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Abstract
Photonic crystal slabs (PCS) are a promising platform for optical biosensing. Yet, flexible applications based on PCS for biosensing have been limited, as the mechanical properties influence the optical ones. Here, we show the suppression of the mechanochromism effect for flexible PCS. We obtained flexible photonic crystal slabs by sputtering of a dielectric 100 nm Nb2O5 high refractive index layer onto a flexible nanostructured polydimethylsiloxane (PDMS) substrate with 370 nm grating period. The PCS exhibit a guided mode resonance at around 650 nm. We demonstrate that these flexible photonic crystal slabs show less than 0.5 nm resonance shift for 4% strain and call them stabilized PCS (sPCS). We compare this to a resonance shift of ∼21 nm for ∼4% strain of a flexible photonic crystal with a flexible nanoparticle high index layer (mechanochromatic PCS, mPCS). This high resonance shift is expected from the Bragg equations, where 4% grating period change correspond to approximately 4% change of the resonance wavelength (i.e., ∼26 nm at a resonance wavelength of 650 nm), if changes in the mode effective refractive index are neglected. In a stretch series we obtain color-to-strain dependencies of 4.79 nm/% strain for mPCS and 0.11 nm/% strain for our stabilized sPCS. We analyze the suppression of the mechanochromism with detailed microscopy results. We observe that fissures and fractures form in the rigid waveguiding layer of the sPCS upon mechanical stress. An algorithm based on Holistically-Nested Edge Detection (HED) is used for automated counting of cracks. Rigid photonic crystal cells with sizes on the order of 10 µm to 100 µm are formed that explain the stable optical properties. Even more stable optical properties with less than 0.03 nm wavelength shift per 1% strain are demonstrated for sPCS with an additional dielectric 100 nm SiO2 low index layer beneath the Nb2O5 waveguide layer decoupling the waveguide further from the flexible PDMS substrate.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The last decade has seen a surge in research activity regarding flexible materials for wearable applications [1–3]. Tracking and knowing essential health data is of importance for the wellbeing of patients and facilitates the treatment administered by physicians. A high fraction of wearable applications is based on electrical transducers, which are beneficial for the incorporation into a read-out system [4]. These advantages are offset by the need of wires connected to the read-out system or by a stored energy source within the system. Optical readout of passive wearable patches is beneficial as it eliminates cables and energy storage. For instance, Kim et al. have shown incorporated pH sensitive dyes on fingernails as an optical wearable sensor [5]. Other flexible optical transducer are based on periodic materials, also known as photonic crystals. Flexible photonic crystals have seen an uptake in research activity within recent years [6,7]. They have been studied for various applications, such as flexible optical elements [8–13], as anticounterfeiting marks in information security [14,15], as an embedded sensor for food security [16], for label-free biosensing [17], and for strain gauging [18–23]. The latter is based on the mechanochromism effect, which is a change of resonance wavelength induced by external mechanical stress [24]. This effect poses a great challenge for optical biosensing with flexible photonic crystals. Considering an application in wearable health care, a change of signal might either be induced by mechanical strain, caused by the patient movement, or by a true binding event at the surface of the photonic crystal. This interdependency needs to be solved for a potential use in wearable healthcare. Recently, Pan et al. introduced a flexible photonic crystal based on colloids, which retains its optical properties when bent [25].
In this work we show an approach, where we suppress the mechanochromatic effect of flexible photonic crystal slabs (PCS) via the formation of photonic crystal cells of rigid waveguiding layers under external stress. In essence, a PCS is a one-dimensional nanostructure integrated with a high refractive index layer, which acts as a waveguide. When illuminated, the grating couples light into the waveguide. This light is coupled out again interfering with the incident light and causing guided mode resonances in the transmission and reflection spectra [26]. The guided light’s mode distribution is not completely confined to the waveguide layer [27]. This renders the PCS sensitive to refractive index changes close to its surface. When capturing proteins such as antibodies are immobilized to the surface, the PCS is a label-free transducer platform for biosensing [28]. Other label-free optical transducers such as surface plasmon resonance (SPR) structures [29], ring resonators [30], slot waveguides [31], and reflectometric interference spectroscopy (RIfS) exist [32], but have mainly been studied on rigid surfaces.
A distinction needs to be made regarding one dimensional photonic crystals based on multilayer stacks of high and low refractive index materials. Due to the stacking a stop band is created, which prohibits the transmission of light at that wavelength through the stack and reflects the light [33]. The thickness of the layers determines the position of the resonance. They are set to be a quarter of the designed resonance wavelength. This effect is increased, when multiple layers of alternating high and low refractive index material are deposited and is tailored by choosing dielectrica with different permittivities. Further, the resonance wavelength would be at around 400 nm, as the thickness of the layers is 100 nm. The resonance observed here is at around 680 nm, as it is caused due to the grating enabling a coupling to the waveguide grating and not due to the thin film interference.
We demonstrate the optical stability under external stress and relate it to the formation of photonic crystal cells formed under external stress. We investigate three different PCS types – two types of stable PCS (sPCS) referred to as type I and type II and a mechanochromatic PCS (mPCS) developed by Karrock et al. [22] as a reference. Figure 1(a) illustrates the three different concepts. The sPCS flexibility concept is based on fracturing of a rigid dielectric waveguiding layer into smaller fragments with constant properties as depicted in in Fig. 1(b). The mPCS concept uses a highly flexible TiO2 nanoparticle layer as high-index waveguide layer that deforms with the substrate and thus exhibits mechanochromism. The flexibility of the sPCS is shown in Fig. 1(c). Furthermore, we develop an algorithm based on convolutional neural networks for the detection and quantification of the appearing fractures. The paper is structured as follows. Section 2 contains the methods, experimental setups and concept of the detection algorithm. In section 3 results are shown and discussed. Conclusions are drawn in section 4.
Fig. 1. a) Sketches of the investigated photonic crystal slabs (PCS). The term sPCS stands for stable PCS, whereas mPCS indicates mechanochromatic PCS. b) Visualization of a photonic crystal slab on polydimethylsiloxane after exposure to mechanical strain. The external stress leads to a fracturing of the homogeneous waveguiding layer into smaller fragments. c) Photographs of an sPCS. The waveguiding layer remains on the PDMS also under bent conditions.
2. Methods and experimental section
2.1 Mathematical modelling
The Bragg equation describes the resonance wavelength λGMR of the PCS as a function of the effective refractive index neff of the mode and grating period Λ of the nanostructure [34]. For perpendicular illumination the first order Bragg equations is given by Eq. (1),
The strain ε is expressed by
where ΔL is the induced displacement and L0 is the initial length [23]. In a simplified model we assume that the effective refractive index neff of the waveguide is approximately constant under strain. We expect a change in the resonance wavelength proportional to the grating period under deformation. In a more accurate analysis the change of neff due to the thickness change of the waveguide layer, the grating shape deformation, and the refractive index change of the waveguide materials under strain need to be included in the calculation. For the mPCS in Fig. 1(a) the high-index nanoparticle layer gets thinner under strain thus reducing neff. This counteracts the increase of λGMR with increasing Λ under strain to some extent.2.2 Fabrication of stable photonic crystal slabs (sPCS)
We fabricate stable photonic crystal slabs (sPCS) based on a nanoimprint lithography process [17,35]. The process is depicted in Fig. 2. PDMS (Dow, Sylgard 184 and curing agent in a ratio of 8:1) is cast onto a nanostructured glass master with a period length of 370 nm, a duty cycle of 0.4 and a depth of 45 nm. After degassing the PDMS, it is placed in an oven and cured for 30 minutes at 130° C. After cooling, it is peeled off and cut into pieces of 25 mm x 25 mm in size. The PDMS contains now the nanostructure from the master glass. The thickness of the PDMS is approximately 1.8 mm.
Fig. 2. Visualization of the two fabrication processes of stable photonic crystal slabs (sPCS) based on polydimethylsiloxane (PDMS). They are referred to as sPCS type I and sPCS type II. The waveguiding layer is deposited by sputtering.
2.3 Measurement setup
As shown in Fig. 1(a), we investigate two different types of sPCS. For both types the PDMS is placed on a support glass during sputtering, which minimizes mechanical effects and enables transport without deformation before investigation. For sPCS type I we directly sputter 100 nm niobium pentoxide (Nb2O5) (Kurt J. Lesker, EJUNBOX353TK4) onto the PDMS as a high refractive index layer. For sPCS type II we add 100 nm of silicon dioxide via sputtering (SiO2) (Kurt J. Lesker, EJUSIO2453TK4) as a low refractive index material before depositing 100 nm Nb2O5. All deposition were performed at 100 W. According to data supplied by the manufacturer, it is to be expected that a deposition power of 100 W leads to a surface temperature between 60 °C to 70 °C. PDMS is intended to withstand temperature up to 150 °C [36]. Nb2O5 was used as a waveguide as it exhibits similar waveguiding properties as TiO2, has a sufficiently high refractive index and was readily available at our chair [37].
As a reference, we investigate the mechanochromatic photonic crystal slab (mPCS) developed by Karrock et al. [22]. The nanoparticles were dispersed on a nanostructured PDMS membrane via spincoating of a solution with a mass concentration of titanium dioxide (TiO2) nanoparticles of 6%. The resulting nanoparticle layer serves as a high refractive index layer forming the optical waveguide. The membrane thickness is approximately 100 µm.
In order to investigate the effects of mechanical strain on the optical properties, the three types of PCS are mounted in a stretching setup, which allows for displacement within the micrometer range. This setup is placed into a microscope and is positioned between two orthogonally crossed polarizers. All three types are positioned at 45° with respect to the direction of the crossed polarizers. The diameter of the illumination spot is approximately 1 cm and the spectra and images were taken at a 10-fold magnification. The crossed polarizers suppress the excitation light and lead to peak resonances in transmission [38]. The emitted light is collected by an objective and directed onto and recorded with a spectrometer (Andor Solis, Shamrock 500i). Two different gratings are used. Grating 1 has 149 lines/mm and enables a measurement over a range of 355.88 nm with a step width of 0.343 nm. Grating 2 has 1149 lines/mm and has a spectral coverage of 43.54 nm, with a step width of 0.043 nm. Mechanical strain is applied to all PCS configurations by displacing the bracket with the micrometer screw. We use displacement steps of either 50 µm or 100 µm. At each step an image of the surface and a spectrum is recorded. The setup is illustrated in Fig. 3.
Fig. 3. a) Schematic of the measurement setup. b) Photograph of the measurement setup of a). c) sPCS mounted in the micrometer screw drive brackets. d) Image of c) without clamping brackets.
2.4 Fracture detection with computer vision
The fractures induced by external mechanical stress are evaluated by a fracture detection algorithm. As a basis, we generate maps distinguishing between fractures and fragments. The maps are created using Holistically-Nested Edge Detection (HED), which detects edges in images using a deep learning model [39]. HED enables image to image prediction and when trained appropriately can achieve a similar performance to manual detection. This is shown in Fig. 4(a) through Fig. 4(c). For images of stretched PCS, HED outperforms classical edge detection approaches such as Canny or Sobel [40,41]. An HED model is trained on a dataset containing pairs of RGB images and ground truth edge annotations. We manually created maps for five images of size 1632 × 2464 pixels. Through data augmentation, a dataset is obtained from these pairs of images and maps. We mirror the images in four directions - none, vertical, horizontal, both - and rotate the obtained images in 12 steps by 30 degrees. This enlarges the number of images by a factor of 48. Furthermore, we go through these 240 images with a step length of 192 pixels in horizontal as well as vertical direction and cut squares of 256 pixels edge length. The resulting dataset contains 15241 square images together with their corresponding maps. From this dataset 80 percent are used for training and the remaining 20 percent for validation. In both cases a batch size of 64 is used and the best model based on training loss and validation error is observed after 2356 epochs. Images larger than 256 × 256 pixels are cut into overlapping snippets for fracture detection. Each snippet is run through the model independently and an overall map is combined from the obtained maps. With the generated maps further analysis is possible. We generated binary edge maps by applying a threshold between 110 and 195, depending on the brightness and presence of noise in the input image. The aim is to minimize noise in the binary map although this leads to minor holes in the detected fractures. This is shown in Fig. 4(d). Then, we colorize and count horizontal edges. A fracture is defined as horizontal, when the slope is between -45° and 45°. A copy of the binary maps is investigated from top left to bottom right in column major order. Whenever a white pixel is found, the height of the fracture gets observed and is traced from left to right until another colored or black area is reached. Afterwards the fracture is counted and colored in one of 20 distinct colors. Fractures that are not classified as horizontal are colorized in dark gray. This is shown in Fig. 4(e).
Fig. 4. Illustration of the different steps of the fracture detection algorithm. a) Original image. b) Hand drawn edge detection. c) Edge detection via a Holistically-Nested Edge Detection (HED) model. d) Binary maps via thresholding of c). e) Colorizing and counting of detected horizontal fractures. Non-horizontal fractures are colored in dark gray. Coloring and counting is based on the binary map obtained in d).
3. Results
3.1 Optical properties and mechanochromism
3.1.1 mPCS
As a reference for later comparison we first investigate the mechanochromism of the flexible nanoparticle-based mPCS described in [22]. Figure 5 shows the optical transmission spectra of the mPCS for different strain values ε. The dip in transmission is attributable to incoherent illuminations, as was suggested by Frank et al. [42]. During clamping of the mPCS in the stretching device, the thin membrane bulges. This is compensated by prestretching the mPCS until a small mode shift is detectable. In Fig. 5(a) the mPCS is stretched orthogonal to the grating grooves and the guided mode resonance exhibits a red-shift upon external strain, as is expected from Eq. (1). In Fig. 5(b) the maximum position is tracked, as the overall spectral form is not affected by the stretching, which facilitates processing. After prestretching the mPCS exhibits a linear resonance wavelength change with strain. Applying a linear fit to the linear part of Fig. 5(b) gives a slope of 4.79 nm/% strain, which is in a range of previously published investigations [22,23]. The calculated R-value of 0.999 shows an excellent linear behavior. The mPCS exhibits this behavior as the waveguiding layer itself is stretchable and therefore the grating period is increased proportional to the strain. For a strain of ε = 3.9% the grating period Λ is also increased by 3.9%. Without any change of the effective refractive index neff we expect also a change of the resonance wavelength of 3.9%, which would be a red shift of ∼27 nm for the initial wavelength of 682 nm. In the experiment a resonance wavelength shift of 21 nm is observed. This is a resonance wavelength increase of ∼3% compared to the initial resonance wavelength of 682 nm. We attribute this lower rate of change while maintaining a linear behavior to an approximately linear combined effect of the deformation of the grating, change in the waveguide refractive indices, and the thinning of the waveguide. PDMS has been shown to have a nearly constant refractive index under strain [10]. Thus, the substrate refractive index should not contribute to the change in neff.
Fig. 5. Resonance shift of a mechanochromatic PCS (mPCS) for orthogonal stretching. The mPCS is prestretched until a small resonance shift is observed. a) Normalized spectra of the guided mode resonance measured between crossed polarizers for different mechanical strains. b) Tracking of the peak position of a).
3.1.2 sPCS Type I
Figure 6 shows the resonance behavior for an sPCS type I with strain. The sPCS was stretched up to a strain of ɛ = 4.9% in a forward and backward motion. At each position a spectrum with grating 1 (described in section 2.2) was recorded and the dip position of the resonance was tracked. The dip tracking was performed via parabolic fitting of the minimum. Here, we performed dip tracking, as the shape of the spectra is influenced by stretching, as is visible in Fig. 6(a) and Fig. 6(c). The dip form remains rather constant during the experiment. In Fig. 6(a) and Fig. 6(c) the spectral effect of stretching orthogonally and in parallel with respect to the nanostructure grating grooves is shown. The observed resonance shifts are significantly lower compared to an mPCS for corresponding strain values. In Fig. 6(b) the resonance wavelength shift for orthogonal stretching with respect to the grating grooves is analyzed. A redshift of only 0.6 nm is observed for a strain of ɛ = 4.9%.
Fig. 6. Stretching effects of a stable photonic crystal slab (sPCS) type I. Forward and backward motion are abbreviated by FWD and BWD, respectively. a) Recorded spectra for different strain values orthogonal to the grating grooves. b) Detected dip position via parabolic fitting. c) and d) Same as a) and b), but for stretching parallel to grating grooves.
When stretching in parallel to the grating, a blue shift is observed. This is shown in Fig. 6(d). PDMS is known to have a Poisson ratio of 0.5, meaning that upon external strain a length elongation is compensated by a perpendicular contraction [43]. The observed blue-shift of 0.9 nm might be attributed to this effect. The sPCS type I shows a slope of 0.11 nm/% strain and -0.18 nm/% strain for orthogonal and parallel stretching, respectively. In addition, the calculated R-values of 0.932 and -0.949 show that the linear dependency of stretch-to-shift is reduced. We want to point out that parallel stretching induces a greater shift than orthogonal stretching.
For both experiments it is observed that the spectrum slightly changes under mechanical stress. This might stem from the birefringent effect of PDMS [44,45]. Since the sPCS is positioned between two crossed polarizers, an effect on the polarization state will be visible in transmission. However, it is to be noted that the birefringence effect is different for the orthogonal and parallel orientation, indicating an anisotropy of the PDMS. The increase in transmission above approximately 720 nm is due to the diminishing suppression efficacy of the polarizers.
3.1.3 sPCS Type II
The remaining dependency of the resonance wavelength position to the straining might arise from the overlap of the mode distribution with the PDMS substrate and the changing interface region between substrate and dielectric waveguide layer. In order to minimize this overlap, we included a low refractive index SiO2 layer beneath the waveguide layer. Figure 7 shows the results of stretching this sPCS type II. In order to investigate smaller changes of the resonance position grating 2 is used. As before, the behavior for orthogonal and parallel stretching in relation to the grating grooves is investigated. Figure 7(a) and Fig. 7(c) show the spectral response under mechanical stress. The fitted dip positions for both scenarios are depicted in Fig. 7(b) and Fig. 7(d). The dip tracking was chosen due to the same reasons as mentioned in section 3.1.2. Again, a redshift and blueshift for orthogonal and parallel stretching is observed, respectively. Yet, the shifts are further reduced as compared to the sPCS type I and the mPCS. For orthogonal stretching a maximum shift of 0.17 nm is recorded. For the parallel stretching a shift of -0.26 nm is detected. A linear fitting of the dip positions gives a slope of 0.027 nm/% strain and -0.030 nm/% strain for orthogonal and parallel stretching respectively. This shows that adding an additional layer of low refractive index material, is highly beneficial to the suppression of the mechanochromatic dependency. The respective R-values of 0.772 and -0.770 indicate a further diminishing of the strain-to-shift ratio. The orientation dependency as portrayed in Fig. 6 is observed, as well. For orthogonal stretching an increase in transmission below the guided mode resonance is detected. In contrast, for parallel stretching an increase above the guided mode resonance is visible.
Fig. 7. Overview of the stretching effect on an sPCS type II. a) Spectral behavior of the sPCS for orthogonal stretching. b) Fitted dip position of a). c) Spectral behavior of the sPCS for parallel stretching. d) Fitted dip positions of c).
These finding support the optical framework given in the introduction. The observed resonance effect is not induced due to the thin film interference of the layers, as this should lead to a blue shift in both directions upon external stress [46]. The observed shifts arise from the change of the period length induced by stretching and is therefore governed by guided mode resonances.
An overview of the mechanochromatic effects for all three configurations is given in Fig. 8 Photographs and algorithmic evaluation of an sPCS type II. The sputtering was performed with a glass substrate for support. The arrow indicates the direction of stretching. The grating grooves of the sPCS were orthogonal to the stretching direction. Images a) through d) were taken between crossed polarizers. a) An image of the surface taken directly after sputtering. b) A photograph of a) on the stretching device after being taken off the glass slide, yet before being stretched. c) Image of the surface stretched by ɛ = 3.5%. d) Image of the surface at ɛ = 5.8%. e) Amount of detected horizontal lines for each strain position. f)-h) Algorithmically detected and colorized fractures for stretching by ɛ = 0.0%, ɛ = 3.5%, ɛ = 5.8%. i) and j) Stitched images of the surface taken with a confocal laser microscope before i) and after j) manual bending of the sPCS (rf. Figure 1(c)).
Fig. 8. Photographs and algorithmic evaluation of an sPCS type II. The sputtering was performed with a glass substrate for support. The arrow indicates the direction of stretching. The grating grooves of the sPCS were orthogonal to the stretching direction. Images a) through d) were taken between crossed polarizers. a) An image of the surface taken directly after sputtering. b) A photograph of a) on the stretching device after being taken off the glass slide, yet before being stretched. c) Image of the surface stretched by ɛ = 3.5%. d) Image of the surface at ɛ = 5.8%. e) Amount of detected horizontal lines for each strain position. f)-h) Algorithmically detected and colorized fractures for stretching by ɛ = 0.0%, ɛ = 3.5%, ɛ = 5.8%. i) and j) Stitched images of the surface taken with a confocal laser microscope before i) and after j) manual bending of the sPCS (rf. Figure 1(c)).
Fig. 9. Various SEM images of one sPCS type I surface. In all four images an underlying ‘withering’ effect similar to damp paper is visible. a) Image of different photonic crystal cells. b) Image of a region, where the high refractive index layer shows a behavior of a shattered glass. c) The photonic crystals are cutting into each other. d) Zoom in of c).
In summary, it is observed that the newly introduced sPCS show a significantly suppressed mechanochromism (Table 1). The absolute suppression of the mechanochromatic effect is by a factor of 44 for the sPCS type I and 180 for the sPCS type II as compared to the reference mPCS. It is to be noted that the sPCS type I and II are an order of magnitude thicker than the mPCS. This renders both sPCS types more mechanically stable. However, we assume that thinner sPCS would still exhibit a similar behavior, as the suppression is not caused by the thickness of the substrate but by the fracturing of the waveguiding layers. A thinner substrate will probably lead to a different type of fracturing. Further research into this assumption needs to be performed.
Table 1. Overview of the mechanochromatic dependency of an mPCS, an sPCS type I and an sPCS type II
3.2 Mechanical flexibility and formation of photonic crystal cells
We have seen that the sPCS exhibit flexible behavior with stable optical properties. In this section we shall investigate the sPCS microstructure and nanostructure to understand why the optical properties show such an impressive stability under strain. Figure 8(a) to Fig. 8(d) show a first series of images of an sPCS type II from fabrication to first stretching. The images were taken between crossed polarizers. Figure 8(a) depicts the surface directly after sputtering. Due to the stacked layers thin film interference is observed [47]. Furthermore, the surface is quite homogeneous and shows few cracks. The interference is not visible around the crack, indicating a change of surface conformation. In Fig. 8(b) the effects of pulling the sPCS from the supporting glass and mounting it onto the stretching device is visible. In comparison to Fig. 8(a) more fractures are evident, resulting from the manual handling. Again, the interference fringes disappear in the vicinity of the cracks. Figure 8(c) and Fig. 8(d) show the increase of cracks for a strain of ɛ = 3.5% and ɛ = 5.8%, respectively. The observed fractures are predominantly aligned with the nanostructure grooves that are orthogonal to the direction of stretching. This shape distribution is induced by the dedicated one-directional displacement via stretching. The visibility of horizontal fractures is improved by the algorithm, which is shown in Fig. 8(f) through Fig. 8 (h), as the black background and rotating colors ease the perception. The identified cracks are quantified in Fig. 8(e). For a strain of ɛ = 5.8% 45 horizontal fractures are identified, which corresponds to an average photonic crystal cell height of approximately 85 µm. These values are calculated by dividing the height of the observed images by the amount of observed cracks plus one.
Manual deformation as shown in Fig. 1(c) leads to a less homogenous shape distribution of the sPCS cells, as is contrasted from Fig. 8(i) to Fig. 8(j). In Fig. 8(i) a stitched image series taken with a laser confocal microscope (Keyence, VK-H1XMD) of the sPCS surface directly after sputtering is illustrated. Similar to Fig. 8(a) the surface is homogeneous with cracks towards the edges of the high refractive index layer, which is induced by the lift-off of the sputtering fixation tape. The major cracks in Fig. 8(j) are present in Fig. 8(i), as well. Yet, due to the manual deformation the sPCS is fragmented into smaller cells. Contrasting Fig. 8(d) and Fig. 8(j) illustrates that the photonic crystal cell shape distribution is influenced by the type of mechanical stress the sPCS is exposed to.
The effect of the fracturing of the dielectric layers on the nanoscopic level is shown in the SEM images Fig. 9. All four images were taken on the same sPCS type I sample and show an underlying ‘withering’ effect, similar to damp paper. This effect has been reported by Markou et al. [48] They have shown that direct deposition of single and double metal layers onto nanostructured PDMS via sputtering leads to similar wrinkling structures as observed here. This is due to the thermal expansion during sputtering and successive contraction upon finishing of the PDMS. They report that the height difference of about 250 nm induced by the wrinkling does not destroy the nanostructure on the PDMS. Figure 9(a) illustrates an area, where different photonic crystal cells are facing one another. The fractures are visible. In Fig. 9(b) an area is illustrated, where the photonic crystal cells show a behavior similar to shattered glass. Figure 9(c) and Fig. 9(d) depict how different cells move into one another. Furthermore, Fig. 9(d) visualizes the nanostructures within the cells, indicating, similar to the findings of Markou et al., that the wrinkling does not destroy the grating structure.
It follows from the photographs and the SEM images that the rigid photonic crystal cells exhibit typical sizes in the range of 10 to 100 µm diameter.
4. Discussion and conclusions
We have reported a fabrication method for flexible photonic crystal slabs with stable optical properties. It is observed that the resonance wavelength shift of sPCS type I and type II is reduced by a factor of 44 and 180, respectively, compared to a flexible reference mPCS based on a nanoparticulate high index layer. By analysis of microscopy and SEM images we observe that during deformation rigid photonic crystal cells of sizes on the order of 10 to 100 µm form. In the literature it has been demonstrated that the quality factor of a guided mode resonance and the propagation length of the mode are related [49–52]. For our resonance quality factors of ∼100 the propagation length is on the order of 5 µm. Comparing this to the typical cell size of the fractured photonic crystal waveguide, it is observed that the cell size still exceeds the mode propagation length. This is in agreement with the stable resonance mode profile under strain. Thus, each individual cell of the fractured waveguide is sufficiently large to support a photonic crystal mode. The stability of the resonance wavelength under strain shows that the photonic crystal cells do not deform under lateral strain but rather “float” on the flexible substrate like floes.
The properties of the photonic crystal cells are further decoupled from the flexible substrate by the rigid low-refractive SiO2 layer below the Nb2O5 waveguide layer. Using this approach, the macroscopic flexible mechanical properties are determined by the substrate, but the microscopic rigid waveguide properties are determined by the rigid waveguide materials. To our best knowledge this concept has not been studied previously. Previously, flexible photonic crystal slabs such as the reference mPCS have been introduced that deform under strain [22]. Also, rigid waveguide layers on flexible substrates have been considered, but these structures were tailored to achieve nominal break points of the rigid waveguide in each period in order to achieve mechanochromism [21,23]. Therefore, the flexible photonic crystals slabs studied so far followed the Bragg Eq. (1). In our concept this is not the case as the cracks ‘absorb’ the mechanical stress and the photonic crystal cells remain intact. The fracture detection algorithm based on Holistically-Nested Edge Detection introduced here serves as a basis for automated analysis of photonic crystal cell formation and targeted crack design. The effect of changing the PDMS substrate thickness on the fracturing and the sPCS optical properties remains to be investigated. Also, lithographically predefining nominal breaking lines in the rigid waveguide or using a shadow mask in the sputtering process may be a feasible route to achieve a more deterministic and homogeneous photonic crystal cell size distribution.
For the practical application of sPCS in wearable applications, thermal effects need to be considered in addition to mechanical effects, as thermal changes also influence the optical properties. Here, we give an estimation of the amplitude of these effects. The resonance is modelled to be affected by two thermal dependencies, which are accounted for by the thermo-optical coefficient and the thermo-mechanical coefficient. The former describes the changes in refractive index induced by a temperature change and the latter the expansion or contraction in size due to external temperature variations. The thermo-mechanical coefficient for Nb2O5, SiO2 and PDMS are 5.8 ppm/K [53], 0.45 ppm/K [54] and 310 ppm/K [36]. Changes in the period length will mainly affect Nb2O5 and SiO2. Averaging the coefficient for Nb2O5 and SiO2, a change of 1 K on a PCS leads to an expansion of the period unit cell of approximately 1 pm, which is of relevant magnitude and similar to reported effects by Privorotskaya et al. [23].
The thermo-optical coefficient for Nb2O5, SiO2 and PDMS are 14.3 ppm/K [53], -19.2 ppm/K [54] and -450 ppm/K [55]. It is evident that the biggest temperature influence is exerted by the PDMS. Yet, the distribution of the electrical field needs to be taken into account. Depending upon how much of the mode extends into to PDMS the net effect on the thermo-optical coefficient of the PDMS might be in the same range as for Nb2O5 and SiO2. Considering that the coefficient for PDMS and SiO2 are negative and positive for Nb2O5 it might be possible to compensate the thermo-optical coefficient by a smart design. Especially the design differences between sPCS type I and type II might play an important factor in regards of temperature stability.
In conclusion, the new concept of sPCS opens the path for considering photonic crystal slabs for biosensing in wearable sensors in combination with an optical readout system. For example, Choi et al. reported resonance shifts for label-free sensing with photonic crystals in the range of 100 pm to 1000 pm [56]. The here reported sPCS type II would need to be strained by 5% to cloud the lowest observed signal.
Funding
Deutsche Forschungsgemeinschaft (DFG) Open Acces-Publizieren.
Acknowledgments
The authors thank Muhammad Hamza for fabricating the PDMS moulds prior to sputtering. Furthermore, we are grateful for the valuable discussion input given by Johannes Bläsi regarding the predefining of nominal breaking lines for deterministic fabrication of photonic crystal cells and to Moritz Paulsen for his expertise regarding temperature effects.
Disclosures
Parts of this work were presented at the Optical Sensors and Sensing Congress in 2022, Nanostructured Floes on PDMS as a Basis for Strain-Invariant Photonic-Crystal Slabs [57].
Data Availability
Data underlying the results presented in this paper are not publicly available at this time and can be obtained from the author upon reasonable request.
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