Electrically Tunable Plasmonic Absorber Based on Cu-ITO Subwavelength Grating on SOI at Telecom Wavelength

An electrically controlled optical absorption is numerically proposed in a plasmonic waveguide on silicon-on-insulator (SOI) consisting of copper-indium tin oxide (ITO) based subwavelength grating at 1.55 µm wavelength. The Cu-ITO subwavelength grating in a form of a discontinuous Cu layer filled with ITO together with electrically tunable permittivity of ITO provides us with a tunable absorption and efficient guidance of plasmonic mode. An n-type ITO is used which exhibits a significant change in the carrier concentration with the applied voltage resulting in a change in optical absorption at a telecom wavelength of 1.55 µm. We numerically observe maximum tuning in absorption at a grating period of 600 nm and a duty cycle of 50%. The proposed device shows a smaller effective mode area of Am = 0.01421/µm2 and a plasmonic confinement factor of 34.67%. The device is reported to have an extinction ratio of 10.28 dB for a 100-µm-long device at a low voltage of 6 V.


Introduction
The absorption of light energy is an important property of light in which the energy of an electromagnetic wave striking on an object is transferred to several usable types of energies, for example, thermal, electrical, chemical, and mechanical. These kinds of devices can be used in a variety of ways like photodetection [1], local heating [2], biosensing [3,4], imaging [5], and energy harvestings [6][7][8]. Noble metals such as copper, gold, and silver are excellent plasmonic materials in the infrared regime (IR). By pattering such types of metals at the nanoscale level, strong absorption can be produced due to the excitation of surface plasmon polaritons (SPPs) [9][10][11][12][13][14][15]. For the integration of nanoscale devices on a single chip, the control and confinement of the light beyond the diffraction limit are major challenges that can be overcome by plasmonic [16][17][18][19]. Surface plasmon (SP) excitations in metals allow light to be trapped in the deep subwavelength zone, which can improve strong light-matter interactions; plasmonic has allowed us to miniaturization of components at a nanoscale level so we can integrate a large number of optical and electronic components on a single chip [20,21]. Controlling and guiding light in on-chip devices via electrical means is a key technology for high-speed computing and embedding data on an optical carrier for efficient data transmission [22]. In that situation, the electrical tuning of a waveguide remains an important function for a variety of devices that can be generated by electrically tuning the charge carrier density of the material to change the optical parameter of the guided wave [23][24][25][26]. The carrier concentration of transparent conducting oxides (TCOs) can be changed to tune the optical properties of light. Among the number of TCOs, indium tin oxide (ITO) is the preferred candidate to tune optical properties. It has received interest as an active electro-optical material because of the significant refractive index change owing to permittivity changes at NIR wavelengths, including the 1.55 µm telecommunication wavelength [27,28]. An integrated platform based on surface plasmon polaritons (SPPs) waveguide can be promising for making photonic devices at the nanoscale. Plasmonic waveguide structures offer confinement of optical energy by coupling electromagnetic wave to the oscillation of free charge carriers present at metal-dielectric interface called surface plasmon polaritons (SPPs). The oscillation wavelength of resulting plasmon polaritons is considerably smaller as compared to the wavelength of light energy in the vacuum [29].
In this paper, an electrically tunable plasmonic absorber on a silicon-on-insulator (SOI) is proposed. The device consists of copper-indium tin oxide (ITO) based subwavelength grating at 1.55 µm wavelength. The slow light propagates in the device arising from light confinement in the small mode area. The effective mode area of Am = 0.01421/µm 2 and plasmonic confinement factor of 34.67% is observed, resulting in enhanced light-matter interaction and significant change in the imaginary part of effective refractive index which shows the absorption of light. The Cu-ITO subwavelength grating in form of a discontinuous Cu layer filled with ITO together with electrically tunable permittivity of ITO provides us with a tunable absorption and efficient guidance of plasmonic mode. An n-type ITO is used which exhibits a significant change in carrier concentration with the applied voltage of 4 V, resulting in a change in optical absorption at telecom wavelength. In this work, the significant change of the imaginary part of the effective refractive index varies the duty cycle at the grating period of 600 nm, and we observe maximum tuning in absorption at a grating period of 600 nm and a duty cycle of 50%. The propagation length of the device with varying the duty cycle and with increasing the duty cycle the propagation length decreases. The device has an extinction ratio of 10.28 dB for a 100-µm-long device at a very low voltage of 6 V.

Device Structure and Working Principle
The proposed device indium tin oxide (ITO) is used as an active absorber material; light absorption can be controlled electrically; the ITO has established itself as one of the highly electrically controllable material; and the optical characteristics of the material can be varied significantly by electrical tuning of free charge carrier [30]. ITO exhibits unity order change of effective refractive index due to change in permittivity of the material which can be used for tunable absorber device [31]. Figure 1 shows the 3-D geometry of the proposed electrically tunable plasmonic absorber device. Here, x-axis depicts the device's width, the y-axis denotes the device's thickness, and the z-axis represents the propagation direction of the electromagnetic wave. The silicon rib waveguide's thickness (t) and width (w) are 200 nm and 300 nm, respectively, and the device has a buried oxide layer for isolation from the silicon substrate for better confinement of light.
The device consists of a 10-nm-thick silicon dioxide layer over which an alternating Cu and ITO grating is formed. Distributed Cu layer is used to reduce metal absorption and to enhance propagation length. ITO material filled between two Cu strips interacts more with SPPs which enhances tuning of carrier concentration ITO layer. The refractive index of Cu and ITO at telecom wavelength (1550 nm) makes a good contrast for the slow light effect which can Cu-ITO subwavelength grating assisted electrically tunable plasmonic absorber at 1550 nm wavelength on p-type SOI wafer. Cu-ITO subwavelength grating is utilized to change the imaginary part of the effective refractive index (κ) of the propagating plasmonic mode of the device. Si rib waveguide width is 300 nm, Si thickness is 200 nm, Cu-ITO grating thickness is 40 nm, Cu-ITO grating period is 600 nm, the duty cycle is 50%, and ITO capping layer is 40 nm and plasmonic mode (TM mode) confinement at dielectric and Cu-ITO grating interface of the device. Inset shows confinement of the guided plasmonic TM mode enhance the light-matter interaction of the device. The grating period of the device is 600 nm, and the duty cycle is 50%. The optimized thickness of both Cu and ITO grating is 40 nm each over which a 40-nm-thick capping layer of ITO is used for better electrical tuning of the device. A 10-nm layer of silicon dioxide dielectric material is used to excite the SPPs at the metal-dielectric interface and to enhance the plasmonic mode. For the simulation of the device lumerical eigenmode, finite difference solver is used to study the field confinement of the plasmonic mode and observed that the device supports transverse magnetic ™ polarized wave propagation and mode confined at the interface of dielectric and Cu-ITO grating. The working principle of the device is when we shine the light having the wavelength of 1550 nm. The TM polarized plasmonic mode propagates with a high confinement factor and tiny mode area at the Cu-ITO grating and dielectric interface; the inset shows the mode confinement of the device. The charge carrier accumulates at Cu-ITO grating and dielectric interface, and the accumulated carriers efficiently coupled by propagating electromagnetic waves and form surface plasmon polaritons (SPPs) which changes the permittivity of ITO material. The imaginary component of the effective refractive index of the waveguide changes when the permittivity of the ITO changes, indicating a change in light.

Analysis of Effect of ITO and Propagation Characteristics
The device's optical properties can be electrically modified by varying the carrier (electron) concentration in the ITO layer. It's a good material for tuning intensity at telecom wavelengths with high modulation efficiency because of the substantial fluctuation in carrier concentration caused by the applied voltage. The mobile electron concentration density of the ITO, which acts as a free electron Drude material, is used to monitor its optical characteristics [32].
The optical permittivity of the ITO is denoted by where ∞ represents dielectric constant of the material, depicts the angular frequency of propagating electromagnetic wave and the carrier collision frequency in the ITO layer of the device is denoted by Γ , p is the plasma frequency of the ITO layer, N e is electron charge magnitude, and m * ce is the effective mass of the electron. The permittivity of the ITO layer can be changed by applying the electrical bias due to the variation of charge carrier density of the ITO layer. Lumerical charge solver is used to analyzing the variation of charge carrier density with applied bias. Figure 2a shows the change of carrier with applied voltage at different ITO thickness, and Fig. 2b shows the change of carrier concentration versus vertical distance (thickness) of the waveguide, and it is observed that the carrier accumulates at the Cu-ITO grating and SiO 2 interface, and the accumulated carrier changes the permittivity of the ITO material. A significant change of carrier concentration at the applied voltage of 4 V is observed. The change of carrier concentration results in changes in the effective refractive index of the material due to a change of permittivity of the ITO layer. The perturbed carrier concentration of the lumerical charge solver due to the applied bias is imported in lumerical finite difference time domain (FDTD) to observe the change of  Figure 3a shows the wave propagation; at no bias, the plasmonic wave propagates at the interface of dielectric and Cu-ITO grating; and we can say that ON state of the device and when we use perturbed carrier concentration at an applied bias of 4 V, the intensity of wave propagation reduces, and the device acts as an absorber as shown in Fig. 3b, and we can say OFF state of the device. In the simulation of the device, we have used the lumerical finite difference eigenmode (FDE) solver for the analysis of mode confinement.
The effective mode area of the guided mode will be the measure of the nature; whether the localized field is optical or plasmonic mode and it would be the merit of confinement ability, the effective mode area (A m ) of the device can be calculated by taking the ratio of total mode energy flux density and the maximum energy flux density at active region. The effective mode area is denoted by [33] Figure 4a shows the variation of effective mode area with increasing the thickness of the ITO layer and light confined at a very small mode area of 0.01421 /µm 2 at the active region of the device.
The propagation length of the plasmonic wave is depicted as the distance at which the intensity of the propagating wave reduces to a factor of 1/e of the total coupling intensity of the light and the propagation length of the guided plasmonic mode is denoted by [34]: where is the operating wavelength and (n eff )img is an imaginary component of the effective refractive index and the model propagation loss is given by: where k 0 = 2 0 denotes the propagation constant of the plasmonic mode and the negative sign indicates lossy materials. Figure 4b shows the propagation length versus duty cycle of Cu-ITO grating, and the propagation length decreases by increasing the duty cycle of grating; this is due to the high model propagation loss of the device. So, there is a tradeoff between model propagation loss and propagation length.
The optical energy confinement of the device is the propagation of power flowing through the active zone to the total power flowing through the system [35][36][37]. Figure 4c shows the plasmonic mode confinement of the device with varying the thickness of the active layer (ITO), and the confinement factor increases with increasing the thickness of the ITO layer, and Fig. 4d depicts the device's plasmonic mode confinement as a function of Cu layer thickness, demonstrating that the mode confinement decreases as Cu layer thickness increases. So, the device exhibits the confinement factor of 34.67% at the optimized layer of 40 nm of the copper layer and 40 nm of the ITO layer.

Electrically Tunable Absorption
The electrical behavior of the device is numerically investigated by using a lumerical charge transport solver. The device simulation yields charge transport data of change of charge carrier density of Cu-ITO junction with applied bias. The perturbed charge carrier density of the device is introduced from the lumerical device simulation tool through the index perturbation into the lumerical mode solution for analysis of change of light properties due to applied bias. The Drude model is used to calculate the change in the effective refractive index of the Cu-ITO subwavelength grating. The change of the charge carrier density of the ITO at different voltages has ability to change the effective refractive index of the device. The complex permittivity of the material is related to its charge carrier density, according to the Drude model hypothesis and depicted as Δn = Δ 2 √ ; the variation of charge carrier density(accumulation or depletion) has ability to change the complex permittivity which yields the change of effective refractive index. The change of complex effective refractive index (real and imaginary components) of the device with variation of carrier density is calculated as: and where N e and N h represent electron and hole carrier densities, e represents electronic charge, λ 0 represents operation wavelength, e and h represent electron and hole mobility, and m * ce and m * ch represent the effective mass of electron and hole, respectively.
The carrier concentration of the ITO layer is 1 × 10 20 cm −3 and when we applied the voltage carrier concentration of the ITO changes as shown in Fig. 2. and electron accumulated at c Plasmonic mode confinement factor at the different thickness of Cu layer of the device; confinement factor decreases with increasing the thickness of Cu layer. d Plasmonic mode confinement at the different thickness of ITO layer of the device; confinement factor increases with increasing the thickness of ITO layer the interface of dielectric and ITO which alters the permittivity of the material yields change in the refractive index of the device when no voltage is applied the refractive index of the material is 2.402 + 0.0349i and when we applied voltage of 6 V, the refractive index of the material changed to 2.335 + 0.048i at the operating wavelength of 1550 nm. The change in carrier concentration (accumulation of electron at Cu-ITO grating and dielectric interface) due to applied bias, there is a change of real and imaginary components of the effective index of the device. The change of the real part represents the phase shift, and the change of the imaginary part represents the attenuation of plasmonic wave propagation. The electromagnetic wave's intensity can be changed by changing the imaginary components, which can be done with the applied voltage. Figure 5a shows the graph between change in the imaginary component of effective refractive index versus applied voltage with varying the thickness of the Cu layer of the device, and it shows that the imaginary component of the effective refractive index increases with decreasing the thickness of the Cu layer. We have observed that the maximum tunability of the device is achieved at copper and ITO thickness of 40 nm each. We have optimized the grating period and duty cycle of the device to achieve higher tunability of the plasmonic wave, and Fig. 5b shows the graph between the change of imaginary component of the effective refractive index with varying the grating period of the device. The change of the imaginary component of the effective refractive index is maximum at the grating period  Fig. 5c depicts the variation of the imaginary component of the effective refractive index versus the duty cycle of Cu-ITO grating, and the device yields the maximum tunability at the duty cycle of 50%. We optimized the device for an electrically tunable absorber and observe that at the grating period of 600 nm and duty cycle of 50%, the device yields a maximum change in effective refractive index which represents the absorption of electromagnetic wave. The change in the imaginary component of the effective refractive index of the device can be used to tune the attenuation of the intensity (absorption) of the electromagnetic wave. We can calculate the absorption of the light in terms of effective refractive index which is given by = 2 k eff . The extinction ratio or modulation depth of the device can be calculated by: Figure 5d shows the extinction ratio versus voltage. The ER of the 100-µm-long device is calculated to be 10.28 dB. The device length must be increased or a greater voltage must be provided to improve the extinction ratio. The higher driving voltage is incompatible with CMOS driving circuits, and the rising device length is incompatible with high-density integration; therefore, there is a tradeoff between high extinction ratio and small device footprint.

Conclusion
An electrically tunable plasmonic absorber on SOI is numerically reported. The device consists of copper-indium tin oxide (ITO) based subwavelength grating which operates at a telecom wavelength of 1.55 µm. The device design with Cu-ITO structure efficiently utilizes electrically tunable permittivity of ITO. We observe the maximum tuning of absorption at a grating period of 600 nm and 50% duty cycle of the Cu-ITO grating. The device shows a very small mode area of A m = 0.01421/ µm 2 and a higher plasmonic confinement factor of 34.67%. Our device exhibits the extinction ratio (ER) of 10.28 dB at a very low voltage of 6 V for a 100-µm-long device. This tunable absorber can be used in many applications where attenuation of intensity is a prime requirement such as intensity modulator, biosensing, and imaging.

Data Availability
The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code Availability
The computer codes used during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics Approval I have read plasmonic's ethical guidelines and state that I have not violated them in any way.

Consent to Participate
Informed consent was obtained from all individual participants included in the study.

Conflict of Interest
The authors declare no competing interests.