Boosting Optical Nanocavity Coupling by Retardation Matching to Dark Modes Rohit Chikkaraddy1 Junyang Huang1 Dean Kos1 Eoin Elliott1 Marlous Kamp1 Chenyang

2025-05-08 3 0 1.87MB 16 页 10玖币

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Boosting Optical Nanocavity Coupling

by Retardation Matching to Dark Modes

Rohit Chikkaraddy1†, Junyang Huang1, Dean Kos1, Eoin Elliott1, Marlous Kamp1, Chenyang

Guo1, Jeremy J. Baumberg1*, Bart de Nijs1*

1 NanoPhotonics Centre, Cavendish Laboratory, Department of Physics, JJ Thompson Avenue, University of

Cambridge, Cambridge, CB3 0HE, United Kingdom

Abstract

Plasmonic nano-antennas can focus light to nanometre length-scales providing intense field

enhancements. For the tightest optical confinements (0.5-5 nm) achieved in plasmonic gaps, the gap

spacing, refractive index, and facet width play a dominant role in determining the optical properties

making tuning through antenna shape challenging. We show here that controlling the surrounding

refractive index instead allows both efficient frequency tuning and enhanced in/output-coupling

through retardation matching as this allows dark modes to become optically active, improving

widespread functionalities.

Keywords: plasmonics, nanocavity, impedance matching, dark modes, SERS

1. Introduction

Plasmonic nano-constructs with nanometre gaps confine light far below the diffraction limit, with

potential applications in single-molecule sensing1, adatom-catalysis2, room temperature quantum

optics3–5, and photon harvesting.2,6,7 Nanoconstructs which incorporate plasmonic nanogaps8 yield

some of the highest9 and most reproducible10,11 field enhancements. Strong optical interactions with

the metal surfaces slow down light in tightly confined modes, giving effective refractive indices  

, dependent on the gap thickness , refractive index , and metal permittivity.8 Inconveniently for

applications, the tightest confined modes emit at high angles () to the nanogap normal, leading to

poor in/out-coupling.12 As a result, net optical efficiencies of most nanocavity processes are ripe for

enhancement,21 essential for transitioning nascent technologies into practical applications.

While plasmonic nano-gaps support a few bright nanocavity modes, many modes are dark and only

accessible via the near-field.13–20 Making these bright and accessible at near normal incidence (=0),

would greatly improve optical access as it provides more operational frequencies and scattering

angles, but how to do so is poorly understood and difficult to achieve. Plasmon resonances tune with

the surrounding refractive index ,21–28 although antenna size, metal, and shape are more commonly

employed to tune plasmon resonances instead as these effects have been well characterised and

documented. Here, by mapping how  enhances specific plasmonic nanocavity mode coupling, we

highlight improvements beyond simple wavelength shifts. We attribute this coupling enhancement to

improved retardation matching between the slow light of the plasmon and retardation from the high

refractive index surrounding medium. Finite-difference time-domain (FDTD) modelling matches

comprehensive experimental characterisation of plasmonic nanogap constructs coated in a range of

dielectric media of different refractive index. We show how modes shift across the visible, and how

dark antisymmetric modes become optically active. These amplified dark modes couple to the far field

over a much wider angular range, and critically are experimentally more accessible.

2. Results and discussion

To robustly form identical plasmonic nanogap constructs, a nanoparticle-on-mirror (NPoM) construct

is used where a flat Au surface is coated with a molecular self-assembled monolayer (SAM) to form a

uniform spacer layer, here biphenyl-4-thiol (BPT) creating a 1.3 nm thick spacer.29 Colloidal =80nm

Au nanoparticles (AuNPs) are then deposited on top, forming a NPoM construct of high

reproducibility.11 The optical hotspot in such nanogaps reaches intensity enhancements of 106 and

supports a set of optical modes dependent on facet size, shape, polarisation, and gap.30

Figure. 1. (a) Left: NPoM geometry in air (=1.0) on a Au surface with thin dielectric spacer (1.3 nm, =1.45),

right: NPoM embedded in =1.5 dielectric layer of increasing height . (b) FDTD-simulated near-fields of four

lowest energy modes in nanocavity, just above the mirror. (c,d) Effect of dielectric layer height () on the gap

modes under (c) high-angle and (d) normal-incidence illumination.

Full-wave FDTD simulations of these NPoMs truncate the NP to form a 20 nm circular bottom facet,

capturing the faceting of colloidal gold nanoparticles (Figure 1a: left).31 The plasmonic cavity formed

between the AuNP and mirror supports a set of optical modes with the four lowest labelled

(,,,).30 These display characteristic field distributions (Figure 1b), with symmetric ‘even’

modes (,  ) and antisymmetric ‘odd’ modes (,; denoted as 1).30,32 In air

(=1), the even modes dominantly contribute to the far-field optical properties, whilst the odd

modes are non-radiative (dark) and absent from the scattering spectrum. Introducing a high refractive

index medium around the metal slows down the incident light, introducing a phase delay between

antenna (NP top) and nanocavity (NP bottom), which matches the confined plasmons. Our simulations

show that increasing the =1.5 dielectric film height () around the constructs shifts the even modes

towards the infrared (Figure 1c) whilst the odd modes steadily become more radiative, as evidenced

in scattering intensities (Figure 1d). The scattering strength of () mode is comparable to scattering

intensities of () mode for >80nm, indicating efficient coupling to () at normal incidence in

contrast with high angle coupling to () mode.

Figure. 2. (a) Scheme depicting two regions of dielectric layer height. (b) Tuning of resonance peak wavelengths

extracted from scattering (solid lines) and near-field (dotted lines) spectra for each mode vs . (c) Near-field

enhancement (/) at spectral peaks of each mode vs . (d) Near field enhancement vs refractive index of

embedding dielectric material. (e) Optical field  (out of page) around NPoM for odd modes ( , )

embedded in dielectric coating of =1.5, =100 nm.

The nanoparticle’s optical properties change most strongly when a film intersects with the spill-out

field of the gap and the nearfield of the nanoparticle, Figure 2a region I), and saturates for   

(region II). This is clearly observed in both near-field and scattering resonance wavelengths

(Figure 2b,c). Upon embedding, the nearfield of odd modes is enhanced more than the even modes

(Figure 2d), with () increasing by 250% and () by 100% compared to 30% for () and 10% for

() modes (Figure S1a). Using fully embedded geometries (=100 nm) and instead increasing 

shows the nearfield of the radiative (10) mode decreases (Figure 2d), primarily as its red-shifting

resonance is less well confined within the nanogap. The nearfield of the non-radiative () mode

however greatly increases because of improved in-coupling, becoming comparable to the

fundamental () mode at =1.8. For (,) strongest nearfields are observed near =1.4 from the

two competing effects. The larger field spill-out of the NP facet for odd modes is visualised from the

magnetic field,  (Figure 2e). The resonance shifts, increase in scattering intensities and near-field

enhancements clearly highlight the importance of refractive index from the surrounding medium in

determining the optical properties of plasmonic nanogap constructs.

To evidence these changes experimentally, NPoM geometries are prepared with a range of different

refractive index coatings (Figure 3). Dielectric layers 100 nm thick with refractive index =1.49, 1.59

or 1.78 are spin-coated onto the NPoMs described above. Averaged dark-field (DF) spectra (Figure 3a)

of many hundred NPoMs show how the plasmonic modes evolve with increasing refractive index. The

scattering intensity from polymer-coated NPoM nano-antennas is over three-fold brighter than

NPoMs in air (=1), due to the improved in-/out-coupling of light. Upon coating, the dominant ()

mode visible at 810 nm in air disappears (red shifting out of the detection range) and higher-order

modes red shift and increase in intensity. Extracting the dominant peak position for each refractive

index (Figure 3b) shows higher-order modes at 650 nm, 695 nm, 710 nm for =1.49, 1.59, 1.78

respectively.

Figure 3. (a) Experimental dark-field (DF) scattering spectra for NPoMs (=80 nm, 1.3 nm spacer) inside

progressively higher refractive index coatings (= 1.0, 1.49, 1.59, 1.78), note =1.0 multiplied 3x for visibility.

Black line is average of 1550, 313, 438, 2235 NPoMs respectively, 50% confidence interval in grey. Insets: average

DF scattering images. (b) Relative occurrence of main DF visible spectral peak, which red-shifts with increasing

refractive index. The () mode at =1.0 redshifts outside the detection range (>900 nm) for ≥1.2.

Figure 4. (a) Calculated DF scattering spectra in dielectric media of refractive indices = 1.0-1.8 showing

increasing redshifts. Simulations use two different illumination conditions: (top) high-angle with   mirror

surface, and (bottom) normal illumination. Insets show ,  directions. (b) Experimental DF scattering spectra

for =1.0, 1.49, 1.59, 1.78 using unpolarised illumination at high angles. Spectra separated into optical modes

using multi-Gaussian fit, assigned to different modes. (c) Extracted (solid) and modelled (open) peak positions

vs surrounding refractive index. (d) Angle-resolved DF scattering spectroscopy of NPoMs shows high angles

dominate for =1.0 (top), but low angles dominate for =1.59 (bottom).

Modelling the effect of refractive index on the fully embedded NPoMs (>100 nm) reproduces the

redshifts and rise in scattering intensity of all modes with increasing  (Figure 4a). Comparing the

simulations with experimental DF spectra (Figure 4b) enables assignment of the dominant modes,

(): red, (): yellow, with the satellite peaks tentatively assigned to (,). The peak positions of

these modes are in agreement with predictions (Figure 4c), except for =1.49 where all peaks are

blue shifted (possibly due to coating morphology under NPs). We note that simulations here also do

not capture variations in nanoparticle facet shape, which further breaks the degeneracy of (1)

modes.30,33

The simulations predict a significant increase in scattering intensity from the initially-dark odd modes,

which emerge as satellite peaks in the DF spectra (Figure 4b,c). The modes can be distinguished by

characterising their different out-coupling angles. Even modes (with vertical dipoles) should emit at

high angles, and dominate radiation for =1.0 when separating high-angle (emitted flux at = 55-

64°) from low-angle (= 0-10°) scattering in -space spectroscopy (Figure 4d:top, Figure S3a).34 In

contrast, for =1.59, nearly equal radiant intensities are simulated for low and high collection angles

(Figure 4d:bottom, Figure S3b). This confirms that out-coupling from high-index coated NPoMs is at

lower angles, yielding high collection efficiencies even in low numerical aperture systems.

Modelling the scattering from different incident angles (Figure 5) shows that even NPoM modes

(which dominate for =1.0) only accept incident light above 45°, whereas odd modes couple to

incident light at angles from 0-60° (Figure 5b). Increasing the efficiency of the latter modes is thus

critical as most incident light arrives at angles <45°, even for a high NA illumination, as illustrated for

a collimated Gaussian beam over-filling the back-aperture of a 0.9 NA objective (Figure 5a, ‘laser

irradiation’). The angular scattering of DF light from NPoMs is experimentally measured using -space

imaging on =1.0 and 1.59 samples (Figure 5c, see supporting information note 3, Figure S3 for

details). At =1 NPoMs scatter near 60° as predicted, while =1.59 coated NPoMs scatter over a

wide angular range between 0-55°. This confirms that odd modes dominate emission when NPoMs

are embedded in higher refractive index surroundings.

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BoostingOpticalNanocavityCouplingbyRetardationMatchingtoDarkModesRohitChikkaraddy1†,JunyangHuang1,DeanKos1,EoinElliott1,MarlousKamp1,ChenyangGuo1,JeremyJ.Baumberg1*,BartdeNijs1*1NanoPhotonicsCentre,CavendishLaboratory,DepartmentofPhysics,JJThompsonAvenue,UniversityofCambridge,Cambridge,CB30HE,United...

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Boosting Optical Nanocavity Coupling by Retardation Matching to Dark Modes Rohit Chikkaraddy1 Junyang Huang1 Dean Kos1 Eoin Elliott1 Marlous Kamp1 Chenyang

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