SUPPLEMENTAL INFORMATION
Fig SI1 shows the calculated reflectance spectrum of the HB-PVS:CA DBR compared to the experimental
one.
Reflectance (%)
100
75
50
25
0
300
400
500
600
700
800
900 1000
Wavelength (nm)
FIGURE SI1 Calculated (red line) and experimental (black line) reflectance spectrum of a ten bilayers HBPVS:CA DBR.
Concerning spectral tunability of the DBR, we would like to remember that it is possible to tune the PBG
in different spectral regions as reported in the figure SI2 for an HB-PVS polymer slightly different than
the one described in in the manuscript and possessing a lower processability. There, the reflectance
spectrum of a 5 bi-layers system is reported. The first order PBG is observed at about 1900 nm, the
second one at 950 nm, the third one at 600 nm, and the fourth one is observed at about 350 nm with a
sigmoid line shape since it overlapped with the absorption of HB-PVS. This DBR however, possesses a
lower uniformity over the surface.
80
Reflectance (%)
70
I° order
60
50
40
II° order
30
20 IV° order
III° order
10
0
300 450 600 750 9001050 1500
2000
2500
Wavelength (nm)
FIGURE SI2 Reflectance spectrum of a DBR with the main PBG tuned deep in the Near Infrared. Notice
that the HP-PVS used for this sample is slightly different that the one mainly used in the manuscript (a
naphthyl group replaces a phenyl one)
100
0°
4°
8°
12°
16°
20°
24°
28°
32°
36°
40°
44°
48°
52°
56°
60°
75
50
25
(a) P-polarization, experiment
Transmittance (%)
Transmittance (%)
100
75
50
25
(b) P-polarization, theory
0
0
500
600
700
800
900
500
1000
700
800
900
1000
900
1000
100
Transmittance (%)
100
Trasmittance (%)
600
Wavelength (nm)
Wavelength (nm)
75
50
25
75
50
25
(c) S-polarization, experiment
(d) S-polarization, theory
0
0
500
600
700
800
900
500
1000
Wavelength (nm)
600
700
800
Wavelength (nm)
FIGURE SI3 Experimental (a, c) and Calculated (b, d) transmittance spectra as a function of the incidence
angle for the HB-PVS:CA DBR for both P- (a, b) and S-polarization (c, d).
A very general (and rough) expression for the low incidence angle dispersion of the PBG wavelength ()
as function of the incidence angle () is provided by the Bragg-Snell law which is widely used for opal
structures (ref. 57)
2
𝑚𝜆 = 2𝐷√𝑛𝑒𝑓𝑓
− 𝑠𝑖𝑛2 𝜃
(Eq. SI1)
Where m is the diffraction order and neff is the effective refractive index of the structure (the averaged
refractive index over the volume fraction of composing materials). By considering that in the optics the
incidence angle is measured form the normal to the surface, while in crystallography from the surface,
this equation is the well-known Bragg diffraction expression where the refractive index of void (n=1) is
replaced by neff (ref. 57-58). In the case of DBR, neff can be written as
𝑛𝑒𝑓𝑓 = 𝑛1
𝑑1
𝑑1 +𝑑21
+ 𝑛2
𝑑2
𝑑1 +𝑑2
(Eq. SI2)
These simple expression provides a rough description of the angular dispersion and do not take into
account the polarization properties and the correlated effective medium theory (ref. 57-58).
For DBR in the /4th condition and for low dielectric contrast, a more detailed analytical expression is
available (ref. 41 and 59).
1
𝜆
1
𝜆
= 4(𝑑
1
𝑛1 𝑐𝑜𝑠𝜃1 +𝑛2 𝑐𝑜𝑠𝜃2
1 +𝑑2 ) 𝑛1 𝑛2 𝑐𝑜𝑠𝜃1 𝑐𝑜𝑠𝜃2
1
= 4𝑛
𝑛1 𝑐𝑜𝑠𝜃2 +𝑛2 𝑐𝑜𝑠𝜃1
2
2
1 𝑛2 (𝑑1 𝑐𝑜𝑠 𝜃1 +𝑑2 𝑐𝑜𝑠 𝜃2 )
for S-polarization
(Eq. SI3a)
for P-polarization
(Eq. SI3b)
Where 1 and 2 are the refraction angles inside the layers and are connected to the external angle
(the one experimentally used) through the Snell law at the different interfaces
𝑛𝑎𝑖𝑟 𝑠𝑖𝑛𝜃 = 𝑛1 𝑠𝑖𝑛𝜃1 (interface air-material 1)
𝑛1 𝑠𝑖𝑛𝜃1 = 𝑛2 𝑠𝑖𝑛𝜃2 (interface material 1 – material 2)
(Eq. SI4a)
(Eq. SI4b)
However, since our DBR are not tuned to the /4th condition, we did not report such expression and we
showed in the Supporting Information (Fig. SI2 c and d) the full numerical calculations of the angle
dependent spectra. In order to account for the referee comment, in the revised version of the
manuscript the dispersion formula for the DBR in the /4th condition are reported in the Supporting
Information.
Reflectance (a.u.)
Fig. SI4 shows the reflectance spectra of a microcavity where HB-PVS plays the role of cavity layer within
a two PVK:CA DBR mirrors. Spectra are recorded in different position of the sample thus indicating an
imperfect uniformity of the structure over a layer larger than one squared inch.
400
500
600
700
800
Wavelength (nm)
FIGURE SI4 Reflectance spectra of the microcavity containing HB-PVS as recorded in different spots on
the sample surface.
We explain here in more details the role of the field enhancement within the microcavity. The simplest
way to explain the fluorescence enhancement is to describe it in terms of density of photonic states (phDOS) as a function of photon energy. The ph-DOS is roughly inversely proportional to the first derivative
of the band structure (E(k))
𝑝ℎ − 𝐷𝑂𝑆 ÷
1
(Eq. SI5)
𝑑𝐸
𝑑𝑘
Indeed, when the light is allowed to propagate through a medium this relation is parabolic (panel (a) in
Figure SI5). The presence of the photonic band gap modifies this picture generating a spectral region
where the ph-DOS is almost zero (panel (b)). Indeed, in such region photons are not allowed to
propagate. The microcavity is a defect of the periodical dielectric lattice. It generates a new state within
the PBG where the electromagnetic field is spatially confined. There, the ph-DOS increases since its first
derivative is zero showing a very sharp peak. The width of the peak is related to the thickness
uniformity. The sharp peak in the ph-DOS for the microcavity corresponds to a strong enhancement of
the Electromagnetic field within the structure.
(c)
(b)
DOS
(a)
Energy
Energy
Energy
FIGURE SI5 Sketch of the photonic DOS for (a) free photons in a homogeneous medium, (b) photons in
a DBR and (c) photons in a planar microcavity.