1. INTRODUCTION

Over the past decade, researchers have made much effort toward constructing traditional semiconductor-based photonic devices and circuits in different soft materials [1–10]. This work not only meets the requirements of rapidly developed wearable devices and systems but also provides more possible applicability and usage in different platforms and environments. In this architecture, the micro- and nanocavities based on the total internal reflection (TIR) effect [1–6] or different meta-structures [7–10] are usually used for manipulating light in the subwavelength scale and realizing various functional core devices. Most embedded photonic devices and circuits based on continuous dielectric structures reasonably show structural stability and stable optical properties under deformations because of the huge differences in the mechanical properties between the semiconductor and soft materials. This feature was well understood in the earlier development stage, which guarantees their reliability and robustness in such flexible platforms.

In addition to their structural and optical stability, researchers have recently become more interested in the tunability of photonic devices by deforming soft carriers in this architecture [11–25]. In such a case, the embedded photonic devices are usually with deformable structures, whose optical modes inside can be significantly altered under the applied strain. The changes of the optical modes (usually in wavelength) can directly serve as tunable devices or quantity for optical sensing. Take photonic crystal (PhC) devices for example. Resonators consisting of discontinuous PhC lattice embedded in a deformable material can show a large wavelength response to the applied strain. This architecture has been reported for use in realizing tunable lasers [14–17], dynamic filters [18–21], and mechanical and chemical sensors [16,17,22–25]. In these reports, the large tunability, dynamic range, or high sensitivity can be achieved by enlarging their optical wavelength responses to the lattice structure variations led by strain. However, once the lattice structures and resonance modes inside are chosen, the wavelength responses to the strain are given, and further optimizations become very tough. Previously reported values usually lie within the range of 2–8 nm for every percent strain variation by different optical modes. In this report, to break through this limitation by lattice types and modes, we propose and demonstrate herein a new concept of strain shaping by inserting artificial mechanical structures in PhC resonators.

2. SHAPING THE STRAIN IN A PHC NANOCAVITY

Figure 1(a) shows the PhC resonator utilized herein. The periodically arranged nanorods in one dimension consist of 1D PhCs, which are embedded in a deformable polydimethylsiloxane (PDMS) substrate. The lattice width $w_n$ and constant $a_n$ are both linearly increased in 10 nm increments from the center to the edge of the 1D PhCs. This lattice design shown in Fig. 1(b) forms a nanocavity for locally confining the dielectric band (i.e., the first band) by the mode gap effect [26,27]. This waveguide-based architecture with small device footprint could facilitate integration with photonic circuits via different ridge-waveguide coupling arrangements [28,29], and its large wavelength response to strain is beneficial for demonstrating a tunable nanolaser with a wide wavelength tuning range and a high strain sensitivity in our previous reports [17,25]. The wavelength tuning mechanism is simply illustrated in Fig. 1(c). When the PDMS is linearly compressed from the length of $L_{\mathrm{tot}}$ to $L_{\text{tot}}^{\prime }$, it defines the total applied strain ${\xi }_{\mathrm{tot}}$ by $L_{\text{tot}}^{\prime }/L_{\mathrm{tot}}$. In this case, the dielectric mode (in $E_y$ fields, red curves) confined within the nanocavity will also be homogenously compressed with the entire PhC structure (presented by black dashed rectangle) and show a blue shift of ${\lambda }^{\prime }-\lambda$ in wavelength. This homogeneous tuning mechanism is the basis of most reported tunable PhC devices, which currently face the same bottleneck in further enhancing the wavelength response mentioned earlier.

 

Fig. 1. (a) Structure of 1D PhCs buried within a PDMS substrate and (b) the nanocavity design on it, where the $t$, $l$, $a_1$, and $w_1$ are 220, 930, 340, and 130 nm, respectively. Schematic of resonance mode profiles (in $E_y$ fields) variation in cavities consisted of (c) homogeneous and (d) hetero-materials with different mechanical properties under compressive strain. (e) Theoretical $x$-strain distributions of PDMS with different embedded InGaAsP rods topologies.

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To break through this bottleneck, a method of locally enhancing the strain is presented in Fig. 1(d). In Fig. 1(d), the PhC structure is embedded crossing a double-hetero-interface consisting of materials 1 and 2 with different elasticity, where the cavity region (yellow dashed rectangle) is located in material 1 and the outer PhCs (black dashed rectangles) lie in material 2. In this case, under the same ${\xi }_{\mathrm{tot}}$ as in Fig. 1(c), different strains will be produced in materials 1 and 2 by their different elasticities. If material 2 is relatively rigid, the embedded outer PhCs will show much smaller local strain, while the strain of the cavity region (${\xi }_{\mathrm{int}}$, defined as $L_{\mathrm{int}}^{\prime }/L_{\mathrm{int}}$) in material 1 will be enhanced. This is because the total strain crossing the entire double-hetero-interface has to be the same as ${\xi }_{\mathrm{tot}}$ in the homogeneous case. Thus, this local strain enhancement of the cavity region can lead to an enhanced wavelength shift (${\lambda }^{\prime \prime }-\lambda$) of the dielectric mode confined inside under the same ${\xi }_{\mathrm{tot}}$. However, in realizing this idea in the structure of Fig. 1(a), it is difficult to create such double-hetero-materials with a significant mechanical difference only by polymer-based carriers. Without changing the material composition, creating a difference in structural scale through the entire device reported recently in other fields [30–32] seems to be feasible. Unfortunately, this kind of method will significantly enlarge the device footprint and/or complicate the nanocavity design.

As an alternative, we proposed a method of slightly modifying the nanocavity topology by inserting certain semiconductor (i.e., InGaAsP herein) nanostructures nearby, which can locally change the mechanical properties of the PhC nanocavity in Fig. 1(a). To explain this proposal, we set a single InGaAsP rod (with length, width, and thickness of 5, 1, and 0.22 μm, respectively) embedded within PDMS and simulate the strain in the $x$ direction ($x$ strain) under ${\xi }_{\mathrm{tot}}$ of 0.95 along the $x$ axis by a 3D finite-element method (FEM) [33]. For the “single rod” case shown in Fig. 1(e), the $x$ strain of PDMS outside the rod (yellow dotted line) remained constant (${\xi }_{\mathrm{tot}}=0.95$, yellow curve). Along the rod (white dotted line), the $x$ strain (white curve) is equal to 1.00 within the rod because of the relatively large Young’s modulus of InGaAsP (5 orders larger than that of PDMS), and it shows exponential enhancement and reaches its maximum value of 0.80 near the rod ends. This film-edge induced strain [34] comes from the significant stiffness variation near the interface between the InGaAsP rod and PDMS. If we further place two identical InGaAsP rods shoulder by shoulder along the $x$ axis with a gap of 1 μm [the case of “double rods along $x$” in Fig. 1(e)], the $x$ strain within the gap (${\xi }_{\mathrm{int}}$) is significantly enhanced to 0.67 as we have shown in Fig. 1(d). In contrast, when we placed these two rods parallel to each other with a gap of 1 μm along the $y$ axis [the case of “double rods along $y$” in Fig. 1(e)], the gap region between the rods will be “clamped” instead. In this case, ${\xi }_{\mathrm{int}}$ shows a relatively small value of 0.99 at the center of the gap under the same ${\xi }_{\mathrm{tot}}$ of 0.95. These results strongly imply that we can use different arrangements of rigid nanostructures to locally shape the strain of PDMS near the PhCs. Based on the effects shown in Fig. 1(e), our proposed design in Fig. 2(a) consists of four InGaAsP rods (i.e., nanoclamps) with length $l$ and height $h$ and sets symmetrically near the 1D PhC nanocavity.

 

Fig. 2. (a) Design and parameter definitions of the 1D PhC nanocavity with nanoclamps. Theoretical $x$-strain distributions and lattice constant shifts along the PhCs of the (b) unclamped and (c) clamped PhC nanocavities. Their cavity mode profiles in the $|E|$ fields under ${\xi }_{\mathrm{tot}}=0.95$ are also shown as the insets. (d) Theoretical $Q$ and $V_{\mathrm{eff}}$ of the clamped nanocavity under different ${\xi }_{\mathrm{tot}}$.

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In Fig. 2(a), rods A and B are separated along the $x$ direction by an opening $o$. This opening corresponds to the nanocavity region and forms a similar topology to “double rods along $x$” in Fig. 1(e) to enhance the strain within the nanocavity under compressive strain. Meanwhile, along the $y$ direction, rods A and B are both with distance $d$ to the 1D PhCs. This will form a similar topology to “double rods along $y$” in Fig. 1(e) for clamping the outer PhCs. This design was then verified by calculating its structure deformation under strain, followed by simulating the optical properties in sequence using 3D FEM. In the simulations, $d$, $h$, $o$, and $L$ were chosen as 250 nm, 150 nm, 4, and 12 lattices, respectively. Figures 2(b) and 2(c) illustrate the simulated $x$-strain distributions of the clamped and unclamped PhC nanocavities under ${\xi }_{\mathrm{tot}}=0.95$. Figure 2(d) shows the theoretical $Q$ and effective mode volume [$V_{\mathrm{eff}}$, as a function of ${(\lambda /n)}^3$, where $n=3.4$ represents the refractive index of InGaAsP] of a clamped PhC nanocavity under different ${\xi }_{\mathrm{tot}}$ from 1.0 to 0.9. For the unclamped PhC nanocavity shown in Fig. 2(b), ${\xi }_{\mathrm{int}}$ between each lattice shows a uniform enhancement near the value of 0.85, which results in the wavelength response to ${\xi }_{\mathrm{tot}}$ ($R_s$, defined as the wavelength shift per 0.01 ${\xi }_{\mathrm{tot}}$ variation) of $-7.8\mathrm{nm}$. In contrast, for the clamped PhC nanocavity shown in Fig. 2(c), ${\xi }_{\mathrm{int}}$ between each lattice shows a significantly non-uniform distribution, which reaches extreme values smaller than 0.80 within the nanocavity region and leads to an enlarged $R_s$ of $-11.0\mathrm{nm}$. Meanwhile, ${\xi }_{\mathrm{int}}$ of the outer PhCs mostly becomes larger than 0.90, thereby agreeing quite well with our proposal in Figs. 1(d) and 1(e). These strain distributions of the clamped and unclamped PhC nanocavities are also directly reflected on their lattice constant variations as shown in Figs. 2(b) and 2(c). The induced non-uniform lattice variation turns the gradual PhCs from a linear to Gaussian-like distribution, leading to the increased $Q$ from 13,700 to 23,800. The dielectric mode profile with slightly enhanced field in the clamped PhC nanocavity caused by increased dielectric confinement factor ($\gamma$, defined as the ratio of ${|E|}^2$ field of the mode concentrating within the PhC lattice, from 0.295 to 0.318) under compression is also shown in the insets of Fig. 2(c), which lead to slightly reduced $V_{\mathrm{eff}}$ from $0.74{(\lambda /n)}^3$ to $0.72{(\lambda /n)}^3$. We should also note that $Q$ and $V_{\mathrm{eff}}$ are almost the same before and after adding the nanoclamps without applying strain. In addition, such $R_s$ enhancement highly depends on the spatial overlapping between the mode profile and strain-enhanced region. For the first and second modes with more fields distributing in the outer clamped PhC regions (strain-prohibited regions), they only show slight enhancement in $R_s$.

3. EXPERIMENTAL RESULTS AND DISCUSSION

Figure 3(a) briefly shows the flowchart for manufacturing our proposed design. Electron beam lithography and dry etching processes (reactive ion etching and inductively coupled plasma for etching ${\mathrm{SiN}}_x$ and InGaAsP, respectively) were utilized in sequence to define and fabricate the PhC nanocavity with nanoclamps on the InGaAsP multi-quantum wells (MQWs) (Steps 1 and 2) as shown by the top- and tilted-view scanning electron microscope (SEM) pictures in Fig. 3(b). Before transferring the PhC structure into PDMS, we partially removed the underlying InP by selective chemical wet etching ($\mathrm{HCl}:{\mathrm{H}}_2\mathrm{O}=1:1$, at 2°C for 5 s) and formed post-standing lattice structures (Step 3) as shown by the SEM images in Fig. 3(c) along two different crystal orientations of InP. This step ensured that the PDMS can tightly hold the lattice and the nanoclamps during the stress release in the following step of removing the entire InP substrate. The PhC nanocavity was then embedded into a PDMS (Sylgard 184, Dow Corning, SylgardA and SylgardB with a volume ratio of 5:1) substrate by bonding with PDMS (Step 4), removing the InP substrate by chemical wet etching ($\mathrm{HCl}:{\mathrm{H}}_2\mathrm{O}=3:1$ at room temperature) (Step 5), and sealing by PDMS (Step 6) in sequence. Figure 3(d) shows a picture and an optical microscope (OM) image of the clamped PhC nanocavity array. It is clear that all the devices are successfully transferred, which means a high yielding rate (usually $>85\%$) of the above fabrication process. More details of the above process can be found in our previous reports [17].

 

Fig. 3. (a) Flowchart of manufacturing 1D PhC nanocavity with nanoclamps buried in a PDMS substrate. (b) Top- and tilted-view SEM pictures of the clamped nanocavity before embedding within the PDMS substrate, whose $h$, $d$, $o$, and $L$ are 150 nm, 250 nm, 4, and 12 lattices, respectively. (c) The SEM pictures show the partially removed InP along different crystal orientations beneath the lattices. (d) Picture and OM image of the clamped PhC nanocavity array after embedding within the PDMS substrate. (e) OM images of the clamped PhC nanocavity under ${\xi }_{\mathrm{tot}}=1.00$ (top) and 0.96 (bottom). (f) Lasing spectra and OM image of the (top) unclamped and (bottom) clamped nanocavities under ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.96. (g) Optical excitation curves of the clamped PhC nanocavity under ${\xi }_{\mathrm{tot}}$ of 1.00 and 0.95. The inset shows the emission spectra of the nanolaser under excitation below (40 and 64 μW) and above (88, 123, and 248 μW) threshold. (h) The linewidth and wavelength variations of the nanolaser under different excitation powers. The lasing spectra under ${\xi }_{\mathrm{tot}}$ of 1.00 and 0.95 are shown with the emission spectra of InGaAsP MQWs.

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In the measurements, these devices were excited by optical pulse (with wavelength of 850 nm, pulse width of 20 ns, and repetition rate of 0.9 MHz) at room temperature under different ${\xi }_{\mathrm{tot}}$. Figure 3(e) illustrates the OM images of the clamped nanocavity before and after compression (${\xi }_{\mathrm{tot}}=1.00$ and 0.96). The length of the clamped PhCs is almost invariant, while that of the unclamped region is significantly compressed. This is the direct evidence of a non-uniform strain distribution as we predicted in our simulation. The lasing spectra of the devices with and without nanoclamps under ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.96 shown in Fig. 3(f) indicate a significantly raised experimental $R_s$ from $-7.7$ to $-10.7\mathrm{nm}$, which also agrees with the simulation results. Therefore, the capability of shaping strain within the PhC nanocavity by our proposed nanoclamps was preliminarily confirmed based on the abovementioned theoretical and experimental results. In addition, we also show the optical excitation curves of the clamped PhC nanocavity under ${\xi }_{\mathrm{tot}}$ of 1.00 and 0.95 in Fig. 3(g). The emission spectra, linewidth, and wavelength variation of the clamped nanocavity under ${\xi }_{\mathrm{tot}}$ of 1.00 and different excitation powers are shown in Figs. 3(g) and 3(h). The significant changes in slope of all the curves further confirm the lasing action. Because there is only slight difference between their theoretical $Q/V_{\mathrm{eff}}$ values [$1.84\times {10}^4{(\lambda /n)}^{-3}$ and $3.28\times {10}^4{(\lambda /n)}^{-3}$, respectively], the gain misalignment shown in the inset of Fig. 3(h) is responsible for the threshold degrading from 70 to 120 μW.

The influences on $R_s$ and the optical properties of the clamped nanocavities with different nanoclamp parameters were investigated after the preliminary verification. With fixed $d$, $o$, and $L$ of 250 nm, 4, and 12 lattices, respectively, Fig. 4(a) shows the theoretical Q and wavelength shifts of the nanocavities with different nanoclamp heights $h$ from 100 to 400 nm under ${\xi }_{\mathrm{tot}}=0.95$. In Fig. 4(a), the wavelength shift remains almost invariant under different $h$, while Q shows a significant decrease when $h>200\mathrm{nm}$. This degradation is attributed to the increased optical loss by the nanoclamps with a large $h$ acting as a side-coupled optical waveguide. Therefore, we can conclude that the height of nanoclamps seems to be independent of $R_s$, but it is harmful to the Q value when it becomes too high. Figure 4(b) depicts the measured $R_s$ from the clamped PhC nanolasers with different $h$ in the experiments, where the SEM images of the clamped PhC nanolasers with $h=125$ and 220 nm are shown as insets. The almost invariant $R_s$ agrees with the simulation prediction in Fig. 4(a).

 

Fig. 4. Theoretical Q, wavelength shifts under ${\xi }_{\mathrm{tot}}$ of 0.95, and measured $R_s$ of the clamped nanocavities with different (a), (b) $h$, (c), (d) $L$, and (e), (f) $d$. The lasing spectra of the clamped nanolaser with $d=200\mathrm{nm}$ under ${\xi }_{\mathrm{tot}}=1.00–0.96$ are shown as the inset in (e).

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We then further studied the effect given by different $L$ of the nanoclamps. With fixed $d$, $h$, and $o$ of 250 nm, 150 nm, and 4 lattices, respectively, Fig. 4(c) shows the theoretical Q and wavelength shifts of the clamped nanocavity with different $L$ from 8 to 16 lattices under ${\xi }_{\mathrm{tot}}=0.95$. In Fig. 4(c), Q exhibits a very small variation under different $L$, while the wavelength shift monotonically increases with $L$. The wavelength shift is enhanced to $-70.0\mathrm{nm}$ (corresponding to $R_s=-14.0\mathrm{nm}$) when $L=16$ lattices. This phenomenon can be simply understood in Fig. 1(d). To keep the strain continuously crossing the entire PDMS, the longer clamped region will concentrate more strain within the unclamped region (nanocavity), thereby increasing $R_s$. Figure 4(d) shows the measured $R_s$ from the clamped PhC nanolasers with different $L$ in the experiments, where the SEM images of the clamped PhC nanolasers with $L$ of 8 and 14 lattices are shown as insets. The monotonically increased $R_s$ from $-7.7$ to $-11.4\mathrm{nm}$ agrees with the predicted trend in Fig. 4(c). Although one can enhance $R_s$ by simply elongating $L$, this approach will result in fragile narrow nanoclamps under stress release during fabrication, and the device footprint will also be significantly enlarged at the same time.

Alternatively, a more robust and delicate parameter design for a large $R_s$ would be changing $d$ of the clamped nanocavity, whose theoretical Q and wavelength shift under ${\xi }_{\mathrm{tot}}=0.95$ are shown in Fig. 4(e). The parameters $h$, $o$, and $L$ were fixed as 150 nm, 4, and 12 lattices, respectively. In Fig. 4(e), the wavelength shift exponentially increases with the decreasing $d$ and reaches $-71.1\mathrm{nm}$ (corresponding to $R_s=-14.2\mathrm{nm}$) when $d=100\mathrm{nm}$. However, the Q value shows a significant degradation when $d<150\mathrm{nm}$. This is attributed to the increased side-coupled loss to the nanoclamps with a small coupling distance. Figure 4(f) shows the measured $R_s$ from the clamped PhC nanolasers with different $d$ in the experiments, where the SEM images of the clamped PhC nanolasers with $d=200$ and 800 nm are shown as the insets. The exponentially increased $R_s$ with the decreased $d$ agrees with the prediction in Fig. 4(e). When $d=200\mathrm{nm}$, we obtained an experimental wavelength shift of $-50.8\mathrm{nm}$ (corresponding to $R_s=-12.7\mathrm{nm}$) from the lasing spectra under ${\xi }_{\mathrm{tot}}=1.00–0.96$ in the inset of Fig. 4(e). Compared with $h$ and $L$, tuning $d$ is an efficient method of enhancing $R_s$ while the device footprint is still kept compact.

Based on above understanding, more complicated nanoclamp topologies can be designed for further $R_s$ enhancement. Take the case of $d=200\mathrm{nm}$ in Fig. 4(f) for example; when we slightly elongated the $L$ by 1 μm along the $x$ direction, $R_s$ significantly increased from $-13.0\mathrm{nm}$ to $-15.1\mathrm{nm}$. When we further connected the nanoclamps at both ends of outer PhCs, the clamped region became more immobilized under the same ${\xi }_{\mathrm{tot}}$, leading to an enhanced strain within the central unclamped region (nanocavity) and an enlarged $R_s$ of $-16.1\mathrm{nm}$. These simple examples implied that one can sculpt the optical properties on demand by shaping the strain using different nanoclamp topologies.

4. RECONFIGURABLE HIGH-$Q$ PHC NANOCAVITY BY STRAIN SHAPING

So far, we have disclosed the capability of shaping the strain inside/outside the PhC nanocavity and enhancing $R_s$ by our proposed nanoclamps. Note that the resulting nonlinear strain shown in Fig. 2(d) gives the nanocavity an extra Gaussian-like lattice shift distribution. That means one could actually create a double-hetero PhCs with mode gap confinement on 1D PhC waveguide by our proposed nanoclamps by applying strain. To confirm this, the nanoclamps were applied in the 1D PhC waveguide with uniform lattice constant $a$ and width $w$ in Fig. 5(a). In the simulations, Fig. 5(b) shows the lattice constant distribution of this device under different ${\xi }_{\mathrm{tot}}$. When ${\xi }_{\mathrm{tot}}=0.95$ and 0.90, the lattices both show Gaussian-like distributions as we predicted, while those without nanoclamps shown in Fig. 5(c) are merely compressed uniformly under the same strain. These properties can also be clearly seen from their $x$-strain distributions as shown as insets in Figs. 5(b) and 5(c). Figure 5(d) further illustrates the theoretical Q and $V_{\mathrm{eff}}$ of the clamped PhC waveguide under different ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.90. When ${\xi }_{\mathrm{tot}}=1.00$, the band-edge mode is with a typically low Q of 4200, a large $V_{\mathrm{eff}}$ of $2.85{(\lambda /n)}^3$, and an extended field profile as shown in Fig. 5(d). Once the device was compressed, Q and $V_{\mathrm{eff}}$ significantly increased and decreased, respectively, with the strain because of the nanocavity formation by the nanoclamps under strain. When ${\xi }_{\mathrm{tot}}=0.92$, the band-edge mode turns into the cavity mode with a very localized and enhanced field shown in Fig. 5(d), whose Q reaches its maximum value of 115,000 and $V_{\mathrm{eff}}$ greatly reduces to $1.08{\lambda }^3$. For comparison, in Fig. 5(e), the theoretical Q of the band-edge mode in the unclamped PhC waveguide slightly increases from 4100 to 6400 when ${\xi }_{\mathrm{tot}}=0.92$ because of the slightly increased dielectric filling factor under compression [17], while $V_{\mathrm{eff}}$ decreases from $3.01{(\lambda /n)}^3$ to $2.77{(\lambda /n)}^3$ based on the same reason. The mode profile under ${\xi }_{\mathrm{tot}}=0.92$ in the inset of Fig. 5(e) still exhibits an extended field distribution.

 

Fig. 5. (a) Schematic of the 1D PhC waveguide with nanoclamps. Theoretical lattice constant distributions of the (b) clamped and (c) unclamped PhC waveguides under ${\xi }_{\mathrm{tot}}$ of 1.00, 0.95, and 0.90. Their $x$-strain distributions are shown as the insets. Theoretical $Q$ and $V_{\mathrm{eff}}$ of the (d) clamped and (e) unclamped PhC waveguides. The confined mode profiles (in the $|E|$ field) of these two devices under ${\xi }_{\mathrm{tot}}$ of 1.00 and 0.92 are shown as the insets.

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To confirm the abovementioned results in the experiments, the device shown in Fig. 6(a) was manufactured by the same processes shown in Fig. 3(a). The lasing spectra of the clamped and unclamped PhC waveguides under ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.95 in Fig. 6(b) exhibit similar total wavelength shifts of $-38.6$ and $-38.0\mathrm{nm}$ (corresponding to $R_s$ of $-7.7$ and $-7.6\mathrm{nm}$, respectively), which agree with the theoretical values of $-8.1$ and $-8.0\mathrm{nm}$ in the simulation. This different result from the $R_s$ enhancement in the clamped nanocavity before is mainly caused by the spatial mismatching between the strain-enhanced region and the band-edge mode distribution.

 

Fig. 6. (a) SEM image of the 1D PhC waveguide with nanoclamps. Parameters $a$, $w$, $d$, $h$, $o$, and $L$ are 340, 130, 200, 130 nm, 4, and 14 lattices, respectively. (b) Lasing spectra of the clamped (right) and unclamped (left) PhC waveguides under ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.95. (c) Optical excitation curves of the clamped PhC waveguide under ${\xi }_{\mathrm{tot}}$ of 1.00 and 0.95, whose lasing spectra are shown with the emission spectra of the InGaAsP MQWs in the inset. (d) Theoretical Q of the clamped PhC waveguides with $d$ from 150 to 600 nm under different ${\xi }_{\mathrm{tot}}$.

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Figure 6(b) shows the excitation curves of the clamped PhC waveguide under ${\xi }_{\mathrm{tot}}=1.00$ and 0.95. First, the higher thresholds of $P_{\text{th}}=250$ and 200 μW than those in Fig. 3(g) are attributed to the large $V_{\mathrm{eff}}$ of the band-edge modes before and after compression. Second, in spite of the gain misalignment shown in the inset of Fig. 6(c), the device still shows a lower threshold under ${\xi }_{\mathrm{tot}}=0.95$ ($P_{\text{th}}=200\mathrm{\mu W}$) than that under ${\xi }_{\mathrm{tot}}=1.00$ ($P_{\text{th}}=250\mathrm{\mu W}$). This is caused by the significantly increased $Q/V_{\mathrm{eff}}$ with strain, which is very different from the results dominated by gain misalignment in Fig. 3(g). Third, the device also shows a larger slope efficiency under ${\xi }_{\mathrm{tot}}=0.95$ than that under ${\xi }_{\mathrm{tot}}=1.00$ because the optical loss along the waveguide will be blocked during nanocavity formation by the nanoclamps under strain, thereby increasing the collectable emission into the vertical direction in the measurements. According to these phenomena, we can conclude the capability of strain shaping to create a reconfigurable nanocavity on the PhC waveguide by our proposed nanoclamps in a deformable platform.

Furthermore, because different nanoclamp topologies will lead to different strain shaping, forming a nanocavity with a higher $Q$ value than that in Fig. 5(d) is possible. Here, we chose $d$ as the tuning parameter based on the same reason we discussed in Figs. 4(c)–4(f). Figure 6(d) shows the theoretical Q of the clamped PhC waveguides with $d$ from 150 to 600 nm under ${\xi }_{\mathrm{tot}}$ from 1.00 to 0.80, while $h$, $o$, and $L$ were fixed as 150 nm, 4, and 14 lattices, respectively. The maximum $Q$ ($Q_{\max }$) increases with $d$ and degrades when $d>500\mathrm{nm}$. The nanoclamps extremely concentrate the strain within the opening region when $d$ is small. This will form a nanocavity with a “sharp” lattice modulation, wherein the confined mode profile is with a low Q because of the significantly high spatial frequency components within the light cone in Fourier space. In contrast, when $d$ increases, the clamping effect for the outer PhCs becomes weaker, indicating that “gentler” strain shaping and lattice modulation will be given for achieving a high $Q$. The $Q_{\max }$ reaches $4.9\times {10}^5$ under ${\xi }_{\mathrm{tot}}=0.86$ when $d=500\mathrm{nm}$ and then starts to degrade when $d>500\mathrm{nm}$ because of a more uniform lattice modulation with insufficient mode-gap confinement by weakened clamping and strain shaping effects. This strain-induced waveguide–nanocavity conversion with a 1–2 order difference in Q would be useful in dynamic switching (response time in milliseconds, ms [35,36]), filtering, and buffering applications in flexible photonic circuits.

5. CONCLUSION

In conclusion, we proposed herein a novel concept of strain shaping by semiconductor nanoclamps embedded in deformable environments, which can form hetero-structures with significant differences in mechanical properties. Local strain enhancement and inhibition of neighboring 1D PhC devices can be produced under the applied linear strain by our proposed nanoclamps setting nearby. For the nanocavity lasers, the measured wavelength response to strain is enhanced from $-7.7$ to $-12.7\mathrm{nm}$ via theoretical and experimental studies of the effects given by different nanoclamp parameters. Furthermore, for the PhC waveguide without defects, the nanoclamps are capable of creating a reconfigurable conversion between the waveguide and the nanocavity with more than a 2-order difference in Q. These demonstrations provide the possibility of on-demand sculpturing optical properties of tunable PhC devices in the nanoscale by inserting additional nano- or micro-structures. It is also foreseeable that this nanoclamp design can enhance the wavelength response to more complex deformations (e.g., bending or twisting) accompanied by lattice elongation or compression. We also believe that these findings will lead to extending issues about how the accessing devices (e.g., optical waveguides) or similar clamping structures can further stabilize or destabilize the optical properties of core devices (tunable or untunable) in a mechanical manner in flexible photonic circuits.