Introduction

The dynamic loading behavior of composites and particulate materials is highly complex as their macroscopic behavior is driven by mesoscale interactions. Despite their prevalence and importance, a comprehensive understanding of such materials is deficient due to a lack of diagnostic tools with desired spatial and temporal resolution. Thus, sensor designs that are capable of providing material state information with high spatial and temporal resolutions are critical to advance the understanding of dynamic behavior in complex, heterogeneous material systems.

Currently, there are few diagnostic tools that simultaneously have sufficient temporal and spatial resolution to capture the highly transient dynamic events controlling mesoscale interactions. For instance, while piezoelectric/piezoresistive stress gauges can provide accurate stress-time profiles with nanosecond temporal resolution [1] their spatial resolution is on the order of millimeters, thus providing only an averaged response of the system. Similarly, laser velocity interferometers, such as the velocity interferometer system for any reflector (VISAR) [2], Fabry-Perot [3, 4] and heterodyne systems [5], all provide accurate velocity profiles with nanosecond resolution, but only for a single spatial point presenting a certain volume. A more capable system; the optically recording velocity interferometer system (ORVIS), has demonstrated sub-nanosecond temporal resolution and sub-mm spatial resolution but only along a one dimensional line profile [6].

In contrast to the limitations of these existing methods, optical microcavities (OMCs), can potentially provide two-dimensional surface data, with comparable temporal resolution. OMCs are composed of an optical medium (cavity layer) placed between two reflecting mirror layers whose principal optical characteristic, the resonant frequency, depends predominantly on the thickness and the refractive index of the cavity layer. The resonant frequency, or cavity mode, corresponds to the particular wavelength of light that can be transmitted. Furthermore, cavity modes of OMCs are typically very sharp with narrow full-width-half-maximum (FWHM) and high transmission. Under dynamic compression, the thickness of the cavity layer along with its refractive index change due to the applied pressure, cause a spectral shift in the transmission peaks or complementary reflectivity minima. By monitoring the shift of a particular cavity mode using time-resolved spectroscopy, it is possible to capture two-dimensional data corresponding to the area of the OMC structure under dynamic loading. These promising characteristics were recently published in an in-depth theoretical study assessing the potential of OMC structures for use in dynamic compression sensing by Scripka et al. [7]. In this work, modeling of an OMC structure with a TiO₂ cavity layer surrounded by Distributed Bragg Reflectors (DBR) composed of alternating TiO₂/SiO₂ layers was performed which showed a shift of the characteristic cavity mode under uniaxial shock compression with a rapid temporal response. Therefore, further design and experimental studies were initiated, with an emphasis on optimizing the design and fabrication processes for dynamic load sensing [8].

In this study, asymmetrical OMC (AOMC) designs and fabrication processes for dynamic loading diagnostics were investigated. The effect of different materials and structural designs on sensor performance were simulated and optimized, and the feasibility of required fabrication processes validated. AOMCs instead of OMCs were chosen to maximize the amount of reflected light from the sample by depositing a thicker mirror layer as the final surface of the multilayer and to provide some additional mechanical stability under shock compression conditions. The optimized designs of the AOMC structures have attributes suited for use as dynamic loading sensors. A fabricated AOMC structure was then subjected to laser-driven shock compression, and the time-resolved position of the characteristic spectral peak was recorded using a streak camera coupled spectrograph.

Design methodology

Figure 1 shows the device design developed during the course of this investigation. The AOMC structure is epoxied to the shock-compression package which has several layers: BK-7/Carbon/Al/Al₂O₃. The AOMC structure was configured to permit optical interrogation from one side (the substrate side) such that the shock front from the opposite side directly impacts the active cavity layer. The shock is generated by the carbon/aluminum layers in the package absorbing the energy of the incident laser pulse, which produces a rapidly expanding plasma cloud, or “explosion” at the interface of the carbon/aluminum layers and shock package substrate. This drives a shock wave into the AOMC, as shown in Fig. 1 (a). Simultaneously, broadband light from a Xenon flash lamp is reflected off the AOMC substrate, and is collected and directed into a grating spectrograph. The spectrograph separates the component wavelengths, and additional optics focus the output from the spectrograph onto the input slit of a fast streak camera, which records the temporal evolution of the spectra with a resolution down to 0.5 ns.

 

Fig. 1 Schematic of a SiO₂ (or Al₂O₃) AOMC structure under dynamic loading experiment and the reflectance spectrum simulated for a Ag/SiO₂/Ag AOMC with a 500 nm thick SiO₂ cavity layer (continuous blue line), and after being compressed to the fracture limit (dotted red line). The inset depicts the calculated shift in the reflectance minimum due to the maximum static compression at the strain to failure point.

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The reflectance and transmission spectra of various AOMC structures were simulated using the OpenFilters software which includes the dispersion properties of the optical materials used in this investigation [9]. Device parameters such as layer thicknesses, reflectivity, and material refractive index, were used as input parameters to simulate the effect of each parameter on the optical properties of the AOMC. In fabricating sensor devices, it is extremely important to achieve highly reliable structures that reflect the true value of their component materials. Thus, in addition to device design, the selection of materials and deposition systems are critical and must take into consideration the resulting optical and structural properties. For example, OMCs are typically fabricated using Distributed Bragg Reflectors (DBR), but the thickness (~2μm) of these structures can result in their response to strain or shock obscuring the cavity effect and lead to a very complex analysis. Thus, thin Ag reflectors were chosen whose optical (reflective) properties are less affected by stress and which directly and rapidly transfer the stress to the cavity material. Although some of the energy of the shock wave is dissipated in the mirrors due to the impedance mismatch between Ag and SiO₂, in comparison to the thicker (2 μm) multilayer DBR design, the energy loss is very small. This is due both to the thinness of the Ag layer and the moderate difference in impedance that results in very little shock energy loss at the interfaces. Therefore, for this application, these simplified designs significantly reduce device complexity and consequently enhance reliability without any loss in performance. This structure also addresses an additional design requirement; namely, that the shock be transferred instantaneously to the sensor layer so as to enhance the temporal response of the device. Using the appropriate material parameters (elastic modulus, density, etc) for a 125 nm thick Ag mirror and a 500 nm thick SiO₂ cavity layer the device response to shock compression was estimated to be <200 ps. To our knowledge, the number of optical materials for which reliable shock parameters are known is very small (SiO₂, TiO₂, Al₂O₃ and LiF). Thus, for this proof-of-principle study we selected SiO₂ and Al₂O₃ as the best cavity materials as their deposition and fabrication techniques have also been well studied.

Figure 1(a) shows a schematic of the simplified SiO₂ (n = 1.46 at 535 nm) and Al₂O₃ (n = 1.77 at 535 nm) AOMC stress-sensors consisting of just three layers: two Ag mirror layers and a cavity layer. The reflectance spectrum was simulated for a 500 nm thick SiO₂ cavity layer and a 35 nm thick semi-transparent (11% transmittance at 535 nm) front Ag mirror layer and ~98% back reflecting 125 nm thick Ag layer. The top Ag layer is designed to be thicker for two reasons: (a) to provide a buffer layer for shock pressure, (b) enable high reflectivity for better optical signal. Although the thickness, refractive index, and reflectivity of each layer all affect the reflectance spectrum, the positions of the reflectance minima are mostly affected by a change in the cavity layer thickness. The dotted red curve shows the simulated effect of a dimensional change in the SiO₂ cavity layer under static compression. It has been previously reported [10] that a-SiO₂ micropillar array exhibits a strain to rupture failure value of 0.15 in uniaxial compression at around 7GPa. By employing this number in simulation, a blueshift of the reflectance minimum by ~70 nm is obtained. It should be noted that the blueshift obtained is an over-estimation as it is under static compression, and also it does not consider other effects such as densification which can result in modification of refractive index. For an Al₂O₃ AOMC structure with the same design parameters, a smaller spectral shift is predicted due to its superior hardness and inherent lower strain at failure compared to SiO₂ [11]. Thus, a SiO₂ based design is expected to be significantly more sensitive to pressure.

The accuracy to which a particular minimum can be measured directly determines the sensitivity of the device to changes in length and/or refractive index. This will depend on how narrow the particular FWHM minimum is and requires a standardized procedure for measuring and comparing data. For the latter we employed a Rayleigh-like criterion to distinguish two adjacent peaks, such that when the first minimum of a peak lies under the maximum of an adjacent peak then the dip between them is 20% less than the maximum intensity of either. For a Gaussian or Lorentzian line shape this is approximately equivalent to the FWHM of the peak. Thus, for example for SiO₂ cavity designs with FWHMs of 9 and 1.5 nm, as discussed later, the percentage accuracy in measuring the position of a peak is determined by the ratio FWHM/(peak position); ~1.64% and ~0.27% respectively, for a peak position of 550 nm centered at the maximum response of the measuring system. To calculate the sensitivity in terms of the minimum strain that can be measured for a given material, we can obtain an estimate from the wavelength shift expected at the strain to fracture limit. For SiO₂, this is 70 nm and gives 13% (9/70 x 100) and 2.1% (1.5/70x100), respectively for the two designs. In principal by judicious curve fitting, and since we are not differentiating two peaks but a shift of a peak, it is estimated that the accuracy can be improved, potentially by a factor of five. Therefore, the designed device must have a sharp transmission peak (which from now on is referred to as a reflectance minimum as we collect reflectance spectrum) and positioned to match the maximum spectral sensitivity of the spectrograph and streak camera: in this case between 400 and 700 nm. Additionally, for maximum device sensitivity, the FWHM must be narrow compared to the free spectral range (FSR) between reflectance minima (shown in Fig. 1) and the bandwidth of the measuring instrumentation. Additionally, a strong overall reflectance is required to enhance the capture and collection of light during the short duration of dynamic loading. We have therefore, rigorously investigated the impact of both material and structural parameters and fabrication issues on the optimization of AOMC structures designed for dynamical loading applications.

Figure 2 shows the dependence of the spectral reflectance, as calculated using the OpenFilters software, on the structural dimensions of the AOMC. Additionally the AOMC can be analyzed in terms of the theory for Fabry-Perot structures, where the reflectance minima (cavity modes) can be obtained from the expression:

 

Fig. 2 (a) Shape of reflectance spectra simulated for different modes of AOMCs tuned for reflectance minimum at 535 nm (b) dependence of FWHM and cavity thickness (as required to achieve a reflectance minimum at 535 nm) on cavity mode number.

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Figure 2(a) shows a collection of reflectance spectra for AOMC structures designed to position the reflectance minimum at λ = 535 nm for each mode number. As the mode number increases, the cavity layer thickness must also increase in order to keep the reflectance minimum positioned at λ = 535 nm. Figure 2(b) shows the dependence of FWHM (δλ) and the required cavity layer thickness, l, on the cavity mode number, m. The FWHM, δλ, at λ = 535 compliance increases from ~100 to 1200 nm. This can be explained from the expression:

As l increases, λ_o decreases because according to Eq. (1), there are more reflectance minima in a given spectral range which means that adjacent minimum become closer to the minimum of interest, λ = 535 nm. Therefore, the increase in l results in a decrease in λ_o and Δλ, which ultimately decreases δλ, as desired. However, even though a higher cavity mode is beneficial, it should be noted that the required cavity layer thickness increases linearly. Thus, it is essential to find the optimum cavity layer thickness for each material while also considering the impact of the fabrication process on the deposited film quality. From these considerations and the data shown in Fig. 2 for a SiO₂ AOMC structure, it was determined that the 3rd order reflection minimum was sufficiently narrow (FWHM ~9 nm) while also keeping the thickness of the cavity layer thin.

Figure 3 shows the OpenFilters computations performed to establish the mirror properties that gave the best reflectance minimum depth and narrowest FWHM [13]. Figure 3(a) shows that the mirror reflectivity at 535 nm increases exponentially as the thickness increases. The reflectivity is close to 1 at 60 nm. From the simulation, it was found that AOMC with Ag mirror layers had the best spectral characteristics (in terms of the depth of minima and FWHM) compared to other metal such as Al and Au mostly due to its excellent reflectivity in visible light range. Furthermore, it was determined from the simulation that the thickness of mirror layer 2 has minimal effect on the reflectance spectrum and the characteristic features above 60 nm. Therefore, we decided to make it ~125 nm as it also acts as the shock buffer layer. Figure 3(b) shows the effect of the thickness of Ag mirror layer 1 on the characteristic minimum’s (m = 3) FWHM (red markers) and depth (blue markers) of AOMC with a fixed SiO₂ cavity thickness (500 nm) and mirror layer 2 (125 nm). As the thickness of mirror layer 1 increases, the FWHM of the characteristic cavity mode decreases drastically. On the other hand, the depth of the characteristic minimum increases initially, but then starts to decrease past a certain thickness. The inset image in Fig. 3(b) shows the zoomed graph of the region of interest. The relative minimum depth is maximized at 25 nm, but the FWHM is too wide (~16.5 nm). Thus, even though there is a drop in the depth of minimum at 35 nm, it is still relatively high at 87% and the FWHM is acceptably narrow at 9 nm. Therefore, the thickness of the mirror layer 1 was optimized to be at 35 nm.

 

Fig. 3 (a) Dependence of reflectivity of Ag mirror at 535 nm on Ag thickness (b) dependence of characteristic minimum (m = 3) FWHM and depth on Ag mirror layer 1 thickness for a fixed SiO₂ cavity thickness of 500 nm and Ag mirror layer 2 thickness of 125nm; inset image shows zoomed in graph of a region of interest.

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Using the same procedures for the Al₂O₃ AOMC, it was determined that the AOMC consists a 990 nm Al₂O₃ cavity layer and front and back Ag mirror layers 105 nm and 53 nm thick, respectively, with a 7th order transmission peak FWHM of 1.5 nm. The Al₂O₃ AOMC length was chosen to utilize a higher order reflecting feature since the deposition process for Al₂O₃ is more uniform and stable than SiO₂. We note that an even higher order mode could have been utilized for the Al₂O₃ AOMC structure but as shown in Fig. 2 the decrease in FWHM after the 7th order was minimal.

AOMC fabrication procedure

For this investigation, the AOMC structures were fabricated on commercially available 1” square aluminoborosilicate glass substrates or 2” diameter sapphire substrates sectioned into quarters. Substrates were thoroughly cleaned using organic solvents and acid (methanol & hydrochloric acid). Ag mirror layers were deposited by electron-beam evaporation which was chosen over sputtering to provide higher surface and interface smoothness. The cavity layers were deposited using ion-assisted deposition (IAD); selected for its capability for high spatial uniformity, simultaneous deposition of different dielectric layers, and particularly its accurate control over the deposition rate and application of plasma excitation for enhancing atomic mobility so as to achieve high density film depositions and sharp interfaces at low temperatures (20 °C). Note that achieving a high density cavity layer is very important as the density directly affects the refractive index and the dynamic loading behavior of the structure. Therefore, the use of IAD which provides precise control over the deposition rate is very important and is a less invasive deposition technique compared to techniques such as sputtering.

The thicknesses of the deposited layers were characterized using test coupons and a profilometer and the reflectance spectra and refractive indices were measured using a Filmetrics thin film interferometer system. After successful validation of the static spectral behavior, the fabricated AOMC structures were epoxied to a laser shock compression package for the dynamic loading experiment. Details of the dynamic loading experiment have been reported [8].

Result and discussion

Figure 4 shows the reflectance spectra of the simulated designs, along with the experimental data from the fabricated structures and refitted simulations based on these results. The parameters obtained from the original simulations and those measured for the fabricated structures are compared in Table 1. As shown on Fig. 4(a), the spectrum measured for the SiO₂ AOMC structure is shifted by 15 nm to shorter wavelengths compared to the targeted design, while no such shift is observed for the Al₂O₃ AOMC. For both structures, the fabricated devices have wider FWHMs and shallower minima than those predicted from simulations. The shifts in the reflectance spectrum and cavity modes for SiO₂ OMC structures are attributed to differences in the thickness and/or refractive index of the cavity layer as shown from the Eq. (1). Thus, the refractive indices and thicknesses of the deposited cavity layers were independently measured. The re-computed predictions employing these corrections reveal that the simulated peak locations are in excellent agreement with experiment. However, a disparity still exists in the depth of the reflectance minimum and FWHM between the experiment and simulations and this is attributed to the mirror layers. As discussed previously in Fig. 3, the depth of the minimum and FWHM in an asymmetrical OMC structure can be greatly influenced by the reflectivity of mirror layer 1. A decrease in the reflectivity of mirror 1 lowers the finesse, F, according to Eq. (3). This also increases the FWHM following the Eq. (2). The FWHM can also be affected by the small difference in refractive index of the cavity layer as it affects FSR according to Eq. (4). The fitted simulation results for both SiO₂ and Al₂O₃ AOMC structures reflecting the corrections of both the refractive index/thickness of the cavity layer and the reflectivity of the mirror layers reveal reflectance spectra in excellent agreement with the fabricated structures. However, it should be noted that some of the SiO₂ AOMC structures were unstable and exhibited different reflectance spectra (in green), as shown in Fig. 4(a). The SiO₂ AOMC structures were found to degrade even more over time and with light/atmosphere exposures due to the poor adhesion between SiO₂ and Ag [14]. Under dynamic loading, the signal-to-noise ratios were very low and spectral responses relied heavily on significant data processing/filtering to distinguish and monitor spectral shifts. This was due to insufficient depths in the characteristic minima exhibited for both fabricated SiO₂ and Al₂O₃ AOMC structures which can hinder their utility as dynamic loading sensors. Therefore, different designs with increased sample stability, minima depth, and narrower FWHM were developed and further investigated.

 

Fig. 4 Reflectance spectra of the simulated design, fabricated structures and the fitted simulation based on experimental results of (a) SiO₂ and (b) Al₂O₃ AOMC structures.

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Table 1. Comparison between simulated and experimental spectral characteristics

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Figure 5(a) shows a schematic of a modified SiO₂ AOMC structure designed to address the instability in the original SiO₂ AOMC structure due to poor adhesion between SiO₂ and Ag. As shown, a thin layer of Al₂O₃ was deposited at each SiO₂/Ag interface to enhance adhesion. Figure 5(b) compares the simulated and measured reflectance spectra of both the modified and the original SiO₂ AOMC structures and Table 2 lists comparisons of their key parameters. When comparing the experimental results, the modified design shows improvements in both the relative minimum depth and FWHM (9 versus 5 nm theoretical and 20 versus 8.5 nm measured) of the characteristic minimum. This is because the poor adhesion and high interfacial energy between Ag and SiO₂ not only affects sample stability but also its spectral properties. High interfacial energy leads to uneven thickness, high interface roughness, defects, and porosity of the deposited Ag layer which decreases its reflectivity as the evaporated Ag atoms minimize their interfacial energy by preferentially growing on previously deposited areas, leading to non-uniform thickness. Therefore, the incorporation of thin Al₂O₃ layers improved the stability and the reflectivity of the mirror layers and the increase in reflectivity of the mirror layers enhanced the spectral properties by narrowing the FWHM and increasing reflectance minimum depth for the modified SiO₂ AOMC structure.

 

Fig. 5 (a) Schematic of SiO₂ AOMC structure fabricated using Al₂O₃ adhesion layers and (b) comparison of simulated and measured reflectance spectra of modified and the original SiO₂ AOMC structure.

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Table 2. Comparison of parameter values between simulated and measured spectra for both the original and modified SiO₂ AOMC structures

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Figure 6 shows the spectral response of the modified design under application of ~4 GPa shock pressure, which was chosen to be significantly below the estimated Hugonist Elastic Limit (HEL) for fused SiO₂ [15]. This preliminary result clearly shows the high promise and feasibility of properly designed SiO₂ AOMC structures as very sensitive, fast response, dynamic loading sensors. At t = 0 (immediately before shock impact), the reflectance minimum is centered at 580 nm. The shock impact was almost instantaneously observed as a blueshift in the reflectance minimum of 22 nm within 3.3 ns of the shock wave impact, which is the approximate rise-time for the pressure pulse in the present laser-driven shock experimental setup. After 27.5 ns the reflectance minimum has decreased to 574 nm indicating that the structure quickly relaxes. For longer times, the magnitude of the blueshift decreases at a slower rate, and after 136 ns, displays a small redshift of ~0.8 nm, which is within the experimental error, and can possibly be due to a ringing effect. Figure 6(c) indeed clearly shows a two-step recovery exhibiting fast and slow release regimes with the relaxation times of 18.1 ns and 78.1 ns, respectively. This two-step behavior can mostly be attributed to the shape of the pressure pulse that laser-driven shock produces: a sharp rise followed by a slow, drawn out release back to low pressure. Also, some of the behavior can be due to the layers surrounding the cavity layer as they also release down from a higher pressure and will have their own behavior applying stress on the cavity layer. Lastly, there could be other contributing factors from the non-linear elastic decompression behavior of the SiO₂ to chemical bond length and bond angle restoration and crystallization [16], but it is very difficult to determine these phenomena and their effects accurately. Regardless, the monitoring cavity mode’s wavelength shifts observed and the data recorded after 3.3 ns, which is very close to the estimated response time of the structure, demonstrate that AOMC devices can be designed and fabricated with very fast response times for use as diagnostics for measurements of nanosecond resolution dynamic effects.

 

Fig. 6 (a) Spectral and temporal response of a modified SiO₂ AOMC device to a 4 GPa shock front. The spectra were recorded using a streak camera at different times to capture the shift in the reflectance minimum (mode 3) caused by the applied shock pressure. (b) The reflectance minimum over time and (c) change in the reflectance minimum position over time after shock propagation.

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Conclusions

In this study asymmetrical metallic OMC structures (AOMC) were shown to significantly enhance device utility for dynamic strain measurements with high temporal resolution (and the potential for high spatial resolution): limited only by the designed linewidth of the resonant mode. The study supports result of previous simulations [7] and initial experimental data that the thickness (and refractive index) of the cavity layer plays a major factor in determining the spectral position, mode number and FWHM of the reflectivity minima. As such, the reflectivity of the mirror layers is also shown to be critical to optimizing device design and required fabrication processes that ensured high stability, as well as ease of processability. The experimental results show that further improvements can be made in this area. It is concluded that for Ag/SiO₂/Ag AOMC structures, thin Al₂O₃ adhesion layers are best suited for this application and lead to the successful detection of a dynamic compression with a blueshift of 22 nm after 3.3 ns. At present, cavity materials with low refractive index and high modulus are shown to be most suitable, however, the lack of values of shock parameters of materials subjected to shock loading, and recent observations that device geometry is very important in determining these limits, illustrates the further potential to not only extend the sensitivity of these devices but also their use as a platform for monitoring the extreme limits of shock compression.