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Abstract
Research on terahertz (THz) spectrum is encountering an enormous booming due to its inherent and promising applications. In recent years, an utmost interest shown by the researchers towards a hollow-core anti-resonant fiber (HC-ARF) based THz bio-sensor because of its sublime sensing performance. In this paper, Zeonex based five-circular cladding tube hollow-core node-less negative-curvature fiber (HC-NNCF) has been proposed for sensing of chemical specimens in THz frequency range. By filling the proposed HC-NNCF sensor with targeted specimens of different refractive indices such as water (n = 1.330), ethanol (n = 1.354), and benzene (n = 1.366), the sensing characteristics of the sensor are numerically investigated using full vectorial finite-element-method (FEM) based COMSOL software. The simulation results show that the proposed HC-NNCF sensor exhibits a total propagation loss magnitude of 10−01 dB/m and a sensitivity response of 98.90%, 99.04%, and 98.90% for water, ethanol, and benzene, respectively, at 1 THz operating frequency. The practical implementation of this propose HC-NNCF sensor is feasible by the existing fabrication methodology. Consequently, the proposed terahertz sensor can be a promising candidate in food, biomedical, and industrial chemical research for opto-fluidic sensing applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) spectrum consists of a band of frequencies ranging from 0.1 THz to 10 THz or 0.03 mm to 3 mm in terms of wavelength has attracted significant interest in recent years. Basically, THz spectrum ties the discontinuity between microwave band and infra-red band bearing the characteristics of both in the electromagnetic frequency spectrum also being the switching region between photonics and electronics. Such radiation has numerous inherent and promising applications boosting from the conventional fields of time domain spectroscopy [1] to the advanced dynamic fields including imaging [2], medicine [3], sensing [4], security surveillance [5], terahertz communications [6,7], drug testing [8], military works [9]. Moreover, THz radiation possesses an alluring non-ionizing characteristic on organic cells and specimens and not harmful to human health which provides a greater advantage over X-ray. Consequently, in these areas THz based sensor have attained notable advancement in biotechnology [10], medical and clinical diagnostic such as analysis of RNA, DNA, and proteins [11–13], breast cancer [14], colon cancer [15,16], skin cancer [17], and tumor detection [18].
Over the past few years, porous core photonic crystal fiber (PC-PCF) operating at THz regime have drawn much interest by the researchers because of its notable and promising characteristics in opto-fluidic sensing applications [19–22]. It has a periodical arrangement of micro-structured air holes in the center defected core surrounded by cladding region throughout the whole length of the fiber. In a PC-PCF, the periodic cladding structure form a photonic bandgap (PBG) that strongly encloses light in the low RI core region and when the core holes are filled with analytes like gases or chemicals, it provides powerful light-analytes interaction thus making it a promising candidate for sensing applications. Moreover, PCFs offers tunable high birefringence, single mode propagation, flattened dispersion, low effective material loss (EML) by varying geometrical parameters such as core diameter, pitch or shape of air holes etc. Due to these lucrative characteristics, PCFs have been used to build up different types of sensors e.g. temperature sensor [23], bio-sensor [24], pressure sensor [25], salinity sensor [26], voltage sensor [27], gas sensor [28], chemical sensor [19], and refractive index sensor [29,30]. In the fields of PC-PCFs based chemical sensing, a remarkable development has been observed for better detection of chemicals analytes by the researchers all over the world. In 2016 Arif et al. [19] proposed a hexagonal photonic crystal fiber with relative sensitivity of 59.07%, and 55.83% for benzene and ethanol, respectively. Later in 2018, Sultana et al. [20] proposed another modified hexagonal lattice PCF with elliptical shape core region and achieved sensitivity of 68.87% for ethanol operating at 1 THz. In the same year, paul et al. [21] reported a micro-structured quasi-PCF with a relatively higher sensitivity of 78.8%, 77.8% and 69.7% for ethanol, benzene and water, respectively, operating at 1.3 THz. Islam et al. [22] came up with a PC-PCF having rectangular core and kagome cladding and attained sensitivity of 85.6%, 85.75%, and 85.9% for water, ethanol, and benzene, respectively, at 1.6 THz. At the same time, Islam et al. [31] proposed another asymmetrical hollow-core PCF with a comparatively higher sensitivity of 96.69%, 96.97% and 97.2% for water, ethanol, and benzene, respectively, at 1.4 THz operating frequency. After in 2019, Sen et al. [32] suggested a rotated hexa-core PCF for chemical sensing and achieved sensitivity of 76.44%, 77.16% and 73.20% for ethanol, benzene, and water, respectively, at 1 THz.
Despite all these developments and advantages of using PCFs based sensors [33], it faces several limitations in practical implementation such as its micron-scale hole size makes analyte filling process time consuming mostly for viscous liquids, fabrication difficulties of kagome lattice with strong power overlap, and high group-velocity dispersion. On the other hand, although, Bragg waveguides exhibit better sensing performance [34,35], have relatively narrow working bandwidth.
As a consequence to mitigate the limitations of PCFs, here comes another fiber which is called hollow-core fiber (HCF).Though, this kind of photonic crystal fibers still have narrower transmission bandwidth than a solid core or PC-PCF [36,37], the main advantages of HCFs are that the larger air core eases liquid infiltration resulting in strong analyte-light interaction, low attenuation, high mode quality, better thermal stability, and low light-dielectric overlap. Based on light guiding principle, HCFs are can be categorized as hollow-core photonic bandgap fiber (HC-PBG) and hollow-core anti-resonant fiber (HC-ARF). In HC-ARFs, the light guiding mechanism is based on anti-resonant reflecting waveguide (ARROW) [38] in which the core modes can radiate and oscillate through the cladding and under anti-resonant condition reflecting from high RI cladding region are confined in the low RI core region in a leaky mode fashion. Based on this guiding mechanism various opto-fluidic sensors have been proposed [39,40]. Though hollow-core anti-resonant fiber (HC-ARF) have a larger core size than PCFs, the optical performance is attenuated by un-engineered core shapes and glass nodes between core defining cladding tubes. To moderate these limitations, very recently node-less (cladding surfaces are non-touching) negative curvature ARFs have been proposed [41,42]. This new kind of hollow-core node-less negative curvature fiber (HC-NNCF) shows outstanding optical performance and has been demonstrated for biochemical sensing [43], nonlinear optics, high power-beam delivery, pulse compression, etc. and could be an auspicious applicant for sensing applications.
In this work, we propose an HC-NNCF sensor for chemical sensing applications in the THz regime. In this proposed sensor, the cladding consists of five circular anti-resonant tubes arranged in node-less configuration. Zeonex has been chosen as the fiber background material because of its improved characteristics at THz regime. The air core of the proposed sensor can be filled by any chosen chemicals and numerically investigated essential sensing parameters such as relative sensitivity, power fraction of core-cladding, effective refractive index, and propagation losses. The practical implementation of this proposed HC-NNCF sensor is feasible by existing fabrication methodology and can be a promising candidate in food, biomedical, and industrial chemical research for opto-fluidic sensing applications in THz technology.
2. Structure, simulation and fabrication methodology
In this paper, we consider a Hollow-core Node-less Negative-curvature Fiber (HC-NNCF) THz fiber for our targeted chemical sensing. Here the term "negative-curvature" depicts that the core defining cladding surfaces that are normal to the core boundary is directed the opposite way from the core [41]. The light guidance mechanism of this propose sensor is based on inhibited-coupling (IC) between the cladding modes and higher-order-core modes by the isotropic anti-resonant elements [44]. This inhibited-coupling mechanized fiber sensor ensures effectively single mode guidance with reduced attenuation, low dielectric overlap, and broad band characteristics [42].
In hollow-core ant-resonant fiber (HC-ARF), when the core modes are phase matched with the cladding modes, higher transmission losses occur at a specific frequency range known as resonant frequency. On the contrary, at anti-resonant frequencies, light is strongly enclosed in the core, leading to lower transmission losses. The anti-resonant frequency of $m_{th}$ order resonance can be calculated as [42]:
where m, c, $n_{mat}$, $n_{air}$ and t indicate the resonance order (integer value), velocity of light in free space, RI of material, RI of Air, and anti-resonant tube thickness, respectively.The geometry of the considered HC-NNCF sensor is shown in Fig. 1. The cladding consists of five circular anti-resonant tubes arranged in node-less configuration. In order to suppress the appearance of unwanted resonance from the reflecting anti-resonant elements, the cladding tubes maintains a constant thickness of t, made from cyclo olefin polymer (COP) commercially known as Zeonex. Zeonex has been chosen as the fiber background material because of its improved characteristics at THz frequency regime including a constant index of refraction of 1.53, lower material absorption coefficient of 0.2 $cm^{-1}$, lower dielectric loss tangent with higher transmittance, excellent optical stability with bio compatibility, higher glass transition temperature, negligible material dispersion over commonly used fiber materials like Silica, PMMA, HDPE, Teflon, etc. [42,45].
Fig. 1. 2D cross sectional view of the proposed HC-NNCF sensor when the fiber is filled with chemical analyte. The fiber has a core diameter Dc = 3 mm, cladding diameter d = 2.1 mm, and cladding tube thickness t = 0.15 mm.
The most common commercially available fiber fabrication techniques that have been used over a prolonged period are stack and draw, drilling, capillary stacking and extrusion, 3D printing [46–49] etc. Recent 3D printing technology eases the way for fabrication of complex asymmetrical structure. Researchers in [50] have fabricated micrometer based simple HC-NNCF using stack and draw method. Lately complex nested and co-joined HC-NNCF [41,51] structure also been able to fabricate using the stack and draw method. Thus, using the existing stack and draw methodology, this proposed HC-NNCF sensor can be fabricated.
Here, we used full vectorial finite-element-method (FEM) based COMSOL software available for analyzing the characteristics of photonic devices to investigate the sensing properties of the proposed HC-NNCF sensor. The gross mesh area $5.534 \times 10^{-05}$ $m^{2}$ consisted of 3334 triangular elements, where 667 and 56, respectively, were the edge and vertex elements. A perfectly matched layer (PML) absorbing boundary condition with a depth of 10% of the total fiber radius is being imposed on the outer periphery of the fiber so that it can act as an anti-reflecting layer and absorbs outgoing waves of the fiber. Three chemicals has been targeted to be sensed and they are water (n = 1.330), ethanol (n = 1.354) and benzene (n = 1.366) [32]. The free space of the fiber can be filled by any chosen chemicals and the desired sensing characteristics can be investigated.
The most ruling type propagation loss that’s affect the optical performance of a THz fiber is the material absorption loss also known as effective material loss (EML). It can be defined as the product of the bulk material loss and fraction of the power in the background material. It mainly depends on the used fiber polymer and physical structure of the sensor and can be measured using the following expression [52]:
In the above expression, $\epsilon _{0}$ is the permittivity and $\mu _{0}$ is the permeability of the free space, n is the Refractive Index (RI), $\alpha _{mat}$ is the material absorption of Topas and $S_{Z}$ is denoted as the Poynting vector in the direction of propagation, which is defined as $S_{Z}=R_{e}(E\times H^{*})z$. Here, E is the electric field component and H is the magnetic field component.
Another propagation loss that’s determines the light-confining ability of a THz fiber called leakage loss or confinement loss (CL). The CL basically depends on the number of rings used in cladding to define the core and sizes, shapes of the core and can be measured by the following expression [42]:
where $k_{0}$ is the free space vector, and defined as $k_{0}=(2\pi f)/c$ and $Im(n_{eff} )$ is the imaginary effective refractive index of analytes. Then the confinement loss is added with effective material loss to calculate total propagation loss or Total Loss. It should be included that we have considered the fundamental mode $(LP_{01})$ for loss calculation. We have found that for $(LP_{01})$ mode the EM field is strongly confined in the core region that leads to the very low confinement loss which is important parameter of chemical sensors. In contrast, for higher order modes, the core mode field easily extended into the gaps between adjacent tubes. However, we avoided all kinds of higher modes $(LP_{11}, LP_{21})$, due to higher confinement loss.First of all, to optimize the geometrical parameter of the proposed sensor, we have investigated the effect of core diameter, Dc and cladding tube diameter, d on total loss when the air core is filled with water. Total loss of the proposed sensor as a function of frequency with the variation of core and cladding diameter is shown in Figs. 2 and 3, respectively. From Fig. 2, it can be observed that an increment in core diameter Dc results decrement on total loss. But a larger core diameter increases overall fiber diameter which further increases critical bend radius [53]. In addition from Fig. 3, it can also be seen that total loss decreases as cladding tube diameter increases. But this time after certain cladding diameter, it results no decrement in total loss as cladding tube diameter increases. Considering all these facts mentioned above we set core diameter, Dc = 3 mm and cladding tube diameter, d = 2.1 mm, where confinement loss (CL) is $7.20 \times 10^{-03}$ dB/m, effective material loss (EML) is $1.14\times 10^{-01}$ dB/m, total loss is $1.21\times 10^{-01}$ dB/m and overall fiber diameter is 8.34 mm. The field distribution of the proposed HC-NNCF sensor for analytes of different refractive indices such as water, ethanol, and benzene are shown in Fig. 4, respectively, maintaining optimal design parameters.
Fig. 2. Total loss of the proposed sensor as a function of frequency with the variation of core diameter. Here, the fiber is filled with water (n = 1.330).
Fig. 3. Total loss of the proposed sensor as a function of frequency with the variation of cladding diameter. Here, the fiber is filled with water (n = 1.330).
Fig. 4. Field distribution of the proposed HC-NNCF sensor when the fiber is filled with (a) water, (b) ethanol and (c) benzene. Here Dc = 3 mm, d = 2.1 mm and cladding tube thickness, t = 0.15 mm.
From the earlier mentioned Eq. (1), it can be seen that, the position of high loss resonant window in hollow-core HC-ARFs mostly depends on tube thickness, t. If the air core of the proposed HC-NNCF sensor is filled with water, then putting $n_{water}$ = 1.33, $n_{zeonex}$ = 1.53, t = 0.15 mm and m = 1 (for first order) in Eq. (1), the resonance frequency can be found at $f_{c}$ = 1.3 THz. Similarly, in case of ethanol and benzene, the resonance frequency can be found at 1.4 THz, and 1.45 THz, respectively. That means theoretically resonant window starts for water, ethanol and benzene from 1.3 THz, 1.4 THz, and 1.45 THz, respectively in frequency band. In resonant regions, core modes are phase matched with the cladding modes, consequently, causes high propagation loss. Here, Fig. 5 illustrates the total propagation loss profile of the proposed HC-NNCF sensor when the air core is filled with water, ethanol, and benzene and the dotted lines indicate the starting edge of resonant windows for respective chemical analytes. From the simulation result presented in Fig. 5, it can be seen that the propagation losses escalate briskly around 1.3 THz, 1.4 THz and 1.45 THz for water, ethanol, and benzene, respectively. Therefore, it can be concluded that the simulation results agree with the theoretical results. However, we have chosen 1 THz as the operating frequency because it is the center frequency of the low loss region (as shown in Fig. 5).
Fig. 5. Total propagation loss of the proposed sensor as a function of frequency when the fiber is filled with targeted analytes of different refractive indices. Here Dc = 3 mm, d = 2.1 mm and cladding tube thickness, t = 0.15 mm.
3. Results and Discussion
The relative sensitivity of a THz fiber based chemical sensor mainly depends on how strongly light interacts with chemical analytes. According to the Beer-Lambert law, the absorption coefficient at a particular frequency can be defined as [19]:
where I(f) and $I_{0}$(f) represent the intensities of light when the fiber is filled with and without desired analyte. And the rest factors r, $\alpha _{mat}$, f, and $l_{c}$ represent the relative sensitivity, bulk material absorption, operating frequency, and channel length, respectively.The absorbance of the chemical analytes to be detected can be measured by [32]:
The relative sensitivity of a THz fiber based sensor can be calculated by [21]:
where $n_{r}$ denotes the RI of the analyte needed to be detected which is 1.33 in case of water, 1.345 in case of ethanol and 1.366 in case of benzene, $n_{eff}$ is the effective refractive index of the guided mode and the rest $P_{c}$ represents the proportion of light interaction with the analyte and that can be calculated by [19]:Since relative sensitivity mostly depends on effective refractive index and core power fraction, therefore these two parameters have been considered first. Figure 6 represents the variation of the effective refractive index of water, ethanol, and benzene as a function of frequency. From Fig. 6, it can be seen that throughout the entire frequency band the effective refractive index of water, ethanol, benzene is being increased steadily with the expansion of frequency.
Fig. 6. Effective refractive index of the proposed sensor as a function of frequency for water, ethanol and benzene with Dc = 3 mm, d = 2.1 mm and tube thickness, t = 0.15 mm.
The core and cladding power fraction for water, ethanol, and benzene are plotted against frequency in Fig. 7. It can be observed that the power fraction increases according to the increment of frequency. But after a certain portion of the frequency band, the core power fraction decreases as the frequency increases. Since core and cladding power fraction are opposite to each other, cladding power fraction shows minimum values in the frequency range of 0.7 to 1 THz and further increment of frequency increases the cladding power fraction.
Fig. 7. Core and cladding power fraction of the proposed sensor as a function of frequency for water, ethanol and benzene with Dc = 3 mm, d = 2.1 mm and tube thickness, t = 0.15 mm.
Figure 8 depicts the variation of sensitivity of water, ethanol, and benzene as a function of frequency. According to the earlier mentioned in Eq. (6), relative sensitivity is proportional to the RI of the analyte and core power fraction and inversely proportional to the effective refractive index. The higher RI of analytes trends to create much more analyte-light interaction, which results higher sensitivity. That’s why the sensitivity of benzene exhibits higher sensitivity response compared to the other analytes. Since effective refractive index increases throughout the entire frequency range and core power fraction decreases after a certain portion of the frequency band, relative sensitivity decreases. Here, the proposed HC-NNCF sensor shows a sensitivity response of 98.90%, 99.04%, and 98.90% for water, ethanol, and benzene, respectively, at 1 THz operating frequency. Moreover, this proposed HC-NNCF sensor demonstrates a frequency response of over 98% for all the targeted analytes in the frequency range of 0.7 to 1.1 THz, as shown in shade gray region.
Fig. 8. Relative sensitivity of the proposed sensor as a function of frequency for water, ethanol and benzene with Dc = 3 mm, d = 2.1 mm and tube thickness, t = 0.15 mm.
The consequences of varying cladding tube thickness on the sensitivity of the proposed fiber is being considered in Fig. 9 for water, ethanol, and benzene, respectively. It can be observed that incresement of tube thickness results lower sensitivity. On the contrary, reduction in tube thickness results higher sensitivity. This occurs due to higher light absorption by the thicker cladding tube material. In order to maintain a balance among sensor parameters and considering fabrication feasibility with sensor rigidity, t = 0.15 mm has been chosen as the optimal tube thickness for the proposed HC-NNCF sensor. Under these circumstances, this proposed sensor achieved a sensitivity response of 98.90%, 99.04%, and 98.90% for water, ethanol, and benzene, respectively, at 1 THz operating frequency.
Fig. 9. Relative sensitivity and total loss with the variation of cladding tube thickness for (a) water, (b) ethanol and (c) benzene as a function of frequency with with Dc = 3 mm, d = 2.1 mm and tube thickness, t = 0.15 mm.
Fig. 10 depicts the effect of hollow cladding tubes on fiber performance. Overall, the sensing performance improves with the decreasing of cladding tube diameter. At 1 THz frequency, the relative sensitivity is achieved of 99.21%, 99.08%, 98.90%, and 98.67% for cladding tube diameter of 1.7 mm, 1.9 mm, 2.1 mm, and 2.3 mm, respectively, when the fiber is filled with Water. However, we have chosen the cladding tube diameter of 2.1 mm, as the smaller tube increases chemical infiltration difficulty.
Fig. 10. Relative sensitivity of the proposed sensor as a function of frequency with the variation of cladding diameter. Here, the fiber is filled with water (n = 1.330).
A comparison has drawn in Table 1 in terms of fiber material, operating point, sensor structure, and relative sensitivity response of the proposed HC-NNCF sensor with the prior chemical sensors. Considering sensing performance and fabrication feasibility this proposed HC-NNCF chemical sensor well in advance of others.
Table 1. Comparision of the proposed HC-NNCF sensor with other prior chemical sensor.
4. Conclusion
In conclusion, a hollow-core node-less negative-curvature fiber (HC-NNCF) chemical sensor has been demonstrated for its sensing application in THz regime. Using Zeonex as the fiber background material, the optical properties of the proposed HC-NNCF sensor have been investigated over a wide THz regime ranging from 0.5 to 1.6 THz aiming to achieve higher relative sensitivity with lower propagation losses. This proposed sensor has able to achieve a total propagation loss magnitude of $10^{-01}$ dB/m and a sensitivity response of 98.90%, 99.04%, and 98.90% for water, ethanol, and benzene, respectively, at 1 THz operating frequency. The practical implementation of this proposed HC-NNCF sensor is feasible by the existing fabrication methodology. With such notable sensing properties, this proposed HC-NNCF based sensor opens a new track for terahertz sensor and can be a promising candidate in food, biomedical and industrial chemical research for sensing applications.
Disclosures
The authors declare no conflicts of interest.
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