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