An application of deterministic
aperiodic structures :
Sensing with Plasmonic quasicrystals
Ata Akatay
July 24, 2009
Photonic Crystals - Romuald Houdré
Application idea
periodic media
=> the formation of well-defined energy gaps
disordered random media
=> the presence of localized eigenstates with high
field enhancement and Q-factors
deterministic aperiodic structures
=> Suggest solutions in between
deterministic aperiodic structures
« defined by the iterations of simple mathematical
rules, rooted in symbolic dynamics, prime number
theory and L-system inflations »
Dal Negro, L. and N. N. Feng (2007)
Periodic
Fibonacci quasi-periodic
structures
quasiperiodic
singular continuous
Thue–Morse and
aperiodic structures
absolutely continuous
Rudin–Shapiro
structures
Dal Negro, L. and N. N. Feng (2007)
Fractal Fourier spectra
Fibonacci quasi-periodic
structures
Thue–Morse and
aperiodic structures
Rudin–Shapiro
structures
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L. and N. N. Feng (2007)
Aperiodic nanoparticle chain
Dal Negro, L., N. N. Feng, et al. (2008)
Transfer matrix approach valid
within the dipole approximation
The dipole equations of motion :
In frequency domain :
Simplifies to :
where,
and gives :
Dal Negro, L. and N. N. Feng (2007)
Analysis
the integrated density of states (IDS) of the chain:
participation ratio yields a quantitative measure of the localization degree
of the eigenstates:
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L., N. N. Feng, et al. (2008)
Dal Negro, L., N. N. Feng, et al. (2008)
Conclusion
whispering-gallery (WG) mode microcavities
low shifts of modal frequencies
SP sensors, which benefit from high values of field intensities in the detection
region
broad resonance linewidths (low Q-factors), which is a limiting factor in the
spectral resolution of such devices.
deterministic aperiodic structures
Can be designed for more flexible solutions
References
1.
2.
Dal Negro, L. and N. N. Feng (2007). "Spectral gaps
and mode localization in Fibonacci chains of metal
nanoparticles." Optics Express 15(22): 14396-14403.
Dal Negro, L., N. N. Feng, et al. (2008).
"Electromagnetic coupling and plasmon localization in
deterministic aperiodic arrays." Journal of Optics aPure and Applied Optics 10(6): -.