# Molecular strong coupling: an exploration employing open, half- and full
planar cavities

Kishan S. Menghrajani  [<EMAIL_ADDRESS>Adarsh B. Vasista  [
Wai Jue Tan  [  William L. Barnes  [

###### Abstract

We explore the modification of photoluminescence from dye-doped open, half and
full optical microcavities. For each configuration, an analysis of the
reflectivty data indicates the presence of strong coupling. We find that an
open cavity, i.e. a dye-doped dielectric slab placed on a silicon substrate,
shows little if any modification of the photoluminescence spectrum. For the
half-cavity, in which a thin metallic film is placed between the dye-doped
dielectric and the substrate, we find a limited degree of modification of the
photoluminescence. For the full-cavity, for which the dielectric layer is
bound both above and below by a metallic mirror, we find very significant
modification to the photoluminescence emission, the photoluminescence clearly
tracking the lower polariton. To learn more about the photo-physics we compare
reflectivity, absorption and photoluminescence dispersion data, making use
where appropriate of numerical modelling. We discuss our results in the
context of harnessing open cavities to modify molecular photo-physics through
molecular strong coupling .

University of Exeter] Department of Physics and Astronomy, University of
Exeter, Exeter, EX4 4QL, United Kingdom ETH Zurich] Nanophotonic Systems
Laboratory, ETH Zurich, Switzerland University of Exeter] Department of
Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, United Kingdom
University of Exeter] Department of Physics and Astronomy, University of
Exeter, Exeter, EX4 4QL, United Kingdom

keywords: Strong-Coupling, Photoluminescence, Optical Microcavity, Polaritons.

##  1 Introduction

When molecules are placed inside an optical microcavity, the interaction of
molecular resonances with the cavity mode may lead to the formation of hybrid
states called polaritons - states that inherit characteristics of both the
optical cavity modes and the molecules from which they are formed 1. This
process, known as molecular strong coupling, has been extensively explored in
the context of both excitonic 2, 3, 4 and vibrational resonances 5, 6, 7. In
the context of vibrational strong coupling there is much excitement at present
owing to the prospect of modifying chemical processes 1, 8, 9, 10, 11, a
prospect that is still somewhat controversial 12, 13, 14. A range of ‘cavity’
structures have been explored, most frequently planar (Fabry-Perot) optical
microcavities in which the molecules are located between two closely spaced
metal or dielectric mirrors. Indeed, planar microcavities have been the work
horse for molecular strong coupling studies for many years, in both excitonic
and vibrational regimes. However, such structures do not offer good access to
the molecules involved, thereby limiting their applicability to modified
chemistry. As a result alternative ‘open’ geometries have been explored,
including surface plasmon modes 15, dielectric microspheres 16, and surface
lattice resonances 17. More recently so-called ‘cavity-free’ geometries have
been investigated 18, 19, 20, and extensive mode splitting observed, these
cavities do not use metallic or dielectric multi-layer (DBR) mirrors, instead
they rely on reflection from the interface of the molecular material with
another dielectric, including air, to produce optical modes. Whilst some of
these works noted changes to the molecular absorption, it remains to be seen
whether such structures can be used to control chemistry effectively. Since
modification of photoluminescence is a more stringent measure of strong
coupling than reflectance, transmittance and scattering 21, 22, 23, here we
chose to explore the photoluminescence process for open, half and full
cavities, in an attempt to gain better insight into cavity free strong
coupling.

In the work reported here we made use of three different planar cavity
structures in our study, shown in figure 1, these were: (a) an open cavity,
i.e. a layer of polymer containing dye molecules supported by a silicon
substrate; (b) a half-cavity, similar to (a), but with the addition of a
metallic (gold) mirror between the substrate and the dye-doped polymer, and;
(c) a full-cavity, similar to (b) but now with a second metallic mirror added
to the top of the structure. In the work reported here we made use of the
J-aggregated dye TDBC
(5,5′,6,6′-tetrachloro-1,1′-diethyl-3,3′-di(4-sulfobutyl)-benzimidazolocarbocyanine)
in two forms, one simply dispersed in the polymer PVA for the open and half
cavities, and the other assembled using a layer-by-layer technique (see
methods) for the full cavity. Our choice of two different forms of TDBC for
these experiments was motivated by our desire to produce comparable levels of
Rabi splitting in the (reflectivity-based) anti-crossing for the three
structures, something we only partially accomplished. We used a silicon
substrate, and made use of gold for the metallic mirrors; further details of
fabrication etc. are given in the methods section. We analysed the
experimental data using a transfer matrix model to calculate the reflectance,
transmittance and absorption, whilst we made use of a coupled oscillator model
to determine the modes of each system; again, details of both are given in the
methods.

Figure 1: Schematic of Cavity Structures: (a) Open Cavity consisting of a
TDBC-doped polymer (PVA) film on a silicon substrate, doped-PVA thickness
$\sim$340 nm. (b) Half Cavity, as (a) but now a thin gold film is included
between the substrate and the dye-doped polymer, doped-PVA thickness $\sim$600
nm. (c) Full Cavity, similar to (b) but with the addition of a top gold layer
to form the second mirror of a closed cavity. Here the TDBC/PVA has been
replaced by a combination of polymer (PMMA) layers and TDBC in the form of
molecular layers deposited by the layer-by-layer technique, thickness of
cavity $\sim$375 nm.

##  2 Results and Discussion

Experimental data were acquired from the different cavity structures so as to
produce dispersion plots. Specifically reflectance and photoluminescence (PL)
were acquired as a function of wavelength and angle. For reflectance
measurements a white-light source was coupled to an objective lens (100x, 0.8
NA) and focused on to the sample. The reflected light was then collected using
the same objective lens and projected onto the Fourier plane 24. For PL
measurements, a 532 nm green diode-laser source was focused onto the sample
and the PL was collected by the same objective lens in the back-scattering
configuration. Details of the optical setup are provided in section S1 of the
supplementary information.

### Open Cavity

Figure 2: Open Cavity. In panel (a) we show an experimentally measured
dispersion, based on p-polarised reflectance, indicated as a colour plot (see
methods re: normalisation). In panel (b) we show the calculated reflectance,
the white dotted lines represent the limit of the collection numerical
aperture used in the experiment. Panel (c) is the same as panel (b) except
that in the calculation we have set the oscillator strength of the dye to
zero. In panel (d) we show an experimentally measured dispersion plot acquired
from photoluminescence data. In panel (e) we show the calculated absorption in
the TDBC-doped layer. In panels (a-e) the polariton dispersion is shown, as
determined from the coupled oscillator model described in the methods section.
The polariton positions are shown as white dashed lines, and the molecular
resonance (2.08 eV) by a black dotted line; just one cavity mode was used in
the model (see panel (c)), and the polymer thickness was $\sim$340 nm. In
panel (f) the polariton positions (normal incidence) are indicated by black
dashed lines.

In figure 2 we show, in the upper row, dispersion data based on reflectance
for the open cavity, i.e. for a $\sim$340 nm TDBC-doped PVA layer on a silicon
substrate. On the left (a) we show the measured reflectance, in the middle the
calculated reflectance (b), and in (c) we again show the calculated
reflectance, but this time we set the oscillator strength of the dye to zero.
In the lower row we again show a dispersion plot, panel (d), this time based
on the measured photoluminescence. In panel (e) we show the calculated
absorption in the TDBC-doped PVA layer, whilst in panel (f) we show normal
incidence line spectra for the measured reflectance, the measured
photoluminescence and the calculated absorption in the TDBC. The white dashed
lines in panels (a-e) indicate the positions of the polariton modes as
determined from our coupled oscillator model (see methods), the polariton
positions at normal incidence are indicated in panel (f) by black dashed
lines. Further details are given in the figure caption.

Looking first at the reflectance, panels (a) and (b), the presence of modes of
the open cavity system is indicated by regions of low reflectivity (blue).
Also shown are the positions of the polaritons as determined by our coupled
oscillator model (details in methods). We see that overall there is a
reasonable match between the experimental data, the calculated data, and the
coupled oscillator model (which here employed a single cavity resonance). The
calculated dispersion for a ‘bare’ cavity and the ‘bare’ coupled oscillator
model is shown in panel (c). Here ‘bare’ refers to the oscillator strength in
equation (4) being set to zero. From the modelling we determine that in this
case the reduced oscillator strength is 0.15, the splitting is $\Omega=0.50\pm
0.04$ eV, and $\beta=1.3$ ($\beta$ is a parameter that ensures the bare cavity
dispersion is correctly included in the coupled oscillator model, see
methods). The splitting exceeds the sum of the TDBC linewidth, $0.053\pm
0.003$ eV, and the width of the cavity modes, $0.18\pm 0.04$ eV, so, if we
accept reflectance as a good indicator of the allowed modes, then we are in
the strong coupling regime. Panel (d) shows the measured photoluminescence
dispersion, we see that there is no sign of any influence of polaritons on the
photoluminescence for this open cavity. One might argue that when the lower
polariton mode is this far in energy from the un-modified photoluminescence
that no change would be expected. However, we have observed before that this
is not the case 23, provided there are phonon/vibrational modes that can
scatter emission via the polariton. Nonetheless, to investigate this aspect
further we looked at a thicker open cavity, where the lower polariton is much
closer in energy to the molecular resonance (less de-tuned). The results of
that investigation, shown in figure S2 of the Supplementary Information, lead
to the same observation, i.e. that the PL is not really modified in the open
cavity configuration. Finally, to investigate the absorption we made further
use of transfer matrix modelling, the results are shown in panel (e). Although
there is a significant change in the absorption (which in the bulk would be a
single peak) it is clear from panel (e) that the distortion is not due to the
presence of polaritons. The ‘double’ nature of the absorption in this
seemingly simple sample arises from the complex interplay between absorption
and the impedance the TDBC-layer presents to incoming light 25. In summary,
whilst the reflectivity is strongly modified in the open cavity system, the
photoluminescence is unaffected, and the absorption shows little if any sign
of the influence of polaritons. As noted above, we reached a very similar
conclusion by looking at a second, thicker, open cavity sample, see
supplementary information section S2. We defer a fuller discussion of these
results until we have looked at data for the half and full cavities.

### Half Cavity

Figure 3: Half Cavity. Data for the half cavity are shown in figure 3, where
the layout is similar to that used for the open cavity data shown in figure 2.
In panel (a) we show an experimentally measured dispersion, based on
p-polarised reflectance, indicated as a colour plot (see methods re:
normalisation). In panel (b) we show the calculated reflectance, the white
dotted lines represent the limit of the collection numerical aperture used in
the experiment. Panel (c) is the same as panel (b) except that in the
calculation we have set the oscillator strength of the dye to zero. In panel
(d) we show an experimentally measured dispersion plot acquired from
photoluminescence data. In panel (e) we show the calculated absorption in the
TDBC-doped layer. In panels (a-e) the polariton dispersion is shown, as
determined from the coupled oscillator model described in the methods section.
The polariton positions are shown as white dashed lines, and the molecular
resonance (2.08 eV) by a black dotted line; just one cavity mode was used in
the model (see panel (c)), and the polymer thickness was $\sim$600 nm. In
panel (f) we show normal incidence line spectra for the measured reflectance,
the measured photoluminescence and the calculated absorption in the TDBC. In
panel (f) the polariton positions (normal incidence) are indicated by black
dashed lines.

Looking first at the reflectance, panels (a) and (b ), the presence of modes
of the half cavity system are again indicated by regions of low reflectivity
(blue). Also shown are the positions of the polaritons as determined by our
coupled oscillator model, where we made use of two cavity modes. We note that
overall the match between the experimental data, the calculated data, and the
coupled oscillator model are not as good as they were for the open cavity. The
calculated dispersion for a ‘bare’ cavity and the ‘bare’ coupled oscillator
model is shown in panel (c). From the modelling we determine that in this case
the reduced oscillator strength is 0.15, the splitting is $\Omega=0.50\pm
0.03$ eV, and $\beta=1.1$. The splitting exceeds the sum of the TDBC
linewidth, $0.053\pm 0.003$ eV, and the width of the cavity modes, $0.11\pm
0.02$ eV, so that we are again, on the basis of reflectivity data anyway, in
the strong coupling regime. Panel (d) shows the measured photoluminescence
dispersion, things are now slightly more interesting than they were for the
open cavity. The PL spectrum is significantly different from the open cavity
case, but we see that there is barely any mapping of the PL onto the position
of the polariton modes. Calculated data for the absorption in the TDBC are
shown in panel (e). There is again a significant change in the absorption
compared to that of the bulk (a single absorption peak), and further, compared
to the case of the open cavity, there is now an indication of the absorption
tracking the lower polariton mode, at least to some limited extent. In
summary, the reflectivity is strongly modified in the half cavity system, as
is the absorption, however the photoluminescence shows only very modest signs
of change. Similar conclusions can be drawn from data based on a 1630 nm thick
half cavity sample, figure S3 in the supplementary information.

### Full Cavity

Figure 4: Full Cavity. In panel (a) we again show an experimentally measured
dispersion plot, based on p-polarised reflectance, indicated as a colour plot.
In panel (b) we show the corresponding calculated reflectance, the white
dotted lines again represent the limit of the collection optics used in the
experiment. In panel (d) we show the photoluminescence, whilst the calculated
absorption in the TDBC is shown in panel (e). In all plots the polariton
dispersion is shown, as determined from the coupled oscillator model described
in the methods section. The polariton positions are shown as white dashed
lines, and the molecular resonance, this time at 2.13 eV, by a black dashed
line; only one cavity mode was used in the model. The cavity was 355 nm thick.
In panel (f) we again show normal incidence line spectra for the measured
reflectance, the measured photoluminescence and the calculated absorption in
the TDBC. In panel (f) the polariton positions (normal incidence) are
indicated by black dashed lines.

Again, as for the open and half cavities, in figure 4 we show the reflectance,
panels (a) and (b), the presence of modes of the half cavity system are again
indicated by regions of low reflectivity (blue). Also shown are the positions
of the polaritons as determined by our coupled oscillator model, where we made
use of two cavity modes. We see that overall there is a reasonable match
between the experimental data, the calculated data, and the coupled oscillator
model. The calculated dispersion for a ‘bare’ cavity and the ‘bare’ coupled
oscillator model is shown in panel (c). In panel (f) we show normal incidence
line spectra for the measured reflectance, the measured photoluminescence and
the calculated absorption in the TDBC.

Looking first at the reflectance, panels (a) and (c), the presence of modes of
the full cavity system are, as before, indicated by regions of low
reflectivity (blue). Also shown are the positions of the polaritons as
determined by our coupled oscillator model, showing a good match between the
experimental data, the calculated data, and the coupled oscillator model.
Notice that for the full cavity the molecular resonance is at 2.13 eV rather
than 2.08 eV for the open and half cavities; this difference is due to the
different nature of the systems, TDBC-doped PVA in the open and half cavities,
TDBC in molecular layer-by-layer films in the full cavity 23. The calculated
dispersion for a ‘bare’ cavity and the ‘bare’ coupled oscillator model is
shown in panel (c). From the modelling we determine that in this case the
reduced oscillator strength is 0.03, the splitting is $\Omega=0.23\pm 0.03$
eV, and $\beta=0.65$. The splitting exceeds the sum of the TDBC linewidth,
$0.053\pm 0.003$ eV, and the width of the cavity modes, $0.11\pm 0.02$ eV, so
that we are again, on the basis of reflectivity data, in the strong coupling
regime. Panel (d) shows the measured photoluminescence dispersion, and now the
influence of polaritons is very clear. The PL spectrum is significantly
different from the open and half cavity cases, the the PL clearly tracking the
lower polariton. Calculated data for the absorption in the TDBC are shown in
panel (e). As for the PL, there is now a very significant change in the
absorption, and it also clearly tracks the polariton modes. Experimental data
for a slightly thicker (390 nm) full cavity are shown in figure S4 of the
supplementary information, they show similar trends to those described above.

It is useful at this point to compare the line spectra for the PL, the
absorption and the reflectance at normal incidence (i.e. $k_{\parallel}=0$ )
for each cavity type, i.e. panels (f) in figures 2, 3 and 4, we also refer the
reader to figures S2, S3 and S4 of the supplementary information. These data
encapsulate much of what we see in the full dispersion data.

Open cavity: For the open cavity the absorption is modified, but doesn’t track
well with polariton position. The PL is unperturbed. Indeed, a comparison of
the PL data in figure 2(f) with the data in figure S5 of the Supplementary
Information shows that the weak PL shoulder at $\sim$1.97 eV is present in the
thin film and is thus unlikely to be a consequence of the open cavity
structure.

Half cavity: For the half cavity the absorption shows clear signs of being
modified by the polaritons, and the PL is also very clearly modified, although
does not track the polariton position, there is only very weak dispersion of
some of the PL features, see figure 3(d). The thicker half-cavity does show
extra features in the PL, and these may be linked to the (lower) polariton
modes supported by this structure, see figure S4(d,f).

Full cavity: For the full cavity the absorption and the PL both track the
lower polariton very nicely. We also note that, as commonly found 26, 27, 28,
we observe PL from polaritons at energies lower than the molecular resonance
energy, see figures 4(e) and 4(f), i.e. we do not see any PL associated with
the upper polariton. Looking at the dispersion of the PL from the lower
polariton we see that it is not uniform, PL is typically produced by the
relaxation of reservoir states through the loss of vibrational energy 29 so
that PL emission is strongest when the difference between the bare molecular
resonance energy (reservoir) and the polariton branch are equal to the energy
of a vibrational mode 23.

## Conclusions

We have compared the photoluminescence from TDBC aggregates located in three
different cavity structures: open, half and full cavities. In all three case
the reflectivity data indicate the strong coupling regime has been reached.
The calculated absorption shows a somewhat different picture, with significant
changes in the absorption by the TDBC for all three cavity types, but only in
the case of the full cavity does the absorption track the (lower) polariton
fully. The situation for photoluminescence is that there is no modification
for the open cavity, some modification for the half cavity, and – as for the
absorption – in the case of the full cavity the PL maps onto the lower
polariton very well.

Previously we have looked at whether absorption by the dye is modified in the
strong coupling regime, and for an open cavity we found that there is some
modification. However, that study 19 made use of a broad spectrum dye (whereas
TDBC is narrow-band), and no PL measurements were undertaken. Other work
looking at strong coupling between dye molecules and particle plasmon modes
found that there was clear PL arising from the lower polariton in the strong
coupling regime 22.

What are we to make of these results? Our work raises a number questions
concerning the use of planar open cavities for molecular strong coupling.
First, whilst it is well known that measurements of reflectance on their own
are not sufficient to confirm the presence of strong coupling 30, 31, we are
left with the question of what level of modification of the absorption would
make a convincing case? Second, and perhaps more importantly given the results
reported here, does an absence of any sign of modification to the PL spectrum
indicate that the changes seen in reflectivity, albeit very substantial, are
not due to strong coupling? The data from our intermediate half cavity system
perhaps provides a clue, showing that changes to absorption for this system do
show signs of the presence of polaritons whilst the PL, although not showing
clear polaritonic behaviour, is nonetheless significantly modified. For the
full cavity the situation is clear, absorption and PL are determined by the
polariton modes of the system, as observed previously 26, 27, 28. It would be
very beneficial if more complete theoretical models, ones that go beyond the
simple coupled oscillator model we have used here, could be developed to
explore the absorption and especially the PL in these structures, perhaps
along the lines of previously reported models 32. It would also be useful if a
future investigation looked to see if different PL excitation wavelengths lead
to similar conclusions 23; such an investigation was beyond the scope of the
present study.

In summary, whilst further work is clearly needed, our investigation prompts
us to question the effectiveness of planar open cavities as a means to harness
strong coupling. Our results from planar half cavities lead us to suggest that
these structures perhaps deserve greater attention/investigation; they are
still ‘open’ yet seem to offer a greater degree of ‘cavity’ control. It would
be especially interesting to see whether similar observations arise if these
different cavity structures are explored in the vibrational (IR) regime 17,
and perhaps using metamaterial analogues 33. Before closing we should
emphasise that here we have looked at planar cavities, and have question
whether planar cavity-free structures offer an effective means of providing
open cavity strong coupling. We note that there are other open cavity systems,
for example those based on the plasmon modes of metallic nanostructures, that
do exhibit clear signatures of strong coupling via photoluminescence 22.

## Methods

Solution preparation: Poly Vinyl Acetate (PVA, molar weight 450 000) was used
as a host matrix for TDBC. PVA was dissolved in water. TDBC was then dissolved
in the PVA-water solution. TDBC/PVA films were deposited on a silicon wafer by
spin-coating. This produced film thicknesses over the range 300-1500 nm.

### Sample preparation

For the open-cavity a TDBC/PVA solution was spun on top of a silicon
substrate. For the half-cavity a thin gold layer of 30 nm was deposited on top
of silicon substrate by thermal evaporation. Later, TDBC/PVA was spun on top
of gold thin film. For the full-cavity, the lower mirror was prepared by
thermally evaporating 40 nm of gold onto a silicon substrate. A 100 nm thcik
layer of PMMA was then added by spin coating to create part of the cavity.
Then the TDBC film was deposited on top of this PMMA layer using a layer-by-
layer approach 34. Briefly, we used a cationic poly(diallyldimethylammonium
chloride) (PDAC) solution as the polyelectrolyte binder for anionic TDBC J -
aggregate solution. A typical deposition step consists of subsequent dipping
the substrate inside a beaker of PDAC solution (20$\%$ by weight in water -
diluted 1:1000) and TDBC solution in water (0.01M diluted 1:10) for 15 minutes
each. The substrate was washed with DI water after each immersion and same
steps were repeated to deposit multiple layers of PDAC/TDBC. To increase the
adhesion we first coat one layer of anionic polystyrene sulfonate (PSS) using
the above mentioned process and continue with PDAC - TDBC. Finally the TDBC
layer was protected by depositing a layer of PDAC molecules. The superstrate
was then prepared by spinning a second layer of PMMA and finally the top
mirror was prepared by thermally evaporating a further 40 nm of gold.

### Reflectance Measurements

Whilst substrate-only spectra for the reflectance should provide
normalisation, in our samples a non-trivial level of scattering meant that the
normalisation process was not as effective as hoped. Accordingly the
reflectance spectra were scaled to provide a better match with calculated
data.

### Coupled Oscillator Models

We made use of a standard coupled oscillator model to help us interpret our
data. The number of cavity resonances included in each model depended on the
details of the sample (thickness etc.). For a molecular resonance at a
frequency (angular) of $\omega_{\textrm{mol}}$ interacting with a single
cavity resonance (whose energy depends on in-plane wavevector, i.e.
$\omega_{\textrm{cav}}(k_{\parallel})$, the coupled oscillator model allows
the new dispersion of the new hybrid (polariton) modes to be determined. They
are found by solving for those frequencies $\omega$ for which the determinant
of the coupling matrix is zero, i.e. $|\mathbf{M}|=0$. The coupling matrix for
a single molecular resonance interacting with a single cavity (photonic) mode
is given by,

$\displaystyle\mathbf{M}=\begin{pmatrix}\omega_{\textrm{mol}}-\omega&\Omega/2\\\
\Omega/2&\omega_{\textrm{cav}}(k_{\parallel})-\omega\end{pmatrix}$ (1)

where $\Omega$ is the extent of the interaction, and is equal to the frequency
splitting (anti-crossing) at the value of $k_{\parallel}$ where the uncoupled
resonances cross. For the $n^{th}$ cavity resonance we described the
$k_{\parallel}$ dependence, $\omega^{n}_{\textrm{cav}}(k_{\parallel})$, as,

$\omega^{n}_{\textrm{cav}}=\frac{\omega^{n}_{k_{0}=0}}{k_{0}}\sqrt{{k_{0}}^{2}+\beta{k_{\parallel}}^{2}/{\varepsilon_{b}}},$
(2)

where $\omega^{n}_{k_{0}=0}$ is the angular frequency of the resonance at
$k_{\parallel}=0$. The factor $\beta$ was used to match the dispersion of the
bare cavity modes with the calculated bare reflectance (needed because the
coupled oscillator model ignores the angle-dependant phase change on
reflection from an interface). We chose to work with the simplest model that
we could, and therefore assumed no damping of the modes. The values of the
$\omega^{n}_{k_{0}=0}$, of $\Omega$ and of $\beta$ were determined by
simultaneously trying to match the eigenvalues to the calculated and measured
reflection data. When more thean one cavity mode was involved we made use of
the 2N coupled oscillator model 35, 36. The values for the Rabi splitting we
report here are based on the parameters used in the coupled oscillator model
that best fit our data.

### Transfer Matrix modelling

We made use of a standard multi-layer optics approach to calculations of the
reflectance and absorption 37, 38, and assumed all media were isotropic. The
reflectance was calculated by taking the square of the modulus of the
amplitude reflection coefficient. For the permittivities, we used the
following:

Silicon substrate: we took the permittivity to be 11.76 + 0.001i.

Gold films: we used a Drude-Lorentz model for the frequency/energy dependant
permittivity of gold, $\varepsilon_{\rm{Au}}(\omega)$, given by,

$\varepsilon_{\rm{Au}}(\omega)=\frac{f_{d}\,\omega_{p}^{2}}{\omega^{2}+i\gamma_{d}\omega}+\sum_{j}{\frac{f_{j}\omega_{p}^{2}}{\omega_{j}^{2}-\omega^{2}-i\gamma_{j}\omega}},$
(3)

with the Lorentz oscillator parameters given by,

$j$ | $f_{j}$ | $\omega_{j}(eV)$ | $\gamma_{j}(eV)$
---|---|---|---
1 | $0.024$ | $0.451$ | $0.241$
2 | $0.010$ | $0.830$ | $0.345$
3 | $0.071$ | $2.969$ | $0.870$
4 | $0.601$ | $4.304$ | $2.494$
5 | $4.385$ | $13.32$ | $2.214$
Table 1: Lorentz oscillator model parameters for gold films, as determined
from ellipsometry

TDBC j-aggregates: we used a Lorentz model, with the energy dependant
permittivity $\varepsilon_{\rm{TDBC}}(E)$ being given by,

$\varepsilon_{\rm{TDBC}}(\omega)=\varepsilon_{b}+\frac{f\,\omega^{2}_{0}}{\omega^{2}_{0}-\omega^{2}-i\gamma\omega},$
(4)

where for the open and half cavities (TDBC dispersed in PVA) we took:
$\omega_{0}=2.08$ eV, $\gamma=0.0459$ eV, and $\varepsilon_{b}=2.292$; for the
full cavity (TDBC layer-by-layer and PMMA) we took $\omega_{0}=2.13$ eV. The
value of the reduced oscillator strength, , was determined for each sample by
seeking a best ’by eye’ match of the calculated and measured reflectance data.

## Acknowledgements

K.S.M. acknowledges financial support from the Leverhulme Trust research grant
“Synthetic biological control of quantum optics”. K.S.M. also acknowledges the
support of Royal Society International Exchange grant (119893R). The authors
acknowledge the support of European Research Council through the photmat
project (ERC-2016-AdG-742222 :www.photmat.eu). Data associated with these
results can be found at XXXXXXXXXX.

Supporting Information Available: Optical Fourier setup; second samples/data
sets for open, half and full cavities; PL spectra of thin films of TDBC, and
comparison of PL spectra from open, half and full cavities. This material is
available free of charge via the Internet at *************

##  Appendix A S1: Optical Fourier setup

Figure 5 shows a schematic of the experimental setup. To measure angle
resolved reflectance, a white light source was focused onto the sample using a
0.8 NA 100x objective lens and the reflected signal was collected using the
same lens. Lens L4 and L5, together, project the back-focal plane of the
objective lens onto either the spectrometer or the camera, depending on the
position of the flip mirror FM2. Lens L6 was a flip-lens used to project the
real plane to the spectrometer/camera. For Photoluminescence (PL)
measurements, a beam-expanded diode-pumped 532 nm source was focused onto the
sample using the objective lens, and the PL was collected in the back-
scattering configuration. The laser line was then rejected using spectral edge
filters placed after lens L5. For k$\sim$0 excitation (normal incidence), we
place a lens, L7, in the input path such that the laser was focused onto the
back aperture of the objective lens, resulting in an approximate parallel beam
with k$\sim$0 at the sample plane.

Figure 5: Schematic of the Fourier optical setup

##  Appendix B S2: Open Cavity (1030 nm)

Figure 6: Open Cavity (1030 nm). In panel (a) we show an experimentally
measured dispersion, based on p-polarised reflectance, indicated as a colour
plot (see methods re: normalisation). In panel (b) we show the calculated
reflectance, the white dotted lines represent the limit of the collection
numerical aperture used in the experiment. Panel (c) is the same as panel (b)
except that in the calculation we have set the oscillator strength of the dye
to zero. In panel (d) we show an experimentally measured dispersion plot
acquired from photoluminescence data. In panel (e) we show the calculated
absorption in the TDBC-doped layer. In panels (a-e) the polariton dispersion
is shown, as determined from the coupled oscillator model described in the
methods section. The polariton positions are shown as white dashed lines, and
the molecular resonance (2.08 eV) by a black dotted line; three cavity modes
were used in the model (see panel (c)), and the polymer thickness was
$\sim$1030 nm. In panel (f) the polariton positions (normal incidence) are
indicated by black dashed lines.

In figure 6 we show, in the upper row, dispersion data based on reflectance
for the open cavity, i.e. for a $\sim$1030 nm TDBC-doped PVA layer on a
silicon substrate. The sample was similar to that used for the open cavity
data shown in figure 2 of the main manuscript, the primary difference being
that here the thickness of the cavity was 1030 nm rather than 340 nm used for
the sample discussed in the main manuscript. On the left (a) we show the
measured reflectance, in the middle the calculated reflectance (b), and in (c)
we again show the calculated reflectance, but this time set the oscillator
strength of the dye to zero. In the lower row we again show a dispersion plot,
panel (d), this time based on the measured photoluminescence. In panel (e) we
show the calculated absorption in the TDBC-doped PVA layer, whilst in panel
(f) we show normal incidence line spectra for the measured reflectance, the
measured photoluminescence and the calculated absorption in the TDBC. The
white dashed lines in panels (a-e) are indicate the positions of the polariton
modes as determined from our coupled oscillator model (see methods), the
polariton positions at normal incidence are indicated in panel (f) by black
dashed lines. Further details are given in the figure caption.

Looking first at the reflectance, panels (a) and (b), the presence of modes of
the open cavity system is indicated by regions of low reflectivity (blue).
Also shown are the positions of the polaritons as determined by our coupled
oscillator model (details in methods). We see that overall there is a
reasonable match between the experimental data, the calculated data, and the
coupled oscillator model (which here employed three cavity resonances). The
calculated dispersion for a ‘bare’ cavity and the ‘bare’ coupled oscillator
model is shown in panel (c). Here ‘bare’ refers to the oscillator strength in
the Lorentz oscillator model being set to zero. From the modelling we
determine that in this case the reduced oscillator strength is 0.28, the
splitting is $\Omega=0.67\pm 0.04$ eV, and $\beta=1.1$ ($\beta$ is a parameter
that ensures the bare cavity dispersion is correctly included in the coupled
oscillator model, see methods). The splitting exceeds the sum of the TDBC
linewidth, $0.053\pm 0.003$ eV, and the width of the cavity modes, $0.18\pm
0.04$ eV, so, if we accept reflectance as a good indicator of the allowed
modes, then we are in the strong coupling regime. Panel (d) shows the measured
photoluminescence dispersion, we see that there is no sign of any influence of
polaritons on the photoluminescence for this open cavity. Finally, to
investigate the absorption we made further use of transfer matrix modelling,
the results are shown in panel (e).

##  Appendix C S3: Half Cavity (1630 nm)

Figure 7: Half Cavity (1630 nm). In panel (a) we show an experimentally
measured dispersion, based on p-polarised reflectance, indicated as a colour
plot. In panel (b) we show the calculated reflectance, the white dotted lines
represent the limit of the collection numerical aperture used in the
experiment. Panel (c) is the same as panel (b) except that in the calculation
we have set the oscillator strength of the dye to zero. In panel (d) we show
an experimentally measured dispersion plot acquired from photoluminescence
data. In panel (e) we show the calculated absorption in the TDBC-doped layer.
In panels (a-e) the polariton dispersion is shown, as determined from the
coupled oscillator model described in the methods section. The polariton
positions are shown as white dashed lines, and the molecular resonance (2.08
eV) by a black dotted line; three cavity modes were used in the model (see
panel (c)), and the polymer thickness was $\sim$1630 nm. In panel (f) the
polariton positions (normal incidence) are indicated by black dashed lines.

The sample used here was similar to that used for the half cavity data shown
in figure 3 of the main manuscript, the primary difference is that here the
thickness of the cavity was 1630 nm rather than 600 nm used for the sample
discussed in the main manuscript. Looking first at the reflectance, panels (a)
and (b), the presence of modes of the half cavity system are again indicated
by regions of low reflectivity (blue). Also shown are the positions of the
polaritons as determined by our coupled oscillator model, where we made use of
three cavity modes. We see that overall there is a reasonable match between
the experimental data, the calculated data, and the coupled oscillator model.
The calculated dispersion for a ‘bare’ cavity and the ‘bare’ coupled
oscillator model is shown in panel (c). From the modelling we determine that
in this case the reduced oscillator strength is 0.07, the splitting is
$\Omega=0.23\pm 0.03$ eV, and $\beta=1.1$. The splitting exceeds the sum of
the TDBC linewidth, $0.053\pm 0.003$ eV, and the width of the cavity modes,
$0.11\pm 0.02$ eV, so that we are again, on the basis of reflectivity data, in
the strong coupling regime. Panel (d) shows the measured photoluminescence
dispersion. As for the 600 nm thick half cavity, things are now slightly more
interesting than they were for the open cavity. The PL spectrum is somewhat
different from the open cavity case, and there is perhaps some slight mapping
of the PL onto the position of the lower polariton modes. Calculated data for
the absorption in the TDBC are shown in panel (e). There is again a
significant change in the absorption compared to that of the bulk (a single
absorption peak), and further there is now an indication of the absorption
tracking the polariton modes, at least in some very limited way.

##  Appendix D S4: Full Cavity (390 nm)

Figure 8: Full Cavity (390 nm). In panel (a) we show an experimentally
measured dispersion, based on p-polarised reflectance, indicated as a colour
plot. In panel (b) we show the calculated reflectance, the white dotted lines
represent the limit of the collection numerical aperture used in the
experiment. Panel (c) is the same as panel (b) except that in the calculation
we have set the oscillator strength of the dye to zero. In panel (d) we show
an experimentally measured dispersion plot acquired from photoluminescence
data. In panel (e) we show the calculated absorption in the TDBC-doped layer.
In panels (a-e) the polariton dispersion is shown, as determined from the
coupled oscillator model described in the methods section. The polariton
positions are shown as white dashed lines, and the molecular resonance (2.13
eV) by a black dotted line; just one cavity mode was used in the model (see
panel (c)), and the cavity thickness was $\sim$390 nm. In panel (f) the
polariton positions (normal incidence) are indicated by black dashed lines.

The sample used here was similar to that used for the full cavity data shown
in figure 4 of the main manuscript, the primary difference being that here the
thickness of the cavity was 390 nm rather than 355 nm used for the sample
discussed in the main manuscript. Looking first at the reflectance, panels (a)
and (b), the presence of modes of the full cavity system are again indicated
by regions of low reflectivity (blue). Also shown are the positions of the
polaritons as determined by our coupled oscillator model, where we made use of
one cavity mode (see panel (c)). We see that overall there is a reasonable
match between the experimental data, the calculated data, and the coupled
oscillator model. The calculated dispersion for a ‘bare’ cavity and the ‘bare’
coupled oscillator model is shown in panel (c). From the modelling we
determine that in this case the reduced oscillator strength is 0.04, the
splitting is $\Omega=0.27\pm 0.03$ eV, and $\beta=0.7$. The splitting exceeds
the sum of the TDBC linewidth, $0.053\pm 0.003$ eV, and the width of the
cavity modes, $0.11\pm 0.02$ eV, so that we are again, on the basis of
reflectivity data, in the strong coupling regime. Panel (d) shows the measured
photoluminescence dispersion. As for the 355 nm thick full cavity, the PL
spectrum is very clearly different from the open and half cavity cases, the PL
nicely mapping onto the position of the lower polariton mode. Calculated data
for the absorption in the TDBC are shown in panel (e). There is again a very
significant change in the absorption compared to that of the bulk (a single
absorption peak), the absorption now tracking the polariton modes.

##  Appendix E S5: Photoluminescence from different thin TDBC layers

Figure 9: Photoluminescence from thin TDBC layers. Three spectra are shown: PL
from TDBC produced by the layer-by-layer technique, deposited on Si; PL from
TDBC-doped PVA on Si; PL from TDBC-doped PVA on Au coated Si.

Note that the PL for TDBC-doped PVA peaks at a lower energy ($\sim$2.08 eV)
than the TDBC produced using the layer-by-layer technique ($\sim$2.13 eV).
Note also that for the TDBC-doped PVA on Au coated Si, the low energy shoulder
of the TDBC PL is enhanced in relative strength. This is consistent with a
recent observation based on squarine dyes Quenzel_ACSNano_2022_16_4693.

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