3.1.

Conventional Semiconductors

Conventional semiconductors, such as silicon, germanium, and III-V semiconductors, have been thoroughly studied and widely applied in the microelectronic and optoelectronic industries. Since integrating plasmonic devices on the mature and developed platforms provided by conventional semiconductors is an inevitable trend, it is of great importance to explore and realize the potential for plasmonic properties from conventional semiconductors. The solution is a widely known technique: doping. The free carrier concentration in doped semiconductors in industry is usually smaller than ${10}^{17}{\mathrm{cm}}^{-3}$, far less than that in metals, which is in the order of ${10}^{22}{\mathrm{cm}}^{-3}$ (Ref. 5). In order to achieve semiconductor plasmonics, a much higher doping level is a necessity. Some research on highly doped semiconductors exhibiting metallic behavior has already been reported.^26–30 However, the solid solubility in conventional semiconductors sets an upper limit for the doping level. For example, it is almost impossible to achieve a carrier concentration of ${10}^{21}{\mathrm{cm}}^{-3}$ in silicon.¹⁹ As a result, plasmonics based on conventional semiconductors could work only at mid-infrared (MIR) or even a lower frequency regime. It is still challenging to use conventional semiconductors for near-infrared (NIR) applications.

3.2.

Metal Compounds

As it needs abundant free carriers to support SPs, most of the alternative plasmonic materials contain a metal component. On the other hand, compared with metals, the carrier concentration in these materials has been reduced due to nonmetallic elements, which would result in lower optical losses. Silicides, germanides, and metal nitrides are typical metal compounds used as plasmonic materials. These materials are important and are also advantageous from the perspective of standard fabrication methods and integration with existing CMOS platforms.¹⁹ Besides, they offer the possibility to be optically tuned by varying their composition. According to previous studies,^31–35 they do not perform better than noble metals as plasmonic materials. However, they have a great potential to be optimized by exploring more complicated compounds or better compositions.

Transparent conducting oxides (TCOs) are doped metal oxides that receive much research focus. They have a large bandgap, which make them visibly transparent. They can be heavily doped to exhibit high electrical conductivity, and more importantly, their plasma frequencies lie in the NIR regime. The exploration of TCOs as the plasmonic metamaterial for NIR applications can be traced back to decades ago.^36–38 Some comparative studies have been reported.^19,32,39,40 Indium tin oxide (ITO), a well-known representative of TCOs, has been widely used as transparent electrodes in solar cells and for displays.^41–44 The carrier concentration in TCOs can be controlled by manipulating the concentration of oxygen vacancies and interstitial metal dopants, which result a change in optical properties. TCOs can be fabricated with a standard physical vapor or chemical vapor deposition process and integrated with other standard technologies. ITO is expensive due to the limited source of indium. Other widely investigated TCOs include aluminum zinc oxide (AZO), gallium zinc oxide, and so forth.^39,45 TCOs have been shown as a promising candidate for tunable plasmonic devices. Some applications of TCOs as tunable plasmonic materials, especially in EO modulators, will be further addressed in this article.

3.3.

2-D Materials

In recent years, great effort has been made on the investigation of 2-D plasmonic materials, especially graphene.^46–50 Their unique properties have made them attractive in many applications.^51–56 Graphene-based plasmonics for surface-enhanced Raman spectroscopy, photodetection, modulation, and sensing has been predicted,^57–60 mainly relying on the tunability of its optical conductivity. Other 2-D atomic crystals under investigation for plasmonic applications include ${\mathrm{MoS}}_2$, BN, ${\mathrm{TaS}}_2$, ${\mathrm{NbSe}}_2$, and ${\mathrm{WS}}_2$.^53,61,62 The major problem for 2-D materials is the difficulty in mass production. Besides, their application in NIR or visible range still remains a challenge.

4.1.

Introduction

As one of the most critical devices in optoelectronic integrated circuits, EO modulators have long been suffering from the poor EO properties of conventional materials, even for some well-known EO materials, such as lithium niobate,^63,64 which inhibit significant modulation within a compact modulator. Some phase modulators are on the order of millimeters.^65,66 In recent years, many EO modulators have been proposed for the purpose of a small footprint and better performance. For instance, silicon resonator modulators enhance the EO effect due to the large quality factor of the resonant cavity and, thus, can shrink their dimensions to tens of micrometers.^67–69 However, resonator modulators usually suffer from bandwidth limitation and temperature fluctuation as well as fabrication tolerance. On the other hand, nonresonant modulators exhibit broadband performance, but they lose compactness.⁷⁰

Development in plasmonics also opens a new vista for EO modulators.^71–75 Some EO modulators utilize a metal-oxide-semiconductor (MOS) structure and show a hybrid plasmonic mode,^75,76 thus having the advantages of lower losses and easy integration with CMOS platforms. A recent reported plasmonic phase modulator has a very small length ($29\mu \mathrm{m}$) and high speed ($40\mathrm{Gbit}/\mathrm{s}$), which realizes EO modulation by exploiting the Pockel effect in nonlinear polymer.⁷⁰ The choice of an active EO material is another important concern that affects device performance. In addition to lithium niobate, silicon, and polymers, graphene has also been reported as an active material for a nanoscale EO modulator working around telecommunication wavelengths.⁷⁷ As previously mentioned, the family of TCOs plays an important role in novel EO modulators.

The optical dielectric constant of TCOs can be approximated by the Drude model:

The absorption coefficient of some specific materials can also tuned by optical signals, which leads to another kind of plasmonic modulator, namely all-optic modulators.^82–84

4.2.

EA Modulators Based on ITO MOS-Like Structure

4.2.1.

ITO/Electrolyte Gel modulator

In our recent study,⁸⁵ we employed a similar structure as MOS but replaced the sandwiched oxide material with electrolyte gel to form simple multilayer modulators based on ITO. The interface between a metal (or heavily doped semiconductor) and electrolyte is of interest in most electrolyte applications, where two parallel layers of positive and negative charges called an electric double layer (EDL) are formed. To some degree, an electrolyte can be treated as a medium with a huge dielectric constant. Another advantage of using an electrolyte as the gating material is that the device behavior can be conveniently controlled by varying the concentration of chemical compounds in the electrolyte.^86,87

We fabricated an ITO film on transparent glass by physical vapor deposition. After applying a thin layer of electrolyte gel on the surface of the ITO, a heavily doped silicon chip or another identical ITO sample with the ITO side facing the electrolyte gel is tightly pushed toward the substrate ITO to form the multilayer modulator, as shown in the inset of Figs. 1(a) and 1(b), respectively.

Fig. 1

Reflectance as a function of incident angle for (a) the heavily doped Si/electrolyte gel/indium tin oxide (ITO) and (b) the ITO/electrolyte gel/ITO modulators with different applied voltages. Inset: illustration of the modulators.

We built an experimental setup⁵⁶ to measure the light reflectance of the modulators by sweeping the incident angle. The reflectance was measured in a sequence of (1) without an externally applied voltage, (2) with an externally applied voltage $V_{\mathrm{P}}$, and (3) with an externally applied voltage that has a reversed polarity but the same magnitude. The modulation depth, $M({\theta }_1)$, is defined as: $M({\theta }_1)=|R_{+Vp}-R_{-Vp}|/R_0$, where $R_0$ is the measured reflectance without an applied voltage, and $|R_{V_{\mathrm{P}}}-R_{-V_{\mathrm{P}}}|$ is the magnitude of the difference of the two reflectances with applied voltages. For $\lambda =1520\mathrm{nm}$ TM-polarized light, the modulation depth at a specific angle of ${\theta }_1=70\mathrm{deg}$ can be calculated as $M(70\mathrm{deg})=20.7\%$, as shown in Fig. 1(a). The double EDLs shown in Fig. 1(b) result in an even higher modulation depth, $M(70\mathrm{deg})=38.8\%$, with TE-polarized light at $\lambda =1520\mathrm{nm}$. We attribute the modulation to the change of the free carrier concentration in either the 5-nm-thick depletion layer or accumulation layer in the ITO at the interface, which is assisted by the redistribution of the ions in electrolyte gel induced by the applied voltage. The results also show that the ITO-based multilayer modulator is not sensitive to the polarization of the incident light beam.

The measured reflectance of the ITO modulator was numerically fitted by calculating the reflectance through the multilayer structure based on the transfer matrix method.⁸⁸ Table 1 summarizes the carrier concentration and corresponding dielectric constant of the active ITO layer (5 nm) induced by an externally applied voltage at $\lambda =1520\mathrm{nm}$.

Table 1

Carrier concentration and dielectric constant of active Indium tin oxide (ITO) layer.

Voltage (V)	Carrier concentration (${\mathrm{cm}}^{-3}$)	Dielectric constant
0	$N_0=9.82\times {10}^{20}$	${\epsilon }_{\text{untuned}}=3.7+j1.0$
10	$N_{\mathrm{dep}}=5.34\times {10}^{20}$	${\epsilon }_{\mathrm{dep}}=4.23+j0.5$
$-10$	$N_{\mathrm{acc}}=4.75\times {10}^{21}$	${\epsilon }_{\mathrm{acc}}=-0.47+j4.9$

The switching speed of the modulator is directly influenced by the relaxation of the ions in the electrolyte gel. For the modulator structure shown in Fig. 1(a), another experiment was carried out to test this relaxation effect.

As shown in Fig. 2, we applied a 30 s positive pulse at time $t_1$ and a 30 s negative pulse at $t_2$. We can observe relatively fast modulation when the pulses are excited; however, a very long time is needed for the ITO-gel modulator to recover to the baseline level. The phenomenon could be caused by the different mobilities of the major carriers in the 5-nm region in the ITO at the interface. Both the ions in the electrolyte gel and the free carriers in the ITO needed to form the EDL will probably limit its applications at high frequencies. This experiment was conducted with $\lambda =1310\mathrm{nm}$ TM-polarized light, where the modulation depth $M(65\mathrm{deg})=12.4\%$, so the ITO/electrolyte gel modulator is a potential broadband device. The problem is the modulator has a short lifetime and a very slow switching speed.

Fig. 2

Ionic relaxation effect of the electrolyte gel, at an angle of ${\theta }_1=65\mathrm{deg}$.

4.2.2.

ITO$/$HfO₂$/$Al modulator

In order to make more efficient modulators, we apply high-k dielectric material in our designed EO modulator structure,^85,89 as illustrated in Fig. 3(a). High-k material ${\mathrm{HfO}}_2$ is utilized as the gate oxide for its ultrahigh permittivity as well as process stability.⁹⁰ Aluminum is chosen here for its excellent conductivity, low absorption in the NIR regime, as well as low cost. Another advantage of using an aluminum layer is that light absorption can be directly measured by $1-R$ ($R$ is the power reflectance).

Fig. 3

(a) Schematic for $\mathrm{ITO}/{\mathrm{HfO}}_2/\mathrm{Al}$ modulator. (b) Fitting dielectric constant (real and imaginary part) of active ITO layer (the rest ITO layer keeps untuned with the value of the blue markers): blue, green, and red markers correspond to parameters with zero bias, positive bias, and negative bias, respectively; solid and dashed lines are from further fitting by the Drude model. (c) to (f) Reflectance as a function of incident angle for the modulator under different applied voltages for different wavelengths (solid lines) and the fitting curves (dashed lines).

The modulator was measured the same way as the ITO/electrolyte gel modulator. The measured reflectance as a function of the incident angle at different wavelengths is shown in Figs. 3(c)–3(f). The results were also numerically fitted to find the change of the optical constant of the active ITO layer. The fitting parameters of the active ITO layer (5 nm), together with further Drude model fitting curves, are shown in Fig. 3(b). From Fig. 3, broadband EO modulation has been achieved and the largest modulation depth obtained at a specific angle, ${\theta }_1=78\mathrm{deg}$, is $M_{\max }(78\mathrm{deg})=37.42\%$ for ${\lambda }_0=1620\mathrm{nm}$. We call the angle where the maximum modulation depth is achieved the modulation angle.

We attribute the modulation mainly to the change of the free carrier concentration in the 5-nm-thick voltage-induced active layer in ITO. For instance, when a negative bias is applied, excess electrons will be induced at the $\mathrm{ITO}–{\mathrm{HfO}}_2$ interface, which results in carrier accumulation in the active ITO layer; on the contrary, the active layer will be depleted under a positive bias.

Besides, we examined the variation of modulation depth with regard to applied voltages of different magnitudes. Starting from 0 V, we measured the power reflectance at the modulation angle at a $\pm 2\mathrm{V}$ step. The measured results for ${\lambda }_0=1550\mathrm{nm}$ are shown in Fig. 4(a). According to our observation, there may exist a threshold voltage around 2 V for the modulator to start working. After that, the modulation depth and applied voltage follow almost a linear relation.

Fig. 4

(a) Power reflectance as a function of applied voltage at the modulation angle for ${\lambda }_0=1550\mathrm{nm}$. (b) and (c) Power reflectance as a function of time at the modulation angle for ${\lambda }_0=1550\mathrm{nm}$. (b) Fast modulation and (c) slow modulation. Inset: reflectance change within 60 s.

Furthermore, we have investigated the modulation speed of the $\mathrm{ITO}/{\mathrm{HfO}}_2/\mathrm{Al}$ modulator. We observed two stages of modulation, namely, fast modulation and slow modulation, as shown in Figs. 4(b) and 4(c). In fast modulation, the reflectance almost instantly shifts up or down with the applied voltages and quickly recovers to the baseline level when turned to zero bias. However, the fast modulation contributes to a small magnitude of modulation depth. After the first stage, the reflectance keeps increasing or decreasing under the applied voltage. We can see that the slope gets smaller and smaller as time elapses, which indicates a slower and slower absorption change. The imperfection in fabrication, the device resistance-capacitance (RC) delay, and the role of the $\mathrm{ITO}–{\mathrm{HfO}}_2$ surface states may be the factors that limit the performance of the modulator.

The ITO-based modulators could be very compact and work over a large wavelength spectrum. The switching speed still needs further optimization. In our study, another key point we are focusing on is tuning the active ITO into the dielectric constant epsilon-near-zero (ENZ) state, where the potentially largest modulation depth would be observed. In the next section, we will review some of our theoretical study on TCOs working as ENZ materials.

5.1.

ENZ Material and Slot Waveguide

The development of metamaterials enables material permittivity to be engineered to almost any arbitrary value.⁹¹ Particularly, some recent research has been focused on ENZ, or index-near-zero material, which has a dielectric constant (or refractive index) with a small magnitude in a frequency range of interest. Novel applications of ENZ materials have been investigated, such as tunneling and squeezing electromagnetic energy through subwavelength narrow channels,^92,93 design of matched zero-index materials,^94,95 and shaping the radiation pattern of a source.^96,97

According to the Drude model [Eqs. (1) and (2)], the ENZ effect of a material shows up when $\omega \approx {\omega }_p$. Metals have such a high plasma frequency that they exhibit a large real dielectric constant in NIR range. Most semiconductors have doping limitations that result in their plasma frequencies located beyond MIR. The appropriate carrier concentrations in TCOs (${10}^{19}$ to ${10}^{21}{\mathrm{cm}}^{-3}$), together with advantages of low intrinsic loss and tunable optical properties, as well as easy fabrication and integration, have made them excellent plasmonic materials in NIR.¹⁹ Several other ENZ metamaterials have also been reported.^98–100

In our recent work, we studied a structure combining ENZ material with a slot waveguide, namely ENZ-slot waveguide, and found some unprecedented properties. A slot waveguide^101,102 consists of a narrow low refractive index slot sandwiched at the center of a single-mode high-index waveguide, which can greatly confine light and enhance optical fields in the slot region. The slot waveguide works well only for the TM mode where the magnetic field is parallel to the slabs. When the free carrier effect is considered in complex dielectric constants, the continuity of electric flux density between two media holds, i.e., ${\epsilon }_1{E}_{1n}={\epsilon }_2{E}_{2n}$ or $E_{1n}=({\epsilon }_2/{\epsilon }_1)E_{2n}$. If ENZ materials were applied as the slot, enormous enhancement of the E-field would take place and more power could be confined in the ENZ-slot.

As a simple example showing field enhancement and power confinement of the ENZ-slot waveguide, the structure shown in Fig. 5(a) is analytically examined. Figure 5(b) plots the electromagnetic field intensity, power percentage in the slot, and effective index of the structure as a function of slot dielectric constant ${\epsilon }_{\text{slot}}$. We can see the dramatic change of these terms when ${\epsilon }_{\text{slot}}$ is approaching zero. In particular, the effective index sharply decreases from 1.6 to $\sim 1$ when ${\epsilon }_{\text{slot}}$ decreases from 0.1 to nearly zero due to the larger power confinement within the low index slot.

Fig. 5

(a) Structure of a simple three-layer waveguide (value of $n_{\text{silicon}}$ used for ${\lambda }_0=1550\mathrm{nm}$ is 3.47). (b) Plots of electric field, magnetic field, power percentage in the slot, and effective index of the structure versus slot dielectric constant.

5.2.

EA Modulators Based on TCO-Slot Waveguide

According to the experimental data in Ref. 78, ITOs with different carrier concentrations could work as ENZ materials at specific wavelengths.¹⁰³ As shown in Fig. 6(a), the ENZ effect of ITO is achieved at ${\lambda }_0=1136\mathrm{nm}$ and ${\lambda }_0=843\mathrm{nm}$ under carrier concentrations $N_1=1.65\times {10}^{22}{\mathrm{cm}}^{-3}$ and $N_2=2.77\times {10}^{22}{\mathrm{cm}}^{-3}$, respectively. As suggested, the accumulation of carriers could be realized by electric signal in an MOS-like structure [Fig. 6(b)], which indicates the optical tunability of ITO.

Fig. 6

(a) Real part of the dielectric constant of ITO as a function of wavelength at three different carrier concentrations based on the Drude model.⁸⁷ (b) Illustration of the epsilon-near-zero (ENZ)-slot waveguide.⁸⁰

The dielectric constant of ITO at epsilon-far-from-zero (untuned) state and ENZ state is shown in Table 2, where we can see the magnitude has changed tens or even hundreds of times due to the externally applied voltage. The huge change in the magnitude of the dielectric constant may find applications in EA modulators. In dielectric heating theory, the power dissipation density can be written as

Table 2

Dielectric constant of ITO at untuned and epsilon-near-zero (ENZ) state.

ITO EA modulators based on a dielectric waveguide [Fig. 7(a)] and a plasmonic waveguide [Fig. 7(b)] were proposed and simulated. Their modes were solved by the finite-difference time-domain (FDTD) method. Note that we applied a 10-nm-thick ITO in the waveguides, of which 5 nm at the $\mathrm{ITO}–{\mathrm{SiO}}_2$ interface were assumed to be tuned. From the results, we can see significant field enhancement and confinement within the ENZ-slot and a considerable shift in the effective index. More importantly, a huge change in waveguide attenuation ($21.85\mathrm{dB}/\mu \mathrm{m}$ for dielectric waveguide and $20.64\mathrm{dB}/\mu \mathrm{m}$ for plasmonic waveguide) is achieved.

Fig. 7

The electric field profiles, effective indices, and propagation loss for different ITO-slot waveguide at untuned state and ENZ state, respectively: (a) in a dielectric rib waveguide and (b) in a plasmonic waveguide.

The insertion loss of the EA modulators was evaluated by three-dimensional (3-D) FDTD simulation. For a 150-nm-long modulator embedded in a plasmonic rib waveguide, the insertion loss is 0.48 dB and the modulation depth is 3.42 dB, which is very close to the one predicted by the 3-D mode solver. A 200-nm-long modulator embedded in a dielectric rib waveguide shows an insertion loss of 0.56 dB and a modulation depth of 3.53 dB.

In Ref. 81, we utilized a similar theory and demonstrated EA modulation based on an ENZ-slot waveguide, where another TCO material, AZO, is serving as the tunable slot. We also showed that the optical bandwidth of these modulators can be over several terahertz due to slow Drude dispersion. These TCO-slot waveguide-based EA modulators are compact and could potentially work at ultrahigh speed, being mainly limited by the RC delay introduced by electric circuits.

Actually, the EA modulators we proposed in Sec. 4 are mainly based on this theoretical study, and we intend to search for the ENZ effect in an active ITO layer, which was supposed to produce the maximum modulation depth. According to the parameters in Table 1 and Fig. 3(b), more effort is still needed in optimizing the design and the fabrication process.

5.3.

Laser Beam Steering by TCO-Slot Waveguide

In both the analytical calculation of a simple ENZ-slot waveguide in Sec. 5.1 and the numerical simulation of the EA modulators, we see that the effective indices of the waveguides undergo the considerable change. Thus, we can engineer the effective index of the ENZ-slot waveguide by tuning the refractive index of ITO film. This phenomenon may find applications in laser beam steering.⁹¹ Laser beam steering techniques are being widely investigated because of their applications in laser-based sensing, communication and power projection, and other fields. Mechanical and nonmechanical methods, such as beam steering with a rotating (Risley) prism, macro-optical mirrors, microlens arrays, and liquid crystal polarization gratings, have been proposed,^104–106 heading to the purposes of compactness, low power, high speed, lightweight, and a large field of regard. To advance this technique, we proposed a novel beam steering structure based on the tunable ENZ-slot waveguide.

In order to realize beam steering, we added periodic gratings on top of the ITO-slot waveguide [Fig. 8(a)] and made use of the tunable effective index of the structure to steer the incident laser beam. According to the grating equation,

Fig. 8

(a) Illustration of beam steering based on ENZ-slot waveguide with periodic gratings. (b) Complex effective index in terms of carrier concentration.

For an incident beam of ${\lambda }_0=1136\mathrm{nm}$, the attenuation would be too large for the waveguide when ITO is at the ENZ state. Since long-distance propagation is a major concern here, in order to achieve easy detection we chose the working wavelength to be 843 nm, which is the cross-wavelength for ITO under $N_2$. Here the damping factor $\gamma \approx 0$,⁷⁸ so the attenuation of the ENZ-slot waveguide decreases quite a bit: ${\alpha }_0=0.328\mathrm{dB}/\mu \mathrm{m}$ when untuned and ${\alpha }_2=0.107\mathrm{dB}/\mu \mathrm{m}$ under $N_2$. Besides, the effective index is also significantly shifted from 2.29 to 1.65, which promises a wide steering angle.

For convenience, in Eq. (4), we assume $\mathrm{\Lambda }=653\mathrm{nm}$, ${\lambda }_0=843\mathrm{nm}$, and $l=1$, which make $l{\lambda }_0/\mathrm{\Lambda }=1.29$. Figure 8(b) plots the complex effective index of the waveguide in terms of the carrier concentration. The effective index that can be obtained ranges from 1.53 to 3.22 (values $>2.29$ may correspond to a higher harmonic mode). Therefore, the value range for $\sin \theta$ that can be achieved is from 0.24 to 1, which also results in a steering angle $\theta$ from 14 to 90 deg. Note that the minimum effective index is achieved when the active ITO layer (5 nm) at the $\mathrm{ITO}–{\mathrm{SiO}}_2$ interface is at the ENZ state.

FDTD simulations were performed to verify the predictions. The phase plot, normalized intensity magnitude plot, and far-field intensity plot of the dominate electric field $E_y$ for the steering angles of 14 and 60 deg are shown in Fig. 9.

Fig. 9

Phase, normalized magnitude, and far-field intensity of $E_y$ for steering angles of (a) 14 deg and (b) 60 deg.

The phase and magnitude plots illustrate the propagation direction of the steered beam in the near-field, which is normal to the phase line, or along the magnitude trend. Note that the magnitude plots show only the electric field above the ENZ-slot due to a much higher electric field in the slot. Far-field intensity plots can clearly identify the steering angle. According to the figures, laser beam steering is achieved by the effective index change of the ENZ-slot waveguide. The maximum steering angle we got from simulations is $\theta \approx 75\mathrm{deg}$.

As one example, we showed some theoretical studies of TCOs behaving as the ENZ material in ENZ-slot waveguides and their applications in EA modulation and laser beam steering. ENZ-slot waveguides highly confine electromagnetic fields in the slot region, so the behaviors of the waveguides can be greatly changed by tuning the slot material. Besides, they can be easily fabricated layer by layer. With the advantages of TCOs in low intrinsic loss, excellent tunability as well as ease of fabrication and integration, the combination, TCO-slot waveguides, is of great promise in building novel optoelectronic devices for NIR applications.