Abstract

In this paper we review the resonance conditions of periodic indentations in metallic layers and evaluate their potential for surface sensing of analytes. A review of significant contributions of nanohole arrays for sensing is presented in a first section. It is then followed by a theoretical analysis of their optical properties using coupled mode theory and an evaluation of their potential for sensing. The sensitivity, resolution, and field distribution are presented as a function of the different parameters of the metal film (periodicity, hole size, and thickness) to determine the optimal design for sensing. The focus of this paper is made on 1-D nanoslit arrays and 2-D square nanohole arrays to identify general considerations regarding sensing experiments using these types of structure. We include a MATLAB user interface, also available as a standalone application, that plots the transmission and reflection spectrum as well as the field distribution of nanohole arrays.

© 2017 Optical Society of America

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2017 (2)

M. Soler, A. Belushkin, A. Cavallini, C. Kebbi-Beghdadi, G. Greub, and H. Altug, “Multiplexed nanoplasmonic biosensor for one-step simultaneous detection of Chlamydia trachomatis and Neisseria gonorrhoeae in urine,” Biosens. Bioelectron. 94, 560–567 (2017).
[Crossref]

X. Li, M. Soler, C. I. Özdemir, A. Belushkin, F. Yesilkoy, and H. Altug, “Plasmonic nanohole array biosensor for label-free and real-time analysis of live cell secretion,” Lab Chip 17, 2208–2217 (2017).
[Crossref]

2016 (3)

J. P. Monteiro, J. H. de Oliveira, E. Radovanovic, A. G. Brolo, and E. M. Girotto, “Microfluidic plasmonic biosensor for breast cancer antigen detection,” Plasmonics 11, 45–51 (2016).
[Crossref]

S. T. Seiler, I. S. Rich, and N. C. Lindquist, “Direct spectral imaging of plasmonic nanohole arrays for real-time sensing,” Nanotechnology 27, 184001 (2016).
[Crossref]

A.-P. Blanchard-Dionne and M. Meunier, “Optical transmission theory for metal-insulator-metal periodic nanostructures,” Interface 6, 349–355 (2016).

2015 (5)

A. E. Cetin, D. Etezadi, B. C. Galarreta, M. P. Busson, Y. Eksioglu, and H. Altug, “Plasmonic nanohole arrays on a robust hybrid substrate for highly sensitive label-free biosensing,” ACS Photon. 2, 1167–1174 (2015).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

A. B. Dahlin, “Sensing applications based on plasmonic nanopores: the hole story,” Analyst 140, 4748–4759 (2015).
[Crossref]

J. Zhang, M. Irannejad, M. Yavuz, and B. Cui, “Gold nanohole array with sub-1  nm roughness by annealing for sensitivity enhancement of extraordinary optical transmission biosensor,” Nanoscale Res. Lett. 10, 238 (2015).
[Crossref]

J. W. de Menezes, A. Thesing, C. Valsecchi, L. E. Armas, and A. G. Brolo, “Improving the performance of gold nanohole array biosensors by controlling the optical collimation conditions,” Appl. Opt. 54, 6502–6507 (2015).
[Crossref]

2014 (6)

Y. Wang, A. Kar, A. Paterson, K. Kourentzi, H. Le, P. Ruchhoeft, R. Willson, and J. Bao, “Transmissive nanohole arrays for massively-parallel optical biosensing,” ACS Photon. 1, 241–245 (2014).
[Crossref]

J. W. Yoon, J. H. Lee, S. H. Song, and R. Magnusson, “Unified theory of surface-plasmonic enhancement and extinction of light transmission through metallic nanoslit arrays,” Sci. Rep. 4, 5683 (2014).
[Crossref]

H. Im, H. Shao, Y. I. Park, V. M. Peterson, C. M. Castro, R. Weissleder, and H. Lee, “Label-free detection and molecular profiling of exosomes with a nano-plasmonic sensor,” Nat. Biotechnol. 32, 490–495 (2014).
[Crossref]

A. Barik, L. M. Otto, D. Yoo, J. Jose, T. W. Johnson, and S.-H. Oh, “Dielectrophoresis-enhanced plasmonic sensing with gold nanohole arrays,” Nano Lett. 14, 2006–2012 (2014).
[Crossref]

A. E. Cetin, A. F. Coskun, B. C. Galarreta, M. Huang, D. Herman, A. Ozcan, and H. Altug, “Handheld high-throughput plasmonic biosensor using computational on-chip imaging,” Light Sci. Appl. 3, e122 (2014).
[Crossref]

A. F. Coskun, A. E. Cetin, B. C. Galarreta, D. A. Alvarez, H. Altug, and A. Ozcan, “Lensfree optofluidic plasmonic sensor for real-time and label-free monitoring of molecular binding events over a wide field-of-view,” Sci. Rep. 4, 6789 (2014).
[Crossref]

2013 (4)

P. Jia, H. Jiang, J. Sabarinathan, and J. Yang, “Plasmonic nanohole array sensors fabricated by template transfer with improved optical performance,” Nanotechnology 24, 195501 (2013).
[Crossref]

G. A. C. Tellez, S. Hassan, R. N. Tait, P. Berini, and R. Gordon, “Atomically flat symmetric elliptical nanohole arrays in a gold film for ultrasensitive refractive index sensing,” Lab Chip 13, 2541–2546 (2013).
[Crossref]

M. Huang, B. C. Galarreta, A. E. Cetin, and H. Altug, “Actively transporting virus like analytes with optofluidics for rapid and ultrasensitive biodetection,” Lab Chip 13, 4841–4847 (2013).
[Crossref]

C. Escobedo, “On-chip nanohole array based sensing: a review,” Lab Chip 13, 2445–2463 (2013).
[Crossref]

2012 (4)

K.-L. Lee, P.-W. Chen, S.-H. Wu, J.-B. Huang, S.-Y. Yang, and P.-K. Wei, “Enhancing surface plasmon detection using template-stripped gold nanoslit arrays on plastic films,” ACS Nano 6, 2931–2939 (2012).
[Crossref]

N. J. Wittenberg, H. Im, X. Xu, B. Wootla, J. Watzlawik, A. E. Warrington, M. Rodriguez, and S.-H. Oh, “High-affinity binding of remyelinating natural autoantibodies to myelin-mimicking lipid bilayers revealed by nanohole surface plasmon resonance,” Anal. Chem. 84, 6031–6039 (2012).
[Crossref]

H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51, 1729–1741 (2012).
[Crossref]

J. B. Wright, K. N. Cicotte, G. Subramania, S. M. Dirk, and I. Brener, “Chemoselective gas sensors based on plasmonic nanohole arrays,” Opt. Mater. Express 2, 1655–1662 (2012).
[Crossref]

2011 (6)

L. Lin and A. Roberts, “Light transmission through nanostructured metallic films: coupling between surface waves and localized resonances,” Opt. Express 19, 2626–2633 (2011).
[Crossref]

L. Guyot, A. Blanchard-Dionne, S. Patskovsky, and M. Meunier, “Integrated silicon-based nanoplasmonic sensor,” Opt. Express 19, 9962–9967 (2011).
[Crossref]

A. Blanchard-Dionne, L. Guyot, S. Patskovsky, R. Gordon, and M. Meunier, “Intensity based surface plasmon resonance sensor using a nanohole rectangular array,” Opt. Express 19, 15041–15046 (2011).
[Crossref]

H. Im, S. H. Lee, N. J. Wittenberg, T. W. Johnson, N. C. Lindquist, P. Nagpal, D. J. Norris, and S.-H. Oh, “Template-stripped smooth Ag nanohole arrays with silica shells for surface plasmon resonance biosensing,” ACS Nano 5, 6244–6253 (2011).
[Crossref]

C. Escobedo, S. Vincent, A. Choudhury, J. Campbell, A. Brolo, D. Sinton, and R. Gordon, “Integrated nanohole array surface plasmon resonance sensing device using a dual-wavelength source,” J. Micromech. Microeng. 21, 115001 (2011).
[Crossref]

T.-Y. Chang, M. Huang, A. A. Yanik, H.-Y. Tsai, P. Shi, S. Aksu, M. F. Yanik, and H. Altug, “Large-scale plasmonic microarrays for label-free high-throughput screening,” Lab Chip 11, 3596–3602 (2011).
[Crossref]

2010 (4)

K.-L. Lee and P.-K. Wei, “Enhancing surface plasmon detection using ultrasmall nanoslits and a multispectral integration method,” Small 6, 1900–1907 (2010).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
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H. Im, A. Lesuffleur, N. C. Lindquist, and S.-H. Oh, “Plasmonic nanoholes in a multichannel microarray format for parallel kinetic assays and differential sensing,” Anal. Chem. 81, 2854–2859 (2009).
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Supplementary Material (2)

NameDescription
» Code 1       Matlab user interface for the transmission and reflection spectra of nanohole arrays and the field distribution.
» Code 2       Standalone applet (Matlab Runtime) for the transmission and reflection spectra of nanohole arrays and the field distribution.

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Figures (46)

Figure 1
Figure 1

Principle of sensing with a nanohole array. As molecules bind to the surface of the structure the resonant wavelength shifts and the change in intensity or of the position of the maximum is used as the signal.

Figure 2
Figure 2

1A and 1B, scanning electron microscopy images of a typical array of sub-wavelength holes. The image in part B is an enlargement of the array presented in part A. 1C, normalized transmission spectra of white light through three arrays of sub-wavelength holes. All arrays were patterned in a 100-nm-thick gold film deposited on the glass slide, and the diameters of the holes were about 200 nm. The lattice parameters (periodicities) of arrays a–c were 618, 545, and 590 nm, respectively. 2, normalized transmission spectra of normally incident white light through an array of sub-wavelength (200 nm diameter) holes on a 100-nm-thick gold substrate deposited on a glass slide. Curve 1, bare (clean) Au surface; curve b, Au modified with a monolayer of MUA; and curve c, Au-MUA modified with BSA. Reprinted with permission from Brolo et al., Langmuir 20, 4813–4815 (2004) [19]. Copyright 2004 American Chemical Society.

Figure 3
Figure 3

(a) Optical image of a 10×10 microarray on a glass slide. (b) SEM image of a 600-nm-period gold nanohole array. (c) SEM image of a 600-nm-period gold nanoslit array. Reprinted with permission from [35]. Copyright 2009 Optical Society of America.

Figure 4
Figure 4

(a) Conceptual diagram of the 2-D nanohole-array-based SPR sensor. The input and output polarization states of a tunable laser are controlled, providing variable spectral or angular Fano-type profiles. A microfluidic channel is used to transport the analyte fluid to the surface of the sensing area and can be used to control the refractive index on the metal–dielectric interface to tune the SPP resonance frequency. Also shown is a scanning electron microscopy image of a representative sample. (b) Normalized transmission as a function of panel (a) energy (wavelength). Reprinted with permission from [20]. Copyright 2006 Optical Society of America.

Figure 5
Figure 5

(a) SEM image of a 16×16 nanohole array with a 200 nm hole size and 380 nm periodicity. (b) A bright-field microscope image of a 5×3 microarray of nanohole arrays (partially shown). Each sensing element, a 16×16 nanohole array as in (a), is separated by 50 μm. (c) The PDMS chip is shown with microfluidic flow cells and tubing. Reprinted with permission from [22]. Copyright 2008 Optical Society of America.

Figure 6
Figure 6

Flow-through nanohole arrays. (a) Schematic of the optical and fluidic test setup employed for both fluorescence tests and transmission spectroscopy. (b) Comparison of response to surface adsorption achieved with flow-over and flow-through formats as indicated in the inset. Measured peak shift (625 nm peak) is plotted as a function of time during flow through/over of an ethanol/MUA solution. As indicated in the inset, the flow-through sensor is operated with flow from the nonparticipating silicon nitride side to the active gold surface. The flow-through case results in a characteristic rate constant of kabs) 3.8×102  min1 as compared to kabs) 6.4×103  min1 for the flow-over case. Adapted with permission from Eftekhari et al., Anal. Chem. 81, 4308–4311 (2009) [26]. Copyright 2009 American Chemical Society.

Figure 7
Figure 7

(a) Real picture of the portable biosensing device, weighing 60 g and 7.5 cm tall, designed for point-of-care applications. In the picture, the hand of the author highlights the compactness of the device. Reprinted by permission from Macmillan Publishers Ltd.: Cetin et al., Light: Sci. Appl. 3, e122 (2014) [59]. Copyright 2014. (b) A prototype miniaturized nPLEX imaging system developed for multiplexed and high throughput analysis of exosomes. The system uses a CMOS imager to record the transmitted light intensity from an nPLEX chip. Reprinted by permission from Macmillan Publishers Ltd.: Im et al., Nat. Biotechnol. 32, 490–495 (2014) [62]. Copyright 2014.

Figure 8
Figure 8

(a) Example of antibody O4 binding to the surface of a live immature rat oligodendrocyte. (b) SPR kinetic curves for IgM autoantibodies binding to supported lipid bilayers (SLBs). (a) O4 binding to SLBs containing 2% Sulf. Reprinted with permission from Wittenberg et al., Anal. Chem. 84, 6031–6039 (2012) [63]. Copyright 2012 American Chemical Society. (c) SEM indicates specific exosome capture by functionalized nPLEX. (d) Putative ovarian cancer markers (EpCAM, CD24, CA19-9, CLDN3, CA-125, MUC18, EGFR, HER2), immune host cell markers (CD41, CD45) and a mesothelial marker (D2-40) were profiled on exosomes [(b), using an nPLEX sensor]. Reprinted by permission from Macmillan Publishers Ltd.: Im et al., Nat. Biotechnol. 32, 490–495 (2014) [62]. Copyright 2014.

Figure 9
Figure 9

(a) Definition of the FWHM and depth of the resonant peak. (b) Definition of the different sensitivities used in this paper: bulk sensitivity (Sb) is relative to a change of refractive index in media 1 and 2, surface sensitivity Ss is relative to a change of refractive index in medium 1 only, and the layer sensitivity Sl is relative to a change of refractive index occurring in a layer of thickness L at the surface of the structure. These sections define the volume of the field integral involved in Eq. (3).

Figure 10
Figure 10

Schematic representation of a unit cell of a periodic nanoslit (or square nanohole) array.

Figure 11
Figure 11

Electric field definition for each medium of the structure. Tangential parts of the fields are contained in the bracket factor. The fields in regions 1 and 3 are represented as a sum of diffracted plane waves, while in region 2 the fields are given by the waveguide mode, which depends on the geometry.

Figure 12
Figure 12

(a) Electric field inside a PEC and a real metal waveguide. (b) Principle of the effective index method for rectangular waveguides, which are separated into the modes of two parallel plate waveguides. The propagation constant of the TM modes of the first waveguide is introduced as an effective dielectric constant εeff=β1/kw into the TE modes of the second waveguide.

Figure 13
Figure 13

Schematic representation of a nanoslit array.

Figure 14
Figure 14

(a) Transmission spectra of nanoslit arrays obtained using the model based on CMT (black line) and a numerical simulation using the FEM (red dotted line) for a period of 0.55 μm with slit size a=0.1  μm for three different thicknesses. (b) Dispersion relation of a slit array with parameters d=0.55  μm, a=0.1  μm, and h=0.4  μm. The red lines correspond to the ZOA dispersion relation given by Eq. (44) for the symmetrical and asymmetrical cases. The black lines are resonance conditions given by Eq. (42).

Figure 15
Figure 15

(a) Sensitivity and (b) FWHM of the slit array obtained using CMT as a function of period with slit width a=0.2d and thickness h=0.2d. The sensitivity equation given by the ZOA of Eq. (46) is given by the dashed black lines.

Figure 16
Figure 16

(a) Transmission spectra and (b) reflection coefficient for a nanoslit array of period d=0.45  μm and thickness 0.2 μm for three different slit widths.

Figure 17
Figure 17

Resolution of the array [Eq. (2)] for three different cases. 1. (Solid black line): the slit width and thickness (a=0.4h=0.2d) are kept proportional to the period. 2. (Red dashed line): thickness is kept proportional (h=0.4d) while slit width is constant (a=0.1  μm). 3. (Blue dashed–dotted line): slit width is kept proportional to the period (a=0.2d) while the thickness is kept constant (h=0.2  μm).

Figure 18
Figure 18

(a) Electric fields norm |E| obtained using CMT for a nanoslit of period d=0.55  μm, slit width a=0.1  μm, and thickness h=0.2  μm. (b) Fields in regions 1–3 given by the diffraction orders (+1), (+2), and (+3) and fields inside the slit for TM modes 0, 2, and 4. These last three graphs have been cropped for improved visualization.

Figure 19
Figure 19

(a) Transmission spectra for slit period 0.55 μm and slit opening a=0.1  μm with three different thicknesses and different refractive indices for the different regions. The red line corresponds to a refractive index of 1.33 for all regions. The black dashed lines are the transmission with a change of refractive index to 1.43 for the surfaces of the slit only. The black line represents the shift for a change of refractive index in all regions. (b) (Black line): percentage of the shift in the resonance peak position due to the change of refractive index at the surface as a function of thickness. (Red dashed line): field integral percentage of the field contained on the surface of the array.

Figure 20
Figure 20

(a) Transmission spectra of nanoslit arrays obtained using CMT for period of 0.55 μm with slit size a=0.1  μm with gold as the metallic layer (black lines) for three different thicknesses. The red dashed lines correspond to numerical simulations using FEM. (b) Dispersion relation of nanoslit array of dimensions d=0.55  μm, h=0.4  μm, and a=0.1  μm. The red lines are the dispersion relation obtained under the ZOA [Eq. (50)]. The black lines are resonance conditions given by Eq. (42). The red dashed line corresponds to the dispersion of an SPP on a flat surface, and coincides with Wood’s anomaly following Eq. (48).

Figure 21
Figure 21

Sensitivity of the nanoslit array as a function of period for a slit width of 0.2d and thickness 0.2d. The black line accounts for the total sensitivity (change of refractive index in all regions) and the black dashed-dotted line for bulk sensitivity only (change if refractive index in region 1–2 only). The red dashed curve represents λ/n.

Figure 22
Figure 22

(a) Transmission spectrum and (b) reflection coefficients as a function of wavelength for a nanoslit array of period 0.45 μm and thickness 0.2 μm for three different slit widths.

Figure 23
Figure 23

Real and imaginary values of the propagation constant as a function of wavelength for a nanoslit array of period 0.45 μm and thickness 0.2 μm for three different slit widths. The dashed line corresponds to the value for a PEC of width a=0.025  μm.

Figure 24
Figure 24

(a) Resolution of the array at the optimal thickness and slit width. Inset: resolution as a function of slit width and array thickness for a period of 0.7 μm. (b) Optimal thickness and slit width as functions of the period.

Figure 25
Figure 25

(a) Electric field norm |E| for a nanoslit array of period 0.55 μm and slit opening 0.1 μm for three different thicknesses: h=0.1  μm, 0.2 μm, and 0.4 μm. (b) Field percentage contained within a layer of thickness L on the top surface of the array for three different thickness of the metal film considered. The dashed lines correspond to the field percentage for the whole surface.

Figure 26
Figure 26

(a) Transmission spectra obtained with CMT for a nanoslit array of period 0.55 μm and slit width 0.1 μm for three different thicknesses with the refractive index of glass (n3=1.51) for region 3. The dashed red line is the result obtained with numerical simulation based on FEM. (b) Dispersion relation for a nanoslit array of dimensions d=0.55  μm, a=0.1  μm, and h=0.4  μm with gold as the metal and glass as the substrate. The black line corresponds to the resonance condition given by Eq. (42). The red dashed lines correspond to the dispersion of SPPs on a flat surface with the indices of regions 1 and 3, and coincide with Wood’s anomaly following Eq. (48).

Figure 27
Figure 27

(a) Bulk sensitivity as a function of period of a nanoslit array with gold as the metal for the case of matching refractive index (solid black line) and glass as the substrate (dashed red line) for a slit array of thickness 0.4d and slit width 0.2d. (b) Reflection coefficient product ρ21 and ρ23 as a function of wavelength for a slit array of period d=0.55  μm, slit width a=0.2d, and thickness h=0.4d.

Figure 28
Figure 28

(a) Resolution of the array at the optimal thickness and slit width. Inset: resolution as a function of slit width and array thickness for a period of 0.7 μm. (b) Thickness and slit width that gave the optimal resolution.

Figure 29
Figure 29

(a) Electric field norm |E| for a nanoslit array of period 0.45 μm and slit opening 0.1 μm for three different thicknesses: h=0.1  μm, 0.2 μm, and 0.4 μm with glass as a substrate. (b) Field percentage contained within a layer of thickness L on the top surface of the array for three different metal film thicknesses considered.

Figure 30
Figure 30

Schematic representation of a square nanohole array.

Figure 31
Figure 31

(a) Transmission spectra of square nanohole arrays obtained using CMT (black lines) for period of 0.55 μm with hole size a=0.20  μm for three different thicknesses. The red dashed lines correspond to numerical results obtained using FEM. (b) Dispersion relation of a square hole array with parameters d=0.55  μm, a=0.25  μm, and h=0.075  μm. The red lines correspond to the ZOA dispersion relation given by Eq. (54). The black lines are resonance conditions given by Eq. (51).

Figure 32
Figure 32

(a) Sensitivity and (b) FWHM of the square nanohole array obtained as a function of period with constant opening of the slit a=0.45d and thickness h=0.2d. The sensitivity equation given by the ZOA of Eq. (46) is given by the dashed black lines.

Figure 33
Figure 33

(a) Transmission spectra and (b) reflection coefficient for a square hole array of period d=0.55  μm and thickness h=0.075  μm for three different hole sizes.

Figure 34
Figure 34

(a) Resolution of the square hole array [Eq. (2)] for three different cases. 1. (Black line): the hole size and thickness a=0.5h=0.25d are kept proportional to the period. 2. (Red dashed line): thickness is kept proportional h=0.25d while the hole size is constant a=0.1  μm. 3. (Blue dashed–dotted line): hole size is kept proportional to the period a=0.5d while the thickness is kept constant h=0.2  μm.

Figure 35
Figure 35

(a) Electric field norm |E|2 at plane coordinate Y=0 of a square hole array of period 0.55 μm, thickness h=0.075μ, and hole width a=0.225  μm. (b) Fields at the upper interface of the hole (Z=h/2). (c) Fields inside the hole (Z=0) that correspond to the summation of rectangular waveguide TM and TE modes.

Figure 36
Figure 36

(a) Transmission spectra for a square nanohole array of period d = 0.55 μm and slit opening a=0.2  μm for three different thicknesses and different refractive indices for the different regions. Black line is for a refractive index of 1.33 for all regions. The red line represents the shift for a change of refractive index in all regions, while the black dashed line is for a change at the surface of the holes only (region 1 and 3). (b) Black line: percentage of the shift in resonance peak position due to the change of refractive index at the surface as a function of thickness. Red dashed line: field integral percentage of the field contained on the surface of the array.

Figure 37
Figure 37

(a) Transmission spectra of square nanohole arrays obtained using CMT for period of 0.55 μm with hole size a=0.2  μm for the case of gold (black lines). Results of FEM simulation are plotted in red dashed lines. (b) Dispersion relation of nanoslit array of dimensions d=0.55  μm, h=0.075  μm, and a=0.2  μm. The red dashed line is the dispersion relation obtained using the ZOA [Eq. (50)]. The black lines are resonance conditions given by Eq. (51). The red dashed line corresponds to the dispersion of an SPP on a flat surface, and coincides with Wood’s anomaly following Eq. (48).

Figure 38
Figure 38

Sensitivity (black line) of a square hole array as a function of period for a hole size of a=0.35d and thickness, and comparison with the perfect conductor case equation λr/n (red dashed line) and the SPP sensitivity for a flat surface (blue dotted line). The bulk sensitivity, corresponding to a change of refractive index in regions 1 and 2 only is shown by the black dashed–dotted line.

Figure 39
Figure 39

(a) Transmission spectra and (b) reflection coefficients for a gold square hole array of period 0.55 μm and thickness h=0.150  μm for three different hole widths.

Figure 40
Figure 40

Imaginary and real components of the propagation vector inside the holes for three different hole widths. These values are compared with the propagation constant of a square hole of 0.225 μm for a PEC (magenta).

Figure 41
Figure 41

(a) Resolution of the square hole array at optimal thickness and hole size as a function of the period of the array for the case of a matching index substrate. Inset: resolution of the array as a function of hole size and thickness for a periodicity of d=0.45  μm. (b) Value of the optimal thickness and hole width for each period of the square hole array.

Figure 42
Figure 42

(a) Electric field norm |E| for a nanosquare hole array of period 0.55 μm and hole opening 0.225 μm for three different thicknesses: h=0.075  μm, 0.15 μm, and 0.3 μm, with an index-matching substrate. (b) Field percentage contained within a layer of thickness L on the top surface of the array for three different thicknesses of the metal film considered.

Figure 43
Figure 43

(a) Transmission spectra of square nanohole array with a glass substrate obtained using CMT. The period is 0.55 μm with hole size of a=0.2  μm, and the case of gold (black lines) is plotted. The red dashed lines correspond to numerical calculation made using FEM. (b) Dispersion relation of nanoslit array of dimensions d=0.55  μm, h=0.1  μm, and a=0.20  μm with glass as the substrate. The black line is the resonance condition given by Eq. (51). The red dashed lines correspond to the dispersion of an SPP on a flat surface (on interface 1 and 2), and coincide with Wood’s anomaly following Eq. (48).

Figure 44
Figure 44

Bulk sensitivity (black line) of square hole array as a function of the period for a hole size of a=0.3d and thickness of h=0.25d. The values are compared to the sensitivity of a PEC given by λ/n (red dashed line) and the sensitivity of a SPP on a flat surface (blue dotted line)

Figure 45
Figure 45

(a) Resolution of the square hole array at optimal thickness and hole size as a function of the period of the array for the case of a glass substrate. Inset: resolution measurements as a function of hole size and metal thickness for period d=0.7  μm. (b) Optimal values of the thickness and hole size for each period considered.

Figure 46
Figure 46

(a) Electric field norm |E| for a nanosquare hole array of period 0.55 μm and hole opening 0.2 μm for three different thicknesses: h=0.075  μm, 0.15 μm, and 0.3 μm with glass as the substrate. (b) Field percentage contained within a layer of thickness L on the top surface of the array for three different thicknesses of the metal film considered.

Tables (1)

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Table 1. Sensitivity and Resolution of Nanohole Arrays

Equations (57)

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Sensitivity=dλrdn.
Resolution=FWHMsensitivity·depth.
ω˜ω0˜ω0˜ΔεE02dVεE02dV,
|ko=Ckeik0rx^|k=[Ckxx^+Ckyy^]eikr.
k=(kwsinθ+mx2πd)x^
k=(kwsinθ+mx2πd)x^+my2πdy^
|α=Cαacos(bπa(x+a2))x^,
qzα=kw2ε2(bπ/a)2.
|α=Cα[Cqxsin(qy(y+a2))cos(qx(x+a2))x^+Cqysin(qx(x+a2))cos(qy(y+a2))y^],
qz=(n2kw)2(bxπa)2(byπa)2
tanh(a2qz2kw2ε2ibπ2)+ε2qz2kw2εmεmqz2kw2ε2=0.
qz=kwε2(1+2kwεm1+εdεm).
|α=Cαcos(qxx+bπ/2)x^,
Cαc=2qxaqx+sin(aqx/2)cos(πb),Cαs=2qxaqxsin(aqx/2)cos(πb),
coth(a2qz2kw2εeffbyiπ2)+qz2kw2εmqz2kw2εeff=0.
qz=kwεeff(λ2a)2,
|α=[CqxCαccos(qxx+bxπ2)Cαssin(qyy+byπ2)x^+CqxCαssin(qxx+bxπ2)Cαccos(qyy+byπ2)y^].
k|α=Ic(b)=CαcCkcos(bπ/2)[2bsin(ab/2)cos(ak/2)2kcos(ab/2)sin(ak/2)b2k2],
k|α=Is(b)=CαsCksin(bπ/2)[2iksin(ab/2)cos(ak/2)2bcos(ab/2)sin(ak/2)b2k2]
k|α=[CqxIc(bx)Is(by)+CqyIs(bx)Ic(by)],
E=zsH×n^z,
(Gααfαfk++Yα)τα12+αβGαβfβfk+τβ12=iYk0fk0+k0|α,
ρk12=δk0,σ0fk0fk0++αk|ατα12fαfk,
(Gγγfαfk++Yγ)ραγ23+βγGαβfαfk+ραβ23=YγδγαGγαfα+fk+,
τ23=αk|αfα+fk++βk|βfαfk+αραβ23,
Gαβ=kYkk|αβ|k
τ012=2Yk0fk0+k0|0G00f0fk++Y0,ρk12=δk0,σ0fk0fk0++k|0τ012f0fk,
ρ0023=Y0G00fα+fk+G00f0f0++Y0,τk23=k|0fα+fk++k|0f0fk+ρ0023.
l(α,β)=ρβα23eiqzαhραβ21eiqzβh.
tk=ατα12τα,k23eiqzαh(1+Mα),
Mα=Vαin[ITα]1Vαout,
Vαin=[l(α,α)l(α,β)],Tα=[aααααl(α,α)aαααβl(α,β)aαββαl(β,α)aααββl(β,β)],Vαout=[b(α,α)b(α,β)]T.
rk=ρk12+αβτα12eiqzαhρα,β23eiqzβhτβ,k21(1+Mα).
T=|t|2,R=|r|2.
Bβ=ατα12eiqzαhρα,β23eiqzβh/2(1+Mα),Aα=βτα12eiqzαh/2(1+Mβ).
t=τ12τk23eiqzαh1ρ21ρ23e2iqzαh.
k=kwεmnd2εm+nd2,
k||2c2=ω2+1ωpl2ω264a4w4π4d4,
G=n2icot(qzh/2),
G=n2itan(qzh/2),
kz=0.
T=|t|=11+4R(1R)2ei(θ+2qzh),
θ+2qzh=2π.
βs=kwns1+S04cot2(qzh/2)ns2nh2,
βa=kwns1+S04tan2(qzh/2)ns2nh2,
λr=nd1+S04tan2(qzh/2).
S=dλdn=λrn.
R=|ρ|2=|YαG|2|Yα+G|2,
kz+zskwns2=0.
βa=nskw1ns2(itan(qzh/2)S02/Yα+zs(S021))2,
βs=nskw1ns2(icot(qzh/2)S02/Yαzs(S021))2.
|ρ12||ρ23|=1/e2|qx|h.
S0=22aπd.
qz=(kwn2)2(π/a)2.
βs=kwn1+S04tan2(ϕ)kw2n2(kwn)2(π/a)2,βa=kwn1+S04cot2(ϕ)kw2n2(kwn)2(π/a)2.
λr=dn1+S04tan2(ϕ)kw2n2(kwn)2(π/a)2.
S=dλrdn=λrn.

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