An application of deterministicaperiodic structures :

Sensing with Plasmonic quasi-crystals Ata Akatay

July 24, 2009

Photonic Crystals - Romuald Houdré

Application ideaperiodic media=> the formation of well-defined energy gapsdisordered random media=> the presence of localized eigenstates with highfield enhancement and Q-factorsdeterministic aperiodic structures=> Suggest solutions in between

« 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)

deterministic aperiodic structures

Periodic Fibonacci quasi-periodic structures

Thue–Morse and aperiodic structures

Rudin–Shapiro structures

absolutely continuoussingular continuous

quasiperiodic

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)

The dipole equations of motion :

Transfer matrix approach valid within the dipole approximation

Simplifies to : where,

In frequency domain :

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 microcavitieslow shifts of modal frequenciesSP sensors, which benefit from high values of field intensities in the detection regionbroad resonance linewidths (low Q-factors), which is a limiting factor in the spectral resolution of such devices.

deterministic aperiodic structuresCan be designed for more flexible solutions

References1. 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.

2. Dal Negro, L., N. N. Feng, et al. (2008). "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays." Journal of Optics a-Pure and Applied Optics 10(6): -.