3. Kishan Menghrajani, Bill Barnes
Physics and Astronomy department
University of Exeter, Exeter, UK
3
Strong coupling beyond the light-line
4. 4
Placing ensembles of molecules that possess an optically active transition inside a confined light field such as
an optical microcavity may lead to a phenomenon known as strong coupling, in which new hybrid states called
polaritons are created that are part molecule, part light.
Strong coupling- Background
To observe strong coupling the Rabi splitting (ћ Ω) has
to be larger than decay rate of each system.
ћ Ω > (Γ𝑎 𝑜𝑟 Γ𝑏)
Confined vacuum
fluctuations
Energy
Molecule P+
P-
• Micro-cavity
• Plasmon resonance
ћ Ω
Matter in a cavity:
energy exchange
ћ Ω= Rabi splitting
ω
θ
System a
System b
ћ Ω
ћ Ω ∝
𝑁
𝑉
Number of
molecules
Mode volume
5. Outline
Microcavity: strong coupling seen for:
• Multiple vibrational modes
Plasmon mode:
• Strong coupling of plasmonic mode with vibrational mode
Coupled plasmon mode:
• Strong coupling beyond the light-line
5
6. Outline
Microcavity: strong coupling seen for:
• Multiple vibrational modes
Plasmon mode:
• Strong coupling of plasmonic mode with vibrational mode
Coupled plasmon mode:
• Strong coupling beyond the light-line
6
7. strong coupling of single molecular vibrational mode in
an optical microcavity
FTIR (Fourier Transform InfraRed)
transmission spectra of PMMA
θincident
kx
IR source
40-60 THz
7
sin
2
xk
PMMA=Poly(methyl methacrylate)
Drude- Lorentz model
Nature Comm. 2015, 6, 1–6; ACS Photonics 2015, 2, 130–136.
ћ Ω
Calculated dispersion plot
of empty microcavity
Transmittance(%)
Transmittance(%)
Transmittance(%)
Calculated dispersion plot of
microcavity with vibrational mode (C=0) Hopfield coefficient which indicates
the relative strength of each mode
Hopfield coefficient of vibrational
mode (C=O)
Au
Au
PMMA
Hopfieldcoefficients
Kx/2π (cm-1)
8. Experiment Computational
C=0
CH2
CH3
Hybridization of multiple vibrational modes via strong coupling
in an optical microcavity
CH3 CH2
C=O
Hopfield coefficient of Middle Polariton (MP)
mode showing energy exchange between
vibrational mode CH3, CH2 with C=O
8
Bare cavity mode
Menghrajani. K, et al. (Advanced Optical Materials 2019, 1900403)
Dispersion plot of optical microcavity
with multiple molecular vibrational modes
9. Outline
Microcavity: strong coupling seen for:
• Multiple vibrational modes
Plasmon mode:
• Strong coupling of plasmonic mode with vibrational mode
Coupled plasmon mode:
• Strong coupling beyond the light-line
9
10. P. Torma and W. L. Barnes, Reports on Progress in
Physics 78, 013901 (2015)
10
Plasmonic mode
Plasmonic mode
Vibrational mode
Vibrational mode
Here we investigate the strong coupling of vibrational molecular resonances
with the infrared surface plasmon modes associated with metal surfaces.
Strong coupling in open plasmonic cavities
We make use of periodic grating
structures to probe (momentum
match to) the hybrid polariton modes
that arise from such strong coupling
scattered surface
plasmon modes
Menghrajani. K, et al. (ACS Photonics 2019 6 (8), 2110-2116)
11. 11
Strong coupling of plasmonic modes with
molecular vibrational mode
E-Beam Lithography
Atomic Force Microscopy showing
30nm Au grating on CaF2
The period of the grating is 4.5 μm with a 1 μm gap between metal stripes.
The PMMA thickness is 1.5 μm.
The dashed blue and green lines are the ±1 scattered air and ±2,3 scattered silicon light-lines
respectively.
Menghrajani. K, et al. (ACS Photonics 2019 6 (8), 2110-2116)
ExperimentComputational
Dispersion plot of plasmonic modes
without molecular vibrational mode
Dispersion plot of plasmonic modes
with molecular vibrational mode
12. 12
Strong coupling of polariton stop band edges
COMSOL plot
Here we are varying the period, keeping the spacing
between metallic elements fixed at 1 um.
The upper and lower band
edge undergo an anti-crossing.
Electric field distribution
Field concentrated for the lower band edge on metal slab
whilst the upper band edge has field maxima over both
metallic and gap region.
Physical review B 1996, 54,6227-6244 Menghrajani. K, et al. (ACS Photonics 2019 6 (8), 2110-2116)
13. Outline
Microcavity: strong coupling seen for:
• Multiple vibrational modes
Plasmon mode:
• Strong coupling of plasmonic mode with vibrational mode
Coupled plasmon mode:
• Strong coupling beyond the light-line
13
15. Dispersion plot of coupled plasmon mode
with vibrational mode
15
Strong coupling of coupled plasmon mode
Schematic of coupled plasmon
mode structure
ExperimentComputational
TM-1
Menghrajani. K, et al. (under revision)
Frensel coefficient model
16. Rabi splitting vs cavity thickness
16
Single-molecule strong coupling at room temperature in
plasmonic nanocavities
Chikkaraddy et al. Nature volume535, pages127–130, 2016
Rabi splitting as a function of cavity thickness
The error bars represent the confidence range in
the Rabi splitting from Fresnel-derived dispersion data
17. 17
Menghrajani. K, et al. (under revision)
Schematic showing DBR
cavity structure
DBR based cavity
Dispersion plot based on Fresnel-type
calculations.
The absolute value of the TM polarised Fresnel coefficient is shown as a function of frequency (wavenumber)
and in-plane wavevector
Dispersion of DBR cavity modes for
zero oscillator strength
18. Conclusion
• I have shown strong coupling of multiple molecular
vibrational modes of same molecular species (PMMA) with
micro-cavity mode. (radiative)
• Later, I have shown strong coupling between plasmon mode
and molecular vibrational mode. (non radiative)
• Finally, I have shown strong coupling between coupled
plasmon mode (below cut-off) and molecular vibrational
mode. (non radiative)
18
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