periodic photonic systems by Kin Hung Fung Department of Applied - - PowerPoint PPT Presentation
Pre se nta tio n in Ao E Wo rksho p (2016) Adva nc e d Co nc e pt in Wa ve Physic s T o po lo g y a nd PT Symme try PT symmetries & Non-reciprocity in periodic photonic systems by Kin Hung Fung Department of Applied Physics The
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by Kin Hung Fung Department of Applied Physics The Hong Kong Polytechnic University
Pre se nta tio n in Ao E Wo rksho p (2016) Adva nc e d Co nc e pt in Wa ve Physic s T
Symme try
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ο Topological Photonics
Static magnetic field
A recent review: Topological Photonics
Edge mode breaks spectral reciprocity: π(π) β π(βπ)
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ο Our recent works related to spatial-temporal
symmetries such as PT symmetry are also provided as examples:
There is a difference between spectral reciprocity and Lorentz reciprocity.
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Spectral reciprocity
π π
T: time reversal (π¦, π§, π¨, π’) β (π¦, π§, π¨, βπ’) P: spatial inversion (π¦, π§, π¨, π’) β (βπ¦, βπ§, βπ¨, π’) Px: spatial inversion (π¦, π§, π¨, π’) β (βπ¦, π§, π¨, π’)
PT symmetry
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ο Can this periodic system support
Unit cell
Static magnetic field
One-way?
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ο Can this 1D periodic system support
Unit cell
Static magnetic field
One-way? A waveguide
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ο What if the materials have small gain/loss
Unit cell One-way? The time reversal symmetry is still broken! A waveguide
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ο We need to break enough symmetries to
ο Well-known examples of symmetries to break
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To have TRS, we want the following after time-reversal of fields:
We say that a system of given π(π²) and π(π²) has TRS if The macroscopic Maxwellβs equations and the constitutive relations for the same π and π are still satisfied by time- reversing the oscillating fields,
These new equations may NOT be satisfied. Original: If they are satisfied, then we have these conditions on π and π.
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Symmetry in band structure
π π
even when there is no spatial symmetry other than periodicity
Ref: Optical Properties
by K. Sakoda
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ο We need to break enough symmetries to
ο Well-known examples of symmetries to break
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ο We need to break enough symmetries to
ο Well-known examples of symmetries to break
Lorentz Reciprocity
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Sπππππ β ππππππππ
Conditions of reciprocal medium:
Case A: Case B:
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π = π πππ βπππ π π3 π = π πππ βπππ π π3 e.g., gyromagnetic materials
Broken TRS Broken Lorentz reciprocity
Observe the difference
(representation in frequency domain)
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ο What if the materials have small gain/loss
Unit cell One-way? The time reversal symmetry is still broken! A waveguide
NO because of Lorentz reciprocity.
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ο Can this 1D periodic system support
Unit cell
Static magnetic field
One-way? A waveguide
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ο We need to break enough symmetries to
ο Well-known examples of symmetries to break
Lorentz Reciprocity
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ο Can this 1D periodic system support
Unit cell
Static magnetic field
One-way? A waveguide
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ο To break
Unit cell
Static magnetic field
A waveguide
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π = 1 β ππ
2
π2 β ππ
2
π = π πππ βπππ π π3
ππ = β ππ π ππ
2
π2 β ππ
2
ππ: Plasma frequency ππ: Cyclotron frequency βDiatomicβ chain of nanoparticles
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π = 1 β ππ
2
π2 β ππ
2
π = π πππ βπππ π π3
ππ = β ππ π ππ
2
π2 β ππ
2
ππ: Plasma frequency ππ: Cyclotron frequency βDiatomicβ chain of nanoparticles
Light line
Notes: 4 bands due to 4 degrees of freedom in unit cell.
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Protected by RT symmetry T = time reversal R = 180Β° rotation about x-axis We need to break this RT symmetry too!
βDiatomicβ chain of nanoparticles CW Ling et al. Physical Review B 92 165430 (2015)
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T R
Protected by RT symmetry T = time reversal R = 180Β° rotation about x-axis We need to break this RT symmetry too!
βDiatomicβ chain of nanoparticles CW Ling et al. Physical Review B 92 165430 (2015)
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Did we break enough symmetries? Yes.
βDiatomicβ chain of nanoparticles CW Ling et al. Physical Review B 92 165430 (2015)
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Result: Non-reciprocal bands Did we break enough symmetries? Yes, It breaks P , T, RT, β¦
Wave vector k Plasmon frequency
Break inversion Break reflection & T
(π¬ β βπ¬) CW Ling et al. Physical Review B 92 165430 (2015)
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Did we break enough symmetries? Yes.
Case A Case B
CW Ling et al. Physical Review B 92 165430 (2015)
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Only forward propagation is allowed at some frequencies no matter what kind of excitation.
CW Ling et al. Physical Review B 92 165430 (2015)
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ο Conclusion of part A:
to achieve non-reciprocity
ο Can we keep PT symmetry while having
ο Next part:
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x y
Domain 1 Domain 2 The surface mode dispersion has been considered before:
but there is something missingβ¦
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x y
T: time reversal (π¦, π§, π¨, π’) β (π¦, π§, π¨, βπ’) P: spatial inversion (π¦, π§, π¨, π’) β (βπ¦, βπ§, βπ¨, π’) Py: spatial inversion in y (π¦, π§, π¨, π’) β (π¦, βπ§, π¨, π’)
Domain 1 Domain 2 Domain 1 Domain 2
P operation T operation The system has PT but not PyT symmetry.
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Jin Wang et al. Physical Review B 91 235410 (2015) Domain 1 Domain 2 ππ/ππ ππ/ππ bulk bulk
This flat band is for ππ < 0 only
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Jin Wang et al. Physical Review B 91 235410 (2015)
π|| π||
This ideal system gives on-way tunneling with perfect transmission. Notes: PyT (or RT) symmetry is broken to give π(π) β π(βπ). PT symmetry is kept to give perfect transmission mode.
x y
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ο We demonstrated that
ο We found
Asymmetric Bands Jin Wang et al. PRB 91 235410 (2015) CW Ling et al. PRB 92 165430 (2015)
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Contact info: Kin Hung Fung* khfung@polyu.edu.hk
Hong Kong Polytechnic University Other collaborators involved in this work: C.W. Ling Jin Wang
Hong Kong University of Science & Technology (HKUST) Southeast University (China)
Supported by Hong Kong RGC through the Area of Excellence Scheme & The Hong Kong Polytechnic University Jin Wang et al. PRB 91 235410 (2015)
The Hong Kong Polytechnic University (PolyU)
http://ap.polyu.edu.hk/apkhfung CW Ling et al. PRB 92 165430 (2015) (my PhD student) Other PT / Topology β related stuff PT and zero extinction (see poster no. 10) Topological plasmon chain: C.W. Ling et. al. Optics Express 23, 2021(2015)