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1D photonic crystal strain sensors Tsan-Wen Lu, Chia-Cheng Wu, and Po-Tsung Lee ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00560 • Publication Date (Web): 05 Jul 2018 Downloaded from http://pubs.acs.org on July 5, 2018
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ACS Photonics
1D photonic crystal strain sensors Tsan-Wen Lu*, Chia-Cheng Wu, and Po-Tsung Lee* Department of Photonics, College of Electrical and Computer Engineering, National Chiao Tung University, Rm. 401 CPT Building, 1001 Ta-Hsueh Road, Hsinchu 30010, Taiwan. KEYWORDS: photonic crystals, nanocavity, optical sensors, strain sensing, semiconductor nanolasers
We introduce a photonic crystal nanocavity consisting of one-dimensional periodic nanorods embedded in a deformable polydimethylsiloxane substrate, which exhibits a high-quality factor and a large wavelength response to the applied strain. By further investigating its wavelength response to non-axial planar strains, we propose and experimentally demonstrate a sensor unit that can precisely identify different planar strains, including their application direction, type, and value. This sensor prototype with small footprint and feasible coupling with optical waveguides could provide additional flexibility for strain analysis in a wide range of fields.
Photonic crystals1 (PhCs) are artificial materials with unique photonic band-gap and band structures. Their capability for on-demand guiding and banning photon flows in wavelength-scale spaces is well-document. Over the past decades, various functional PhC devices that are crucial for constructing versatile nano-photonic chips and replacing electronic integrated circuits2 had been proposed and demonstrated. Among the numerous functions, optical sensing via PhC waveguides3 and cavities4 is interesting and practical to our daily lives. This is typically achieved by measuring and analyzing the change of tailored optical fields within welldesigned PhC nanostructures caused by perturbations of interest (physical quantities that are sensed). According to the perturbation type, the PhC sensors can be roughly classified into groups such as biological, chemical and mechanical. Bio/chemical sensing is usually based on the effective refractive index change of the PhC cavities and waveguides with predesigned lattice structures, and the functionalized layers for specific analyte.5−7 On the other hand, unlike the bio/chemical sensors, mechanical/deformation sensing usually utilize PhC nanostructures with mechanically variable lattices or flexible platforms. For example, PhC devices can be integrated as actuators into micro-electromechanical systems8,9, whose actuating distances are monitored by their corresponding change in optical coupling wavelength. As an alternative, one can integrate PhC cavities and waveguides into mechanically unstable platforms10, for example, fibers11, cantilevers12, and deformable carriers13−19, under applied strain. In such a case, the lattice or device structure can be easily deformed to produce a significant change in the optical properties, and this serves as the basis for sensing deformations. Among these methods, the placement of PhC devices on/within deformable carriers has yielded high flexibility for on-chip integration and ease of manufacturing. In recent years, various PhC mechanical sensors13−19 based on this architecture have been proposed and demonstrated for measuring curvature, strain, displacement, pressure, etc. However, there are still limitations associated with these procedures. Firstly, most of them still utilize 2D PhCs with large device footprints and their band-edge modes
with extended mode profiles also show low compatibility with planar waveguides. Secondly, all the presented sensors are operated under predetermined strain types and directions. This means they actually did not identify an unknown planar strain. In this report, we introduce a tunable 1D PhC nanolaser with a large wavelength response to structural deformation. By further investigating its optical properties under non-axial planar strains, a sensor unit prototype that can identify an unknown planar strain, including its application direction, type, and value, is proposed and demonstrated.
Figure 1. (a) Structure and parameter definitions of a 1D PhC waveguide buried within a PDMS substrate. (b) Schematic of wavelength shift of propagating photonic mode in PhC waveguide under lattice elongation. (c) Theoretical transverse-electric-like dielectric bands (the 1st band) of the 1D PhCs (with w, L, and a of 135, 920, and 340 nm respectively) under ξ of 0.1, 0, and -0.1. (d) PhC nanocavity design based on the modulated lattice constants (a, a1, a2, …) and widths (w, w1, w2, …). (e) Theoretical mode profiles in |E|2 fields of the extended (left, without nanocavity) and locally confined (right, with nanocavity) dielectric modes in PhC waveguides.
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Figure 2. (a) Schematic of PhC nanocavity under compressive strain oriented to the lattice direction by an angle α and the orthogonally induced stretching strain. (b) The FEM simulation setup of the PhC nanocavity with α = 45° embedded within PDMS under ξ = -0.05 along the x-axis, (c) the accumulated displacement distribution of the PDMS in the x- and y-directions, and (d) the calculated positions of the displaced lattices.
Figure 1(a) shows the schematic of a 1D PhC waveguide formed by periodically arranged dielectric nanorods with lattice constant a, width w, and length L, buried in a deformable polydimethylsiloxane (PDMS) substrate. Due to its structural discontinuity, the lattice structure can be easily changed along with the surrounding PDMS when a deformation is applied, which accompanies the wavelength shift ∆λ of the propagating photonic mode within, as illustrated in Fig. 1(b). Figure 1(c) shows the 1st photonic bands (dielectric bands) of the PhC waveguide under applied stretching and compressive strains ξ of 0.1 and -0.1 along the lattice direction, where ξ is defined as the ratio of the deformed (∆l = l- l0) and the original length (l0) of the PDMS substrate. The shifting of these bands results in a ∆λ of 8.0 nm for ξ of 0.01, which indicates a relatively large wavelength response to the applied strain compared to previously reported values.14−17,19 To locally confine the propagating dielectric mode with low loss, w and a of the nanorods are both linearly increased in 10nm increments from the center to the edge of the waveguide to form a nanocavity with mode gap confinement, as shown in Fig. 1(d). Figure 1(e) shows the theoretical dielectric mode profiles for the |E|2 fields in the PhC waveguide with (right) and without (left) a nanocavity for an applied ξ from 0.1 to 0.1 by 3D finite element method (FEM). With mode-gap confinement along the waveguide, the nanocavities show much higher quality factors (Qs) and stronger field intensities (smaller effective mode volumes (Veff)) than those without nanocavities. When ξ is varied from 0.1 to -0.1 in both cases, the increased w/a ratios accompanied by the increased dielectric confinement (γ) factor of the modes will simultaneously result in an increased Q and a decreased Veff. In addition, the nanocavity shows very large wavelength responses of ±7.8 nm to ξ of ±0.1, which has been demonstrated experimentally in our previous report as a tunable nanolaser.18,20 This wavelength response also indicates a minimum detectable displacement of less than ±2 nm for a device length of 10 µm (minimum detectable ξ < ±2×10-4) and a Rayleigh distinguish-
able spectral linewidth of 0.16 nm after lasing. This is promising for realizing a highly sensitive strain sensor, especially for small strain variation. Although the limited gain spectrum linewidth (~150 nm) of the quantum-wells (QWs) we used in the following manufacturing process would restrict its sensible range (∆ξ < 0.2) for large strain, this could be improved by realizing our present design in a passive manner. However, similar to other reports, the strain application direction was still predetermined along the waveguide (x-axis) in our previous demonstration. To further investigate its capability to detect an unknown planar strain, we studied its optical properties under different strains along different directions. Figure. 2(a) shows the schematic for lattice deformations of the PhC nanocavity under compressive strain oriented to the lattice direction at an angle of α. Because of the positive Poisson ratio (ν ~ 0.495) of PDMS, the application of a compression ξL to the PDMS along the x-axis as shown in Fig. 2(a) will lead to an induced elongation νξL that is orthogonal (yaxis) to the strain application direction. This gives rise to displacements of cosα·ξL (compressive) and sinα·νξL (stretching) to the lattices in two orthogonal directions respectively, which are represented by blue and red arrows in the inset of Fig. 2(a). A similar phenomenon will occur when applying stretching strain along the x-axis. The prediction in Fig. 2(a) was then verified by 3D FEM. In the simulation setup shown in Fig. 2(b), the planar forces are applied on two opposite planes of the PDMS substrate to deform the device embedded inside. And the other planes are set as free in all directions. Figure 2(c) shows the accumulated displacement distributions of the PDMS with the nanocavity in the x- and y-directions, which clearly indicates the origin of the lattice deformation. Fig. 2(d) shows the displaced lattice positions of the PhC nanocavity with α = 45° under an applied ξ of -0.05 along the x-axis. The lattice contour color represents the accumulated total displacement. The magnified displaced lattices in the inset of Fig. 2(d) agree with our expectation in Fig. 2(a) quite well. The simulated deformed meshes are then used to calculate the change of the optical resonance of the nanocavity. Figures 3(a) and (b) show the theoretical ∆λ of the nanocavities with different α under ξ from 0 to ±0.05 along the x-axis. In Fig. 3(a), the blue-shift of the wavelength is completely attributable to the applied compression along the x-axis when α = 0°. However, in the range of 0° < α < 90°, it gradually decreases because of the reduced lattice compression and the increase of the lattice elongation with the increased α along and orthogonal to the direction of applied deformation. When α > 57°, the ∆λ changes to a red-shift due to the domination of the orthogonally induced elongation. When α = 90°, the induced elongation is completely responsible for the red-shift. A similar process alsooccurs during the application of a stretching strain to the nanocavity. Figures 3(c) and (d) show the theoretical mode profiles of the |E|2 fields of the nanocavities with α = 30° and 75° under ξ of ±0.05 along the x-axis via FEM. In Fig. 3(c), the nanocavity with α = 30° shows a higher Q value than that with α = 75° under ξ of -0.05. This is because the resultant lattice deformation of the latter is stretched, which leads to a degraded γ factor, as we discussed in Fig. 1(e). The nanocavity with α = 30° exhibits a lower Q value than that of α = 75° under ξ of 0.05 as shown in Fig. 3(d), for the same reason. The slight Q fluctuations (in the same order) and the very small field intensity variation shown in Figs. 3(c)
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ACS Photonics and (d) can guarantee mode stability under strain for high sens i t i v i t y
Figure 3. Theoretical (curves) and measured (open squares and circles) ∆λ of the nanocavities with different α under ξ from 0 to (a) 0.05 and (b) 0.05 along the x-axis. Theoretical mode profiles of the |E|2 fields of the nanocavities with different α of 30° and 75° under ξ of (c) -0.05 and (d) 0.05 along the x-axis.
application. In addition, it is interesting that all the curves in Figs. 3(a) and (b) intersect at α = 57°, where the ∆λ caused by the applied and induced lattice displacement compensate for each other, and therefore shows no response to the applied strain. This insensitive angle αin is determined by the Poisson ratio of the PDMS substrate and could be useful in the following sensing operations. Figure 4(a) briefly shows the flowchart of the manufacturing process for the device presented in Fig. 1(a). Firstly, the PhCs are fabricated by a series of electron beam lithography and dry etching processes on InGaAsP QWs. Then the PhCs are embedded into a PDMS substrate, and the underlying InP substrate is removed. The exposed surface is then sealed by PDMS.20 Figure 4(b) shows a tilted-view scanning electron microscope (SEM) image of the PhC nanocavity before embedding into the PDMS substrate. The nanocavities with different α from 0 to 90° (denoted as A to L) shown in the optical
microscopic and SEM images in Figs. 4(b) and (c) are also manufactured via the described process. In measurements (see Fig. S1(a) in the supplementary data), the excitation laser pulse with 1 MHz repetition rate and 15 ns pulse width is used to excite the nanolasers at room temperature (see Fig. S1(b) in the supplementary data). During measurements, a strain is applied to the PDMS substrate with ξ from 0 to -0.05 along the x-axis via our strain testing stage. Under excitation by a laser pulse at room temperature, their acquired lasing spectra are shown in Fig. 4(d). Taking ξ = 0.05 for example, the nanocavity A shows a wavelength shift (∆λ-0.05) of -35.7 nm (blue-shift), while the nanocavities B to G show gradually decreased blue-shifts (from -34.8 nm to -1.1 nm). For nanocavity H (α = 60°), the ∆λ-0.05 becomes a redshift of 3.0 nm, where the induced elongation along the y-axis dominates the ∆λ as we predicted from the simulation. For nanocavity L (α = 90°), the ∆λ-0.05 shows a red-shift of 17.4 nm that is completely attributed to the induced stretching strain along the y-axis. The measured ∆λ-0.05 of the nanocavities with different α are recorded by open circles and squares in Fig. 3(a), as well as those under ξ of 0.05 (∆λ0.05) in Fig. 3(c). (Their spectra are shown in Fig. S2(a) in the supplementary data) They all agree with the simulation results quite well. Figure 4(e) further shows the spectra of device G with α = 53° under ξ from 0 to -0.05 along the x-axis. In this case, a very small ∆λ-0.05 of -1.1 nm is observed. This is very close to the invariant ∆λ at αin = 57° we predicted in Fig. 3(a). In addition, a small ∆λ0.05 of 1.4 nm for nanocavity G under an applied ξ of 0 to 0.05 along the x-axis is also confirmed. (See Fig. S2(b) in the supplementary data) According to the aforementioned simulation and experimental results, a database can be built in the process of designing a sensor unit capable of identifying an unknown planar strain, including its direction, type, and value. Figure 5(a) shows the schematic of our proposed sensor unit which consists of three PhC nanocavities V1, V2, and V3 arranged at arbitrary angles ϴ12 and ϴ13 in the first planar quadrant. The titled view SEM and optical microscopic images in Fig. 5(b) show the fabricated sensor unit with ϴ12 and ϴ13 of 20° and 85° respectively, relative to the x-axis. By recording the ∆λ of the nanocavities under strain and fitting them with the built data bases based on Figs. 3(a) and (c), the information for the applied planar strain can be precisely analyzed. During the experiments, blind sensing tests are performed by different executors and analyzers. For example, the lasing spectra measured
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Figure 4. (a) Flowchart of the manufacturing process for the PhC nanocavity buried in a PDMS substrate. (b) (top) Tilted-view SEM image and (bottom) microscopic images of PhC nanocavities before and after embedding within the PDMS substrate. (c) Top-view SEM images of the PhC nanocavities with different α from 0° to 90° (denoted as A to L). (d) Lasing spectra of nanocavities A to L under ξ from 0 to -0.05 (in -0.01 increments) along the x-axis. (e) Lasing spectra of nanocavity G (α = 53°) under ξ from 0 to -0.05 along the x-axis.
Figure 5. (a) Schematic, (b) tilted-view SEM (before embedding in PDMS), and optical microscope images (after embedding in PDMS) of our proposed sensor unit consisted of three nanocavities V1, V2, and V3. (c) (e) Lasing spectra and (d) (f) the ∆λ fitting with the simulation results of the sensor unit under ξ of 0.012 at -60° (actually applied: ξ of 0.01 at -60°) oriented to the x-axis and ξ of -0.033 at -40° (actually applied: ξ of -0.03 at -40°) oriented to the x-axis.
from nanocavities V1, V2, and V3 in Fig. 5(c) exhibit ∆λ of -1.0, -4.0, and 4.9 nm respectively. By fitting them with the data base shown in Fig. 5(d), we can easily identify that the applied ξ is 0.012 in the direction of -60° relative to the x-axis. For the test shown in Figs. 5(e) and (f), the ∆λ fitting clearly identifies an applied ξ of -0.033 from the direction of -40° relative to the x-axis. In addition, because the nanocavity V3 shows an almost invariant ∆λ of 0.2 nm in this case, one can approximately identify the strain direction as close to ±57° (±αin) oriented to nanocavity V3. Then, the strain type and value can be identified by fitting the ∆λ to an arbitrary one of the other nanocavities within the database. This means that the insensitive angle αin can simplify the sensing operation for specific strains. Other tests for different applied strains are provided in Figs. S3(a)−(c) in the supplementary data. Comparing with the actually applied strains indicated in the captions of Figs. 5(c)-(f) and Figs. S3(a)-(c), the fitting results correctly identify the applied strain directions, but show small deviations of 0.0010.003 in strain value identification. These deviations might be caused by the different fluctuations arisen from the varied effective excitation power (thermal dissipation of the nanolaser) or non-uniform deformation during measurement of each data point. Nevertheless, these results still clearly show the capability to identify an unknown planar strain using the proposed sensor unit. To further realize dynamical strain sensing, the nanocavities in this sensing unit can be excited at the same time by a single pumping spot or integrated with coupling waveguides for leading in/out their optical signals in a passive manner for practical applications. Furthermore, due to the small device footprint of the PhC nanocavity, the size of the sensor unit shown in Fig. 5(b) is smaller than 80 µm2. Although this can be further reduced by constructing the sensor unit with only two nanocavities, invalid sensing results may occur under certain strain conditions (see Figs. S4(a) and (b) in the supplementary data). Therefore, three nanocavities are the minimum number required to con-
struct our proposed sensor unit with reliable sensing results. Indeed, with an admissible increase in the footprint of the sensing unit, one can reasonably add as many nanocavities as required, which means more data points for fitting with the curves in the database. This could minimize the deviation caused by the fluctuations for each measured data point we mentioned above for better sensing accuracy. In conclusion, based on the 1D PhC nanolaser embedded in a PDMS substrate with a large wavelength response to strain, we theoretically and experimentally studied its optical properties under different planar strains in different directions, in this report. The results can serve as a database for our proposed sensor unit composed of three nanocavities arranged at arbitrary angles in the first planar quadrant. By fitting their wavelength shifts with the database, the sensor unit can precisely identify different unknown planar strains, including their direction, type, and value. To the best of our knowledge, this capability to identify strain based on a PhC device has been proposed and demonstrated for the first time in reported literature. The compact device footprint and feasible coupling via different waveguide architectures21-22 can also facilitate high flexibility for on-chip integration. We believe that this demonstrated sensor prototype in a polymer-based architecture could be easily integrated into different platforms and provide new possibilities for strain analysis in a wide range of fields.
ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: Figure S1 show the measurement setup and lasing properties of 1D PhC nanolaser. Figure S2 shows the lasing spectra of PhC nanocavities with different α under different stretching ξ. Figure S3 shows other tests for different applied strains. Figure S4 and Note S1 predict the invalid sensing results from sensor unit composed of two nanolasers under certain strain conditions.
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ACS Photonics
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected]. *E-mail:
[email protected].
ORCID Tsan-Wen Lu: 0000-0003-4108-1815 Po-Tsung Lee: 0000-0003-4116-3781
ACKNOWLEDGMENT The authors acknowledge the financial support from Ministry of Science and Technology (MOST), Taiwan, under 106-2221-E009-124-MY2. We also sincerely thank the Center for Nano Science and Technology of the National Chiao Tung University of Taiwan for the assistance in fabrication facilities.
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1D photonic crystal strain sensors Tsan-Wen Lu*, Chia-Cheng Wu, and Po-Tsung Lee*
Figure Description: 1D PhC nanolasers under different planar strains in different directions and the sensor unit composed of three PhC nanolasers.
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