Dual-channel sensing by combining geometric and dynamic phases with an ultrathin metasurface

Qilong Tan; Qilong Tan; Hongchao Liu; Hongchao Liu; Shuang Zhang

doi:10.1364/OE.395364

1. Introduction

Metasurfaces consisting of monolayer ultrathin plasmonic or dielectric resonators have been designed to exhibit exotic electromagnetic properties and functionalities, which significantly enhanced the control of the propagation of electromagnetic (EM) waves. By spatially varying the structure of the unit cells across the surface, both transmitted and reflected EM wavefront can be elaborately manipulated with desired features. There have been in general two approaches for the wavefront control: one based on dynamic phases, and the other one on geometric phase. The dynamic phase can be generated through either structural resonance in thin plasmonic structures or the propagation phase of guided mode supported by high aspect ratio dielectric rods. Dynamic phases are usually highly dispersive. Independent and arbitrary phase profiles can be engineered for the two orthogonal linear polarizations [1–4]. On the other hand, the geometric (or Pancharatnam-Berry) phase is controlled by spatially rotating the subwavelength resonators with anisotropic electromagnetic responses. The geometric metasurfaces are capable of imparting dispersionless and spin-dependent phase profiles for the two circular polarizations, and generating spin-multiplexed optical functionalities, such as anomalous refraction [5–7], unidirectional excitation of surface plasmon polariton [8,9], tunable orbital angular momentum [10–12] and helicity multiplexed holograms [13–15]. However, the two phase profiles for different incident spin states are conjugated to each other, meaning that the spin dependent functionalities are correlated to each other.

Because the localized surface plasmon (LSP) is highly sensitive to the change in refractive index [16], resonant plasmonic metasurfaces have shown great potential for achieving highly sensitive sensing applications, in a similar way as the widely employed surface plasmon resonance (SPR) technique [17]. By engineering individual plasmonic resonators and their spatial arrangements, resonant EM spectra can be readily tuned by the change in the refractive index of the surrounding environment. Such resonant properties have been continuously attracting enormous interest. However, their practical implementations are still limited, especially in optical frequencies, owing to the unavoidable intrinsic losses in plasmonic systems due to ohmic dissipation and radiation. The quality (Q) factors of resonances are hence quite low, putting a severe constraint on the signal-to-noise ratio (SNR). In other words, while the resonance peaks of plasmonic structures could sensitively shift with the changes in the refractive index of the external environment, their generally broad linewidths pose challenge to probe and distinguish in practical implementations. Apparently, overcoming the losses or improving Q factors of plasmonic resonances would greatly enhance the performance of resonant sensing with approaches including use of dielectric materials [18,19], Fabry-Perot (F-P) resonance [20,21], plasmon induced transparency (EIT) [22–24], plasmonic perfect absorbers [25,26] and optimizing the artificially designed structures. However, these sensing schemes usually involve some expensive instruments, such as spectrometers with high resolution, stable broadband sources or supercontinuum light sources. Moreover, other factors, such as temperature fluctuation, mechanical vibrations, and intensity random noise, will significantly affect the sensing performance.

In this work, we propose a new sensing method by combining geometric phase, which is spin-dependent, and resonance-induced dynamic phase in an ultrathin hybrid metasurface grating (HYMG). Our work is different from some previous works wherein only polarization state of anomalous diffraction can be regulated [27,28]. By accurately controlling the orientations or resonant features of gold antennas, the phase profiles of different spin components can vary dynamically and independently with the change in external environment. As shown in Fig. 1, the metasurface consists of two sets of gold nanorods with different geometries, rectangular and ‘I’ shape. The A and B sub-units, consisting only of the rectangular and I-shaped nanorods, respectively, are arranged interdigitally along y direction. Each sub-unit contains four gold nanorods with a π/4 step in the angle difference between two neighboring nanorods along x-axis, corresponding to a relative geometric phase of π/2. The rotation directions of four nanorods in A and B are the same, but with a relative offset of one lattice constant along x direction. For a linearly polarized light with polarization along x direction normally incident onto the metasurface, the anomalous right circularly polarized light (RCP) and left circularly polarized light (LCP) are diffracted to ± 1 orders, respectively. Due to the interplay between the different shapes of the antennas in the two sub-units and their offset in x direction, the intensities of ± 1 orders diffracted by the HYMG exhibit opposite variations with the change in external environment. The simulation shows the responsivities of the two channels (±1 diffraction orders) respectively reaches 28.1 dB/RIU (refractive index unit) and −25.5 dB/RIU for the sensing of liquid refractive index. The responsivity can be further increased by improving the Q factor of the “meta-atoms” mentioned above.

Fig. 1. (a) Excitation of dipole moment when illuminating one nanorod with the orientation angle $\varphi$ along the x-axis. (b) The geometric phase variation with the orientation angle $\varphi$ for LCP and RCP components. The resonance wavelength (c) and corresponding dynamic phase (d) of the polarized field with the refractive index n variation for a general case. (e) The coherent superposition of different spin components diffracted by the two sub-units consisting of different antenna geometries. (f) The top view of the gold nano antennas and configuration of the structures.

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2. Theoretical analysis

To understand the underlying mechanism of the designed metasurfaces, we start with the description of a single metallic nanorod with orientation angle $\varphi$ shown in Fig. 1(a). The antenna can be modeled as an electric dipole due to its deep subwavelength size. Its resonant properties depend on both the surrounding refractive index and the structural parameters. When an x-polarized light is normally incident onto the nanorod, an LSP resonance is excited. The induced electric dipole moment of each nanorod is expressed as:

(1)$$\begin{aligned}\vec{\textbf{p}} &= p({\omega ,n} ){e^{i\psi ({\omega ,n} )}}\left[ {\begin{array}{cc} {{{\cos }^2}\varphi }&{\sin \varphi \cos \varphi }\\ {\sin \varphi \cos \varphi }&{{{\sin }^2}\varphi } \end{array}} \right]\left[ {\begin{array}{c} 1\\ 0 \end{array}} \right]{e^{i\omega t}} \\ &=\frac{1}{4}p({\omega ,n} ){e^{i\psi ({\omega ,n} )}}\left( {2\left[ {\begin{array}{c} 1\\ 0 \end{array}} \right] + {e^{ - i2\varphi }}\left[ {\begin{array}{c} 1\\ i \end{array}} \right] + {e^{i2\varphi }}\left[ {\begin{array}{c} 1\\ { - i} \end{array}} \right]} \right){e^{i\omega t}}, \end{aligned}$$

where ω is the angular frequency; n is the refractive index of the surrounding environment; p(ω,n) and $\psi$(ω,n) are the dispersive magnitude and phase of the electric polarizability at a given refractive index n of the surrounding medium, respectively; [1, i] and [1, -i] refer to the left circular polarization (LCP) and right circular polarization (RCP), respectively. Therefore, there are three components in the radiation field of the dipole. The two spin polarized components carry both resonance-dependent dynamic phase ($\psi$(ω,n)) and spin-dependent geometric phase ($2 \sigma \varphi$), where σ = ±1 correspond to RCP and LCP states, respectively. By linearly varying the orientation angle $\varphi$ of nanorod along x direction shown in Fig. 1(b), opposite geometric phase gradient can be formed for the two orthogonal spin components. Figure 1(c) and (d) respectively indicate the shifts of resonance wavelength and the corresponding change in the dynamic phase $\psi$(ω,n) for each metallic nanorod with the refractive index n. Importantly, the phases of the two spin components ($\psi (\omega, n)-2 \sigma \varphi$) can be independently engineered by changing the refractive index n, the resonance properties of nano antennas, and the orientation angle $\varphi$.

By arranging different kinds of nanorod structures in an array with a constant gradient of the orientation angle $\varphi = \pi/4$ along the x-axis as shown in Fig. 1(e), spatially varying geometric phase introduces photonic spin Hall shift in the momentum space, leading to different diffraction angle for the different spin components. As illustrated by Fig. 1(f), each unit cell of the periodic array is constructed by two kinds of nanorod structures with a rotation angle $\theta$ between them. By selecting appropriate structural parameters for the periodic array and nanorod structures, diffraction of the grating only appears in x direction. The 1^st order diffraction fields E_±1 consist of coherent superposition of the different spin components diffracted by the two sub-units consisting of different antenna geometries, which can be expressed as follows:

(2)$${E_{ - 1}} = LC{P_A} + LC{P_B} \propto {p_A}({{\omega_0},n} ){e^{i{\psi _A}(n)}}\left[ {\begin{array}{c} 1\\ i \end{array}} \right] + {p_B}({{\omega_0},n} ){e^{i[{{\psi_B}(n) - 2\theta } ]}}\left[ {\begin{array}{c} 1\\ i \end{array}} \right],$$

(3)$${E_{ + 1}} = RC{P_A} + RC{P_B} \propto {p_A}({{\omega_0},n} ){e^{i{\psi _A}(n)}}\left[ {\begin{array}{c} 1\\ { - i} \end{array}} \right] + {p_B}({{\omega_0},n} ){e^{i[{{\psi_B}(n) + 2\theta } ]}}\left[ {\begin{array}{c} 1\\ { - i} \end{array}} \right],$$

where ω₀ is the angular frequency of the incident wave; the sub-indices A and B refer to the two different types of nanorods, respectively. Interestingly, the phase differences of radiation fields between A and B sub-units for E_±1 are $\psi$_B(n)-$\psi$_A(n) ± 2$\theta$, respectively. As the resonant properties are associated with the structural parameters of nano-antenna, $\psi$_B(n)-$\psi$_A(n) can be engineered to vary with the refractive index n, providing the same dynamic phase difference both in ± 1 diffraction orders. Moreover, the phase difference ± 2$\theta$ can be accurately controlled by rotation angle $\theta$, providing the opposite and dispersionless geometric phase difference for ± 1 diffraction orders. Assuming that the two types of dipoles have very close electric polarizability (|p_A-p_B|<<p_A) and that the phase difference between A and B monotonically increases with the refractive index n (d[$\psi$_B(n)-$\psi$_A(n)]/dn>0), the intensities of ± 1 diffraction orders can change independently with the refractive index n.

Assuming that the dispersive magnitude p(ω,n) is a constant, the normalized intensities of first order diffractions versus the dynamic phase $\psi$_B(n)-$\psi$_A(n) can be shown in Fig. 2. When the rotation angle $\theta$ = 0, the phase differences of radiation fields between A and B are only modulated by the dynamic phases. Thus, intensities of ± 1 diffraction orders exhibit the same trend with refractive index, as shown in Fig. 2(a). In addition, different intensity variation between ± 1 diffraction orders can be realized by combining the geometric and dynamic phases, as shown in Fig. 2(b-d). This distinctive phenomenon can be used for dual-channel sensing.

Fig. 2. Normalized intensities of first order diffractions depend on the dynamic phase $\psi$_B(n)-$\psi$_A(n) with the rotating angle (a) $\theta$ = 0, (b) $\theta = \pi/8$, (c) $\theta = \pi/4$, (d) $\theta = 3\pi/8$.

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3. Sensing performance of the HYMG

We numerically investigate the performance of dual-channel refractive index sensing for liquid by means of finite-difference time-domain (FDTD) method. Here, dual-channel detection of reflection is adopted. The condition of liquid refractive index sensing is calculated with the following parameters: L₁ = 330 nm, L₂ = 360 nm, w = 160 nm, d₁= d₂ = 80 nm and $\varphi = \pi/4$, operating at the communication wavelength λ = 1.55 µm. The lattice constant of the antennas is 450 nm, forming a periodic supercell with lattice constant of 1.8 µm × 0.9 µm, as shown in Fig. 3(b). The thicknesses of the two types of antennas are both h = 50 nm, which is much less than the incident wavelength. Moreover, as the periodicity along y direction is less than the wavelength of light, such that the diffraction of the reflected fields only occur along the x direction. The corresponding diffraction angles of ± 1 orders are about ± 59.4^° in free space, respectively. An x-polarized beam with normalized intensity is applied to incident from the silica substrate.

Fig. 3. (a) The diagram of refractive index sensing for liquid. (b) The structural parameters of the HYMG. The FDTD simulated polarizations of −1 (c) and + 1 (d) diffraction orders when $\theta = \pi/4$. The light intensities of first diffraction orders with the change in the refractive index of the surrounding liquid for $\theta$ = 0 (e) and $\theta = \pi/4$ (f). (g) The parameter S with the variation of n.

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Owing to the precise phase control and strong spin-orbit coupling of the HYMG, the ± 1 diffraction orders are formed by different spin components. When the rotation angle $\theta$ = 0, the simulation shows that the intensities of ± 1 order diffracted waves barely change with the liquid refractive index, as shown in Fig. 3(e). Because the phase differences of radiation fields between A and B are only modulated by the dynamic phases, the diffractions of metasurface exhibit a similar response with conventional periodic gratings. When the rotation angle $\theta = \pi/4$, the geometric phase and dynamic phase both affect the diffracted fields. Figure 3(c) and (d) respectively show the calculated polarization states of first diffraction fields, wherein the arrows indicate the handedness of the circular polarization, the colors represent different refractive indices of the surrounding liquid. The simulation shows that the ± 1 diffraction orders are mainly composed by RCP and LCP components, respectively. Importantly, their intensities show opposite trends with the change in liquid refractive index n, as shown in Fig. 3(f). The intensities I_±1 of two channels respectively change by 5.6 dB and −5.1 dB when the liquid refractive index varies from 1.3 to 1.5. The sensing range covers most of aqueous solutions and parts of organic liquids. Thus, the responsivities of two channels reach 28.1 dB/RIU and −25.5 dB/RIU, respectively.

Usually the performance of sensing is affected by the noise in practical applications, such as that originating from external vibrations, temperature fluctuations, measurement errors, and instabilities of laser. It is difficult to effectively suppress noises with compact dimensions and low costs. For our sensing scheme, as the noises of two channels are caused by the same external factors mentioned above, the SNR can be further enhanced utilizing a dual-channel measurement. Here we adopt a parameter S to characterize the sensing performance, which is expressed as:

(4)$$S = \frac{{{I_{ + 1}} - {I_{ - 1}}}}{{{I_{ - 1}} + {I_{ + 1}}}},$$

where I₋₁ and I₊₁ represent the intensities of the −1 and + 1 orders, respectively. Figure 3(g) shows the variation of S with the changes of refractive index n. By compared with a conventional gradient grating (when the rotation angle $\theta$ = 0), the sensing performance is significantly enhanced. The corresponding responsivity defined as $\eta = \textrm{d}S/\textrm{d}n$ is 267.2% RIU⁻¹, which is higher than the famous Fresnel-reflection based dual-channel sensing (115.1% RIU⁻¹) [29,30].

Benefitting from the enormous local enhancement of LSPs evanescent field, the resonance properties of nano antenna are sensitive to the variation of media near metal surface, such as the change of refractive index due to biomolecular interactions that occur in analyte layers. Thus, metasurfaces are promising for sensitive and label-free detection of biochemical assays, with potential applications in various chemical and biological sensing technologies. As shown in Fig. 4(a), an ultrathin film of 10 nm thick coated on the HYMG in solution is adopted as an example to investigate the sensing performance for detection of biomolecules. The coated HYMG has identical scheme with Fig. 3(b). The refractive index of water is 1.31 at the communication wavelength. The simulated results shown in Fig. 4(b) indicate that the intensities I_±1 of two channels respectively change by 6.3 dB and −3.3 dB when the refractive index of the thin film increases from 1.3 to 2.3. Figure 4(c) shows the variation of S with the refractive index n, which varies from −0.46 to −0.01. The corresponding responsivity is 45% RIU⁻¹. By engineering individual antennas and their arrangements, the operating wavelength of HYMG can be adjusted to accommodate various biosensing applications, such as the biomolecular binding or dissociation. Compared with spectrum detection, dual-channel detection depresses the influence arising from the absorption and the resonance of the biomolecules.

Fig. 4. (a) The diagram of sensing for ultrathin layer. The light intensities of first diffraction orders (b) and the parameter S (c) with refractive index n of the ultrathin layer.

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4. Conclusion

In conclusion, we propose a dual-channel sensing method by incorporating geometric phase and resonance-induced dynamic phase utilizing an HYMG. By assembling two different types of nano gold antennas along the interface, the phase profiles of diffraction field vary dynamically and independently with external environment. The simulated results show that the intensities of ± 1 orders diffracted by the HYMG exhibits opposite variation tendency with the external environment including liquid refractive index and monomolecular layer. The dual-channel sensing [27,31] strategy improves the sensing performance of the optical system. Importantly, it only requires a mono-wavelength laser and a number of simple optical devices to carry out intensity detection, which are cost effective and compact. Furthermore, as the individual antennas and their arrangements can be engineered flexibly and arbitrarily, abundant physical mechanisms can be introduced to further improve the performance of sensing, such as EIT, symmetry breaking and asymmetric Fano resonance. These features enable HYMG to have potential applications in biosensing, precision manufacturing, monitoring of environment, optical regulations and nonlinear interactions [32,33].

Funding

Start-up Research Grant of University of Macau (SRG2019-00174-IAPME); South China Normal University Young Teachers Research and Cultivation Foundation (300014); China Postdoctoral Science Foundation (2018M643108); Horizon 2020 Framework Programme (648783, 734578).

Disclosures

The authors declare no conflicts of interest.

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Dual-channel sensing by combining geometric and dynamic phases with an ultrathin metasurface

Abstract

1. Introduction

2. Theoretical analysis

3. Sensing performance of the HYMG

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (4)

Equations (4)

Optics Express