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A holey cladding dielectric waveguide with square cross section is designed, simulated, fabricated and characterized. The TOPAS waveguide is designed to be single mode across the broad frequency range of 180 GHz to 360 GHz as shown by finite-difference time domain simulation and to robustly support simultaneous TE and TM mode propagation. The square fiber geometry is realized by pulling through a heat distribution made square by appropriate furnace design. The transmitted mode profile is imaged using a vector network analyzer with a pinhole at the receiver module. Good agreement between the measured mode distribution and the calculated mode distribution is demonstrated.
© 2016 Optical Society of America
1. Introduction
The generation of pulsed Terahertz (0.1 THz to 10 THz) electromagnetic waves began in the 1970s and early 1980s when optical pulses from mode-locked lasers became short enough (picosecond pulses) to yield the necessary THz bandwidth [1, 2]. In very early experiments the ultra-short optical pulse was rectified by a photoconductor antenna (PC) comprised of two metal electrodes on a semiconductor substrate separated by a gap [3, 4]. Since then, THz electromagnetic waves have been generated through a variety of techniques, including optical rectification, quantum cascade lasers (QCLs), optical beating, and air plasma THz generation [5–7]. Solid state electronic devices have also been used to generate THz radiation by mixing two signals having slightly different frequencies that yield the generated wave frequency [8]. THz wave generation was also recently demonstrated in a lens-less silicon CMOS architecture [9].
A variety of THz wave detectors have been developed. An unbiased photoconductor antenna and optical rectification can be used to detect THz waves [10]. The electro optic responses of birefringent crystals has also been used as a THz detector [11]. CMOS Schottky diode detectors [12] and diode-connected NMOS transistors [13] are examples of THz detectors used for imaging.
The use of THz radiation in experimental systems or commercial applications invariably requires additional components to focus, guide or otherwise manipulate the signal. Since THz waves fall between the infrared (IR) and microwave spectral regions, most passive THz components have been inspired by either optical/IR or microwave components. For instance, parabolic mirrors and dielectric lenses similar to optical components, are routinely used in THz applications. Since the wavelength of THz radiation is much larger than optical wavelengths, fabrication precision is not typically a challenge. Material considerations, however, do limit the translation of components from the optical/IR spectral region to the THz region. THz lens materials include Picarin (a cyclo olefin based polymer also known as Tsurupica) [14], Zeonex Cyclo Olefin Polymer (COP) [15], and TOPAS cyclic olefin copolymer (COC) lenses which are optically transparent and easily aligned. Teflon is used for low THz frequencies [14], and polyethylene (PE), HDPE, and TPX (4-methylpentene-1 based polyolefin) are also commonly used. Graded index (GRIN) lenses are made using metamaterials [16] and variable focal length THz lenses [17] are also demonstrated. THz filters may be made of PTFE based Fluorogold [14] and other materials. Most mirrors are metal or metal-coated glass. Gold mirrors are excellent reflectors of THz waves. Aluminum coated glass is a cheaper alternative and relatively easy to align, since aluminum is a good reflector in the visible region.
Examples of THz components evolved from the microwave region are rectangular and circular cross section metallic waveguides. Circular cross section waveguides [18] are made of metallic shells and exhibit ohmic loss due only to the metallic surface. Metallic parallel plate waveguides [19] exhibit ohmic loss due to the plates and divergence loss at the open sides of the waveguide. Bare metal wires [20] are made of thin wires that form boundary conditions for propagation. Propagating waves are loosely confined to the wire and mostly propagate in the air surrounding the single wire. This results in lower ohmic loss but also less mode confinement. The mode confinement can be increased by using two metal wires [21, 22]. When components are scaled from the microwave region to the THz region, fabrication challenges including manufacturing precision and ohmic loss impairments are encountered. Dielectric THz waveguides have emerged as an alternative to side-step ohmic loss principally due to metal surface roughness.
The fabrication processes of dielectric waveguides have been adopted from optical and IR fibers. THz dielectric waveguides are divided into hollow, solid and porous core designs. Hollow core waveguides offer low loss since waves propagate in the hollow core but lack bending flexibility [23] since they are a few millimeters thick. There is a large variety of thin flexible hollow core fibers based on anti-resonant reflection [24, 25] and solid core waveguides, though they suffer from material loss. To lower the material loss a low loss material may be chosen as well as reducing the size of the core. However, core reduction also reduces mode confinement. In light of these considerations, solid core holey waveguides are an attractive solution for lower material loss, good mode confinement, and support for broadband transmission.
In this paper we describe a dielectric holey cladding THz waveguide having a square cross section that supports both polarizations. While doping the dielectric to create a core raises the loss tangent, holey cladding fibers offer a lower loss solution. Holey cladding fibers also benefit from ease of fabrication and lower fabrication costs in the same manner as photonic and hollow photonic crystal fibers. To this end, the present design uses the lowest possible number of holes to provide higher fabrication yield. The square holey geometry described herein allows a broad band (180 GHz to 360 GHz) of single mode propagation. A cyclic olefin copolymer (COC) known as TOPAS was chosen from among a variety of dielectric materials for its low loss [23]. The proposed square waveguide is smaller than cylindrical holey TOPAS [26] and Zeonex [27] waveguides. Further, square waveguides offer the advantage of close-packing a ribbon of waveguides. A square fiber geometry was additionally chosen because of its resistance to polarization mode coupling between TE and TM modes providing less crosstalk unlike circular fiber and polarization mode dispersion when there is a break in symmetry compared to conventional cylindrical waveguides [28, 29]. we show below good performance in our experiment on imperfect fibers as fabricated. Similarly, modeling of these imperfect fibers also supports the robustness of the square geometry. Polarization multiplexing for a data communication application is thus more robustly implemented.
The design and simulation of square holey cladding TOPAS waveguides is presented. A calculation of a refractive index profile is given for comparison to cylindrical waveguides. The fabrication process, including differences between our draw tower and conventional fiber drawing processes, is designed to facilitate the square waveguide geometry. The transmitted waveguide mode profile is measured using a vector network analyzer (VNA) by stepping a pinhole across the output facet of the waveguide.
2. Design and simulation
The intended application of this work is chip-to-chip communication using native THz radiation. The waveguide channel must be low cost, easy to fabricate, support a wide frequency band, and facilitate polarization multiplexing. A square holey cladding fiber geometry is designed [using the finite-difference time-domain (FDTD) software package Rsoft] to support TE and TM single-mode polarization states over the frequency range of 180 GHz to 360 GHz. This broad frequency range is specified by the application and is hard to realize, especially at higher frequencies when higher order modes may be excited, particularly in presence of imperfections. To improve fabrication yield, it is desirable to minimize the number of holes and the hole configuration. Figure 1(a) shows the simulated cross sections of the designed 2 mm × 2 mm waveguide with eight 400 µm diameter holes and approximately 1 mm core size. The core size of the waveguide is in the order of the wavelength or smaller. The simulations are shown for both TE and TM polarizations. Figures 1(b) and 1(c) indicate good mode confinement at 360 GHz for both polarizations. Figures 1(d) and 1(e) show the simulation at 180 GHz for both polarizations.
Fig. 1 (a) The cross section of the designed 2 mm × 2 mm waveguide with eight holes (400 µm). The electric field at the cross section of the waveguide at 360 GHz is shown for (b) TE and (c) TM modes. The electric field at the cross section of the waveguide at 180 GHz is shown for (d) TE and (e) TM modes.
The refractive index of the waveguide is calculated as a function of square contours of half width ρ [µm] as shown in the inset of Fig. 2. The core refractive index is considered to be 1.5258 [26] since the center is only TOPAS. The cladding refractive index, is calculated as a weighted average using [30] while is the refractive index of material i, and is the volume fraction covered by material i. Here, instead of a volume fraction, a fraction of areas covered by the material is used.
Fig. 2 The averaged refractive index of the waveguide as a function of square contours is shown radiating outward from ρ = 450 µm to ρ = 1000 µm. The refractive index from ρ = 0 to ρ = 450 µm is a constant value for TOPAS, 1.5258. At ρ = 500 µm the refractive index begins to decrease due to presence of eight holes. At ρ = 850 µm the refractive index is minimum, and begins to increase, since at ρ = 900 µm the area of the air holes stop increasing and the area of TOPAS increases. (Inset) A schematic cross section of the waveguide showing a square contour ρ [µm]. The cladding holes were 400 µm in diameter and the overall dimension of the waveguide is 2 mm × 2 mm.
The refractive index of the holey waveguide is the weighted average of the core and cladding. The latter consists of air holes and TOPAS. The total refractive index was calculated using:
Importantly, the area of holes,, was calculated by integrating over a circle in Cartesian coordinates as a function of the rectangular distance parameter ρ in units of micrometers. The areas of TOPAS between holes were calculated by subtracting the square contour area from the area covered by air holes. The use of square contours allows comparison with the refractive index profiles of typical cylindrical waveguides. Figure 2 shows the averaged refractive index as a function of ρ.3. Fabrication
A number of different processes are used to fabricate holey fibers, including tube stacking, micro-structured molding, and a drill-and-draw technique [31]. The most widely used method is tube stacking, in which capillary tubes are stacked and arranged to create a preform from which a fiber is drawn. Microstructure molding may be done by casting the desired material into a mold to create a preform. In this case, the drawn fibers are kept under solvent for days to etch the cast and yield structured holey fibers. In another microstructure molding technique, the preform is made by casting the desired material into a mold. The mold is then pulled out to make the holey preform structure from which fibers will be drawn. The drill and draw technique was chosen here due to its ease of fabrication with a small number of holes. TOPAS COC was purchased from TOPAS Advanced Polymer Company. The material loss, about 0.2dB/cm (at 0.3 THz) [26], is lower than that found in commonly used dielectric materials such as PMMA (8.6 dB/cm at 0.3 THz) [26] and polycarbonate (PC) (8.7 dB/cm at 0.3 THz).
The drill and draw fabrication process consists of three steps: making preform, drilling holes into preform and, under temperature fiber drawing from preform. To make preforms a custom mold was designed and machined from stainless steel. The cross sectional dimensions of a typical preform is 35 mm × 35 mm as precisely determined by the mold and calculated based on empirical preform-to-fiber shrink ratio data. To ensure sufficient material for fiber drawing, a typical preform is approximately 9cm tall.
A mold was sprayed with boron nitride to prevent the material from sticking to the sidewalls. Molds were preheated using a hot plate at 157°C. The temperature was then increased to 210°C and 10 layers of 20ml of TOPAS beads were sequentially added every 20 minutes. The preform was final-annealed for 40 minutes in a convection oven at 230 °C. The hot plate temperature and melting time were controlled to give a uniform block of TOPAS.
Next, holes were precisely drilled through the TOPAS preform at their designed locations (10 mm pitch) using a mechanical drill press and drill bit size of 3/16”. The shrink factor of preform-to-fiber dimensions was experimentally determined. The core shrink factor is 15.8 ± 1, the cladding shrink factor is 17.5 ± 1, and the shrink factor of holes is 13 ± 1. Using shrink factor data, the 3/16” drill bit was used on the preform to achieve a 400 µm diameter hole size in the fiber. The hole-drilling process was done very slowly using water as lubricant to ensure optically smooth holes in the drawn fiber.
Finally, the waveguide was drawn from the TOPAS preform in a custom built draw tower (shown schematically in Fig. 3). The oven includes two stainless steel pieces, an outer surface to maintain the process temperature and an inner surface to shape the temperature field around the preform. Four heaters with a slightly curved surface of approximately 6 cm × 6 cm (Ceramic E-Mitters, CRS00009 from TEMPCO Electric Heater Corporation) are symmetrically placed between the two shells. The shape of the temperature field affects the geometry of the resulting waveguide cross section. The square geometry of the oven follows the geometry of the preform and is specifically chosen to shape the temperature field to preserve the square cross section of the preform and fiber. The inner piece is a 24 cm tall hollow square tube with 6.5 cm × 6.5 cm cross section and the outer piece has a 17 cm × 17 cm cross section and 24 cm height. The fiber was pulled at the rate of 1.6 cm/s after neck-down occurred at 257°C using a collecting spool with a variable rotation speed. During fiber pulling the preform was lowered using a vertical pico-motor driven translational stage with the speed of 0.019 mm/s to ensure proper preheating. A final fiber thickness of 2 mm was achieved by empirically determining, then controlling draw parameters such as temperature and pulling tension [32].
Fig. 3 The draw tower is comprised of an oven and motion control for the preform and the drawn fiber. The oven has two hollow metal shells to contain and shape the temperature field. Four (CRS00009) heaters positioned between the shells. A collecting spool maintains and regulates the drawn fiber and stores the final product. A pico-motor stage keeps the necking region of the preform at the correct height and temperature.
4. Results and measurements
A variety of waveguides with lengths ranging from 15 cm to 200 cm were successfully fabricated with a cross section of about 2 mm × 2 mm and thickness variation ranging from 3.7% to 8.0% along the waveguide length.
Figure 4 shows photographs of pulled fiber samples and cross section micrographs. Distortion is occasionally present in both sidewall and hole cross-sections. To study the effect of geometric distortion in the drawn fibers, simulations were designed to model the mode profile in the condition of breaks in symmetry. Figure 5(a) shows the photographed cross section of a fabricated fiber and Fig. 5(b) shows the simulation at 230 GHz for the same fiber. A new FDTD simulation was designed to account for fabrication defects such as hole size variations, noncircular holes and curved edges as shown in Fig. 5(b). The simulated mode was found to be well confined to the core area despite these geometric imperfections.
Fig. 4 (a)Fabricated waveguide samples. (b-c) Composite optical microscope images show fabricated waveguide cross sections of two different segments of fiber from the same preform. (d) Composite optical microscope image of a fabricated waveguide cross section.
Fig. 5 (a) Micro-graph of the cross section of a fabricated waveguide. (b)TE Mode propagation simulation for the fabricated waveguide, considering all geometric imperfections at 230 GHz. The plot shows the magnitude of the electric field on a linear scale. Similar results were observed for TM polarization.
The mode profile of a 30cm long waveguide was mapped using a pinhole mode profilometer described in the following section. The setup consist of a VNA (Agilent E8361C) along with two frequency extenders (OML V03VNA2-T/R) at the transmitter and receiver ends. The VNA and extenders provided a source and detector for radiation from 220 GHz to 325 GHz. The waveguide was placed on an X-Y-Z stage with tilt stages between the two frequency extenders allowing proper alignment of the source into the fabricated waveguide. A 250 µm pinhole was mounted to the receiver module, which was then stepped in an X-Y array to map the transmitted mode from the fiber in steps of 250 µm. Figure 6 shows the resulting transmitted mode profile of the fabricated waveguide averaged over the frequency range of 220 GHz to 325 GHz. Transmission in the fiber core was measured to be 10dB higher than near the edges of the waveguide. Note that this is a relative measurement; data do not represent exact transmission values. This pinhole profilometer technique provides an imaging measurement consistent with the FDTD simulation of Fig. 5(b).
Fig. 6 Mode profile of the waveguide as mapped with a 250 µm pinhole in a 250 µm grid using a VNA with two frequency extenders.
5. Discussion
A square dielectric holey cladding waveguide was designed to work in the THz frequency range and support two modes of polarization, thus multiplexing the data transfer rate. The manufacturing process included a well-defined temperature field to preserve the square geometry of the waveguide. The refractive index of the waveguide was calculated. At the center of the waveguide the refractive index is 1.5258. At ρ = 500 µm (where the holes start), the refractive index decreases since air holes lower the overall refractive index. As ρ increases, the refractive index decreases with a slower slope since hole areas increase at a lower rate. Around ρ = 900 µm the refractive index starts increasing. Since the area of the holes are not increasing after that point and edges are filled with TOPAS only. Simulations designed to model geometric imperfections in fabricated waveguides indicate good mode confinement under breaks in symmetry and external perturbations, thus demonstrating a low cost fabrication process that relaxes manufacturing constraints. A less distorted square cross section waveguide may be achieved by pre-emphasis of the original preform geometry to accommodate for the wall distortions of the drawn fiber. Figure 7 shows the effective refractive index (obtained by simulation in Rsoft) of a waveguide with perfect square geometry (Fig. 1) and refractive index of a realized waveguide with broken symmetry (Fig. 5(b)) across the frequency range of interest for TE and TM states of polarization. The refractive index of a waveguide with broken symmetry approaches the refractive index of a perfect square geometry at higher frequencies since the mode is more confined to the core at lower wavelengths. Negligibly slight differences in refractive index between TE and TM polarizations are observed for a waveguide with broken symmetry at lower frequencies, which shows the impact of hole and sidewall imperfections.
Fig. 7 Effective refractive index of the waveguides shown in Fig. 1 and 5(b) across the frequency range of interest for TE and TM polarizations.
Mode profiles of fabricated fibers measured using a pinhole mode profilometer are in agreement with simulations which show mode confinement in waveguide centers. The slightly off-center maximum transmission area, along with nonsymmetrical transmission across the waveguide in measured data is shown in Fig. 6. This could be a result of off-center pinhole position while scanning the cross section of the waveguide. Also low resolution grids (steps of 250 µm) can lead to slight differences between the measured data and simulated data.
The demonstrated waveguide can be integrated into a multi- waveguide ribbon as a chip-to-chip THz communication system. Low loss coupling between the chip and waveguide may be achieved using a horn reflector antenna made with the same dielectric material (TOPAS COC).
Acknowledgment
This work was supported in part by Semiconductor Research Corporation (SRC). The authors would like to acknowledge the anonymous reviewer for the perspective of pre-emphasis of original preform to accommodate for the distortion of the drawn fiber.
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