Terahertz (THz) radiation has important applications in spectroscopy, imaging, and space science. Fiber optics for the THz region have been limited to rigid hollow metallic waveguides or short lengths of solid-core transparent dielectrics such as sapphire and plastic. We have fabricated flexible, hollow polycarbonate waveguides with interior Cu coatings for broadband THz transmission using simple liquid-phase chemistry techniques. The losses for these hollow-core guides were measured using a tunable, cw single-mode far IR laser. The losses for the best guides were found to be less than four dB/m and the single mode of the laser was preserved for the smaller bore waveguides.
©2004 Optical Society of America
THz waveguides have traditionally been fabricated from metals such as Cu, brass, and stainless steel with rectangular, square, and circular cross sections. Grischkowsky and his co-workers have described their work on circular and rectangular waveguides made from stainless steel (hypodermic) and brass tubing with bore sizes of about 300 μm and lengths up to 25 mm [1,2]. Their measured loss at 1 THz for a 280-μm bore stainless steel waveguide was 0.7 cm-1 or about 300 dB/m. For their loss and dispersive measurements they used a short pulse, broadband THz source. These same investigators also studied parallel plate waveguides made from Cu plates . A somewhat unusual approach was taken by Hidaka et al.  who proposed using ferroelectric polyvinylidene fluoride (PVDF) as the inner wall material of a hollow waveguide. The idea is that the dielectric constant of ferroelectric materials such as SrTiO3 and some polymers becomes very high at THz frequencies. This leads to high reflectivity of PVDF in the THz region. Hidaka et al.  found that the loss for an 8-mm bore, 30-cm long PVDF waveguide in the 1 to 2 THz frequency regime was 1.5 m-1 or about 6.5 dB/m. Their results for a similar Cu waveguide were more that 3 times larger than that for the PVDF waveguide. Solid-core THz waveguides have also been made from rectangular strips of high-density polyethylene and slab waveguides of LiNiO3 have also been studied. Jamison et al.  studied the THz properties of single-crystal sapphire fibers.
The approach that we have taken to produce waveguides for THz frequencies is to adapt the technology that we have successfully used to fabricate low loss, hollow waveguides for the mid-IR region between 2 and 12 μm [6,7]. The hollow waveguide technology used involves coating the inside of either silica or polymer tubing with metallic and dielectric coatings using liquid-phase chemistry methods. The most common approach is the deposition of a thin Ag layer followed by an iodization process to form an AgI layer of the correct optical thickness to enhance the reflectivity. In a similar manner we have also deposited thin films of Cu and CuI . For this study we have chosen to use Cu for the metallic layer and plastic tubing for the substrate tubing. Copper was chosen because it is one of the best reflectors at THz frequencies. For example, the measured reflectivity for Cu, Ag, and Au at 513.02 μm is 0.997, 0.996, and 0.994, respectively . We have chosen polycarbonate tubing for making the waveguides for two reasons. The first is that this polymer tubing has a very smooth inner surface nearly equal in roughness to silica glass and this has enabled us to fabricate hollow polycarbonate waveguides (HPWs) with the lowest loss to date in the mid-IR region. The second reason is that we are able to use tubing with relatively large bore sizes and still have the guides be quite flexible. The polycarbonate tubing used for this study has bore sizes ranging from 2 to 6.3 mm. In contrast, glass tubing with bore sizes in this size range would be inflexible.
Copper films are deposited inside polycarbonate tubing using an electroless, liquid-phase chemistry process . The first step is to sensitize the polycarbonate using an aqueous solution of PdCl2 and SnCl2. Next a copper bath solution is prepared consisting of copper sulfate, formaldehyde, Rochelle salt, and sodium hydroxide with a pH of 12.5. This solution is pumped through the plastic tubing at a flow rate of 5 ml/min. The formaldehyde reduces the Cu ions and Cu metal is plated out on the tubing. The duration of the deposition process is 30 to 45 min and the estimated thickness of the Cu layer formed is 0.5 to 0.7 μm. This thickness is much greater than the skin depth of about 0.05 μm for Cu at THz frequencies.
The THz source used for the measurement was an optically pumped SIFIR-50 laser made by Coherent-DEOS. The CO2 pump laser excited the rotational bands of low pressure CH3OH or CH2F2 and laser radiation could be obtained at a series of wavelengths between 42 and 1020 μm. The laser delivered a polarized, TEM00 output beam with a maximum power at the input end of the waveguide of about 25 mW. The laser energy was focused into the waveguide using a 25-cm fl, high-density polyethylene lens. The spatial profiles of the input laser beam and the output beam from the waveguide were measured using a Spiricon Pyrocam III.
3. Results and discussion
3.1 Straight waveguide loss
The losses for the Cu-coated HPWs were measured at three different laser wavelengths. The initial measurements were made on straight waveguides. Table 1 summarizes the losses at the different laser wavelengths for three bore sizes. The losses reported in Table 1 were obtained using a cut-back method in which the loss for the long guide was ratioed against the loss for a short segment of the same waveguide. In this way we were able to correct for coupling losses. In addition, the losses in Table 1 are corrected for atmospheric absorption at each wavelength. The atmospheric absorption of air was taken to be 0.48, 1.13, and 1.35 dB/m at 118.83, 158.51, and 184.31 μm, respectively . The mode launched into the guide was TEM00 but this mode was not always preserved at the output of the waveguide as will be discussed in Sec. 3.3. In general, the spot size of the input beam was adjusted to be approximately 0.6 to 0.7 times the diameter of the guide as this gives optimal coupling into the waveguides.
The data in Table 1 show that the lowest loss of 3.9 dB/m was obtained for a 3-mm bore fiber at 158.51 μm. In fact, the losses were generally lower at this wavelength compared to the other wavelengths. There is, however, one somewhat unusual aspect to the loss data. That is, normally the losses for hollow waveguides depend strongly on the bore size . Specifically, the absorption coefficient, α, varies as 1/a 3, where a is the bore radius. The data in Table 1 do not scale as 1/a 3. The primary reason for this is the generation of higher order modes in the large bore guides. A general expression for the attenuation of the Irnth mode in a straight hollow guide is,
where ulm is the usual fiber optic mode parameter equal to the zeroes of the Bessel function; and Re(Vl) is a term that depends on the mode, the complex refractive index of the inner wall material, and the cross-sectional geometry of the waveguide . In our case the reflective layer is only Cu so the Re(Vl) term contains the complex refractive index of Cu. From Eq. (1) we see the loss for the higher order modes increases rapidly as the square of the mode parameter. Another reason for the higher loss for the 6.3-mm bore guide is that the Cu coating may not be as uniform as it is for the smaller bore waveguides. This is a result of poorer flow conditions during the coating of the large bore tubing. The lowest loss for the 3-mm bore guide of 3.9 dB/m is quite low compared to other THz waveguides. McGowan et al.  reported a loss of about 0.7 cm-1 or 300 dB/m for their stainless steel hypodermic tubing and Hidaka, et al. a loss of 0.015 cm-1 or 6.5 dB/m for their PVDF tubing .
As mentioned above, Cu has the highest reflectivity of any metal at THz frequencies. The lowest loss mode for a metallic waveguide is the TE01 mode. Roser, et al.  have calculated the loss for Cu waveguides for different bore sizes and for different TElm modes. Their calculations give losses for the TE01 mode at 160 μm of about 0.6, 0.08, and 0.005 dB/m for 1, 2, and 5 mm bore Cu waveguides, respectively. Clearly our losses are much higher than those calculated by Roser, et al. One reason for this discrepancy is that we have not launched the lowest loss TE01 mode into the guides as this mode is not easy to generate. Nevertheless, even though only the HE11 mode propagated in the smaller bore guides, the losses are still high.
3.2 Bending losses
In the mid-IR region it has been shown that there is an additional loss on bending hollow waveguides which varies as 1/R, where R is the radius of curvature . This loss dependence has been verified for many different metallic and single-layer dielectric coated hollow guides from 2 to 12 μm. While it is possible to eliminate this bending loss effect for hollow waveguides by fabricating a photonic bandgap or omnidirectional hollow guide structure , this has not been done for the THz region. In essence, a 1D photonic bandgap structure may be formed by depositing multiple dielectric layers of alternating high/low refractive index materials for which the pair of materials has high index contrast. This type of structure has been made for wavelengths up to about 12 μm but not for longer wavelengths. Therefore, we would expect some sort of bending loss in the THz region especially since we are not propagating the TE01 mode.
The total loss for bent waveguides is shown in Fig. 1. These losses were measured for a 2mm bore waveguide at 184.31 μm. For these measurements, the amount of waveguide under bend was kept constant and the laser radiation was perpendicular to the plane of bending. The data in Fig. 1 show that the losses increase as the curvature increases. For a bending radius of 20 cm (curvature of 5 m-1) the 110-cm long waveguide was bent 180°. The solid line in Fig. 1 is a quadratic fit to the data rather than the linear fit that would be expected for the 1/R dependence on loss normally found in the mid-IR region. That is, as the radius of the bend decreases the losses increase less rapidly than expected. This may be seen from the data in Fig. 1 where the decrease in bend radius from 40 to 20 cm (increase in curvature from 2.5 to 5 m-1) leads only to a slight increase in total loss from 9.9 to about 10 dB/m. We are not sure why this is the case as the modal properties of the guides do not change significantly as the guides are bent.
3.3 Modal properties of the hollow waveguides
One of the most important and yet intriguing aspects of hollow waveguides is the propagation of low order modes. It is possible to propagate near single mode radiation through hollow guides whose bore size is substantially larger than the wavelength of light. Matsuura, et al.  showed that the lowest order HE11 mode was preserved when the TEM00 mode of a CO2 laser operating at 10.6 μm was launched into a 250-μm bore, Ag/AgI-coated hollow glass waveguide. In this case the bore size was over 20 times the wavelength yet the waveguide preserved the single mode input beam quality. We have seen some similar qualitative results for our Cu-coated guides. An example of the modal dependence of the waveguides is shown in Fig. 2. The mode profiles are given for a straight 2-mm bore waveguide at the three laser wavelengths used for our loss measurements. For the shortest wavelength of 118.83 μm we see that the output mode is not single mode (Fig. 2(a)) but as the wavelength increases to the longest wavelength of 184.31 μm the output becomes distinctively single mode (Fig. 2(c)). That is, when the bore size is about 17λ the guide is multimode but when it is 12λ or less then the waveguide becomes essentially single mode. An interesting aspect of this data is that the waveguide loss at the shortest wavelength (Fig. 2(a)) is less than at the longest wavelength (Fig. 2(c)) as may be seen from the data in Table 1. This result is in contrast to what is observed for the dielectric-coated hollow waveguides for which the lowest loss mode is the HE11 mode. A reasonable explanation for the Cu-only waveguides studied here is that we are propagating some of the lowest loss TE01 mode (Fig. 2(a) shows a mixed mode) and, therefore, the overall loss is lower than for the purer HE11 mode seen in Fig. 2(c).
The effect of bending on output mode quality is shown in Fig. 3 for the 2-mm and 3-mm bore guides at 184.31 μm. Again we see that the smaller 2-mm bore waveguide distorts the input mode very little (Fig. 3(b)) but that when the 3-mm bore guide is bent to a radius of 60 cm there is mode coupling and the resultant output mode is not longer single mode (Fig. 3(c)).
Therefore, we conclude that the use of the smaller bore guides, while a little higher in loss, are the best choice if it is desired to transmit single mode laser energy.
3.4 Dielectric-coated Cu HPWs
The losses in Cu hollow waveguides can be significantly reduced if a dielectric coating of the correct optical thickness is deposited over the metallic layer. That is, dielectric coatings are a well known means of enhancing the reflectivity of metal mirrors and it is assumed that the reflectivity of Cu could be greatly improved if suitable transparent dielectric coatings could be found to coat the inside of the Cu guides. This technique has worked well in the mid-IR where AgI and CuI have been deposited over Ag and Cu metallic films in hollow waveguides. Normally these dielectric coatings, which are formed by the conversion of part of the metallic layer into the metal iodide, are from 0.2 to about 0.8 μm thick. This is the appropriate quarter-wavelength thickness for single-dielectric coatings operating in the 2 to12 μm region. The challenge to adapting this technology at THz frequencies is to first find suitably transparent materials and then second to be able to deposit them inside the bore with the correct uniformity and optical thickness required for these very long wavelengths.
What we have done in this preliminary study is to measure the optical losses for a 2-mm bore Cu/CuI coated polycarbonate waveguide that was prepared for optimal performance at 10 μm. The thickness of the dielectric layer was, therefore, not at all optimized for the longer wavelengths of the THz laser. Nevertheless, we wanted to at least test this combination as an early indication of the efficacy of CuI at these long wavelengths. The results for the straight-loss measurements at 158.31 μm on a 99.0 cm long Cu/CuI waveguide were 8.7 dB/m. As may be seen from Table 1, this is higher than the best loss for a straight 2-mm bore Cu-only guide of 6.5 dB/m. What we conclude from this measurement is that CuI has a non-negligible absorption at 158.31 μm. The thickness of the CuI that we used provided only a protective coating to inhibit oxidation of the Cu film. It did not enhance the reflectivity of the Cu. We are now looking at other coating materials that are more transparent at THz frequencies and that we can deposit with the requisite rather thick film. One category of coating materials is polymer films. Matsuura, et al.  have very successfully used a variety of polymer films deposited over Ag for the mid-IR hollow glass waveguides. This may be a good approach for the longer wavelengths.
THz waveguides are just now beginning to be studied as an efficient means of transmitting this long wavelength radiation. There are many applications of THz waves in sensor and power delivery systems which should benefit from a viable THz fiber optic. Our approach to studying THz waveguides is to draw on the technology of metal-coated hollow waveguides used successfully in the mid-IR. The Cu-coated hollow polycarbonate guides used in this study are simple in design and inexpensive to fabricate. The lowest loss of 3.9 dB/m at 158.31 μm for the 3-mm bore fiber is not nearly as low as the calculated loss for a Cu waveguide but it is reasonably low at this long wavelength compared to reported losses for other THz fiber optics. There are several reasons for our high loss. The lowest loss TE01 mode was not launched into the guide and there may be some corrosion of the Cu layer. The oxidation of the Cu layer, however, is not thought to be that important here as the guides were freshly prepared before measurement. In the future, it would probably be best to deposit dielectric coatings over the metallic film to both enhance the reflectivity and lower the loss as well as to protect the Cu surface from contamination. Just a single-layer dielectric coating could significantly reduce the straight and bending losses for the guides. For example, Ag/AgI or Cu/CuI waveguides at 10.6 μm have losses that are at least a factor of 10 less than for the Ag or Cu-only guides.
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