We demonstrate fiber Bragg gratings written in polymer fiber for use in the THz window for the first time. A KrF excimer laser operating at 248 nm was used to inscribe notch-type gratings in single component Topas subwavelength fiber. A transmission loss at the centre wavelength of the grating of 60 dB is observed in short gratings containing only 192 notches. Experimental results and modeling are presented. The gratings are expected to find use in THz signal filtering and chemical or biosensing applications.
©2012 Optical Society of America
THz radiation spans the region of the electromagnetic spectrum between the mid infrared and microwaves (approximately 300 GHz – 10 THz, wavelength 30 µm – 1 mm) and is increasingly being used in the fields of security scanning , biological imaging  and wireless communication . However, this region of the spectrum suffers from a poor choice of components. Techniques used to generate such radiation and components designed to operate within the THz window draw on technologies which are used in both the optical and microwave regions. A prime example is the waveguide which can be either a metal component similar to that used with microwaves or a fiber as is used in optical communications. It is common for components designed to operate at THz frequencies to be fabricated in bulk form [4, 5], and those employing waveguides are rare . In this paper we report on what we believe is the first production of fiber Bragg gratings (FBGs) written in polymer optical fibers for use as THz filters.
2. Grating fabrication
The fiber used in our experiment was produced by the direct extrusion technique . Compared with the conventional fiber drawing method which uses a furnace and drawing tower, extrusion eliminates the requirement for fabrication of a preform and has the dual advantages of low cost and the ability to fabricate fiber continuously.
Figure 1 depicts a simplified diagram of an extruding machine. Raw materials, usually in pellet form, are fed into the hopper and the motor driven screw extrudes the material through the nozzle. By selecting an appropriate die, different fiber cross-sections and multi-component fibers with conventional core and cladding can be extruded, though for the purposes of this experiment a single component fiber was fabricated. The temperature of the extrusion head is precisely controlled and the temperature profile usually increases from the feed zone to the die. The fiber is wound onto a capstan and by controlling the drawing speed and optimizing the temperature profile, fibers with different diameters can be drawn. In this experiment, Topas 6013F04 grade purchased from Polyplastics was adopted as the fiber material. Topas is a cyclic olefin copolymer which exhibits low loss at THz frequencies  and has a refractive index of 1.51 in the range 220 GHz – 500 GHz. The extruded fiber was an air-clad sub-wavelength fiber with a diameter of either 0.6 mm or 0.3 mm for gratings centered at 265 GHz and 400 GHz respectively, which corresponds to a calculated mode overlap with the fiber of 46% and 19%. Subwavelength THz polymer fiber has the advantage of low loss compared to conventional fibers which possess a core and cladding . As the name suggests, the fiber diameter is smaller than the operating wavelength. Reducing the diameter-to-wavelength ratio decreases the percentage of field guided inside the lossy core, resulting in reduced fiber loss. Minimizing the fiber diameter also has the advantage of making the fiber more flexible, which is desirable for practical use. This flexibility comes at the expense of introducing some bend loss, although this will not be a problem in a small, packaged FBG. Specifically for THz, a subwavelength fiber fabricated using the extrusion process is also low cost. In addition, exposing the outer field of the THz signal offers an effective means of incorporating bio- and chemical sensing functionality.
The FBGs were written point-by-point using a Coherent Compex Pro 102 KrF laser operating at 248 nm with a pulse energy of 200 mJ and at a repetition rate of 5 Hz. The grating strength was controlled by varying the number of laser pulses each element received.
As depicted in Fig. 2 , the laser was focused to a line 11.5 mm by 150 µm using two crossed UV fused silica plano-convex cylindrical lenses. In this way, up to 10 FBGs could be fabricated at one time. The fiber was moved through the stationary beam using a Newport M-ILS100CCHA linear translation stage with a resolution of 0.3 μm.
A picture of a typical FBG is shown in Fig. 3 . The gratings consisted of a series of 192 equally exposed elements with a pitch of either 509 µm in 0.6 mm fiber, or 361 µm in 0.3 mm fiber, for FBG center frequencies of 265 GHz and 400 GHz respectively. The approximate lengths of the gratings were 98 mm and 69 mm. The FBGs are similar to those produced by reactive ion etching into the core of silica single mode fiber . It should be noted that an equivalent scaled photorefractive FBG written in conventional telecom fiber for use at λ = 1.5 µm would be only 130 µm long.
The FBG transmission spectrum was measured using an Agilent N5245A PNA-X microwave network analyzer connected to mixer modules from OML Inc. which scaled the frequency range to 500 GHz (see Fig. 4 ). In this configuration, the measurement system has a dynamic range of approximately 70 dB and a display limited resolution of approximately 50MHz. Hollow metallic waveguides were used for ease of coupling of the transmitted and reflected THz signal between the mixer modules and the fiber without the need for bulk optics. Two x-y-z stages (not shown) were used to position the ends of the fiber which was held in specially fabricated polystyrene mounts in order to minimize the loss. The fiber was held as straight as possible in order to eliminate bend loss.
The output of the waveguides was linearly polarized. The nature of the spectrum analyzer was such that bidirectional measurements of both the transmitted and reflected signals were possible without the need to re-arrange the experiment.
Typical FBG transmission spectra at 265 GHz and 400 GHz are shown in Fig. 5 . The reflection spectrum of a FBG at 265 GHz is shown in Fig. 6 (linear scale). The spectra have been normalized to remove waveguide to fiber coupling losses and fiber loss, typically totaling <10 dB. The small out of band ripple is due to Fabry-Perot interference from the ends of the fiber. Since the gratings are formed by removing material from the fiber, the refractive index change is negative and the center frequency of the FBG increases with increasing strength. Each notch of the grating was exposed for 30 s and 8 s respectively. The FBGs had a transmission loss of approximately 60 dB at 265 GHz and 45 dB at 400 GHz, limited by the dynamic range of the network analyzer.
As the gratings are fabricated by ablation and not the photorefractive effect, it is difficult to obtain the required refractive index profile along the fiber, and a conventional approach based on coupled mode theory is not suitable. In our study, we adopted a combination of numericalmethod and conventional transfer matrix method  in order to model the fabricated gratings. Each UV laser inscripted notch, or a few of the notches, are simulated by the commercial High Frequency Structure Simulator (HFSS) software package which is a 3D full-wave electromagnetic field simulator based on the finite element method. This software is widely used in microwave engineering and is able to extract parasitic parameters, e.g. scattering parameters comprising transmission and reflection, from the simulated structure. The scattering parameters are then converted to the transfer matrix and cascaded to obtain the frequency response of the whole grating.
The geometrical model of the FBG is simply a solid cylinder with multiple notches removed, modeled on the experimental FBGs. As depicted in Fig. 7 , the notches are triangular from a side view and homogeneous along that direction. The fibers were exposed to the laser for different durations, resulting in different notch depths. As the exposure time increases, the notch also becomes wider. The depth and width of the notches were measured from microscopic photos and used in the model, and none of the parameters were optimized to improve the fit to the experiment. Sixteen notches were simulated, and the corresponding scattering parameters were extracted for transfer matrix method processing.
Figure 8 shows comparisons between the simulated and experimental results for gratings centered at 260 GHz. It should be noted that the coupling efficiency from a hollow metallic waveguide to the subwavelength fiber we used, as calculated by the overlap integral of the two modes, is around 0.53. Hence operating in transmission mode we should observe a total waveguide to fiber coupling loss of 5.5 dB. Experimental results shown in Fig. 8 suggest that the measured insertion loss is around 7-8 dB which, taking into account the measured fiber loss of approximately 0.2dB/cm, is consistent with the calculated value.
All the experimental data presented in Fig. 8 were measured with horizontally polarized waves. Figure 9 shows the effects of birefringence. The responses due to the two polarizations are clearly different with horizontally polarized waves experiencing a stronger grating. For gratings with a depth of 179 μm, the suppression difference at the center frequency of the simulated FBG is 11 dB. This is mostly due to the distribution of the etched grating not being radially symmetric, hence the interactions with the notches are different. However, as the fiberwe used was not polarization maintaining, we only observed a difference of around 6 dB experimentally.
It can be observed in Fig. 8 that sometimes the Bragg frequency predicted by the simulator deviates from the experimental one. This can be explained by diameter variation of the fiber which is not always exactly 600 μm. Figure 10 provides a parametric study on the diameter of the fiber. Smaller diameter fiber exhibits a smaller mode index and hence the peak shifts to higher frequency. We confirmed that the Bragg frequency shift observed in Fig. 8 is caused by diameter variation by carefully measuring the diameter of the fiber used.
The performance of the FBG can be affected by the fiber diameter variation. If the diameter is consistent along the gratings, the Bragg frequency will alter according to the fiber size. If the diameter varies within the grating however, the performance will be degraded. Figure 11 shows two examples.
If the fiber diameter is smaller at one end and increases linearly towards the other end, the grating will become chirped. Figure 11(a) records the simulated spectrum of a FBG with respect to diameter change. It can be seen that the bandwidth of the grating becomes wider as the diameter change increases and the center moves to higher frequency, as expected for a chirped FBG. This can be explained by the fact that as the diameter decreases, the effective refractive index becomes smaller which results in a higher Bragg frequency. Figure 11(b) depicts the situation when the fiber diameter is smaller in the middle of the grating. As the diameter decreases from the ends towards the middle, effectively the FBG is modulated and forms a superstructure FBG . As a result, multiple reflection peaks appear, which is consistent with the transmission spectrum shown in Fig. 11(b). Meanwhile, the same blue shift phenomenon also exists. Therefore in order to get FBGs with good quality, diameter control is a key factor.
For the first time to our knowledge, FBGs have been fabricated point by point in polymer fiber in the THz region. Measurement limited transmission loss of up to 60 dB has been observed. The FBGs consisted of only 192 elements resulting in very short, ultra-strong gratings compared with their optical counterparts. Good agreements have been achieved between experimental results and HFSS numerical simulations. The gratings should find applications in THz signal filtering and chemical or biosensing.
This work was supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project no. City U 110608).
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