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Bloch-like surface waves in Fibonacci quasi-cyrstals and Thue-Morse aperiodic dielectric multilayers
SPIE Optics + Photonics 2016 [9929-23] San Diego, CA
August 31, 2016
Vijay Koju, William M. Robertson
Computational Science Program Middle Tennessee State University
λ2 λ1
Photonic band structure/diagram
Light cone in air Radiative zone
Allowed region
Forbidden region
Defect mode
Region beyond light cone Non-radiative zone
Region beyond light cone Non-radiative zone
Defect layer with extra thickness
λ1
Bloch surface wave in 1D periodic dielectric multilayer
Periodic dielectric multilayer
Photonic band structure/diagram
Light cone in air Radiative zone
Allowed region
Forbidden region
Region beyond light cone Non-radiative zone
Region beyond light cone Non-radiative zone
Defect mode lies in the forbidden region beyond the light cone.
It lies in the non-radiative zone.
Defect mode cannot be excited directed by incoming light from the air side.
Such defect modes are called Bloch surface wave (BSW) modes
Need for prism coupling or grating coupling to excite them.
Defect mode
Bloch surface wave in 1D periodic dielectric multilayer
Bloch surface wave in 1D periodic dielectric multilayer
Bloch surface waves widely studied in periodic multilayers.
Not realized in aperiodic and quasi-crystals yet.
Other optical properties like dispersion and band-gap, perfect transmission, propagation, and localization of light studied well.
Periodic structures are used for applications largely because it has not been recognized that aperiodic structures can also provide such functionalities.
When compared to their periodic counterparts, aperiodic structures can add significant flexibility and richness when engineering the optical response of devices in ways that have yet to be realized.
We show that Bloch-like surface waves can be excited in Fibonacci quasi-crystals (FQCs) and Thue-Morse aperiodic dielectric multilayers (TMADMs).
Motivation to go aperiodic
Fibonacci quasi-crystals and Thue-Morse aperiodic multilayers
Fibonacci sequence generation rule:
Thue-Morse sequence generation rule:
Some examples: Fibonacci Thue-Morse
Dielectric materials used in our simulations
A = TiO2
B = SiO2
Loss introduced through the imaginary part of the refractive index. 0.00016 for TiO2 and 0.000034 for SiO2.
Wavelength dependent refractive indices over the range of 430 – 800 nm.
1.44
1.45
1.47
1.46
2.5
2.6
2.8
2.7
2.9
450 550 650 750 Wavelength [nm]
nTi
O2
nSi
O2
34-layered (S7) Fibonacci quasi-crystal (FQC)
Two Bloch-like surface modes (BLSMs) found over the wavelength range of 430 – 800 nm. Modes lie beyond the lightline.
Highly confined electric field at the surface layer. Exponentially decaying field profile in the air side. Field confinement in the multi- layer side not necessarily exponential.
ABAABABAABAABABAABABAABAABABAABAAB
A = TiO2 , 71.9 nm thick B = SiO2 , 108.4 nm thick
λ = 443.2 nm θ = 45.670
λ = 760 nm θ = 42.140
32-layered (S5) Thue-Morse aperiodic dielectric multilayer (TMADM)
Four Bloch-like surface modes (BLSMs) found over the wavelength range of 430 – 800 nm. Modes lie beyond the lightline.
Highly confined electric field at the surface layer. Exponentially decaying field profile in the air side. Field confinement in the multi- layer side not necessarily exponential.
ABBABAABBAABABBABAABABBAABBABAAB
A = TiO2 , 71.9 nm thick B = SiO2 , 108.4 nm thick
λ = 762.4 nm θ = 420
λ = 701.4 nm θ = 420
λ = 488.1 nm θ = 41.860
λ = 465.1 nm θ = 41.860
Comparison with a periodic counterpart
Bloch surface wave in a 32-layered periodic dielectric multilayer (PDM) with a surface defect. Exponentially decaying field at the multilayer side as well as the air side.
ABABABABABABABABABABABABABABABAB’
A = TiO2 , 71.9 nm thick B = SiO2 , 108.4 nm thick B’ = SiO2 defect layer, 120 nm thick
λ = 440 nm θ = 53.160
Comparison with a periodic counterpart
|E|2 Electric filed intensity at the surface, normalized by input electric field intensity.
PD e-1 penetration depth of the exponentially decaying field beyond the surface.
Both |E|2 and PD highly enhanced in FQC and TMADM compared to their periodic counterpart. High |E|2 field and PD can be utilized for improving the quality of fluorescence based detection and surface-enhanced Raman spectroscopy.
Bloch-like surface waves in different generations of FCQs
13 layered (S5) FCQ
89 layered (S9) FCQ
λ = 475 nm θ = 42.360
λ = 440 nm θ = 46.530
Bloch-like surface waves in different generation of TMADM
8 layered (S3) TMADM
λ = 460 nm θ = 42.460
λ = 700 nm θ = 43.630
Conclusions
We show the existence of Bloch-like surface waves in Fibonacci quasi-crystals and Thue-Morse aperiodic dielectric multilayer structures.
Bloch-like surface waves also exist for different generation of FCQs and TMADM.
Bloch-like surface waves exhibit enhanced electric field at the surface layer.
They also have extended penetration depth beyond the surface of the multilayer.
Have applications in the field of label-free detection, fluorescence detection and surface enhanced Raman spectroscopy.
References
Koju, V. and Robertson, W. M., “Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers,” Opt. Lett. 41, 2916-2918 (2016)
Vardeny Z. V., Nahata, A. and Agrawal, A., “Optics of photonic quasicrystals,” Nat. Phot. 7, 117 (2013).
Delfan, A., Liscidini, M. and Sipe, J. E., “Surface enhanced Raman scattering in the presence of multilayer dielectric structures,” J. Opt. Soc. Am. B 29, 1863 (2012).
Robertson, W. M. and May, M. S., “Surface electromagnetic wave excitation on one-dimen- sional photonic band-gap arrays,” Appl. Phys. Lett. 74, 1800 (1999).
Toma, K., Descrovi, E., Toma, M., Ballarini, M., Madracci, P., Fiorgis, F., Mateescu, A., Jonas,
U., Knoll, W. and Dostalek, J., “Bloch surface wave-enhanced fluorescence biosensors,” Biosensors and Bioelectronics, 43, 108 (2013).
Thank you