Abstract

We demonstrate that 3D printing, commonly associated with the manufacture of large objects, allows for the fabrication of high quality terahertz (THz) plasmonic structures. Using a commercial 3D printer, we print a variety of structures that include abrupt out-of-plane bends and continuously varying bends. The waveguides are initially printed in a polymer resin and then sputter deposited with ~500 nm of Au. This thickness of Au is sufficient to support low loss propagation of surface plasmon-polaritons with minimal impact from the underlying layer, thereby demonstrating a useful approach for fabricating a broad range of plasmonic structures that incorporate complex geometries. Using THz time-domain spectroscopy, we measure the guided-wave properties of these devices. We find that the propagation properties of the guided-wave modes are similar to those obtained in similar conventional metal-based waveguides, albeit with slightly higher loss. This additional loss is attributed to roughness associated with limitations that currently exist in commercial 3D printers.

© 2013 Optical Society of America

1. Introduction

In contrast to naturally occurring materials, where the atomic and molecular substituents of the materials determine its physical properties, artificially structured materials offer the ability to engineer the physical properties of the resulting medium based on the geometrical properties of the imprinted pattern. In the field of plasmonics, such texturing allows for control over electromagnetic waves bound to the interface between a metal and the adjacent dielectric medium [1,2]. These surface plasmon-polaritons (SPPs) display unique dispersion characteristics that depend upon the plasma frequency of the medium. In the long wavelength regime, where metals are highly conductive, it has been shown, both theoretically [35] and experimentally [6,7], that such texturing can create an effective medium that can be characterized by an effective plasma frequency that is determined by the geometrical parameters of the surface structure.

The terahertz (THz) spectral range offers unique opportunities to utilize such materials. While there has been significant work on developing coherent sources and detectors, relatively few other device technologies currently exist [8]. A major issue that has constrained this development is the fact that most conventional dielectrics and semiconductors are highly lossy in this spectral range. Since metals are highly conductive, SPPs experience very low propagation loss when air acts as the adjacent dielectric medium. One representative device structure where this has been well demonstrated is in the area of THz waveguides. Over the last decade, a broad range of metal-based waveguides has been developed [916]. Recently, we showed that a one-dimensional array of rectangular apertures that either partially or completely perforate a planar metal film could be used to create a variety of guided-wave devices [12,15]. In fact, using this approach, we have fabricated not only straight and curved waveguides, but also y-splitters and 3 dB couplers. While the fabrication approach used in those implementations is promising for developing other types of guided-wave structures, it is a time-consuming process that is generally limited to planar geometries. As an example, in the case of blind aperture-based waveguides, the final structure requires the bonding of three separate layers, in which one layer requires laser ablation. Therefore, the development of relatively easy fabrication techniques to create non-planar guided-wave devices may create new opportunities in a variety of emerging THz applications.

In this submission, we demonstrate the use of conventional 3D printing to create both planar and non-planar THz plasmonic waveguides. While 3D printing has been used extensively to print large objects, the use of 3D printing for THz devices has not been well studied, although a few examples exist [1719]. The devices discussed here are printed using a professional-grade commercially available 3D printer in a polymer resin and then subsequently overcoated with a thin layer of Au, allowing the structure to support SPPs. Using this approach, we fabricate and characterize a variety of geometries that cannot easily be fabricated using other conventional techniques. We use THz time-domain spectroscopy (THz-TDS) to fully characterize the propagation properties of the waveguides and compare them to devices that have previously been fabricated in conventional metals.

2. Experimental details

We fabricated a variety of guided-wave structures using an Objet EDEN 260V 3D printer, including straight waveguides, 3D bends, 3D y-splitters and U-shaped structures. The printer had a resolution of 600 dpi along the x- and y-axes and 1600 dpi along the z-axis. The structures were printed using a Vero White polymer resin onto a plastic printing platform. After printing, the resin solidified as a rigid white opaque plastic. In general, the total printing time was volume dependent. However, for the structures described here, the printing time was typically on the order of an hour. After detaching the device from the support platform, we sputter deposited ~500 nm of Au. Sputter deposition allowed for metal deposition on all surfaces, including inside the blind holes. Nevertheless, there may be some non-uniformity in the Au thickness, particularly on the sidewalls of the rectangular blind holes. Based on measurements using larger equivalent structures, we estimate that the minimum Au thickness on any surface is at least 300 nm. We have previously shown that once the metal thickness is greater than approximately two skin depths (δ~150 nm at THz frequencies), the properties of the surface waves are determined by the properties of the top metal film [20]. Thus, SPPs launched on the metal surface have minimal interaction with the underlying medium, allowing for waveguide fabrication that is independent of the fabrication medium.

In Fig. 1, we show a schematic diagram of a planar guided-wave structure, along with the corresponding excitation and detection scheme and blind aperture dimensions. In order to couple freely propagating THz radiation into SPPs, we fabricated a 1 mm long, 300 µm wide by 100 µm deep straight groove into a 1 mm thick stainless steel metal piece. This groove was physically abutted against the waveguides and allowed for reproducible coupling from device to device (not shown). All of the waveguide devices described here utilized rectangular blind holes (rectangular holes that do not perforate the medium) as the basis for the device topology. These blind holes had design dimensions of s = 550 µm, a = 150 µm, h = 450 µm, and d = 250 µm. The devices were typically fabricated to have a total length of 10 cm. Compared to the wavelength (λ) of the lowest order mode, discussed below, the aperture width was ~λ/7 and the periodicity was ~λ/4, indicating that we were operating in the long wavelength limit.

 

Fig. 1 Schematic drawing of the printed THz waveguide, including the excitation and detection scheme. The groove at the input end is used to couple normally incident broadband THz radiation to SPPs. For detection purposes, the optical probe beam propagates parallel to the THz guided-wave SPPs. A <110> ZnTe crystal is used for coherent detection of the Ez component of the guided-wave SPP. The design dimensions of the rectangular blind holes are: length s = 550 µm, width a = 150 µm, depth h = 450 µm, and periodicity d = 250 µm.

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We used a modified THz time-domain spectroscopy setup to characterize the propagation properties of SPPs on these devices. Although the details related to the experimental apparatus have been discussed elsewhere [21], we briefly present them here. We used a 1 mm thick <110> ZnTe crystal for generation of broadband THz pulses. This radiation was collected and collimated using an off axis parabolic mirror. We then used a 150 mm focal length TPX (polymethylpentene) lens to focus the THz radiation onto the input coupler at normal incidence. After propagation along the surface, the THz SPPs were measured using a second 1 mm thick <110> ZnTe crystal via electro-optic sampling [21]. Because of the crystal orientation and the polarization of both the optical probe and THz SPP beams, we were only sensitive to the Ez component of the surface field. By moving the optical probe beam and electro-optic crystal relative to the surface of the patterned structure, we were able to measure the spatial distribution and loss properties of the propagating modes.

3. Experimental results and discussion

We begin by describing the spectral and spatial properties of a planar straight waveguide fabricated using 3D printing. In Fig. 2(a), we show the experimentally measured waveguide transmission spectrum obtained at the end of a 10 cm long linear waveguide. There are several notable features in the spectrum. First, it is apparent that there are three separate modes, each with its own distinct dip (anti-resonance frequency). These appear at 0.27, 0.47 and 0.54 THz. As we have discussed earlier, these dips on the high frequency side of each resonance are the relevant parameter, not the frequencies associated with the resonance peaks [22]. Thus, the locations of the anti-resonant frequencies can be viewed as effective cavity resonance frequencies of the individual apertures. These frequencies are approximately given by [15]

νmnp=c2π(mπs)2+(nπa)2+((p+0.25)πh)2
where, m, n, and p are integers (m = 1,2,3… and n,p = 0,1,2…) and c is the speed of light in vacuum.. In the case of blind holes, we previously showed that the conventional description for the cavity modes required that the value of p be offset by 0.25. This modification may be the result of having an asymmetric rectangular cavity (i.e. a bottom metal surface and open on top). With this refinement, the lowest order anti-resonance frequency can still be indexed as m = 1, n = 0, and p = 0. In order to fit the anti-resonance frequencies to Eq. (1), a slight adjustment in the blind hole dimensions is necessary to achieve good agreement. Specifically, we use s = 560 µm instead of the design value of s = 550 µm and h = 470 µm instead of the design value of h = 450 µm. Since n = 0 for all three modes, the exact value of blind hole width, a, is not critical. Given the details of the printing process, the need for making such small changes in the geometrical parameters is not surprising. With these modified values, the frequencies associated with the anti-resonance frequencies obtained from Eq. (1) are 0.28 THz for the (100) mode, 0.48 THz for the (101) mode and 0.54 THz for the (200) mode, which is in good agreement with the experimental data. Modes that operate beyond the Bragg frequency, νB = c/2d = 0.6 THz are strongly damped, as demonstrated in the spectrum.

 

Fig. 2 Propagation properties for a planar straight waveguide with periodically spaced rectangular blind holes. (a) Measured transmission spectrum for the waveguide. The arrows show the anti-resonance frequencies associated with the different effective cavity modes. These dips occur at 0.27, 0.47 and 0.54 THz. (b) The field amplitude |Ez| measured along the x-axis at different positions along the length of the waveguide. The dots represent the measured field value normalized to the value at the input. The black line is an exponential fit to the data, corresponding to a 1/e decay length of ~5.9 cm. (c) The |Ez| component of the electric field measured along the z-axis at different heights above the sample surface. The dots represent the measured field value normalized to the value at the surface. The black line is an exponential fit to the data, corresponding to a 1/e decay length of 2.6 mm. (d) The |Ez| component of the electric field measured along the y-axis 5 cm from the waveguide input. The dots represent the measured value, while the black trace is a Gaussian fit to the data, yielding a (FWHM) width of ~3.4 mm.

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In all of the subsequent data, we describe only the propagation properties of the lowest order mode. Specifically, we show the magnitude of the Ez component of the THz electric field taken at the peak of the lowest order mode (0.27 THz). In Fig. 2(b), we show the loss properties for propagation along the waveguide. An exponential fit to the data yields a loss parameter of 0.17 cm−1, corresponding to a 1/e propagation length of ~5.9 cm. In Fig. 2(c), we show the magnitude of the Ez field component as a function of distance above the waveguide surface (along the z-axis). The field decays exponentially from the metal dielectric interface with a 1/e decay length of ~2.6 mm. Finally, in Fig. 2(d), we show the magnitude of the Ez field component measured along the y-axis of the waveguide, 5 cm from the waveguide input. The lateral field distribution at the cross-section exhibits a Gaussian mode profile with a full-width at half maximum (FWHM) mode size of ~3.4 mm, indicating reasonably tight confinement along the lateral direction. At this point, it is instructive to compare the properties of this printed waveguide, with one that was previously fabricated in stainless steel and using laser ablation to fabricate the blind holes [15]. In that device, the 1/e propagation length along the x-axis was ~12 cm, the 1/e out-of-plane spatial extent of the THz electric field was ~2.5 mm, and the FWHM lateral width of the lowest order guided-wave mode was 2.8 mm. These properties are generally consistent with the fact that the stainless steel waveguide exhibits lower loss.

Clearly, the fact that the propagation loss associated with a Au coated waveguide is greater than that in a nearly identical device stainless steel device is somewhat counter-intuitive. To understand this, we consider the different aspects of the fabrication process. First, 3D printing, by its nature, does not currently allow for the fabrication of smooth surfaces. In fact, the measured surface roughness of the printed device is ~3 µm rms, which is substantially larger that the ~50 nm rms surface roughness associated with stainless steel foil used to fabricate the waveguides using more conventional techniques. We expect a similar difference in the surface roughness within the blind apertures. Such irregularities on the waveguide surface and inside the apertures are expected to lead to increased radiative losses. Second, it is likely that the thickness of the deposited Au is not uniform, especially on the aperture sidewalls. However, as we noted earlier, we do not expect the metal thickness to be less than approximately two skin depths on any surface. Thus, this is unlikely to play a significant role in determining the loss properties of the waveguide.

Having established properties for guided-wave propagation using a simple planar structure, we now discuss the advantages of 3D printing technology. In this case, designs are no longer limited to waveguiding along only a single plane. To demonstrate this, we design a series of structures that incorporate two separate out-of-plane bends, such that the output plane and input plane are parallel to one another. A schematic drawing of the geometry is shown in Fig. 3(a). Based on this configuration, a simple planar waveguide corresponds to a device that incorporates two 0° bends into the device. We printed 8 different 3D structures, each 10 cm long, that incorporate two identical bends with angles varying between 5° to 40°. For each waveguide, we measured the total propagation loss, subtracted the propagation loss expected from a planar 10 cm long waveguide [see Fig. 2(b)], and divided the result by 2 assuming that both bends contributed equally to bend losses. In Fig. 3(b), we present the excess bend loss as a function of the bend angle. As expected, the loss increases with increasing bend loss. However, somewhat surprisingly, the loss in dB appears to increase in an approximately linear fashion until θ = 35°.

 

Fig. 3 Properties of abrupt out-of-plane bends. (a) Schematic drawing for the printed bend structures. Devices were fabricated with bend angles from 5° to 40°, in 5° increments. (b) Excess loss per bend as a function of the bend angle measured at 0.27 THz.

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Based on the excess loss properties obtained from the 3D bend structures, we are now able to extend this approach to develop a 3D Y-splitter that is composed of the same periodically spaced rectangular blind holes used in the structures described above. In Figs. 4(a) and 4(b), we show a schematic diagram of the device with the relevant parameters and a photograph of the device, respectively. The Y-splitter consists of a planar 6 cm long Y-splitter that has 20° angle between the two split arms. The left arm is then bent 10° upward out-of-plane, while the right arm is bent 10° downward out-of-plane. After 2 cm, both arms are again bent by 10°, so that the two output planes are parallel to the input plane. Based on the angle (10°) of the out-of-plane bends, the two output arms are vertically offset from one another by ~7 mm and horizontally offset from one another by 11 mm.

 

Fig. 4 Properties of a 3D Y-splitters. (a) Schematic diagram of a 10 cm long Y-splitter, in which the two arms branch off both in-plane and out-of-plane. In both cases, the branches are at ± 10 ° relative to the preceding waveguide. (b) Image of the Y splitter after sputter deposition with Au. (c) & (d) The field amplitude |Ez| along y-axis at the end of the Y-splitter for both arms of the waveguide. The black dots correspond to experimental data and the solid black traces are fits to the experimental data using Gaussian functions. The FWHM widths are ~3.5 mm for both arms.

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We measured |Ez| along the output face of the device, as shown in Fig. 4(c). Because the two output arms are at different vertical heights, with the right arm lower than the input to the Y-splitter, we had to make two separate measurements to obtain the lateral guided-wave properties of the device. Since the left arm is vertically higher than the input, the measurement is straightforward, in terms of having the THz SPP and the optical probe beam co-propagate. For the right arm, the optical probe beam is made to co-propagate with the THz SPP only over the last 2 cm of the device. We use a thin (100 µm) sapphire slide that has a high reflection coating optimized for 800 nm. The THz data for the right arm is corrected for the reflection associated with the sapphire mirror. We fit the experimentally measured data for both arms to Gaussian functions and found that the FWHM widths were 3.53 and 3.48 mm, respectively, which is in good agreement with the mode size shown in Fig. 2(b).

Finally, in order to more fully demonstrate the utility of 3D printing for fabricating THz devices, we fabricated a series of curved waveguides that incorporate a U-shaped arc. In Figs. 5(a) and 5(b), we show a schematic diagram of the general structure and a photograph of several finished devices, respectively. Each of the devices is 60 mm in total length and includes 5 mm long planar sections (sections A-B and F-G in the schematic) on the input and output side that allow for coupling of THz radiation into the device and placement of the detection crystal at the output. The central portion of the curve (section C-D-E) incorporates an arc that varies between 5 mm and 15 mm. In order to connect the arc (section C-D-E) with the planar sections (sections A-B and F-G), the intervening sections (B-C and E-F) are required to change geometry in order to maintain a smoothly varying curve. Thus, measurements are reported not in terms of radius of curvature, but rather the total vertical depth change, H. In Fig. 5(c), we show the excess loss for each structure, once the propagation loss associated with a 6 cm straight waveguide, found in Fig. 2, has been subtracted. As expected, the excess loss increases with increasing depth.

 

Fig. 5 Properties of 3D curved waveguides. (a) Schematic drawing of the 60 mm long curved waveguide with the various sections delineated. The input (A-B) and output (F-G) sections are 5 mm long planar waveguides used to facilitate input coupling and detection of the guided wave at the out put. The central arc (C-D-E) has a radius of curvature that varies between 5 mm and 15 mm. The connecting sections (B-C and E-F) are adjustable to ensure a smoothly varying curve. (b) Images of the four fabricated devices. (c) Measured excess loss as a function of the depth, H.

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4. Conclusion

In conclusion, we have demonstrated experimentally that conventional 3D printing is well suited for fabricating THz plasmonic devices. We made a variety of different devices, including straight waveguides, 3D bends, 3D Y-splitters and curved waveguides. Although the basic structures described here were printed in a polymer resin, once they were coated with a metal layer that was sufficiently thick, they supported relatively low loss propagation of SPPs. In straight waveguides, we observed a propagation loss parameter of 0.17 cm−1, corresponding to a 1/e propagation length of 5.9 cm. This loss is higher than was observed with waveguides fabricated using conventional metal foils [15]. We attribute the higher loss in the printed devices to greater surface roughness that results from the printing process. In devices that included abrupt out-of-plane bends and continuously varying bends, we measured an excess loss associated with those geometries that increases with increasing angle. In the former case, for example, a 10° abrupt out-of-plane bend resulted in an excess loss of ~2 dB and increased with increasing angle. We have discussed only a few select geometries here. However, the fabrication approach can be used to make a broad range of artificially structured materials. Ongoing advances in printing technology are likely to have significant impact on the utilization of this technique.

Acknowledgments

This work was supported by the NSF MRSEC program at the University of Utah under grant # DMR 1121252.

References and Links

1. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef]   [PubMed]  

2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef]   [PubMed]  

3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]   [PubMed]  

4. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]  

5. S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006). [CrossRef]   [PubMed]  

6. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef]   [PubMed]  

7. A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express 16(13), 9601–9613 (2008). [CrossRef]   [PubMed]  

8. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]  

9. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]   [PubMed]  

10. J. A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express 12(21), 5263–5268 (2004). [CrossRef]   [PubMed]  

11. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef]   [PubMed]  

12. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef]   [PubMed]  

13. D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express 18(2), 754–764 (2010). [CrossRef]   [PubMed]  

14. W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express 18(20), 21498–21503 (2010). [CrossRef]   [PubMed]  

15. G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys. 13(3), 033024 (2011). [CrossRef]  

16. X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102(15), 151912 (2013). [CrossRef]  

17. Z. Wu, J. Kinast, M. E. Gehm, and H. Xin, “Rapid and inexpensive fabrication of terahertz electromagnetic bandgap structures,” Opt. Express 16(21), 16442–16451 (2008). [CrossRef]   [PubMed]  

18. Z. Wu, W.-R. Ng, M. E. Gehm, and H. Xin, “Terahertz electromagnetic crystal waveguide fabricated by polymer jetting rapid prototyping,” Opt. Express 19(5), 3962–3972 (2011). [CrossRef]   [PubMed]  

19. J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett. 103(3), 031104 (2013). [CrossRef]  

20. X. Shou, A. Agrawal, and A. Nahata, “Role of metal film thickness on the enhanced transmission properties of a periodic array of subwavelength apertures,” Opt. Express 13(24), 9834–9840 (2005). [CrossRef]   [PubMed]  

21. A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007). [CrossRef]   [PubMed]  

22. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007). [CrossRef]   [PubMed]  

References

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  1. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
    [CrossRef] [PubMed]
  2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
    [CrossRef] [PubMed]
  3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
    [CrossRef] [PubMed]
  4. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
    [CrossRef]
  5. S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
    [CrossRef] [PubMed]
  6. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
    [CrossRef] [PubMed]
  7. A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express16(13), 9601–9613 (2008).
    [CrossRef] [PubMed]
  8. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
    [CrossRef]
  9. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett.26(11), 846–848 (2001).
    [CrossRef] [PubMed]
  10. J. A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express12(21), 5263–5268 (2004).
    [CrossRef] [PubMed]
  11. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature432(7015), 376–379 (2004).
    [CrossRef] [PubMed]
  12. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express16(9), 6216–6226 (2008).
    [CrossRef] [PubMed]
  13. D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
    [CrossRef] [PubMed]
  14. W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express18(20), 21498–21503 (2010).
    [CrossRef] [PubMed]
  15. G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
    [CrossRef]
  16. X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
    [CrossRef]
  17. Z. Wu, J. Kinast, M. E. Gehm, and H. Xin, “Rapid and inexpensive fabrication of terahertz electromagnetic bandgap structures,” Opt. Express16(21), 16442–16451 (2008).
    [CrossRef] [PubMed]
  18. Z. Wu, W.-R. Ng, M. E. Gehm, and H. Xin, “Terahertz electromagnetic crystal waveguide fabricated by polymer jetting rapid prototyping,” Opt. Express19(5), 3962–3972 (2011).
    [CrossRef] [PubMed]
  19. J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
    [CrossRef]
  20. X. Shou, A. Agrawal, and A. Nahata, “Role of metal film thickness on the enhanced transmission properties of a periodic array of subwavelength apertures,” Opt. Express13(24), 9834–9840 (2005).
    [CrossRef] [PubMed]
  21. A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express15(9), 5616–5624 (2007).
    [CrossRef] [PubMed]
  22. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
    [CrossRef] [PubMed]

2013

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
[CrossRef]

2011

Z. Wu, W.-R. Ng, M. E. Gehm, and H. Xin, “Terahertz electromagnetic crystal waveguide fabricated by polymer jetting rapid prototyping,” Opt. Express19(5), 3962–3972 (2011).
[CrossRef] [PubMed]

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
[CrossRef]

2010

2008

2007

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express15(9), 5616–5624 (2007).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

2006

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

2005

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

X. Shou, A. Agrawal, and A. Nahata, “Role of metal film thickness on the enhanced transmission properties of a periodic array of subwavelength apertures,” Opt. Express13(24), 9834–9840 (2005).
[CrossRef] [PubMed]

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

J. A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express12(21), 5263–5268 (2004).
[CrossRef] [PubMed]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature432(7015), 376–379 (2004).
[CrossRef] [PubMed]

2001

Agrawal, A.

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Cui, A.

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
[CrossRef]

Cui, T. J.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Eldaiki, O. M.

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Fernandez-Dominguez, A. I.

Gao, X.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Garcia-Vidal, F. J.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

García-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Gehm, M. E.

George, R.

Grischkowsky, D.

Harrington, J. A.

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Jiang, W. X.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Kinast, J.

Kumar, G.

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
[CrossRef]

Li, L.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Liu, J.

J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
[CrossRef]

Lu, Z.

Ma, H. F.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Martin-Cano, D.

Martin-Moreno, L.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

Martín-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Mendis, R.

J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
[CrossRef]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett.26(11), 846–848 (2001).
[CrossRef] [PubMed]

Mittleman, D. M.

J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
[CrossRef]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Moreno, E.

Mueller, E.

Nahata, A.

Nesterov, M. L.

Ng, W.-R.

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Pandey, S.

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
[CrossRef]

Pedersen, P.

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Sambles, J. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Shen, X.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Shi, J. H.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Shou, X.

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

Vardeny, Z. V.

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Wang, K.

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature432(7015), 376–379 (2004).
[CrossRef] [PubMed]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Wu, Z.

Xin, H.

Yang, R.

Zhao, W.

Zhu, W.

Appl. Phys. Lett.

X. Gao, J. H. Shi, X. Shen, H. F. Ma, W. X. Jiang, L. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett.103(3), 031104 (2013).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Nat. Photonics

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1(2), 97–105 (2007).
[CrossRef]

Nature

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature432(7015), 376–379 (2004).
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

New J. Phys.

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated films,” New J. Phys.13(3), 033024 (2011).
[CrossRef]

Opt. Express

J. A. Harrington, R. George, P. Pedersen, and E. Mueller, “Hollow polycarbonate waveguides with inner Cu coatings for delivery of terahertz radiation,” Opt. Express12(21), 5263–5268 (2004).
[CrossRef] [PubMed]

Z. Wu, J. Kinast, M. E. Gehm, and H. Xin, “Rapid and inexpensive fabrication of terahertz electromagnetic bandgap structures,” Opt. Express16(21), 16442–16451 (2008).
[CrossRef] [PubMed]

Z. Wu, W.-R. Ng, M. E. Gehm, and H. Xin, “Terahertz electromagnetic crystal waveguide fabricated by polymer jetting rapid prototyping,” Opt. Express19(5), 3962–3972 (2011).
[CrossRef] [PubMed]

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express16(9), 6216–6226 (2008).
[CrossRef] [PubMed]

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express18(20), 21498–21503 (2010).
[CrossRef] [PubMed]

A. Agrawal, Z. V. Vardeny, and A. Nahata, “Engineering the dielectric function of plasmonic lattices,” Opt. Express16(13), 9601–9613 (2008).
[CrossRef] [PubMed]

X. Shou, A. Agrawal, and A. Nahata, “Role of metal film thickness on the enhanced transmission properties of a periodic array of subwavelength apertures,” Opt. Express13(24), 9834–9840 (2005).
[CrossRef] [PubMed]

A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express15(9), 5616–5624 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett.97(17), 176805 (2006).
[CrossRef] [PubMed]

Science

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic drawing of the printed THz waveguide, including the excitation and detection scheme. The groove at the input end is used to couple normally incident broadband THz radiation to SPPs. For detection purposes, the optical probe beam propagates parallel to the THz guided-wave SPPs. A <110> ZnTe crystal is used for coherent detection of the Ez component of the guided-wave SPP. The design dimensions of the rectangular blind holes are: length s = 550 µm, width a = 150 µm, depth h = 450 µm, and periodicity d = 250 µm.

Fig. 2
Fig. 2

Propagation properties for a planar straight waveguide with periodically spaced rectangular blind holes. (a) Measured transmission spectrum for the waveguide. The arrows show the anti-resonance frequencies associated with the different effective cavity modes. These dips occur at 0.27, 0.47 and 0.54 THz. (b) The field amplitude |Ez| measured along the x-axis at different positions along the length of the waveguide. The dots represent the measured field value normalized to the value at the input. The black line is an exponential fit to the data, corresponding to a 1/e decay length of ~5.9 cm. (c) The |Ez| component of the electric field measured along the z-axis at different heights above the sample surface. The dots represent the measured field value normalized to the value at the surface. The black line is an exponential fit to the data, corresponding to a 1/e decay length of 2.6 mm. (d) The |Ez| component of the electric field measured along the y-axis 5 cm from the waveguide input. The dots represent the measured value, while the black trace is a Gaussian fit to the data, yielding a (FWHM) width of ~3.4 mm.

Fig. 3
Fig. 3

Properties of abrupt out-of-plane bends. (a) Schematic drawing for the printed bend structures. Devices were fabricated with bend angles from 5° to 40°, in 5° increments. (b) Excess loss per bend as a function of the bend angle measured at 0.27 THz.

Fig. 4
Fig. 4

Properties of a 3D Y-splitters. (a) Schematic diagram of a 10 cm long Y-splitter, in which the two arms branch off both in-plane and out-of-plane. In both cases, the branches are at ± 10 ° relative to the preceding waveguide. (b) Image of the Y splitter after sputter deposition with Au. (c) & (d) The field amplitude |Ez| along y-axis at the end of the Y-splitter for both arms of the waveguide. The black dots correspond to experimental data and the solid black traces are fits to the experimental data using Gaussian functions. The FWHM widths are ~3.5 mm for both arms.

Fig. 5
Fig. 5

Properties of 3D curved waveguides. (a) Schematic drawing of the 60 mm long curved waveguide with the various sections delineated. The input (A-B) and output (F-G) sections are 5 mm long planar waveguides used to facilitate input coupling and detection of the guided wave at the out put. The central arc (C-D-E) has a radius of curvature that varies between 5 mm and 15 mm. The connecting sections (B-C and E-F) are adjustable to ensure a smoothly varying curve. (b) Images of the four fabricated devices. (c) Measured excess loss as a function of the depth, H.

Equations (1)

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ν mnp = c 2π ( mπ s ) 2 + ( nπ a ) 2 + ( (p+0.25)π h ) 2

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