Ultra-compact nonvolatile plasmonic phase change modulators and switches with dual electrical–optical functionality Open Access

In the last few years, photonic integrated circuits (PICs) became very attractive as they offer broad bandwidth and very efficient information transport, processing, and storage.^1,2 Large-scale PICs are based on the silicon photonics platform that is compatible with the well-established CMOS technology. To realize large-scale photonic systems, active components, such as photodetectors, modulators, and switches, are very essential to detect and control the light flow within the network.³ Apart from the photodetectors that perform optical to electrical signal conversion, the on-chip modulators and switches convert the electrical signals into the optical ones, and thus they are key components in photonic links. They should be characterized by low static and dynamic power consumption, high switching contrast, low optical loss, compact footprint, dense integration, and ultrafast switching speed. Furthermore, they should operate under CMOS driving voltages of 1.2 V.

Most of the available modulators and switches can be classified as volatile devices as they require a constant supply of the electric power to hold each switching state. However, for high-performance operations and neuromorphic computing, the nonvolatile functionalities are essential. The term nonvolatile means that no static energy or holding power is required to retain any of the states once it is set. In consequence, it enables a low power consumption as no power is required to keep a switching state and brings new possibilities to the existing platform.⁴ A huge impact is expected to technologies, such as programmable photonics,⁵ photonic memories,⁶ neural networks,⁷ LIDAR systems,⁸ or power-efficient switching in data centers.⁹ 

In terms of a switching mechanism, the modulators can operate based on the plasma dispersion effect,^1,10 thermo-optic (TO) effect,^11–14 or electro-optic (EO) effect^15,16 where the modulation is achieved by either changing the real part (n) of the modal refractive index leading to optical modulators (OM)^16,17 or by modulating the imaginary part (k) of the modal refractive index leading to absorption modulators (AM).¹⁸ Thus, OMs relate to the phase of the light, whereas AMs to the intensity absorption of the light. In both types, the fundamental complex index of refraction is altered thermally or electrically in the active material, which in turn modifies the propagation constant of the mode inside the respective waveguide.

For the optimal operation conditions, the phase modulators require a large variation of the real part of the mode effective index (Δn) while losses should stay low, i.e., small variation of the imaginary part between the on and off states (Δk = 0). On the other hand, the intensity modulators require a large variation of the imaginary part (Δk) with the minimum losses, i.e., minimum k for the on or off states. Furthermore, the phase modulation always requires a reference phase for comparison; thus, the modulator requires the interferometric arrangement^{12,13,17,19,20} (Fig. 1). In comparison, the absorption modulators can operate under even linear waveguide arrangement.

Thermo-optic Mach–Zehnder interferometers (MZIs) or micro-ring resonators (MRRs) are the most extensively studied TO phase modulators (switches) where the index of propagating modes is changed through the resistive metal contact on top of the waveguides.¹⁹ While MZIs are relatively temperature insensitive and provide very high bandwidth of modulation, they suffer, however, from high power switching, low switching time, and large footprint.²¹ On the contrary, MRRs can provide lower power consumption, reduced footprint, and still very high bandwidth; however, they are not as temperature insensitive as MZI and require more fabrication precision.²¹ 

In electro-optic modulators, the electrical signal modifies the refractive index of the material through the Pockels effect, Kerr effect, quantum confined Stark effect, or free carrier dispersion effect.¹⁶ In terms of the modulators and switches that are based on free carrier dispersion effect, they show low power consumption and faster modulation speed; however, they suffer from a large device footprint as a result of small refractive index change (<10⁻³).³ Furthermore, each modulation schema requires specific application-defined design.

Thus, most modulators and switches suffer from a high power consumption,¹⁹ a low operation speed,^11–13 a high optical insertion loss,¹⁷ a low modulation depth, or a large footprint.²⁰ Furthermore, some of them are not suitable for operation at temperature above 100 °C due to a material degradation tendency at moderate temperatures.²² Finally, all of them require a constant supply of the electric power as they are volatile. As a result, finding a better material and design platform is of great interest for the industry. In the last few decades, it has become obvious that further progress can be made through an implementation of new materials,^23–27 integration with plasmonics,^28,29 or both.

Plasmonics can squeeze light much below the diffraction limit, which reduces the device footprint.²⁸ Furthermore, a small device volume means a higher density of integration and, simultaneously, lower power consumption, easier heat dissipation, and faster operation speed.²⁹ 

The proposed modulators are based on the long-range dielectric-loaded surface plasmon polariton (LR-DLSPP) waveguide arrangement with the metal stripe placed between the ridge and buffer layer that supports the TM-polarized mode (Fig. 2). Thus, the metal stripe is an essential part of the LR-DLSPP waveguide and can serve as one of the electrodes.^30–33 

In a balance condition, the mode effective index below the metal stripe is close to the mode effective index above the metal stripe. In consequence, the absorption in the metal stripe is minimalized, and the propagation length is enhanced. When the active material is deposited either on top of the buffer layer in the “inverse” design [Fig. 2(a)] or on top of the ridge in the “normal” design [Fig. 2(b)], even a small change in the refractive index of the active material can disturb the balance (Fig. 3). Depending on the refractive index of the buffer layer and the ridge, the mode is pushed either to the ridge or the buffer layer [Fig. 3(a)]. As a result, the absorption in metal arises, and the propagation length of the mode decreases. This effect can be highly enhanced when the active material is placed directly at the contact with the metal stripe, i.e., in the electric field maximum of the propagating mode.

The simulations were performed for the ridge width of 300 nm and heights of 140 nm and 180 nm while the buffer layer thickness was kept constant at 120 nm. Two different scenarios (cases) of phase change material (PCM) location were considered here: in the first case, the PCM constituted for the buffer layer [Fig. 3(a)], and in the second case, it constituted for a ridge [Fig. 3(b)]. As the second material that constitutes for a LR-DLSPP waveguide, the Si was chosen due to a refractive index that is close to most of the PCMs. To avoid oxidation from air and, consequently, excessive optical losses, the PCM was covered by SiO₂ that additionally covered the Si.

The proposed LR-DLSPP waveguide ensures low attenuation below 0.0075 dB/μm that can be achieved with the Si platform [Fig. 3(a)]. Consequently, assuming even 10 µm long active region of the modulator, the insertion losses (IL) below 0.075 dB can be achieved. Even further reduction in absorption losses can be achieved with lower index waveguide materials in which the propagation length of 700 µm was measured at telecom wavelength for CMOS-compatible silicon nitride (SiN).²⁵ 

Furthermore, the proposed plasmonic waveguide ensures high coupling efficiency with the photonic platform that was numerically estimated at 97% [Fig. 3(a)].^30,31 Thus, the coupling losses per interface as low as 0.05 dB can be achieved. It was experimentally validated, where the coupling efficiency exceeding 75% per interface was achieved. The difference between numerical calculations and experimental results was attributed to the presence of a thin layer of titanium used for improving adhesion between the gold stripe and substrate that introduces substantial mode absorption.³³ 

In consequence, apart from an efficient conversion mechanism, the proposed plasmonic waveguide provides an excellent platform for the realization of on-chip modulators and switches.

Compared to the volatile modulators and switches that require a constant power supply to maintain the switching state, the nonvolatile optical modulators and switches do not necessitate static energy or holding power (continuous power supply) to retain (keep) the switching state. The phase change materials (PCMs) have been recently proposed as very promising materials for the realization of such a task as they are able to hold the switching state in the absence of the applied voltage.^23,26,34,35

They provide extremely high refractive index contrast (Δn = 0.6–3.0), ultrafast transition (>1 ns), energy-efficient reversible switching, nonvolatility (leading to zero-static power consumption), high scalability, long-term retention (<10 years), and high cyclability (10¹² switching cycles).^36–39 The mechanism of switching in the PCM is realized through a phase transition between its two different phases—amorphous and crystalline.^37,38 It can be performed by Joule heating of the PCM using external heaters (thermal effect),^40,41 electrical pulses (electro-thermal effect),^23,29,42 or optical pulses (photo-thermal effect).^26,29,35,43 In photonic nonvolatile phase-change switches, the heat-induced refractive index change of PCM induces change in transmitted light.

Ge₂Sb₂Te₅ (GST) and Ge₂Sb₂Se₄Te₁ (GSST) are the most commonly used PCMs for the integrated phase-change devices owing to its wide availability, well established technology, relatively low switching temperature, and very large refractive index shift.^37,41,42 The crystalline state in PCMs is achieved by heating the material above the crystallization temperature of 160 °C, while the amorphization is achieved by heating the material above the melting temperature of 600 °C and then quenching by rapid cooling (nanoseconds).⁴ In terms of switching time between the states, it is generally slower for crystallization and physically limited to hundreds of picoseconds.⁴⁴ 

The refractive index contrast between the amorphous and crystalline states at the wavelength of 1550 nm for GST was calculated at Δn = ∼2.74 while for GSTT at Δn = ∼2.03. As observed [Fig. 4(a)], the refractive index of both a-GST and a-GSST is very close to the refractive index of Si, n = 3.47, which provides a good mode matching. However, both materials show large absorption losses in the crystalline phase with k = ∼1.09 and k = ∼0.42 for c-GST and c-GSST, respectively. As a result, the transmitted light through GST- or GSST-based waveguides undergoes much larger change in amplitude than in phase during a transition. This limits their use to amplitude modulation rather than to phase modulation.

Recently, a new class of low loss PCMs, such as Sb₂S₃ and Sb₂Se₃, was demonstrated that can be considered as reversible alternatives to the standard commercially available chalcogenide GST and GSST.²⁷ They offer zero loss in both the amorphous and crystalline states at both 1310 and 1550 nm and a large index change, which makes it an ideal candidate for nonvolatile phase change switches [Fig. 4(b)]. At a wavelength of 1550 nm, Sb₂S₃ shows a complex refractive index n = 2.71 + 0i for the amorphous phase (a-SbS) and n = 3.31 + 0i for the crystalline state (c-SbS), while for Sb₂Se₃, it is n = 3.28 + 0i and n = 4.05 + 0i for the amorphous phase (a-SbSe) and crystalline (c-SbSe) phase, respectively. Thus, a contrast of refractive index of Δn = 0.60 for Sb₂S₃ and Δn = 0.77 for Sb₂Se₃ is achieved while maintaining extremely low losses, k < 10⁻⁵ [Fig. 4(b)].

In a photonic nonvolatile PCMs arrangement, the complex optical refractive index is tuned, which affects both the optical absorption level and the phase and, therefore, the transmitted light.

The proposed PCM-based plasmonic modulator enables reversible switching the state of PCM between its amorphous (high resistance, high transmission) and crystalline (low resistance, low transmission) states by sending either electrical pulses through the metal electrodes or optical pulses through the waveguide. When the electrical current flows through PCM that forms the circuit, the Joule heating of PCM causes the phase change. This switching method is often called “memory switching.” However, the main limitation with this type of switching mechanism is that only a small volume of the PCM can be switched due to filamentation.⁴⁵ To switch larger area of PCM, the state of PCM can be switched by Joule heating using one of the metal electrodes that can work as a heater.

In most of the presented up to day PCM switches, the heating mechanism needs some extra space, which reduces the computing density (TMACs/s/mm²) and also increases the insertion loss. Thus, the approach of using PCM on integrated photonics still needs to be understood on how to do that in an ultra-compact and scalable way.

The metal stripe is an essential part of the proposed LR-DLSPP waveguide and can be implemented as an internal heater.^30–33 As it is in direct contact with PCM, the heating process can be very efficient. Furthermore, the metal stripe is placed in the electric field maximum of the propagating mode; thus, even a small change in the refractive index of PCM close to the metal stripe can highly influence the propagating mode. However, to enhance the performance of the PCM-based modulator, few aspects of the heat flow should be considered.

Under an applied voltage to the metal stripe, the electrical energy is dissipated into heat. The heat from the metal stripe dissipates to any materials that are in contact with the metal through conductive heat transfer.¹⁴ The amount of heat transferred to the area of interest (ridge or buffer layer) depends upon the thermal conductivity coefficients of the materials that are in contact with the metal stripe, contact area, and thickness of the buffer layer and ridge. Thus, to ensure an efficient heat transfer to the PCM, the second material that constitutes for the LR-DLSPP waveguide should own lower thermal conductivity coefficient.¹⁴ 

The proposed LR-DLSPP-based modulator can be arranged, as well with the external heaters, as shown in Figs. 5 and 6. They can be arranged in two different configurations: lateral [Figs. 5(a) and 6(b)] and vertical [Figs. 5(b) and 6(a)]. The lateral configuration consists of two resistive heaters placed directly in contact with the PCM [Figs. 5(a) and 6(b)] that is part of the waveguide, thus providing more heat to the PCM locally, which lowers the switching threshold. In comparison, the vertical configuration consists of a metal heating electrode placed on top of either the buffer layer [Fig. 5(b)] or the ridge [Fig. 6(a)]. Depending on the requirements, the heating electrode can be separated from the PCM layer through a very thin conductive layer to minimize the mode-overlap with the metal and eventual scattering while still providing an efficient heat transfer to the PCM.

As the LR-DLSPP mode is tightly bounded to the metal stripe, the external electrodes can be placed very close to the propagating mode without influencing the propagation length. Thus, the ohmic losses due to the presence of external metals are minimalized. As it has been previously shown for a lateral configuration,⁴⁶ the external electrodes can be placed as close as 50 nm away from the ridge without introducing any additional losses. For comparison, an essential increase in additional losses was observed for a similar arrangement but realized with a Si photonic waveguide, where the presence of external electrodes contributed to 0.11 dB/μm additional losses for the propagating TM mode.⁴¹ 

The direct contact of PCM with the electrode allows lowering the threshold voltage for delivering the right amount of heat for inducing a phase transition in the PCM. A resistive heater optimized for efficient switching and contemporary not generating insertion losses can be made in doped silicon or in silicide positioned next to the waveguide.³⁴ Furthermore, the external heater can be made from transparent conductive oxides (TCOs) [Figs. 5(b) and 6(a)], such as indium tin oxide (ITO)^40,41 that is characterized by low optical losses at 1550 nm.^17,47 Apart from it, graphene can be very efficient platform for the realization of such a task.^23,24

Moreover, the proposed arrangements provide strong light confinement inside PCM and without introducing excessive parasitic optical losses. Furthermore, the heat is highly localized within PCM; thus, the thermal mass is significantly lowered. In consequence, the switching voltage and current of the device can be highly minimalized.

Under the heating of PCM through the light (optical pulses) or electrical contacts, the PCM undergoes a transition to a crystalline state that is characterized by a much higher refractive index (Table I). Thus, the balance in the mode effective indices is broken as one side of the LR-DLSPP waveguide (upper or lower) with PCM shows a higher mode effective index. In consequence, most of the optical energy is now pushed out of the PCM to the opposite side of the LR-DLSPP waveguide [Fig. 3(a)]. As the balance is broken, the absorption losses in metal arise that give rise to the increase in the temperature of the metal stripe. The heat generated in such a way by a metal stripe dissipates its energy to any materials that are in direct contact with it. Depending on the materials surrounding the metal stripe, the amount of heat transferred to the PCM can change significantly. However, it provides an additional heat source that can provide further increases in the temperature of the PCM.

The proposed LR-DLSPP plasmonic mode is tightly bounded to the metal stripe; thus, the external electrodes can be placed very close to the propagating mode without substantial influence on the attenuation (Fig. 7). In consequence, the ohmic losses due to the presence of external metals can be minimalized. As shown in Fig. 7, the external electrodes can be placed as close as 50 nm away from the ridge without introducing substantial losses even being 200 nm thickness (Fig. 7).⁴⁶ As such, in the lateral electrodes’ arrangement [Fig. 7(a)], the minimum attenuation coefficient of 0.226 dB/μm was achieved for the electrodes placed just only 50 nm away from the ridge. Further decreases of an attenuation were observed for longer electrodes’ spacing that drops below even 0.06 dB/μm for a distance between the electrode and ridge at 250 nm.

Under the heating of PCM that constitutes a buffer layer, the refractive index of PCM increases. As shown in Fig. 7(a), for a distance between the electrodes and the ridge of 150 nm, the change of a refractive index of the buffer layer from n = 3.47 to n = 5.25 corresponds to the same level of an attenuation of 0.3 dB/μm. However, the real part of the mode effective index in the same interval changes from n_eff = ∼2.08 to n_eff = ∼2.91 that corresponds to the mode effective index change Δn_eff = ∼0.83 and a phase shift of ∼1.07 π/μm. This corresponds to an ultra-compact phase shifter of only ∼930 nm in length needed to attain a full π phase delay. The small device footprint also yields a low theoretical insertion loss of 0.26 dB when switching the refractive index of PCM from n = 3.47 to n = 5.25. Even higher change of the mode effective index Δn_eff = ∼0.86 can be achieved for the electrodes placed 250 nm away from the ridge with a significant reduction of an attenuation that is kept constant at 0.19 dB/μm for the buffer layer refractive index of n = 3.2 and n = 5.0. This change of mode effective index corresponds to a phase shift of ∼1.11 π/μm and, consequently, requires only ∼900 nm long phase shifter to provide a full π phase delay while the losses are kept at ∼0.17 dB.

The distance of 50 nm between the electrodes and the ridge is much smaller compared to a previously presented configuration with a Si rib waveguide, where the distance between the electrodes and the rib was 500 nm.²⁴ The presence of metal electrodes contributed to an additional loss of 0.01 dB/μm, while the presence of graphene that was used as a heater led to an additional loss of 0.1 dB/μm. Thus, the overall losses calculated for an amorphous state of GST exceeded 0.11 dB/μm for a distance between the electrodes and a rib of 500 nm that is ten times higher than in the LR-DLSSP waveguide organized in a lateral configuration proposed here. The insertion loss of ∼0.11 dB/μm is only two times lower than ∼0.226 dB/μm that was calculated for our configuration [Fig. 7(a)]. Furthermore, the distance between the electrodes and the active region of the waveguide influences the energy efficiency since part of the generated heat is dissipated around the long region. Thus, a shorter distance is highly desired as it enhances the heat transfer efficiency and reduces the power consumption. In Ref. 24, under a switching of GST from an amorphous state to a crystalline state, the real part of the mode effective index changed from n_eff = ∼2.66 to n_eff = ∼2.87, while an attenuation arises from ∼0.01 to ∼1.46 dB/μm. It corresponds to the mode effective index change Δn_eff = ∼0.21 and an attenuation change of ∼1.45 dB/μm. Thus, the presented configuration can serve only for an amplitude modulation.

In another example of the lateral electrode configuration, a phosphorus-doped silicon was used as a heater.²⁵ Under the heating of Sb₂Se₃ and the transition of an amorphous to a crystalline phase, the mode effective index change, Δn_eff = ∼0.071, was calculated that corresponds to a phase shift of ∼0.09 π/μm. Thus, to attain a full π phase shift, a 11 µm long shifter is needed for which an insertion loss of ∼0.1 dB was theoretically calculated. A small difference in attenuations between the amorphous and crystalline states of Sb₂Se₃ was calculated at ∼0.007 dB for a 11 µm long shifter. However, a significant reduction in attenuations was possible as the metal contacts were far away from waveguide to reduce losses. It allows us to avoid some additional losses but at the cost of power efficiency as more heat is dissipated before reaching the active part of the waveguide.

In comparison, as proposed in this paper, the arrangement with a lateral electrodes’ configuration requires only ∼900 nm long shifter to attain a full π phase delay while losses for both states of PCM are kept constant at ∼0.19 dB/μm. Thus, over 11 times reduction in the length of a shifter was achieved while the losses are kept constant for both phases of PCM. Furthermore, a direct contact of the external electrodes with the PCM and very close distance to the center of the waveguide provides huge benefits in terms of heat delivery and power consumption.

As mentioned earlier in this paper, the thickness of PCM for the proposed design can range from 50 nm to hundreds of nanometers, which depends on where the PCM is deposited—in a buffer layer or a ridge. However, in most of the articles that can be found in the literature,^{24,25,41,48,49} the thickness of PCM is in the range of 10–30 nm as strong increase of an attenuation was observed for thicker PCMs.²⁴ For example, when Sb₂S₃ of different thicknesses was deposited on the SOI waveguide, the simulations performed for the TE mode show the mode effective index change Δn_eff = ∼0.022 and change of attenuation from ∼0.009 to ∼0.282 dB/μm for a 20 nm thick Sb₂S₃ and under a phase transition. However, for a 66 nm thick Sb₂S₃ on the SOI waveguide, the mode effective index change was calculated at Δn_eff = ∼0.038, while the attenuation grows from ∼0.014 dB/μm for an amorphous phase to ∼0.335 dB/μm for a crystalline phase. Even a higher influence of PCM thickness and width on the attenuation was observed for the GST material where an increase of attenuation from 1 dB/μm for a 5 nm thick c-GST to up to 30 dB/μm for a 50 nm thick c-GST was calculated. In comparison, for a-GST, the increase of attenuation was from 0.01 to 0.1 dB/μm with an increase of thickness from 5 to 50 nm.²⁴ Thus, to avoid additional losses, most of the authors limit the thickness of PCM to 20–30 nm.

In the second proposed arrangement with a vertical electrode configuration and with the PCM placed in the ridge [Fig. 7(b)], an attenuation below ∼0.185 dB/μm was calculated for a heating electrode placed only 110 nm away from the ridge and for the PCM refractive index of n = 4.0. When the heating electrode is more closer to the ridge, the attenuation arises and reaches ∼0.48 dB/μm for an electrode placed just only 50 nm from the PCM ridge, with a minimum corresponding to the PCM ridge refractive index of n = 4.4. As observed, the attenuation of ∼0.43 dB/μm was calculated for a ridge refractive index of n = 3.2 and n = 5 that corresponds to the mode effective index change from n_eff = ∼2.15 to n_eff = ∼4.90. Thus, the change of the mode effective index exceeds Δn_eff = ∼2.75 and a phase shift ∼3.55 π/μm. In consequence, only ∼280 nm long active area is needed to attain a full π phase delay with an insertion loss of ∼0.12 dB.

For comparison, an essential increase of additional losses was observed for a similar arrangement but realized with a Si photonic waveguide where the presence of external tungsten electrodes contributed to 0.11 dB/μm additional losses for a lateral arrangement and 0.06 dB/μm for a vertical arrangement with the heating electrode placed 250 nm above the silicon waveguide.⁴¹ In this case, when a GSST transfers from an amorphous state to a crystalline state under a heating approach, the mode effective index of the propagating TM mode changes from n_eff = 1.942 to n_eff = 2.154 + 0.045i. The change of the mode effective index can be calculated at Δn = ∼0.212 while an attenuation arises from 0 to ∼1.59 dB/μm. Thus, the proposed arrangement can be utilized to an absorption modulation rather than a phase modulation.

One of the ways to change the phase of PCM can be realized through a thermal heater. In such a case, the heating element that is properly biased dissipates energy in the form of Joule heat to the surrounding media.

Under an applied voltage to the metal stripe [Fig. 8(a)] or external electrodes [Figs. 8(b)–8(e)], the electrical energy is dissipated into heat. The heat from the metal electrodes (metal stripe or external electrodes) dissipates to any materials that are in contact with the metal through conductive heat transfer.¹⁴ The amount of heat transferred to the area of interest (ridge or buffer layer) depends upon the thermal conductivity coefficients of any materials that are in contact with the metal electrode, contact area, and thickness of the materials. Thus, to ensure an efficient heat transfer to the PCM, the second material that is in contact with the metal electrode should possess low thermal conductivity coefficient.¹⁴ Furthermore, the direct contact of PCM with the electrodes in the proposed modulator allows lowering the threshold voltage for delivering the right amount of heat for inducing a phase transition in PCM.

To evaluate the heat transfer to PCM, the thermal resistance and thermal capacitance should be considered. The thermal resistance of an object is defined as R_th = L/(κ · A), and it describes the temperature difference that will cause the heat power of 1 W to flow between the object and its surroundings. In comparison, the thermal capacitance of an object, C_th = C_p · ρ · V, describes the energy required to change its temperature by 1 K if no heat is exchanged with its surroundings.¹⁴ Here, L is the length of the substrate along the heat transfer direction, A is the cross-section area of the substrate, V is the heated volume of the material, κ is the thermal conductivity of the material, C_p is the specific heat, and ρ is the mass density. Thus, the lower the thermal capacitance the higher the temperature for a given amount of heat delivered to the material. Furthermore, the materials with lower thermal conductivity coefficient are characterized by higher thermal resistance, so lower electrical powers are required to increase the material temperature as the heat loss is reduced.

Here, the Joule heating process and heat dissipation model were performed using a 3D finite-element method simulation in COMSOL Multiphysics. We used the Joule heating module where the Sb₂Se₃ was considered as the PCM. For a heating mechanism, three electrode configurations were considered: internal with a metal stripe [Fig. 8(a)], vertical [Figs. 8(b) and 8(c)], and lateral [Figs. 8(d) and 8(e)].

The metal stripe that is a part of the LR-DLSPP waveguide can serve simultaneously as a heating electrode, efficiently providing heat to the area of interest—either to the ridge or the buffer layer [Fig. 8(a)]. As it is placed in the electric field maximum of the propagating LR-DLSPP mode, even a slight change of the PCM refractive index will highly influence a propagating mode. Additionally, the heat is very efficiently provided to the PCM; thus, high reduction in power consumption is expected. The amount of heat provided to the PCM can be highly enhanced by a proper choice of the material that is in direct contact with the metal stripe on the opposite interface. As observed from Fig. 8(a), most of the heat from the metal stripe is dissipated into the Si ridge due to an enormous difference in the thermal conductivities between PCM and Si. As observed from Table I, the thermal conductivity coefficient of most PCMs ranges from 0.2 to 1.0 W m⁻¹ K⁻¹, while for Si, it reaches 148 W m⁻¹ K⁻¹. To enhance a heat transfer to the PCM, a thin layer of the material with a lower thermal conductivity coefficient compared to Si can be deposited between the metal stripe and Si. However, this material should possess a refractive index that is close to the refractive index of Si. In another solution, the Si can be replaced by SiN that is characterized by much lower thermal conductivity coefficient of 30 W m⁻¹ K⁻¹. As the refractive index of SiN is much lower compared to Si and most of PCMs, the waveguide dimensions should be optimized.

In the case of the vertical configuration, the metal heating electrode is placed at a certain distance from the PCM ridge that consists of the LR-DLSPP waveguide [Figs. 8(b) and 8(c)] and is surrounded by an oxide layer to avoid oxidation from the air and, consequently, an excessive optical loss. As shown in Figs. 8(b) and 8(c), the heating electrode placed closer to the PCM ridge provides more efficient and faster heat transfer to PCM. Thus, a lower power/voltage is required to increase the temperature of PCM. This statement is obvious; however, in conventional photonic waveguides, it is hard to realize it as the heating electrode has a strong effect on the propagating mode. When it is placed close to the photonic waveguide, the photonic mode is pushed to the electrode, and, in consequence, the absorption losses highly arise. In comparison, the LR-DLSPP mode is strongly bounded to the metal stripe, which allows us to place an electrode close to the LR-DLSPP waveguide without introducing significant losses [Fig. 7(a)].

In the case of the lateral configuration, the heating electrodes are in direct contact with the PCM and are placed on both sides of the LR-DLSPP waveguide [Figs. 8(d) and 8(e)]. In consequence, a heat transfer to PCM that consists of the buffer layer is more efficient. Compared to the similar arrangement realized with the photonic waveguide that shows higher insertion losses compared to the vertical configuration,⁴¹ the losses associated with the presence of the external electrodes in the lateral arrangement are much lower compared to the vertical configuration (Fig. 7). For the external electrodes placed only 50 nm away from the ridge, the minimum attenuation was calculated at 0.225 dB/μm [Fig. 7(a)], while for the vertical configuration with the heating electrode placed 50 nm below a ridge, the minimum attenuation was calculated at 0.486 dB/μm [Fig. 7(b)]. The lateral configuration allows us to utilize both the electrodes as heating electrode [Fig. 7(d)] or only one of them [Fig. 7(e)].

Apart from the external heater(s), the state of PCM that is a part of the waveguide can be reversibly switched between the amorphous and crystalline phase by sending light (optical pulses) through the LR-DLSPP waveguide (Figs. 5 and 6). The guiding properties of the LR-DLSPP waveguide depend on the state of PCM. Under a design, the LR-DLSPP waveguide can work in a low-loss regime, either for PCM in the amorphous state [Fig. 7(a), solid blue line] or crystalline state [Fig. 7(b), solid blue line]. For low-loss operation conditions, the LR-DLSPP waveguide is in balance as the mode effective index below the metal stripe (in a ridge) is close to the mode effective index above the metal stripe (in a buffer layer). However, when under either a design or an applied voltage, the balance is disturbed, the absorption in the metal stripe arises, and attenuation increases. Thus, the metal stripe can serve as an internal heater that does not require an external voltage [Fig. 8(a)].⁵⁰ In consequence, a heating process can be realized all-optically. Compared to standard on-chip optical switching that cannot switch wide bandgap PCMs that have zero absorption in the near IR (Fig. 4),⁴³ the arrangement proposed here takes an advantage of plasmonics and the presence of an internal metal stripe that is part of the waveguide.

The optical power absorbed by the metal stripe is dissipated into any materials that are in contact with the metal stripe, and an amount of heat dissipated into PCM depends on thermal resistance and capacity of the surroundings materials [Fig. 8(a)]. The dissipated power by the metal stripe depends on the surface plasmon polariton attenuation coefficient and the length of the active region. Thus, the higher the attenuation coefficient, the higher the metal stripe temperature. As it has been previously shown, the increase of the temperature of the materials that are in contact with the metal stripe is proportional to the power coupled to the plasmonic waveguide.⁵⁰ 

Let us now compare a heating mechanism of the photonic waveguide with the proposed LR-DLSPP waveguide in terms of the optical switching.

In a photonic waveguide, a thin layer of PCM (10 nm GST) is deposited on top of the Si or SiN waveguide and covered with indium tin oxide (ITO) (10 nm thick) to prevent oxidation of PCM [Fig. 9(a)].^51,52 As observed from Fig. 9(a), the PCM is placed far away from the electric field maximum of the propagating mode; thus, the interaction of light with PCM is weak.

In comparison, for a LR-DLSPP waveguide, the PCM can be placed either in a buffer layer or in a ridge that are in direct contact with the metal stripe, i.e., in the electric field maximum of the propagating plasmonic mode [Fig. 9(b)]. Furthermore, as the electric field is much more enhanced in the plasmonic waveguide compared to the photonic waveguide, the electric field of the propagating LR-DLSPP mode [Fig. 9(b)] that interacts with PCM is much stronger compared to the photonic waveguide [Fig. 9(a)].

Furthermore, as it was mentioned earlier, the optical switching in the proposed waveguide can be highly enhanced through the heat transfer from the metal stripe under the absorption of light to the PCM that is in a direct contact with the metal stripe.⁵⁰ Thus, a two stage heating process of PCM can take place in the proposed LR-DLSPP arrangement that is related with (a) a direct absorption of light by PCM and (b) a heat transfer from the metal stripe to the PCM under the absorption of light by the metal stripe.

Furthermore, when considering either a vertical configuration with the external electrode in direct contact with the PCM placed either in a ridge or a buffer layer [Fig. 8(a)] or lateral with the PCM placed in a buffer layer [Fig. 8(d)], the external electrode and the metal stripe can be in direct contact with the PCM, and the distance between the electrodes can be below 100 nm. Thus, the PCM is connected into a circuit, which enables the electrical (memory) switching. When the electrical current flows through PCM that is part of the circuit, the Joule heating of PCM itself causes the phase transition. One of the main limitations of this switching mechanism is that only a small volume of PCM can be changed, as it has been previously shown in Ref. 29. In our case, a small volume in the range of hundreds of nanometers is required to attain either a full π phase delay or provide high optical contrast. Our proposed LR-DLSPP waveguide is extremely sensitive to any changes of the refractive index of PCM. Under a change of refractive index of PCM that is placed in the ridge from n = 4.0 to n = 5.8, the attenuation arises from ∼0.183 to ∼2.4 dB/μm; thus, only 1 µm long waveguide is required to introduce an optical contrast exceeding 2.2 dB [Fig. 7(b)], or only 280 nm long waveguide is needed to provide a full π phase delay with an insertion loss below ∼0.12 dB [Fig. 7(b)] when the PCM refractive index changes from n = 3.2 and n = 5.

The arrangement proposed in this paper provides a nanoscale volume of PCM, which reduces the volume of the material that needs to be heated during switching and, in turn, reduces switching energies. Furthermore, the process of switching is enhanced by a plasmonic structure. In consequence, the small PCM volume, the high volume/surface ratio, and the implementation of plasmonics can contribute to a remarkably effective switching process.

In this work, the simulations and calculations were performed for Au as a metal stripe and a heating electrode; however, any other “plasmonic” metals^28,53,54 can be used as a metal that supports the LR-DLSPP mode, and any other metals can be implemented as the external electrodes that can provide even higher benefits in terms of heat generation efficiency.

The proposed arrangement allows modulation of the optical signal under an applied voltage. The state of PCM that is a part of the waveguide can be reversibly switched between the amorphous and crystalline states by sending electrical pulses through the metal stripe and/or metal electrode(s) [Figs. 5(b) and 6(a)]. The guiding properties of the LR-DLSPP waveguide depend on the state of PCM. For an amorphous state of PCM, the LR-DLSPP waveguide works in a low-loss regime as the mode effective index below the metal stripe is close to the mode effective index above the metal stripe. Thus, the LR-DLSPP waveguide is in balance. For a crystalline state of PCM, the balance in mode effective indices is broken as one side of the LR-DLSPP waveguide (upper or lower) with PCM shows higher mode effective index. In consequence, the absorption in the metal stripe arises, resulting in the shorter propagation length of the mode and, in turn, lower optical transmission. For example, the attenuation change from 0.183 to 2.4 dB/μm was calculated under a change of PCM refractive index placed in the ridge from n = 4.0 to n = 5.8 [Fig. 7(b), blue solid line]. Further enhancement is possible as no optimization was provided at this stage of the research.

Under a change of the refractive index of PCM, the mode is pushed to one interface of the metal stripe that is characterized by a lower mode effective index. As the distance between the metal stripe and an external electrode can be in a range of from tens to hundreds of nanometers, the mode propagating on one side of the metal stripe can couple to the external electrode, thus creating a gap surface plasmon polariton mode propagating in the metal–PCM–metal structure. Compared to the LR-DLSPP mode that is characterized by a long propagation distance in the range of hundreds of micrometers,^30–33 the metal–insulator–metal (MIM) mode propagation distance does not usually exceeds ten of micrometers.¹⁴ Thus, under the phase transition of PCM, an enormous difference in the propagation length of the plasmonic mode can be observed ranging from few micrometers to up to hundreds of micrometers. In comparison, a previously reported MIM plasmonic modulation with the GST placed in the gap showed the optical contrast (a change in a light transmission) lower than 1% at telecom wavelength of 1550 nm under a transition of GST from an amorphous to a crystalline state (Table II).²⁹ As observed in this example and Table II, the absorption modulation of PCM-based photonic straight waveguides is not very impressive; thus, PCMs are often integrated with photonic cavities where both optical phase and absorption modulation effect of PCMs contribute to high extinction ration.³⁵ 

Here, it should be emphasized that the results provided for the LR-DLSPP waveguide in an absorption modulation schema are based on the assumption of zero loss PCMs for both the amorphous and crystalline states. Thus, the results mostly refer here to low-loss or even zero-loss PCMs, such as Sb₂S₃ and Sb₂Se₃. If GST or GSST integrated in such a LR-DLSPP waveguide, a huge enhancement in the extinction ration should be observed.

The proposed modulation arrangement that is based on the PCM can minimize the switching voltage and current as the PCM is placed in the electric field maximum of the propagating mode. Thus, it provides a strong light confinement inside PCM without introducing excessive optical losses (Table II).³⁹ Furthermore, as PCM is in direct contact with the electrodes, it enhances heat localization within PCM to effectively lower thermal mass and it enhances the speed of switching the PCM device.³⁹ 

The main obstacles in achieving phase modulation are due to the small refractive index perturbation, which result in a large device footprint, significant optical losses, and long switching time. Moreover, all the switching mechanism are volatile, which require a constant power supply to operate.^10,15–20

Phase modulation requires interferometric schema, such as Mach–Zehnder interferometers.^12,13,17,19 The operation of the MZI is based on changing the mode propagation constant in one arm, resulting in the phase difference of two modes interfering at the output Y-junction/the length of the MZI arm required to ensure complete modulation, i.e., switching the light off in the Y-junction, is related to the phase difference π between the arms (Fig. 1).

Low-loss PCMs, such as Sb₂S₃ and Sb₂Se₃ [Fig. 4(b)], enable the realization of nonvolatile phase modulation with the LR-DLSPP waveguides where the change of phase of PCM effect rather the mode effective index than attenuation of the LR-DLSPP waveguide [Fig. 7(a), green dashed line]. In this example, the attenuation for both the PCM phases are kept constant at 0.28 dB/μm; however, further reduction is possible as no optimization was provided at this stage of the research. While the attenuation is kept constant on the same level, the mode effective index change Δn_eff = ∼0.83 was calculated that corresponds to a phase shift of ∼1.07 π/μm. Thus, only ∼930 nm in-length phase shifter is required to attain a full π phase delay. The small device footprint also yields a low theoretical insertion loss of ∼0.26 dB when switching the refractive index of PCM from n = 3.47 to n = 5.25.

In Table III, we compare the PCM-based plasmonic phase shifter proposed here with the state-of-the-art PCM phase shifters and other phase shifters realized in different technologies in terms of the change in the effective index, Δn_eff, the total length to achieve a π phase shift, L_π, the insertion losses, IL, the accompanying attenuation, α_att, and a distance from a heater to the waveguide. In terms of the PCM phase shifters, the distance between the heater and waveguide defines the energy/power consumption and the switching time as less generated heat is dissipated around the long distance. Thus, smaller the distance the lower energy/power required to achieve a π phase shift and faster switching time. On the other hand, most of the traditional photonic PCM phase shifters place the electrodes far away from the waveguide to avoid high insertion losses.^{23–25,48,49} Thus, a trade-off between the insertion loss and the energy efficiency exists. In the case of the plasmonic PCM phase shifter proposed here, this trade-off can be largely avoided as a plasmonic mode is tightly bounded to the metal stripe; thus, the external electrode(s) can be placed very close to the plasmonic waveguide (see Table III).

The static phase-shifter or phase modulator that does not consume any energy to hold the state is a key component of the on-chip self-reconfigurable optical network that can perform any linear operation or couple between any input and output. Most of the available or proposed switches suffer from high insertion loss, slow switching speed, small modulation depth, and high energy consumption (Table III). Thus, the phase shifter proposed here, operating in a low loss regime and under a low power consumption, is of deep interest.

For an optimum operation conditions, the overall losses of the system need to be kept at the minimum. The figure of merit (FoM) in Mach–Zehnder Modulators (MZM) that are based on the Mach–Zehnder Interferometer (MZI) arrangement is the product of the half-wave voltage and the active modulator length, V_πL.^17,19 However, as some of the plasmonic modulators show very good FoM, most of them, simultaneously, suffer from very high insertion and coupling losses to the active modulator area exceeding 8 dB.^16,17,22,29 Thus, even being very compact, the insertion losses exceeding 4.5 dB for just 3 µm long active region were measured for ITO deposited on top of the waveguide.¹⁷ Simultaneously, a doped silicon heater with PCM leads to high insertion losses exceeding ∼0.5 dB/μm.⁴² Therefore, most of them become impractical for large-scale PIC platforms where light is guided through numerous photonic routers.

The proposed modulators can provide extremely low insertion losses even below 0.0075 dB/μm when the external electrodes are placed 500 nm away from the ridge [Fig. 3(a)]. As we can expect that some imperfections in the fabrication process can increase this value to about 0.02 dB/μm, it still exceeds previously reported values for other plasmonic modulators.^16–18,22 Thus, even assuming a 5 µm long active area of the phase modulator, the insertion losses below 0.1 dB can be obtained. Simultaneously, the coupling losses between the photonic waveguide and the LR-DLSPP waveguide per interface as low as ∼0.05 dB were calculated.^30,31 Assuming again some imperfections in the fabrication process, the value ∼0.2 dB per interface seems reasonable. In conclusion, even a 5 µm long photodetector can provide the overall losses below 0.5 dB under an assumption of some imperfections during the fabrication process. However, from a theoretical point of view, the overall losses as low as ∼0.115 dB can be achieved.

As it has been previously shown, the proposed arrangement can be used as well as a photodetector and an activation function unit⁶⁰ or/and can serve as a building block for future plasmonic neural networks.⁶¹ 

As the energy-per-bit scales with the length of the modulator and power consumption required to switch its state, the proposed arrangement that is based on the LR-DLSPP waveguide offers high reduction in energy consumption. The direct contact of the external or internal heater(s) with PCM that has strong influence on the propagating mode highly reduces power requirements and enables low voltage operation (Tables II and III). As it was shown in this paper, the length of the proposed switches operating based on the amplitude or phase modulation effects does not exceed 1 µm.

In conclusion, we have proposed a new class of electrically and optically driven plasmonic nonvolatile switches operating based on a phase shift and/or amplitude modulation that achieves zero-static power consumption in a device being extremely compact. Such a nonvolatile phase shifter requires only ∼230 nm long active area to attain a full π phase delay while an insertion loss is kept below ∼0.12 dB. In comparison, a nonvolatile switch operating on an amplitude modulation can show an extinction ratio exceeding ∼2.2 dB/μm and insertion loss of ∼0.185 dB/μm. Compared to any other nonvolatile devices that are based on the phase change materials, the heating of the material can be realized through either external or internal heater(s), memory switching or optical switching. They can be exploited separately or linked to provide further enhancement of temperature increases.

The author thank the “ENSEMBLE3 - Centre of Excellence for nanophotonics, advanced materials and novel crystal growth-based technologies” project (GA No. MAB/2020/14) carried out within the International Research Agendas programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund and the European Union’s Horizon 2020 research and innovation programme Teaming for Excellence (GA. No. 857543) for support of this work.

The author have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.