We demonstrate the ability to directly generate broadband THz surface plasmons via optical rectification on a cylindrical metal wire. This is accomplished by milling a single circumferential groove into the wire and overcoating it with a poled polymer that exhibits a bulk second order susceptibility. An attractive feature of this approach is the potential to generate THz pulses that are limited in duration only by the duration of the optical pump pulse. While a photoconductive detector is used in the present demonstration, we discuss further refinements to the system that should allow for significant enhancement of the nonlinear optical conversion efficiency and detection bandwidth.
©2008 Optical Society of America
In recent years, there has been significant activity in examining the properties of surface plasmon-polaritons (SPPs) for a broad range of photonics applications . While much of the work has been performed at optical frequencies, because of the potential utility in developing nanophotonic devices, there is growing interest in understanding and exploiting the properties of SPPs at terahertz (THz) frequencies. One recent example involves the demonstration of low loss, low distortion propagation of broadband THz pulses on cylindrical metal wires , which have potential applications in near-field microscopy and spectroscopy. With regard to the former application, it has recently been predicted using numerical simulations that wires, either corrugated [3,4] or uncorrugated  along the shaft, may allow for unique capabilities including that of subwavelength focusing of THz radiation.
The dominant propagating mode on a cylindrical metal wire is an azimuthally symmetric transverse magnetic wave, commonly referred to as a Sommerfeld wave . The radial nature of this mode creates challenges in efficiently launching THz radiation along the wire. In general, there are two approaches that may be used: coupling THz radiation onto the wire from an external source or directly generating THz radiation on the wire. To date, only the former approach has been employed, and then, only in conjunction with photoconductive emitters. Within this approach, one technique that was devised in an effort to optimize the coupling efficiency of broadband THz radiation onto the wire required the fabrication of a radially symmetric photoconductive antenna to generate a broadband THz field pattern that was compatible with the dominant mode of the wire . In this case, radiation was coupled by placing the wire in contact with the center conductor of the antenna. While this approach is attractive for optimizing the coupling efficiency, photoconductive antennas are inherently limited in their frequency response, particularly in light of the minimum size features required. This frequency limitation, as well as limitations associated with the correspondingly longer temporal duration of the THz pulse, can constrain the ensuing applications. It is worth noting that other approaches to coupling freely propagating THz radiation to metallic wires have also been demonstrated. These have relied on the use of metallic microstructures on or around the wire to enhance the coupling efficiency [8,9].
Optical rectification represents an interesting alternative technique, either for directly generating or indirectly coupling to SPPs at THz frequencies. As an example of the latter approach, Chang and co-workers demonstrated the generation of radially polarized THz pulses using velocity-mismatched optical rectification in second order nonlinear media and mentioned the possibility of using this radiation to obtain enhanced coupling to SPP waves on cylindrical metal wires, because of mode matching considerations . More generally, optical rectification is commonly used for generation of broadband THz radiation, because numerous materials are known to exhibit a nonlinear susceptibility that is primarily electronic in nature, corresponding to ultrafast response times. While much of the work in this area has focused on inorganic crystals, poled polymers exhibit a number of very attractive features for this application, as demonstrated in a number of prior publications in both bulk [11,12] and guided-wave geometries [13,14]. These features include the potential for large electro-optic coefficients [15,16], relatively low dispersion between the optical and THz refractive indices , and processing ease. This last attribute is particularly important in working with non-planar geometries, as is the case here.
In this submission, we describe a proof-of-principle demonstration of the direct generation of surface propagating broadband THz pulses directly on a single cylindrical metal wire via optical rectification. The basic technique is based on our recent demonstration of coupling freely propagating broadband THz radiation to a single cylindrical metal wire using grooves fabricated directly into the wire . In that demonstration, we found that each groove was able to couple the incident THz radiation to a propagating surface wave. Thus, by varying the number of grooves and the groove separation, both the linewidth and center frequency could be straightforwardly manipulated. Here, we fabricate a single groove into a metallized cylinder. This groove acts to couple freely propagating ultrafast near-infrared optical pulses to propagating SPP pulses bound to the metal-dielectric interface. By overcoating the groove and the surrounding region with a thin poled polymer layer that is processed to exhibit a macroscopic second order optical nonlinearity, the surface propagating optical pulse generates a broadband THz pulse directly in a co-propagating geometry on the wire. While a single groove is used here to generate broadband THz SPP waves, multiple grooves could be used to generate narrow band THz surface waves that propagate along the wire . We discuss future refinements to this demonstration that should allow for significant enhancement of the nonlinear conversion efficiency.
2. Experimental details
We begin by describing the fabrication process for the polymer coated metallic wire. Our previous demonstrations of coupling THz radiation to cylindrical metal wires used commercially available 1 mm diameter stainless steel wires [8,9]. However, these wires are unsuitable for the present purposes, since they exhibit a surface roughness ~100 nm RMS. Therefore, an effective cylindrical metal wire was fabricated using a 1 mm diameter glass fiber, which exhibited a surface roughness ~ several nm RMS. The basic fabrication process is shown in Fig. 1(a). The fiber was uniformly over-coated with 5 nm of Cr, followed by ~300 nm of Ag. Using a focused ion beam machine, we milled a single 375 nm wide rectangular groove that was 100 nm deep, which has previously been shown to be well suited for coupling ultrafast optical pulses at 800 nm . Silver was used to maximize the propagation length of the coupled optical pulse, since most metals exhibit sufficient conductivity at THz frequencies to allow for low loss propagation over the lengths discussed here. Furthermore, the 300 nm metal coating thickness was used since the thickness corresponds to approximately 2 skin depths at THz frequencies and more than 15 skin depths at 800 nm . The groove and the surrounding region, approximately 5 mm in length, were dip coated with a ~2 µm thick layer of a nonlinear optical polymer (Disperse Red #1 covalently attached to a methyl methacrylate backbone). The chemical structure, synthesis, polymer properties, and linear and nonlinear optical properties have been described elsewhere .
In order to effect dipolar alignment, we constructed a simple corona poling apparatus, as shown schematically in Fig. 1(b). In corona poling, an electrical discharge is used to align mobile nonlinear moieties . The discharge creates mobile ions that collect on one surface of a dielectric medium, while the other surface is grounded, resulting in a strong electric field across the medium. Thus, corona poling is well suited for applications where deposition of the two electrodes directly onto the poling medium is not suitable. As shown in Fig. 1(b), the polymer clad wire sat at the center of the apparatus, with the wire axis pointing out of the plane of the figure. The metal film on the fiber was connected to ground. The corona discharge section of the apparatus consisted of eight 25 µm diameter tungsten wires, oriented parallel to the distributed azimuthally about the polymer clad wire. These corona discharge wires were connected electrically to one another and to a high voltage source. We placed the entire system in an oven and heated the sample to the glass transition temperature of the copolymer (137° C) and applied a discharge voltage of -5000 V to the tungsten wires. The sample was then cooled to room temperature with the field in place. It should be noted that upon poling, the polymer remained completely amorphous, although it was rendered uniaxial with the c-axis parallel to the poling field (i.e. radially oriented) and exhibited the properties of a uniaxial nonlinear optical medium (symmetry group C∞v) . The dominant nonlinear tensor component χ(2) zzz can be accessed if both the fundamental and THz electric fields are polarized along the crystallographic c-axis (i.e. normal to the metal surface). Indeed, this is the dominant vector component for propagating SPPs at both optical and THz frequencies.
The experimental setup for coupling optical radiation onto the metallic wire, as well as the generation and detection of THz radiation is shown in Fig. 2. A mode-locked Ti:sapphire laser operating at 820 nm with a repetition rate of 89 MHz was used as the optical source. The optical pump beam, with an average power of 20 mW, was horizontally polarized (parallel to the wire axis) and focused to a spot size of ~100 µm centered on the single groove fabricated into the metal clad fiber. The surface propagating optical pump pulses generated broadband THz pulses via optical rectification. For reference purposes, we heated the polymer above its glass transition temperature, which depoles the polymer so that it does not exhibit a second order nonlinear optical susceptibility. A photoconductive detector was situated approximately 5 mm beyond the end of the wire waveguide, with the receiver offset from the center of the wire by approximately 3 mm and oriented to detect horizontally polarized THz pulses. The distance between the groove and the laterally offset photoconductive detector was approximately 5 cm. The detector was placed at different positions surrounding the wire to ensure that the measured wave was radially polarized, which would correspond to a Sommerfeld wave.
3. Experimental results and discussion
In Fig. 3(a), we show the measured THz time-domain waveforms radiated from the 5 cm long poled polymer clad metallized wire under several different conditions. The top red waveform was obtained with the optical pump beam centered on the poled polymer clad groove, while the center blue waveform was obtained after shifting the optical pump beam laterally away from the groove, but still incident on the poled polymer. Thus, interaction between the optical pulse and the groove appears to be necessary to generate surface propagating THz pulses, at least in this specific cylindrical geometry. The bottom black waveform was obtained with the optical pump beam once again focused on the groove; however, in this case, the polymer was depoled so that it did not exhibit a macroscopic second order optical nonlinearity. As expected, in the absence of a macroscopic χ(2), no generation of THz pulses can occur. In Fig. 3(b), we show the amplitude spectrum of the top red waveform in Fig. 3(a). The spectral content was limited to less than 1 THz and determined primarily by the spectral response properties of the photoconductive detector. We confirmed the limitation imposed by the dipole detector by replacing the coated wire with a 1 mm thick <110> ZnTe crystal  and measuring the generated radiation (not shown). In the discussion below, we discuss the need for using photoconductive detection in the present measurements and future refinements that we believe will eliminate the need for this detection.
We noted above that the dominant propagating mode on the wire is radially polarized. In order to demonstrate this, we measured the time-domain properties of the THz waveform for two different detector positions: 3 mm to the right of the wire center and 3 mm to the left of the wire center. These two waveforms are shown in Fig. 4. The two waveforms are clearly related through a simple sign inversion, demonstrating that the polarization direction is reversed between these two positions. This is consistent with earlier results reported by Wang and Mittleman .
These results lead to a simple interpretation for the generation of THz SPP waves guided on the metallized wire: (1) normally incident ultrafast optical pulses are coupled to optical SPP pulses on the metallized wire via interaction with the groove, which is consistent with earlier observations [8, 17] (2) the bound SPP pulses at optical frequencies mix within the poled polymer to generate SPP pulses at THz frequencies via optical rectification over an interaction length determined by the attenuation properties of the interacting waves and (3) the bound radially polarized THz SPP mode propagates along the wire. Although this sequence of events is conceptually simple, it raises several questions regarding the coupling process and the spatio-temporal evolution of the optical and THz SPP modes. While we have begun examining these issues, a detailed study is beyond the scope of the present work.
Finally, we discuss the need for photoconductive detection in the present work and future refinements that should allow for far greater detection bandwidth. For the optical SPP waves at ~800 nm propagating along a smooth silver-air interface (εAg=-33+3i ), the 1/e propagation distance is ~50 µm . The 1/e propagation length remains unchanged if we now consider a silver film overcoated with a 2 µm thick poled polymer layer, since the polymer exhibits smaller attenuation than the metal at this wavelength . Because of the short interaction length for nonlinear conversion, a sensitive photoconductive detector was necessary and careful consideration of phase-matching constraints over the frequency range observed was not required. We believe that by simply changing the poled polymer and shifting the optical excitation wavelength to 1.55 µm, the conversion efficiency could be dramatically improved. The Disperse Red #1 copolymer used in this demonstration exhibited an electro-optic coefficient, r33, of ~8 pm/V at 800 nm . At 1.55 µm, polymers exhibiting an electro-optic coefficient, r33, of ~150 pm/V have been reported . Furthermore, the 1/e propagation length of SPP waves at this optical frequency for a silver-air interface is ~1 mm [18,23]. The significant increases in the polymer nonlinearity and the interaction length should allow for significant enhancement in the THz conversion efficiency. In this case, careful consideration of phase-matching is necessary (i.e. the optical group velocity for the optical SPP pulse should be approximately equal to the phase velocity for the THz SPP pulse ). Specifically, SPP pulses at ~1.55 µm would propagate wholly within the poled polymer, since the 1/e out-of-plane spatial extent at this wavelength is typically less than a wavelength . Thus, the group velocity of the optical SPP pulse would be determined by the mode properties of the guided-wave within the poled polymer. On the other hand, since the spatial extent of the THz SPP pulse typically extends several wavelengths along the out-of-plane direction , the THz phase velocity would require consideration of the THz field in both the poled polymer and air. Exploiting these refinements would also allow for the use of electro-optic sampling , enabling broader bandwidth detection.
In summary, we have directly generated broadband THz pulses on a cylindrical metal wire by integrating a broadband coupler and a nonlinear conversion medium directly onto the wire. The current proof-of-principle demonstration relies on a poled polymer that exhibits a relatively modest second-order susceptibility and a photoconductive detector. By using more optimal polymers and electro-optic detection, we expect significant enhancement in the nonlinear conversion efficiency and detection bandwidth, thereby expanding the applicability of these wires in broadband spectroscopy and THz near-field applications.
References and links
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