1. Introduction

Over the past years, the physics of optical quasi-bound states in the continuum (quasi-BIC) has found numerous fascinating applications ranging from sensing, lasing, chirality and nonlinear effects to controlled enhancement of quantum emitters [1–11].

The concept of BICs initially emerged from electronic systems, [12] but recently found direct analogies in optics and became a major trend of research in this field [13–15]. Optical BICs represent a class of states that remain localized despite residing in the continuum of radiating modes [13]. The lack of coupling to the incident radiation or, equivalently, the impossibility of radiation emission, lead to inherently infinite radiative $Q$-factors of BICs [13]. BICs can be classified into different types regarding the origin of radiation suppression. The symmetry-protected BICs appear when the spatial symmetry of the mode is not compatible with the symmetry of the radiating waves [15]. These BICs are manifested in metasurfaces, gratings, waveguide arrays, and other geometries [16–20]. Another type of BICs is related to the accidental vanishing of the coupling coefficients to the radiative waves by means of continuous tuning of certain parameters of the system [21–23]. These BICs are known as accidental BICs and can be observed even in isolated nanoparticles.

The infinite $Q$-factors of BICs cannot be experimentally attained due to the finite size of the samples, parasitic scattering, absorption or structural disorder [14]. In realistic scenarios, BICs are transformed into leaky modes, known as quasi-BICs [8,24,25]. In the experimentally measured spectra, this state usually interacts with a broad background resonance and manifests itself as a Fano resonance, characterized by asymmetric lineshape and high $Q$-factor values [9]. In the case of symmetry-protected BICs, the BIC can be transformed in a quasi-BIC by breaking the symmetry of the metasurface, opening a radiation channel. Quasi-BICs in all-dielectric metasurfaces were already utilized to enhance the emission of different emitters like 2D materials or quantum dots [26–29].

For practical applications, the tuning of the emission wavelength is also a crucial functionality. However, conventionally the parameters of quasi-BICs are fixed by the metasurface design. From this perspective, phase change materials (PCMs) present a viable platform for achieving tunable performance [30–33]. PCMs exhibit a considerable change of their optical properties upon transition from the amorphous to the crystalline phase that can be induced via thermal, electrical [34] or optical [35] stimuli; importantly, the phase transition is non-volatile, fast (down to nanoseconds), reversible and reproducible across many cycles [31]. Recent developments in the field of phase change nanophotonics yielded several materials that provide large refractive index contrast in different spectral ranges [32]. In particular, Ge$_2$Sb$_2$Te$_5$ (GST) and Ge$_2$Sb$_2$Se$_4$Te (GSST) were used for applications in the near- to mid-infrared ranges [36,37]. However, the small bandgaps of these materials (of the order of 0.5 eV) limit their efficiency in the visible light applications. Recently, the binary antimony compounds Sb$_2$S$_3$ and Sb$_2$Se$_3$ emerged as promising candidates to bring the phase change functionality to the visible and ensure low-loss operation in the technologically relevant telecom spectral range [38]. These materials are characterized by a much larger bandgap (up to 2.05 eV for antimony trisulfide) while maintaining high absolute value of the refractive index and its contrast between different phases (3 to 3.5). Based on these unique properties, tunable Mie resonances and color imprinting in the visible have been experimentally demonstrated [33,39].

The combination of the high $Q$-factors provided by quasi-BIC states with the tunable optical properties of PCMs opens exciting opportunities for the realization of active nanophotonic devices. Some of the most important functionalities of PCMs are in tuning and switching devices. It should be noted that in some previous works the tuning of quasi-BICs excited in all-dielectric metasurfaces was investigated by means of adjusting the Fermi level of a graphene monolayer , heating of a nematic liquid crystal [40], or controlling the temperature of strontium titanate materials integrated on the top of the metasurface [41]. In [42] the tuning effect was achieved through a metasurface made of a photosensitive chalcogenide glass of As$_2$S$_3$.

In a recent work by Bochek et al. [43], a switching effect of a photonic Friedrich-Wintgen quasi-BIC resonance excited in an isolated cylinder or disk made of GST was reported. It was demonstrated that by changing the GST state from amorphous to crystalline, the quasi-BIC practically dissapears, and only a background signal is observed in the spectrum.

In this work, for the first time to our knowledge, we numerically show the possibility of switching (“on”/“off”) and tuning of the quasi-BIC state excited in all-dielectric metasurfaces using phase change materials. To this end, we design a silicon-based metasurface supporting a quasi-BIC mode enabled by the asymmetry of its unit cell. A thin layer of PCM placed on top of the resonators allows for tuning of the BIC state’s properties. Our metasurface is designed to support the quasi-BIC resonance at $\lambda \approx 1550$ nm. Depending on the PCM material that we introduce to our structure, we demonstrate “on”/“off” switching of the quasi-BIC mode or its spectral fine-tuning in the telecom spectral range. When Ge$_2$Sb$_2$Te$_5$ is considered as PCM, the quasi-BIC resonance is manifested only for the amorphous state and is strongly suppressed when the material is switched to the crystalline state due to increased absorption. In contrast to previous work [43], here we focus on symmetry protected quasi-BIC resonances in dielectric metasurfaces rather than on accidental quasi-BICs attained in isolated nanoparticles. Morever, due to our particular design with low volume of PCM, we show that instead of complete suppression of BIC mode, spectral tuning of quasi-BIC resonance can also be achieved. To this end, we employ the large bandgap phase change material Sb$_{2}$Se$_{3}$. Due to its low absorption in both amorphous and crystalline phases in the telecom range, upon phase transition, the quasi-BIC resonance is shifted spectrally while the total $Q$-factor is kept at a relatively high value. This functionality is of particular importance for applications involving light emission (e.g. from quantum dots [29]), as it allows simultaneous strong and narrow-band enhancement and tuning of this band across the spectral range of emission. Furthermore, inspired by recent experimental demonstrations of the multilevel switching of PCMs, [34,35] we suggest that the control over the tuning can be extended by changing the crystallization fraction of the PCM.

2. Results

2.1 Design of the metasurface

Our metasurface design is inspired by the recently proposed concept of quasi-BIC in high-refractive-index (HRI) resonator lattices with asymmetric unit cell [11,15,44] and optimized for achieving the quasi-BIC resonance at telecom wavelengths. Figure 1(a) shows the sketch of our metasurface and its unit cell, which consists of two nanobars with different widths made of silicon and functionalized with a thin PCM layer. The optical properties of the constituent materials (silicon as the primary resonator material and Sb$_2$Se$_3$ for the top layer) were determined by our ellipsometric measurements. For GST, literature values were used [35]. The thickness of the PCM layer was fixed at $t = 50$ nm for both GST and Sb$_2$Se$_3$. This value was chosen to account for practical considerations: while larger PCM thickness would increase the tuning range, the low thermal conductivity of PCMs hinders the re-amorphization of large volumes of the material, which requires fast cooling rates [31,32]. The other dimensions in our design were taken as follows (see Figure 1(a)): bar length $l_{\mathrm {x}} = 435$ nm, bar widths $l_{\mathrm {y1}} = 315$ nm, $l_{\mathrm {y2}} = 230$ nm, gap between the two bars $g = 90$ nm and thickness of silicon layer $h = 273$ nm. The period of the metasurface is $P_{\mathrm {x}} = 570$ nm and $P_{\mathrm {y}} = 725$ nm (Fig. 1(b)). The substrate is assumed to be glass with refractive index $n = 1.51$. Finally, to avoid the surface oxidation (in case of GST) or gradual emission of Se and segregation (in case of Sb$_2$Se$_3$) in practical realizations, the metasurface is immersed into glass from top as well.

 

Fig. 1. (a,b) Sketch of the considered hybrid Si/PCM metasurface. (a) The unit cell is composed of two asymmetric bars embedded in glass ($n = 1.51$). (b) The period of the metasurface is $P_\mathrm {x} = 570$ nm and $P_\mathrm {y} = 725$ nm. (c,d) Optical properties of the amorphous (solid line) and crystalline (dashed line) phase of different PCMs: (c) Sb$_2$Se$_3$ and (d) GST [35]. The blue and red curves represent the real and imaginary parts of the refractive index, respectively. The black circles in (c) and (d) show the real part of the refractive index for Si.

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In order to investigate the switching behaviour of the hybrid metasurfaces, we performed numerical simulations of their transmission spectra using the finite-difference time-domain method implemented in Lumerical [45], Additionally, eigenmode field distributions were calculated using the finite element method implemented in COMSOL Multiphysics [46].

2.2 Optical properties

The performance of our metasurface critically depends on the optical properties of the amorphous and crystalline phases of the chosen PCMs. In Fig. 1(c) and (d) we present the optical constants of Sb$_2$Se$_3$ and GST for both states (amorphous and crystalline) that were used in our calculations, respectively. We have also included the real part of the refractive index of silicon for reference; its imaginary part is omitted as it exhibits negligibly small values in the spectral region of interest. Both PCMs have large values of the real part of the refractive index: $n = 4.09$ for GST and $n = 3.28$ for Sb$_2$Se$_3$ in amorphous phase at $\lambda \approx 1550$ nm. Regarding the imaginary part, the amorphous phase shows values lower than 0.03 in both cases ($k = 0.03$ for GST and $k = 0.018$ for Sb$_2$Se$_3$; note that even smaller losses for Sb$_2$Se$_3$ were reported in the work by Delaney et al. [38]). For the crystalline phase, $n$ increases to values of $n = 6.98$ for GST and $n = 4.66$ for Sb$_2$Se$_3$. The main difference in the material behavior is manifested in the absorption for the crystalline phase: for GST it increases considerably, reaching values of $k = 1.2$, whilst for Sb$_2$Se$_3$ the increase in $k$ is quite minor, $k = 0.17$. As we show further, this difference enables distinct functionality of GST- and Sb$_2$Se$_3$-based devices.

2.3 Tuning the resonance wavelength of quasi-BIC states with Sb$_2$Se$_3$

In Fig. 2(a) we present the transmission spectra of the described metasurface, considering Sb$_2$Se$_3$ as the PCM, for both its phases, amorphous and crystalline. For the amorphous phase, we can observe the quasi-BIC resonance at $\lambda = 1549$ nm. For the crystalline phase, the resonance is shifted to $\lambda = 1607$ nm, leading to a spectral shift of $\Delta \lambda = 58$ nm. The nature of the observed quasi-BIC resonance is revealed by the calculated eigenmode field distributions (Fig. 2(b) and (c)) which shows a pair of magnetic dipoles in each of the bars of the unit cell, oriented in opposite directions along the $x$-axis, which give a non-zero net magnetic dipole moment of the unit cell. By fitting the transmission spectra with a Fano curve, we extracted the $Q$-factor of the modes, which changes from $Q = 96.8$ for amorphous phase $Q = 38.2$ for crystalline phase. The decrease of the $Q$-factor is mainly due to the moderate increase of losses of Sb$_2$Se$_3$ in the crystalline state ($k$ = 0.018 vs. $k$ = 0.16 at the resonance wavelengths in the two phases, $\lambda = 1549$ nm and $\lambda = 1607$ nm for amorphous and crystalline states, respectively). In spite of the absorption increase, it is still possible to observe moderately-high $Q$-factors for the quasi-BIC resonance in the crystalline phase. The spatial distributions of the electric field intensity of the quasi-BIC mode for amorphous phase, shown in Fig. 2(b) and (c), reveal the field enhancement both inside the resonators and in the gaps between them. This suggests a potential application: realizing tunable emission enhancement by embedding nanoscale emitters directly into silicon resonators or in the silica matrix. The final design can be implemented using standard e-beam lithography combined with reactive ion etching, the most technologically challenging feature being the small gap between the neighboring bars within the unit cell. The incorporation of emitters in the design can e.g. be achieved in a multi-stage process demonstrated for Ge/Si QDs [47] or by spin-coating the device with colloidal QDs [48].

 

Fig. 2. (a) Transmission spectra for the optimized a-Si metasurface with a 50 nm layer of Sb$_2$Se$_3$ on top of the resonators. The structure was illuminated under normal incidence with linearly polarized incident light along the $y$-axis. The inset indicates the direction of polarization of the incident radiation ($\mathbf {E}$) with respect to the unit cell of the metasurface. (b,c) Eigenmode field distributions of the quasi-BIC state ($\lambda = 1549$ nm marked with a dashed line in panel a) for the amorphous state of Sb$_2$Se$_3$ in XY (b) and ZY (c) planes that intersect the bars at their center (marked with a dashed line in each panel). Black solid lines represent the edges of the resonators.

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The limited decrease of the mode $Q$-factor upon switching to the crystalline state of Sb$_2$Se$_3$ inspires the use of our design for continuous tuning of the resonance wavelength e.g. for applications in tunable filters or light sources, which can be achieved by fractional crystallization of the PCM. Experimentally, it was demonstrated that the crystallization fraction can be controlled through the formation of critical nuclei and their subsequent growth by applying a customized electrical pulse [34] or by applying a sequence of optical pulses with controlled fluence [35]. In order to understand how the crystallization fraction affects the tuning, we have analyzed the changes in the $Q$-factor (Fig. 3(a)) and the evolution of the transmission spectra (resonance wavelength and the dip value) (Fig. 3(b)) for different crystallization fractions. The effective dielectric constant ($\epsilon _{\mathrm {eff}}$) of the PCM for different crystallization fractions can be calculated using the Lorentz relation [37]:

 

Fig. 3. (a) $Q$-factor as a function of the crystallization factor $m$. (b) Evolution of the transmission spectra (resonance wavelength, red points, and minimum value, blue points) for different crystallization fractions.

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Naturally, the $Q$-factor decreases as the crystallization factor increases $m$ (Fig. 3(a)). We also observe a minor change in the depth of the transmission minimum with the increase of the crystallization fraction at the quasi-BIC resonance (Fig. 3(b)). In addition, a red-shift of the mode spectral position is attained.

2.4 Switching of the quasi-BIC resonance with GST

In the previous section we showed that due to the small losses of Sb$_2$Se$_3$ in the telecom spectral range, it is possible to observe quasi-BICs with high $Q$-factors in the amorphous and crystalline phases. Here, we show how the metasurface behaviour changes when GST is chosen as the PCM material, which exhibits a considerable increase of losses in the crystalline state. In the amorphous phase, we observe a quasi-BIC resonance at $\lambda = 1584$ nm, with a $Q$-factor of 65.9. When GST is changed from the amorphous to the crystalline phase, the resonance transforms considerably, as it can be observed in Fig. 4(a). Apart from the spectral shift to $\lambda = 1721$ nm ($\Delta \lambda = 137$ nm), the resonance exhibits a substantial drop of the $Q$-factor (down to 10.8), as well as a drastic change of the depth of the transmission minimum, from $T = 0.015$ (amorphous phase) to $T = 0.26$ (crystalline phase). The increase in the absorption $k$ at the resonant wavelength in this case is from 0.021 at $\lambda = 1584$ nm for the amorphous phase, to $k = 0.82$ at $\lambda = 1721$ nm, for the crystalline one.

 

Fig. 4. (a) Transmission spectra for the a-Si metasurface with a 50 nm layer of GST on top of the resonators, described in Fig. 1. The structure was illuminated under normal incidence with linearly polarized incident light along the $y$-axis. The inset indicates the direction of polarization of the incident radiation ($\mathbf {E}$) with respect to the unit cell of the metasurface. (b,c) Eigenmode field distributions of the quasi-BIC state ($\lambda = 1584$ nm marked with dashed line in panel a) for amorphous state of GST in XY (b) and ZY (c) planes that intersect the bars at their center (marked with dashed lines in each panel). Black solid lines represent the edges of the resonators.

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It is important to remark that the origin of the quasi-BIC is the same as that described in the previous section, which is confirmed by the eigenmode field intensity distributions shown in Fig. 4(b) and (c). In contrast to the Sb$_2$Se$_3$ design, the maps suggest that an “on-off” switching of the high-$Q$ state can be performed, which could e.g. be employed for the dynamic switching of brightness of nanoscale light sources integrated into the metasurface architecture.

2.5 Evolution of the $Q$-factor with the asymmetry parameter

The influence of the asymmetry parameter ($\alpha$) on the radiative $Q$-factor of quasi-BIC resonances was theoretically studied in Refs. [15,44]. It was shown that as the asymmetry parameter increases, the $Q$-factor decreases following a square-law dependence ($Q \propto \alpha ^{-2}$). This law is independent of the kind of geometry constituting the metasurface.

In this section, we analyze the evolution of the $Q$-factor with the asymmetry parameter for the two PCMs considered in the previous sections when they are in the low-loss amorphous state. By decreasing the asymmetry parameter, it is possible to determine the maximum values of the $Q$-factor that can be obtained with the designed metasurfaces, which are limited by the optical losses of the respective material.

Fig. 5 shows how the $Q$-factor decreases with the asymmetry parameter. For small asymmetry parameters ($\alpha = 0.01$), the maximum values obtained for Sb$_2$Se$_3$ and GST are $Q = 1182$ and $Q = 3203$, respectively. These values are typical for most of all-dielectric metasurfaces designed to exhibit quasi-BIC in the near-infrared (NIR) spectral region. For two dielectric nanobars geometries, $Q$-factor values ranging from 150 to 300 were experimentally achieved for wavelengths between $\lambda = 855$ nm and $\lambda = 1500$ nm [6,14]. However, larger $Q$-factors have been obtained theoretically by means of novel geometries. For example, a metasurface composed of silicon nanodisk dimers was designed to achieve $Q$-factors as large as $10^9$ at $\lambda = 1100$ nm owing to the excitation of toroidal dipole BICs [49].

 

Fig. 5. $Q$-factor as a function of the asymmetry parameter $\alpha$ for the different PCMs considered on the top of the silicon resonators when they are in amorphous state: (a) Sb$_2$Se$_3$ and (b) GST. As an inset in (a) it is represented an scheme of the definition of the asymmetry parameter $\alpha$.

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We also analyze the contributions of $Q_{\mathrm {loss}}$ and $Q_{\mathrm {rad}}$ to the $Q$-factor. $Q_{\mathrm {loss}}$ was obtained by simulating a lossless metasurface. In that case, the total $Q$-factor is determined by $Q_{\mathrm {rad}}$. Once $Q_{\mathrm {rad}}$ is known and, under the assumption that $Q_{\mathrm {rad}}$ is independent of the losses in each one of the resonators, we can retrieve $Q_{\mathrm {loss}}$ for our designed metasurface from the $Q$-factor value and using Eq. (2).

For an asymmetry parameter corresponding to $\alpha = 0.01$ and the amorphous state, we have obtained the $Q_{\mathrm {loss}}$ and $Q_{\mathrm {rad}}$ contributions. For Sb$_2$Se$_3$ $Q_{\mathrm {loss}}$ and $Q_{\mathrm {rad}}$ correspond to $1.22\cdot 10^3$ and $4.07\cdot 10^4$, respectively. For GST, the following values were found: $Q_{\mathrm {loss}} = 3.31\cdot 10^3$ and $Q_{\mathrm {rad}} = 9.55\cdot 10^4$. For both materials $Q_\mathrm {rad}$ is larger than $Q_\mathrm {loss}$.

For the asymmetry parameter used in our design, $\alpha = 0.27$, the $Q_{\mathrm {loss}}$ and $Q_{\mathrm {rad}}$ contributions to the total $Q$-factor were calculated for both amorphous and crystalline states, and for Sb$_2$Se$_3$ and GST, obtaining: Sb$_2$Se$_3$ amorphous state: $Q_{\mathrm {loss}} = 772.8$ and $Q_\mathrm {rad} = 110.7$. Sb$_2$Se$_3$ crystalline state: $Q_{\mathrm {loss}} = 143.1$ and $Q_\mathrm {rad} = 52.1$. GST amorphous state: $Q_{\mathrm {loss}} = 1.11\cdot 10^3$ and $Q_\mathrm {rad} = 70.0$. GST crystalline state: $Q_{\mathrm {loss}} = 41.7$ and $Q_\mathrm {rad} = 14.6$.

For the amorphous state, $Q_{\mathrm {loss}}$ is much larger than $Q_{\mathrm {rad}}$. However, as the crystallization fraction increases, both contributions take similar values, being close to the critical coupling regime for the crystalline state. When the critical coupling condition is satisfied ($Q_\mathrm {rad}$ = $Q_\mathrm {loss}$), a complete exchange of energy between a propagating mode in a coupler device and the given resonator mode can occur [49]. This suggests that our design is closer to the optimum for the crystalline state than for the amorphous one.

In order to determine the asymmetry parameter requiring to achieve critical coupling, we have used the well-known dependency of the $Q$-factor on the asymmetry parameter, which is given by Eq. (3) [50].

By the inspection of Eq. (3), it is possible to conclude that by the fitting of the $Q$-factor for different asymmetry parameter values to that equation, we can retrieve both the $Q_{\mathrm {loss}}$ contribution and the asymmetry value for obtaining the critical coupling condition. By following this procedure, we have obtained $\alpha _\mathrm {cr}$ for Sb$_2$Se$_3$ and GST for amorphous and crystalline states. Sb$_2$Se$_3$ amorphous state: $\alpha _\mathrm {cr} = 0.065$. Sb$_2$Se$_3$ crystalline state: $\alpha _\mathrm {cr} = 0.18$. GST amorphous state: $\alpha _\mathrm {cr} = 0.067$. GST crystalline state: $\alpha _\mathrm {cr} = 0.22$.

Several works have investigated the effect of the fabrication imperfections and structural disorder in the $Q$-factor values of structures exhibiting BIC resonances. From a careful review of these articles, we give an estimation of the $Q$-factor for our design when these effects are taken into account. In [51], it was studied both numerically and experimentally, how the sample imperfections during the fabrication process affect the $Q$-factor values. It was shown that even for small geometrical changes, the $Q$-factor and the amplitude of the resonances are significantly reduced. In that manuscript, the effect of the tolerances in nanofabrication, such as random geometrical variations, on different BIC metasurface designs was analyzed. In particular, they considered three different broken-symmetry geometries: tilted ellipses, asymmetric double rods, and split rings. The second geometry is very similar to the one used in our work. The authors demonstrated that the $Q$-factor of the different BIC designs is proportional to the standard deviations ($\sigma$) of the geometrical variation by means of the following equation:

Experimentally, a tolerance in fabrication of $\sigma = 0.9$ nm was obtained. This leads to a reduction in the $Q$-factor of about a 35% for the two-bars geometry. By using the same reduction for our designs, we can estimate a $Q$-factor of 770 and 2100 for the Sb$_2$Se$_3$ and GST metasurfaces, respectively.

In [52] the effect of structural disorder on the transition from BICs to quasi-BICs by the example of a periodic photonic structure composed of two layers of parallel dielectric rods was studied. It was established that for a structure of finite size, consisting of $N$ periods, presenting structural disorder, the total $Q$-factor is contributed by two parts:

The authors analyzed the disorder effect for both: accidental and symmetry-protected quasi-BIC. However, this type of disorder is only characteristic for self-assembled structures. In our case, e-beam fabrication would be used, as it was already explained. This suggests that, for our design, mainly deviations of the exact sizes of the metasurface elements from their target values as reported in [51] would play a role.

3. Conclusions

In this work we have numerically analyzed different functionalities of a hybrid metasurface based on a-Si nanobars functionalized by a thin layer of phase change material. The metasurface was designed to exhibit a quasi-BIC resonance at telecom wavelengths driven by the asymmetry of its unit cell. We showed that the change of the refractive index, provided by switching the phase state of PCM, enables effective control over the quasi-BIC resonance that in turn provides distinct functionalities dependent on the phase change material that is used in the design.

For the low loss PCM Sb$_2$Se$_3$, the switching of the phase state provided strong spectral tuning of the resonance that maintains relatively high $Q$-factors even for the crystalline state. We also showed that in this case the control of the crystallization fraction allows for continuous tuning of the spectral position of the resonance. On the other hand, the use of GeSbTe, as the phase change material in the same design, provides “on-off” switching of the resonance that follows from much stronger optical losses for its crystalline phase in comparison with Sb$_2$Se$_3$.

We also analyzed the maximum achievable $Q$-factors for such hybrid metasurface that are limited by the absorption of the PCMs in their amorphous state. In particular, for an asymmetry parameter of $\alpha = 0.01$, $Q = 1182$ and $Q = 3203$ were attained for Sb$_2$Se$_3$ and GST, respectively.

The proposed platform of quasi-BIC metasurface functionalized by PCM may find applications for tunable spectral shaping, dynamic wavefront shaping, tunable filters, sensors, and enhancement and fine control of light emission.