Photonic Bragg waveguide platform for multichannel resonant sensing applications in the THz range.

In this paper, we study a photonic Bragg waveguide sensor for resonant sensing applications in the THz range. In order to enhance the resolution and detectivity of the sensor, we modify the relatively broad transmission spectrum of the Bragg waveguide with spectrally narrow transmission dips by creating a geometrical defect in Bragg reflector and causing anti-crossing phenomenon between the core-guided mode and defect mode. The spectral position of the resonant dip is highly sensitive to the thickness variation in the vicinity of the waveguide core. By designing and manufacturing a Bragg waveguide which includes several sections with different defect layer thicknesses, we can interrogate more than one sample simultaneously and thereby realize multichannel resonant sensing by directly tracking the independent resonant dips. Furthermore, we demonstrate the waveguide platform for online monitoring of the thickness variation of lactose powders, which is captured on the waveguide core via a centrifugal force using a home-built rotating setup. Additionally, we also demonstrate the waveguide for fingerprint detection of powder analytes, which further enriches the sensing scenario of the sensing platform. Finally, we discuss the advantages and the spectral tailoring flexibility of the THz Bragg waveguides sensors for future implementations.


Introduction
Over the past decades, ultrasensitive optical sensing based on engineered structures with resonant sensing features has attracted considerable interests in a variety of fundamental and practical applications [1][2][3][4][5]. Currently, most of the investigations of the developed resonant sensors are typically operating in the visible and near-infrared regions. Since the probing lengths of the evanescent fields in these spectral ranges are deeply sub-wavelength, detection of larger targets (such as bacteria with sizes of 0.5µm-10µm) is found to be problematic. In order to extend the probing depth of the surface wave to longer distance for macromolecular or bacteria detection, one solution is to develop resonant sensors operating at longer wavelengths (such as THz).
The THz range, with frequencies lying between 100GHz and 10THz, has strong application potential for a wide range of industrial and scientific fields, including biosensing, imaging, communications, and spectroscopy [6][7][8][9]. Among these applications, THz biosensing has attracted considerable interest due to many appealing properties of THz waves. First, THz waves are non-ionizing, therefore, they pose no damage to the biological samples. Second, many molecules have vibrational and rotational modes in the THz regime, thereby showing unique absorption fingerprints. Third, the probing length of THz surface wave is a natural candidate for detection of macromolecules, cells, and bacteria of relatively large sizes.
Designing of THz waveguides for flexible delivery of THz radiation with low loss and efficient light-matter interactions is an important step towards practical sensing implementations. The concept of using waveguides for sensing is well established in other frequency ranges, but has only recently started maturing in the THz range. One principal difficulty for realizing low-loss THz waveguides is that most materials exhibit large absorption losses in the THz region. In order to circumvent the loss limit imposed by the absorption of fiber material, subwavelength [10][11][12][13], porous [14][15][16], and hollow-core THz waveguides with various structures [17][18][19], are developed. In particular, hollow-core or porous waveguides are of great interest for biosensing applications. Such configurations allow the test samples to conveniently access to the waveguide core and the evanescent tail of the guided waves. Moreover, the relatively large channels could be further functionalized with bio-recognition elements (such as phages) that can bind and progressively accumulate target bacteria, thus enabling detection of specificity.
One of the most common configurations of THz waveguides for sensing applications is based on anti-resonant reflecting hollow waveguide (ARRHW), which features a hollow core surrounded by a ring-shaped dielectric cladding [20,21]. In this configuration, the core modes can oscillate and radiate through the cladding since the refractive index of the waveguide core is smaller than that of the cladding material. A thin bilayer attached to the cladding of the THz-ARRHW results in resonant-frequency shifts. Thus, one can sense the tiny variations in the refractive index or thickness of an adsorbed molecular film near the ring cladding. Based on this mechanism, various sensing applications have been proposed. For example, in [20], the authors experimentally demonstrated the use of a simple hollow tube for the detection of sub-wavelength-thick molecular overlayer adhered to the inner-core surface of tubes. In another implementation [21], the authors demonstrated a similar pipe waveguide as a terahertz refractive index sensor for powder and liquid-vapor sensing. The demonstrated sensors based on ARRHW have the advantages of flexibility and compactness, as well as remote sensing capability. They are potentially suitable for applications, such as biomedical or industrial sensing applications, and environmental pollutant monitoring.
Parallel plate waveguides (PPWG) have also been extensively studied for THz guidance and sensing experiments [22][23][24]. THz pulses propagating in the PPWG allows characterization of analyte liquids or dielectric films loaded in the vicinity of the waveguide. In such sensors, sensing of thin dielectric films is based on the analysis of resonant frequency or pulse delay in the presence of the test sample. In 2009, the authors [23] described a THz resonator integrated with a parallel-plate waveguide for highly sensitive, and noninvasive liquid refractive index monitoring. Later in 2012, the same research group [24] realized a similar parallel-plate waveguide sensor with two independent integrated resonant cavities. The resonant frequency of each cavity exhibits an approximately linear dependence on the refractive index of the material inside the cavity, and each cavity is demonstrated to respond independently with no measurable crosstalk.
Another major category of waveguides that have been studied for THz sensing applications is micro-structured waveguides [25][26][27]. These waveguides offer better confinement and lower losses due to less material residing in the core compared to solid-core waveguides, and they have great potential for sensing applications. For example, in [25], the authors used a suspended core polyethylene THz fiber for the detection of E. coli bacteria based on an amplitude modality. In another implementation [26], the authors proposed a planar porous dielectric waveguide featuring periodic sequence of deeply sub-wavelength air/dielectric bi-layers for potential applications as low-loss waveguides and sensors in the THz spectral range. The design of this waveguide maximized the fraction of power guided in the air to reduce the waveguide loss due to material absorption, thus providing a conveniently accessible microfluidic channels for sensor measurements. Such micro-structured THz waveguides sensors are fabricated by using traditional fiber drawing technique. One typically prepares preform with designed cross section and then draws it in to waveguides with desired diameter.
Nevertheless, in this method, the waveguide cross-section is most determined by the geometry of the preform, which is relatively difficult to produce waveguide with sophisticated geometry in their cross-sections. This inevitably limits the versatility in their spectral features and many industrial applications.
With the success and commercialization of additive manufacturing and 3D printing technology, many THz functional and sensing devices have been reported [27][28][29][30][31][32]. For example, in 2019, the authors reported a hollow-core Bragg waveguide-based fluidic sensor, where the liquid analyte is flowing in the microfluidic channel integrated into the waveguide cladding [32]. The analyte refractive index-dependent resonant defect state supported by the fluidic channel is probed by tracking the resulting absorption dip and phase change of the core guided mode on waveguide transmission spectra. The sensor sensitivity is found to be ∼110 GHz/RIU.
In practical industrial application, one key capability for resonant sensing platform is parallelism, i.e., the ability to interrogate more than one sample simultaneously and independently [24]. In this work, we demonstrate that by properly designing and manufacturing Bragg waveguides with wellcontrolled geometries, one can achieve multichannel resonant sensing. This can be accomplished by employing a single piece waveguide, which includes several sections of Bragg waveguides with different defect layer thickness, and therefore, different and independent resonant dip positions in the transmission spectra. In this way, each section can be biologically or chemically functionalized to selectively detect specific analytes. By tracking each independent resonant dip in the transmission spectrum of the waveguide, one can monitor changes in the thickness or quantity of different analytes by exploiting a single-cycle terahertz pulse. Furthermore, we use the 3D printed waveguide for online monitoring the thickness variation of lactose powder, which is captured on the waveguide core inner surface via centrifugal force using a home-built rotating setup. Then, a form of fingerprint detection of powder analyte is also experimental demonstrated. Such waveguides are fabricated by 3D technology, which has greatly simplified the fabrication of THz waveguide sensors and devices without sacrificing the performance. The ability to tailor the spectral properties of the sensors by properly designing their geometric parameters means that our Bragg waveguides become a viable platform for a wide range of application, such as detection of powers, films, and bacterial interactions, as well as monitoring of liquid analytes, etc. Finally, we discuss the advantages, limitations, as well as the spectral tailoring flexibility of the 3D printed THz Bragg waveguides sensors for future sensing implementations.

Fabrication of the Bragg waveguide using 3D printing technology
With the advent of dramatic resolution improvement of 3D printing technology, researchers and engineers have widely employed 3D printing for the fabrication of THz waveguides and components [30][31][32][33][34]. In particular, stereo-lithographic apparatus (SLA) has been proven to be an effective method for the fabrication of THz waveguides and devices. In this approach, the photosensitive resin is cured layer by layer with a specific pattern defined with UV radiation at the build plane. In this work, we choose ASIGA Pro 2 with photosensitive resin for the fabrication of Bragg waveguides. This printer has a transverse resolution of 50µm and a longitudinal resolution of 1µm (along the waveguide). In order to remove the unreacted photosensitive resin, the printed components are immersed into isopropanol for 4-6 hours and then dried in air. The schematic design of the THz Bragg waveguide is shown in Fig. 1(a). The gray region and white region represent the high refractive index layer (printing resin) and low refractive index layer (air), respectively. This resin has a refractive index of n = 1.63 and absorption loss α = 0.95 cm −1 in the vicinity of the interested spectral range as measured using a cut-back method [31,32]. This is also the value we use in our theoretical simulations in the following section. The green region in the waveguide geometry represents the defect layer. (c) Transmission spectrum of a waveguide with uniform layer in the reflector (blue curve). The numerically calculated loss spectrum of the HE 11 mode is shown in cyan color. The inserts represents the modal profile at 0.18THz marked on the spectrum. (d) Transmission spectrum of a waveguide with a defect. (e) Schematic of the THz-TDS system with a fiber-coupled detector, which can perform both THz spectroscopy and imaging. Waveguide is mounted on a U-shaped holder, which has an aperture at both the input and output facet. (f) Transmission spectra of two Bragg waveguides with different defect thicknesses.

Design and characterization of the Bragg waveguide with and without a defect
Single-mode operation is generally favored for sensing applications. We, therefore, start by designing a single-mode Bragg waveguide by gradually reducing the diameter of waveguide core. In order to confirm the propagation modes supported in the bandgap, we compute the band diagram of the Bragg waveguide at selected core diameters using COMSOL software. We find that when the waveguide core diameter is reduced to 4.5mm, an effectively single HE 11 mode propagation could be achieved in the fundamental bandgap region. In Fig. 1(a), we plot the modal effective refractive indices of the guided modes as a function of frequency in the frequency range of 0.1-0.3THz. The color code indicates the fraction of the modal power guided within the hollow core. As shown in Fig. 1(a), the bandgap, in fact, features several types of modes, which can be identified as core-guided modes and defect modes. The core-guided mode is the Gaussian-type HE 11 modes [red-colored curve in Fig. 1(a), mode profile shown in the insert]. Additionally, some defect modes are observed within the fundamental bandgap due to the presence of micro-bridges. Nevertheless, these modes only have very small power in the core, and therefore, difficult to excite with the linear polarized THz beam used in this work. As a result, such Bragg waveguide operates in an effectively single mode regime.
In order to confirm this, we then characterize the transmission of a 3D printed Bragg waveguide with a uniform reflector (no defect) using a fiber-coupled TDS spectroscopy and imaging setup, as shown in Fig. 1(e). In this setup, a femtosecond Ti: Sapphire laser is used as a pump source. A free space coupled high power interdigitated antenna is used as the THz emitter, and a fiber-coupled photoconductive detector is mounted on an automatic micro-positioning stage, which enables both spectroscopy characterizations and model imaging by raster scanning the fiber-coupled detector. A grating-based dispersion management module is employed with a goal to compensate the pump pulse broadening due to the fiber dispersion [31,39]. The 3D printed waveguides are mounted on a U-shaped holders, as shown in Fig. 1(e). In Fig. 1(c), we present the transmission spectra of the Bragg waveguides with a uniform reflector. The experimentally measured fundamental bandgap is centered at 0.17THz, which is slightly displaced compared to the theoretical value (0.18THz). This can be easily rationalized by noting that the thickness of the high-refractive-index layer is in fact somewhat thicker than the designed values due to the swelling of the resin during postprocessing, which induces a blue frequency shift in the bandgap center position. In order to confirm an effective mode operation, we perform the modal imaging of the waveguide output facet using the same setup by raster scanning the detector with a step resolution of 250µm. The mode profile at 0.18THz is presented in the insert of Fig. 1(c), which confirms an effective single-mode operation of the waveguide. Furthermore, we note that the bandgap looks asymmetric and the mode confinement is weaker compared to that of the HE 11 mode based on numerical calculations, as shown in Fig. 1(c). This is probably due to the variation and deformation in the geometry of the printed Bragg reflector from that of the designed one with perfectly uniform reflector. Additionally, since the Bragg waveguide characterized in this work is only 2.5cm, the optical confinement is weak, resulting a relatively broad transmission window. Such a broad bandgap window will inevitably limit its sensitivity and detection of limit in sensing applications. One straightforward solution is employing a longer waveguide with increased bilayer number in the Bragg reflector, which could enhance the optical confinement and generate smaller transmission window. Nevertheless, this will sacrifice on the compactness of the sensing system. In fact, another feasible approach is to introduce geometrical defects into the structure of a Bragg reflector, which can confine localized states, and thereby modify the relatively broad transmission window with spectrally narrow dips [31,32]. To verify this phenomenon, we compute the band diagram of a Bragg waveguide featuring a defect in the form of a thicker first reflector layer (thickness increase of 300µm, the light green region represents the so-called defect layer). As shown in Fig. 1(b), the introduction of a defect layer into the waveguide core results in anti-crossing between the core-guided mode and the defect modes which are typically localized to the defect layer and lossy. On typical defect mode is shown in the insert of Fig. 1(b). Over a certain frequency range, there is a resonant power transfer from the core-guided mode into the defect mode, resulting in a significant increase in the propagation loss, forming a narrow resonant transmission dip inside the waveguide transmission bandgap. As is observed in Fig. 1(d), the spectrum of the Bragg waveguide with a defect features two loss peaks inside of the waveguide bandgap, which correspond to the two anti-crossing regions shown in Fig. 1(d). Next, we characterize Bragg waveguides with a defect layer with thicknesses of 300µm and 400µm on the first layer of the reflector, respectively. The experimentally measured transmission spectra for the Bragg waveguides are present in Fig. 1(f). The anti-crossing frequency (or resonant dip position) depends strongly on the defect layer thickness and refractive index, and features a blue shift when the thickness of the defect layer is increased. The resonant dips feature narrow linewidths, which can significantly improve the detection limit and sensitivity of such sensors. Additionally, since the resonant dip position is dependent on the defect layer thickness, one quickly arrives at the intriguing idea of modifying the transmission spectrum of the Bragg waveguide with several independent resonant dips by incorporating multiple defects along the waveguide, one could realize multichannel sensing. In this way, one could potentially interrogate more than one samples simultaneously by a single THz pulse, as will be studied in the next section.

Bragg waveguide with defect layers for multichannel resonant sensing
One important capability of resonant sensors is parallelism. Specifically, in practical industrial implementation, more than one samples need to be interrogated simultaneously and independently. Realization of parallelism relies on the development of sophisticated and versatile waveguide platforms with well-controlled geometry. In traditionally fiber drawing technique, the waveguide is manufactured by preform heating and drawing in a fiber-drawing tower. Geometry of the final waveguide can be controlled by adjusting the parameters in the drawing process, such as temperature distribution in the furnace, fiber drawing, and preform feed speeds, as well as the pressurization of the hollow core. Nevertheless, in our practical demonstrations, we find that the waveguide cross-section is most determined by the geometry of the preform, and it is relatively difficult to produce waveguides with sophisticated geometry in their cross-sections or introducing any changes along the waveguides, which limits the versatility in their spectral features and the capability for interrogating more than one samples simultaneously and independently. The advent of 3D printing technology with significantly improved resolution enables development of waveguides with ever-sophisticated geometries, which also opens a pathway to develop waveguide platforms with enriched spectral features to realize advanced sensing application, e.g., parallelism.
In Fig. 2(a), we present the schematic operation principle of a multichannel sensing based on the Bragg waveguide. In this configuration, two pieces of Bragg waveguides with different defect thicknesses are butt-coupled together. In the transmission spectrum, it is reasonable to expect multiple independent resonant dip positions, by assuming there is no cross talk among these resonant dips and the experimental setup has a high-enough frequency resolution to resolve them. In this case, each section of the Bragg waveguide could be functionalized in order to detect specific targets (e.g., the left section to target analyte 1 and the right section to target analyte 2 marked in red and green in Fig. 2(a), respectively), independently, and thereby enabling multichannel sensing . The analyte changes in the vicinity of the waveguide core of each section can be monitored by analyzing the independent resonant dip potions in the transmission spectrum of the waveguide.
In order to study the possibility of parallelism sensing, we, therefore, fabricate one single 4cm-long Bragg waveguide with its first layer in the reflector modified by two different defects (i.e., 300µm and 500µm, respectively). Such a geometry configuration is chosen in order to avoid the cross talk between the resonant dips of the two sensing sections based on our preliminary experimental trials and observations. We then characterized the spectrum of the waveguide in a continuous wave (CW) THz setup. A CW system has a very high frequency resolution of ∼10MHz, which is essential to resolve the resonant dips and spectral shift in the transmission spectrum. This is generally impractical due to the frequency limitation of a TDS setup, as detailed in Section 6. The spectrum of the Bragg waveguide is shown in black in Fig. 2(b), which features as four resonant dips, which correspond to the anti-crossings between the core mode and four different defect modes. The two dips at high frequency regions (e and f) are due to the hybridization between the core-guided mode and a defect mode localized in thinner layer (i.e.,  ). This is also consistent with our experimental observations in Section 2. In fact, this phenomenon can also be rationalized with the variational theorem detailed in [42]. When the defect thickness is increased, the frequency will decrease because the mode has more space to oscillate.
In order to test the independence of the resonant dips for multichannel sensing, we increase the defect thickness of one section (e.g., defect 1) by 10µm, and the transmission spectrum is shown in pink curve in Fig. 2(b). We note that the high frequency fluctuations in the signal are due to the standing waves between the waveguide facet and the detector, which can be removed by applying a low pass filter [31]. The filtered spectral regions of interests marked as dash circles are illustrated in Fig. 2(c-f). It is well observed that two of the resonant dips on the right experience a blue frequency shift of ∆υ ∼ 1.4GHz, while the other two resonant dips are retained at the same frequency position. The projected sensitivity is 0.14GHz/µm, which is consistent with our previous results [31]. This clearly demonstrates the independent nature of the resonances. Therefore, by tracking the positions of the resonant dips, one can achieve multichannel sensing by employing a relatively long waveguide, which incorporates several sections of Bragg waveguides with different defect layer thicknesses and different resonant dip positions in the transmission spectra. In practical implementations, each section could be biologically or chemically functionalized to selectively detect specific analytes. By tracking each independent resonant dip in the overall transmission spectrum of the long waveguide, one can thereby monitor changes in the thickness or quantity of different analytes by exploiting a single-cycle terahertz pulse.
It is important to note that one potential difficulty in realizing parallelism sensing based on the waveguide platform is the cross talk between the resonant dips, which could also limits the dynamic range of the sensors. This issue can be circumvented based on the following two approaches. First, by carefully optimizing the geometry of the Bragg waveguide cross-section, one can fine tune the positions of the corresponding resonant dips in order to avoid such cross talk and interference. For the other, we note that the number of resonant dips is dependent on the thickness of the defect layer. When the defect thickness is decreased, fewer modes can be localized on the defect layer, and vice versa. In the limit when the defect layer thickness is close to zero, no defect modes can be found [42]. Therefore, by choosing proper defect layer thickness, we can achieve Bragg waveguide with single resonant dip in the transmission spectrum, which is another approach to avoid such crosstalk. Our group is currently working on optimizing the Bragg waveguide geometry and demonstrating them for practical multichannel sensing applications, and we will report our findings in future publications.

Demonstration of the THz Bragg waveguide for lactose powder sensing and fingerprint detection
In this Section, we demonstrate the Bragg waveguide for on-line monitoring the biolayer thickness changes and explore the repeatability of the sensor, as well as demonstrate it for the fingerprint detection. A powder analyte named α-lactose monohydrate (molecular structure shown in Fig. 3(a)) is chosen as the target analyte, since it has fingerprint in THz region [40]. Such powder is captured on the waveguide inner core surface via the centrifugal force by employing a rotating setup shown in Fig. 3(b-c), which has been detailed in [31]. The Bragg waveguide is hosted in a bearing, which is connected to a motor via a strap. The lactose powder is loaded into the waveguide core by using a home-built feeder which enables onsite capturing of lactose powders when the waveguide is rotating fast, at the same time, guarantee consistent coupling condition. We then characterize the transmission spectra of the Bragg waveguide before and after dispersing the powder analyte onto the waveguide inner core. Minute amount of lactose powder with a mass increment of 0.002g is dispersed into the waveguide core, which is expected to induce a thickness variation of 3µm on the waveguide core by assuming a uniform layer formation during fast rotation based on the waveguide geometry. The transmission spectra of the Bragg waveguide with three different analyte layer thicknesses of the 3µm, 6µm, and 12µm respectively) are characterized. We note that, after each measurement, the waveguide core is purged with nitrogen in order to remove the residual powder analyte and guarantee consistent thickness at same amount of loading. The transmission spectra of the Bragg waveguide sensor before and after introducing the powders onto the waveguide inner surface are presented in Fig. 3(d). A continuous and consistent frequency shift in the resonant dip positions is well observed when increased amount of lactose power is introduced, which projects a spectral sensitivity of 0.145GHz/µm. Repeatability is a key performance when developing sensors for industrial sensing applications. In order to verify the repeatability of our waveguide sensor, at each mount of lactose powers, the measurements are repeated by 4 times. As shown in Fig. 3(d), the Bragg waveguides show a good agreement in the spectral positions of the resonant dips, which suggests a very good repeatability of the Bragg waveguides sensor.

Demonstration of the waveguide for fingerprint detection
Furthermore, terahertz radiation has unique properties which allows fingerprint detection and identification of substance in biomedical research, because many chemicals and molecules shows their characteristic absorption frequencies located in the THz regime resulting from rotation, intra-and inter-molecular vibrational signatures. This technique can be used for many applications including security screening of illicit drugs and explosives, biomedical diagnosis and pharmaceutic industry. In this part, a form of THz absorption spectroscopy, using α-lactose monohydrate powder as the analyte, is shown as a proof-of-principle demonstration of waveguide sensors for fingerprint detection. As shown in Fig. 4, we present the transmission spectrum of a Bragg waveguide when the core is loaded with lactose powders. As a reference, we also plot the reference spectrum of the waveguide with an empty core. The absorption peak at ∼0.53THz is the absorption signature of α-lactose monohydrate in THz range due to intermolecular interactions [40]. The other absorption peak at ∼0.57THz is one of the water lines in THz range [41]. The enhanced confinement and interaction between the waveguide transmission mode and substance filling the waveguide core of means that the waveguide can also be used as a very promising platform for online characterization and identification of substance in a contained, and highly integrated manner. Furthermore, we note that by adjusting the waveguide geometry, one can target specific frequency range of interest, and enrich the sensing scenarios. For example, as proposed in this manuscript, by designing the operation frequency of the sensor near the absorption peak of α-lactose monohydrate (at 0.53THz), one can simultaneously monitor the layer thickness and the lactose concentration in the powders using the anti-crossing frequency and the absorption peak strength, respectively. To our knowledge, this multiparameter sensing modality has never been reported before, and it is beneficial for the design of the versatile highly integrated sensors that offer a comprehensive multiparameter material characterization by a single device and a single pulse. Fig. 4. Experimental transmission spectrum characterization of the Bragg waveguide before and after manually filling lactose powders in the waveguide core. The spectrum is characterized with a TDS setup.

Advantages of the Bragg waveguide sensor
In this Section, we would like to summarize several distinct advantages of the proposed waveguide sensors. First, the developed waveguide sensor is based on resonant phenomenon between the coreguided and defect modes localized in the defect layer, therefore, it is more advantageous and robust than traditional free-space-transmission-mode spectroscopy for layer thickness measurement, which records the phase variations in the THz waves passing through a thin film. Second, in our method, the relatively broad transmission window of the Bragg waveguides is modified by spectral narrow loss peaks, which enables resolving minute spectral shift caused by small changes in the defect layer thickness of refractive index. Third, we demonstrate the capability for multichannel sensing simultaneously and independently by employing a relatively long waveguide, which incorporates several sections of Bragg waveguides with different defect layer thicknesses and different resonant dip positions in the transmission spectra. Each section can be biologically or chemically functionalized to selectively detect specific analytes. By properly designing of the Bragg waveguides, one can fine tune the number and position of resonant dips and the position in order to avoid crosstalk. By tracking each independent resonant dip in the overall transmission spectrum of the long waveguide, one can thereby monitor changes in the thickness or quantity of different analytes by exploiting a single-cycle terahertz pulse. In applications when high sensitivity and resolution are required, one can pursue to a CW THz setup capable of ∼10MHz spectral resolution [35], which is potential to revolve sub-100nm thickness variation on the waveguide inner surface. Finally, the demonstrated waveguides offers a flexible platform for the delivery of analytes (e.g. liquids, powders, gases), at the same time, achieves considerable model overlap between the waveguide modes and the test analyte. Again, to our knowledge, this multi-channel sensing modality has never been reported before, and it is beneficial for the design of versatile, and highly integrated sensors, which enables a comprehensive material characterization by a single device and a single shot of the THz pulse. Such THz porous waveguide sensors can be conveniently fabricated using 3D printing technologies. 3D printing technologies enable the fabrication of waveguides with significantly complex transverse profiles, which means that this method could have a considerable impact on the developments of practical terahertz waveguides and enrich their application scenarios in numerous industrial fields.

Spectral tailoring capability of the Bragg waveguide sensor
Additionally, we would like to highlight the flexibility of tailoring the spectral features of the THz waveguides by properly designing their geometric parameters. In what follows, we indicate three possible independent "knobs" (the location of the defect, the size of the defect, and the overall scaling of the structure) that can be used to tailor the spectral properties of the waveguide in intuitively predictable ways. The first knob is the depth of the defect within the Bragg reflector, which controls the interaction strength of the core-guided mode and the defect mode. According to the coupled-mode theory [38], the magnitude of the frequency range over which the modal interaction takes place depends on the strength of the interaction between the core-guided mode and the defect mode (or in other words the degree of overlap between the fields of the two modes). In this work, we have demonstrated the waveguide for resonant surface sensing when the defect layer is located in the first layer of the Bragg reflector. In this case, the defect modes have relatively strong interactions with the core-guided mode. In fact, when the interaction is weaker, which will be the case if the defect is located further from the waveguide core, the frequency range over which the avoided crossing occurs will be narrower, resulting in even sharper loss peaks in the waveguide transmission spectrum. This is highly attractive for resonant sensing applications if the target analytes could be loaded in the vicinity of the defect layer.
The second knob is the structure of the defect, and in particular the size of the defect layer, which controls the anti-crossing frequency between the core-guided mode and the defect modes. One can shift the frequency of modal interaction up or down by decreasing or increasing the size of the defect, respectively.
A third knob is the overall scaling of the waveguide structure. By changing the periodicity or, equivalently, the individual layer in the Bragg reflector, one can perform sensing at selectable wavelengths. We note that although the materials of the cladding may be highly lossy at these wavelength regions, these properties can be suppressed by many orders of magnitude for the core-guided modes, which have almost all of their fields within the hollow core. This knob is particularly useful when designing waveguide for the detection target analytes, which have absorption signatures over certain frequency regions.

Spectral resolution of TDS THz spectroscopy and CW spectroscopy
The desirable characteristic in spectroscopy is high spectral resolution, which is critical for observing resonances with narrow line widths. In TDS, the THz spectrum is calculated by numerical Fourier transformation of the measured temporal waveform. From the Fourier theory, the spectral resolution of a TDS system is determined from the span of the time delay sweep, and is given by c/2L, where L is the physical length of the mechanical delay line. A higher spectral resolution can be obtained by extending the temporal window, which corresponds to the scanning distance. In a noise-free system with an unlimited delay line, the resolution would be limited by the pulse repetition rate of the pump laser. The longest duration that can be sampled is equal to the time between the two consecutive pulses. However, in the presence of a noise, the achievable frequency resolution is much poorer and is determined by the signal-to-noise ratio (SNR) of the system in time domain. This is because as the signal amplitude diminishes with an increased delay from the main pulse, the SNR approaches unity. From a certain point onwards, scanning to longer delay spans gives no further data. Therefore, the usable delay span is limited by the SNR of the system. In practice, it is advisable to limit the scan length to the region where the SNR is higher than 2.
On some occasions, it is common practice to increase the frequency resolution of a TDS measurement by zero-padding [36,37]. This is accomplished by extending the time-domain data set with a string of zeros. Zero-padding uses the information contained in the existing time span and interpolate additional frequency data points, which trace out the spectra with greater resolution. In fact, the additional supplementary data points carry no additional information, but rather interpolate the existing information. When the measured spectrum lacks narrow-resonant features, this technique works well and produces spectra that are negligibly different from high-resolutions ones. However, when the spectra of interest feature narrow-resonant features such as the sharp transmission dips, the zero-padded spectrum does not entirely succeed in reproducing the detailed long-scan spectrum, because that narrow spectral features require extended time data in order to be determined accurately. To explicitly illustrate the effects of zero-padding, in Fig. 5, we plot the spectrum of a Bragg waveguide with two sharp transmission dips obtained with high resolution and low resolution, as well as that with zero-padding. It is well observed that for the region with broad spectral features (e.g., 0.2THz-0.4THz), the zero-padding technique with interpolated data points has refined the spectral profile. However, the zero-padded spectrum fails to reproduce the two sharp dips as shown in the detailed long-scan spectrum.  5. Spectral characterization of a Bragg waveguide (with a defect of 300µm). The measurements are conducted with a 50mm scan with 3 GHz resolution, a 12.5 mm scan with 12 GHz resolution, a 12.5mm scan with zero-padding to 50 mm with a nominal resolution of 3 GHz.
In contrast, in a continuous wave (CW) spectroscopy setup, the frequency resolution is determined by the quality of the laser beat. Therefore, it is dependent on the frequency stability and linewidth of the lasers sources. In such systems, distributed feedback (DFB) lasers, which feature a grating structure within the active region of the semiconductor, are frequently used to restrict the emission spectrum to a single longitudinal mode. In general, a typical CW system can achieve a frequency resolution on the 10MHz range. This is of great significance when precise detection of small volume of target analytes is required.

Summary
In this paper, a THz photonic Bragg waveguide platform has been demonstrated for multichannel resonant sensing applications using both numerical analysis and experimental characterization. The waveguide operates in the effectively single mode regime and features a spectral narrow loss peak (or transmission dip), which has enhanced resolution and detection of limit. The capability of the waveguide platform for multichannel resonant sensing applications has also been investigated. Additionally, the waveguide platform is demonstrated for online monitoring the thickness variation of lactose powder dispersed onto the waveguide inner surface. A form of fingerprint detection of powder analyte is also demonstrated. Finally, we discussed the potential applications of the demonstrated waveguide sensor and point out some future directions. The results of our study confirm strong potential of the 3D printed photonic Bragg waveguides in various branches of THz science and technology, for which high resolution and multichannel sensing capabilities are required.

Funding
National Natural Science Foundation of China (11904135).