Supplementary Information: Large spontaneous emission rate
enhancement in grating coupled hyperbolic metamaterials
Kandammathe Valiyaveedu Sreekanth1*, Koduru Hari Krishna1, 2, Antonio De Luca2 and
Giuseppe Strangi1, 2**
1
Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland,
Ohio. 44106-7079, USA
2
Department of Physics and CNR-IPCF UOS di Cosenza, University of Calabria, 87036 - Rende
(Italy)
Correspondence authors: E-mail: *sxk923@case.edu , **giuseppe.strangi@case.edu
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1. Transmission and reflection measurements of GCHMM
The transmission measurement of GCHMM at normal incidence is carried out and shown in Fig.
S1. It is evident from the figure that the resonant transmission peaks are located around the same
positions of the reflectance minima. The obtained transmission plot also shows the existence of
plasmonic modes in GCHMM. The plasmonic modes of metal-dielectric multilayered
metamaterial can be experimentally probed by studying the reflectance spectra as a function of
incident angle at a particular wavelength. The excitation of bulk plasmon modes at different
excitation wavelengths are shown in Fig. S2. It should be noted that the investigated wavelength
spectral region supports the bulk plasmon modes. As reported before, the number of dielectric
layers in the multilayer decides the total number of bulk modes 1. Here, we observed only one
bulk mode for both 430 nm and 450 nm excitation wavelength that represents the fundamental
mode. However, two bulk modes are present for 480 nm excitation wavelength that represent the
fundamental and first order mode, respectively. Note that the higher order bulk modes are absent
in the reflectance spectra because of the coupling issue due to large modal indices of the higher
order guided modes. The reflectance spectrum of GCHMM geometry is simulated using
scattering matrix method (Fig. S3). Here the incident grazing angle is set to be 50ο. It shows that
the simulation curve is exactly matching with experimental curve in Fig. 3. We theoretically
verified that the reflectance minimum close to 400 nm wavelength is due to surface plasmon
modes of metallic diffracting grating and other three (above 450 nm) reflectance minima are due
to bulk plasmon modes of HMM2.
Reflectance spectra of Ag film deposited samples in the absence and presence of dye
doped PMMA layer are shown in Fig. S4 (a) and (b), respectively. In comparison to absence of
dye doped PMMA layer, presence of dye doped PMMA layer shows a broad reflectance
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minimum at higher wavelength (750 nm), which is due to the presence of Ag scatterers
intermixed at the interface with dye doped PMMA layer.
Figure S1 Transmittance spectrum of GCHMM at normal incidence. The obtained four
prominent transmission maxima correspond to the excitation of plasmonic modes from
GCHMM.
Figure S2 Reflectance spectra of GCHMM as a function of incident angle. (a) 430 nm, (b) 450
nm and (c) 480 nm.
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Figure S3 Simulated reflectance spectrum of GCHMM at 50ο incident angle.
Figure S4 Reflectance spectra of Ag film deposited samples in the absence (a) and presence (b)
of dye doped PMMA layer.
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2. Experimental set up
As shown in Fig. S5, an ultrafast optical set up has been used to measure the lifetimes of the
samples. The optical set up consists of a Ti: Sapphire tunable femtosecond laser (Chameleon
Ultra II from Coherent), Pulse Picker (by Coherent), Second Harmonic Generator (by Coherent),
and a spectrofluorometer for time-correlated single photon counting (TCSPC) instrument (by
Edinburgh instruments). The time resolution of the TCSPC instrument is ≤ 5 ps. In the
experiments, the Coumarin 500 dye was excited by using a pulsed laser at 380 nm with a pulse
width of about 120 fs and a repetition rate of 4 MHz. Here the emission wavelengths were varied
using a monochromator that belongs to the TCSPC instrument.
Figure S5 Experimental set up used for the lifetime photoluminescence measurements.
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4. Absorption and steady state photoluminescence measurements
The absorption spectrum of Coumarin 500 dye dissolved PMMA (reference sample) is shown in
Fig. S6 (a). The maximum absorption is observed at 380 nm wavelength. We conducted steadystate photoluminescence measurements using spectrofluorometer to verify the coupling of dye
emission into the metamaterial states. The detection method was based on a reflection geometry
in which dyes were excited using a mercury lamp and the emitted signals were detected using a
last generation multichannel photomultiplier tube. For 380 nm excitation wavelength, the
maximum emission wavelength of Coumarin 500 dye dissolved PMMA is observed at 470 nm
wavelength (Fig. S6(b)).
Figure S6 (a) Absorption spectrum of dye dissolved PMMA (for reference sample). (b) Steadystate photoluminescence measurements of dye on reference sample.
5. Lifetime photoluminescence measurements
The time decay curves of Ref and HMM samples for three different emission wavelengths are
shown in Fig. S7. The transition from elliptical to hyperbolic dispersion is very clear from the
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figures that there is a large variation in time decay for HMM compared to reference sample when
the emission wavelength is increased from 420 nm to 450 nm.
In
order
to
obtain
the
lifetime,
the
data
are
fitted
using,
R(t )  B1 e t / 1  B2 e t / 2  B3e t /  3 , where τi is the lifetime. The obtained shorter lifetimes (τ1 and
τ2) of Ref and HMM samples as a function of emission wavelengths are shown in Fig. S8. In
hyperbolic region, a large difference in spontaneous emission lifetime of dye onto the HMM
compared to reference sample is observed. Also, dye on reference sample show an increase in
lifetimes with emission wavelengths; however lifetime of dye onto HMM is almost constant in
the hyperbolic region of the emission spectra. The observed behaviour of HMM is attributed to
the existence of high-k modes as well as non-radiative and SPP modes present in the HMM3. The
time decay curves of HMM with Ag and GCHMM samples for three different emission
wavelengths are also shown in Fig. S9.
Figure S7 Time-resolved photoluminescence measurements of Coumarin dye on Ref and HMM
samples. (a) in elliptical region (λe=420 nm), (b) at critical wavelength (λc=430 nm), and (c) in
hyperbolic region (λe=450 nm). Black lines represent the corresponding fit.
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Figure S8 Variation of spontaneous emission lifetimes of the Coumarin dye on Ref and HMM
samples, as a function of emission wavelength. (a) first decay time and (b) second decay time.
Figure S9 Time-resolved photoluminescence measurements of Coumarin dye on HMM with Ag
and GCHMM samples. (a) in elliptical region (λe=420 nm), (b) at critical wavelength (λc=430
nm), and (c) in hyperbolic region (λe=450 nm). Red lines represent the corresponding fit.
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References
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nanoscale metal-dielectric multilayers. Phys. Rev. B 75, 241402 (2007).
2. Sreekanth, K. V., De Luca, A. & Strangi, G. Experimental demonstration of surface and bulk
plasmon polaritons in hypergratings. Sci. Rep. 3, 3291 (2013).
3. Krishnamoorthy, H. N. S., Jacob, Z., Narimanov, E., Kretzschmar, I. & Menon, V. M.
Topological transitions in metamaterials. Science 336, 205-209 (2012).
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