are not truly exact complementary fractals. This is because; the 2µm wide circumscribing strip lines were needed to have the same electric field concentration at the antenna’s gap. This is the reason why the self-similar surface plasmon current distribution is not obvious in the Fig. 7. For the purpose of comparison, we chose to investigate an exact fractal (Sierpinski fractal) to shed light on the current distribution on the surface. From Fig. 8(c,d), it can be observed that the surface plasmon current density maps of these emitters do not show the self-similar patterns. Both THz PC emitters showed equal THz radiation emission power to the bow-tie PC THz emitter which is 18% and 30% lower than those obtained from the i = 1 and i = 2 Sierpinski PC THz emitters, respectively. In these PC THz emitters, the lack of self-similarity reveals itself by lowering the coherent interference and coupling of the generated PC THz radiation by the perforations to fee-space. This finding supports the fact that the self-similar current distribution is the key in the observed enhanced THz emission. The self-similar geometry can be thought of as an intermediate configuration between periodic and non-periodic geometry. As shown in Fig. 6(b-d), the apertures present on the Sierpinski’s fractal antennae are configured in a self-similar fashion. If the apertures on the antenna surface were configured in a periodic manner, the output emission would show a resonance radiation at specific frequencies governed by the periodicity parameters. On the other hand, if the apertures were distributed in a non-periodic fashion, the emitted radiation would not result in optimal construction interference at the far-fields. For a self-similar surface structure, each segment of the antenna is a replica of the whole antenna, with its size being scaled down according to the fractal order. In such a configuration, the radiation emitted by each segment will be added coherently to result in the overall radiation pattern. That is, the overall radiation pattern of the fractal antenna is the summation of all the individual radiators that are configured in a self-similar architecture.
4. Conclusion
In this work a new class of plasmonic photoconductive THz emitters based on complementary Sierpinski gasket fractal geometry was presented. By engineering the antenna surface to have perforations of dimensions less than the wavelength of the excited radiation, the THz generated from the PC gap is coupled to the sub-wavelength structures through surface plasmons. Through utilizing THz-TDS, photoconductive THz emitters exhibiting ~80% increase in the emitted THz radiation power to conventional bow-tie and Sierpinski gasket THz emitters are demonstrated. It is shown that the self-similar current distribution is the key in the observed enhanced THz emission. Due to their higher radiation power and better signal to noise (S/N) ratios, these emitters are ideal for situations when higher THz signals (S/N) are required such as in THz-TDS systems.
Acknowledgments
This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Canada Research Chairs (CRC). P. M. acknowledges Alberta Innovates Technology Futures Funds for their support.
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