rigorous quality factor calculation in contemporary
TRANSCRIPT
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1School of Electrical and Computer Engineering, Aristotle University of Thessaloniki
2Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas
Rigorous Quality Factor Calculation in Contemporary
Optical Resonant Systems
Thomas Christopoulos,1 Odysseas Tsilipakos,2 Georgios Sinatkas,1 and Emmanouil E. Kriezis1
Optical Wave & Waveguide Theory and Numerical Modelling (OWTNM) 2019
10-11 May, 2019 – Malaga, Spain
10/05/2019: RESONANT STRUCTURES
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
2
Motivation
o Resonant structures are ubiquitous in modern photonics integrated circuits
o Contemporary platforms (plasmonics) and materials (graphene) exhibit distinct characteristics
o Quality factor calculation is non-trivial
Objectives
o Collectively present the Q-factor calculation techniques using commercially available software implementing FEM (COMSOL Multiphysics, ANSYS HFSS, CST Microwave studio)
o Highlight the effect of material dispersion, ohmic loss and light leakage on the calculations
o Propose alternatives routes
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Presentation outline
3
Computational methods for calculating the Quality Factor
1. Eigenvector
2. Field distribution
3. Eigenfrequency
4. Spectral response
Application range of the methods via examples
o Silicon ring resonator at the NIR
o Graphene tube resonator at the FIR
o Polaritonic rod at the FIR
o Plasmonic core-shell at the visible
Conclusions
School of Electrical & Computer Engineering | Aristotle University of Thessaloniki
Photonics Group | www.photonics.ee.auth.gr
Computational methods for calculating the Quality Factor
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
o Stored energy on resonance
o Power loss
Quality factor definition (1): the eigenmode and the field distribution methods
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Q-factor calculation
Quality Factor definition
• Resistive
• Radiation
• External (coupling)
IntrinsicLoaded
[D. M. Pozar, Microwave Engineering]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
o Stored energy on resonance
o Power loss
Quality factor definition (1): the eigenmode and the field distribution methods
6
Q-factor calculation
Quality Factor definition
• Resistive
• Radiation
• External (coupling)
IntrinsicLoaded
Energy and Losses calculation
Material dispersion
Dielectric lossOhmic loss
[D. M. Pozar, Microwave Engineering]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Quality factor definition (2): the eigenmode and the field distribution methods
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Q-factor calculation
o and diverge but is constant
1. The eigenmode method
Commercial FEM eigenvalue implementations do not incorporate dispersion
o Complex eigenvalue
o Temporal decay
o Spatial exponential divergence!
EIGENMOME METHOD FAILS IN HIGHLY DISPERSIVE SYSTEMS
[L. D. Landau, Electrodynamics of continuous media]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Quality factor definition (2): the eigenmode and the field distribution methods
8
Q-factor calculation
FIELD DISTRIBUTION METHOD REQUIRES CAREFUL CHOICE OF THE INTEGRATION WINDOW
2. The field distribution method
o Driven harmonic simulation @
o Physically incorporates dispersion
o Spatial and temporal mode decay
o and diverge but is constant
1. The eigenmode method
Commercial FEM eigenvalue implementations do not incorporate dispersion
o Complex eigenvalue
o Temporal decay
o Spatial exponential divergence!
o depends on the integration windowo diverges with radius
EIGENMOME METHOD FAILS IN HIGHLY DISPERSIVE SYSTEMS
[L. D. Landau, Electrodynamics of continuous media]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Alternative approaches: the eigenfrequency and the spectral response method
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Q-factor calculation
3. The eigenfrequency method
Commercial FEM eigenvalue implementations do not incorporate dispersion
o Complex eigenvalue
EIGENFREQUENY METHOD FAILS IN DISPERSIVE SYSTEMS
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Alternative approaches: the eigenfrequency and the spectral response method
10
Q-factor calculation
4. The spectral response method3. The eigenfrequency method
Commercial FEM eigenvalue implementations do not incorporate dispersion
o Complex eigenvalue
EIGENFREQUENY METHOD FAILS IN DISPERSIVE SYSTEMS
ω0
Δω
Tmin
( )/2Tmin max + T
Tmax
ω0
Δω
Tmin
( )/2Tmin max + T
Tmax
o Driven harmonic simulation @ frequencies around
SPECTRAL RESPONSE METHOD IS ALWAYS CORRECT
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Alternative approaches: the eigenfrequency and the spectral response method
11
Q-factor calculation
4. The spectral response method3. The eigenfrequency method
Commercial FEM eigenvalue implementations do not incorporate dispersion
o Complex eigenvalue
EIGENFREQUENY METHOD FAILS IN DISPERSIVE SYSTEMS
ω0
Δω
Tmin
( )/2Tmin max + T
Tmax
ω0
Δω
Tmin
( )/2Tmin max + T
Tmax
o Driven harmonic simulation @ frequencies around
SPECTRAL RESPONSE METHOD IS ALWAYS CORRECT
School of Electrical & Computer Engineering | Aristotle University of Thessaloniki
Photonics Group | www.photonics.ee.auth.gr
Application range of the methods via examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
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Study examples
o Weak dispersion
o Absence of ohmic loss
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
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Study examples
o Weak dispersion
o Absence of ohmic loss
[Bogaerts, Laser Photonics Rev. 6, 47, 2012][Pendry, Science 312, 1780, 2006]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
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Study examples
o Weak dispersion
o Absence of ohmic loss
[Bogaerts, Laser Photonics Rev. 6, 47, 2012][Pendry, Science 312, 1780, 2006]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
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Study examples
o Weak dispersion
o Absence of ohmic loss
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
17
Study examples
o Weak dispersion
o Absence of ohmic loss
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // Intrinsic Q
18
Study examples
o Weak dispersion
o Absence of ohmic loss
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // External and Loaded Q
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o Weak dispersion
o Absence of ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // External and Loaded Q
20
o Weak dispersion
o Absence of ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // External and Loaded Q
21
o Weak dispersion
o Absence of ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // External and Loaded Q
22
o Weak dispersion
o Absence of ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Silicon slab ring resonator @ Near Infrared spectrum // External and Loaded Q
23
o Weak dispersion
o Absence of ohmic loss
Study examples
[H. A. Haus, Waves and Fields in Optoelectronics]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Graphene tube resonator @ Far Infrared (THz) spectrum
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o Strong dispersion
o Absence of radiation
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Graphene tube resonator @ Far Infrared (THz) spectrum
25
o Strong dispersion
o Absence of radiation
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Graphene tube resonator @ Far Infrared (THz) spectrum
26
o Strong dispersion
o Absence of radiation [Christopoulos, Phys. Rev. E 94, 062219, 2016]
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Graphene tube resonator @ Far Infrared (THz) spectrum
27
o Strong dispersion
o Absence of radiation [Christopoulos, Phys. Rev. E 94, 062219, 2016]
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Graphene tube resonator @ Far Infrared (THz) spectrum
28
o Strong dispersion
o Absence of radiation [Christopoulos, Phys. Rev. E 94, 062219, 2016]
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Dielectric rod resonator/metasurface @ Far Infrared (THz) spectrum
29
o Weak dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Dielectric rod resonator/metasurface @ Far Infrared (THz) spectrum
30
o Weak dispersion
o Radiation and ohmic loss
Study examples
[J. A. Stratton, Electromagnetic Theory]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Dielectric rod resonator/metasurface @ Far Infrared (THz) spectrum
31
o Weak dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Dielectric rod resonator/metasurface @ Far Infrared (THz) spectrum
32
o Weak dispersion
o Radiation and ohmic loss
[Ruan, J. Phys. Chem. C 114, 013901, 2010]
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Dielectric rod resonator/metasurface @ Far Infrared (THz) spectrum
33
o Weak dispersion
o Radiation and ohmic loss
[Ruan, J. Phys. Chem. C 114, 013901, 2010]
[H. A. Haus, Waves and Fields in Optoelectronics]
Study examples
[Tsilipakos, Adv. Opt. Mater. 6, 1800633, 2018]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Plasmonic core-shell @ Visible spectrum
34
o Strong dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Plasmonic core-shell @ Visible spectrum
35
o Strong dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Plasmonic core-shell @ Visible spectrum
36
o Strong dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Plasmonic core-shell @ Visible spectrum
37
o Strong dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Plasmonic core-shell @ Visible spectrum
38
o Strong dispersion
o Radiation and ohmic loss
Study examples
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Conclusion
39
Summary
o Presentation of the Q-factor calculation in contemporary photonic resonant structures
o Evaluation in four judiciously chosen structures
o In depth examination of their applicability range with commercially available software
Results
o Strong influence of dispersion on the correct calculation of Q
o Light leakage also hardens the calculation
[arXiv:1902.09415]
Photonics Group | School of ECE | AUTH
w w w . p h o t o n i c s . e e . a u t h . g rThomas Christopoulos
Thank you!
web: w w w . p h o t o n i c s . e e . a u t h . g r
e-mail: c t h o m a s a @ e c e . a u t h . g r
This research was co-financed by Greece and the European Union (European Social Fund-ESF)through the Operational Program “Human Resources Development, Education and LifelongLearning 2014-2020” in the context of the project “Nonlinear phenomena in graphene-comprisingresonators” (MIS 5004717).