1. Introduction

In recent years, several studies have focused on photonic crystals (PhCs), which exhibit several novel optical phenomena and properties [1–3]. One of the most important features of PhCs is the ability to form ultrasmall nanocavities thanks to their strong light confinement with photonic bandgaps. A large variety of PhC resonators, formed by specially-arranged point defects or local modulation of line defects in PhCs, have shown wavelength-sized ultrasmall cavity modes with strong light confinement and high Q-factors [4–7]. These properties give rise to a large enhancement in various light-matter interactions, and are expected to be promising for energy-efficient on-chip optical processing in photonic integrated circuits. For example, all-optical switches and optical memories with extremely low energy/power consumption were demonstrated by employing PhC nanocavities [8–10]. These high performances are attributed to the small cavity mode volume and the strong light confinement, which enable us to alter the device output by extremely small optical input. The same scenario can be hold for many types of devices, such as lasers [11,12], electro-optic modulators [13], and optical transistors [14].

As one of the interesting features of PhC nanocavities, their resonance wavelength can be tuned by small perturbation and even created and eliminated in a reconfigurable way. Previous studies have proposed cavity mode tuning via the thermo-optic effect of Si [15] or photorefractive effect of chalcogenide glasses [16,17], etc. Cavity formation can also be achieved by modulating the refractive index distribution rather than the spatial structure. For example, Ref. [18] proposes a reconfigurable nanocavity that can be formed in a graphene-loaded Si photonic crystal waveguide. Cavity formation and modulation are induced by electrostatic gate-tuning of graphene, and this structure allows the cavity formation to be manipulated within the picosecond order leveraging the ultrafast response time of graphene [18].

Although these device characteristics of PhC nanocavity devices are promising to form energy-efficient photonic integrated circuits, they are mostly volatile devices. The structures proposed in these previous studies require specific external mechanisms to tune or maintain the mode modulation effect. However, recently non-volatile photonic devices attract increasing interest because they give rise to less power consumption and memory/logic functions, which is especially important for integrated optical computing. For such purpose, phase change materials (PCMs) have exhibited significant potential for non-volatile photonic functionalities. Particularly, $\mathrm {Ge}_2\mathrm {Sb}_2\mathrm {Te}_5$ (GST) is a well-established PCM with distinctive properties, including a high refractive index contrast, two stable states, and a reversible phase change [19,20]. It has a complex refractive index of $4.39 + 0.16i$ for the amorphous state and $7.25 + 1.55i$ for the crystalline state at a wavelength of 1.55 µm [21]. The refractive index contrast $\Delta n/n = 0.65$ is much larger than those commonly used in optics, such as the Kerr effect with $\Delta n/n \sim 10^{-3}$ [22], the thermo-optic effect with $\Delta n/n \sim 10^{-2}$ [15], and the carrier-induced nonlinearity with $\Delta n/n \sim 10^{-3}$ [10]. GST undergoes phase transition at a temperature range close to 150 to 170$^\circ$C [23], or by applying electric pulse [24] or laser pulses reversibly with durations of few tens of nanosecond [21] for crystallization or few hundreds of femtosecond order [25] for amorphization. The ability to undergo phase transitions in less than a few tens of nanoseconds in an amorphous-to-crystalline state and in a few hundreds of femtoseconds in a crystalline-to-amorphous state is promising for applications in switches and memories [25–28]. It does not require any external fields or special equipment to maintain the GST state, since both the amorphous and crystalline states are stable at room temperature for at least 10 years [20]. GST is a great candidate as a material for low power consumption optical devices thanks to the reversible phase change with short pulse and and non-volatility. $\mathrm {VO}_2$ is another well-known PCM that undergoes the phase transition at a temperature close to 70$^\circ$C or when an electric field is applied [29]. However, GST is more promising for our purpose than $\mathrm {VO}_2$ since the change in the real part is smaller than that of GST.

Several studies have reported on the application of GST to optical devices, such as resonators [24,30], modulators [21,31,32], optical switches or filters [33–35], and reconfigurable metasurfaces [35–37]. Particularly, Rios et al. proposed the optical devices with GST that can be switched by semi-nanosecond pulses passing through a waveguide [32]. GST is therefore an excellent candidate for enabling non-volatile small-footprint reconfigurable optical devices.

In these optical devices, however, the area of GST on a single device is generally rather large, typically several square micrometers [21,24,30–32,38], which should lead to large power consumption and footprint. Hence, our purpose of this study is to combine ultrasmall GST patterns and ultrasmall PhC nanocavities to achieve non-volatile tuning and even non-volatile cavity creation/elimination. Some previous studies have numerically shown the reconfigurable PhC resonator with GST [39–42], but these studies assume challenging techniques in fabrication, such as the using of nanoscale GST rods [39–41] and selective GST coating around the wall of air-holes [42], and no specific procedures provided for their fabrication. Keitz et al. demonstrated mode tuning of the resonant mode in one-dimensional PhC cavities, but the GST area is not in a sub-micrometer range [43]. In fact, the patterning of sub-micron GST on PhCs requires elaborate nanofabrication technologies with fine alignment accuracy, which is not a trivial task. Although there have been submicron GST patterns on simple waveguides, there has been no report of submicron GST pattern formation on PhCs.

In this work, we propose and experimentally demonstrate a PhC nanocavity post-process tuning and cavity formation by incorporating a sub-micron square GST film within a center of 2D Si PhC point and line-defect devices. Utilizing a sub-micron square GST within a PhC nanocavity allows us to attain a significant modulation effect despite the small volume of GST. As far as we know, there has been no report for post-tuning or on-demand creation/elimination of PhC nanocavities with submicron GST. Furthermore, the proposed devices are non-volatile because the tuning effect for the resonant wavelength or Q-factor is maintained without external power due to the stability of the GST phase. This characteristic holds promise as a component of optical memory devices. Our work ultimately paves the way for non-volatile devices that can be switched with ultra-low power consumption.

The overview of this study is as follows:

The compact and simple geometry in our proposed structure is realized due to the stability and high refractive contrast of the GST. GST will allow for repeated control of the properties of the PhC resonators through bidirectional phase transitions. Our structures can potentially be applied to the ultrahigh efficiency writing, and non-volatile nanoscale optical devices.

2. Mode tuning in L5-type PhC resonator

In this section, mode tuning via phase change of GST in the L5-type PhC resonator is considered. First, the characteristics of the L5-type PhC resonator are briefly described. Next, the results of numerical calculations to estimate the amount of expected wavelength shift and Q-factor are discussed. The fabrication process and results are then explained. Finally, the experimental results of the transmittance measurement before and after phase change of GST are considered. We discuss the agreement with the simulation results and consider whether the resonant wavelength shift and Q-factor shift are achieved with the phase change of the GST.

All numerical calculations in this paper were performed using finite-element-method calculations (COMSOL Multiphysics).

2.1 Numerical calculations

Figure 1 (a) shows a schematic of the GST-loaded L5 resonator, which consists of five in-line missing-holes. The geometry is based on a triangular lattice Si-PhC slab. We employed an L5 resonator in this study, but in principle, an L3 or L7 resonator structure could also be employed. In this study, we adopted the L5 resonator to balance the sizes of the PhC and GST with the Q-factor. We use the lattice contrast $a = 400$ [nm], slab thickness $h = 200$ [nm], and the radius of air-holes $r = a/4$. Note that two end holes are slightly shifted toward outside by 80 nm. The refractive indices in each region are set as follows: $n_{\mathrm {Si}} = 3.48$, $n_{\mathrm {SiO}_2} = 1.45$, $n_{\mathrm {air}} = 1$. We also omit the input/output waveguides from the numerical calculations. The cavity modes are modulated by loading the GST at the center of the cavity.

Figure 1 (b) denotes the list of sizes of GST blocks loaded onto the PhC resonators. The unit size of a GST block is $a/4 \times (\sqrt {3}/8)\, a$, which is approximately equal to 100-nm square. Here, the vertical and horizontal numbers of GST blocks are denoted as $N_x \times N_y$ in the following text. The refractive indices of GST blocks are set as $n_\text {a} = 4.49+0.124i$, $n_\text {c} = 7.36+1.52i$, where $n_\text {a}$ and $n_\text {c}$ denote the values in the amorphous and crystalline states, respectively. $n_\text {a}, n_\text {c}$ are obtained by our ellipsometric measurement of the GST film deposited on the bulk Si substrate. Here, we focus on the two types of cavity modes located within the photonic bandgap. Figure 1 (c) shows the electric field distribution of the cavity modes in the L5 resonator. While the electric field of the 1st mode has an anti-node, the node of the 2nd mode is located at the center of the cavity. As seen in Fig. 1 (c), there is no noticeable change in the electric field distribution due to loading the $2 \times 2$ GST block. The electric field distributions of both the 1st and 2nd mode are confined to several lattice constant squares, which is more compact than the electric field distributions of nanobeam resonators [43].

The eigenmodes in the geometry shown in Fig. 1 (a) with 30-nm-thick GST patterns of different sizes are calculated by the finite element method. Figures 2 (a) and (b) show the resonant wavelength $\lambda _\mathrm {a} - \lambda _\mathrm {a0}$, $\lambda _\mathrm {c} - \lambda _\mathrm {c0}$ and Q-factor $Q_\mathrm {a}, Q_\mathrm {c}$ as a function of the GST blocks in the (a) amorphous and (b) crystalline states, respectively. Here, $\lambda _\mathrm {a0}$ and $\lambda _\mathrm {c0}$ represent the wavelength in the absence of GST and $\lambda _\mathrm {a0} = \lambda _\mathrm {c0}$ holds in the numerical calculations. Figure 2 (d) denotes the caption which shows the relationship between the marker type and the direction of GST block. It can be seen from Fig. 2 (a) that the redshift in the resonant wavelength and Q-reduction for the 1st mode become larger as the block number increases due to the change in the effective refractive index by the deposition of amorphous GST. Furthermore, the shift and Q-reduction size tends to be larger in the crystalline state, as shown in Fig. 2 (b), which is due to the larger complex refractive index in the crystalline state. In some large GST samples, the resonant wavelength in the 1st mode is blue shifted after phase change. We regard that this blue shift is due to the deformation of the cavity field distribution induced by the presence of large GST (in Appendix A for details). Note that this happens only for large GST. The changes through phase change of GST in the wavelength $\Delta \lambda := (\lambda _\mathrm {c} - \lambda _\mathrm {c0}) - (\lambda _\mathrm {a} - \lambda _\mathrm {a0})$ and Q-factor ($Q_\mathrm {c} / Q_\mathrm {a}$) are shown in Fig. 2 (c). The wavelength increases and the Q-factor decreases as the size of GST block increases except for the case with $4 \times 2$ and $4 \times 4$ GST blocks. The shift of wavelength and Q-factor are induced by the change in complex refractive associated with the phase change of GST.

 

Fig. 1. (a) Schematic of the GST-loaded L5-type PhC resonator. (b) The size of GST-film patterns used for calculation, which is same as the designed value for experiments. We fabricated three devices in the case of the $2\times 2$ and $4\times 4$ blocks. (c) Electric field distribution of two types of cavity modes in the L5 resonator.

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Fig. 2. (a), (b) The relationship between the number of GST blocks and resonant wavelength and Q-factor in (a) amorphous and (b) crystalline state in the numerical simulations. All results in resonant wavelength are based on the wavelengths without GST loading $\lambda _\mathrm {a0}, \lambda _\mathrm {c0}$. (c) The wavelength shift and change in the Q-factor after phase change of GST. (d) The correspondence table of the marker type and the direction of GST block.

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The same trends are confirmed in the results of the 2nd mode as shown in Figs. 2 (a), (b), and (c). The shift of both resonant wavelength and Q-factor in the 1st mode is larger than that of the 2nd mode, indicating that the 1st mode is selectively modulated by loading GST on the center of PhC cavity. Further, the results for GST 2, 4, 8 blocks suggest that the modulation effects by the GST blocks with $N_x > N_y$ are larger than those with $N_x < N_y$ in the 1st mode, and the opposite is true in the 2nd mode. Note that the facts that the GST blocks with $N_x > N_y$ have a large modulation effect for the 1st mode and vice versa for 2nd mode are consistent with the following: 1. The electric field of the 1st and 2nd mode have an anti-node and node at the center of the cavity. 2. The anti-node of the 1st mode and the node of the 2nd mode extends in the $x$- and $y$-directions, respectively.

2.2 Fabrication

Figure 3 (a) shows the fabrication process. A GST-loaded PhC slab was fabricated from a silicon-on-insulator (SOI) wafer with a top Si layer of 205-nm thickness. The fabrication process is as follows. The resist pattern for the PhC layer was defined by electron beam (EB) lithography and the Si PhC strcture is formed by dry etching. The resist patterns for the GST films were also defined by EB lithography on the Si PhC. The alignment accuracy between the Si PhC and GST pattern is better than 20 nm. Next, a GST film of a thickness of approximately 30 nm was deposited by magnetron sputtering by using an alloy target in an Ar atmosphere of $1.6\times 10^{-2}$ Pa and a rate of 0.19 nm/s on PhC patterns. The deposition rate was measured by a quartz resonator. Sub-micron GST pattern was subsequently formed by a lift-off process. After a series of measurements in the amorphous state, the samples were annealed to cause the phase change from amorphous to crystalline in an oven at a temperature of 280$^\circ$C, which is above the crystallization temperature of around $\sim$170$^\circ$C [44] with a duration of 75 min.

Figures 3 (b) and (c) are the Atomic Force Microscope (AFM) images of the fabricated GST patterns of $200 \times 200 \sqrt {3}/2$ nm$^2$ in the amorphous and crystalline states, respectively. These figures show good accuracy of the size and position of the patterned GST films. Here, the edges of GST patterns exhibit a distinct bump shape, which is thought to be due to the deposition of GST on the sidewalls of the resist pattern. The average GST thickness measured by AFM was approximately 25 nm to 30 nm for both the amorphous and crystalline states.

 

Fig. 3. (a) The fabrication process of the GST-loaded PhC resonator. (b), (c) Measured AFM images and cross-sectional height views for the structure shown in Fig. 1(a) in the amorphous state (b) and the crystalline state (c). The red dashed lines and the cross marks in the AFM images show the line where the cross-sectional height views are taken.

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2.3 Experimental demonstration of mode tuning by phase change of GST

To evaluate the wavelength tuning experimentally, we measured the transmittance between the input and output waveguide through the cavity. Figure 4 (a) shows a schematic for a transmittance measurement. A wavelength tunable laser source with a wavelength between 1500 nm and 1600 nm was used as the continuous-wave light source. The power to the input fiber was set to 1 mW. A polarizer and lens were attached to the tip of the fiber in front of the sample chip, and the TE mode light was focused onto the end faces of the Si waveguide. Polarization-maintaining single-mode fibers were used. The light from the Si waveguide was coupled to the Si-PhC slab waveguide, whose width are set to $1.1\sqrt {3}a$ (W1.1 waveguide). The output light from the sample was coupled to a fiber connected to a photodiode by the similar setup for the input fiber. The light from the fiber was detected by a photodiode.

Before presenting the measured results of the transmission experiments, we show the analytical transmission spectrum in the cavity-waveguide coupled structure as shown in Fig. 4 (a). The analytical function is derived using temporal coupled mode theory [45]:

 

Fig. 4. (a) Schematic of the L5-resonator and transmittance measurement. (b),(c),(d) Transmission spectrum of the L5-resonator (b) without GST, (c) with $2 \times 2$ GST blocks, and (d) with $4 \times 4$ GST blocks. The green and red lines show the peak curve in the amorphous or crystalline states fitted by the Lorentzian function given by Eq. (3). The left columns indicate the number of GST blocks.

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Here, $\omega _0$ is the resonant frequency, $Q_\text {coup}$ denotes the coupling Q-factor, and $Q$ is the total Q-factor which includes the contribution from coupling $Q_\text {coup}$, absorption $Q_\text {abs}$, out-of-plane radiation $Q_\text {rad}$: $Q^{-1} = Q_\text {coup}^{-1} + Q_\text {abs}^{-1} + Q_\text {rad}^{-1}$. Since GST has a relatively high absorption near the telecom wavelength, the approximate expression for the transmittance at $\omega = \omega _0$ is derived by assuming $Q_\text {abs} \gg Q_\text {coup}, Q_\text {rad}$.

Next, we show the measured transmission spectra in Fig. 4 (b), (c) and (d). Curves denote the spectra for different GST blocks for the amorphous phase (before annealing) and the crystalline phase (after the annealing). The left columns indicate the number of GST blocks: (b) without GST loading, (c) with $200 \times 200 \sqrt {3}/2$ nm$^2$ GST-film, (d) with $400 \times 400 \sqrt {3}/2$ nm$^2$ GST-film. See Appendix B for the other transmission spectums. Here, we fit these measured transmission spectra by analytical spectra to deduce cavity parameters.

The peak curves in amorphous or crystalline state are fitted by the Lorentzian function given in Eq. (3):

Figure 4 (c) shows the transmittance with the $200\times 200\sqrt {3}/2$ nm$^2$ GST pattern. The vertical black-dashed lines in the figures represent the baseline wavelength: $\lambda _{\mathrm {base}} := \lambda _\mathrm {a} + (\lambda _\mathrm {c0} - \lambda _\mathrm {a0})$. Therefore, $\lambda _\mathrm {c} - \lambda _{\mathrm {base}} = (\lambda _\mathrm {c} - \lambda _\mathrm {c0}) - (\lambda _\mathrm {a} - \lambda _\mathrm {a0}) =: \Delta \lambda$ represents the net wavelength shift due to the phase change of GST. Compared to the spectrum without GST (Fig. 4 (b)), the 1st peak is broadened and red-shifted by approximately 4 nm in the amorphous state and 5 nm in the crystalline state, suggesting that GST apparently modulates the cavity modes. Moreover, the shift of the 2nd peak due to phase change is too small to confirm the effect of GST, which is consistent with the numerical calculations as shown in Fig. 2 (c). Due to the small size and the high alignment accuracy of GST, there are differences in the influence of refractive index changes depending on the position of the mode nodes.

Next, we investigate the case for larger GST block. Figure 4 (d) shows the transmittance with the $400\times 400\sqrt {3}/2$ nm$^2$ GST pattern. In this case, the 1st peaks are eliminated in both the amorphous and crystalline states. We regard that this cavity mode elimination is due to the strong absorption by GST. The 2nd peaks are broadened and red-shifted by 4 to 5 nm through phase change of GST. Based on Eq. (2), the increase of absorption should lead to the decrease in transmittance and disappearance of resonant peaks. Hence, the wavelength shift and the cavity elimination are both explained by the phase change of GST.

Finally, we investigate how the resonant wavelength and Q-factor change at the phase change as a function of the area of GST. Figures 5 (a) and (b) show the resonant wavelength and Q-factor of the peaks as a function of the number of GST blocks. The origin of the wavelength shift was based on the resonant peak wavelength of the no-GST (unloaded) sample. We omit the point of the 1st peak at 16 GST blocks in the experiment, since the Q-factor is too small to identify the peak. First, we discuss the result in the amorphous state shown in Fig. 5 (a). The resonant wavelength of both the 1st and 2nd modes increases in proportion to the number of GST blocks. The magnitudes of the wavelength shifts are in good agreement with the results in the numerical results shown in Fig. 2 (a). A good agreement of overall trends between simulation and experiment are also confirmed for Q-factor. There, the agreement for the Q-factor between the experiment and the numerical calculation is not perfect, and it may be due to that fact that since the numerical calculations ignore the existence of the coupled input/output waveguides. Furthermore, for samples with the same number of GST blocks, it was observed that the wavelength shift of the 1st mode by GST deposition tends to be larger than that of the 2nd mode. For example, among five samples with 4 GST blocks, the average $\lambda _\mathrm {a} - \lambda _\mathrm {a0}$ of the 1st mode was 2.69 nm, whereas for the 2nd mode, it was 0.64 nm. This difference suggests that GST has been precisely patterned and can independently control the 1st and 2nd modes, since The simulation results depicted in Fig. 2 (a) imply that the selectively patterned GST at the center of the PhC cavity can more effectively modulate the 1st mode compared to the 2nd mode. Therefore, the contrast of $\lambda _\mathrm {a} - \lambda _\mathrm {a0}$ between the 1st and 2nd mode are considered to stem from the presence of an anti-node and a node at the center of the PhC cavity for the 1st and 2nd modes, respectively. On the other hand, the directional dependence of GST loading (portrait or landscape) for the samples with GST 2, 4, 8 blocks could not be confirmed clearly in the experimental results.

 

Fig. 5. (a), (b) The relationship between the number of GST blocks and resonant wavelength and Q-factor in (a) amorphous and (b) crystalline state in the experiment. All results in resonant wavelength are based on the wavelengths without GST loading $\lambda _\mathrm {a0}, \lambda _\mathrm {c0}$. (c) The wavelength shift and change in the Q-factor after phase change of GST. (d) The correspondence table of the marker type and the direction of GST block.

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Next, we investigate the result after phase change shown in Fig. 5 (b). We omit the experimental data with eight or more GST blocks from the graph about the 1st mode, since it is difficult to measure the 1st peak due to the strong absorption of GST. It can be seen that the size of the wavelength shifts and Q-factor shifts become larger than that for the results in the amorphous state, which is consistent with the numerical results. Here, the magnitude of the Q-factor in the crystalline state obtained from the measurements is up to four times higher than that in the simulation. There are two possible reasons for this difference: (i) errors in the refractive index used in the simulation: In general, it is more difficult to accurately determine the extinction coefficient $\kappa$ by ellipsometry than the real refractive index $n$. We also notice that the optical constants of patterned film may differ from those of uniform thin film, depending on the substrate and the size of the GST. (ii) Difficulties in determining the Q-factor from the transmission spectrum: As shown in Fig. 4(c), the peak of the 2nd mode in the crystalline state is significantly broadened (the measured Q-factor is approximately 200 for the sample GST block 16), which makes it difficult to identify the exact Q-factor. From the transmittance measurement in both the amorphous and crystalline states, we were able to identify only the resonance peaks whose Q-factor is greater than about 300 for the 1st mode and 200 for the 2nd mode. The lower limit of the measurable Q-factor is determined by the coupled Q of each mode and the transmission loss that can be tolerated in the experimental system, according to the CMT equation Eq. (2).

Figure 5 (c) summarizes the wavelength shift and change in Q-factor at the phase change. Here, $\Delta \lambda = (\lambda _\mathrm {c} - \lambda _{\mathrm {c}0}) - (\lambda _\mathrm {a} - \lambda _{\mathrm {a}0})$ and $\lambda _{\mathrm {a}0}, \lambda _{\mathrm {c}0}$ represent the resonant wavelength of the no-GST sample before and after phase change, respectively. In this plot, one can clearly observe that the wavelength shift increases and the Q-factor decreases as the number of GST blocks increases. This suggests that the size of the GST blocks corresponds to the size of wavelength shift and change in Q-factor. From the above results, we conclude that we have successfully tuned the resonant wavelength and Q-factor of PhC nanocavities by the phase change of submicron-sized GST.

Table 1 shows a comparison with previous studies on the experimental demonstration of resonator tuning in typical photonic crystal resonators and ring resonators. First, we compare the device size. Apparently, the PhC cavities are much smaller than ring resonators [30,46]. This is the most important advantage when we employ PhC nanoresonators. Among this table, there is a fundamental difference between non-volatile and volatile devices. Non-volatile devices do not need a power to keep the switched state, which is fundamentally different from volatile ones such as in thermo-optic effect [15] and photo refractive effect [16]. In volatile devices, the switching energy is proportional to the volume of the phase change materials. As for the GST volume, our devices is superior to the previous GST devices. We employ typically $2\times 2$ ($200$ nm $\times$ $200 \sqrt {3} /2$ nm $\times$ 30 nm) and $4\times 4$ ($400$ nm $\times$ $400 \sqrt {3} /2$ nm $\times$ 30 nm) GST blocks, which are approximately $1/10$ and $1/3$ of those of the design for a 1D GST-loaded PhC cavity [43]. Next, we examine the resonant wavelength shift. The intrinsic refractive index change of the phase change is much larger than that of optical nonlinearity. In the present case, however, the achieved wavelength shift of our devices, $\Delta \lambda / \lambda \sim 0.3{\% }$ (2nd peak, $4\times 4$ GST block) is comparable to those reported in previous studies for thermo-optic effect [15] and photorefractive effect [16]. This is because we load a GST thin film as a perturbation to the host PhC. In fact, if we employ GST for the host PhC, a much larger shift can be obtained, but then the required switching energy should increase. When we compare the wavelength shift with other GST devices, the achieved shift in our devices is about an order of magnitude larger than that in the results of the 1D PhC cavity [43], which is due to the strong optical confinement in our 2D PhC cavity. The strong moduation with a smaller GST volume can be attributed to the strong optical confinement of the 2D PhC resonant modes. Finally, we examine the Q-factor. Q of our cavity is comparable to or slightly lower than that of other devices in Table 1. This is due the strong light-matter coupling in our device configuration, but this is not fundamental limitation. The Q-factor can be improved by using transparent phase-change materials such as Sb$_2$S$_3$ or Sb$_2$Se$_3$ to suppress absorption losses, as demonstrated in the ring resonator [46]. Consequently, Table 1 shows that our device exhibits strengths in terms of non-volatility, small footprint, and small volume of the phase-change material together with a relatively large resonant wavelength shift, which indicates that our device is promising for a tuning device with a small switching energy and no extra holding power.

Table 1. Comparison with previous studies of experimentally demonstrated resonator tuning. 1st, 2nd, 3rd denote the orders of the resonance peaks. The 1st and 2nd of our research correspond to the results of $2\times 2$ and $4\times 4$ GST blocks, respectively. The Q-factor is compared based on the values in the amorphous phase.

View Table

The simulation and experimental results shown in Fig. 2 (c) and Fig. 5 (c) suggest a strong correlation between the Q-factor shifts and the resonant wavelength shifts by phase change of GST. For the samples with less than four GST blocks for which the resonant peak in the crystalline state could be confirmed by transmittance measurements, Fig. 6 show the shifts of rate of inverse Q as $\Delta Q^{-1} / Q^{-1}$ in the 1st peaks with respect to the shift in resonant peak wavelength $\Delta \lambda / \lambda$. The black line indicates the fitting lines: $\Delta Q^{-1} / Q^{-1} = \alpha (\Delta \lambda / \lambda )$. The linear relationships in the region where $\Delta \lambda / \lambda$ is small are identified in both the simulation and experimental results. The values in the sample of $1\times 4$ GST blocks in simulations deviate significantly from the fitting line (i.e. $\Delta \lambda / \lambda \sim 0.06{\% }, \Delta Q^{-1} / Q^{-1} \sim 9$), which is due to the highly distorted electric field distribution by GST modulation. The determination coefficient $R^2=0.925$ is obtained from the simulation results when this point is removed. Further, the wavelength shift in the experiment is smaller than that in the simulation, which can be attributed to the error in the estimation of the complex refractive index of GST and difficulties in determining the Q-factor. The strong correlation between the $Q^{-1}$ shifts and the wavelength shifts can be explained by the changes in the complex refractive index of GST.

 

Fig. 6. $Q^{-1}$ shift by the phase change of GST as a function of wavelength shift.

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3. Cavity formation in PhC line-defect waveguide

In this section, we investigate the cavity formation in the PhC line-defect waveguide by selectively loaded GST patterns. The first part describes the schematic of the PhC line-defect waveguide with GST. Next, we show that the resonant mode is formed by the effective refractive index modulation by loading of GSTs. The creation and modulation or annihilation of the cavity is then experimentally confirmed by transmission measurements.

Figure 7 (a) shows a schematic of the PhC line-defect waveguide loaded with the patterned GST-film and the configurations of the GST-film patterns we employed. The lattice constant $a$, hole radius $r$, and slab thickness $h$ are the same as those that as for the L5 resonator in the previous section. The total length of the waveguide for the $x$-axis is $50a$ (20 µm). The width of the waveguide is set to $1.1\sqrt {3}a$ (W1.1 waveguide), and the center of the waveguide is modulated with a width of $0.98\sqrt {3}a$ (W0.98 waveguide). The length of the modulated region is $2 \times 6a$. GST-film patterns are located at the center of the W0.98 waveguide, and the configurations of the GST-film patterns are shown in the bottom of Fig. 7 (a), which are the same as those in L5-type cavities. Note that in contrast to the previous section, here, there is no pre-fabricated cavity before loading GST. As explained below, a nanocavity is automatically formed around the GST region in the line defect due to the local refractive index modulation. The refractive index modulation by GST shifts the mode gap to the lower frequency. The cavity is then formed in the region surrounded by the modulated mode gap. The fabrication and measurement process are the same as that for the L5-type cavities in the section 2.2 and 2.3, respectively. The input incident light is incident from the left toof the W1.1 waveguide, and are coupled to the center cavity in the W0.98 region and transmitted to the right-hand side waveguide.

 

Fig. 7. (a) Structural design of a PhC line-defect waveguide with a $400 \times 200 (\sqrt {3}/2)$ nm$^2$ GST-film and the size of GST-film patterns used for calculations and fabrications. The waveguides with two different line-defect widths are interconnected. (b) The diagram for describing the mechanism of cavity formation by GST loading. Top: The simple PhC line-defect waveguide. The right side shows the structure with GST patterns. Middle: The simplified drawing for the frequencies of the modes in the above structures. Bottom: The electric field distributions for the band-edge mode (left) and the resonant mode (right).

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Figure 7 (b) describes the mechanism of cavity formation by GST loading. Figure 7 (b) top shows the simple line-defect waveguide with a width of $0.98\sqrt {3}a$ (the left part) and that with patterned loaded GST-films (the right part). The frequencies of the modes in the corresponding structures are shown in the middle part of Fig. 7 (b). The cavity is formed by the red shift of the band-edge mode by the same mechanism as in the case where the position and size of the holes are modulated. Figure 7 (b) bottom shows the electric field distributions for the band-edge mode (left) and the resonant mode (right). The periodic boundary conditions are imposed along the $x$-axis. The band-edge mode is distributed throughout the waveguide, indicating that this is not a localized mode. Additionally, the cavity mode shown on the right part is localized near the GST deposition, suggesting that it is a localized mode.

The left side of Fig. 8 (a) shows the measured transmission spectra of the PhC structure in Fig. 7 (a) without GST block. The gray and orange line denotes the spectrum before and after annealed, respectively. The blue shift of the overall spectrum after annealing by 2.24-nm is due to the oxidation of the surface of the Si-PhC layer, similar to which is consistent with the results in the L5 resonator. The transmission reduction due to the existence of the mode gap in the W0.98 waveguide is observed, but no Lorentzian resonant peaks are observed in the spectrum. The right side of Fig. 8 (a) illustrates a magnified diagram of the area near the band edge. The wavelength of band edge is given by fitting with the following function $f_{\mathrm {bandedge}}(\lambda )$:

Here, $c, b, \lambda _0$ are the fitted parameters denoting slope of the transmission tail near the band-edge, offset of the spectrum and band edge wavelength. and we estimate the band edge wavelength as the origin of wavelength shifts $\lambda _0$ as $\lambda _\mathrm {a0} = 1525.00$ [nm] for the amorphous state and $\lambda _\mathrm {c0} = 1522.76$ [nm] for the crystalline state. The left side of Fig. 8 (b) shows the transmission spectrum with the $200 \times 200 \sqrt {3}/2$ nm$^2$ GST-film. The gray and orange line denotes the spectrum before and after phase change of GST. Note that we can now see bump structures in the spectra. We also plot the green and red lines in the spectrum as the fitted curve, which is the product of the Lorentz function and exponential functions:

The coefficients $A$ and $c$ are identified from the fitting by Eq. (5). Figure 8 (b) indicates that resonant modes are formed by loading GST. Furthermore, the resonant wavelength is red-shifted and the Q-factor of the peak decreases after the phase change of GST, which is consistent with the simulation and can be explained by the increase in the complex refractive index through phase change. Figure 8 (c) shows the transmission spectrum with the $400 \times 200 \sqrt {3}/2$ nm$^2$ GST-film. There is a resonant peak in the amorphous state as well as in the case with the $200 \times 200 \sqrt {3}/2$ nm$^2$ GST-film, On the other hand, the resonant peaks disappear in the crystalline state, suggesting that the increase in material absorption led to a significant decrease in the Q-factor of the resonant mode, as in the case of the L5 resonator. These results demonstrate the cavity formation through the introduction of amorphous GST, and its characteristics were dynamically altered, nearly vanishing, during the phase change of GST.

Figures. 9 (a) to (f) show the resonant wavelength and Q-factor of the peaks as a function of the number of GST blocks. Here, (a) to (c) show the result of the numerical calculations, and (d) to (f) show the corresponding experimental results. The origin of the wavelength shift $\lambda _\mathrm {a0}, \lambda _\mathrm {c0}$ are calculated from the eigenfrequency analysis in numerical calculations as the wavelength in the edge of waveguide mode in the W0.98 waveguide without GST loading. Further, $\lambda _\mathrm {a0}$ and $\lambda _\mathrm {c0}$ in the experiment are defined as the wavelength in band edge depicted in the right part of Fig. 8 (a). A trend of red-shift of the resonant wavelength and Q-reduction with increasing the number of GST blocks are observed in the experimental results for both the amorphous and crystalline states, as shown in Figs. 9 (d) and (e). This result is consistent with the numerical calculations in Figs. 9 (a) and (b). There are discrepancies of approximately 2-nm between the simulation and experimental resonant wavelengths, which can be attributed to the error in estimating the band-edge wavelength. Here, since no resonant peaks were observed in the transmittance measurements for the samples with GST blocks $1\times 1$, $1\times 2$ and $1\times 4$, they are not depicted in Figs. 9 (d) and (e). We regard that this is because the modulation effect by GST loading is too small and the resonant wavelength is too close to the mode gap of the W0.98 waveguide (See Appendix C for details). The resonant wavelengths exhibit a variation of approximately $\pm 1$ nm, which is considered to be due to the fabrication errors of GST patterns similar to that in the L5 resonator. The positive wavelength shift and Q-reduction by the phase change are also observed in the experiments, as shown in Fig. 9 (f), indicating that the cavity modulation by the phase change of GST has been achieved in addition to the cavity formation by GST deposition. The blue-shift in the crystalline GST and the negative wavelength shift by the phase change indicated by numerical calculations in Figs. 9 (b), (c), which are in particular relevant in the samples with the (GST block of 4, 8, and 16) are not observed in the experiment. This may be because, since in such situations Lorentzian peak cannnot be observed resolved due to very low-Q factor by when the distortion of the electric field distribution is too large.

 

Fig. 8. (a), (b), (c) Transmission spectrum of the PhC structure shown in Fig. 7 (a) (a) without GST, (b) with $2 \times 2$ GST blocks, and (c) with $4 \times 4$ GST blocks. The green and red lines show the peak curve in the amorphous or crystalline states fitted by the Lorentzian function given by Eq. (3). The left columns indicate the number of GST blocks. The right part of (b), (c) denote the details of the spectrum and fit curve with exponential background removed.

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Fig. 9. (a), (b) The relationship between the number of GST blocks and resonant wavelength and Q-factor in the numerical calculations. (a) and (b) show the results for the amorphous and crystalline states, respectively. (c) The wavelength shift and change in the Q-factor after phase change of GST. (d), (e), (f) the same as (a), (b), (c) in the experiment. (g) A caption for (a)$\sim$(f).

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Consequently, we have experimentally observed a fairy good agreement in the overall trends between numerical calculations and experiments for the cavity formation, in terms of the resonant wavelength, Q-factor, and wavelength shift by the phase change of GST.

4. Conclusion

We have proposed and fabricated non-volatile and reconfigurable 2D PhC nanocavities with patterned GST-films of several hundred nanometer square, and the nanocavity tuning by phase change of $200 \times 200 \sqrt {3}/2$ nm$^2$ or more GST are confirmed. The properties of the PhC nanocavities loaded with sub-micron-scale GST films have been investigated by numerical calculations, and it was verified that the cavity modes are modulated by both deposition and phase change of the GST. We fabricated Si PhC nanocavities loaded with sub-micron-scale GST films and confirmed that $200 \times 200 \sqrt {3}/2$ nm$^2$ or more thin GST blocks were patterned on the PhC with sufficiently high accuracy. The transmission spectra have been measured before (amorphous phase) and after phase change (crystalline phase), and it was found that the wavelength and Q-factor of the resonant mode are switched by the loading and phase change of GST. Notably, we successfully confirmed a direct correlation between the phase change of GST and the large of shifts of the wavelength and Q-factor of the resonant mode. This demonstrates that one can control the characteristics of the nanocavities by the phase-change of GST, which will be employed for various non-volatile reconfigurable nanocavity devices. Furthermore, it may be worth noting that the GST volume employed in our study is approximately one order of magnitude smaller than that in previous studies [43], which is attributed to the fact that our devices are based on ultrasmall nanocavities. Together with the smallness, by employing a technique that enables a precise control of the number and positions of GST films, our method is promising for enhancing the potential of post-processing using GST loading. There are advantages in terms of non-volatility and reconfigurability in our structure, and there is a potential for improvement in the choice of material. Cavity formation was also confirmed by GST loading on the PhC line-defect waveguide. The formed cavities were modulated by the phase change and vanished in the crystalline state when the number of GST blocks is 8 or above.

The experimental demonstrations of the mode tuning and cavity formation by patterned sub-micron scale GST on photonic crystals are the first important step towards the realization of optical devices with a non-volatility and ultra-low power consumption. We have used GST as the phase change material in this study, and other reconfigurable materials are also available. GSST ($\mathrm {Ge}_2\mathrm {Sb}_2\mathrm {Se}_4\mathrm {Te}_1$), Sb$_2$S$_3$ and Sb$_2$Se$_3$, which can reduce optical attenuation around telecom bands, have been proposed and fabricated in recent years [19,38,46–50]. Our proposed structures have the potential to be developed into higher Q resonators by adopting transparent materials instead of GST, which can lead to improved performance as resonators. Moreover, the fabrication techniques of GST nanopatterns can be applied not only to resonators and waveguides, but also to topological and non-Hermitian systems. Thus, our study will be the basis for future research on optical devices using phase change materials.

Appendix A: mode deforms due to too strong modulation

GST loading leads to an increase in the effective refractive index of the mode if its perturbation effect is not strong. Phase change of GST is also expected to lead to a positive wavelength shift of the resonant mode within the range of perturbations, since the effective refractive index increases with the phase change from amorphous to crystalline [19–21,23]. However, too strong modulation effects deform the electric field distribution and lead to a decrease of the effective refractive index. This explains the negative wavelength shift confirmed by numerical calculations.

Figure 10 shows the electric field distribution of two types of cavity modes in the L5 resonator. Here, (a), (c), (e) and (b), (d), (f) denote the electric field distribution of the 1st and 2nd cavity modes. The upper and lower rows represent cross sections in the $xy$-plane (at $z=0$) and $xz$-plane. The electric field distribution in the GST $2\times 2$ block (Figs. 10 (c),(d)) is almost the same as the electric field distribution when GST is not loaded as shown in Figs. 10 (a),(b). This means that the effect of refractive index modulation by GST can be treated as a perturbation when the area of GST is small. This result is consistent with the linear relationship between wavelength shift and inverse Q-factor in Figs. 6 (a), (b) of the main text. On the other hand, in the GST $4\times 4$ block (Figs. 10 (e),(f)), it is observed that the electric field distribution is strongly modulated for both the 1st and 2nd modes in the crystalline GST. Especially, the cross section of the $xz$-plane as shown in Figs. 10 (e) shows that the electric field distribution of the 1st mode leaks outward from the PhC slab, which is thought to cause the blue shift of resonant wavelength. The strong deformation of the electric field distribution also significantly reduces the Q-factor of the mode, which is due to the increased out-of-plane radiation. Such low-Q modes were not observed in the transmission experiments for too small transmittance.

 

Fig. 10. The electric field distribution of two types of cavity modes in the L5 resonator (a), (b) without GST film, (c), (d) with $2\times 2$ GST blocks, and (e), (f) with $4\times 4$ GST blocks. (a), (c), (e) and (b), (d), (f) denote the electric field distribution of the 1st and 2nd cavity modes. The upper and lower rows represent cross sections in the $xy$-plane (at $z=0$) and $xz$-plane, respectively.

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Appendix B: transmission spectrum of the L5 resonator in other GST blocks

Figure 4 of the main text only shows the transmission spectrum with 2$\times$2 and 4$\times$4 GST blocks. Here, we lists spectra for 1$\times$1, 2$\times$1, 1$\times$2, 4$\times$1, 1$\times$4, 2$\times$4, and 4$\times$2 GST blocks. The results for 1$\times$1, 2$\times$1 and 1$\times$2 GST blocks as shown in Figs. 11 (a), (b) and (c) show little change in the resonance peak associated with the GST phase transition. The results for the 4$\times$1 block as shown in Fig. 11 (d) shows a change in the resonant peak due to the GST phase transition comparable to that of the 2$\times$2 block. The results for the 1$\times$4 block showed little change due to the GST phase transition (Fig. 11 (e)). The cause has not been identified, but in general, the more elongated the GST block, the more susceptible it is to fabrication errors. The results for the 4$\times$2 and 2$\times$4 GST blocks as shown in Figs. 11 (f) and (g) show intermediate features between the results for the 2$\times$2 and 4$\times$4 GST blocks: the 1st peak in the crystalline state is not observable (or indistinguishable from noise) due to a drastic decrease in Q-factor, which is similar to the result for the 4$\times$4 GST block. Moreover, the 2nd peak undergoes a net redshift of about 1 nm due to the GST phase transition.

 

Fig. 11. Transmission spectrum of the PhC structure shown in Fig. 1 (a) in the main text (a) with $1\times 1$, (b) with $2\times 2$, (c) $1\times 2$, (d) $4\times 1$, (e) $1\times 4$, (f) $4\times 2$, and (g) $2\times 4$ GST blocks. The left columns indicate the number of GST blocks.

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Appendix C: transmission spectrum of the W1.1 & W0.98 heterostructures in small GST blocks

In Section 3 of the main text, we show that cavities are formed by loading GST in a photonic crystal waveguide. However, in certain samples with small GST size, we could not identify the resonant peaks from transmission measurements. This section shows and briefly discusses the behavior when the effec of GST is small.

Six transmission spectrum are shown in Figs. 12 (a) to (f), where the left columns indicate the number of GST blocks. There are some signs of resonant peak near the original band edge in Figs. (b) to (c), but it cannot be determined to be a peak. Moreover, no signs of resonant peak were observed in the spectrum in the sample of GST $4\times 1$ block as shown in Fig. (d). It is possible that the GST is not patterning correctly in this sample. The sample of GST $1\times 2$ block as shown in Fig. 12 (e) is the smallest sample in which the cavity formation is confirmed. The resonance peak formed by loading amorphous GST is clearly present, whereas the peak shift due to the phase change of GST is hardly confirmed. This result suggests that the GST size is too small to achieve the phase change. We can confirm both the cavity formation and cavity tuning by phase change of GST in the sample of GST $1\times 4$ block as shown in Fig. 12 (f) as well as the sample of GST $2\times 2$ block in Fig. 8 (b) of the main text.

 

Fig. 12. Transmission spectrum of the PhC structure shown in Fig. 7 (a) in the main text (a) without GST, (b) with $1\times 1$, (c) $2\times 1$, (d) $4\times 1$, (e) $1\times 2$, and (f) $1\times 4$ GST blocks. The left columns indicate the number of GST blocks.

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Funding

Japan Society for the Promotion of Science (JP21K14551, JP20H05641).

Acknowledgement

We acknowledge the invaluable contributions of Dr. Toshiaki Tamamura, Toshifumi Watanabe and Osamu Moriwaki for nanofabrication techniques and Shinichi Fujiura for AFM measurements.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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