Mechanisms of Fano-resonant biosensing: Mechanical loading of plasmonic oscillators

Optics Communications 469 (2020) 125780

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Mechanisms of Fano-resonant biosensing: Mechanical loading of plasmonic oscillators Xiangchao Zhu a , Ning Cao b , Brian J. Thibeault b , Benjamin Pinsky c , Ahmet Ali Yanik a ,∗ a

Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA c Department of Medicine, Stanford University School of Medicine, Palo Alto, CA 94305, USA b

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Keywords: Biosensing Label-free detection Fano resonances Plasmonics Extraordinary light transmission Plasmonic nanoholes

ABSTRACT Distinctively narrow and asymmetric line shape Fano resonances arise due to resonant interactions of sub-radiant and super-radiant modes in plasmonic nanostructures and metamaterials. A number of recent experimental studies have shown unique opportunities provided by highly dispersive Fano resonances in biosensing applications. However, there is limited understanding of Fano resonant optical response to biomolecular accumulation. Here, we introduce a phenomenological model that can precisely describe the intricate nature of the Fano resonances in plasmonic nanohole arrays and provide unambiguous physical insights into biosensing experiments. Using rigorous electromagnetic simulations and experimental measurements as benchmarking tools, we show that the non-trivial contribution of molecular accumulation to Fano resonant plasmonic response can be incorporated as a mechanical loading effect in a coupled-oscillator model. Quite remarkably, our phenomenological approach captures the complex spectral response of the Fano resonance profile and asymmetric linewidth broadening upon molecular accumulation. Furthermore, in strong agreement with our experimental measurements, we show that our parameterized model has predictive power in fine tuning the Fano resonant extraordinary light transmission lineshape using structural design parameters without resorting to electromagnetic simulations. Our phenomenological model provides a general analytical method that can be adapted to understand biomolecular detection measurements in different plasmonic and metamaterial systems.

1. Introduction Fano resonant plasmonic nanostructures and metamaterials, offering exciting opportunities for biomolecular detection purposes, has recently attracted significant attention of the scientific community [1– 14]. In plasmonic systems, distinctly asymmetric Fano resonances emerge from the interference of narrow-band dark (sub-radiant) and broad-band bright (super-radiant) modes [15–24]. An abrupt reversal of the interference condition from a constructive to destructive nature within a narrow spectral window leads to the spectrally sharp transmission–reflection characteristics in these systems [3,25–27]. This is an attractive feature that can be exploited in realization of ultrasensitive biosensors [2,4,19,28–33]. In particular, plasmonic nanohole arrays (NHAs) exhibiting extraordinary optical transmission (EOT) spectra with Fano resonance lineshape offer some unique opportunities for biosensing applications [4,11,31,34–38]. Most recently, researchers have succeeded in employing these nanostructures for labelfree naked-eye detection of protein monolayers [4]. However, while the asymmetric EOT resonances can be precisely captured using Fano formula [4,39–41], a parameterized understanding of the underlying

mechanisms behind the Fano resonant behavior is still lacking. An intuitive and parameterized model capturing the microscopic origins of Fano resonances in NHAs and their spectral response to the surrounding dielectric medium is still needed. Development of an analytical model can help effective utilization of Fano resonances in equipment-free biosensing applications. Furthermore, Fano resonances in NHAs emerge from the transmission peak-dip pairs, each showing strong dependence to the dielectric environment with varying strengths. Hence, questions arise regarding how EOT spectra evolve with molecular accumulation on NHA surfaces and what is the dynamic range within which one can exploit the EOT signal in biosensing applications without degrading its distinctly advantageous Fano resonance lineshape. In this paper, we introduce an intuitive and quantitative model elucidating the microscopic origins of the Fano resonant EOT effect and shedding light into our experimental observations in biomolecular diagnostics measurements [4,42]. Our coupled-oscillator model consists of mechanical analogues of the three plasmonic excitations responsible for EOT effect: the surface plasmon polariton (SPP) modes on the in-coupling (SPPin ) and out-coupling (SPPout ) surfaces, and localized

∗ Corresponding author. E-mail address: [email protected] (A.A. Yanik).

https://doi.org/10.1016/j.optcom.2020.125780 Received 25 November 2019; Received in revised form 15 March 2020; Accepted 16 March 2020 Available online 20 March 2020 0030-4018/© 2020 Elsevier B.V. All rights reserved.

X. Zhu, N. Cao, B.J. Thibeault et al.

Optics Communications 469 (2020) 125780

of 10 nm (7.4 nm) is obtained for an adsorbed protein layer with a surface mass density of 8.4 ng/mm2 (see Methods) in agreement with our experimental measurements (Fig. 1b). In the following sections, experimental measurements and FDTD calculations will be used as benchmarking tools for our coupled-oscillator model that elucidates the microscopic origins of the Fano resonances in NHAs and the non-trivial impact of molecular accumulation processes.

surface plasmon (LSP) modes at the rims of the nanoholes [43–45]. Our phenomenological model offers a parameterized understanding in tailoring Fano resonance spectral behavior using structural parameters of the nanoholes in excellent agreement with our experimental measurements. It inherently captures the NHA spectral response and tuning of Fano resonant behavior upon accumulation of proteins on surfaces. In our analysis, molecular accumulations within the dramatically enhanced field regions (hot spots) are incorporated as mechanical loading of the corresponding plasmonic oscillators, leading to modulations in the coupled-oscillator resonances of the NHA system. Our model provides an intuitive and quantitative description that is in excellent agreement with the analytical Fano formula, finite difference time domain (FDTD) calculations and our experimental measurements. Furthermore, we demonstrate that biomolecular accumulation leads to minimal degradation of the highly dispersive EOT signal in NHAs. Hence, our analysis confirms the feasibility of using highly dispersive Fano resonant EOT spectra for equipment-free detection of molecular accumulation on NHAs over a broad dynamic range.

2.2. Extraordinary transmission effect Coupled oscillators used in phenomenological model can be understood using finite difference time domain (FDTD) simulations (Fig. 2). Here, a self-suspended NHA with identical features with our experimental measurements is analyzed. In NHAs, for incident light to pass through the subwavelength nanohole efficiently, a series of excitation and coupling of plasmonic modes (SPP → LSP → SPP) at different interfaces and boundaries is needed [34,43,44,47]. In principle, the EOT resonance peak should occur at wavelengths corresponding to the grating matching condition required for the excitation of SPPs on the Au dielectric interface [48], √ √ √ 𝜀𝐴𝑢 𝑛2 𝑑 𝑑 √ (1) 𝜆𝑠𝑝𝑝 = √ 𝜀𝐴𝑢 + 𝑛2𝑑 𝑖2 + 𝑗 2

2. Results 2.1. Fano resonant biosensing We performed biomolecular detection experiments as a robust testbed in refining and validating our microscopic model of Fano resonances in NHAs. We used suspended NHAs to investigate the underlying mechanism of Fano resonant EOT effect and evolution of the asymmetric resonance profile with molecular accumulation. To fabricate our devices, we employed a high-throughput Lift-off-Free Evaporation (LIFE) lithography technique (see Methods and Fig. S1) following a technique introduced in an earlier work [4]. Nanoholes with 160 nm diameter and 450 nm pitch are fabricated within a 125 nm thick gold (Au) film that is suspended on a low-pressure chemical vapor deposition (LPCVD) silicon nitride (Si3 N4 ) membrane (Fig. 1a). Spectral transmission measurements are performed using an optical setup with a broadband light excitation source and a high-resolution spectrometer (see Methods). A high-quality asymmetric Fano resonance profile with a transmission maximum at ∼700 nm and a minimum at ∼650 nm is observed for pristine (pre-functionalized) NHAs in water (Fig. 1b, blue curve). To investigate the impact of biomolecular accumulation on the Fano resonance profile, biomolecular sensing experiments are carried out following surface activation of NHAs (see Methods). A protein bilayer consisting of protein A/G (Thermofisher Inc.) and mouse protein IgG (Sigma-Aldrich) are immobilized on the activated NHA device [4,36]. Upon bilayer protein immobilization a red shifting of ∼10 nm (∼7 nm) is observed for the transmission peak (minimum) as shown in Fig. 1b (red curve). Three prominent experimental observations are consistently noted in our experimental measurements: (i) EOT spectrum overall red-shifts with the increased effective refractive index following replacement of water molecules with proteins on NHA surfaces, (ii) a larger sensitivity to molecular accumulation is observed for the EOT peak with respect to transmission minimum (resonance window), (iii) the asymmetric Fano resonance profile is slightly broadened following biomolecular accumulation. Our experimental observations are validated using full-wave electromagnetic three-dimensional finite difference time domain (3D FDTD) simulations for varying biomolecular surface densities (Fig. 1c). In our analysis, following earlier work [2,46], the conformal protein layer is incorporated as a fixed height (𝑡 = 8 nm) thin film with an effective refractive index (RI) that linearly changes with mass density of the accumulated molecules (see Methods and Fig. S2). We analyzed the impact of the surface protein accumulations on the Fano resonant characteristics in a broad dynamic range spanning from pristine surfaces (0 ng/mm2 ) to protein multilayers (∼27 ng/mm2 ). Linear red shifting of EOT spectra with increased mass, albeit with a larger sensitivity for the transmission peak is observed (Fig. 1c). A transmission peak (dip) shift

where (i, j) are the grating orders along the x- and y-directions, d the periodicity of the square array, 𝜀𝐴𝑢 the permittivity of gold, 𝑛𝑑 the RI of the dielectric material in contact with the upper grating interface. In practice, a transmission minimum, instead of a transmission maximum, is routinely observed at this particular resonance wavelength [4,40,47]. This counterintuitive observation is associated to the fact that the grating matching condition defined above is for SPPs propagating on a perfectly uniform and continuous Au layer. Enhanced light transmission requires strong coupling of SPPs to the LSPs at the rims of the nanoapertures [43,45]. The SPP excitation condition given in Eq. (1) is only matched when there is minimal perturbation (coupling of SPPs to LSPs) leading to a resonant transmission minimum, a scenario that is illustrated in Fig. 2a. Our FDTD simulations provide electromagnetic field profiles in understanding this observation. In Fig. 2b, the magnetic field profiles within the xy-plane are shown for x-polarized incident light propagating along the z-direction (normal to the NHA surface) at a wavelength corresponding to the transmission minimum. Magnetic field profiles at the incident Au/water interface, in the middle of the nanohole, at the exit Au/water interface and within a plane 50 nm below the exit surface are shown. Incident light efficiently launches two coherent counter-propagating SPP waves on the upper grating interface with parallel wave vectors ±2𝜋/p in the xdirection. As shown in Fig. 2b (top left), this leads to surface plasmon polariton Bloch waves (SPP-BWs), standing waves corresponding to the coherent superposition of counter propagating SPPs with a wave pattern that bypasses the nanoholes [43,49]. Coupling of SPP-BWs with the LSPs around the rims of the nanoholes is minimal for this excitation wavelength, an effect that leads to minimal funneling of incident electromagnetic waves through the nanohole TEM01 waveguide modes (Fig. 2b, top right) [45]. Weak coupling results in minimal transmission of the incident electromagnetic wave to the bottom surface (Fig. 2b, bottom left). Notably, this distinct null-field profile is responsible for the transmission minimum (Fig. 2b, bottom right), commonly referred as resonant ‘‘Wood’s anomaly’’ at the grating matching condition given in Eq. (1) [39,40,50]. Further analysis focused on charge distribution profiles within the nanoholes confirms that the anti-symmetric electric quadrupole mode within the nanoaperture. This result is consistent with our expectations for the diminished coupling of the SPP-BWs to nanohole modes, leading to transmission minimum (Fig. S3a). In plasmonic NHAs, light transmission efficiencies can be drastically modulated from a nearly null value to beyond the unity within a narrow spectral window (∼10–20 nm) [4]. EOT peak emerges at specific wavelengths where strong coupling of SPP-BWs (black sinusoidal waves) 2

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Optics Communications 469 (2020) 125780

Fig. 1. (a) Schematic of the Fano resonance based biomolecular detection experimental setup that consists of a broadband light source, a 10× objective, a reflection mirror, a convex lens, and a high-resolution spectrometer. SEM image of a suspended plasmonic nanohole array (𝑑 = 160 nm, 𝑃 = 450 nm) is shown (inset). (b) Experimentally measured transmission spectra before (blue curve) and after (red curve) surface accumulation of protein A/G and IgG antibodies on the NHA are shown. (c) Sensitivities of the Fano resonant EOT transmission dip and peak to protein accumulation are compared. Full wave electromagnetic FDTD simulations demonstrate that transmission minimum and EOT peak wavelength red shifts with increasing protein surface density (defined in units of ng/mm2 ). A larger shift is observed for the EOT peak with respect to transmission minima. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

to LSPs (hot spots at the rims of the holes) takes place [4,45], as illustrated in Fig. 2c. At a wavelength corresponding to the transmission maximum, SPP-BWs exhibit a symmetric standing field pattern that strongly overlaps with the rims of the nanoholes (Fig. 2d, top left). This overlap results in efficient excitation of LSPs around the rims of the apertures (Fig. 2d, top left) and funneling of the incident light to the TEM01 waveguide mode of the cylindrical holes (Fig. 2d, top right). At the out-coupling surface, TEM01 waveguide mode couples back to the SPP-BWs through the LSPs at this interface (Fig. 2e, bottom left). SPP-BWs and LSPs excited at the out-coupling surface can radiate to the far-field due to strong coupling to the continuum, leading to extraordinary optical transmission maxima [43,45]. In the near field regions (50 nm away for the out-coupling surface), the field profile of the transmitted light reflects the SPP-BWs and LSPs distribution along the out-coupling surface (Fig. 2d, bottom right). Our analysis on the charge distribution (Fig. S3b) reveals that the nanohole acts as a Hertz-type electric dipole antenna effectively coupling the incident electromagnetic wave to the out-coupling surface.

2.3. Mechanical model of Fano resonant EOT effect

Lorentz model provides a remarkably accurate description of dipolar light-matter interactions as a result of bound charge oscillations within a neutral atom. The frequency dependent polarization of the electronion pair is obtained using a damped harmonic mass–spring system, consisting of a mass m attached to a rigid support through a spring with force constant 𝜅, representing the electron-nucleus binding. In this classical model, an electromagnetic field acting on the bound charges is incorporated by introducing an external harmonic force 𝐹 (𝑡) = 𝐹0 𝑒−𝑖(𝜔𝑡) driving the mechanical oscillator. Similarly, emergence of Fano resonances in plasmonic NHAs can be explained using an equivalent coupled-oscillator system driven by an external harmonic force. Following our FDTD analysis above, our equivalent mass–spring system consists of three mechanical oscillators corresponding to SPP modes on the in-coupling (SPPin ) and out-coupling (SPPout ) surfaces, and LSP modes at the rims of the nanoholes (Fig. 3a). Effective masses of 𝑚SPPin , 𝑚SPPout and 𝑚LSP with the spring constants of 𝑘SPPin , 𝑘SPPout 3

X. Zhu, N. Cao, B.J. Thibeault et al.

Optics Communications 469 (2020) 125780

Fig. 2. Coupled plasmonic excitations leading to a Fano resonant extraordinary light transmission effect. (a) Weak coupling in between in-coupling SPP-BWs and nanoaperture LSPs is illustrated. Minimum light transmission occurs due to the diminished light funneling in between in-coupling and out-coupling surfaces. (b) Magnetic field profiles within the nanohole surface plane (xy-plane) are shown for x-polarized incident light propagating along the z-direction (normal to the NHA surface). Field profiles at the incident Au/water interface, in the middle of the metallic film, at the exit Au/water interface and within a plane 50 nm below the exit surface are shown. (c) Strong coupling of SPP-BWs to the LSPs leading to EOT peak is illustrated. (d) Magnetic field profiles at interfaces listed in (b) are shown for the wavelength corresponding to the peak transmission. Hot spots around the rims of the nanoapertures lead to efficient light funneling in between the in-coupling to out-coupling surfaces.

and 𝑘LSP control the natural oscillation frequencies of the corresponding plasmonic excitations. The coupling between the 𝑚SPPin and 𝑚SPPout oscillators is realized through 𝑚LSP , the localized plasmonic excitations at nanoaperture rims. The coupling strengths between the neighboring oscillators are determined by the spring constant 𝜅. A symmetric coupling strength (𝜅) and pre-loading equal mass for all the oscillators (𝑚SPPin = 𝑚LSP = 𝑚SPPout = m) is assumed for convenience. The natural frequency (plasmon resonance frequency) of each oscillator in the absence of damping is defined by its mass and spring constant, i.e., 𝜔SPPin = (𝑘SPPin ∕𝑚SPPin )1∕2 , 𝜔LSP = (𝑘LSP ∕𝑚LSP )1∕2 , 𝜔SPPout = (𝑘SPPout ∕𝑚SPPout )1∕2 . Optical excitation of the coupled plasmonic oscillator systems is incorporated using an external harmonic driving force acting on the first oscillator 𝑚SPPin . Note that the incident field cannot excite LSP and out-coupling SPPout directly, but only through the SPPin excited on the in-coupling surface via a grating assisted coupling mechanism. Plasmonic decay due to non-radiative and radiative losses are introduced using frictional constants 𝛾SPPin , 𝛾LSP , and 𝛾SPPout . The mechanical motion of the coupled-oscillator system is a complex

superposition of its normal modes with varying phases. Hence, we determine the displacements of the oscillators from their respective equilibrium positions, a measure of the induced electric dipole moment of the corresponding plasmonic mode, using following set of equations of motion 𝑚SPPin 𝑥̈ SPPin + 𝛾SPPin 𝑚SPPin 𝑥̇ SPPin + 𝑘SPPin 𝑥SPPin − 𝜅 2 𝑚LSP 𝑥LSP = 𝐹0 𝑒−𝑖𝜔𝑡 2

(2a)

2

𝑚LSP 𝑥̈ LSP + 𝛾LSP 𝑚LSP 𝑥̇ LSP + 𝑘LSP 𝑥LSP − 𝜅 𝑚SPPin 𝑥SPPin − 𝜅 𝑚SPPout 𝑥SPPout = 0

(2b) 𝑚SPPout 𝑥̈ SPPout + 𝛾SPPout 𝑚SPPout 𝑥̇ SPPout + 𝑘SPPout 𝑥SPPout − 𝜅 2 𝑚LSP 𝑥LSP = 0

(2c)

We use Eqs. (2a)–(2c) to calculate the power transferred to SPPin , 𝑃 (𝑡) = 𝐹0 𝑒−𝑖(𝜔𝑡) 𝑑𝑥SPPin ∕𝑑𝑡 (see Eq. (S1) in the supplementary document), the mechanical counterpart of the transmitted light intensity [15,51]. Using optimized parameters 𝑚SPPin = 𝑚SPPout = 𝑚LSP = 1, 𝑘SPPin = 𝑘SPPout = 4.71, 𝑘LSP = 4.41, 𝛾SPPin = 𝛾SPPout = 0.04, 𝛾LSP = 0.001, 𝜅 = 1, and 𝐹0 = 1 in standard units, we obtained an asymmetric Fano lineshape for P(t ) (Fig. 3b, solid blue curve) with spectral features in 4

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Optics Communications 469 (2020) 125780

Fig. 3. (a) The coupled-oscillator model capturing the Fano resonant EOT behavior. Masses 𝑚SPPin , 𝑚LSP , 𝑚SPPout represent plasmonic oscillators on the in-coupling metal/dielectric interface (SPP), at hole aperture rims (LSP) and SPP at the out-coupling metal/dielectric interface, respectively. An external driving force 𝐹 (𝑡) = 𝐹0 cos(𝜔𝑡) is introduced as the mechanical analogue of the incident light excitation. (b) Power transfer spectrum derived from the mechanical model (blue solid curve) is compared with 3D FDTD simulations (black dashed curve) and experimentally measurements (black solid curve). (c) Normal modes of the coupled-oscillator system are illustrated. The oscillation amplitudes (d) and phases (e) of each oscillator as a function of the excitation wavelength are shown. Wavelengths corresponding to the normal modes (I, II, III) and the Wood’s anomaly (WA) are indicated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

excellent agreement with our FDTD simulation (black dashed curve) and experimental measurements in water (𝑛water = 1.33) (black solid curve).

the LSPs around the rims of the hole apertures, which is responsible for the enhanced light transmission (Fig. 2c–d and Fig. S3b). With increasing excitation frequency, the oscillation amplitudes (𝑚SPPin , 𝑚LSP and 𝑚SPPout ) diminish (Fig. 3d). At the resonance minimum, the phase response of the third oscillator 𝑚SPPout to external driving force abruptly switches from 𝜋 to −𝜋 (Fig. 3e, bottom). At this wavelength, the amplitude and phase responses indicate destructive interference between the (I) and (II) normal modes of the system. Null amplitude response of the mechanical system emulates the minimal light transmission through the NHAs at Wood’s anomaly (Fig. 3b). This scenario corresponds to an electromagnetic field distribution where the launched SPP-BWs on the incident nanohole array surface skip over the nanoapertures, leading to minimal coupling between the SPP and LSP modes and light transmission in agreement with our FDTD simulations (Fig. 2a–b and Fig. S3a) [52]. As shown by Fig. 3d, spectrally close amplitude dip (highlighted in dark gray) at ∼ 658 nm and the amplitude peak at the natural frequency of the first normal mode (∼ 700 nm) leads to a typical asymmetrical Fano-type resonance. Furthermore, the wavelength (∼ 658 nm) at which null amplitude appears is in excellent agreement with the predicted resonance condition from the phase matching condition (∼ 650 nm) in Eq. (1). Our coupled-oscillator analysis is focused on the grating coupled (1, 0) transmission peak for two primary reasons: (i) it is the resonance peak routinely used in experimental measurements, and (ii) Fano resonance behavior of this (1, 0) grating order can be accurately described using our one-dimensional (1D) oscillator model.

We first find the normal modes of the oscillator system and subsequently analyze the amplitude and phase responses of each oscillators to the external driving force [51]. Fig. 3c summarizes the characteristic normal modes of a three-coupled-oscillator system. Black arrows indicate the relative oscillation directions and amplitudes. The first normal mode (I) corresponds to oscillations where all masses swing together back and forth with the second mass 𝑚LSP . This oscillation pattern is similar to the symmetrical mode of a typical two-coupled-oscillator system. The second normal mode (II), which has a higher natural frequency than the symmetrical mode, is a consequence of the first 𝑚SPPin and third 𝑚SPPout masses oscillating in opposite directions while the second mass 𝑚LSP is nearly stationary. This mode corresponds to the anti-symmetrical mode in a typical two-coupled oscillator system. The third normal mode (III) represents an oscillatory motion where the second mass 𝑚LSP experiences a full phase reversed oscillation relative to the 𝑚SPPin and 𝑚SPPout . This mode has the highest natural frequency. The displacement amplitudes and phases of the individual oscillators for these normal modes are shown in Fig. 3d–e (highlighted in gray). At a low driving energy of about 1.77 eV (∼ 700 nm in wavelength), all the masses oscillate in-phase (Fig. 3d–e), indicating the excitation of the normal mode (I) in Fig. 3c. In-phase oscillation of individual oscillators at this wavelength is analogous to the resonant coupling of the SPPs on the upper and lower grating interfaces with 5

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Optics Communications 469 (2020) 125780

We examined how well our coupled-oscillator model captures the asymmetric Fano resonance lineshape by analyzing its spectrum using the Fano formula [4,40]: ( )2 ∑ 1 + 𝑟 𝑞𝑟 ∕𝜀𝑟 (𝜔) (3) 𝑇𝐹 𝑎𝑛𝑜 (𝜔) = 𝑇𝐵 + 𝑇𝐴 (∑ )2 +1 𝑟 1∕𝜀𝑟 (𝜔) where 𝑇𝐵 ∼ (𝑟∕𝜆)4 is the Bethe’s transmission coefficient [53], 𝜀𝑟 (𝜔) = 2(𝜔𝑟 − 𝜔0 )/𝛤𝑟 (𝜔0 the resonant frequency), 𝛤𝑟 and 𝜔𝑟 are the resonance linewidth and frequency of the 𝑟th resonance, respectively. The Fano parameter 𝑞𝑟 controls the spectral dispersion of the 𝑟th resonance. 𝑇𝐴 is the discrete-continuum coupling constant that modulates the amount of light transmission through the NHAs [19,40,54,55]. As shown in Fig. S4, nearly perfect agreement between the Fano formula (red curve) and the coupled-oscillator model (black curve) confirms that the Fano resonance transmission profile of the suspended NHA can be accurately reproduced. Here, the dimensionless asymmetric parameter q = −12 with a negative value indicates a spectral dip (resonant Wood’s anomaly) at a shorter wavelength with respect to the adjacent spectral peak [55]. 2.4. Fine tuning of Fano resonances Structural design of NHAs with highly dispersive Fano resonant EOT characteristics at specific wavelengths is a challenging task. In addition to providing significant insight into the nature of Fano resonant transmission in NHAs, our coupled-oscillator model provides guidelines in fine-tuning of Fano resonances. We demonstrated this capability by examining the impact of the nanohole size on the EOT wavelength and Fano resonance lineshape. In our analysis, the experimental transmission spectra (Fig. 4a) are compared with rigorous full-wave electromagnetic FDTD simulations (Fig. 4b) and the coupledoscillator model (Fig. 4c) for three different nanoaperture diameters. Several experimental observations (Fig. 4a) with decreasing nanohole dimensions are noted: (i) a clear blue shifting of the Fano resonance peak, (ii) increased asymmetry of the Fano resonance profile, and (iii) unaltered null transmission wavelength. Plasmonic oscillators present an effective Hertzian dipole behavior at the transmission peak (Fig. S3). Hence, our first observation is associated to the fact that decreasing hole size leads to stronger dipolar charge oscillations and a √ 𝑘/m). This causes the stiffer resonant free electron ‘‘spring’’ (𝜔 = (blue) shifting of the LSP and resonant transmission peak to shorter wavelengths as predicted by our FDTD simulations (Fig. 4b). The increased asymmetry of the EOT profile with decreasing aperture size, the second observation, is linked to the diminished coupling of SPPs to LSPs, leading to spectral narrowing of the Fano resonance linewidth. Essentially, the coupling strength of the interfering SPPs and LSPs plays an important role in determining the Fano resonance linewidth [44,56]. The complicated interaction between these two plasmonic oscillators for varying nanohole dimensions can be incorporated by changing the spring constant 𝜅 in our coupled-oscillator model. As shown in Fig. 4c, a reduction in the spring constant (𝛥𝜅 < 0) captures optical response of the NHA to the decreasing hole diameter: a blue shifted resonance peak and minimal modulation of the null transmission wavelength. Here, we compare the power absorption spectra for three different spring constants: 0.97 (red curve), 1 (blue curve), and 1.03 (black curve). The resonance peak considerably blue shifts with decreasing spring constant 𝜅, whereas a negligible spectral modulation is observed for the transmission dip around 650 nm in strong agreement with rigorous full-wave electromagnetic FDTD simulations (Fig. 4b) and experimental measurements (Fig. 4a). Furthermore, reducing the coupling strength between the oscillators leads to narrowing of the absorption resonance linewidth and increased spectral asymmetry factors q, a parameter that is strongly correlated to the spectral distance 𝛥𝜆 between the Fano lineshape resonance peak and dip (Fig. 4c). Specifically, we compared three different hole diameters: 150 nm (red curve), 160 nm (blue

Fig. 4. Influence of the nanohole diameter on the Fano resonant EOT wavelength and asymmetrical profile is revealed by the (a) experimental measurements, (b) 3D FDTD simulations, and (c) coupled-oscillator model predictions of the transmission spectra of plasmonic NHAs as a function of wavelength. Three different nanohole diameters, 150 nm (red solid curve), 160 nm (blue solid curve), and 170 nm (black solid curve), are characterized. Dashed curves represent the fit of the Fano formula Eq. (3) to the obtained spectra. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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peak and Fano resonance dip to protein accumulation. This observation demonstrates that the spectral response to protein accumulation can be accurately captured as a mass loading effect within a phenomenological coupled-oscillator model.

curve), and 170 nm (black curve) and demonstrated that our coupledoscillator model accurately predicts our experimental measurements without resorting to computationally demanding 3D FDTD simulations. 2.5. Biosensing as a mechanical loading process

3. Conclusions Fano resonant EOT signal is remarkably sensitive to small alterations in local dielectric environment, a particularly useful feature for biosensing applications [4,11,19,38]. This inherent sensitivity originates from the highly dispersive nature of the Fano resonance and enhanced spectral response of the EOT profile to minor perturbations within the local dielectric environment of plasmonic NHAs [34,47]. Due to the increased light-matter interactions enabled by the plasmonic excitations (Fig. 5a–b), accumulation of higher refractive index (RI) molecules on metallic interfaces can induce large enough spectral shifting of the Fano resonant EOT peak, leading to a discernible transmission intensity change at the resonance wavelength [4,28,32,36,38]. A remarkable demonstration of this includes label-free detection of biomolecular sub-monolayers by visual inspection of the transmitted light intensity over a narrow and highly dispersive spectral window [4]. Our coupled-oscillator model inherently captures the spectral sensitivity of EOT signals by incorporating the surface adsorbed protein monolayer as a mechanical load (Fig. 5c–d). As schematically shown in the top panel of Fig. 5c, only the 𝑚SPPin and 𝑚LSP oscillators are mechanically loaded. Molecular accumulation on the top surface and within the nanohole apertures do not disturb the SPPs on the outcoupling surface (𝑚SPPout oscillator), which is physically sealed by the membrane substrate [11]. Transferred power spectra is shown in Fig. 5e for three different mass loading conditions: 0 (black dashed curve), 0.02 (black solid curve), 0.04 (blue solid curve), and 0.06 (red solid curve) in standard units. A gradual red shifting of the Fano resonant EOT profile is observed with increased mass loading; increased inertia of the individual mechanical oscillators results in red shifting of the coupled resonances to longer wavelengths. We performed rigorous full-wave FDTD simulations to systematically analyze the impact of protein accumulation on Fano resonances and to validate our coupled-oscillator model (Fig. 5f and Fig. S5). Surface accumulated proteins are modeled as fixed height molecular thin films with varying refractive indices proportional to surface concentrations of the proteins [46,57,58]. In line with our experiments (Fig. 1), we considered an accumulated multiprotein bilayer consisting of a protein-A/G capturing layer serving as a recognition moiety and a secondary layer of IgG target antibodies (see Methods) [2,4]. A thin dielectric film with a constant thickness (𝑡 = 8 nm) and varying RI is conformally coated on the incident Au surface and the inner walls of each nanoholes (Fig. 5a–b). Transmission spectra of NHA structures with varying amounts of protein accumulation are shown in Fig. S5. Plotting the relative resonance wavelength shift with respect to the pure water background scenario (𝑛protein = 1.33), we found a linear dependence of the Fano resonance transmission dip and EOT transmission peak shifts on 𝑛protein (red curves in Fig. 5f). A larger spectral sensitivity is observed for the EOT transmission peak (∼ 53 nm/RIUprotein or 1.16 nm/ng mm2 for a protein layer of 𝑡 = 8 nm within a mass density ranging from 0 to 20 ng/mm2 ) with respect to the Fano resonance transmission dip (∼32 nm/RIUprotein or 0.75 nm/ng mm2 for a protein layer of 𝑡 = 8 nm within a mass density ranging from 0 to 20 ng/mm2 ). We subsequently analyzed the optical response of NHAs to protein accumulation by incorporating it as a mass loading effect. Our analysis shows a linear dependence of the mechanical resonance wavelength shift on the square root of the total oscillator mass, as presented by the black solid and dashed curves in Fig. 5f. This observation is associated to the fact that the square of the natural oscillation frequency √ 𝑘∕𝑚). is inversely proportional to the mass of the oscillator (𝜔 = Remarkably, our coupled-oscillator model, yielding an optical response nearly identical to that calculated by FDTD simulations, accurately captures the markedly different sensitivities of the EOT transmission

In conclusion, we have shown that the impact of biomolecular accumulation on Fano resonant systems can be incorporated as a mechanical loading mechanism in widely adapted coupled-oscillator models. The defining characteristics of Fano resonant EOT signal is the highly asymmetric transmission profile due to the spectrally close destructive and constructive interference conditions emerging from resonant interactions in between SPPs and LSPs. Our phenomenological approach inherently captures the intricate spectral response of the coupled SPP and LSP modes and their optical response to biomolecular accumulation. It allows us to understand non-trivial modulations in Fano-resonant EOT spectra. Our theoretical approach incorporating molecular accumulation processes as a mechanical loading is universal and can be exploited in understanding of experimental observations in biomolecular sensing tests utilizing different plasmonic and metamaterial systems. This discovery presents crucial insights into how highly dispersive resonances can be exploited in biosensing applications. Furthermore, we demonstrated that our phenomenological model providing a parameterized understanding of the physical origins of the EOT effect in plasmonic NHAs presents predictive power in finetuning the Fano resonant characteristics. It establishes structural design guidelines without resorting to computationally expensive full-wave electromagnetic simulations. In our analysis focused on fine-tuning of Fano resonances by adjusting nanohole dimensions, we demonstrated excellent agreement between the pairs among our coupled-oscillator mechanical model, rigorous FDTD simulations and experimental measurements. 4. Methods 4.1. Fabrication of suspended open-ended plasmonic nanohole arrays A high-throughput and large-area Lift-off-Free Evaporation (LIFE) lithography technique is employed to fabricate suspended plasmonic NHAs. The fabrication process is summarized in Fig. S1: suspended plasmonic NHAs (𝑑 = 160 nm, 𝑃 = 450 nm) are fabricated on a 100nm-thick low stress low pressure chemical vapor deposition (LPCVD) silicon nitride (Si3 N4 ) thin film deposited silicon (Si) wafer. The wafer is first spin-coated with a 300 nm-thick photoresist (PR) layer and then patterned using deep ultraviolet (DUV, 248 nm) light. Following the reactive-ion etching (RIE) and PR removal processes, a free-standing Si3 N4 thin membrane is created by wet etching in potassium hydroxide (KOH). Finally, suspended plasmonic NHAs are defined by physical vapor deposition of a gold (Au) metal layer (120 nm thick) using a directional electron beam evaporator. 4.2. Immobilization of proteins on nanohole array surface A protein bilayer consisting of protein A/G (Thermofisher Inc.) and mouse protein IgG (Sigma-Aldrich Inc.) is used in the biomolecular detection experiments. Protein A/G selectively binds to the activated Au surface of the NHA chips through physisorption [2,36]. Protein A/G (1 mg/ml, 10 mM phosphate buffer) is drop-casted onto the NHA devices. Following 1-hr incubation and subsequent rinsing (DI water) processes, immobilization of the A/G protein layer on the NHA surface is achieved, and excess unbound protein A/G is removed. Subsequently, the target protein IgG (1 mg/ml) is added and incubated for another hour. Finally, NHA devices are gently rinsed in DI water and loaded into a custom-designed microfluidic chamber prefilled with clean DI water for spectroscopic measurement. 7

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Fig. 5. Top (a) and side (b) near-field profiles of a suspended plasmonic NHA (𝑑 = 160 nm, 𝑃 = 450 nm) that is coated with a 8-nm thick protein layer at a refractive index of 1.6. Near-field enhancements are shown at the EOT transmission peak wavelength (∼ 714 nm). (c) The thin adsorbed protein layer is incorporated in the phenomenological coupled-oscillator model as a mechanical load (𝑚protein ) applied to the 𝑚SPPin and 𝑚LSP oscillators. (d) Schematics of the coating of a fixed-thickness protein layer on the incident Au surface and the inner walls of each nanoholes. (e) Normalized power spectra (a plasmonic analogue of EOT spectra) of the mechanically loaded coupled-oscillator system is shown for varying load masses. (f) Spectral shifting of the Fano resonance dip (dashed) and EOT transmission peak (solid) with respect to the pure water background (𝑛protein = 1.33) as a function of the refractive index of the adsorbed protein layer (𝑛protein ) is shown. FDTD simulations (red) are compared to the coupled-oscillator model (black). Straight lines represent the first-order polynomial fits to the data obtained from the calculations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

light source (550–900 nm) is launched from the Si3 N4 side along +z axis. A pair of periodic boundary conditions are applied to x and y directions. Perfectly matched layer (PML) boundary conditions are applied in the z direction. A mesh size of 5 nm is used. A plane power monitor is employed to obtain transmission spectra. The surface adsorbed protein layers are modeled as fixed-height layers with varying refractive indices based on their surface mass densities [46,58]. Using the fixed-height model, the effective refractive index of a protein layer (𝑛protein ) can be calculated using 𝑛𝑝𝑟𝑜𝑡𝑒𝑖𝑛 = 𝑛𝑚𝑒𝑑𝑖𝑢𝑚 + (N/V) × (𝑀.𝑊 .∕𝑁𝐴 ) × (dn/dc), where 𝑛medium is 1.33, N is the number of molecules, V is the volume of the protein layer, M.W. is the molecular weight of IgG (∼150 kDa), 𝑁𝐴 is Avagadro’s number, and dn/dc is the incremental RI (∼0.18 cm3 /g) [46,57,60]. Using the protein layer thicknesses obtained from ellipsometry measurements [2], approximate refractive indices of 𝑛𝐴∕𝐺 = 1.55 and 𝑛𝐼𝑔𝐺 = 1.6 are determined for

4.3. Optical measurements A normally incident collimated broadband light (400–1100 nm) is used to obtain the transmission spectrum of a plasmonic NHA. Transmitted light is coupled to a high-resolution spectrometer (HR4000, Ocean Optics) using a collection objective and convex lens. Raw spectra are recorded using a commercial software SpectraSuite (Ocean Optics) over a wavelength range from 400 to 1100 nm. The spectral measurement setup is schematically shown in Fig. 1a. 4.4. FDTD simulations and fixed-height model for protein layers In our FDTD simulations, ‘‘Au (Gold) - Palik’’ dielectric constants are used for gold [59]. The refractive indice of Si3 N4 and the water background are set to 2.16 and 1.33, respectively. A linearly polarized 8

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the A/G and IgG monolayers. We analyzed a broad range of effective refractive indices for the combined A/G + IgG (recognition moiety + target) bilayer corresponding to a series of scenarios from pristine NHA structures to the NHAs coated with sparse/complete protein layers and protein multilayers.

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Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Xiangchao Zhu: Methodology, Software, Investigation, Data curation, Validation, Formal analysis, Writing - original draft. Ning Cao: Resources. Brian J. Thibeault: Resources. Benjamin Pinsky: Conceptualization, Methodology, Funding acquisition, Resources. Ahmet Ali Yanik: Conceptualization, Methodology, Writing - review, Project administration, Supervision, Funding acquisition. Acknowledgments This work was partially supported by the NIH, USA Award R21AI139790 and by National Science Foundation, USA [ECCS-1611290]. A.A.Y. gratefully acknowledge support from National Science Foundation, USA through CAREER Award [ECCS-1847733]. X.Z. was supported by a University of California, USA Chancellor’s Dissertation Year Fellowship. We acknowledge Dr. Tom Yuzvinsky for assistance with device fabrication, the W.M. Keck Center for Nanoscale Optofluidics for the use of the FEI Quanta 3D and UC Santa Barbara Nanofabrication Facility for deep-UV lithography. Authors acknowledge the Army Research Office, USA under award number W911NF17-1-0460 for equipment support. Appendix A. Supplementary data Supplementary material related to this article can be found online at https://doi.org/10.1016/j.optcom.2020.125780. References [1] J.N. Anker, W.P. Hall, O. Lyandres, N.C. Shah, J. Zhao, R.P. Van Duyne, Biosensing with plasmonic nanosensors, Nature Mater. 7 (2008) 442–453. [2] C. Wu, A.B. Khanikaev, R. Adato, N. Arju, A.A. Yanik, H. Altug, G. Shvets, Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers, Nature Mater. 11 (2012) 69–75. [3] F. Hao, Y. Sonnefraud, P.V. Dorpe, S.A. Maier, N.J. Halas, P. Nordlander, Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance, Nano Lett. 8 (2008) 3983–3988. [4] A.A. Yanik, A.E. Cetin, M. Huang, A. Artar, S.H. Mousavi, A. Khanikaev, J.H. Connor, G. Shvets, H. Altug, Seeing protein monolayers with naked eye through plasmonic Fano resonances, Proc. Natl. Acad. Sci. 108 (2011) 11784–11789. [5] E. Cubukcu, S. Zhang, Y.-S. Park, G. Bartal, X. Zhang, Split ring resonator sensors for infrared detection of single molecular monolayers, Appl. Phys. Lett. 95 (2009) 043113. [6] R. Gordon, A.G. Brolo, D. Sinton, K.L. Kavanagh, Resonant optical transmission through hole-arrays in metal films: physics and applications, Laser Photonics Rev. 4 (2010) 311–335. [7] S.A.O. Olson, D.A. Mohr, J. Shaver, T.W. Johnson, S.-H. Oh, Plasmonic cup resonators for single-nanohole-based sensing and spectroscopy, ACS Photonics 3 (2016) 1202–1207. [8] J. Ye, F. Wen, H. Sobhani, J.B. Lassiter, P. Van Dorpe, P. Nordlander, N.J. Halas, Plasmonic nanoclusters: Near field properties of the Fano resonance interrogated with SERS, Nano Lett. 12 (2012) 1660–1667. [9] A.E. Cetin, H. Altug, Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing, ACS Nano 6 (2012) 9989–9995. [10] X. Zhu, A. Cicek, Y. Li, A.A. Yanik, Plasmofluidic microlenses for label-free optical sorting of exosomes, Sci. Rep. 9 (2019) 8593. [11] J. Ferreira, M.J.L. Santos, M.M. Rahman, A.G. Brolo, R. Gordon, D. Sinton, E.M. Girotto, Attomolar protein detection using in-hole surface plasmon resonance, J. Am. Chem. Soc. 131 (2009) 436–437. 9

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