Îµ-Near-Zero Materials for Highly Miniaturizable Magnetoplasmonic

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

#-Near-Zero Materials for Highly Miniaturizable Magnetoplasmonic Sensing Devices Edwin Moncada Villa, Osvaldo Novais Oliveira, and Jorge Ricardo Mejía-Salazar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11384 • Publication Date (Web): 22 Jan 2019 Downloaded from http://pubs.acs.org on January 26, 2019

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The Journal of Physical Chemistry

ε-Near-Zero Materials for Highly Miniaturizable Magnetoplasmonic Sensing Devices E. Moncada-Villa,† Osvaldo N. Oliveira Jr,‡ and J. R. Mej´ıa-Salazar∗,¶ †Escuela de F´ısica, Universidad Pedag´ ogica y Tecnológica de Colombia, Avenida Central del Norte 39-115, Tunja, Colombia ‡São Carlos Institute of Physics, University of São Paulo, CP 369, 13560-970, São Carlos, SP, Brazil ¶National Institute of Telecommunications (Inatel), 37540-000, Santa Rita do Sapuca´ı, MG, Brazil E-mail: [email protected]

Abstract We show here the design of a magnetoplasmonic sensing platform consisting of a bilayer of a transparent conducting oxide and a gold film grown on a ferromagnetic substrate. Near the bulk plasmon frequency (ε ≈ 0) of the oxide film, sharp resonances are observed for the transverse magneto-optical Kerr effect (TMOKE), which are used for sensing permittivity changes. As a proof of concept, we demonstrate that the proposed architecture is able to detect glucose at mM concentration levels in aqueous media, even without any surface functionalization. Because no prism coupler is needed, the sensing platform may be miniaturized and employed in microfluidic systems for point-of-care devices.

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Introduction Plasmonics is responsible for the unique ability of overcoming the diffraction limit through resonantly coupling electromagnetic waves to collective electron oscillations at metal-dielectric interfaces, which can be exploited for light enhancement and confinement at dimensions much smaller than the incident wavelength. 1,2 It is just this feature which makes it an ideal candidate for highly integrated nanoscale optoelectronic devices in numerous applications. 3,4 Plasmonic biosensing, in particular, allows for real-time control of adsorption events by monitoring the refractive index, 5–8 but there are two important limitations. First, detection is normally possible only for large molecules or high concentrations that induce large refractive index changes. The second drawback arises from the need of a prism coupler to excite the surface plasmon resonances (SPR), 9 thus hampering miniaturization and fabrication of portable (lab-on-a-chip) point-of-care (PoC) devices. Several strategies have been employed to circumvent the first limitation, including the use of magnetic nanoparticles, 10–12 metamaterial surfaces, 13,14 and magnetoplasmonic structures. 15–26 Magnetoplasmonics exploits the modulation in the intensity of reflected light by a transversally applied magnetic field, in the so-called transverse magneto-optical Kerr effect (TMOKE). 27 TMOKE can be defined as the relative change in the reflected light amplitudes, Rpp (±M), when magnetization (M) alternates between two opposite senses (±) along the perpendicular direction to the plane of polarization TMOKE =

Rpp (+M) − Rpp (−M) , Rpp (+M) + Rpp (−M)

(1)

with Rpp and M indicating the reflectance and the intrinsic magnetization (or an external applied magnetic field), respectively. The subindex pp in the reflectances is used to specify that the effect can only be observed under p-polarized incident light, for which SPRs are excited. The idea behind this mechanism is to distribute the enhanced electromagnetic field associated with SPRs inside an adjacent magneto-optical (MO) layer to increase the MO activity. 28 This technique has improved detection levels by at least three orders of magnitude, especially as

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the sharp TMOKE resonances depend strongly on the surrounding dielectric properties. 15 Although localized surface plasmon resonances (LSPRs), which only need nanostructures that act as nanoantennas and may be implemented in miniaturized devices, 29 can be seen as an alternative to solve the second limitation, 29 there are major hurdles deriving from the need to place nanoparticles at specific regions, in addition to the difficulties in localizing the target molecules at the hot spots on the device. 30 Hence, attempts to circumvent the second limitation include the use of perforated nanolayers 20 and grating couplers, 21 which may require very precise and expensive lithographic techniques. An alternative consists in exciting SPRs with materials working in the permittivity-near-zero or ε-near-zero (ENZ) regime, 31 instead of conventional prism couplers. 32 In the latter strategy both the highly absorbing ε-near-zero and SPR modes are coupled in a hybrid ε-near-zero/metal interface. Following this strategy, giant TMOKE enhancements were predicted for a multilayer deposited on gold, which consisted of alternating layers of the dielectric MO bismuth-iron-garnet:ytrium-irongarnet (BIG:YIG), indium-tin oxide (ITO) and SiO2 . 33 In spite of such promising results, it has to be admitted that the experimental realization of this multilayer architecture is likely to be challenging. In this work, we describe the design of a much simpler architecture for reaching giant TMOKE values. It comprises a transparent conducting oxide film (made of ITO) deposited on a gold(Au)-coated cobalt (Co) substrate, as depicted in Figure 1(a). Working in the ε-near-zero regime, the ITO film serves as the light-to-SPR coupler, with no need of a prism. Therefore, this magnetoplasmonic platform may be miniaturized to be employed in microfluidic and other portable devices. Furthermore, ITO may be functionalized with phosphonates, 34 amines, 35 zirconium complexes, 36 carboxylic acids and thiols, 37 DNA, 38 and silanes, 39 thus opening the way for a variety of sensors and biosensors to be produced.

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(b)

(a)

cob a

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lITO lAu

z lt ( sub stra te)

(d)

(c)

Figure 1: (a) Schematic representation of the proposed system for magnetoplasmonic sensing devices. lAu and lITO correspond to the Au and ITO film thicknesses. (b) Electric field profile for λ = 1250 nm (εITO ∼ 0), with lAu = 5.4 nm, lITO = 6.2 nm, and θ = 71.73◦ . (c) and (d) show the TMOKE, for two different resonance regions, as function of the incident angle and the ITO layer thickness. Solid and dashed lines show the numerical results of Eq. (10) for +M and −M, respectively.

Theoretical Framework The frequency-dependent permittivities for ITO (εITO ), gold (εAu ), and Co (εCo ) were taken from experimental results in Refs. [32,40,41]. The permittivity for ITO was considered as 32

εITO (ν) = ε∞,ITO −

4

2 νp,ITO , ν(ν + iγITO )


(2)

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with ε∞,ITO = 4, νp,ITO = 477 THz, and γITO = 4.775 THz. For the gold layer we used 40

εAu (ν) = ε∞,Au −

2 νp,Au , ν(ν + iγAu )

(3)

with ε∞,Au = 1, νp,Au = 217.5 THz, and γAu = 6.5 THz, which fits experimental results 40 (and is only valid) in the wavelength range λ ∈ [0.45 µm, 3.2 µm]. By using this expression we obtain εAu ≈ −68.47 + 1.73i for the working frequency ν = 240 THz (λ = 1250 nm), for which εITO = 0.048 + 0.079i. For the anisotropic permittivity of the Co substrate, with magnetization along the y-axis (as in Figure 1), we used 



0 εxz  εxx  εˆ =  εxx 0  0  −εxz 0 εxx

  .  

(4)

with εxx = −14.05 + 39.04i and εxz = 0.29 − 1.72i obtained through interpolation of experimental results in Ref. [41] for ν = 240 THz (λ = 1250 nm). As it is noted, Co behaves as a metal for the working frequency considered. Reflectance amplitudes, for ±M, are calculated within the scattering-matrix method (SMM) 42,43 as

Rpp =

−q0 η0 + qITO ηITO q0 η0 + qITO ηITO 2q0 η0 qITO ηITO (qITO ηITO − qAu ηAu )eiqITO dITO − G 1 2 2 − 2q0 η0 qITO ηITO qAu ηAu (q0 η0 + qITO ηITO ) GF ·(qAu ηAu − qCo ηxx + kx ηxz )eiqAu dAu ,

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(5)


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with

G = (q0 η0 + qITO ηITO ) [qITO ηITO (q0 η0 + qAu ηAu ) cos (qITO dITO ) 2 2 −i(qITO ηITO + q0 η0 qAu ηAu ) sin (qITO dITO ) ,

(6)

F = [Q0,ITO cos (qITO dITO ) − iQITO,Co sin (qITO dITO )] cos (qAu dAu ) −iQITO,Au cos (qITO dITO ) sin (qAu dAu ) 2 2 2 2 − q0 η0 qAu ηAu + qITO ηITO (qCo ηxx − kx ηxz ) · sin (qITO dITO ) sin (qAu dAu ) ,

(7)

where the wavevectors, qα , and ηα parameters are calculated as s qα = ηα =

ω2 − kx2 , ηα

1 , εα

(8) (9)

with subindex α = 0 (incident medium), ITO, Au, and Co indicating the corresponding medium along the structure. In the same formalism, we obtain the condition for ENZ modes as

tan (qAu dAu ) =

iQ0,ITO cos (qITO dITO ) + QITO,Co sin (qITO dITO ) , −QITO,Au cos (qITO dITO ) + iQ0,Au sin (qITO dITO )

(10)

where

Q0,ITO = qAu ηAu qITO ηITO (q0 η0 + qCo ηxx − kx ηxz ) , 2 2 QITO,Co = qAu ηAu qITO ηITO + q0 η0 (qCo ηxx − kx ηxz ) ,

(11)

2 2 Q0,Au = qITO ηITO Q0,ITO − q0 η0 qAu ηAu , 2 2 QITO,Au = qITO ηITO qAu ηAu + q0 η0 (qCo ηxx − kx ηxz ) .

(13)

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(12)

(14)

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Results & Discussion Let us begin by considering the incident medium as air, i.e., εair = 1.0, in order to discuss the working principle of the magnetoplasmonic platform in Figure 1(a). Minima in the reflectance spectra, for electromagnetic waves with λ in the ENZ regime (λ ∼ 1250 nm), are observed when the condition established in Eq. (10) is met. Such minima are associated with the corresponding light trapping at the ENZ slab. Hybrid ENZ-SPR modes are excited under the phase-matching condition, i.e., when guided ENZ modes are phase-matched to the corresponding SPR modes along the dielectric-metal (ITO-gold) interface. These resonances must be solved numerically because a simple relation for the phase-matching condition, such as the one for the Kretschmann geometry, 26 cannot be obtained due to the number of interfaces in the structure. 44 Figure 1(b) shows the Ex profile of a resonantly coupled ENZ-SPR mode for this platform, calculated for λ = 1250 nm, lAu = 5.4 nm, lITO = 6.2 nm, and θ = 71.73◦ . Figures 1(c) and 1(d) show the TMOKE around the first two regions of resonant enhancement (ENZ-SPR coupling). Results are separated in two different regions of θ and lITO for the sake of clarity. As we are interested in highly integrable platforms, we will focus on resonances occurring at small lITO values. Solid and dashed lines in Figures 1(c) and 1(d) show the numerical solutions of Eq. (10) for +M and −M, respectively, and the extreme values of the TMOKE, from Eq. (1), are observed when either Rpp (+M) = 0 (for -1) or Rpp (−M) = 0 (for 1), which indicate a way to numerically find the corresponding phase-matching condition. The structure in Figure 1(a) can also be used to design a prototype sensor platform with an SPR transducer mechanism through reflection measurements, which can be done by optimizing TMOKE of the ITO-Au system on a Co substrate, assuming an aqueous incident medium (n0 = 1.333). The working frequency is again taken as ν = 240 THz (λ = 1250 nm). TMOKE was calculated as a function of the ITO and gold layer thicknesses, lITO and lAu , with thickness steps ∆lITO = ∆lAu = 0.2 nm for the angle of incidence, θ, varying from 0◦ to 90◦ with ∆θ = 0.001◦ . For visualization purposes, in Figure 2(a) we show a scatter plot of 7



10

1.0

(a)

1.0

(b)

lITO = 3.4 nm

0.7

8

0.5

0.3

lAu (nm)

TMOKE

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0.0

6 0.0

4

-0.5

-0.3

lAu = 5.4 nm

-0.7

2 -1.0

TMOKE -1.0

1

2

3

4

5

6

7

8

64

65

66

67

68

69

(deg.)

lITO (nm)

Figure 2: TMOKE as a function of gold, lAu , and ITO, lITO , layer thicknesses, and incident angle θ. (a) Results are presented as a function of lITO to identify the range in which TMOKE exhibits maximum values. (b) TMOKE as a function of lAu and θ for lITO = 3.4 nm.

these results only as a function of lITO . Maximum TMOKE values are seen for lITO between 3.2 nm and 3.6 nm. Thus, we selected lITO = 3.4 nm for a prototype structure and show the results for TMOKE as function of lAu and θ in Figure 2(b). TMOKE can take positive or negative large values depending on lAu , as it can be noted. From now on we shall consider lAu = 5.4 nm for the gold film thickness. The corresponding TMOKE in Figure 3(a) shows giant values (TMOKE ≈ 1) with a sharp Fano-like resonance. 20 This enhancement of the MO effect is due to the resonant excitation of a surface plasmon-polariton at the ITO-Au interface. Indeed, very small reflectances are observed in Figure 3(b), represented by solid and dashed lines for Rpp (−M) and Rpp (+M), respectively. In order to demonstrate a potential detection of analytes of biological interest, we consider here the case of glucose. The effects from adding different glucose concentrations to the aqueous incident medium are taken into account by the change in the refractive index (RI), which according to experimental results in Ref. [45] can be expressed as

ninc = 1.333 + 25.76 × 10−6 × C,

8


(15)

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2.0

1.0

(a) 4

(b) 1.5

Rpp (M) x 10

TMOKE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5

1.0

0.0

0.5

-0.5 65

66

67

68

0.0 66.75

69

(deg.)

67.00

67.25

(deg.)

Figure 3: (a) TMOKE and (b) Rpp (−M) (solid line) and Rpp (+M) (dashed line) reflectances, as a function of θ, for a working frequency ν = 240 THz. Geometrical parameters were taken as lITO = 3.4 nm and lAu = 5.4 nm for all calculations in this figure.

where C corresponds to the glucose concentration in units of mM. The numerical results for this biosensing platform are given in Figure 4, where glucose concentration (C) was increased in steps of ∆C = 77.6398 mM to produce refractive index variations of ∆n = 0.002. TMOKE curves corresponding to C = 0 mM, 77.6398 mM, 155.28 mM, 232.9192 mM, 310.559 mM, 388.199 mM and 465.839 mM, are shown in Figure 4(a). The amplitude of the TMOKE peak diminishes for increasing concentration (as depicted by the arrow in the figure), while its position varies linearly with C, as presented in Figure 4(b). The top and bottom horizontal axes present results in terms of RI units (RIU) and glucose concentration, respectively. The corresponding sensitivity, obtained from the slope of the linear fitting, is S = −9.09 × 10−4 deg./mM (S = −35.29 deg./RIU). These results are competitive with recent proposals for magnetoplasmonic biosensing platforms in the Kretschmann geometry. 26 We expect this seminal work to stimulate further studies to lower detection limits down to µM, which was recently reached through the design of an enzymatic-SPR technology. 46 We should stress that the results were calculated with a system optimized for an aqueous medium to make it suitable, but not limited to, for biosensing purposes. Probing analytes in realworld samples, such as blood, urine, tissue, etc, will require surface-functionalization and the 9



increasing RI

Figure 4: (a) TMOKE as a function of θ for increasing concentrations of glucose. Successive peaks from the highest to the lowest one (indicated by the arrow) correspond to C = 0 mM, 77.6398 mM, 155.28 mM, 232.9192 mM, 310.559 mM, 388.199 mM and 465.839 mM. (b) Corresponding angular peak positions and their linear fitting, with S = −9.09 × 10−4 deg./mM (S = −35.29 deg./RIU).

integration with a proper microfluidic system to improve selectivity and ruggedness. 47 The platform can be optimized to work in air for gas sensors as well. In addition, the proposed magnetoplasmonic platform can also be used for monitoring microwave currents flowing in semiconductor circuits. 48

Conclusions In summary, we designed a magnetoplasmonic sensing platform that is amenable to miniaturization, since it does not require a prism coupler. A very simple structure consisting of a gold thin film placed on a ferromagnetic substrate, Co in this case, and covered by an ITO thin film working in the ε-near-zero regime was considered. Giant enhancement of the TMOKE values (∼ ±1) was observed depending on the Au and ITO film thicknesses, which allow us to properly tune the MO properties of these systems. The simulations indicated that a biosensor can be built for glucose, as a proof of concept. We emphasize that the magneto10


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plasmonic structure proposed here is feasible with available technology. 25,32 Significantly, the possible miniaturization makes this proposal of interest for developing point-of-care (PoC) devices for real-time health monitoring.

Acknowledgments We acknowledge the financial support from the Brazilian Agencies CNPq and FAPESP (2013/14262-7).

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