Tunable beam deflection based on plasmonic resonators mounted freestanding thermoresponsive hydrogel

Ata Ur Rahman Khalid; Juan Liu; Naeem Ullah; Shiqi Jia

doi:10.3788/COL202018.062402

Abstract

We propose and numerically demonstrate a dynamic beam deflector based on plasmonic resonator loaded thermoresponsive freestanding hydrogel that swells and collapses in water by temperature. For this purpose, we utilize four-step phase gradients mounted on freestanding hydrated hydrogel. For normal incidence, linearly orthogonal light deflects to 19.44° in the collapsed state and 14.40° in the swollen state of hydrogel. Furthermore, the light deflects at a third angle of 12.29° when the solvent changes from water to ethanol. It is expected that our metadesign will provide a platform for dynamic holography, active lensing, data storage, and anticounterfeiting.

Keywords

beam deflector hydrogel tuning

Metasurfaces, artificially engineered structures, have received tremendous attention because of their unique feature to control electromagnetic (EM) waves. The geometric control of structures results in fascinating phenomena that barely exist in nature such as negative refraction, cloaking, the Doppler effect, and optical focusing^[1–5]. By taking control over the propagation of EM waves, metasurfaces are widely being studied in flat lensing, vortex beam generation, and holograms^[6–11].

Metasurfaces can produce various profiles for outgoing electromagnetic waves. Thus, arbitrary wavefronts can be obtained by simply arranging the meta-atoms. A beam deflector is an important optical component used in steering the light in a specific direction^[12]. Nanostructures are playing a vital role in manipulating outgoing wavefronts and providing new avenues to develop various nano-optics devices. Till now, several approaches have been reported for beam steering by using subwavelength structures such as gratings^[13], metallic slits^[14], slits filled with nonlinear materials^[15], and plasmonic and dielectric metasurfaces^[12,16,17]. However, active steering of light by using metasurfaces is highly desired in practical applications. Among the studies concerning active steering there is some research to actively control the light path by temperature stimulation^[18–22], external strain^[23], and electrical gating^[24,25]. The studies based on phase change material either use separate types of meta-atom that are dominantly reactive or less reactive based on temperature variation degrading the signal to noise ratio, or use complex structures that are difficult to fabricate. Furthermore, an electrical gating restricts the deflection angle range, and external strain structures might not be quite feasible to integrate with practical applications. Here, we are the first time to use functional hydrogel that swells and collapses by temperature stimulation in water instead of external strain.

Hydrogel, poly(N-isopropylacrylamide-based) (pNIPAAM) membrane, extensively swells and collapses vertically (surface-attached hydrogel) or horizontally (freestanding hydrogel) inside water by temperature stimulation. In an aqueous solution, such a hydrophilic polymeric network absorbs a considerable amount of water and attains the equilibrium swelling state below the local critical solution temperature (LCST). The increase of temperature from the LCST oozes the water and results in the collapse of the polymeric network^[26,27]. The swelling and collapse occur with a characteristic response time below 100 ms and are fully reversible up to several hundreds of cycles^[28]. Previously, it has been studied for actively tunable collective surface plasmons^[29], active control of surface plasmon resonance for biosensor applications^[28], and dynamic holography^[30]. Due to the swelling and collapsing feature, metasurface integrated hydrogel has great potential to manipulate wavefronts. The phase discontinuity can be tuned by changing the scattering element, shape, orientation, and position of each element. Among these tuning mechanisms, the relative position of meta-atoms can be changed by using resonator loaded freestanding hydrogel. The freestanding hydrogel swells and collapses in water and provides additional swelling in ethanol. The swelling in ethanol is not reversible by temperature. However, changing the solvent to water, the hydrogel regains its reversible switching^[29]. Here, we demonstrate that by mounting the resonators on freestanding hydrogel, the outgoing wavefront can be tuned at three different angles via temperature modulation and solvent. We believe that our approach can find applications in active photonic fields such as fiber-optics telecommunication, scanning systems, and integrated optical devices.

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Figure 1 illustrates the schematic of the proposed tunable beam deflector. We periodically arrange the resonators on freestanding hydrogel, which swells and collapses in water by temperature. Due to the swelling and collapsing of hydrogel, the linearly orthogonal transmitted light deflects between $θ_{1}$ and $θ_{2}$ by temperature modulation [Figs. 1(a) and 1(b)]. The outgoing light further deflects at $θ_{3}$ due to further swelling in ethanol [Fig. 1(c)]. The light deflection follows the generalized Snell’s law^[31]: $n_{t} \sin θ_{t} - n_{i} \sin θ_{i} = \frac{λ_{o}}{2 π} \frac{d Φ}{d x},$ (1)where $n_{i}$ and $n_{t}$ are the indices of refraction in the incidence and refraction medium, respectively. $θ_{i}$ and $θ_{t}$ are the incidence and refraction angles, respectively, $λ_{o}$ in the freespace wavelength, $d Φ$ is the phase difference between the successive unit cells, and $d x$ is the period of a unit cell. For the normal incidence $θ_{i} = 0$ with hydrogel as the refraction medium, the anomalous refraction angle can be obtained by $| θ_{t} | = \arcsin (λ_{o} / n_{t} Λ)$ , where $Λ$ is the size of the supercell in the x direction. The refraction angle $| θ_{t} |$ can be tuned by $Λ$ , which is in an inverse proportional relationship with $Λ$ . Thus, the refraction angle decreases with the increase in size of the supercell and vice versa.

Our metadesign consists of periodically arranged resonators sitting on the top surface of freestanding hydrogel dipped in a solvent inside the glass container, as depicted in Fig. 2(a). The dotted rectangle is representing a supercell with period of $Λ$ in the x direction. Figures 2(b) and 2(c) represent the supercell and its top view, respectively. The building block of the metasurface consists of circular sectors/segments on the top of the thermoresponsive hydrogel, as shown in the rightmost cell of Fig. 2(b). The 2D illustration of the unit cell is presented in Fig. 2(c), the rightmost cell. The antennas on the top of the hydrogel are called sector resonators throughout this Letter. By varying the first opening of sector $α$ (angle w.r.t. the x axis in the conterclockwise direction), the second opening of sector resonator $β$ (angle w.r.t. $α$ in the counterclockwise direction), and radius R, the amplitude and phase of scattered light can locally be modulated. In this study, we choose freestanding hydrogel that swells and collapses in lateral directions in water. When it interacts with water below LCST, i.e., $32 ° C$ , then it swells and collapses back after the LCST. The hydrogel further expands when it interacts with ethanol. It exhibits a nonthermoresponsive property in ethanol. We take the refractive index of freestanding hydrogel in water as follows: in a swollen state $n_{s} = 1.34$ and in a collapsed state $n_{c} = 1.46$ , while the surrounding water has a refractive index $n_{w} = 1.334$ . In ethanol, the refractive index in the swelling state $n_{s} = 1.37$ , while the surrounding ethanol refractive index $n_{e} = 1.36$ . These indices are taken from Ref. [29]. The operating wavelength is 700 nm.

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To demonstrate the proposed tunable beam deflector, we introduce phase gradients on the surface of hydrogel. We arrange selected four phase gradients $d Φ / d x$ on freestanding hydrogel such that corresponding phases gradually cover a $2 π$ phase distribution with a step of $π / 2$ [Figs. 2(b) and 2(c)], which forms the supercell. This arrangement causes incoming light to deflect in a specific direction according to the generalized Snell’s law as calculated by $θ_{1} = | θ_{t} | = \arcsin (\frac{λ_{o}}{n_{t} Λ_{1}}) = \arcsin (\frac{700 nm}{1.46 \times 1440 nm}) = 19.44 °,$ (2) $θ_{2} = | θ_{t} | = \arcsin (\frac{λ_{o}}{n_{t} Λ_{2}}) = \arcsin (\frac{700 nm}{1.34 \times 2100 nm}) = 14.40 °,$ (3) $θ_{3} = | θ_{t} | = \arcsin (\frac{λ_{o}}{n_{t} Λ_{3}}) = \arcsin (\frac{700 nm}{1.37 \times 2400 nm}) = 12.29 ° .$ (4)

Equations (2)–(4) depict the analytical computed angles for hydrogels collapsed in water, swollen in water, and swollen in ethanol, respectively. When the hydrated hydrogel is in a collapsed state, i.e., $I_{x} = I_{y} = 0$ , then the size of the supercell in the x direction becomes $Λ = Λ_{1} = 4 \times (P_{x} + I_{x}) = 1440 nm$ . For normal incidence, outgoing light deflects at an angle of $θ_{1} = 19.44 °$ in hydrogel. When the solvent temperature is less than the critical solution temperature, the hydrogel swells in both the x and y directions, and thus the size of the supercell in the x direction becomes $Λ = Λ_{2} = 4 \times (P_{x} + I_{x}) = 2100 nm$ , where $I_{x} = I_{y} = 165 nm$ . Thus, under swelling conditions, the light deflects at $θ_{2} = 14.40 °$ . The light further deflects to $θ_{3} = 12.29 °$ by changing the solvent from water to ethanol. This is due to the fact that ethanol serves as a better solvent than water. In ethanol, the period of the unit cell prolonged with the increment of $P_{x} = P_{y} = 240 nm$ in both the x and y directions. Thus, the size of the supercell in the x direction becomes $Λ = Λ_{3} = 4 \times (P_{x} + I_{x}) = 2400 nm$ in ethanol. These analytically computed angles are in accordance with simulated ones at the linearly orthogonal outgoing light when the linearly y polarized light impinges, and the sector loaded hydrogel is dipped in different solvents and stimulated with temperature. Figures 4(a)–4(c) show the phase distribution inside the hydrogel for the outgoing light under swelling and collapsing in water and swelling in ethanol, respectively. The light further deflects at 19.52°, 13.24°, and 11.56° under swelling and collapsing in water and swelling in ethanol, respectively, inside the glass due to mismatch of refractive indices of hydrogel and glass, as shown in Figs. 4(d)–4(f).

$Numerical simulation results. (a)–(c) are the phase distributions of the wavefront inside the hydrogel in a collapsed state in water, swollen in water, and swollen in ethanol, respectively. (d)–(f) are the phase distributions of the wavefront inside the glass in a collapsed state in water, swollen in water, and swollen in ethanol, respectively. θt is the refraction angle in the xy plane for the linearly y-polarized input light and the linearly x-polarized light is calculated at output.$

Figure 4.Numerical simulation results. (a)–(c) are the phase distributions of the wavefront inside the hydrogel in a collapsed state in water, swollen in water, and swollen in ethanol, respectively. (d)–(f) are the phase distributions of the wavefront inside the glass in a collapsed state in water, swollen in water, and swollen in ethanol, respectively. $θ_{t}$ is the refraction angle in the xy plane for the linearly y-polarized input light and the linearly x-polarized light is calculated at output.

The angle deflection in water is dynamic, which exhibits deflection angle switching due to the swelling and collapsing of hydrogel through temperature modulation. In ethanol, hydrogel does not exhibit active deflection by changing the temperature. However, by changing the solvent to water, hydrogel again functions actively by temperature modulation. In the case of reversing the incident polarization to x polarized light, the phase gradients must have to be arranged along the y axis to observe the linearly orthogonal beam deflection. The overall absorption of our water-dipped plasmonic metadesign is high, and thus only a limited amount of energy will be transmitted, i.e., 2%. Furthermore, our proposed design can be fabricated by using the approach reported in Ref. [29]. The fabrication steps are as follows: pattern the sector resonator supercell arrays on glass substrate via state of the art electron beam lithography technique, then attach the pNIPAAM layer by in situ synthesizing via UV light irradiation, and detach the patterned hydrogel from the glass substrate by swelling in ethanol in order to form a freestanding membrane.

In conclusion, we have numerically demonstrated the dynamic deflection of the wavefront by using plasmonic resonator loaded freestanding thermoresponsive hydrogel. By arranging the sector resonators on hydrogel, we observe anomalous refraction. When the solution temperature is greater than the LCST, i.e., collapsed state, the outgoing linearly orthogonal light deflects at 19.46° in hydrated hydrogel from the normal. Similarly, the deflection angle tunes from 19.46° to 14.40° due to the increase in period when the hydrated hydrogel is in the swollen state. This tunability is reversible in water via temperature modulation. Furthermore, the outgoing light further deflects to 12.29° due to better swelling in ethanol. The deflection in ethanol is not reversible by temperature. However, the hydrogel will function actively again when the solvent changes back to water. It is predicted that such active meta devices may serve as a novel platform for active switching, active lensing, anticounterfeiting, and several other flat optical devices in optical fiber-optics communication and scanning systems that demand highly compact light path deflection and fast switching.

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