The ability to control the amplitude, phase and/or polarization of electromagnetic waves remains of critical importance for all technological applications. This is also applicable to Terahertz (THz) radiation, ranging from 100 GHz to 5 THz that is of interest to scientists and technologists because electromagnetic waves at those frequencies can excite intra- and intermolecular resonances due to molecular rotations or vibrations and Van de Waals forces  . Additionally, THz electromagnetic waves exhibit a variety of useful characteristics, namely, THz photons are non-ionizing and most dielectrics are transparent to them, enabling a wide range of applications, from characterization of chemical substances and quality control      to contributions in communications, and conservation of cultural heritage    . In terms of the size of the objects under consideration, it extends from the galactic scale to nanoscale systems     . Interestingly, THz devices are, in general, faster and more sensitive, compared to their counterparts in other regions of the electromagnetic spectrum ; however, the paucity of naturally occurring materials with a suitable performance in the THz regime has made the advance of terahertz devices and applications rather arduous. This shortcoming can be addressed by the judicious utilization of metamaterials, which are artificial media with subwavelength unit cells that can be designed to achieve arbitrary (negative or positive) permittivity and permeability values, and can be custom-tailored to exhibit resonances at a desired frequency even in the THz regime     . The resonance amplitude and frequency of operation of metamaterials are determined by the geometry and the materials utilized, and typically do not exhibit a reconfigurable behavior, which is a requirement in numerous applications. A variety of schemes have been suggested and explored to achieve reconfigurable metamaterial performance including the dynamic adjustment of the dimensions or the spacing of the structures which can be effected either by employing flexible surfaces   or microactuating mechanisms frequently associated with MEMS technology  . The use of phase-change materials, either thermal, electrical or electromagnetically controlled, can also attain such a goal  . However, an all-optical reconfigurable device is highly desirable for THz communication and data transmission applications, and a dynamic reconfigurable performance could be achieved by modulating the dielectric characteristics of the media surrounding the metamaterial unit cell, for instance by the utilization of semiconducting quantum dots (QDs). Specifically, it has recently been reported that Cadmium Telluride (CdTe) QDs exhibit a variation in their dielectric characteristics when they are excited by an ultraviolet (UV) source . However, their ability to modulate the response of a metamaterial array operating in the THz regime has not been demonstrated yet.
2. Experimental Details
2.1. Quantum Dot Synthesis
The CdTe QDs employed as reconfigurable elements, were obtained by a hydrothermal synthesis method. In a typical synthesis, 0.0533 g (0.2 mmol) of Cadmium acetate dihydrate (Cd(CH3COO)2 2H2O, 99.5%) were dissolved in 50 ml of deionized (DI) water in a 125-ml Erlenmeyer flask. Next, 18 µl of thioglycolic acid (TGA) were added and 1 M NaOH solution was incorporated dropwise to adjust the pH to a value between 10.5 - 11. In a separate flask, 0.0101 g (0.04 mmol) of potassium tellurite (K2TeO3, 95%) were dissolved in 50 ml of DI water and added to the first solution. Subsequently, 0.08 g of sodium borohydride (NaBH4, 99.99%) was added to the mixture and the reaction was allowed to stir for 5 min. The solution was transferred to a three-neck round flask and attached to a Liebig condenser and refluxed under atmospheric conditions, at a temperature of 100˚C. QD size is determined by the reflux time. The solution was then washed with acetone and redispersed in deionized water to obtain a clean colloidal solution. A high-resolution TEM micrograph of the synthesized QDs is shown in the inset of Figure 1(b). Since the QDs are capped with TGA, their surfaces contain negatively-charged carboxylate groups  . This makes CdTe QDs a suitable candidate for a layer-by-layer deposition employing positively and negatively charged polyelectrolytes, namely, Poly(diallyldimethylammonium chloride) and Poly(styrene sulfonate), respectively.
2.2. Quantum Dot Characterization
Quantum dot optical absorption characterization was performed employing an Ocean Optics Flame-S-UV-VIS spectrometer (Figure 1(a)). Bandgap energy and absorption are related by the following expression 
where α is the experimentally collected absorption, h is Planck’s constant, υ is the photon’s frequency, Eg is the quantum dot bandgap energy and A is a proportionality constant. The nominal value of r reflects the nature of the optical transition. For a direct allowed transition, r is set to be 2. The optical bandgap can then be estimated graphically employing a method described by Tauc  (Figure 1(b)). The extracted bandgap value of CdTe QDs was estimated to be 3.11 eV. Alternatively, after a mathematical manipulation, the above equation can be rewritten as 
According to the above equation, a plot of vs. should exhibit a discontinuity when . However, due to impurities and QD size inhomogeneity, the discontinuity could be replaced by a maximum. Figure 2 illustrates this method, from which a bandgap value of 3.18 eV was obtained, in reasonable agreement with the previously estimated value employing Tauc’s graphic method.
Additionally, QD size can be estimated using Brus’ quantum mechanical approximation 
where is the radius, is the relative permittivity of bulk CdTe, and are the respective electron and hole effective
Figure 1. (a) CdTe QDs optical absorption; (b) Tauc plot showing the estimated optical bandgap at 3.11 eV. The inset in (a) is an HR TEM of the QDs.
Figure 2. Plot of d(ln(αhν))/d(hν) vs. hν showing the bandgap value at the maximum position.
masses, e is the electron charge, and and are the QD and bulk bandgap values, respectively. Utilizing these parameters, the radius of the synthesized QDs was estimated to be 1.56 nm. Moreover, CdTe QDs size can also be approximated by the empirical equation 
where D is the diameter of the QDs and λ is the wavelength of the first excitonic absorption peak. As shown in Figure 1(a), the first excitonic absorption peak is located at a wavelength of 540 nm, indicating a diameter of 3.2 nm, in close agreement to the quantum mechanical approach. The confinement state of the generated electron-hole pairs can be determined by comparing the previous value to the Bohr radius corresponding to the first excitonic state which is given by the equation 
Since the calculated Bohr radius for the first excitonic state is 7.5 nm for CdTe, and, therefore, larger than the size of the synthesized QDs, it evinces the strong confinement state of electrons and holes .
In order to conduct THz measurements employing colloidal quantum dots, water must be exchanged as the host solvent, due to its extremely high absorption coefficient . A thiol exchange scheme was employed to make the QDs solvable on toluene, which has a much lower THZ absorption coefficient , . To this end, 1 ml of 1-dodecanethiol was added to 1 ml of a clean solution of CdTe QDs. Subsequently, 2 ml of acetone were added to the mixture followed by 2 minutes of vortexing. The solution was then heated to 60˚C until the organic phase was reduced to 1 ml. After the QDs had been transferred to the organic phase, they were diluted with toluene and precipitated with methanol. The product was decanted and diluted once more with toluene.
Quantum dot concentration was measured employing a quartz crystal microbalance (QCM) instrument. The technique is based on the resonance frequency shift of a piezoelectric crystal. The deposition of a liquid drop of colloidal QDs on top of an oscillating quartz crystal provokes a shift in its resonance frequency, which is related to the mass of the residual QDs film after the solvent was evaporated by the following equation 
where is the frequency shift and is the crystal sensitivity factor (56.6 Hz∙μg−1∙cm2). The concentration of CdTe QDs dissolved in toluene was measured by dropping 15 μl of solution on the crystal’s active area. After the solvent was evaporated, the residual mass was measured. This process was repeated 9 times and the results were linearly fitted to obtain the concentration in units of μg/μl (see Figure 3).
Quantum Dot Terahertz characterization was carried out by employing a THz time domain spectroscopy (THz-TDS) technique, operating in transmission mode. The system makes use of a photoconductive antenna to generate an ultrafast, broadband THz pulse when is activated by a femtosecond laser with a wavelength of 800 nm. A second photoconductive antenna is utilized as a detector. Once proper alignment was achieved, the system was thermalized for 2 hours. An ultraviolet lamp (365 nm, 20 mW/cm2) was employed to excite the sample.
The time domain Terahertz signal is transformed into the frequency domain by a Fast Fourier Transform to obtain the amplitude and phase change. Air and the empty cuvette were used as references to calculate the complex permittivity
Figure 3. Mass of the QDs film as a function of the volume dropped on top of the QCM crystal. The slope of the linear fit represents QD concentration
of toluene and colloidal quantum dots . Subsequently, linear effective medium theory was employed to obtain the permittivity of the Quantum dots through the relation 
where c is the volume fraction of colloidal QDs and is the permittivity of the host solvent, which, for CdTe QDs was toluene. Figure 4 shows the real and imaginary part of the permittivity of the QDs, after applying the aforementioned effective medium theory. Ostensibly, the real and imaginary parts of increase when the nanoparticles are excited by an ultraviolet source. This change is thought to be related to the large exciton polarizability of the QDs, due to their atom-like response, which is present in the strong confinement state .
2.3. Metamaterial Simulation
Finite Difference Time-Domain (FDTD) simulations were performed in order to elucidate the electromagnetic response of the metamaterial geometry. This technique solves Maxwell’s equations numerically in discretized time and space and the results are the electric and magnetic field distributions following the interaction of the source fields with the material distribution. The simulations were carried out employing a commercial solver (Lumerical Inc., ND). The dimensions of the simulated metamaterial unit cell are shown in Figure 5(a) employing a design reported elsewhere . The outer black hexagon represents the boundary of the unit cell and the red lines represent a Perfect Electric Conductor (PEC).
The metallic incursions are placed on top of a silicon slab with a refractive index of n = 3.42 + 0.01i . Periodical boundary conditions were set in the directions orthogonal to the electromagnetic source, and a Perfectly Matched Layer (PML) was set in the direction parallel to it. The electromagnetic source
Figure 4. Spectral dependence of the real and imaginary parts of the complex permittivity. The traces in blue correspond to the colloidal samples without UV excitation, while the traces in black correspond to the same samples under UV excitation with a wavelength of 365 nm.
Figure 5. (a) Diagram of the simulated unit cell; (b) Optical microscope image of the fabricated metamaterial.
was a plane wave with the electric field aligned orthogonal to the capacitor plates in the center of the unit cell. An optical image of the microfabricated metamaterial structure is shown in Figure 5(b).
Figure 6 shows the simulated and experimental transmission graphs featuring a resonance at 0.62 THz. The electric field distribution at the resonant frequency is illustrated in Figure 6(b). Ostensibly, the electric field is strongly confined within the capacitor area of the unit cell.
2.4. Metamaterial Fabrication
For Metamaterial fabrication a standard image reversal lift-off procedure was performed on a <100> high resistivity silicon substrate, with a nominal thickness of 400 μm. Silver was chosen as the material for the metallic array due to its relatively low-loss properties . To this end, thermal evaporation was employed to deposit a silver layer with a thickness of 100 nm on top of a 20 nm layer of
Figure 6. (a) Resonant frequency value from computational simulation and experimental observation; (b) Electric field distribution at 0.6 THz, featuring an electric field confinement at the capacitor area.
chromium that was included for adhesion purposes. Terahertz Time-Domain Spectroscopy (THz TDS) in transmission mode was employed to experimentally explore the resonant properties of the metamaterial. The measurements were performed at room temperature with a Menlo Systems TeraSmart K15 equipment. Five thousand waveforms were averaged for each sample, and the time domain waveforms were passed through a Gaussian window to remove the Fabry-Perot oscillations in order to obtain a cleaner signal . Subsequently, a Fast Fourier Transform (FFT) was applied to obtain the amplitude and phase of the transmitted beam as a function of frequency. In order to extract the effect of the metamaterial, we define the transmission as the ratio of the amplitude of the electric field through the metamaterial structure to the one through a blank, 400 um thick silicon wafer. Prior to deploying the synthesized QDs, the substrate with the metamaterial geometry was exposed to an O2 plasma (30 W for 10 minutes) to activate the surface, and two bilayers of alternating positively charged Poly(diallyldimethylammonium chloride) (PDDA) (1.5 wt%) and negatively charged Poly(styrene sulfonate) (PSS) (0.3 wt%) were spin coated at 2500 rpm for 2 min. Subsequently, CdTe QDs were then deployed on the metamaterial by employing a bilayer scheme (Figure 7)  in which a layer of PDDA was spin cast on the surface, followed by a layer of the aqueous solution of negatively charged CdTe QDs. This last alternating bilayer step was repeated 6, 10, 13 and 15 times to evaluate the performance as a function of the number of bilayers employed. The sample surface was rinsed with DI water and dried with a gentle stream of N2 after each individual spin coated layer. Profilometry measurements indicated that, on average, for every pair of PDDA + CdTe QDs layers, the thickness increased by approximately 10 nm.
Transmission modulation (TM) was measured employing an ultraviolet source with a wavelength of 365 nm, which corresponds to an energy of 3.4 eV, i.e., larger than the bandgap energy of CdTe QDs. The UV source was set to illuminate all samples with a different number of bilayers while varying the incident power density from 6 to 20 mW/cm2. At the resonant frequency of 0.62 THz, the TM was observed to increase with all incident power density increases (Figure 8(a)). This is thought to be due to the susceptibility of the photoexcited QDs dependence on the excitation density. That is, the number of incident photons per unit area has an impact on the polarizability of the excitons confined in the QDs .
In terms of the number of bilayers employed, the TM value increased as the number of bilayers increased from 6 to 10 and decreased for subsequent increases in the number of bilayers, i.e., 13 and 15 bilayers. Specifically, for 6 bilayers, the modulation increased from 0.2% to 1.3%, the modulation observed
Figure 7. Process flow illustrating the layer-by-layer method described herein.
Figure 8. (a) Modulation as a function of frequency for the metamaterial with 10 bilayers; (b) Modulation at 0.62 THz for the highest power density as a function of number of layers.
with 10 bilayers increased from 1.84% to 2.68%, and with 13 bilayers, the modulation increased from 1.2% to 1.6%. Lastly, for 15 bilayers, the modulation increased from 0.13% to 0.48%, being the smallest modulation attained. Quenching and shadowing effects are thought to be responsible for the observed decrease in transmission modulation depth when employing 13 or more bilayers which is presented in Figure 8(b).
Colloidal CdTe QDs were chemically synthesized and utilized as a reconfigurable element in a previously fabricated metamaterial structure that exhibited a resonance frequency at 0.62 THz. Modulation due to an ultraviolet source with different power densities and different numbers of polyelectrolyte bilayers were probed. The experimental data revealed that the modulation is largest when 10 layers of QDs + PDDA are deployed and the maximum modulation achieved was 2.68%, with a power density reaching 20 mW/cm2. Furthermore, the proximity to a linear relation suggests that a larger modulation can be achieved at higher power densities. Additionally, the entire process is mass production compatible and can be integrated with other electronic circuitry microfabrication processes, making it attractive for a variety of technological applications
This work was supported by the Air Force Office of Scientific Research (AFOSR) Grant number FA9550-17RYCOR490.
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