Plasmonic switch based on asymmetric cavities with embedding square of gold inside the cavities

Abstract. We proposed an all-optical plasmonic switch based on metal-insulator-metal structures. We used the intrinsic nonlinear properties of gold to implement the switch. The proposed switch consists of a bus waveguide side coupled with a pair of asymmetric vertical cavities. We obtained the transmission spectrum of the structure for low input intensities. The results showed that a sharp dip occurs at the wavelength of 860 nm. Due to the nonlinear properties of gold and the nonlinear Kerr effects, the proposed switch has a high transmission ratio of about 0.8  mW  /  μm2 and a low threshold power of 0.07  mW  /  μm2. The threshold power of the structure with and without using the gold nanostructure shows a reduction of 50%. The result showed that the proposed switch has the potential to be applied in the plasmonic integration circuits.


Introduction
All-optical switches are indispensable in integrated optical circuits, and are widely applied in alloptical networks. 13][4][5][6][7] SPPs are electromagnetic waves propagating at the interface between a metal and a dielectric.In metal structures, only transverse magnetic (TM) polarization excites the SPPs.When light with TM polarization is applied to the metal structure, SPPs are excited. 8,91][12][13][14][15] Plasmonic switches are in the range of nanometers with fast response, low input power, and high transmission efficiency.In recent years, various switching mechanisms have been demonstrated in plasmonic waveguide-cavity coupled devices.One of the important and interesting approaches for the implementation of plasmonic switches is the optical nonlinear Kerr effect.4][25][26] However, to the best of our knowledge, the implementation of a plasmonic switch using the nonlinear Kerr effect and the inherently nonlinear characteristics of the gold has remained unaddressed so far, and hence has been the focus of study in this paper.In this research, we demonstrate an all-optical switch based on the plasmonic cavity.It has the potential to be applied in plasmonic integration circuits.The switching threshold power and the transmission spectra for the plasmonic switch are achieved.The propagation of electromagnetic waves in the time domain is simulated with the finite difference time domain. 27

Theory and Structure
In this study, metal-insulator-metal (MIM) structures, cavities, and nonlinear characteristics of gold are employed to implement a plasmonic switch.Using high Kerr coefficient material, cavities, and inserting a piece of gold inside the cavities, result in an all-optical switch with a low power consumption and fast speed.For the first time, in addition to the material with a high nonlinear Kerr coefficient, the inherently nonlinear characteristics of the gold are the other factor used to implement a plasmonic switch.][30][31][32][33] Figure 1(a) shows the schematic view of the proposed switch comprising a bus waveguide side coupled with a pair of asymmetric vertical cavities.Also, the top view of the switch is shown in Fig. 1(b).The complex dielectric constant of silver is determined by the Drude model where ε ∞ , ω p , γ, and ω are the relative permittivity at the infinite frequency, the plasma frequency, the electron collision frequency, and the angular frequency of the incident light wave, respectively.In this paper, the parameters are the following: ε ∞ ¼ 1.95, ω p ¼ 1.37 × 10 16 ðrad∕sÞ, and γ ¼ 20 × 10 12 rad∕s, which were taken from Ref. 24.
The straight waveguide and the cavities are filled with air and the nonlinear Au∕SiO 2 , respectively.The cavities can enable deep subwavelength confinement of SPPs in all three spatial dimensions.
The dielectric in the straight waveguides is air with a refractive index n air ¼ 1.The dielectric in the cavities is Au∕SiO 2 with high Kerr nonlinearity, which has a refractive index of n 0 ¼ 1.47 and Kerr non-linear coefficient of n 2 ¼ 2.07 × 10 −9 cm 2 ∕W. 34The surface plasmon resonance of Au∕SiO 2 composite can lead to enhanced third-order optical nonlinear susceptibility. 35g. 1  The width of the waveguide and the width of the two asymmetric vertical cavities, w, are assumed to be 150 nm.Also, the distance between the cavities, d, is assumed to be 150 nm.A 100 × 100 nm square of gold is inserted inside the cavities.
As shown in Fig. 1(a) the structure should be placed on a glass substrate, as this will be also the case when it is studied experimentally.To ensure the feasibility of the fabrication technology, the thickness of the substrate, silver, and Au∕SiO 2 are taken at 100, 50, and 50 nm, respectively.Moreover, the thickness of the glass film is set at 100 nm.If fabrication considerations are taken into account, including choosing a glass substrate with the appropriate thickness, the effect of the fabrication tolerances on the results is negligible.
A cavity can be considered a good candidate for achieving strong nonlinear effects.The resonance of light within the cavity increases the light intensity to higher levels at some specific frequencies.Thus, the outcome will be a strong nonlinear Kerr effect.When light with TM polarization is injected into the MIM structure, it couples to the waveguide, and SPP waves propagate along the common metal surfaces.If the wavelength of the applied light is the same as the resonant cavity wavelength, the light does not pass.This wavelength is sensitive to the dielectric constant that can be changed due to the nonlinear Kerr effect of the material.Therefore, by increasing the intensity of the input light, the wavelength changes, and switching is performed. 8Table 1 presents the physical and geometric parameters of the proposed switch.

Design and Simulation
The asymmetric nonlinear cavity pair of the nanostructure, shown in Fig. 1, has a strong resonant wavelength.To investigate the confined SPP modes, we calculated the transmission spectrum for the cavities.Figure 2 shows the transmission spectrum of the structure for low and high input intensities.Fig. 2 at the low intensity (0.01 mW∕μm 2 ), a sharp dip occurs at the wavelength of 860 nm.This indicates that SPPs are strongly confined in the cavities without significant  scattering.If the input light intensity is increased to 0.1 mW∕μm 2 , the dielectric constant of the nonlinear material also increases, and the dip is red-shifted to 880 nm. Figure 3 shows the dependency of signal transmission on the intensity of the input light at the wavelength of 860 nm.If the intensity of the input light changes, the dielectric constant changes and causes a difference in the transmission spectrum of the signal.Therefore, a mechanism is provided for the dual behavior of light at the output regarding the input light intensity.It should be noted that the constant dielectric change is due to the field intensity in the cavities.When the input light intensity is increased to 0.1 mW∕μm 2 , the signal transmission to the output increases suddenly to about 0.8.The threshold power of the signal is about 0.07 mW∕μm 2 ; therefore, only higher light intensity than the threshold power is required to realize the switching operation.
To demonstrate the performance of the incident light signal under on/off conditions, the magnetic field distribution of the structure for low and high light intensities is shown in Fig. 4. As shown, when the input light intensity is about 0.01 mW∕μm 2 , the signal is reflected, and when the input light intensity increases to 0.1 mW∕μm 2 , it can pass the straight waveguide.The results are in good agreement with the signal transmission spectrum response under on/off conditions.
In addition to the nonlinear material with a high Kerr effect, the low light intensity required for switching is due to employing gold nanostructures inside the cavities.To ensure the validity of this issue and study the effect of these square gold nanostructures, the proposed switch structure is studied and simulated in the absence of the gold nanostructures inside the cavities.Considering the transmission spectrum of the structure in Fig. 5 for low input intensity of 0.01 mW∕μm 2 , a sharp dip in the transmission spectrum for through port is observed at a wavelength of 740 nm.The structure is scanned at this wavelength for various light intensities, and the dependency of the signal transmission to the input light intensity is shown in Fig. 6.When the light intensity is increased to 0.2 mW∕μm 2 , the transmission increases to 0.62.The threshold power of the signal is 0.15 mW∕μm 2 .the results, using square gold nanostructures reduces the input light intensity from 0.15 to 0.07 mW∕μm 2 .
To observe the effect of the asymmetry of the structure on the switch performance, the distance between the two cavities is increased from 150 to 300 nm.The structure was simulated for distances of 200, 250, and 300 nm.As the transmission spectrum in Fig. 7 shows, the asymmetry of the structure causes that an appropriate resonant frequency cannot be found for the correct operation of the switch.So, it is concluded that the structure must have symmetry.It should be noted that the inherently nonlinear characteristics of gold are better than other metals, such as copper, silver, etc.
The results of the presented switch surpassed those of several other studies, indicating a significant advancement in the research.To compare the specifications of the proposed switch with other published works in recent years, [36][37][38][39] the results are organized in Table 2.As shown, the proposed plasmonic switch has the highest ON-state transmission and requires the least switching power among all the structures listed in Table 2.

Conclusion
In this study, MIM structures, cavities, and intrinsic nonlinear properties of the gold are used to implement an all-optical plasmonic switch.The proposed switch is comprised of a bus waveguide side coupled with a pair of asymmetric vertical cavities.The dielectric in the waveguide and the two cavities are filled with air and Kerr nonlinear material, respectively.A 100 × 100 nm square of gold is also inserted inside the cavities.The transmission spectrum showed that for low input intensities, a sharp dip occurs at the wavelength of 860 nm.When the input light intensity is  increased to 0.1 mW∕μm 2 , the dip of the transmission spectrum changes and the transmission power increases to 0.8.The threshold power of the structure with and without using the gold nanostructure is 0.15 and 0.07 mW∕μm 2 , respectively, showing a reduction of 50%.
Fig. 1 (a) Schematic and (b) top view of the proposed plasmonic switch.

Fig. 2
Fig. 2 Transmission spectrum of the proposed plasmonic switch for (a) low and (b) high input intensities.

Fig. 3 Fig. 4
Fig. 3 Dependency of signal transmission on the intensity of the input light with gold nanostructures.

Fig. 5
Fig. 5 Transmission spectrum of the proposed plasmonic switch without gold nanostructures.

Fig. 6
Fig. 6 Dependency of the signal transmission to the input light intensity without gold nanostructures.

Table 1
Physical and geometric parameters of the switch.

Table 2
Comparison of the results with previous works.