1. Introduction

All-optical implementations [1] of key on-chip data operations could potentially save energy and increase operational bandwidth, by making electrical-optical conversions redundant, and accessing the high-bandwidths and low transmission losses inherent in the optical domain. There is also a keen interest, currently, in all-optical and hybrid electronic-photonic hardware platforms for neural inference [2,3] to power the next generation of Artificial Intelligence (AI) technology [4] in the form of coherent nanophotonic circuits [5], and neuromorphic photonic integrated circuits [6,7]. The optical properties of silicon and silicon nitride are only modestly tunable and their optical nonlinearities are weak; this makes it difficult to achieve all-optical processing in these platforms. Additionally, active devices like modulators require a large footprint (as they need to rely on resonant structures to achieve performance specifications [8]). Heterogeneous integration with materials like electro-optic polymers, plasmonic materials, 2D materials and phase change materials is an approach being considered to address these shortcomings. Chalcogenide phase-change materials (PCM) embedded in integrated photonic circuits [9–11] are especially promising as they can exhibit wide tunability in both the real and imaginary components of their refractive index [12] and can be switched rapidly between different phases [13,14]. They have been explored in photonic devices for nonvolatile binary and multilevel memory; arithmetic and logic processing [15]; and, neuronal and synaptic hardware mimics. Moreover, these devices can be readily combined into larger-scale systems to provide all-optical non-Von-Neumann computation [9]. While great strides have been made in the development of integrated phase-change photonic devices, there is a need to further improve performance metrics.

At the heart of PCM based reconfigurable integrated photonics lies a waveguide or a resonator-coupled waveguide which embeds small phase-change memory cells atop the waveguides or the resonator. The PCM cell is evanescently coupled to the optical mode and affects its optical transmittance via absorption. The simplest configurations [16] involve PCM cells on silicon [8] or silicon nitride strip waveguides [15,17,18]. In non-resonant configurations, the evanescent coupling is inefficient and requires long GST cells of about 4 µm length for decent performance. Li and coworkers have achieved a maximum contrast of 32% for a GST size of 4 µm x 1.3 µm x 0.01 µm [18]. The write process for this study has a threshold energy of 68 pJ and a figure-of-merit of 10.5×10⁻³ dB pJ⁻¹ [19]. For smaller GST size of 0.25 µm length, Rios and coworkers reported a significantly smaller contrast of 0.67% and a figure-of-merit of 0.52×10⁻³ dB pJ⁻¹ for the write process [19,20]. Even with longer GST cells, the maximum readout contrast and the figure-of-merit for the write process are not very high. This occurs because only a portion of the cell changes state due to the nonuniform absorption profile in large GST sizes. Cheng and coworkers [7] have explored the possibility of using multiple PCM cells to improve transmission contrast. But, this too showed only a marginal improvement as absorption is mostly limited to the first cell.

Configurations using resonant structures can locally enhance electric fields which is equivalent to increasing the absorption path length. Wu and coworkers have reported a micro-ring resonator configuration where the maximum achieved contrast is 87% and the figure-of-merit for the write process is 40×10⁻³ dB pJ⁻¹ [19,21]. However, the device operates at a significantly high threshold energy of 220 pJ. Also, these improvements occur at the cost of vastly increased device footprint. One approach to improve performance without incurring footprint expansion is a theoretical proposal of a waveguide loaded with a plasmonic [19] dimer nanoantenna with a PCM filled gap which resulted in significant improvements in switching speeds and energies. Write/erase speeds in the range 2 ns to 20 ns, and write/erase energies in the range 2 pJ to 15 pJ were predicted, representing improvements of one to two orders of magnitude when compared to conventional device architectures. A potential drawback of the plasmonic approach [19,22], however, is the significant fabrication difficulties (multiple materials and tighter tolerance requirements). Also, the readout contrast is only about a 18%.

We propose a novel configuration of the optically-reconfigurable element based on a resonant metamaterial waveguide (also known as the sub-wavelength grating (SWG) [23] waveguide). SWG waveguides [23–29] have led to performance improvement in a number of integrated photonics devices. Specifically, we consider a silicon nitride on silica platform [30] (air-clad) loaded with a Ge₂Sb₂Te₅ (GST) cell. The threshold energy of our device is 16 pJ for a 10 ns write pulse and is around 3-4 times smaller than conventional ridge waveguide architectures using long GST strips, and an order of magnitude smaller than micro-ring and photonic crystal cavity structures [19]. Our device exhibits a maximum contrast of more than 100% for write pulses of 10 ns which is 2-3 times higher than conventional structures [18]. Using two GST strips and a longer write pulse of 50 ns, a further increase in contrast up to 300% is possible which is a three-fold improvement over micro-ring and photonic crystal cavity structures [21] [31]. The figure-of-merit for the write process in our device is around 140×10⁻³ dB pJ⁻¹ displaying three-fold increase in comparison to micro-ring architecture, and an order of magnitude improvement when compared to conventional and photonic crystal cavity architectures [19]. The proposed structure provides many advantages over the photonic crystal cavity design reported by Von Keitz and coworkers [31]. The mode profile (in particular, the proportion of the mode in the evanescent tail) can be controlled to a greater degree to improve evanescent coupling efficiency. Overall device lengths including the taper can be designed to be less than 50 µm and smaller GST cell dimensions can be used. Additionally, the issue of optimal cell loading that we consider here has not been addressed previously.

The rest of the paper is organised as follows: in section 2, we discuss the proposed geometry and the operating principle of its optical reconfigurability; in section 3, the geometrical parameters are systematically studied and device optimization is discussed; in section 4, the performance of the proposed geometry is assessed and compared with other configurations. The paper concludes in section 5.

2. Device geometry and operation principle

The schematic of the proposed reconfigurable resonant metamaterial waveguide is shown in Fig. 1. It consists of two outer strip waveguide sections and an inner SWG section with a taper interfacing the different sections. The width $W$ and height $H$ of the waveguide remains constant throughout. The SWG section is characterised by the number of grating ribs, the grating period (GP) and the duty cycle (DC). The duty cycle (DC) is a parameter characterizing the fill-fraction of silicon nitride in a grating period. Duty cycle provides control over $n_{\parallel }$ (the refractive index along the width of the waveguide) and $n_{\perp }$ (the refractive index along the propagation direction of the waveguide), and, consequently, over the effective index and dispersion of the mode [23]. $L$ and $L_{c}$ denote the overall device length and length of the cavity respectively. The taper sections are characterized by the taper length (TP). The GST cell is a cuboid lying on a rib; $l$ denotes its length along the $x$ direction, $w$ denotes its width along the $y$ direction, and $h$ denotes its height along the $z$ direction. The position of the GST cell can be specified by the offset of the rib (with respect to the central rib) on which it lies.

 

Fig. 1. A Schematic of the proposed optically reconfigurable waveguide two-level memory. High-power sculpted optical pulses are used to change the phase of the GST material between crystalline and amorphous states. Low powered read pulses can transmit with low (state ’0’) or high (state ’1’) values of transmittance depending on the GST phase. B: 2D cross-section view in the $y-z$ plane. C: Top view with geometrical parameters indicated.

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The transmittance of the waveguide is affected by the GST nanoantenna which is evanescently coupled to the propagating mode of the waveguide. In the pure crystalline state, GST has a high value of $\kappa$ resulting in a large attenuation. Conversely, in the pure amorphous state, the GST nanoantenna has a smaller value of $\kappa$ resulting in a higher transmittance value than the other phase. A GST strip existing in a partially amorphized state will affect the transmittance depending on the degree of crystallinity. The formula used for calculating maximum contrast is $(T_{a}-T_{c})/T_{c}$, where $T_{a}$ is the transmittance through the waveguide when the GST is in its most amorphous state, and $T_{c}$ is the transmittance through the waveguide when the GST is in a complete crystalline state [7,21,32]. However, in some previous works, the formula used for calculating maximum contrast is $(T_{a}-T_{c})/T_{a}$ [19,20]. In our study, we have used the first formula for all the comparisons because crystalline state is the reference for contrast measurements in our application.

The optical transmittance of the waveguide (within predetermined tolerance) is considered as the state of the waveguide and this state can be "read" by determining the transmittance of a low-powered (below the reconfiguration threshold) optical pulse of known signal strength. Optical pulses can induce phase changes in the GST material provided they meet certain threshold power requirements. The reconfiguration of the waveguide is a process by which the state of the waveguide is altered by sending a sculpted high-powered (above the reconfiguration threshold) optical pulse. For a 2-level (binary) reconfigurable waveguide, three different operations can be considered (write, erase and read). Beginning with a GST cell in the crystalline phase, the ’write’ pulse converts it into an amorphous state. Sending an ’erase’ pulse recrystallizes the GST cell. The read, write and erase pulses are distinguished by their shape and power level as seen in Fig. 1(A). The performance metrics of the reconfigurable waveguide include the speed of reconfiguration, the threshold energy for reconfiguration, the transmittance contrast between the levels and the device footprint. Beyond the threshold, the transmittance contrast can be increased using a higher pulse energy. The slope of the contrast change with pulse energy can be considered as a figure of merit (FoM) and is of special relevance for multilevel bit design. The performance metrics depend upon the optical and thermal properties of a particular design; in particular, the optical interaction between the waveguide mode and the GST nanoantenna is a key factor.

2.1 Numerical simulation methodology

The numerical study was performed using the commercial simulation tool CST Studio Suite which includes the optical and thermal solvers. The optical simulations are performed using the high-frequency transient solver in the CST Microwave Studio (MWS) module which uses the Finite Integration Technique (FIT). All the simulations have been performed with open boundary conditions. The structure is divided into hexahedral meshes with a minimum of 10 cells per wavelength to perform the EM simulations. The material parameters used for our simulations are shown in Table 1. The optical excitation uses the fundamental transverse electric (TE) mode injected in the input port of the waveguide. Also, for a particular excitation wavelength, a thermal loss distribution is obtained which calculates power losses in the dispersive materials of the structure. The thermal loss distribution couples the optical simulation to the thermal solver as it imports the 3D power dissipation profile to the multi-physics module of CST Studio Suite. The root-mean-squared power loss obtained for a 1 W mode power needs to be scaled to the power of the excitation pulse envelope before being used as a heat source in the thermal simulations. This heat source is modulated with the excitation signal envelope in the transient thermal solver to mimic the envelope of an optical pulse. The thermal solver step results in a 3D transient temperature profile of the desired structure. The temperature profile is used to determine the phase distribution in the GST strip. The exact phase profile of a GST strip is used again in the EM solver to determine the optical transmittance.

Table 1. Summary of various materials used in this study and their relevant physical parameters. The relevant references in the literature are noted.

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For the SWG structure, the transmittance spectrum and electric field profile was verified against previous papers. The Fabry-perot modes of the SWG cavity obtained are similar to those in our previous work [37]. We have verified our simulation methodology by comparing our results with previously published papers on phase change memories. The electric field magnitudes and distribution profile along the axis of propagation of light matches closely with Cheng et al. for a single GST strip of 6 µm length loaded on a straight waveguide [7]. The power absorption and temperature distribution in the GST material for our simulations is consistent with Cheng et al. for a 2 µm length GST cell loaded on a straight waveguide [15]. We have also verified our temperature distribution with Rios et al. for a 5 µm length GST cell where they had used a different set of material coefficients and excitation signal from the previous case [17].

3. Device design and optimisation

A SWG waveguide can operate in three distinct operational regimes depending on the ratio of the grating period (GP) to the operating wavelength [23]: (1) as a strip waveguide with an effective index proportional to the duty cycle (DC) for large wavelengths; (2) for shorter wavelengths comparable to the GP, it behaves as a bragg grating exhibiting distinct stop bands; and (3) in between these two extremes, the SWG waveguide exhibits a series of narrow transmittance peaks (as seen in Fig. 2(A)). Regime (3) is of interest in this paper. When the operating wavelength coincides with the resonant wavelength of the cavity, an incident pulse undergoes multiple bounces resulting in an enhanced electric field amplitude in comparison to a non-resonant situation. This increase in field amplitude is not accompanied by a widening of the mode cross section resulting in increasing coupling between the mode and the nano-antenna. We previously reported a resonant enhancement of electric field by an approximate factor of 3 (compared to strip waveguides) [37].

 

Fig. 2. Optical study of unloaded resonant SWG waveguide. A Transmittance, Reflectance, and Absorbance spectra highlighting the first three modes (GP = 475, DC = 0.6, Number of ribs = 53, Taper = 15*GP). B Variation of Q-factor with number of ribs in the resonator for the first three modes (GP = 500, DC = 0.5, and zero taper). C Top view of the electric field profile of the first three modes seen in A. D-G Optimisation of the parameters of SWG keeping the number of ribs fixed at 53. D–F: Variation of Q-factor and resonant wavelength for the $1^{\textrm{st}}$ mode as a function of DC for GP values of 450 nm, 475 nm and 500 nm respectively. G Variation of peak transmittance and maximum ER for the $1^{\textrm{st}}$ mode for various taper lengths (GP = 475 and DC = 0.6).

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3.1 Optimizing the bare cavity

The transmittance, reflectance, and absorbance spectra of an unloaded SWG waveguide is shown in Fig. 2(A), and resonant transmission peaks at 1556.7 nm, 1571.2 nm, and 1592.8 nm can be observed. The $1^{\textrm{st}}$ mode at 1556.7 nm which lies in the C-band exhibits the sharpest peak among all the modes. Although the waveguide and the substrates are nearly lossless, some power is lost due to scattering and other leakage. The peak transmittance values at the modes can be increased by the careful design of the taper. The cavity length $L_C$ can be increased to improve the quality factor of the modes as seen in Fig. 2(B). The corresponding electric field profiles for the three modes on the top surface of the waveguide are shown in Fig. 2(C) which exhibit up to four-fold field enhancements compared to strip waveguides of similiar width and height. It can be observed here that $1^{\textrm{st}}$ mode exhibits maximum field enhancement compared to the other modes.

In order to arrive at this optimised bare SWG geometry, we systematically vary the number of ribs, GP, DC and taper length individually while keeping the other parameters constant using the Q-factor and resonance wavelength as metrics. For the analysis of Fig. 2(B), we fix the GP at 500, DC at 0.5, and do not include any taper. Here, it is observed that the Q-factor of $1^{\textrm{st}}$ mode is significantly higher than that of the other modes. It can also be observed that the Q-factor increases rapidly for more number of ribs. In the remainder of the paper, the total number of ribs in the structure is fixed to 53 with 26 ribs on each side of the central rib.

Next, we analyse the dependence of Q-factor and resonance wavelength on GP and DC. In Fig. 2(D), we start with GP = 450, No. of ribs = 53 and zero taper. As the DC is varied, the Q-factor and resonance wavelength are plotted for the $1^{\textrm{st}}$ mode. A similar study is performed in Fig. 2(E) and 2(F), where, the GP value is changed to 475 and 500 respectively keeping other parameters constant. For all the three cases, there is an optimal value of DC for which the Q-factor is highest. Further, increasing DC negatively affects it. As the DC increases and approaches one, the spacing between ribs continues to decrease and the SWG structure starts behaving more like a strip waveguide resulting in the reduction of Q-factor. It is also observed in Fig. 2(D), 2(E) and 2(F) that the $1^{\textrm{st}}$ mode resonance wavelength increases linearly with DC due to the increase in effective index. For values of GP greater than 500, the transmission drops as the Bragg reflection regime is entered. We choose a DC value of 0.6 and fix the GP at 475 for our study as this configuration exhibits a very high Q-factor and the resonance wavelength lies in C-band near 1550 nm.

Finally, a taper is introduced in the structure to increase the transmittance peak value at the modes which also enhances the electric field localized in the cavity. The introduction of taper minimally shifts the resonance wavelength and keeps it within the C-band. To quantify the enhancement of electric field, we use an electric field enhancement ratio (ER) given by $\displaystyle \mathbf {|E|} / \mathbf {|E|}_s$, where $\mathbf {|E|}$ is the maximum electric field amplitude in the cavity on the top surface of the SWG structure corresponding to the $1^{\textrm{st}}$ Fabry-Perot mode, and $\mathbf {|E|}_s$ is the maximum electric field amplitude on the top surface of the strip waveguide of similar dimensions for identical input power. Figure 2(F) shows the variation of $1^{\textrm{st}}$ mode transmittance peak value and ER with taper lengths. The structure used in study has a DC = 0.6, GP = 475 and number of ribs = 53. We can clearly see that with larger taper lengths, the ER and transmittance peak values both improve. This occurs because the taper is gradually reducing the effective index contrast between the strip and the SWG sections. However, for larger taper lengths of 20*GP and more, the SWG portion of cavity reduces as more ribs are incorporated in the taper. As a result, we are left with fewer number of ribs where GST can be loaded. Therefore, we fix the taper length at 15*GP which has a transmittance value greater than 0.8 for $1^{\textrm{st}}$ mode and shows an ER of about 4.

3.2 Optimizing the loaded cavity

Next an SWG structure loaded with a crystalline GST nanoantennae is studied. The first question concerns finding the optimal loading position of nanoantennae which can maximise its coupling with the waveguide. Figure 3(B) and 3(C) show the transmittance and absorbance spectra for various loading positions. Comparisons with the reference spectra for the unloaded waveguides shows that peaks exhibit red shifts as well as increased broadening. For a given mode, the amount of shift and broadening is seen to be strongly dependent on the loading position with respect to the field intensity nodes of the mode. Consistent with the results of cavity perturbation theory [38], the shifts are largest (see Fig. 3(B)) when the loading is coincident with position of maximum field intensity (see Fig. 2(C)). Similarly, the linewidth broadening is also greatest for loading (see Fig. 3(B)) where the electric field intensity is highest (see Fig. 2(C)). For example - In the $1^{\textrm{st}}$ mode, the electric field intensity is highest at the center, and it is observed that the red shift and linewidth broadening is also maximum when the GST is loaded at this point. Whereas, for the $2^{\textrm{nd}}$ mode, electric field intensity is highest at +$8^{\textrm{th}}$ and -$8^{\textrm{th}}$ rib; it is observed that redshift and linewidth broadening is maximum when GST is loaded at these positions. In this paper, our write operation corresponds to the $1^{\textrm{st}}$ mode and we will be optimizing the loading position for it.

 

Fig. 3. Optical response of the loaded resonant SWG waveguide. A Top view of the SWG structure showing how the placement of GST is specified by the offset with respect to the central rib. B,C Transmittance and absorbance spectra respectively for different loading positions. The spectra for the unloaded waveguide is shown for reference. D Peak power loss density in the GST cell and the mode Q-factors for different loading positions, E Variation of the resonance wavelength and peak absorption with loading positions.

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The waveguide transmittance spectra for the $1^{\textrm{st}}$ resonance mode seen in Fig. 3(A) indicate a strong reduction for loading at the center. However, a reduced transmittance does not imply an absorption peak as seen in Figs. 3(B) and 3(E). It was also observed that the reflection is larger compared to that of the bare waveguide; more so, for the cases of loading near the center. The reflection occurs due to impedance mismatch introduced by the loading. Thus, it can be concluded that center loading is not the optimal position to obtain the largest absorption in the GST cell for a given mode power. From Fig. 3(D), it is observed that the peak power loss density is highest for the crystalline GST loaded on +$10^{\textrm{th}}$ rib from the center. This result is also consistent with the absorbance values as +$10^{\textrm{th}}$ offset position exhibits highest peak at the $1^{\textrm{st}}$ mode resonance wavelength. This feature can clearly observed in Fig. 3(E). In other words, even though the electric field is maximum at the centre of cavity, loading the GST at this point perturbs the cavity maximally leading to increased reflection losses. On the contrary, loading the GST furthest away from the cavity perturbs it the least, but, the absorbed power in the GST cell is also low due to the reduced local electric field. As a result of this trade off, the optimal position is found out to be at the +$10^{\textrm{th}}$ rib where the overall GST cell absorption is highest.

After optimising the placement of GST, the effect of the nanoantennae dimensions on the performance is studied next. First, for the optimised waveguide configuration, the length of the GST cell $l$ is varied from 90 nm to 270 nm. The width $w$ and height $h$ of the GST cell are maintained constant at 500 nm and 20 nm respectively. Figure 4(A) shows that while the peak power loss density is highest for the 90 nm GST length case, maximum contrast is achieved for 270 nm GST length. This is because absorption is more localised in smaller GST sizes leading to higher peak values. On the other hand, the total absorption would be higher for larger GST sizes as the volume of absorbing material is greater. The peak power loss density dictates the threshold energy of our device, while the contrast dictates the multi-level operation. Next, we vary the thickness of the GST film from 10 nm to 30 nm maintaining the length and width of the film constant at 180 nm and 500 nm respectively. It can be observed from Fig. 4(B) that the peak power loss density is maximum for a film thickness of 20 nm while the transmittance contrast is highest for the case of 30 nm thickness. For the remainder of the article, we choose a length of 180 nm and GST film thickness of 20 nm.

 

Fig. 4. Parametric study of GST dimensions. Variation of peak power loss density and transmittance contrast with the length $l$ (A) and thickness $h$ (B) of the GST cell. The width $w$ is maintained constant at 500 nm. The GST cell is loaded on +$10^{\textrm{th}}$ rib from the centre where the maximum coupling is obtained.

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The final optimized structure has a DC = 0.6, GP = 475, number of ribs = 53 and taper length = 15*GP with GST loading on the tenth rib from the centre of the structure in the direction of propagation of light. This configuration is used in Fig. 5 to qualitatively show the enhancement of electric field, power loss density and temperature profile for the structured waveguide in comparison to the strip waveguide. For the case of multiple GST cells, a second identical nanoantenna is placed on +$9^{\textrm{th}}$ rib from the centre. The maximum power loss density and highest temperature is less for multiple GST case compared to that of single GST resulting in increased threshold energy. But, the transmittance contrast will be higher for the case of multiple GST as significant portion of both the GST cells undergo amorphisation.

 

Fig. 5. Optical and thermal distribution profiles for crystalline GST loaded strip and SWG structures. A Electric field profile at the top surface of waveguide for strip ((i), (iii)) and SWG ((ii) and (iv)) waveguides loaded with one and two PCM cells respectively. B Cross sectional view ($y-z$ plane) of the electric field profile passing through the center of the GST cell and the waveguide for strip (i) and SWG (ii) waveguides respectively. C and D Comparison of the power absorption profile at middle plane of GST cell ($x-y$ plane) between the strip (i)(iii) and SWG (ii)(iv) waveguides for single and double GST loading respectively. E,F Comparison of steady state temperature profile at the top surface of GST cell for the strip (i)(iii) and SWG (ii)(iv) waveguides for the cases of single and double GST loading respectively. C,D - cw illumination of 1 W, E, F - 50 ns write pulse of 2 mW peak power.

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4. Performance of the reconfigurable waveguide

In the following subsections, we first demonstrate the write and erase operations in our device. Next, we compare the efficiency of our proposed architecture to other GST-waveguide configurations.

4.1 Read, write, and erase operations

The wavelengths at which read, write, and erase operations are to be performed are first determined. Figure 6(A) shows the transmission spectra for the bare SWG waveguide in comparison to the loaded SWG. The read operation involves monitoring the transmittance of low-powered optical pulses to determine the state of the phase change memory. We perform the read operation at 1573 nm where we can observe a maximum peak in the transmission contrast between amorphous and crystalline GST, as shown in Fig. 6(B). Typically, a read operation is performed using sub-nanosecond pulses with an order of magnitude lesser power than write operation [20]. On the other hand, the write process (amorphization) requires heating up of the GST cell to temperatures above the melting point (877 K) [39] followed by quenching at very high cooling rates around 10¹⁰ K s⁻¹ [40] until the glass transition temperature (383 K) [41] to avoid crystallization of the melt. Threshold energy of this switching is signified by the minimum energy needed for any portion of the GST cell to reach the melting temperature and amorphize. Therefore, writing operation of our device is performed at the wavelength where absorbance is highest (as seen in Fig. 6(C)) resulting in faster and efficient heating. To summarize, the write/erase operation of our device is performed at 1560 nm and the read operation is performed at 1573 nm.

 

Fig. 6. Determining the Read-Write wavelengths. A Transmittance spectra of bare SWG and loaded SWG (amorphous and crystalline GST cells placed at the optimised position). B Transmittance contrast between crystalline and amorphous GST loaded structures. Read wavelength is positioned at the point of maximum contrast. C Absorbance spectrum of c-GST loaded waveguide. Write/erase wavelength is positioned at the point of peak absorbance.

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Next the dynamics of the write/erase operations are examined. Here, a pulse with 1.5 mW power and 50 ns width with a rise and fall time of 0.5 ns is supplied to demonstrate the write process. In Fig. 7(B), we can observe the maximum and minimum temperature in our GST cell as a function of time. This is a case of partial amorphization where a significant portion of GST is above 877 K but not the entire volume. When the pulse is removed, the cooling rate of the melt region (black curve in Fig. 7(B)) is in the same order of magnitude as mentioned in the previous paragraph confirming the quenching of these regions to amorphous phase. The blue curve in Fig. 7(B) shows the transient temperature profile of the hottest point in GST for a pulse with threshold energy.

 

Fig. 7. Dynamics of the Write/Erase operations. The GST material is in a completely crystalline state before 0 ns for the write operations in A and B. For the erase operations in C and D, it is in a completely amorphous state before 0 ns. A Write pulse profile (rise and fall times of 0.5 ns) with the 2D temperature profile for the top surface of GST cell at te 50 ns mark shown in the inset. B Temperature variations with time at the maximum and minimum temperature points for threshold and 1.5 mW power. C Double step erase pulse profile with a linearly decreasing first pulse and a constant 1 mW second pulse (inset shows the 2D temperature profile after the first pulse at 20 ns for the top surface of GST cell). D Temperature variation with time for three different points x1 (black), x2 (red) and x3 (blue) in the GST cell, where, x1 denotes the point which has the highest temperature in the entire GST cell, x3 denotes the point with the least temperature in the entire volume, and x2 denotes the mean temperature of the outer region of GST volume not melted after the first excitation signal is applied.

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The erase process (recrystallization) involves heating the GST cell for a particular amount of time above the glass transition temperature (383 K) and below the melting point (877 K) in order to achieve complete phase transition from the amorphous to crystalline state. As opposed to the minimum 100 ns pulse duration required for complete phase transformation of an as-deposited amorphous GST film, melt-quenched amorphous films can be completely erased in 10 ns [42]. This is due to the growth of tiny crystalline nuclei present in the quenched amorphous films [42]. In literature, various combination of pulses have been used to demonstrate the erase function for GST-based photonic phase change memories. Some of these approaches include a train of multiple pulses with decreasing power [20] or a double-step pulse where the power of the second pulse in considerably low compared to the first pulse [32].

Here, we demonstrate a double step pulse, as shown in Fig. 7(C), to recrystallize a completely amorphous film. The first part of the pulse consists a linearly decreasing slope from 10 mW to 6 mW power for a duration of 20 ns. The role of this pulse is to melt to the center portion of GST cell which heats up the fastest, as can be in the inset of Fig. 7(C). The remaining portion of the GST cell heats up to temperatures above 500 K but below the melting point. This is the range where the crystallization rates are the highest [41]. An assumption is made that this remaining portion has crystallized supported by the experimental evidence in literature that melt-quenched amorphous regions recrystallize in as short as 10 ns at specific powers when the crystallization rates are high [41] [42]. The second pulse supplies a constant power of 1 mW for 30 ns to decrease the temperature of the melt and equilibriates it at around 700 K where the crystal growth rate is very high. This pulse also maintains the temperatures of already crystallized regions below the melting point to avoid its re-amorphization. The thermal simulation results of the erase process are shown in Fig. 7(D) where the transient temperature data of three points x1, x2 and x3 are compared. Here, x1 denotes the point which has the highest temperature in the entire GST cell, x3 denotes the point with the least temperature in the entire volume, and x2 denotes the mean temperature of the outer region of GST volume which is not melted after the first excitation signal is applied. The energy required for the entire erase process is 190 pJ.

4.2 Comparative study of reconfigurable waveguides

Next, we analyze the performance of the write operation. Optical pulses with varying power and widths are input into the waveguide. For each pulse, we obtain the 3D temperature distribution profile of the GST. The volume of GST whose temperature is above 877 K is considered amorphized as explained previously. In order to simplify our model, we mark the melt regions in the middle plane of the GST cell that is perpendicular to the thickness in the $z$-direction. The middle plane is chosen because it has the mean temperature among all the planes in the z-direction. This marked area is now extruded in the z-direction covering the entire thickness of the GST component. This results in the insertion of an amorphous volume inside the existing crystalline cell. The optical transmission value obtained for this new hybrid GST component dictates the contrast we can achieve for a particular pulse energy. For different waveguide configurations and pulse widths, the transmission contrast values are plotted in Fig. 8 as a function of pulse energy. The formula used for calculating the contrast is $(T-T_{c})/T_{c}$, where $T$ is the transmittance through the waveguide when the GST is an arbitrary state between amorphous and crystalline state depending on the write pulse energy, and $T_{c}$ is the transmittance through the waveguide when the GST is in a complete crystalline state. The ablation point of GST is denoted in the curves with a star marker. Beyond this ablation point, the temperatures inside GST rises above 1500 K and the material damages [19]. Hence, it wont be feasible to achieve transmittance contrast beyond this point.

 

Fig. 8. Comparative study of pulse energy vs transmission contrast curves for different GST-waveguide configurations including the report by Keitz et al. [31].

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The performance results in Fig. 8 show that for the same size of GST cell and pulse width, the proposed structure (red curve) exhibits a 5-fold reduction in reconfiguration threshold, and a 30-fold improved figure of merit for the write process, in comparison to non-resonant strip waveguides (brown curve). To further increase the transmittance contrast and improve the reconfigurability of our structure at the operating wavelength, we can increase the number of nanoantennae loaded on the structure. The blue curve in Fig. 8 shows the maximum transmittance contrast more than doubles when the SWG is loaded with two GST cells instead of one cell. Further reduction in pulse width can lead to lower thresholds, but ablative hole formation will begin for much lower contrasts adversely affecting the reconfigurability of our device, henceforth, presenting a trade off. The threshold energy lowers for small pulse widths because the boundary of amorphization regime essentially follows the equation $P = \alpha *t^{-0.5}$, where $P$ is the power of the pulse, $t$ is the pulse width, and $\alpha$ is a constant [43]. In comparison to the resonant nanobeam cavity configuration [31], the threshold is reduced to (16 pJ for a 10 ns pulse) and the figure of merit for the write process is an order of magnitude higher at 140×10⁻³ dB pJ⁻¹. Furthermore, the insertion loss in the "on" phase is reduced significantly.

5. Conclusions

To summarize, a resonant metamaterial waveguide with embedded PCM nanoantenna is proposed and numerically studied. The systematic numerical study provides insights to guide further experimental activity in PCM based integrated photonics. We briefly discuss the fabrication aspects of the proposed structure and implications of fabrication defects. The dimensions of the proposed waveguide are well within the range of both electron beam lithography and wafer-scale deep-ultraviolet lithography [23]. Mix and match lithography, combining stepper photo-lithography with wafer scale Electron-Beam lithography is expected to become available in the silicon nitride platform soon [30] which will enable the fabrication of the waveguide with GST loading. The optical response of silicon nitride devices is robust to manufacturing imperfections owing to the lowered effective index [30]. From Fig. 3(D), we note that if the GST strip is misaligned and placed on other ribs near the optimized position (for example - $6^{\textrm{th}}$, $8^{\textrm{th}}$, and $12^{\textrm{th}}$ rib), the absorption would still be high.