Emission Rate Modi cation and Quantum E ciency Enhancement of

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Emission Rate Modification and Quantum Efficiency Enhancement of Er3+ Emitters by Near-Field Coupling with Nanohole Arrays Niccolò T. Michieli, Boris Kalinic, Carlo Scian, Tiziana Cesca, and Giovanni Mattei ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00042 • Publication Date (Web): 22 Apr 2018 Downloaded from http://pubs.acs.org on April 22, 2018

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ACS Photonics

Emission Rate Modication and Quantum Eciency Enhancement of Er3+ Emitters by Near-Field Coupling with Nanohole Arrays Niccolò Michieli,

∗

Boris Kalinic, Carlo Scian, Tiziana Cesca,

∗

and Giovanni Mattei

Department of Physics and Astronomy, University of Padova, via Marzolo 8, I-35131 Padova, Italy. E-mail: [email protected]; [email protected]

Abstract The control of the spontaneous emission properties of quantum emitters with limited losses by near-eld coupling with plasmons-supporting nanostructures is one of the keys for next-generation high-eciency and high-coherence plasmonic devices. In the present work, gold nanohole arrays are demonstrated to be an eective plasmonic system for controlling radiative rate and quantum eciency of the 1540 nm emission of Er3+ ions embedded in silica. Finite elements method electrodynamic simulations were used to describe the interaction between dipolar Er3+ emitters and the nanohole arrays. The results are in agreement with those of photoluminescence measurements performed in dierent coupling congurations. Particularly, we demonstrated that owing to the combination of strong emission enhancement and low level of ohmic losses in the metal, nanohole arrays are able to enhance the far-eld photons yield up to 74%. This in turn is related to an extremely high far-eld quantum eciency: more than 90% of the emitted photons reach the far-eld for the most ecient congurations investigated in

1

ACS Paragon Plus Environment

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which the extraordinary optical transmission peak of the nanohole array is matched with the Er3+ emission.

Keywords Finite Elements Method, Emission Rate Modication, Quantum Eciency Enhancement, Erbium Luminescence, Nanohole Arrays

In the last years the huge advances in micro- and nano-fabrication techniques opened the route to a ner and ner control of the interaction of light with nano-conned modes, such as plasmons.

1

Enhancing and manipulating light-matter interaction at the nanoscale is in turn

the key to improve the performances of nanodevices for a wide range of applications, such as photovoltaics,

2,3

biosensing,

46

light emission,

7

nonlinear optics.

811

In this framework,

engineering the emission properties of quantum emitters by coupling them with localized photonic and plasmonic cavity modes is of particular importance and interest. dates back to the pioneering work by Purcell,

12

The idea

who demonstrated that the presence of con-

ned modes in an optical cavity modies the local density of optical states (LDOS) around an emitter, giving rise to a modication of its spontaneous emission properties. Two regimes of interaction have been recognized, the so-called

strong coupling

and

weak coupling

regimes.

In the rst one, the result of the interaction is that the modes of the emitter and the cavity get hybridized, forming together a quantum system. in various congurations, such as microcavities, mons,

16

or plasmonic nanocavities.

17

14

13

Strong coupling has been reported

graphene plasmons,

15

surface lattice plas-

In the weak coupling regime, instead, the emitter and

the cavity can be considered as separated systems and their interaction can promote a more eective light extraction, which can be described using classical electrodynamics, be done in the present work.

2


13

as it will

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Owing to their strong eld connement properties, plasmonic modes are the ideal candidates for enhancing the emission rate of nearby emitters,

18

but losses limit the overall

performances, at least in the simplest congurations. Ohmic losses are responsible for the poor performances achieved studying the interaction between emitters and localized plasmons (LSPR) supported by noble metals nanoparticles in which the increased interaction is compensated by the occurrence of losses at very short (nanometric) distances.

19

Propagat-

ing surface plasmon polaritons (PSPP) supported by a metal/dielectric planar interface are also known to be a candidate for the emission rate modication since the pioneering work by Drexhage

20

and the development of the analytical classical dipole oscillator model by Chance,

Prock and Silbey tal data.

21

(CPS model) that provided a good description of Drexhage's experimen-

However, despite the signicant emission rate increase that can be achieved by

the presence of a planar interface, a considerable part of the radiatively emitted energy is subsequently dissipated by lossy surface waves or by evanescent PSPPs that, in the absence of proper additional out-coupling mechanisms, are to be considered non-radiative modes for the far-eld.

22,23

Thus, the number of photons that reach the far-eld can be even lower than

in the case of emitters embedded in a homogeneous medium and the far-eld quantum eciency of the emitting system results seriously compromised. Since the increase of radiative decay rates - while limiting non-radiative processes - is the key for maximizing the irradiated energy,

2427

more complex systems have to be considered to overcome the limits of planar

interfaces. A rst step in this direction was carried out considering the eects of interfaces roughness in increasing the intensity and directivity of emission.

28

In the present work, a more features-rich PSPP-supporting system - the nanohole array (NHA)

29

- has been investigated. NHAs have been widely studied in recent years for their

extraordinary optical transmission (EOT) properties, which found interesting applications in biosensing

3033

and nanophotonics.

3437

On the other hand, probably due to the lack of both

analytical and phenomenological models, the NHA-emitter interaction has still to be deeply investigated and only a few works are present in the literature.

3


3843

Here we focused our

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interest on NHAs (compared to planar interfaces) coupled to emitters for two key aspects: (i) the PSPP modes can be modied by acting on the geometry of the lattice

45

44

and (ii) PSPPs

can directly couple to far-eld photons. As the emitting species, we focused this study on

3+ Er ions (embedded in a silica matrix) due to the technological importance of erbium as one of the doping elements of election in the eld of optical communication the realization of planar optical ampliers,

51,52

solid state lasers

53,54

4650

and to its role in

and light sources.

This is due to its sharp and temperature-stable luminescent emission peaked at 1.54 mathces the minimum absorption window for silica-based optical bers. to modify the decay rate of Er

3+

57,58

55,56

µm that

The possibility

ions was demonstrated exploiting the near-eld interaction

with metallic and dielectric lms,

59,60

while the control and amplication of the amount of

light irradiated in far-eld resulted more challenging with those approaches. Our rst goal in the present work is to provide a modeling strategy for the interaction of emitters with more complex nanostructures, which in principle can give more degrees of freedom for the control of the interaction. To this aim, nite elements method (FEM) electrodynamic simulations have been used to model the Er

3+

-NHA interaction. It is important to

point out, however, that the developed strategy is general and can be applied also to dierent nanostructures and/or emitters. The computed emission rates have been compared with the experimental results of photoluminescence measurements, obtaining a very good agreement and also demonstrating that the emission of each Er

3+

ion is not correlated with the others,

qualifying the studied system as a candidate for the development of quantum plasmonic devices. We then used the developed model to show that NHAs are able to provide a strong emission rate amplication while keeping at the same time a high quantum eciency. As a result, a net increment in the far-eld photons ux - i.e., the number of photons that reach the far-eld with respect to that obtained for emitters embedded in a homogeneous matrix was demonstrated (up to 36% enhancement for a homogeneous distribution of emitters and up to 74% for emitters distributions patterned to exploit the most ecient regions provided by the nanohole array). Correspondingly, very high far-eld photons eciencies have been

4


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ACS Photonics

determined for NHAs (larger than 90%, to be compared to about 60% for homogeneous thin lms).

Denitions Far-eld optical features of NHAs The nanostructure investigated in the present work is a nanohole array (NHA) made of an optically thick Au lm (thickness 120 nm) with a periodic (hexagonal) array of subwavelength (∼ 300 nm in diameter) holes, deposited on a silica substrate and covered by 200 nm of silica. Owing to their periodicity, NHAs support several Bloch modes. For this reason, rst we performed nite dierences time domain (FDTD) simulations to nd the band-structure of the investigated NHAs. In particular, we explored the First Brillouin Zone (FBZ) in the reciprocal lattice along the

Γ-M, M-K and K-Γ directions, to nd the dispersion

relation of Bloch modes. In Fig. 1a and 1b we reported the calculated dispersion law for two NHAs with lattice parameter

a0 = 1030

nm and

a0 = 1280

nm, respectively. In the graphs,

the modes are highlighted with yellow-red bands, whereas blue regions indicate the absence of modes. In both panels, the black horizontal line indicates the frequency corresponding to the Er

3+

parameter

emission line at

λP L = 1540

a0 = 1030 nm (Fig.

nm. At this frequency, for the NHA with lattice

1a), along with two modes in the middle of the

Γ-M and K-Γ

directions, a strong mode is present at the M point, which is non-propagating (dω/dk

= 0);

this mode corresponds to band-edge plasmons, as it will be shown shortly. Conversely, the

a0 = 1280

nm NHA has no band-edge modes at the Er

modes with non-zero group velocity (dω/dk

6= 0)

3+

emission frequency (Fig. 1b), but

exist in all the three considered directions.

For the two dierent NHA congurations we simulated the spectral position of the EOT resonance and its shape by nite elements method (FEM) simulations.

Fig.

1c shows

the comparison between the simulated and experimental transmittance spectra: a very good agreement was obtained for both congurations. The results show that the NHA with lattice

5


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parameter

a0 = 1030

emission wavelength. at

λP L = 1540

nm has the EOT peak at The NHA with

Page 6 of 38

λP L = 1540

a0 = 1280

nm, i.e., resonant with the Er

3+

nm, instead, has negligible transmission

nm and the EOT peak at longer wavelengths. Thus, we can conclude that

the band-edge mode visible in the band-structure of the

a0 = 1030

nm NHA (Fig. 1a) is

the plasmon mode responsible for the EOT. We can also note that, correspondingly, for the

a0 = 1280

nm NHA the EOT occurs at the frequency where the band-edge plasmon is

present in that structure (λ

∼ = 1880 nm).

Hereafter we named these two NHA congurations

as resonant (R) and non-resonant (NR), referring to the resonance between the EOT and the Er

3+

emission wavelength at

λP L = 1540

nm. In Figs. 1d and 1e we reported the SEM

images of the fabricated NHAs in the R and NR congurations, respectively. The measured holes radii are

rH = 300 ± 16

nm for the resonant NHA and

rH = 375 ± 23

nm for the

non-resonant one. Looking at the band-structure, we can conclude that an emitter placed close to the resonant NHA can be coupled to the strong band-edge mode and to a weaker propagating mode. In the Supporting Information (Fig.

S3), we reported the maps of eld distribution of

the electric eld component orthogonal to the NHA surface (Ez ) at both surfaces of the NHA (facing and opposite to the emitter), excited by a dipole oscillating orthogonally to the NHA surfaces: the eld modulation has the wave-vector corresponding to the band-edge mode. On the other hand, the non-resonant NHA oers four propagating modes for coupling with the Er

3+

emission. Thus, dierences between the two congurations can in principle

emerge from two main aspects: (i) each mode modies the LDOS in a dierent way, both in terms of amplitude and spatial localization; (ii) PSPPs excited by the incoming photons at the NHA surfaces couple dierently to far-eld light, as the conservation of momentum must be satised.

61,62

Moreover we want to emphasize that PSPPs-light coupling is certainly

fundamental for the explanation of the dierences between NHAs and homogenous lms, as the NHA periodicity behaves as a matching grating and enables the PSPPs re-irradiation. On the other hand, in the presence of thin homogeneous lms, PSPPs are always trapped

6


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ACS Photonics

at the interface and dissipated into ohmic losses in the metal in the absence of additional out-coupling schemes.

22,23

Coupling of Er3+ ions to NHAs To study the interaction between Er

3+

emitters and nanohole arrays, a layered system was

designed, as depicted in Fig. 2a. The substrate is a HSQ300 silica glass slab from Heraeus. On top of the substrate three layers with controlled thickness are considered: doped silica layer, with thickness

1) an Er-

TEr ; 2) a silica spacer layer, with thickness Tspc ; 3) the gold

nanohole array embedded in silica. The Er:SiO2 and the spacer layers have been deposited by means of a magnetron co-sputtering system (see Methods).

27,60

In addition to the high

control over both the lm thickness and the dopant concentration, the sputtering system oered the possibility to deposit the undoped silica layer (spacer) on top of the Er:SiO2 layer in a single process, thus nely tailoring the distance between the Er-doped layer and the sample surface. In the samples investigated in the present work the distribution of Er ions in the silica layer can be described by a box-like function with a plateau concentration of 1% at. and a thickness of

TEr = 20

nm. The thickness was chosen to be large enough

to get a suciently intense emission signal from the Er

3+

ions, and suciently small to

resolve the emission rate modication as a function of the emitters-nanostructure distance

z.

Three sets of samples were fabricated in which silica spacers of dierent thickness (Tspc )

were deposited. Correspondingly, the sets of samples were labelled as A20 (Er-doped layer centered at at

zc = 20 ± 2

zc = 40 ± 2

nm, obtained with

nm, obtained with

Tspc =10 ±

Tspc =30 ±

2 nm), A40 (Er-doped layer centered

2 nm) and A110 (Er-doped layer centered at

zc = 110 ± 2 nm, obtained with Tspc =100 ± 2 nm).

From each sample, three pieces were cut:

one was left as a reference, while the other two were used as substrates on which the gold

◦ NHAs in the two congurations were fabricated. Finally, an annealing at 900 C in vacuum for 2 hours was performed on the samples in order to obtain the Er activation.

60

7


3+

photoluminescence

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FEM simulations Finite elements method (FEM) electrodynamic simulations were carried out in the frequency domain. All the details about the modeled domains are reported in the Methods section. At rst, the simulations were run without gold (substituted by silica) in the NHA domain, to compute the emission resulting from an emitter embedded in a homogeneous silica layer. The total emitted power in this conguration, vector

~=S ~SiO2 S

W 0 , was calculated as the ux of the Poynting

on a closed spherical surface

Z

0

Σ,

placed very close to the dipole (5 nm):

~SiO2 · uˆ dσ. S

W =

(1)

Σ

Since in the case of a homogeneous silica layer there is no absorption within the simulated domains, it results

W 0 = Wf0f ,

Wf0f

where

is the power radiated into the far-eld.

Wf0f

is

calculated as the ux of the Poynting vector on the external boundaries of the model (before the PML), at a surface

5 λP L /n,

where

n

Σout

placed beyond the near-eld region (at a distance of about

is the refractive index of silica):

Wf0f

Z

~SiO2 · uˆ dσ = W 0 . S

=

(2)

Σout

W0

was then used for the normalization of the emitted power in the presence of the NHAs,

to get the change of the radiative decay rate of the emitter. radiative decay rate,

γr ,

We dene the normalized

as the ratio between the modied radiative decay rate

radiative decay rate in a homogeneous silica layer,

Γ0r

γ ).

and the

(in the following, we will follow the

convention that decay rates are indicated with capital letter, are indicated with lowercase letter,

Γr

Γ, while normalized decay rates

Since in a simulation in the frequency domain the

decay rates are proportional to the emitted power, for each conguration of the emitting dipole (in terms of polarization and position), the normalized decay rate was calculated as

8


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ACS Photonics

the ratio between

W

- the total emitted power for the considered conguration - and

W 0:

R ~ S · uˆ dσ Γr W Σ N HA ≡ γ = = . R r ~SiO2 · uˆ dσ Γ0r W0 S Σ

(3)

Moreover, since our simulations can give normalized decay rates only, to compare the simulated results with experimental data we used the denition of

γr

to compute

Γr = γr Γ0r .

The

3+ value of the radiative decay rate of Er ions in a homogeneous silica matrix was taken from the literature decay rate

γr

63

as

(and

Γ0r = 70 Γr ),

−1 s . It is worth noting that in the estimation of the radiative

all the radiative decay events are taken into account, including both

those where the emitted energy is absorbed in the near-eld and those where the power reaches the far-eld as photons.

Results and discussion Radiative decay rate modication Within the described framework, the radiative decay rate can be changed by acting on the following parameters: (i) the distance of the emitter from the interface, of the emitter in the

xy ˆ

plane with respect to the NHA lattice

the dipolar moment of the emitter (p ˆ

= xˆ, yˆ

or

zˆ).

(x, y);

For each position

z;

(ii) the position

(iii) the direction of

(x, y, z),

the average

of the three dipole orientations gives the normalized decay rate for a random distribution of orientations:

γr = γrxˆ + γryˆ + γrzˆ /3.

The corresponding radiative decay rate (Γr

then can be computed for each point. In this way, for each point cell, a decay rate prole

z

(xi , yj , z) in the elementary

Γr (z) as a function of the NHA-emitter distance z

Fig. 3a shows the decay rate proles

= γr Γ0r )

can be obtained.

Γr (xi , yj ; z) ≡ Γij r (z) as a function of the dipole distance

from the NHA (averaged over the three polarization orientations), computed for the 27

lattice positions

(xi , yj , z) in the elementary cell (inset), for the resonant NHA conguration.

The graph shows the dierences arising from nanostructuring the metallic (Au) layer as a

9


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NHA that interacts with the emitters, with respect to the eect of a continuous lm (blue dashed line): dierent radiative decay curves are obtained for the dierent positions of the emitter in the NHA lattice. Lighter curves (corresponding to sites under the metallic region of the NHA) are similar to what is obtained for a continuous lm. Darker curves (i.e., sites under the hole) show a dierent trend: close to the interface the decay rate converges to a nite value, unlike for the continuous lm case, and the starting point of the oscillatory behavior is shifted towards larger

z

distances. Thus, the eect is similar to the lm case for

dipoles under the metal. On the contrary, a more complex situation has to be considered when dipoles lie under the hole, particularly at short

z

distances. Deeper insights into this

behavior can be obtained by analyzing the details in the coupling of dipoles in dierent positions with respect to the NHA unit cell, as it will be presented in the following section. It is worth noting that the decay rate modication factors (Purcell factor) reported in g. 3 are lower than 10, except for dipoles very close to the metal (< values (>

103 )

10

nm). Since much higher

are in general expected for strong coupling regime, this result conrms that

our emitting system can be considered in a weak coupling regime.

Comparison with experimental data.

In order to compare the simulated data to the

experimental ndings, we computed the total photoluminescence signal of a box-like dipole distribution corresponding to the one present in the experimental samples following the approach adopted in Ref. decay rate

60

].

A dipole placed in the position

(xi , yj , z),

with simulated

Γij r (z), contributes to the total photoluminescence with a time-dependent intensity ij

I ij (z; t) = I0 e−tΓr (z) . function

[

f (xi , yj , z)

The total signal from a distribution of emitters described by the

is obtained by summing the signals over the

computational cell and by integrating in

I (t) = A

X ij

(x, y)

positions in the

z:

Z cij

+∞

ij

f (xi , yj , z) e−tΓr (z) dz,

0

10


(4)

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ACS Photonics

where the coecients

cij

are dimensionless weights used to account for the fact that the

points at the edges of the computational cell are shared by nearby cells (cij

cij = 41 for P A = I0 / ij cij

=1

inside the

cell,

cij =

1 for points on the edges, 2

the point in the bottom corners in Fig.2e,

and

cij =

1 for the top corner); 6

is a normalization factor. For the samples

investigated in the present work, the Er distribution is homogeneous in the has a box-like prole in the

zˆ

direction; thus

f = f (z)

depends on the

z

xy ˆ

plane, and

coordinate only

and to a good approximation can be described analytically by the characteristic function

f (z) = {

f0 , z∈[zmin ,zmax ] 0, z ∈[z / min ,zmax ] , where

zmin = zc −

depth, of the Er distribution and

I (t)

TEr

TEr and 2

TEr ; 2

zc

is the center, in

its thickness. The computed time-dependent signal

is then tted with a single exponential decay function

the eective decay rate of the distribution,

F EM

I (t) = I0 e−tΓr

ΓFr EM (zc ) obtained from the simulations of

20 nm-thick box-like distribution of Er ions and centered, in depth, at z = zc

Er concentration in the range

[zc − 10

to determine

ΓFr EM . 60

Fig. 3b shows the integrated radiative decay rate a

zmax = zc +

(i.e., constant

nm, zc +10 nm ]), for the resonant (blue curve) and non-

resonant (orange curve) NHAs, respectively. Dots indicate the corresponding experimental

EXP ) of samples A20, A40 and A110 with resonant (blue) and nonradiative decay rates (Γr resonant (orange) NHAs, determined as described in the following. experimentally measured normalized PL decay curves at

Figs.

λP L = 1540

3c,d report the

nm for the two sets

of samples with resonant (c) and non-resonant (d) NHAs. The Er ions were excited with a cw Ar laser at

λexc = 488

nm, that is resonant with the

4

I15/2 →4 F7/2

transition. PL measurements with out-of-resonance excitation at

3+ Er absorption

λout exc = 476.5

nm were also

performed to check that no energy-transfer mechanism occurs in the excitation of Er possibly due to the presence of the NHAs. this case. For in-resonance excitation at

4750

3+

ions,

As expected, no PL signal was detected in

λexc = 488

nm, instead, all the samples exhibited

a single exponential temporal decay that was tted with the function determine the total decay rate of the Er

3+

distribution,

ΓEXP .

I (t) = I0 e−tΓ

EXP

to

The radiative decay rate of the

emitters in the experimental samples was then determined by subtracting the non-radiative

11


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Page 12 of 38

F EM EXP ) radiative decay ) and simulated (Γr Table 1: Comparison between experimental (Γr rates, for the three samples, with resonant and non-resonant NHAs. For the simulated results, the indicated errors are the

±5%

condence bands as in Fig. 3b. The values of the

non-radiative decay rate (Γnr ) estimated from the analysis of the three reference samples are also reported. Reference Γnr (s−1 ) A20 (zc

= 20 nm) A40 (zc = 40 nm) A110 (zc = 110 nm) decay rate,

Γnr ,

51 73 57

± ± ±

5 5 5

Resonant NHA ΓFEM (s−1 ) r

ΓEXP (s−1 ) r 172 ± 9 102 ± 7 81 ± 6

132 99 85

to the total (measured) decay rate

± ± ±

7 5 4

Non-resonant NHA ΓFEM (s−1 ) r

ΓEXP (s−1 ) r 125 ± 8 82 ± 6 74 ± 5

136 87 76

7 4 4

ΓEXP : 60

ΓEXP = ΓEXP − Γnr . r

Γnr

± ± ±

(5)

was determined for each sample in the following way. Since due to the presence of the

spacer layer the radiative decay rate in the reference samples too is modied with respect to

Γ0r ,

we used the CPS model

decay rate was calculated as

21

to evaluate such modied

Γnr = Γref − Γref r ,

where

Γref

Γref r .

Then, the non-radiative

is the total decay rate in the

reference samples (obtained by PL measurements with the same approach described above to get

ΓEXP ).

The non-radiative decay rates obtained from the analysis of the three reference

samples are reported in Table 1. It is worth stressing that in the present case

Γnr

represents

the intrinsic non-radiative decay rate and it accounts for losses that occur in the near-eld of the emitters (at distances shorter than 1-2 nm), due for instance to the presence of matrix defects, inclusions, other emitters.

Due to the local nature of such non-radiative interac-

tions, it is expected that the presence of the NHA (always more than 10 nm away from the closest emitters) does not modify this intrinsic non-radiative decay rate, as conrmed also in several papers in the literature.

20,21,23,59,60

Table 1 shows also the comparison between the

experimental and simulated radiative decay rates of the three samples, with resonant and non-resonant NHA. A good agreement between the experimental and simulated results was obtained (see Fig.

3b).

Particularly, with both resonant and non-resonant NHA congu-

12


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rations a signicant increment in the Er radiative decay rate at 1540 nm - with respect to

3+ the value for Er ions in a homogeneous silica matrix,

Γ0r = 70

s

−1

- was observed, up

to more than a factor of 2. Such an increment is a function of the distance of the Er:SiO2 layer from the NHA and the eect is higher as the distance decreases. Moreover, the data in Fig. 3b show that the eect of the resonant and non-resonant NHA congurations can be distinguished, especially in the range

[zc ≈ 30

nm, zc

≈ 100

nm ].

However, the dier-

ences are not dramatic, as the maximum separation between the two congurations is about 13% at

zc = 50

nm.

Instead, both NHA congurations behave very dierently from the

homogeneous lm case. The eect of a continuous Au lm (blued dashed curve in Fig. 3b) was evaluated by FEM simulations and the results are in agreement with those obtained by the CPS model.

59,60

It is worth pointing out here that the dierences observed between the

resonant and non-resonant NHA congurations exclude the validity of any kind of eective medium approximation based on the (volume) average of the gold and silica dielectric functions: since the gold/silica ratio is almost the same for the two congurations, if an eective medium approximation were sucient to describe the system, the two resulting decay rates would coincide. Furthermore, the good agreement of the model with the experiments also tells us that the approximation of single emitters used for the simulations is reliable. This means that, under the conditions investigated in the present work, the emitters do not correlate themselves through their emission and thus the studied system can be considered as a valid candidate for future developments in the eld of quantum photonics, particularly as single photon sources.

Far-eld intensity and quantum eciency Since part of the radiation emitted by Er ions is absorbed in the near-eld region, the far-eld quantum eciency experiences a drop. To account for the losses and thus to compute the quantum eciency in far-eld, we introduced the in a similar way as

γr .

far-eld normalized decay rate, γf f , dened

In the simulations, we computed

13


γf f

by integrating the Poynting

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vector on the outer surface

Σout

Page 14 of 38

previously dened and normalizing by

W 0:

R ~ S · uˆ dσ Γf f Wf f Σout N HA ≡ γ = = . R f f ~SiO2 · uˆ dσ Γ0r W0 S

(6)

Σout

γf f

takes into account only the radiative decay events for which the emitted energy reaches

the far-eld.

To eliminate the contribution of energy owing at the interfaces as PSPPs,

we excluded from the integral the region close to the NHA (at a distance shorter than one plasmon-eld decay length in silica in the integrated. We dened the

zˆ

direction), so that only far-eld photons were

far-eld quantum eciency q

as the ratio between the number

of photons that reach the far-eld (which is proportional to photons emitted by the dipole (which is proportional to

q=

where

γabs

γf f )

and the total number of

γr ):

γf f γf f = , γr γf f + γabs

(7)

represents the photons that have been absorbed (dissipated into ohmic losses in

the metal) due to the presence of the gold NHA and

γr

indicates the radiative emission rate,

modied by the presence of NHAs, as previously discussed. When a set of (each one characterized by a normalized far-eld decay rate decay rate

γri

and a quantum eciency

q i = γfi f /γri )

n

congurations

γfi f , i = 1, . . . , n,

a normalized

is considered, the resulting average

quantum eciency is given by the sum of the far-eld decay rates divided by the sum of the radiative decay rates:

Pn i n 1X i i=1 γf f q = Pn i 6= q. n i=1 i=1 γr In this case, congurations with larger

γr

(8)

will dominate in the average on those with smaller

decay rates (the average quantum eciency is not the arithmetical average of the single quantum eciencies). It is worth noting at this point that the simulations were carried out for an ideal emitter (without non-radiative decays, i.e., quantum eciency is

q0 = 1).

If this is not the case (γnr

14

γnr = 0 6= 0),


and the near-eld intrinsic

the total quantum eciency

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of the system

q

qtot

can be obtained by multiplying the computed far-eld quantum eciency

by the near-eld quantum eciency of the real emitter,

qtot = qq00 =

We stress that

qtot .

as follows:

γf f γr γf f = . γr γnr + γr γnr + γr

(9)

is the radiative emission rate modied by the presence of the nanohole

γnr = 0, q00 = q0 = 1

array. For total one

γr

q00 = γr / (γnr + γr ),

The role of

γf f

and the far-eld quantum eciency

q

coincides with the

in the experiments can be better understood by noting that

when the number of excited emitters is maintained constant by continuous excitation with an external pump at

λexc , this quantity is equal to the normalized far-eld photon yield, ηf f :

ηf f =

where

Nph

and

0 Nph

Nph Wf f = γf f , = 0 Nph W0

(10)

are the integrated number of photons that reach the far-eld in the time

unit in the samples with and without the NHA, respectively. Thus, an enhanced normalized far-eld decay rate (γf f

> 1) corresponds to a net increment in the recorded far-eld photon

yield with respect to that generated by emitters in a homogeneous silica matrix for the same pumping intensity (ηf f

> 1).

and the quantum eciency

q

Fig.

4 shows the normalized far-eld photon yield

ηf f

(b) computed for the two NHA congurations (resonant and

non-resonant); a reduced set of emitter-NHA distances was explored in this case (z nm,

z = 50

nm and

z = 100

(a)

= 20

nm).

The presence of the NHA can aect in a dierent way the emission properties of emitters placed in dierent sites within the NHA unit cell and this can be exploited to further enhance the performances of NHAs in modifying the emission properties of emitters. To highlight this we simulated the eect of a patterned distribution of emitters in the

xy ˆ

plane, by considering

also the conguration in which the dipoles are conned below the footprint of the holes only. Fig.

4a shows that, for distributions that are homogeneous in the

ηf f > 1

xy ˆ

plane (full dots),

for all the investigated distances from the NHA (both for the resonant (red) and

15


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Page 16 of 38

non-resonant (blue) conguration), with a maximum enhancement of 36 % for the resonant NHA placed at a distance of patterned,

ηf f

20

nm from the emitter.

When the emitters distribution is

results even higher, leading to an increase of up to the 74% in the far-eld

photon yield for

z = 20

nm (open dots). In contrast, when a continuous gold interface is

considered, although the total radiative emission rate can be enhanced, giving blue dashed line in Fig. is

ηf f < 1,

3a, where

Γr > Γ0r

for

z < 480

γr > 1

(see

nm), the far-eld photon yield

3+ i.e., the number of photons emitted in far-eld for Er ions interacting with a

continuous lm (blue and green dots in Fig. 3a) is smaller than for emitters in a homogeneous silica matrix. To experimentally determine the enhancement in far-eld photons ux due to the presence of NHAs, we carried out integrated PL intensity measurements of the samples with the NHAs and the corresponding reference samples. The results are reported in Fig. S2 of the Supporting Information.

For each distance investigated, the increment in the

far-eld photon yield, passing from the continuous lm to the NHA with a homogeneous distribution of emitters in the

xy ˆ

plane and to the conguration in which the emitters are

under the hole only, corresponds to an increment in the far-eld quantum eciency

q,

as

shown in Fig. 4b. This suggests that such an enhancement is not only due to an increase of the emission rate, but also to the partial suppression of absorption pathways. Moreover, the higher eciency of NHAs with respect to the continuous lm is due to two aspects: 1) as already noted, PSPP modes can couple with far-eld photons and therefore the energy which ows into PSPPs can be re-emitted and is not completely dissipated in ohmic losses, as non-radiative losses are weak for NHA plasmons;

64,65

2) when a dipole is placed under

r from the center of a hole in the xy ˆ plane smaller than the p r = x2 + y 2 < rH ), the distance from the closest point of the metal is

the hole (i.e., at a distance

rH , p d = z 2 + (rH − r)2 > z .

holes radius

Lossy surface waves (LSWs) are responsible for a large part of

absorption when the metal-emitters distance as the distance increases.

23

d is low, but their importance quickly decreases

Thus, emitters placed under a hole experience an enhancement

in the coupling to radiative modes (photons and PSPPs that, in contrast to LSWs, extend

16


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ACS Photonics

also under holes), but not to the dissipative ones.

In contrast, when a continuous lm is

considered, LSW and PSPP modes are competitive with photons as ecient decay channels (as all the emitters are at a distance

d = z , the average coupling is higher with respect to the

NHA, where holes reduce it) and both are completely lossy: as noted before, in the absence of an additional coupling system (i.e., a grating or a prism), PSPP modes are trapped at the metal/dielectric interface and intrinsically non-radiative. Thus, a large part of the emitted energy is absorbed. Since LSWs constitute a weak decay channel for emitters under the hole (due to the increased distance from the metal), the losses associated to LSWs are further suppressed when the Er ions are conned under the hole (see open dots in Figs. 4a and 4b). Thus, the quantum eciency (q

> 90%

q

results the highest for the hole-conned emitters distribution

for all the considered distances). Moreover, the increase of

q

with the patterned

distribution of emitters is even more eective when the NHA-emitter distance is the shortest (see

z = 20

nm), since in this case the derivative

∂d/∂r

is larger and thus the coupling

to LSWs is more aected by the position of the emitter in the for all the congurations investigated, the quantum eciency

q

xy ˆ

plane.

We stress that

results much higher than in

the case of a continuous gold lm. Furthermore, the energy dissipation in the NHA results negligible (q

z ≥ 50

> 90%),

also in the case of homogeneous emitter distributions, already for

nm. Therefore, with a smart design of the system (e.g., by conning the emitters

in the region under the hole and at a distance between

z = 20

possible to get a strong increase of the radiative decay rate

γr ,

nm and

z = 50

nm) it is

keeping at the same time

almost unitary quantum eciencies. As a consequence, a net increment in the far-eld signal can be obtained. Keeping almost unitary quantum eciencies, while enhancing the emission rate, is the key for all those photonic applications that need to suppress losses and increase the far-eld emission, as for example to realize few-photons or even single-photon sources. Moreover, from the experimental point of view, the connement of emitters only under the footprint of the holes of the NHA can be achieved by methods that enable pattering through masks, like for example ion implantation, in which the NHA itself can be used a mask.

17


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Page 18 of 38

Furthermore, the resonant and non-resonant NHA congurations gave comparable results in terms of the far-eld photon yield and only small dierences can be found, mainly in a slightly larger enhancement of

γr

for the resonant NHA. This eect can be explained taking

into account that, as already noted (Fig. 1b), four modes exist for the non-resonant NHA at the Er emission frequency and thus the enhancement of the emission can be obtained due the the coupling with these modes.

The energy transferred to these modes can still

be re-emitted by the NHA, the only dierence is the angle of emission.

61

Thus, as a nal

comment, we want to point out that the possibility to get the coupling of the Er emission with propagating modes allows one to use also non-resonant NHAs with only a limited reduction of performances in terms of the emission enhancement and eciency. Moreover, since the angular pattern of the re-emitted photons is determined by the directional dependence of the dispersion of the modes they couple with, and thus by the lattice constant of the NHA, varying this parameter would permit in principle to control also the direction of the emitted light.

62

Conclusions The modication of the radiative decay rate of Er

3+

ions coupled to Au nanohole arrays was

investigated for two NHA congurations: one in which the extraordinary optical transmission

3+ peak is resonant with the Er emission wavelength, the other in which EOT is at longer wavelengths.

For both congurations, FEM electrodynamic simulations were carried out

and the results were compared with those of photoluminescence measurements performed on experimental samples.

A good agreement between simulated and experimental results

was evidenced which conrmed also that the emitters do not correlate themselves through the emission.

As it occurs for a continuous Au lm, the emission rate results enhanced

in a broad range of distances ranging from zero to hundreds of nanometers away from the interface. On the other hand, in contrast with the case of lms, we found that NHAs are also

18


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ACS Photonics

able to yield a net increment in the far-eld photons yield. Such an enhancement is due to the achievement of high quantum eciency values. This, in turn, is due to two factors. On one hand, the energy that couples to extended plasmons traveling at the NHA surfaces is not lost as in the case of lms: PSPPs couple with far-eld photons making it possible to recover a large amount of this energy. Moreover, the emission from dipoles placed under a hole in the NHA lattice experiences almost no losses due to LSWs, further reducing absorption in the near-eld. As a consequence, the far-eld quantum eciency results increased, passing from values of about 50%-60% obtained with the continuous lm to values over 90% with the NHAs; even higher values (up to 99%) could be obtained if the emitters distribution is patterned so that they are conned in the zone under the holes (with a corresponding enhancement of the far-eld photon yield of 74%). Finally, we evidenced that, owing to the rich band-structure of the NHA, the coupling with Er emitters weakly depends on the NHA lattice parameter (resonant and non-resonant NHA gave comparable results), and this opens the possibility to control other aspects of the emission properties, such as the directionality, without losing in terms of eciency.

Methods Er:SiO2 deposition 2 Er:SiO2 thin lms were deposited by magnetron co-sputtering on 2.5×2.5 cm silica substrates (HSQ300 by Heraeus). Before the deposition, the substrates were cleaned in a piranha solution (30% H2 O2 , 70% H2 SO4 ) for 60 min and copiously rinsed with Milli-Q deionized water. A radiofrequency (RF) source was used for the sputtering of the silica target operated at a power of 250 W, while a DC source (at 3 W) was used for the erbium target. In these conditions, the Er concentration in the samples was of about 1.0% at. (determined by Rutherford backscattering measurements). During the co-depositions, the sample holder was kept in rotation to guarantee the homogeneity of the lm composition and thickness.

19


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Page 20 of 38

Synthesis of the NHAs Hexagonal gold nanohole arrays were fabricated by nanosphere lithography (NSL)

66

in a

three-steps process: 1) a periodic array of polystyrene (PS) nanospheres is made by selfassembly on a silica substrate; 2) reactive ion etching (RIE) with an Ar:O2 mixture is performed on the PS nanospheres to reduce their radius while keeping the periodic pattern; 3) gold deposition by magnetron sputtering on the PS nanospheres and their successive lift-o by dissolution in toluene. Commercial PS nanospheres (Microparticles GmbH) with nominal diameters

D = 1030

nm or

D = 1280

lattice parameters

a0 = 1030

nm and

nm were used to fabricate the NHAs with

a0 = 1280

nm (a0

= D).

All the substrates were

previously cleaned using the piranha solution. The time of RIE was set to reduce the radius of the PS nanospheres (and thus the radius of the obtained nanoholes) by a factor about 2/3 from their original size. A 120 nm thick Au lm was then deposited by magnetron sputtering on the PS nanospheres.

To remove the PS nanospheres, the samples were sonicated in

toluene for 2 minutes. Finally, a silica layer of thickness 400 nm is deposited on the NHAs to get refractive index matching close to the nanoarray, and to preserve it during the high temperature thermal annealing needed for the Er

3+

optical activation (900

◦

C, 2 hours, in

vacuum).

Morphological and optical characterization Before the deposition of the nal silica layer, the fabricated NHAs were characterized morphologically by scanning electron microscopy with a Zeiss Sigma HD eld-emission scanning electron microscope (FE-SEM), operated at 5 kV, with in-lens detector. Atomic force microscopy (AFM) measurements were performed using a NT-MDT Solver PRO-M AFM microscope with a 100

× 100 µm scanner, operated in semi-contact mode.

SEM measurements

were also carried out after the deposition of the silica layer and the subsequent thermal annealing, to check that the NHAs were preserved. Optical transmittance spectra were collected in normal incidence with a JASCO V670 dual

20


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ACS Photonics

beam spectrophotometer. The dielectric properties of the materials used for the synthesis of the samples (gold and silica) were characterized by spectroscopic ellipsometry measurements using a J. Woolham V-VASE spectroscopic ellipsometer. The measurements were performed on homogeneous fthin ilms deposited on Si substrates under the same conditions used for the samples.

Photoluminescence measurements Integrated and time-resolved photoluminescence (PL) measurements were performed at room temperature. A sketch of the experimental setup is reported in Fig. S1 of the Supporting Information. The 488 nm line of a cw Ar laser (mechanically chopped at 6 Hz) was used to excite the samples in-resonance with the

4

I15/2 →4 F7/2

3+ 4750 Er absorption transition.

Since the presence of the NHA causes a (modest) increase of the local electric eld intensity at the pumping wavelength, for each sample we simulated this enhancement by modeling the pump laser beam impinging on the sample with the same geometry of our experiments and we used this parameter as a normalization factor of the pump laser intensity when measuring the emitted intensity. The PL emission was spectrally selected by a single grating monochromator and detected by a liquid N2 -cooled near-infrared photomultiplier tube (Hamamatsu R5509-72). To exclude any possible energy-transfer eect from the nanohole array to nearby

3+ Er ions, PL measurements were also performed with out-of-resonance excitation using the

λexc = 476.5 nm line of the Ar laser (which is not resonant with any Er3+ no PL signal at 1.54 takes place.

67,68

atomic transition):

µm was detected in this case, conrming that no energy-transfer process

The temporal decay curves of the PL emission were obtained by xing the

detected wavelength at 1.54

µm

and collecting the PL intensity evolution as a function of

time with a digital oscilloscope (Tektronix TDS 7104).

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Page 22 of 38

Numerical methods FEM simulations

FEM simulations were carried out using the commercial software COMSOL Multiphysics 5.2a to solve the Helmholtz equation in the frequency domain.

6,69,70

The modeled domains

are embedded in a sphere, surrounded by a perfectly matched layer (PML) which prevents backscattering of propagating waves from the outer surface. nanohole array is placed between the

z=0

and

z = −120

5,6

Inside the sphere, the Au

nm planes. In the

xy ˆ

plane, 61

unitary cells of the NHA lattice are included in the simulation domain. The diameter of the model sphere is about 9 times the lattice parameter of the nanohole array (see Fig. 2b). The comparison with analytical results obtained with the CPS model

21

allowed us to conrm

that such a domain size is larger than what is needed to correctly reproduce the physics of the near-eld interaction with lms: a domain sphere radius of about 5 times the emission wavelength in silica would be sucient (as demonstrated in Ref. [

60

]). Moreover, the size of

the modeled domain is suciently large that, in all the computed congurations, the modes conned at the NHA surfaces carry less than

5%

of the emitted power when they reach the

outer surface. Thus, we neglected this energy and to get conservative results we considered it as dissipated in the simulations.

The dielectric function of the NHA was that of gold.

Apart from the NHA, all the others domains were modeled as silica, consistently with the experimental samples. For all the models, the properties of the materials (gold for NHA, and silica in the remaining space) were described by using their experimental dielectric functions measured by spectroscopic ellipsometry.

3+ The Er emitters were modeled as electric dipoles, oscillating at the frequency corresponding to the their emission at

λP L = 1540

nm.

Each conguration was modeled with a single

emitter placed at a specic position in the NHA unit cell and with a given orientation. The distribution of emitters was modeled by integrating the results obtained from all the single congurations that form the distribution, as described in the following. The dipole is

22


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ACS Photonics

alternately oriented along the

xˆ, yˆ or zˆ axis.

An average over the three orientations gives the

results for randomly oriented emitters distributions in the samples. The

z

coordinate of the

dipole represents the distance from the NHA surface (see Fig. 2c), and it was varied from

6

nm to

1000

nm. The

x

and

y

coordinates dene the relative position of the emitter with

respect to the center of the hole in the center of the model. To exploit all the symmetries, the simulations were performed for a reduced set of dipole positions inside the computational cell. The cell is dened starting from the Wigner-Seitz unit cell, as shown in Fig. 2d (solid black line) and, owing to the symmetry across the

x=0

and

y=0

planes, it was further

reduced to a quarter (solid red line). Inside this cell, the calculations were performed for the 27 dierent positions shown by the dots in Fig. 2e.

FDTD simulations

FDTD calculations were performed using an in-house implementation of Yee's algorithm.

71,72

The principle for the band-structure calculation is to excite all the possible modes, wait until only normal modes survive, and then determine their frequency by performing a Fourier transform. This operation was repeated for several values of the parallel wave-vector,

kk ,

to

get the band-structure along the most important directions of the reciprocal lattice of the NHAs.

15 points in each of the 3 directions,

modeled gold NHAs extend over the cell in the

xy ˆ

xy ˆ

Γ-M,

M-K and K-Γ, were considered.

The

plane and are embedded in silica. The simulation

plane was a centered rectangular one, with a hole in its center.

At the

boundaries perpendicular to the NHA surfaces, Bloch periodic boundary conditions were used to vary the parallel component of the modes wave-vector, by varying the phase shift between corresponding boundaries. PMLs were added at the boundaries of the simulation region parallel to the NHA surfaces to absorb light scattered in that direction. The excitation was made by a set of 20 dipoles, with random position and orientation.

Each dipole was

modeled as a broad-band source, with a frequency band ranging between

fmin = c/(10a0 )

and

fmax = c/a0

for each value of the lattice parameter

23

a0 .


The dipole emission consisted

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Page 24 of 38

in a short pulse of 50 fs. After 250 fs only normal modes were still present: to consider only these modes, a Fourier transform of the eld amplitude was performed after apodization using a Gaussian curve centered at 625 fs and with a width of 500 fs. For the geometry of the NHAs, we used the same parameters as for the FEM simulations. Silica was modeled as a non-dispersive medium with

n = 1.45,

while the optical properties of gold were obtained

from a Drude-Lorentz t of the experimental data used in FEM calculations.

Author Information Author Contributions NM performed the FEM simulations. BK and TC performed integrated and time-resolved PL measurements.

NM, BK and CS fabricated the samples.

TC and GM conceived the

experiments. NM and TC wrote the manuscript. All the authors revised the manuscript.

Conict of Interest The authors declare no competing nancial interest.

Acknowledgement This work was partially supported by the Italian Ministry of Foreigner Aairs and International Cooperation (MAECI) with the Project of Major Importance Italy-Mexico (MX14MO09) and by the University of Padova with the Project BINDER (CPDA153538).

Supporting Information Available Additional information about PL measurements and simulations.

24


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www.

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Graphical TOC Entry

a0

34


Page 34 of 38

0.8 1540

0.6 2000

0.4

Γ

(a)

0.2

M K k points

Γ

5000

Γ

EXP/FEM

Transmittance (%)

Normalized frequency (f a0/c)

1030

1280

1.0

1540

0.8

2000

0.6 0.4

(b)

0.2

M K k points

Γ

(c)

Γ

(d)

Res. NHA (a0=1030 nm) Non-res. NHA (a0=1280 nm)

100

5000

Freespace wavelength (nm)

1.0

Freespace wavelength (nm)

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

ACS Photonics

Normalized frequency (f a0/c)

Page 35 of 38

80

1µm

60

(e)

40 20 0 1000

1200

1400

1600

1800

2000

1µm

Wavelength (nm) Figure 1: (a,b) FDTD-calculated band-structure of (a) resonant (R, (b) non-resonant (NR,

a0 = 1280

a0 = 1030

nm) and

nm) gold nanohole arrays embedded in silica; yellow-red

regions correspond to the presence of a mode, on the blue background. The y-axis on the left is the normalized frequency

f a0 /c,

while on the right the corresponding wavelengths 3+ are indicated. The horizontal white line indicates the frequency of the Er emission. The x-axis spans over the FBZ (in the inset) along the directions

Γ-M,

M-K and K-Γ. (c) Far-

eld transmittance spectra of the two NHA embedded in silica. Black and red lines indicate the resonant and the non-resonant congurations, respectively.

Solid lines represent the

FEM computed spectra, whereas dashed lines are the experimental measurements on the nanofabricated samples.

(d) SEM image in top-view of a resonant gold NHA (a0

nm) and (e) of a non-resonant gold NHA (a0

= 1280

35

= 1030

nm), before the silica deposition.


ACS Photonics 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

Page 36 of 38

SiO2

a) NHA

z=0

Tspc spacer TEr active layer

SiO2

substrate

zc

SiO2

Er:SiO2

z

SiO2-NHA Interface

b)

Au NHA

c) NHA

y z

dipole

̂ ̂

e)

d)

r

Figure 2: (a) Side view of the designed system. The control its distance from the NHA; the

x and y

z

coordinate of the dipole is varied to

coordinates control the position with respect

to the NHA lattice unit cell. (b,c) 3D and transverse views of the model. (d) Wigner-Seitz elementary cell denition and reduction using symmetries (red line).

(e) Sampling of the

elementary cell by 27 points; the color map indicates the distance from the center of a hole.

36


(a) resonant

r 0

a0/2

175

(b)

Au film Res. NHA (a0=1030 nm) Non-res. NHA (a0=1280 nm) EXP Res. NHA (a0=1030 nm) EXP Non-res. NHA (a0=1280 nm)

150 125 100 75 0

50

100

150

200

250

300

z (nm) 1

1

(c) ex=488nm

0.1

Normalized PL

Normalized PL

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

ACS Photonics

Rad. decay rate Gr (s-1)

Page 37 of 38

=7.2ms

em=1540nm

=5.7ms

A110 A40 A20

0.01 0

5

(d) ex=488nm

0.1

15

0.01

20

0

Time (ms) Figure 3: (a) Radiative decay rate

=6.6ms

A110 A40 A20

=4.5ms

10

=7.2ms

em=1540nm

5

=5.9ms

10

15

20

Time (ms) Γij r (z)

as a function of the distance between the emitter

and the NHA-silica interface, for dierent positions in the NHA lattice unit cell; the color scale represents the distance of a hole) in the

xy ˆ

r

of the emitter from the origin of the unit cell (i.e., the center

plane. The inset shows the 27 positions of the emitter considered in the

simulations and the corresponding color. As a comparison, the blue dashed curve indicates the emission rate computed for an optically thick continuous gold lm. (b) Integrated eective decay rates computed assuming a box-like distribution of emitters with a thickness of

20

nm, centered at a distance

z = zc

from the NHA-silica interface. Data were computed

for the resonant (blue) and non-resonant (orange) NHA congurations, and for a continuous Au lm as a reference (blue dashed line). In transparency, the condence bands of are plotted for the two NHA congurations.

±

5%

Dots represent the experimental decay rates

measured on samples A20, A40 and A110 (20 nm-thick Er-doped silica layer centered at a distance of

20

nm,

40

nm and

110

nm from the NHA surface, respectively), both for the

resonant (blue dots) and non-resonant (orange dots) NHA congurations. (c,d) Experimental time-dependent photoluminescence signal for the three samples A20, A40 and A110, in logarithmic scale, for resonant (c) and non-resonant (d) NHAs. Measurements were carried 3+ out exciting the Er ions at λexc = 488 nm and collecting the emission at λP L = 1540 nm. The experimental points in panel (b) were obtained from exponential ts of the decay curves in panel (c) (blue dots, resonant conguration) and (d) (orange dots, non-resonant conguration).

37


ACS Photonics

Hole Hole NR

film FEM film CPS

Quantum efficiency, q (%)

NHA NHA NR

2,0

Normalized far-field photon yield, ηff

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

1,5 1,0 0,5

(a) 0,0

20

40

60

80

Page 38 of 38

NHA NHA NR

Hole Hole NR

film FEM film CPS

100 80 60 40

(b) 20

100

20

40

60

80

100

z (nm)

z (nm) Figure 4: (a) Normalized far-eld photon yield

ηf f

as a function of the distance of the dipole

from the Au NHA-silica interface. The values were obtained by integrating the emission from either the full unit cell (full dots) or from emitters placed under the hole only (open dots), averaging for the three dipole orientations. Black dots refer to the resonant NHA, red dots to the non-resonant NHA. As a comparison, blue and green dots are the results obtained with a continuous Au lm, computed by FEM simulations (blue) and using the analytical CPS model (green). (b) Quantum eciency

q

as a function of the distance from the NHA.

Color codes are the same as in panel a.

38


Emission Rate Modi cation and Quantum E ciency Enhancement of

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