Switching the Localized Surface Plasmon Resonance of Single Gold Nanorods with a Phase-Change Material and the Implementation of a Cellular Automata Algorithm Using a Plasmon Particle Array

We investigate the modulation of the localized surface plasmon resonance (LSPR) of a gold nanorod (AuNR) using a GeSbTe film as an active medium. We demonstrate high-contrast switching of LSPR in an AuNR/GST/Au thin film sandwich structure upon phase change. To go beyond this single-particle switching functionality, we consider a plasmon particle system interacting with a phase-change material (PCM) to discuss the possibility of parallel processing devices with memory functionality, exploiting the plasticity and threshold behavior that are inherent characteristics of PCMs.We demonstrate that the temporal and spatial evolution of a plasmon-PCM array system can be equivalent to a cellular automata algorithm.


Introduction
Control of localized surface plasmon resonance (LSPR) excited on metal nanostructures has drawn attention for applications in dynamic switching and for tuning the functionality of plasmonic optical devices [1,2].Basically, control of LSPR relies on its sensitivity to the optical permittivity of the environment due to dielectric screening and mode hybridization [3,4].As reversible active media for LSPR control, chalcogenide phase-change materials (PCMs) [5] such as GeSbTe are promising for the development of high-contrast robust plasmonic switching devices [6][7][8] owing to significant differences in the dielectric constants of their crystalline and amorphous phases, as well as their stable plasticity at room temperature and their rapid crystallization (within several tens of nanoseconds).More importantly, GeSbTe can be nonthermally amorphized on a subpicosecond timescale with femtosecond laser pulse excitation [9,10].By exploiting these attractive properties of GeSbTe, we have demonstrated the LSPR switching of individual Au nanospheres on a GeSbTe thin film by alternating irradiation by a femtosecond pulse laser for amorphization and a continuous wave (cw) laser for crystallization [11].
The metal-dielectric-metal nanosandwich structure is an effective approach for enhancing LSPR switching contrast.When two metal particles are coupled, their dipoles are hybridized and split into symmetric and antisymmetric modes.The latter mode is called a magnetic dipole mode, in which the dipole moments of the two particles are aligned in opposite directions and generate a current loop [12][13][14][15].The LSPR peak positions of the hybridized modes, particularly the magnetic dipole mode, shift dramatically with the refractive index of the dielectric material owing to the retardation effect.
Owing to the plasticity and the threshold behavior during both amorphization and crystallization of PCMs, PCMbased LSPR switching elements possess a dual functionality of memory and processing.Integration of LSPR switching elements so that they interact with each other will allow us to build a new computing device.In this paper, as a specific demonstration of this idea, we discuss the implementation of a cellular automata (CA) algorithm [16,17]  the modeling of complex and dynamic systems, including natural and social phenomena.Any CA system is composed of cells with a finite number of states, and each cell interacts with neighboring cells.The interaction is local, with the next state of a cell being a function of the current state of itself and its neighbors.In the model we propose that PCM cells, which can be in one of two states (amorphous and crystalline), are allowed to interact with each other by being linked by a gold nanorod (AuNR), whose LSPR peak wavelength is determined by the phase of PCM cells on either side.The CA program proceeds by irradiating with a light pulse train.The local rule set is defined by the temperature rise in the PCM cells induced by the LSPR of the Au nanorod, which is subject to the intensity and wavelength of the irradiating pulse.

FDTD Simulation
Figure 1(a) illustrates the layered configuration of the Au and Ge 2 Sb 2 Te 5 (GST) sandwich structure.Numerical simulations based on the finite-difference time-domain (FDTD) method were conducted to determine the appropriate wavelength at which to monitor the LSPR switching of the AuNR.A scattering spectrum of the AuNR was calculated under broadband plane wave illumination at normal incidence.The spatial discretization was set to 1 nm, and the dielectric constants of Au and GST were obtained from [18,19], respectively.Figure 1(b) shows scattering spectra from the AuNR with crystalline and amorphous phases of the GST layer.The spectrum consists of three dominant bands around 600, 1000, and 1800 nm for amorphous GST and 600, 1500, and 2500 nm for crystalline GST.The electric field distribution (Figure 1(b) inset) confirms that the lowest bands come from interactions between the AuNR and the underlying Au layer.As in the nanosandwich, this band originates from antisymmetric coupling between the AuNR dipole and its image in the Au layer.The magnetic field intensity distribution (not shown) provides support for this peak assignment; the antisymmetric mode generates a magnetic moment due to the induced electrical dipoles, which oscillate out-of-phase to create an effective current loop.
The LSPR peak position and broadening were significantly altered upon phase change (Δ ≈ 500 nm for the intermediate band and Δ ≈ 700 nm for the lowest band).The higher refractive index of the crystalline phase than that of the amorphous phase causes a larger retardation effect, and thus the LSPR occurs at a longer wavelength.The broader LSPR for crystalline GST is due to the larger imaginary component of the GST dielectric constant, which causes a stronger damping of the LSPR.A high switching contrast is expected around 1000 and 1800 nm, so the former band was selected to demonstrate this, and the scattering intensity ratio of the AuNR for GST in the amorphous phase to that of GST in the crystalline phase is larger than 5.

LSPR Switching of a Single Gold Nanorod
After the deposition of a 50-nm-thick Au thin film on a glass substrate, a 20-nm-thick GST film was formed by sputtering.A colloidal solution of AuNRs (140 nm long, 50 nm in diameter) was used, and an AuNR dispersion in ethanol was drop-cast onto the GST film.The substrate was heated to rapidly evaporate the ethanol and prevent the aggregation of AuNRs.
The optical setup for single-AuNR spectroscopy is illustrated in Figure 2. To amorphize the GST, a picosecond pulse from a diode-pumped solid-state laser ( = 532 nm; pulse width: 300 ps) was delivered through a microscope objective.
The pulse fluence was approximately 200 mJ/cm 2 .To induce crystallization, a laser diode (LD) with  = 830 nm was used under cw operation.To monitor the switching behavior of a single AuNR at an LSPR band around 1000 nm, the AuNR was illuminated by a LD with  = 980 nm in dark-field configuration, and the scattered light was detected through the objective.
Figure 3 shows a time trace of the scattered light intensity.Starting with the GST layer in the crystalline phase, amorphization and crystallization were repeated under alternating irradiation by picosecond laser pulses and the cw LD.LSPR switching with good stability and repeatability was observed.Here, we define the switching contrast,   /  , where   and   are the scattered light intensities for substrates in the amorphous and crystalline phases, respectively.The obtained switching contrast of 1.5 was smaller than expected on the basis of the numerical simulations.This may be due to residual background scattered light originating from the roughness of the GST film surface.The amorphization process may be localized, occurring only in a small volume just below the AuNR, where the electric field enhancement occurs.However, we assumed in the simulation that the GST was fully amorphized throughout the entire volume.This could also explain the deviation from the simulation results.
In the initial stage of the switching operation, a gradual increase in the modulation contrast was observed.Although it was difficult to determine what was occurring from the optical measurements alone, one possible explanation is as follows.The modification of the surface morphology due to volume expansion of the GST film may be different after each amorphization process.There is a volume expansion of approximately 10% upon amorphization from crystalline GST [20].Therefore, there could be a slight change in the position or configuration of the AuNR in the initial stage that eventually becomes stabilized.

Implementation of Cellular Automata Algorithm
We attempted to implement a CA [16,17] algorithm into the interacting LSPR switching elements.A CA consists of a uniform array of identical cells in which each cell has a finite number of states and interacts with a few neighboring cells.A rule set is provided to define how each cell is updated at each new time step as a result of its interactions.The rule set may involve some physical mechanism that takes account of local interactions.
One very simple CA is a one-dimensional line of cells, each existing in one of two states (0 or 1).The local transition rule for each cell is defined as a function of the adjacent two neighbors.Figure 4 illustrates a one-dimensional CA composed of plasmon particles and a phase change material.GeSbTe nanopads are arranged in a regular array on an Au film.Each nanopad corresponds to a cell in the CA.Some pads are in the crystalline phase (state "0"), while others are in the amorphous phase (state "1").In order to enable interaction between neighboring nanopads, they are coupled to each other by AuNRs.When the system is uniformly illuminated with laser light at a specific wavelength, some nanorods resonate with the light while others do not, depending on whether the nanopads on both sides are amorphous or crystalline.If a nanorod resonates with the light, the nanopads on both sides absorb more light and are heated, and eventually a phase change may take place depending on what temperature the nanopad reaches.
An electromagnetic simulation was performed to calculate the temperature increase in the nanopads under light irradiation at different wavelengths.The model unit element of the CA used for this calculation is illustrated in Figure 5(a).After solving for the electric field distribution using the FDTD method, we calculated the absorbed power density ( abs ) distribution within the nanopad, employing the imaginary part of the permittivity of crystalline and amorphous GST. Figure 5(b) shows the temperature of nanopads in different configurations as a function of irradiation wavelength.Here, we assume that the temperature increase in a nanopad due to light absorption is proportional to the heat generated, which can be obtained by integrating  abs over the volume of the nanopad.The irradiation light intensity was determined such that the maximum temperature of a nanopad in the crystalline phase exceeded the melting point of GST (∼600 ∘ C).For example, if the wavelength is 1800 nm and the two nanopads adjacent to an Au nanorod are in the amorphous phase, the temperature will reach 350 ∘ C. Furthermore, if one pad is amorphous and the other is crystalline, the temperature of the crystalline nanopad will increase to 950 ∘ C, while the other only reaches 70 ∘ C.
In a one-dimensional CA (array of nanopads), the temperature of each nanopad can be calculated in a similar fashion.The laser irradiation conditions are generally different for amorphization and crystallization.However, although somewhat hypothetical, if we assume an irradiation light pulse with a width longer than the crystallization time and with a fall time much shorter than the crystallization time, the pulse can induce both amorphization and crystallization, these assumptions, at an irradiation wavelength of 1800 nm, we obtained the rule set illustrated in Figure 6, called rule number 54.When the irradiation wavelength is shifted, we can obtain another rule set.

Conclusion
Single-particle spectroscopy of an Au nanosandwich, in which a thin GST layer is sandwiched between interacting AuNRs and an Au film, was conducted.The LSPR band structure was determined using the FDTD method, and its physical causes were discussed.A very large band shift was obtained for the hybridized modes between the AuNR and Au film upon phase change of the GST layer.An experimental demonstration of LSPR modulation was performed for the LSPR band around 1000 nm, at which a switching contrast of >5 would be expected.Stable and repeatable switching with a contrast of 1.5 was obtained.Finally, as an application of high-contrast LSPR switching, the implementation of a onedimensional cellular automata algorithm using Au nanorod and GST nanopad array was discussed.

2 AdvancesGe 2 Figure 1 :
Figure 1: (a) Model of the AuNR/GST/Au nanosandwich structure for numerical calculation.(b) Numerically calculated scattering spectra from an AuNR/GST/Au nanosandwich for crystalline and amorphous GST.The insets show the electric field distributions in the vicinity of the AuNR for the three dominant bands.

Figure 2 :
Figure 2: Experimental setup for dark-field scattering measurement of single Au nanorods.

Figure 3 :
Figure 3: Time trace of scattered light intensity ( = 980 nm) from AuNR/GST/Au nanosandwich demonstrating repeatable modulation of LSPR band by alternate irradiation with femtosecond pulsed laser for amorphization and cw LD for crystallization.The switching contrast for each cycle is also plotted.

Figure 4 :Figure 5 :Figure 6 :
Figure 4: One-dimensional CA model of GeSbTe nanopads.The nanopads are coupled to each other by Au nanorods.