A novel 2D-surface shock pressure sensor is designed and tested based on 1D-Photonic Crystal, i.e., Distributed Bragg Reflector Multilayer (DBR/ML) structures. The fast opto-mechanical response of these structures to changes in layer thicknesses and refractive indices are ideally suited for dynamic pressure sensing. They offer the potential to minimize acoustic impedance mismatch between the material layers, and most importantly, the potential to monitor both temporal and spatial (lateral) variations during shock compression. In this feasibility study, different materials and device designs are investigated to identify material/device design combinations with optimum response to dynamic loading. Structural and material effects are studied in terms of spectral and mechanical properties, structure stability, and the ease of fabrication process. Structures comprising of different numbers of SiO1.5/SiO1.7 bilayer stacks are modeled, and fabricated. A 10-bilayer structure placed under a dynamic compressive load of ~7.2 GPa, exhibits a blueshift of 29 nm with a response time of ~5 ns which is well within the shock pressure rise time measured with PDV velocimetry. This promising result successfully demonstrates the feasibility of the specifically designed DBR/ML structure as a dynamic pressure sensor.
© 2017 Optical Society of America
Mesoscale heterogeneities in materials often play an important role in the macroscopic behavior of a system under dynamic or shock compression loading. Complex loading states driven by mesoscale interactions coupled with the limitation of current experimental diagnostic methods make understanding and predicting the behavior of such systems extremely difficult. Commonly used diagnostic tools employed today, have a temporal resolution sufficient to capture the dynamic response of a material with nanosecond resolution, but often have limited spatial resolution. For example, piezoelectric/piezoresistive stress gauges  typically provide nanosecond time resolution, but have spatial resolution of several millimeters which provides an averaged response. Laser velocimetry systems, such as the Velocity Interferometer System for Any Reflector (VISAR) , provides spatial resolution defined by the diameter of the laser beam (~0.5 mm), in spite of nanosecond time resolution. There are other techniques available such as line-VISAR and the Optically Recording Velocity Interferometer System (ORVIS)  that can provide sub-mm spatial resolution but only along a one-dimensional line profile.
Recently, optical structures have been investigated, to provide enhanced capabilities for dynamic load sensing. For instance, fiber Bragg grating sensors were investigated by Ravid et. al. , and Sandberg et. al. [4,5], demonstrating their capability for dynamic pressure sensing with the added advantages of low cost, potential for temperature sensing, and increased spatial resolution. However, their disadvantages include lower temporal resolution and limited in situ survivability (fiber fracture resulting in lost signal or poor signal quality that complicates analysis).
As a new approach to optical structure dynamic loading sensors, we recently proposed modifications to two mature 2D-surface optical devices: the asymmetrical optical micro-cavity (AOMC) and the Distributed Bragg Reflector Multilayer (DBR) structure . Both devices are typically characterized by an intense, characteristic peak (narrow transmission peak for AOMC, and reflectance peak for DBR), formed by additive interference at specific wavelengths whose position depends on the dimensions and refractive indices of the layers comprising the structure. The response to shock compression is to shift spectral features to shorter wavelengths where the magnitude of the shift is dependent on the change in optical path length (i.e. a decrease in layer thicknesses which in some cases can be partially offset by an increase in refractive index), at high pressure. In our prior work, we demonstrated the potential of AOMC structures as a dynamic loading sensor . This was accomplished by monitoring the pressure-induced shift of a transmission peak under dynamic loading. However, the experimental result demonstrated a few limitations of the AOMC. The AOMC structure investigated had metal mirror (Ag) layers with a dielectric cavity layer (SiO2) and to improve the adhesion between Ag/SiO2, thin layers of Al2O3 had to be incorporated. This combined with an impedance mismatch from the metal/dielectric interfaces can complicate the pressure analysis especially in heterogeneous loading scenarios. In contrast, a DBR structure can be constructed with layers of mechanically similar materials that have a lower impedance mismatch and good fabrication/structure compatibility. However, DBRs can have some disadvantages compared to AOMCs. As we showed in our previous work , the accuracy and sensitivity of the device to shock compression and changes in pressure was, respectively, directly proportional to the position of the characteristic spectral feature and its full-width at half-maxima (FWHM). For optical sensing, the intrinsic response time is determined by the thickness of the active sensor region and the speed of shock wave propagation through the structure. This time is estimated to be longer for the DBR structure due to its larger thickness; on the order of 600 ps as opposed to 100 ps for the AOMC. Furthermore, because of its multilayer structure, the DBR is expected to show a more complicated response than the simple spectral shift observed for the AOMC. Initially, the compression of the first few bilayers (BLs) will signal the emergence of a new peak at shorter wavelengths whose intensity progressively increases as the shock wave propagates through the structure, while in registration, the intensity of the fundamental (original) peak decreases eventually to zero . Thus, after the shock front has passed through the device, only the shifted peak will remain and later will move back to its original position as the device structure relaxes. This is another potential advantage of the DBR structure over the AOMC, whereby it can provide a spatial resolution in the direction of shock wave propagation. An important advantage of both the DBR and AOMC devices is their potential for measuring the 2D surface (areal) pressure profile across the device. Thus, the current theoretical and experimental study complements our prior work on AOMC sensors, to demonstrate the potential of DBR multilayer (ML) structures for dynamic load sensing. In this paper, we report the concept of the DBR/ML device including the criteria used for material selection, simulations of device performance to optimize the design, fabrication methods, and the results obtained from preliminary experimental studies.
2. Design criteria and material selection
For dynamic load sensing, it is extremely important to obtain a highly reliable structure that accurately produces a fast, observable response to the applied shock pressure. Therefore, achieving optimal device characteristics requires careful consideration of the class of materials, their optical and mechanical properties, and the ability to grow the structure in a reliable/reproducible way.
To achieve high spectral discrimination/resolution (positional sensitivity) for dynamic load sensing, a DBR multilayer structure must yield a narrow FWHM with a high reflectance peak for high signal-to-noise ratio. Also, the total thickness of the structure must be a few micrometers for relatively fast temporal resolution (~few nanoseconds). Lastly, the DBR structure should also be composed of layers with similar density and bulk modulus to minimize shock impedance mismatch (acoustic impedance, Z = C0 * ρ, where ρ is the density, C0 is the speed of sound , and is the elastic modulus). Impedance mismatch increases the mechanical equilibration time and causes high stresses to form at interfaces, making it difficult to estimate the pressure transferred to subsequent layers thereby increasing the complexity of the optical response and analysis. Thus, as explained earlier, a well-designed DBR multilayer can in principle offer an advantage over the previously investigated AOMC structure which consists of two metal mirror layers and a dielectric cavity layer that inherently creates a large impedance mismatch as density and modulus greatly differ between metals and oxides (Ag has ~2.2 times higher impedance than a-SiO2: density of Ag = 10.49 g/cm3, elastic modulus of Ag = 74 GPa, and density of a-SiO2 = 2.20 g/cm3, elastic modulus of a-SiO2 = 72 GPa) [8–12].
A search of materials exhibiting these attributes with low optical absorption (high transparency) and suitable mechanical properties led to the identification of polymer or metal- oxide based systems. It was preferable to use a material system, in which the refractive index can be compositionally tuned, to minimize impedance mismatch and also since there is a strong dependence of the peak reflectance and FWHM on the refractive indices and the difference in refractive indices as discussed later. Subsequently, different SiOx (1.0 < x < 2.0) compositions were chosen as the material for each layer as their refractive index is small and can be easily tuned between 1.41 and 1.97 at 500 nm by varying the atomic content of oxygen, x . A schematic of the typical DBR structure using SiOx material system is shown in Fig. 1. Each bilayer is stoichiometrically altered in oxygen content, so the refractive index is different (SiOA & SiOB with AB and ). Mechanical properties of these oxides are very similar for slightly different compositions and subsequently this will minimize the shock impedance mismatch (due to densities of SiO and SiO2 being between 2.13 to 2.20 g/cm3 and their elastic moduli between 92 to 72 GPa for x = 1 to 2, or a maximum of 11% or less shock impedance difference) [8–12]. Detailed examination of the properties of the SiOx system showed that for compositions with x < 1.27, the transmission was poor and that for alloys with x >1.91, the deposition process became difficult. Thus, the SiOA and SiOB (A ≠ B) compositions forming the multilayer were restricted to 1.27 ≤ A < B ≤ 1.91. Within this range the refractive index of SiOx lies between 1.46 and 1.89 at 500 nm, which allows significant flexibility in device design .
With the possible material chosen (and the range of refractive index set), simulations of the reflectance spectra were performed to find the optimized design using the classical Fresnel equation approach, as available in “OpenFilters” ; the Fresnel approach was chosen as it is well proven for both periodic and non-periodic structures and gives greater physical insight. The effects of various parameters such as material properties, thickness, refractive index of each layer, and the number of bilayers were investigated.
For dynamic loading analysis, the fabricated DBR structures were compressed against an ~50 µm thick aluminum layer backed by a borosilicate glass substrate with glycerin layers filling the air gap at every interface. The shockwave was generated by the aluminum layer absorbing the energy of an incident 3 J 1064 nm Nd:YAG laser pulse through the borosilicate glass substrate as shown in Fig. 1. This process produces a rapidly expanding plasma cloud at the substrate/aluminum interface that launches a shockwave through the aluminum layer and into the DBR structure. Simultaneously, broadband light from a Xenon flash lamp was reflected off the rear side of the DBR structure through the substrate. The reflected signal was directed into a custom high-throughput spectrograph and fast streak camera capable of recording a spectrum every ~0.225 ns. As the shock pressure propagates through the DBR structure, the thickness and the refractive index of each layer comprising the DBR structure is altered, resulting in the shift of the characteristic reflectance peak.
3. Simulation study
Simulations were conducted to determine an optimized DBR design for shock sensing with appropriate number of bilayers (BLs), mode number, total thickness and refractive indices for the layers. For our spectrograph/streak camera, the spectral sensitivity is maximized in the range of 400 to 600 nm, hence, the reflectance peak for the fabricated DBR sensor can be anywhere in this range. For the simulation studies, positioning the peak reflectance at 500 nm was used as an example for all the DBR structure calculations. Figure 2 shows simulations of the effects of the number of BLs, mode number (m), and the total device thickness on the peak reflectance and FWHM. The key spectral characteristics can also be analyzed using the following equations :Eq. (1), the condition is set to achieve the same optical path length for each layer in the bilayer. The reflectance peak is narrower and higher in intensity with an extra deposited layer of A, as observed by other researchers [16, 17].
From Eq. (1), the center wavelength of a peak depends on the thickness and refractive index of each layer in the bilayer. As mentioned previously, the refractive index of layer A and B were restricted between 1.46 to 1.89 based on the high transmission property (low absorption) of visible light and the ease of the fabrication process. To first investigate the effects of number of BLs and the mode number, the refractive index of layer A and B were chosen as 1.7 and 1.6, respectively. To position a reflectance peak at 500 nm for different mode numbers, the required thickness of each layer in the bilayer ( and ) should change (the thickness increases with mode number). As seen from Fig. 2(a), the FWHM of a peak, decreases with increasing mode number. The effect of the number of BLs is demonstrated from Fig. 2(a) and Eq. (2); the peak reflectance, R, increases and the FWHM decreases with increasing number of BLs. Therefore, it appears desirable to maximize the number of BLs and the mode number as it minimizes the FWHM (which improves the sensor sensitivity) and maximizes the peak reflectance (which improves the signal to noise ratio). However, the total device thickness as shown in Fig. 2(b), drastically increases causing the transient time of the shockwave through the device to increase, which subsequently decreases the temporal resolution of the sensor. Therefore, the appropriate device thickness for high optimal sensitivity needs to be balanced with the requirement for a sufficiently high temporal resolution. The deposition system used to deposit SiOx (discussed later), Ion Assisted Deposition (IAD) also has a limitation; the total thickness of the SiOx layers that can be deposited in a single run is limited to approximately 5000 nm. This is shown by the red dashed line in Fig. 2(b). This restriction limits us to utilize the 1st order peak with ≤ 30 BLs, 3rd order peak with ≤ 10 BLs, or the 5th order peak with ≤ 5 BLs. As seen from Fig. 2(a), the 5th order peak with 5 BLs would not have sufficient peak reflectance (~33%). The 3rd order peak with just 10 BLs has a high enough peak reflectance (~55%) as well as a narrower FWHM (14.5 nm) than the FWHM of the 1st order peak (27.5 nm) of the 30 BLs structure while having a comparable device thickness (4770 nm vs. 4552 nm). Whereas a structure with 30 BLs would have a higher peak reflectance (~90%), there would be added fabrication complexity and interfaces present in the structure. Therefore, in this study, DBR structures with 3rd order mode number were selected for the design of the shock sensor, with ~10 BLs desired for better sensitivity.
Figure 3 shows the effect of the difference in the refractive indices (Δn) between the layers comprising the bilayers on the reflectance spectra for the 10 BL structure utilizing the 3rd order reflectance peak positioned at 500 nm. The effect of the refractive index difference between the layers on the FWHM of the first order mode is given by the expression :
As observed in Fig. 3(a), a decrease in Δn improves the sensitivity of the device by decreasing the FWHM. However, it also decreases the peak reflectance, which subsequently lowers the signal to noise ratio thus making the tracking of the peak shift under dynamic loading more difficult. For 10 BLs with a 3rd order reflectance peak at 500 nm, the FWHM is minimized (14 nm) when Δn = 0.05 but the peak reflectance value is too low (~35%) compared to Δn = 0.10 (~15 nm, ~50%) as shown in Fig. 3(b). Even though Δn = 0.15 has a higher peak reflectance with moderately low FWHM (~68%, 22 nm), Δn = 0.10 was chosen to minimize the impedance mismatch (as higher Δn increases Δx in SiOx which increases the density and modulus difference thus creating a larger impedance mismatch). Also, fabrication variations (in terms of thicknesses and the refractive indices of the deposited layers compared to simulation values) would affect the FWHM (which widens the peak) more than the peak reflectance value. Therefore, from these simulation studies for the effects of various parameters, it was determined that the SiOA/SiOB DBR structure with Δn = 0.10 (nA = 1.7 and nB = 1.6) has optimized attributes for use as a dynamic loading sensor.
For a 10 BL design, it would have an optical response to shock compression of approximately 0.9 ns (which is basically limited by the acoustic response of the device as light travels orders of magnitude faster than the shock wave velocity); assuming there is no equilibration time required and that the shock travels at around 5500 m/s (0.9 ns = ~5 μm / 5500 m/s). The sensitivity of the device depends on the FWHM, magnitude of the peak shift, as well as the signal to noise ratio of the peak. Using the Equation of State (EOS) and optical property data for SiO2 from Ref . and assuming that the SiOA/SiOB layers will have similar responses to SiO2, it was estimated that the refractive index will increase by 3-4% and the layer thicknesses will decrease by 13-14% under a uniaxial shock compression load of ~7 GPa. The increase in refractive index partially offsets the decrease in layer thickness, resulting in a smaller net change in optical path and a theoretical shift of ~43 nm at a ~7 GPa load using Eq. (1) and the material property data for SiO2. Without considering the signal to noise ratio, the sensitivity of the device may be estimated using the Rayleigh criteria which is used to differentiate two peaks that are present at the same time. The Rayleigh criteria says that two peaks can be distinguishable when they are at least apart by FWHM (15 nm). Thus, according to the Rayleigh criteria, the minimum strain (FWHM) that can be measured compared to the maximum wavelength shift is ~33% (15 nm/45 nm). The absolute accuracy in measuring the position of a peak would be around 3% (FWHM/peak position). However, these are overestimates and the accuracy and the sensitivity of the device are most likely better as we are monitoring a peak shift and not differentiating between two peaks that are present at the same time. On the other hand, we can track the peak shift induced reflection intensity change at the initial peak position, potentially with better sensitivity.
4. Device fabrication and dynamic loading experiments
Following the design phase, DBR structures were fabricated on commercially available 2” diameter fused silica substrates. Immediately prior to growth, the substrates were thoroughly cleaned using solvents and acid (methanol & hydrochloric acid). The alternating layers of SiOA and SiOB (A ≠ B) forming the bilayers were deposited sequentially using Ion-Assisted Deposition (IAD). We started by depositing single layers and characterizing them to determine the deposition parameters used to control the refractive index of the film. IAD is capable of controlling various parameters such as precise plasma conditions for added atomic mobility and oxygen flow for atomic composition of the deposited layer. By using IAD we could precisely control and tune the refractive index of the deposited layer. The stoichiometric oxygen content in SiOx was varied by using a different O2 flow rate from 0 to 30 sccm (standard cubic centimeters per minute) at room temperatures for growth rates of 0.2 nm/s. The range of x values for the deposited SiOx layer was approximated to be in between 1.30 to 1.91 using EDX and the refractive index of the deposited layer was between 1.51 and 1.75 at 500 nm. The deposited layer exhibited high transmission (low absorption) to visible light as in . It should be noted that the total thickness of the SiOx layers deposited in a single run was limited to a maximum thickness of ~5 μm using two different thermal boat sources (2.5 μm per boat). To obtain a thicker DBR structure, the IAD chamber was vented to replenish the raw material. The thicknesses of the deposited layers were characterized using a profilometer. The reflectance spectra and refractive indices were measured using a Filmetrics thin film interferometer system.
After calibrating the thickness and the refractive index of the deposited single layers and obtaining the optimal IAD deposition conditions, DBR structures peaked between 400 and 600 nm were grown using different IAD conditions on multiple test substrates. The DBR structure was fabricated using 10 and 20 sccm oxygen flow rates to deposit layer A and B, respectively in the effort to match the optimized design determined from the simulations. The oxygen composition of the deposited layers A and B was estimated to be 1.51 and 1.8 respectively, and their corresponding refractive index was approximated to be 1.65 and 1.55, respectively. Assuming a linear dependence of both density and modulus between SiO and SiO2, the acoustic impedance mismatch between the layer SiOA and SiOB is estimated to be around 3.3% for the fabricated structures.
Figure 4 shows the reflectance spectra of a (a) 5 BLs and (b) 10 BLs fabricated DBR structures with total thicknesses of ~2 μm and ~5.2 μm, respectively. For the 5 BL sample shown in Fig. 4(a), the simulation shows a peak at λ3 ≈435 nm for layer A and B thicknesses of, dA = 192 nm and dB = 204 nm, which is close to the designed structure using a mode number m = 3 and Δn = 0.1. The FWHM (27.3 nm) of the peak of the fabricated structure is much wider than simulated (19.5 nm), indicating a relatively large thickness variation actually existed in the deposited layers due to fabrication error. However, the relative peak reflectance value remained high (~36.6%) and close to the simulation (32.3%). For a 10 BL sample peaked at λ3 ≈570 nm shown in Fig. 4(b), the fabricated structure was constructed with thicker bilayers (dA ≈252 nm, and dB ≈267 nm). The obtained reflectance spectra also showed a wider FWHM of 23.8 nm than the simulation (16.5 nm) due to fabrication error, but it is narrower than the FWHM of fabricated 5 BLs as expected. Also, a much higher reflectance of 69.5% was obtained which is excellent for improved signal-to-noise under shock sensing. The higher experimental reflectance (69.5%) than the simulation (55.2%) may indicate a higher refractive index and/or Δn in the fabricated structure than that used in simulation. It should be noted that 10 BLs were successfully deposited in a continuous single IAD run. Although they are not as perfect as what we designed using simulations, the 5 and 10 BL DBRs served as excellent testing structures for preliminary shock studies discussed below.
Figure 5 shows the dynamic loading experiment results conducted on a 10 BL sample under an approximately 7.2 GPa peak pressure at different times during laser shock loading. The result clearly shows the promising feasibility of the specially designed DBR structure as a dynamic shock pressure sensor. At t = 18 ns (just before the shock pressure rise), the reflectance spectrum shows a peak reflectance at around 564 nm. Just after the arrival of the shock wave (t = 20 ns), the characteristic peak starts to blueshift until at t = 25 ns it reaches a maximum blueshift of ~29 nm. The rise time is defined as the time required for a pulse rise from 10 to 90% peak amplitude. The blueshift rise time corresponds closely to the measured velocity rise time of ~5 ns from simultaneous Photon Doppler Velocimetry (PDV) monitoring the interface of the aluminum layer and DBR structure as shown in Fig. 1, and is also similar to the temporal response of the SiO2 AOMC structure reported in our previous work . Note that the theoretical transit time of a single pass of an ~7.2 GPa shock wave through the ~5 µm thick DBR structure is about 0.9 ns. At later times the blueshift begins to decrease corresponding to pressure relaxation from the laser-induced shock pressure profile, but with a notable shoulder at t = 35 ns likely due to shock reflection effects at the Aluminum/borosilicate glass interface, again showing excellent correlation with the PDV data. The appearance/disappearance of the original and shifted DBR peaks as proposed in our prior simulation results , was not observed in the experimental data, likely due to the fast pressure rise time and limited temporal resolution of the streak camera (~0.225 ns between individual spectra). Additional bilayers would increase the probability of observing this effect, but to the detriment of the structure’s temporal resolution due to increased overall device thickness.
Comparing the observed shift of ~29 nm for the 10-BL DBR structure to the estimated shift of ~43 nm, it appears that the actual pressure experienced by the DBR is expected to be complicated by reverberations, echoes, and potential reflections of the acoustic waves at interfaces (Al layer/SiOA, SiOA/SiOB & SiOA/Fused Silica). Additionally, the material models used in simulations  may not apply as well to the SiOA/SiOB nano-layers as assumed, thus leads to an overestimated theoretical shift. On the other hand, material production and characterization imperfections will also cause model/experiment quantitative disagreements. The diffusion of O between adjacent layers and roughness likely leads to the effects observed. These considerations make it difficult to estimate the intrinsic response of the structure and require comprehensive simulations to unambiguously analyze the observed shifts and temporal behavior. Additional experimental testing at a series of different pressures is currently underway to provide more evidence to evaluate these theories. As a consequence, we believe that these devices, in addition to their potential sensor applications, have an added importance in that they provide the data to develop rigorous models for understanding of shock propagation in well characterized material structures. Rigorous proofs of these models will then allow their use for accurately analyzing heterogeneous shock-compression loading conditions. Also, empirical pressure calibration can be performed for high accuracy before application of these devices for 2D-surface sensing or as embedded probes. Nevertheless, the preliminary result clearly indicates that DBR optomechanical structures, similar to the AOMC structures, can successfully perform dynamic pressure sensing with nanosecond level temporal resolution. In future studies, an ultrafast camera with band-pass filters at the initial DBR reflectance peak wavelengths will be used for 2D-imaging and determination of the spatial (lateral) resolution of the sensor, potentially demonstrating spatial pressure variations during shock compression.
5. Summary and conclusion
From in-depth simulations, it was determined that finding the optimized DBR design is critical in order to maximize the shock sensor performance; an ideal DBR dynamic pressure sensor should have well defined spectral features (high peak reflectance, narrow FWHM) with good acoustic/structural properties (mechanically similar materials for minimized impedance mismatch, a relatively thin structure and high speed of sound for fast temporal resolution), and fabrication feasibility. A DBR multilayer structure utilizing two different SiOx compositions was chosen as it can be fabricated relatively easily and it provided flexibility in optical properties (variable refractive index) with low acoustic impedance mismatch between the layers. Although utilizing a high order reflectance peak, a large number of bilayers, and a relatively low difference in refractive indices would result in a very high and narrow reflectance peak width, this would tremendously increase the total thickness of the device and consequently decrease its temporal resolution, as well as increase fabrication difficulty. Consequently, the DBR structure was optimized considering the interplay between the optical properties, the temporal resolution and the manufacturing limitations. Working within the total thickness restriction currently set by the fabrication tool, it was determined that the optimized design would be composed of ~10 SiOA and SiOB bilayers with refractive indices of about 1.7 and 1.6 respectively, at a wavelength of 500 nm, with a 3rd order mode peak between 400 and 600 nm. Subsequently, a fabricated 10 bilayer DBR structure was placed under a dynamic load of ~7.2 GPa and the reflectance peak blueshift of ~29 nm was detected in ~5 ns, with a time-resolved blueshift profile in excellent consistence with simultaneous PDV velocimetry data. This preliminary result successfully demonstrates the promising potential of the DBR structure as a shock pressure sensor, complimenting the previously reported AOMC shock sensor with the added advantage of the minimized impedance mismatching between the layers of the structure. Furthermore, it provides robust experimental results to guide and develop rigorous simulation models, which can be used to analyze more complex loading conditions and potential sensing applications.
Defense Threat Reduction Agency (DTRA) (HDTRA1-12-1-0052); National Sciences and Engineering Research Council of Canada (NSERC) (PGS-D); Department of Defense (DoD) (NDSEG); Air Force Office of Scientific Research (AFOSR) (FA9550-151049); Independent Research and Development funding from Georgia Tech Research Institute.
References and links
1. R. A. Graham, F. W. Neilson, and W. B. Benedick, “Piezoelectric Current from Shock‐Loaded Quartz—A Submicrosecond Stress Gauge,” J. Appl. Phys. 36, 1775–1783 (1965).
2. L. M. Barker and R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
3. D. Bloomquist and S. Sheffield, “Optically recording interferometer for velocity measurements with subnanosecond resolution,” J. Appl. Phys. 54, 1717–1722 (1983).
4. A. Ravid, E. Shafir, S. Zilberman, G. Berkovic, B. Glam, G. Appelbaum, and A. F. Gefen, “Fibre Bragg Grating sensor for shock wave diagnostics,” J. Phys. Conf. Ser. 500, 142029 (2014).
5. R. L. Sandberg, G. Rodriguez, L. L. Gibson, D. M. Dattelbaum, G. D. Stevens, M. Grover, B. M. Lalone, and E. Udd, “Embedded optical probes for simultaneous pressure and temperature measurement of materials in extreme conditions,” J. Phys. Conf. Ser. 500, 142031 (2014).
6. D. Scripka, G. LeCroy, C. J. Summers, and N. N. Thadhani, “Spectral response of multilayer optical structures to dynamic mechanical loading,” Appl. Phys. Lett. 106, 201906 (2015).
7. G. Lee, D. A. Scripka, Z. Kang, N. N. Thadhani, and C. J. Summers, “Asymmetrical optical microcavity structures for dynamic pressure sensing: design, fabrication, validation,” Opt. Express 24(20), 23494–23504 (2016). [PubMed]
8. R. B. Ross, Metallic Materials Specification Handbook (Springer US, 2013).
9. A. I. H. Committee, Properties and Selection: Nonferrous Alloys and Special- Purpose Materials (ASM International, 1990).
10. A. Nayar, The Metals Databook (McGraw-Hill, 1997).
11. D. R. Lide, CRC Handbook of Chemistry and Physics, 85th Edition (Taylor & Francis, 2004).
12. M. Bauccio, ASM engineered materials reference book (ASM International, 1994).
13. S. M. A. Durrani, M. F. Al-Kuhaili, and E. E. Khawaja, “Characterization of thin films of a-SiO x (1.1< x <2.0) prepared by reactive evaporation of SiO,” J. Phys. Condens. Matter 15, 8123 (2003).
14. S. Larouche and L. Martinu, “OpenFilters: open-source software for the design, optimization, and synthesis of optical filters,” Appl. Opt. 47(13), C219–C230 (2008). [PubMed]
15. C. J. R. Sheppard, “Approximate calculation of the reflection coefficient from a stratified medium,” J. Euro. Opt. Soc. Part A 4, 665 (1995).
16. M. Kolle, B. Zheng, N. Gibbons, J. J. Baumberg, and U. Steiner, “Stretch-tuneable dielectric mirrors and optical microcavities,” Opt. Express 18(5), 4356–4364 (2010). [PubMed]
17. A. L. Álvarez, J. Tito, M. B. Vaello, P. Velásquez, R. Mallavia, M. M. Sánchez-López, and S. Fernández de Ávila, “Polymeric multilayers for integration into photonic devices,” Thin Solid Films 433, 277–280 (2003).
18. L. R. Brovelli and U. Keller, “Simple analytical expressions for the reflectivity and the penetration depth of a Bragg mirror between arbitrary media,” Opt. Commun. 116, 343–350 (1995).
19. R. E. Setchell, “Index of refraction of shock‐compressed fused silica and sapphire,” J. Appl. Phys. 50(12), 8186–8192 (1979).