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Abstract
In the rapidly changing moisture air, conventional relative humidity (RH) sensors are often difficult to respond in time and accurately due to the limitation of flow rate and non-uniform airflow distribution. In this study, we numerically demonstrate that humidity changes on micro-zones can be monitored in real time using a Bloch surface wave (BSW) ubiquitous in one-dimensional photonic crystals (1DPC). This phenomenon can be observed by leakage radiation microscope (LRM). After theoretically deriving the angular resolution limit of LRM, we obtained the minimum BSW angular change on a practical scheme that can be observed in the momentum space to complete the detection, and realized the dynamic real-time monitoring of small-scale humidity change in experiment for the first time. This monitoring method has extremely high figure of merit (FOM) without hysteresis, which can be used in humidity sensing and refractive index sensing as well as the research on turbulence.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Humidity generally indicates the content of water vapor in moist air. It has widely used in atmosphere, agriculture, medicine and other fields [1–3], and has been described as the most important factors for the performance of some studies that require precise control [4,5]. Especially in some studies on nanofabrication or biopharmaceuticals, environmental monitoring of micro-areas is particularly important [1,6–9]. Small humidity changes or transient humidity drifts often affect the experimental results [5].Conventional Relative humidity (RH) sensors mainly use resistive and capacitive electronic sensors [10,11]. Many sensors have deficiencies such as slow response, low sensitivity, weak corrosion resistance, and poor anti-electromagnetic interference ability. Even for some optical fiber and two-dimensional material sensors to solve the above problems, the fabrication process is relatively complicated. [5,9,12,13]. In addition, sensing based on localized surface plasmon resonance requires the cooperation of various optical components, and its sensitivity and figure of merit (FOM) are generally not high enough due to the wide resonance linewidth.
Multilayer structures based on Bloch surface waves (BSW) have been used in humidity sensing due to their simple in-plane structure and high sensitivity [14,15]. The effective interaction of light and matter is increased through the confinement of modes in the structure, thereby effectively increasing the sensitivity, and the response of this kind of hygrometer is relatively fast, which can measure the ambient humidity on the surface of the structure. However, when such a hygrometer above used to measure humidity, a relatively stable environment is required and the incident angle needs to be accurately controlled. Such precise measurements are rarely seen in experiments and the humidity distribution in the space is not uniform in the complex and changing airflow environment, which is difficult to display the relative humidity value for a micro-area in time when the rapidly changing moisture flow passes through.
In this work, we use leaked radiation microscopy (LRM) to achieve high-precision characterization of BSW in momentum-space on the one hand, and real-time observation of micro-area environmental humidity changes [16–19]. After carefully deriving the actual measurement accuracy of the system, this type of optical sensing with a high response speed and repeated measurement is particularly attractive compared to other techniques. This relative humidity monitoring method also represents a powerful alternative showing very high figure-of-merit (FOM) for monochromatic light in theoretical calculation.
2. Principle of BSW sensing and the simulation results
Bloch surface waves are electromagnetic modes propagating on the surface of a truncated periodic structure [20]. It can be excited in a one-dimensional photonic crystal (1DPC), and the coupling angle is generally outside the total internal reflection angle. BSW on 1DPC is similar to surface plasmon polaritons (SPP) on metal thin films, sharing similar advantages. Besides, the resonance of BSW is much narrower than that of SPP [21–24]. Meanwhile, the angular component of its coupling is wavelength-sensitive, and a wide variety of dielectric structural parameters can be tuned to fabricate 1DPCs to operate at different wavelengths and resonance angles. Therefore, by adjusting the resonance angle and since the coupling angle is greater than the total internal reflection angle, the full width at half maximum (FWHM) of the resonance angle can be continuously squeezed, which also provides an opportunity to make a device with a high FOM.
A typical one-dimensional photonic crystal structure is generally composed of the dielectric multilayer substrate with alternating high and low refractive indices. In order to be consistent with the later experiments, the thickness of alternating layers used in the calculation here are 126 and 78 nm, respectively, and the thickness of top layer with low refractive index is 152 nm. In general, such structures can support three types of modes under the excitation of TE-polarized light, namely internal cavity modes (IM), Bloch surface modes (BSM), and guide wave modes (GWM). They correspond to the upper left, middle and lower right positions in Fig. 1(a), respectively. Due to the low loss characteristics in such a pure dielectric structure, compared with the surface plasmon modes in metal structures, these modes have strict selectivity for angles, which means that their coupling angles are only limited to a very small range. Among them, the range of coupling angle of Bloch surface mode is particularly narrow, which is shown in the figure that the curve corresponding to BSM is much thinner than the other two modes. Not only that, it is also very sensitive to the surface environment. When the surface environment varies, only the coupling conditions of Bloch surface modes change, which has little effect on the coupling conditions of the other two modes. This phenomenon is mainly because the light line will also shift as the equivalent permittivity of the surface layer, Therefore, various surface modes such as the Bloch surface modes or the Tamm modes are extremely sensitive to the changes in the external environment.
Fig. 1. Dispersion relation and electric field properties of BSW with different environment. (a) Simulated dispersion properties of a typical one-dimensional photonic crystal structure for TE-polarized modes via two surface environment. (b) Field distribution of the BSW mode when the surface environment changes. Inset is the electric field intensity distribution along the black dashed line
When the beam of a certain wavelength incidence to the surface as an appropriate excitation angle, the far-field energy could be coupled as Bloch surface mode and propagate in the near-field, that is, Bloch surface wave. The sensitivity of BSW to the environment is also different at each wavelength. It is clear from the enlarged inset in Fig. 1(a) that the BSW coupling angle changes at different wavelengths. In this configuration, its sensitivity increases with wavelength, as shown by the transverse dotted lines of different colors in Fig. 1(a). Therefore, a fixed coupling wavelength and angle (black circle in Fig. 1(a)) are selected to simulate the surface electric field intensity of the 1DPC under different refractive indices through the finite element method, as shown in Fig. 1(b). It can be seen that in an environment with a surface refractive index of n1, The TE beam with a wavelength of 600 nm can efficiently excite the BSW, and the electric field converted from the far-field to the near-field is highly localized on the surface of the 1DPC. However, the surface electric field intensity decreases sharply when the ambient refractive index changes, even if the change of n2’ compared to n1 is only one tenth of that of n2 compared to n1 in Fig. 1(a). Since the coupled excitation angle of BSW is very sensitive to the environment, it can be demonstrated to monitor the tiny changes in humidity on the surface of 1DPC.
It is precisely because the coupling angle of BSW is very small and changes via external environment. The specific realization requires the detection instrument to have very high angular resolution. A comprehensive LRM system can combine the function of microscopic imaging and the characterization of light-matter interaction in momentum space, which has sufficient angle resolution and far beyond the traditional prism based coupling system. It also avoids the mechanical rotation step by step in previous prism structures [14,15]. When TE light is incident at various angles, the light is only coupled from the far field to the near field at a specific very narrow coupling angle range. This also means that a dark arc appears on its back focal plane, oriented orthogonally to the polarization of the incident light. When the external environment changes, the coupling angle of the BSW under a certain wavelength will shift, and the dark arc on the back focal plane will also move. According to the magnitude of this movement, the monitoring of the instantaneous humidity can be completed.
3. Experimental set-up and detection limit
The 1DPC placed on the LRM, and combined with the wet airflow generation device, the experimental setup used in the relative humidity monitoring is shown in Fig. 2. The moisture flow generated by the humidifier flows out along the bifurcated duct, and the surface of 1DPC is used as a sensitive element to sense the humidity change in a section of the duct. Meanwhile, there is a commercial hygrometer on the other end for comparison. A white-light source (halogen lamp, 24 V, 150W) is employed on LRM to generate the collimated beam with an optical fiber and a telephoto lens. A band pass filter (198695, Grand Unified Optics, center wavelength at 600nm) is used to select the near-monochromatic beam about 10nm bandwidth. The wavelength of 600 nm is chosen here because in Fig. 1 (a), the coupling conditions at this wavelength vary more than that of other short wavelengths. The collimated beam is then focused on the 1DPC surface through an objective (×100, NA = 1.45), and the reflected signal carrying the surface wetness information is also collected by the same objective. The collection lens is placed in a suitable position to complete the characterization of the every modes in the momentum space, and the BSWs coupled to the far-field is then captured by a scientific CMOS camera (Dhyana 400D, Tucsen) with large sensing area. Before it, an additional vertically placed polarizer was used to facilitate the observation of appropriate modes.
Fig. 2. (a) Experimental setup for relative humidity monitoring, and (b) the angular resolution limit under this setup
Since the coupling angle of BSW corresponds to the radii of arcs on back focal plane (BFP), such an architecture of LRM can represent different modes and be used for sensing, it is worth exploring the angular resolution limit it can really achieve in practice. The coupling angle and radius satisfy the following relationship [25]
in which r gives the radius of the dark arc, which indicate the excitation angles $\theta$ of BSW in different directions, where $R$ is the radius of the field of view, as shown by the green and yellow arrows in the illustration of Fig. 2(a). The imaging here is not magnified to the maximum, so the field boundary can be clearly seen to facilitate calculation. If the pixels corresponding to the field of view are known, the RH monitoring can be completed only by observing the change. This is different from the traditional LRM system. The previous technology requires a complete field of view. Instead, computational morphology is used to help measuring the radius here, which is only needs to finish the imaging of the corresponding modes. According to the definition of diffraction limit $n\sin \theta = 1.22\lambda /D$, when the angle is small, the following approximation of $\sin \theta \to \theta$ and $\theta \to \delta r/f$ are satisfied. Here, $f$ is the focal length of imaging lens and $\delta r$ is the minimum resolution size on the back focal plane image, which can thus be expressed asWhen the coupling angle changes slightly, the change reflected in the back focal plane image according to (1) is
Therefore, combined with the above relationship, the angular resolution of LRM is
Actually, considering the size and thickness of the dichroic mirror, the focal length is generally at least 50mm. Therefore, in theory, the best angular resolution can below 0.015°, when it corresponds to a coupled emission angle about 40°. It is worth noting that, if the pixel size of the imaging device is assumed to be $a$, since the image needs to be magnified by $a/\delta r$ times, the light path is generally extended, when imaging at the highest resolution. This is not conducive to the construction of actual microscopic imaging equipment. Meanwhile, the angular resolution is always used to distinguish when two coupling angles are very close. Confirmation of angular resolution will help the determination of spectral resolution of future on-chip spectrometers. The slightly shift of a single angle in sensing is generally not restricted, but it is necessary to ensure that its small changes can be detected by different pixels. Therefore, the focal length of imaging lens in our experiments was chosen to be 75mm, which has been proved to be sufficient for sensing humidity monitoring in later experiments. The resolution limit under this condition is shown in Fig. 2(b). When the wavelength is 600 nm, the excitation angle of BSW in a dry air flow is generally around 41°, shown as the black circle in Fig. 1(a). Therefore, the angular resolution of the LRM system can reach 0.03°. Based on this result, according to the subsequent experimental and theoretical data, we can get the detection limit of LRM in refractive index detection or humidity monitoring.
4. Results and discussion
In the specific experimental scheme, we covered a chamber on the surface of 1DPC, and recorded the back focal plane image at several moments when the relative humidity was relatively stable. Because the axis of the polarizer is vertical, the BSW excited by a TE beam appears as two horizontally symmetrical dark arcs. For convenience, only one dark arc in the enlarged image is observed. It can be clearly seen that when the surface humidity on 1DPC changes, the dark arc representing the BSW in the back focal plane moves. When the air gradually becomes humid, the far-field light needs a larger coupling angle to effectively couple into the BSW, and the direct phenomenon on the back focal plane is the increase of the radius of the dark arc. As shown in Fig. 3(a), we analyzed the morphology of the dark arc and obtained its radius instead of calculating the coupled angle in only one direction as traditional method. In addition, the ovalization of dark arc caused by light path deviation can be found in time to avoid calculation error. Thus, this approach has a higher signal-to-noise ratio and is more accurate. The measurement results are listed in the right side of the figure with radii of 1394.2, 1398.0, 1405.1 and 1412.0 pixels, respectively. Since the radius of the field of view is about 2020.3 pixels, from Eq. (1), the corresponding coupled angles can be obtained as 41.24°, 41.37°, 41.63° and 41.88°.
Fig. 3. Experimental sensing results and theoretical predictions under different humidity. (a) The movement of BSW on back focal plane when humidity changes. (b) Near-linear relationship between mode dark arc radius and coupling angle. (c) Relationship between BSW coupling angle and refractive index. (d) Sensitivities and FOMs at different refractive indices
It can be seen that the angle change is very small, and the linearity of the two is therefore very high, as shown in Fig. 3(b). According to the data of relative humidity obtained by hygrometer 21%, 24%, 37% and 43%, we can get its sensitivity of 0.03°/%RH. It should be pointed out here that the response of the commercial hygrometer for measuring RH here is not fast enough, and the results may not be very accurate, which also shows the necessity of our dynamic and fast measurement. Therefore, the relative humidity is converted to the corresponding ambient refractive index according to the coupling angle, and the sensitivity is 51.58°/RIU (the linear ratio of RH and refractive index is approximately 5.247 × 10−4 RIU/%RH). Although linearity is essential as a sensor test, sensitivity is still the most critical factor. Only such a small angle change is not easy to be detected in the measurement, and is also difficult to ensure the measurement accuracy. Fortunately, the humidity monitoring method based on the BSW has a very high figure of merit. According to the calculation of the full width at half maxima (FWHM) of coupled angle, the experimental FOM can reach at least about 17/%RH. It should be noted here that, as mentioned above, in order to avoid the excessive space of the experimental platform, the observation is not under the detection limit of LRM. On the other hand, due to the bandwidth of the filter, the wavelength used in our experiment is not monochromatic light. Therefore, the effect will be better if the imaging light path is extended and the super-continuum light source with good collimation is selected.
If a monochromatic light source is used, the extremely high FOM becomes more obvious due to the low loss of such all-dielectric photonic crystal structures where the BSW is located. We can theoretically calculate the reflectivity of 600nm monochromatic light at different angles. When the refractive index of the surface environment increases slightly, the lowest reflectivity point, that is, the optimal coupled angle, will also shift to a larger value, as shown in Fig. 3(c). Due to temperature or instrumentation, the relative humidity and refractive index relationship measurements obtained from many groups vary widely [26–29]. In order to facilitate unified comparison, we only use the refractive index as the unit here. By calculating its sensitivity (48.91°/RIU, shown as the illustration in Fig. 3(d)) and FWHM, the theoretical FOM can be obtained, as shown in Fig. 3(d). FOM can reach about 3 × 104/RIU when RH is low, and can reach a maximum of 2.8 × 105/RIU through light-line squeeze. This is the best effect that such sensors can achieve today, and even the near-field sensing based on surface plasmon-coupled emission has not reached this level. It is worth noting that this kind of relative humidity measurement has a certain range. When the humidity continues to increase, the surface refractive index changes too much due to the high moisture content in the air, which means that the excitation angle range of BSW will continue to be squeezed to the critical angle, resulting in the decrease of FWHM until BSW at this wavelength cannot be excited. When the relative humidity is greater than a certain humidity, it cannot be excited because it does not meet the BSW excitation conditions of 600 nm light, and the FOM will drop sharply thereafter. From the theoretically calculated at this wavelength, when the refractive index is above 1.0085, the coupling efficiency begins to decrease, that is, the width at half maximum increases. This means that the high-sensitivity relative humidity sensing range of this chip is approximately between 20% and 55%. If still want to monitor humidity, we need to sacrifice a certain sensing sensitivity and choose other shorter wavelengths.
When the humid air flow generated by the humidity generator blows over the 1DPC surface, the relative humidity tends to change instantaneously and recover quickly. Therefore, a high-speed response measurement method is necessary. Due to the high-speed and long-term collection for the data storage, the hard disk space resources are huge. Combined the imaging contrast and the requirement of long-term monitoring, the acquisition time of a single image is generally 50 ms. If required, by increasing the light intensity, the acquisition time can be further reduced to the order of microseconds. Rely on the movement time and movement size of the dark arc of the back focal plane, the real-time humidity change of the 1DPC surface micro-area can be obtained. All steps can be done with automatic graphics processing on the back focal plane for unattended moisture airflow monitoring.
The rapid change of relative humidity in such a small range is difficult to achieve with conventional hygrometers, while it can be easily achieved with LRM. By recording the position and thickness of the dark arc, the relationship between relative humidity and time is shown in Fig. 4. It can be seen that the humidity distribution in the air flow is uneven during the humidification process. The humidity in the micro area will rise rapidly and recover many times. More details can be found in the video as the Visualization 1. This also experimentally proves that in the process of inflation with moist air, the RH of the micro-zone always fluctuates before uniform. All these dynamic monitoring of humid air flow in micro-areas has successfully proved its significance in environments such as micro-nano processing or cell culture requiring highly sensitive humidity control.
5. Conclusions
In summary, the instantaneous monitoring in micro area of moist air is realized in LRM. Based on the environmental sensitivity of Bloch surface waves on 1DPC and their low loss properties, the resonance angle is represents as a sharp dark arc in the back focal plane of LRM. This unattended automatic analysis technology based on morphology can realize single point dynamic monitoring on micro area in unsteady environments. The sensitivity reached 0.03°/%RH, which is about 51.58°/RIU for general comparison. We also theoretically calculate the angular resolution limit of the BSW in LRM can below 0.015° in practice, and the FOM at monochromatic wavelengths can reach 2.8 × 105/RIU, which are substantially higher than those for standard SPR-based sensors. In addition, the dielectric 1DPCs with relatively waterproof property and not as fragile as metal surfaces can extend its service life, which can also be used in coupled emission of fluorescence and other highly sensitive monitoring devices. If an additional two-dimensional galvanometer is added to complete the beam scanning, the monitoring of the spatial distribution of relative humidity in a large range can be completed, which may helpful for studies on gradually moist air or turbulence in the future.
Funding
National Natural Science Foundation of China (11804161); Natural Science Foundation of Jiangsu Province (BK20170818).
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.
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