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Abstract
An on-chip Mach-Zehnder interferometer (MZI) hydrogen sensor, applying a double-slot hybrid plasmonic (DSHP) waveguide composed of a Si waveguide and two Pd disks on both sides as the sensing arm, is designed. The optical confinement factor of the sensing area can be up to 87%. For the MZI hydrogen sensor with a DSHP waveguide of 14 µm, the sensitivity can be as high as 11.935 nm/%, corresponding to a free spectral range (FSR) of 15 nm. Furthermore, the sensor sensitivity is influenced by the MZI structure parameters, which is highly adjustable. The extinction ratio of the interference spectra can reach over 30 dB. A feasible solution is provided in this paper for highly sensitive hydrogen detection.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Hydrogen (H2), as a new type of clean energy, poses a risk of leakage, combustion and explosion during its preparation, storage and use, as a result of its small molecular weight, low ignition energy (0.02 mJ) [1] and lower explosion limit (4%) [2]. It is of great significance to develop hydrogen sensors with high sensitivity and the ability to detect concentrations below the lower explosion limit. Currently proposed hydrogen sensors are including catalytic [3–5], semiconductor [6–9], electrochemical [10,11], mechanical [12–14], thermally conductive [15–17], optical [18–28] and other major types. Compared with other sensors, optical hydrogen sensors have the advantages of small size, strong anti-electromagnetic interference and high reliability. Integrated optical hydrogen sensors own the advantages of optical sensors, while being highly compact and compatible with silicon-on-insulator (SOI) platforms. Utilizing the complementary metal-oxide-semiconductor (CMOS) manufacturing technology enables mass production. Reported integrated optical hydrogen sensors use straight waveguides [26–28], microring resonators [18,19,21–24] and microdisk resonators [20] as sensing elements. Optical waveguide sensors based on Mach-Zehnder interferometers (MZI) have extremely high sensitivity, wide dynamic range and mechanical stability. Its sensitivity is determined by both the waveguide sensitivity and structure parameters, resulting in higher flexibility. However, the hydrogen sensor based on a MZI waveguide has not been reported.
The hybrid plasmonic (HP) waveguide with integrated photonics and plasmonic modes on chip can be applied for temperature [29], liquid concentration [29–32] and gas [21,33] detection, chemical analysis [34,35], electro-optic modulation [30,31] and other aspects. A single-slot hybrid microring resonator applied to hydrogen sensing has been reported [21]. Utilizing the expansion of Pd to bring about changes in the whispering gallery modes (WGM) achieves hydrogen sensing with a sensitivity as high as 11.038 nm/%. The hydrogen sensors using double-slot hybrid plasmonic (DSHP) waveguides for sensing have not yet been reported. The DSHP waveguide supports the polarization mode of TE, and simultaneously has high refractive index contrast and plasmonic enhancement, which can limit the mode to low refractive index slots with ultra-high optical confinement factors and transmit with lower propagation losses [31]. The hydrogen sensor based on Pd-coated SU-8 polymer microresonator, which utilizes lattice expansion of Pd disk after the reaction between Pd and H2, has been experimentally verified [20]. As a hydrogen sensitive material, Pd undergoes volume expansion in the presence of H2 [36]. SU-8 elastic polymer, as a material of the microdisk, can better transfer the changes in Pd disk expansion to the microdisk. The SU-8 polymer is also used as the material of substrates and sensing elements [37] for optofluidic refractive index sensors.
In this paper, we present an asymmetric MZI hydrogen sensor based on DSHP waveguide. In the DSHP waveguide, two open nanogrooves are formed by a high refractive index silicon waveguide and two Pd metal disks on both sides. By adjusting and optimizing the optical confinement factors in the slots, the light-matter interactions in the low refractive index area is enhanced, and the sensitivity of the sensor is improved. In the designed MZI, the sensing arm employs a DSHP waveguide as the sensing element, which supports quasi-TE polarization mode and is compatible with the production process of SOI platform. By utilizing the expansion changes of Pd disks on both sides of the Si waveguide after reacting with hydrogen, the effective refractive index of the hybrid plasmonic waveguide mode is changed, resulting in interference spectrum shift and achieving highly sensitive hydrogen detection. By coating a layer of SU-8 elastic material on SiO2 as the substrate, the effect of Pd disk deformation is better transferred to the DSHP waveguide. In order to better analyze the characteristics of the proposed MZI hydrogen sensor, the finite-difference time-domain (FDTD) solution is adopted for simulation to compare the performance of the sensors under different design parameters.
2. Theory and design scheme
2.1 Design principle
The DSHP waveguide structure composed of a Si waveguide and two Pd disks on both sides is shown in Fig. 1(a). On the substrate composed of SiO2 and SU-8 layers, two low refractive index slots are formed between silicon waveguides and Pd disks, supporting hybrid modes between photonics modes (Si waveguide) and plasmonic modes (Pd disk). Further extending the evanescent field from the waveguide to the environment can enhance the light-matter interactions, resulting in a narrower Si ridge in the DSHP waveguide. The Si tapers on both sides are used to couple the bus waveguide (SOI waveguide) and the sensing area of the DSHP waveguide, and the Pd tapers are used to convert the guided modes from photonics modes to hybrid plasmonic modes, reducing the coupling and propagation losses of power.
Fig. 1. 3D schematic diagram of sensing area. (a) Coupling between the DSHP waveguide and SOI waveguide. (b) Cross section view. The widths of Si waveguide and slot are WSi and Wslot respectively, and the heights of Pd disk and Si waveguide are both HWG = 300 nm (see Fig. S1 of Supplement 1). The surrounding environmental medium is H2.
Figure 1(b) is a cross-sectional view of the DSHP waveguide. A layer of SU-8 elastic material deposited on the SiO2 substrate reduces the shear forces between the Pd disk and the substrate, which is beneficial to transfer the expansion deformation of Pd [20]. The gas to be measured covers the waveguides. Si waveguides and Pd disks are both HWG in height, separated by low refractive index nanogrooves. The widths of the silicon waveguides and slots are WSi and Wslot respectively. The Pd disk utilizes plasmonic technology to confine light energy in nanogrooves. The stronger the light field in the slot, the more intense the interaction between light and matter in the area, and the more sensitive the perception of the external environment. Optimizing the intensity of light-matter interactions requires optimization of the optical confinement factors (Γ) in special regions. Γ is represented by the ratio of the power confined in a specific region to the total power [30], defined as
An MZI hydrogen sensor is constructed using a DSHP waveguide composed of Si waveguide and Pd disks as the sensing arm. The overall structure is shown in Fig. 2(a). The device uses a tunable continuous wave laser. The beam passes through a polarization controller, ultimately, TE polarization light is coupled into the waveguide through a grating coupler. Due to the coupling and transmission losses introduced by the DSHP waveguide, MZI uses an asymmetric Y-splitter to control the splitting ratio of the sensing arm and reference arm, thereby improving the extinction ratio of the interference spectrum. The Y-splitter consists of straight waveguides and curved waveguides with a bending radius of Rref, connecting the input and output terminals, respectively. The reference arm has a width of 400 nm, consists of a total of four curved waveguides with a radius of Rref and three straight waveguides with a length of LRef = 2πRref + LR1 + LR2 + LR3. Figure 2(b) shows a locally enlarged view of the sensing area. The bus waveguide with a width of 400 nm is coupled into the DSHP waveguide through the Si taper. The input and output straight waveguide lengths Lin and Loutput are both equal to 10 µm. The length of Si taper is Ltaper = 3 µm, the length range of Pd taper is Lridge = 3-7 µm, and the length range of DSHP waveguide is LDSHP = 6-14 µm. The total length of the sensing arm is Lsen = 2Lin + 2Ltaper + 2Lridge + LDSHP. As a result of the change in the effective refractive index of the DSHP waveguide during the sensing process, the phase change $\Delta \phi $, depending on the change in the optical path difference (OPD), is expressed as
Fig. 2. Characterization device and structure diagram of the MZI hydrogen sensor. (a) Asymmetric MZI structure. (b) Sensing area. The overall power is split by an asymmetric Y-splitter, and the sensing area includes Si tapers, Pd tapers and DSHP waveguide.
The free spectral range (FSR) of MZI can be calculated by the following equation:
The hydrogen sensor designed in this paper utilizes the expansion effect caused by the reaction between Pd and H2 to change the effective refractive index of the DSHP waveguide, leading to phase change and thus the wavelength shift. The sensitivity (S) of the sensor, which is the variation in wavelength shift relative to the H2 concentration, can be given by
2.2 Sensing material
The hydrogen absorption and release of Pd is a reversible process [40], represented by the following chemical equation:
where x represents the hydrogen concentration in Pd (H/Pd). $\textrm{PdH}x$ is in different phases as the lattice expands during hydrogen absorption process. The $\textrm{PdH}x$ systems typically undergo an irreversible phase transition when the H2 concentration ($C_{hyd}$) exceeds 1% [22]. For 1% H2 concentration, 0.087% lattice expansion occurs in Pd, and the expansion is reversible. $\textrm{PdH}x$ is in the α phase [36]. The $C_{hyd}$ of each hydrogen sensors studied in this paper is between 0% and 1%.The Pd material is described by Lorentz-Drude Model [41] and the calculated refractive index distribution of Pd material is shown in Fig. S2 (see Supplement 1 for supporting information). The refractive index data experimentally measured by Palik is adopted for Si and SiO2 materials [42]. The refractive index of the SU-8 is 1.57 [37].
3. Results and discussion
3.1 Structure optimization
The DSHP waveguides establish two low refractive index slots between the Pd disks and the Si waveguide. Compared with traditional all-dielectric groove waveguides, DSHP waveguides have the advantages of both subwavelength confinement and preventing lateral leakage of evanescent fields. The plasma effect between the metal Pd disks on both sides is used to confine more optical fields in the induction slots, and also enhances the optical confinement of the covering medium area (slot and top covering area) to improve sensor sensitivity. In order to investigate the influence of Si waveguide width, the mode field distribution of the DSHP waveguide is analyzed with a fixed slot width (Wslot) of 20 nm at Si waveguide widths (WSi) of 100 nm, 200 nm, 300 nm and 400 nm, as shown in Fig. 3(a)–(d). The Si ridge corresponding to WSi = 400 nm in the DSHP waveguide confines more optical fields than other small width Si waveguide. When WSi decreases, the optical field extends into the environment, reducing the confinement of photonic modes in Si waveguides and increasing the optical confinement in the slots. When WSi decreases to 200 nm, due to the diffraction limit, there are almost no photonic modes in the Si waveguide, and most of the optical fields are transformed into evanescent fields that extend into the external environment. From Fig. 3(e)-(h), corresponding to the electric field distribution functions on the transverse centerline of the DSHP waveguides in Fig. 3(a)-(d), it can also be seen that the narrower the Si waveguide, the higher the enhancement of the optical field in the slot area, and the more sensitive it is to the external changes.
Fig. 3. Mode field distributions of the DSHP waveguides and normalized field distribution functions |Ex| on the transverse centerlines: (a)-(d) show the mode field distributions at WSi of 100 nm, 200 nm, 300 nm and 400 nm, respectively; (e)-(h) separately correspond to curves of the |Ex| on the transverse centerlines of the DSHP waveguides in cases (a)-(d). The slot widths are all 20 nm.
For a DSHP waveguide with a certain Si ridge, selecting an appropriate slot width to enhance the plasmonic confinement between the Pd disks and the Si waveguide can achieve highly sensitive sensing. To study the influence of slot width in DSHP waveguides, considering the waveguide structure supporting the transmission of TE fundamental mode, WSi is fixed at 100 nm, 200 nm, 300 nm and 400 nm, while Wslot is increased from 20 nm to 60 nm. A more detailed study on how the widths of Si waveguides and slots affect the mode conversion behavior of DSHP waveguides is shown in Fig. S3 (see Supplement 1). The variations of the mode effective refractive index (neff), loss (Loss) and optical confinement of the covering H2 area, slot region and Si waveguide ($\varGamma_{H_2}$, $\varGamma_{slot}$ and $\varGamma_{Si}$) of DSHP waveguides with different Si ridges and slots are studied as shown in Fig. 4.
Fig. 4. Performance parameters of DSHP waveguides with Si waveguide and slots of different widths. (a) Variation of effective refractive index (neff) with slot width (Wslot). (b) Relationship between loss and Wslot, the loss unit is dB/µm. (c)-(e) Change of optical confinement factors for H2 coverage area, slot area and Si waveguide ($\varGamma_{H_2}$, $\varGamma_{slot}$ and $\varGamma_{Si}$) respectively with Wslot.
Figure 4(a) shows that neff decreases with the increase of Wslot for DSHP waveguides at different Si ridges. The neff of the DSHP waveguide with smaller Si ridge width is also smaller due to the high refractive index of Si waveguide. As Wslot gradually increases, the neff of the DSHP waveguide gradually tends to the SOI waveguide due to the reduced influence of plasma. The larger neff of the DSHP waveguide with narrow slots indicates that the DSHP waveguide has greater optical confinement compared to traditional SOI waveguide. But DSHP waveguides also bring greater propagation loss, as shown in Fig. 4(b). When WSi = 100 nm and Wslot = 20 nm, the corresponding maximum loss is 4.28 dB/µm. When WSi = 400 nm and Wslot = 60 nm, the minimum propagation loss is 0.18 dB/µm. In the case of DSHP waveguides with the same Si ridge, the larger the Wslot, the smaller the loss. Meanwhile, due to the photonic mode confinement of Si waveguides, the larger the Si ridge, the weaker the confinement of H2 coverage area, the less the absorption of the optical field by Pd, and the smaller the propagation loss. Therefore, considering the propagation loss in applications, the selection of DSHP waveguide parameters requires a trade-off between optical confinement factors and losses.
Figures 4(c)-(e) show the changes of $\varGamma_{H_2}$, $\varGamma_{slot}$ and $\varGamma_{Si}$ with Wslot. The smaller the WSi, the larger the $\varGamma_{H_2}$ and $\varGamma_{slot}$ values of the DSHP waveguide. Analogous to the narrower the Si waveguide in the SOI waveguide, the weaker the Si waveguide ability to limit the optical field, and the more the optical field is confined to the external environment. However, from Fig. 4(c) and (d), when WSi changes from 100 nm to 300 nm, the trend of $\varGamma_{H_2}$ and $\varGamma_{slot}$ with Wslot shows that the DSHP waveguide with WSi = 200 nm has the $\varGamma_{H_2}$ and $\varGamma_{slot}$ greater than DSHP waveguide with WSi = 100 nm since Wslot is larger than 35 nm and the DSHP waveguide with WSi = 300 nm has larger $\varGamma_{H_2}$ and $\varGamma_{slot}$ than DSHP waveguide with WSi = 100 nm corresponding to Wslot > 58 nm. This indicates that the variation trend of optical confinement factor is not only influenced by photonic modes, but also the plasmonic modes. In the case of WSi = 100 nm and Wslot = 20 nm, $\varGamma_{H_2}$ and $\varGamma_{slot}$ can reach up to 87.33% and 83.99%, respectively. For DSHP waveguides with different WSi and Wslot, $\varGamma_{slot}$ is about 4% lower than $\varGamma_{H_2}$, indicating that most of the optical field in the H2 environment is confined to the slot. Optimizing the optical confinement factor of the slot and external area directly affects the waveguide sensitivity.
For DSHP waveguides with different WSi, as Wslot decreases, plasmonic confinement enhances, $\varGamma_{H_2}$ and $\varGamma_{slot}$ increase. When WSi is equal to 300 nm or 400 nm, the influence of Pd decreases with the increase of Wslot, the confinement of the slot weakens, and $\varGamma_{Si}$ increases, as shown in Fig. 4(e). Diffraction limit is reached when WSi is less than 200 nm, few photonic modes are supported in the Si waveguide, $\varGamma_{Si}$ is very small. At this time, the plasmonic mode dominates in the DSHP propagation modes and the DSHP waveguide is approximated to the plasmonic slit waveguide.
Furthermore, due to the hybrid propagation modes of photonic and plasmonic modes in the DSHP waveguide, propagation loss in the DSHP waveguide is also between the SOI waveguide and plasmonic waveguide. As the Si ridge width increases, the proportion of photonic modes increases and the loss decreases, but at the same time, $\varGamma_{H_2}$ and $\varGamma_{slot}$ in the external environment decrease. To balance the optical confinement factor and propagation loss, the MZI hydrogen sensor in this paper adopts the DSHP waveguide structure with WSi = 300 nm and Wslot = 20 nm, reaching 75.29% for $\varGamma_{H_2}$ and 71.84% for $\varGamma_{slot}$. The fabrication tolerance for this slot width is about ± 5 nm (see Fig. S4 of Supplement 1).
In order to compensate the propagation and coupling losses introduced by the DSHP waveguide, an asymmetric Y-branch composed of straight waveguides and curved waveguides is designed as a beam splitter. Multiple power distributions can be provided by controlling the curvature radius of the curved waveguides in the Y-splitter. For LDSHP of 6-14 µm, different curvature radii are selected to provide optimized power allocations, as shown in Fig. 5.
Fig. 5. Spectral requirements for different lengths of DSHP waveguides: (a) power distribution, and (b) variation of Rref with LDSHP.
The splitting requirements of the reference and sensing arms depend on the propagation and coupling losses of different LDSHP. When LDSHP is 6, 8, 10, 12 and 14 µm, the corresponding mode losses are 5.82, 7.84, 9.17, 10.29 and 11.99 dB, respectively. The input power of the two arms is distributed differently to balance the output power. For the MZI hydrogen sensors with 6, 8, 10, 12 and 14 µm long DSHP waveguide, the input power ratio for sensing and reference arms, represented by Pin-Sen and Pin-Ref, are 0.603, 0.619, 0.652, 0.690, 0.698 and 0.397, 0.348, 0.381, 0.310, 0.302, indicated by black and red lines respectively, as shown in Fig. 5(a). When LDSHP increases, the required Pin-Sen increases and Pin-Ref decreases to compensate for the loss of the DSHP waveguide. This requires regulation of Rref. Larger LDSHP requires smaller Rref to increase the power distribution of the sensing arm, as shown in Fig. 5(b). For 6, 8, 10, 12 and 14 µm long DSHP waveguide, the values of corresponding Rref are respectively 1.625, 1.125, 0.875, 0.575 and 0.5 µm to achieve the different splitting ratios.
3.2 Performance analysis
An important parameter of the MZI sensor is the free spectral range (FSR), which refers to the frequency interval between adjacent interference peaks and determines the detection range of the spectrometer when measuring wavelength shift. From Eq. (3), it can be seen that FSR is related to the lengths of reference and sensing arms, denoted as LRef and Lsen. For different LDSHP, regulating LRef can achieve the regulation of FSR while LDSHP remains unchanged, as shown in Fig. 6. It can be seen that for sensors with fixed LDSHP, a smaller FSR requires a larger LRef.
Fig. 6. Relationship between FSR and LRef under different LDSHP conditions. The black dashed lines represent the LRef values corresponding to fixed LDSHP with FSR of 15 nm and 10 nm, respectively.
The MZI sensors with different LDSHP correspond to different Rref in order to achieve the best light splitting effect. Therefore, the adjustment of LRef only requires controlling the length of the straight waveguide, such as LR1, LR2 and LR3. For the FSR of 15 nm and 10 nm respectively, sensors with the different LDSHP (10, 12 and 14 µm) correspond to different values of the reference arm (LRef = 2πRref + LR1 + LR2 + LR3). The values of various parts are shown in Table S1. And the available fabrication processes, such as e-beam lithography (EBL), inductively coupled plasma (ICP) dry etching, and deep reactive ion beam etching (DRIE), are demonstrated in Fig. S5 (see Supplement 1).
The lattice expansion after the reaction between Pd and H2 (1% H2 corresponds to 0.087% expansion) is utilized by the sensor, and the Pd disk gradually approaches the Si ridge, resulting in enhanced confinement of slot and an increase in the effective refractive index of the DSHP waveguide. Linear interpolation is performed for the 12 µm-width Pd disk expansion process. When the DSHP waveguide with WSi = 300 nm and Wslot = 20 nm is exposed to an environment of 0% - 1% H2, the change in TE mode effective refractive index increment (TE-Δneff) is shown in Fig. S6 (see Supplement 1), and the sensitivity corresponding to the effective refractive index variation of the waveguide mode with H2 concentration reaches 0.104 RIU/%. By utilizing the expansion effect of Pd and the DSHP waveguide with high optical confinement factor, amplify the effect of H2 concentration changes on the effective refractive index of the mode. In addition, the increase in the size of the Pd disk directly affects the increase in the effective refractive index of the mode, so the sensitivity of the DSHP waveguide can be increased by widening the Pd disk. Figures S7(d)-(f) indicate that the sensor with a 14 µm wide Pd disk has a sensitivity of 13.914 nm/%, which is greater than the sensor sensitivity at 12 µm wide Pd disk for the proposed MZI hydrogen sensor with a 14 µm long DSHP waveguide (see Supplement 1 for detailed information).
Figures 7(a)-(c) and (d)-(f) respectively correspond to the transmission spectrums for MZI hydrogen sensors with 10 nm and 15 nm FSR, as well as the DSHP waveguide at 10, 12 and 14 µm. Different colors represent the corresponding transmission spectrums for different H2 concentrations (from 0% to 1%). It can be seen that as the concentration of H2 increases, the optical path difference between the two arms decreases, and the interference peak shifts towards the short wavelength direction (blue shift). As the H2 concentration increases from 0% to 1%, the interference spectrums with 10 nm FSR in Fig. 7(a)-(c) show different blue shifts of 5.71, 6.65 and 7.77 nm, corresponding to LDSHP = 10, 12 and 14 µm. Figures 7(d)-(f) show the blue shift of 8.22, 9.75 and 11.91 nm when the H2 concentration changes from 0% to 1%, corresponding to the MZI sensors with 15 nm FSR and LDSHP of 10, 12 and 14 µm. It can be seen that the larger the FSR, the more significant the wavelength shift of the corresponding device, and the higher the detection sensitivity. Figures S7(g)-(i) show that by reducing the LRef of the MZI hydrogen sensor with a 14 µm DSHP waveguide, the sensitivity of the corresponding sensor with increased FSR to 20 nm is 15.041 nm/%, which is greater than the sensor sensitivity at 15 nm FSR (see Supplement 1 for detailed information). However, excessive FSR increases the difficulty of detecting interference wavelengths in the spectral analyzers (OSA). Therefore, this paper mainly selects the case where FSR is 10 nm or 15 nm for analysis. The coupling and transmission losses in the sensing arm are related to the length of the DSHP waveguide. The longer the DSHP waveguide, the longer the interaction length between Pd and evanescent field of Si waveguide, and the greater the loss. By controlling Rref, the loss of the DSHP waveguide can be compensated to achieve better extinction effect. The insertion losses of 10, 12 and 14 µm DSHP waveguide devices in this paper are about 7.56 dB, 8.56 dB and 9.80 dB, respectively, and the corresponding extinction ratio (ER) reaches 30 dB above. The monotonic decreasing trend in the resonance peak intensity is due to the reversible expansion of the Pd disk. As the hydrogen absorption concentration increases, the Pd disk expands and closes to the Si waveguide, resulting in an increase in the light loss of the sensing arm (see Fig. 4(b)) and a decrease in output power. Therefore, the intensity of the resonance peak shows the monotonic decreasing trend in Fig. 7.
Fig. 7. Output response of MZI hydrogen sensor: (a)–(c) transmission spectra of the MZI hydrogen sensors with 10, 12 and 14 µm long DSHP waveguide at different H2 concentrations, corresponding to FSR of 10 nm, (d)–(f) represent the same at FSR of 15 nm, (a), (d), (b), (e), and (c), (f) correspond to the MZI output spectra of 10 nm and 15 nm FSR with LDSHP of 10, 12 and 14 µm, respectively, (g)-(h) show variation of wavelength shift with H2 concentration under different LDSHP for MZI sensors with 10 nm and 15 nm FSR. The slope of each line represents the sensitivity (S) of the hydrogen sensor. The minus sign of Δλres indicates the blue shift.
So far, the interference wavelength shift of the transmission spectrum is only considered to be caused by the expansion effect of Pd. However, due to the formation of $\textrm{PdH}x$ during the reaction between Pd and H2, the refractive index of the Pd disk also changes leading to the interference spectrum shift [43]. Peak wavelength shift Δλres can be determined by Δλres = Δλexp + Δλn, where Δλexp and Δλn are the wavelength shift caused by the lattice expansion and refractive index changes of Pd, respectively. In order to investigate the impact of changes in Pd refractive index, the MZI hydrogen sensor with FSR = 15 nm and LDSHP = 14 µm is simulated by changing the refractive index of Pd according to Ref. [44] without changing the size of the Pd disk. When $Chyd$ changes from 0% to 1%, the transmission spectrum shifts by 20 pm, while the Δλexp caused by Pd expansion is 11.91 nm, see Fig. 7(f). Therefore, the Δλexp occupies an absolutely dominant position and the influence of Δλn is ignored in calculation.
Figures 7(g) and (h) illustrate the linear relationship between interference peak shift and H2 concentration, corresponding to LDSHP of 10, 12 and 14 µm at FSR of 10 and 15 nm. And the fitted R2 all reach 0.99. The slope of the curve can be expressed as the sensitivity (S) of the sensor. Therefore, the sensitivities of the MZI hydrogen sensors with LDSHP = 10, 12 and 14 µm can reach 5.719 nm/%, 6.652 nm/% and 7.785 nm /%, corresponding to FSR = 10 nm; 8.207 nm/%, 9.783 nm/% and 11.935 nm/% for FSR = 15 nm. It can be shown that for MZI hydrogen sensors with FSR = 10 nm and 15 nm, the larger the FSR and LDSHP, the higher the sensitivity. Figures S7(a) - (c) suggest that the sensitivity of the sensor with FSR of 15 nm can be increased to 12.929 nm/% by increasing the length of the DSHP waveguide to 15 µm (see Supplement 1 for detailed information). For the proposed two types of sensors with 10 - 14 µm long DSHP waveguide, corresponding to FSR of 10 nm and 15 nm, the MZI hydrogen sensor with FSR = 15 nm and LDSHP = 14 µm provides a maximum sensitivity of 11.935 nm/% and achieves reversible transformation, which is at a high level among other reported on-chip optical hydrogen sensors based on wavelength modulation [18,20–22,24,25], as shown in Table 1. Compared with the similar result of Ref. [21], the proposed sensor has some advantages, such as adjustable sensitivity, high extinction ratio, wide dynamic range and good mechanical stability, etc. The detection limit (DL) of the sensor is defined as the ratio of the resolution to sensitivity of the device, expressed as λRes/S. Here the resolution of the device λRes is not only determined by the resolution of the light source and OSA, but also affected by the presence of noise in the detection [45]. The λRes is set to 20 pm for theoretical studies. The detection limits for MZI hydrogen sensors with a DSHP waveguide length of 14 µm have been analyzed, and the detection limits of the sensors with 10 nm and 15 nm FSR are 0.26% and 0.17%, respectively, which are far below the lower explosive limit of 4% for H2 in air.
Table 1. Comparison of sensitivity (S) and reversibility between the proposed MZI hydrogen sensor and other on-chip optical hydrogen sensors based on wavelength modulation in the literatures
Note that according to the literatures [20,21,36], when Pd is exposed to hydrogen, the lattice expansion occurs by absorption effect. But when Pd is exposed to air or nitrogen (N2), the volume of Pd will be returned to the initial state. The temperature stability has been investigated from 290 K to 310 K. In 290 - 310 K temperature range, and the FSR = 15 nm and LDSHP = 14 µm case (see Fig. S8(a) of Supplement 1), the shift of the interference peak is 0.66 nm, which is about 5.5% compared to that of 1% hydrogen. In addition, the temperature sensitivity of the sensor is 32.7 pm/K with fitting parameter R2 of 0.98 (see Fig. S8(b) of Supplement 1), which is much lower than the hydrogen sensitivity of 11.935 nm/%, indicating the weak crosstalk between temperature and hydrogen sensing.
The response time (Tresponse) is defined as the time required for the Pd film to absorb hydrogen from original reaction to 90% of its equilibrium state [46]. The response percentage (η) can be given as [1],
where h is the thickness of the Pd disk, taken as 300 nm; D is the diffusion coefficient of hydrogen in Pd disk, taken as 1 × 10−14 m2/s [47]. Thus, the response time (Tresponse) can be written as,Therefore, the response time of the proposed MZI hydrogen sensor can be theoretically as short as 7.65 s, making it possible for the on-chip hydrogen optical sensor that meets industry standard (10 s interval in detection) [43].
4. Conclusions
In this paper, we propose a DSHP waveguide with Pd disks loaded on both sides of Si waveguide, which supports hybrid photonic-plasmonic modes. The optical confinement factors for low refractive index slots and H2 coverage areas can reach as high as 87.33% and 83.99%, but at the cost of larger propagation loss (4.28 dB/µm). In order to balance the optical confinement factor and propagation loss, the DSHP waveguide with WSi = 300 nm and Wslot = 20 nm is adopted by MZI as a sensing arm. The confinement for H2 coverage area can reach 75.29%, and the optical confinement factor for slots is 71.84%. Using SU-8 polymer as the elastic substrate reduces the shear force between Pd disk and the substrate, which is beneficial for realizing the expansion deformation of the Pd disk. The calculation shows that the wavelength shifts in the spectrum are mainly caused by the lattice expansion of the Pd disk, rather than the refractive index change. For MZI hydrogen sensor with 15 nm FSR and 14 µm long DSHP waveguide, the sensor sensitivity can reach up to 11.935 nm/%, which is at a high level in existing reports of on-chip optical hydrogen sensors. The coupling and propagation losses of the DSHP waveguide are compensated by the unequal power distribution of the asymmetric Y-splitter, achieving an extinction ratio of over 30 dB. It is noteworthy that the geometric parameters in this work don’t represent the basic limitations of the proposed sensor. The sensitivity of the MZI hydrogen sensor with the proposed DSHP waveguide can be improved by further increasing the DSHP waveguide length, expanding the Pd disk width, and reducing the length of the reference arm. For MZI hydrogen sensors with FSR of 15 nm and Pd disk width of 12 µm, the sensitivity of the sensor can be increased to 12.929 nm/% by raising the DSHP waveguide length to 15 µm; for sensors with FSR of 15 nm and DSHP waveguide of 14 µm, the sensitivity of the sensor can reach 13.914 nm/% by increasing the Pd disk width to 14 µm; and the sensitivity of the proposed sensor with increased FSR to 20 nm is up to 15.041 nm/% by reducing the reference arm length of the MZI hydrogen sensor with a 14 µm DSHP waveguide. On the other hand, the high-sensitivity design makes the proposed MZI sensor suitable for detecting different gases by changing the sensing layer, and can also be applied to biological and chemical sensing analysis. Due to the small size and compact design, the proposed MZI sensor can be integrated into on-chip arrays to achieve multi-parameter sensing.
Funding
National Natural Science Foundation of China (51574054); Chongqing Municipal Education Commission (KJZD-K202201107); Chongqing Science and Technology Bureau (CSTB2022NSCQ-MSX0356, cstc2021jcyj-msxmX0493); Joint Fund of Chongqing Municipal Education Commission and Science and Technology Bureau (CSTB2022NSCQ-LZX0032); Chongqing University of Technology (gzlcx20222078).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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