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題目(和文)

フォトニック結晶におけるバレー依存した光学現象とトポロジカルに保護された偏光特異点

Title(English)

Valley-dependent physics and topologically-protected singularities inphotonic crystal slabs

著者(和文)

養田大騎

Author(English)

Taiki Yoda

出典(和文)

学位:博士(理学),学位授与機関:東京工業大学,
報告番号:甲第11364号,授与年月日:2020年3月26日,
学位の種別:課程博士,審査員:納富 雅也,村上 修一,藤澤 利正,金森 英人,西田 祐介

Citation(English)

Degree:Doctor (Science),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第11364号,
Conferred date:2020/3/26,
Degree Type:Course doctor,Examiner:,,,,

学位種別(和文)博士論文Category(English)

Doctoral Thesis

種別(和文)

要約

Type(English)

OutlinePowered by T2R2 (Tokyo Institute Research Repository)

Outline of “Valley-dependent physics and topologically-protectedsingularities in photonic crystal slabs”
Photonic crystals are periodic dielectric structures with periodic modulation of the refractive index.
The periodicity ensures that the dispersion of photons in photonic crystals is described by the photonic
band structure. The photonic band offers many attractive optical phenomena, and thus photonic
crystals are versatile platforms for controlling light. Because the photonic band structure is an opticalanalog of the electronic band structure, photons in photonic crystals sometimes display phenomena
similar to electrons in electronic crystals. In this thesis, we mainly deal with two topics: valleydependent optical physics and topological singularities of far-field polarization vectors.
First, we investigate valley-dependent optical physics in photonic crystals with triangular lattice.
Recently, valleyphotonics, which is an analogy with valleytronics in electronic systems, has been
extensively studied. The optical analogs of inversion-asymmetric graphene are sometimes called
valley photonic crystals. Previous works focus on valley photonic crystal slabs with honeycomb lattice
structures because the lowest two bands form Dirac cones at the K and K’ points in their photonic
crystals. When perturbations breaking the inversion symmetry is introduced, the degenerate two statesat the K and K’ points split, and it has been known that the gapped states display valley-dependent
optical phenomena such as the angular momentum and Berry curvature. The gapped states have thevortex of the Poynting vector, the in-plane circular polarization, and the phase singularity of the fields.
The direction of these circulations is opposite at the K and K’ points. In addition, the structural
asymmetry induces finite Berry curvatures at the K and K’ points. The Berry curvature also has
opposite values at the K and K’ points due to the time-reversal symmetry. Therefore, the chirality ofthe valley state at the K and K’ points couples to the valley degree of freedom. We can distinguish thevalley states via the valley-contrasting quantities. Moreover, the interface state emerges at the interface
between two valley photonic crystals with different valley topologies. All of the previous works relyon photonic crystal slabs with honeycomb lattice structures because this scheme is just analogous tographene with a staggered sublattice potential. However, the Berry curvature and angular momentum
are general properties in systems without inversion symmetry, and thus it is not clear whether thepresence of Dirac cones is essential. In this thesis, we propose another scheme to create valley photoniccrystals. We focus on triangular-lattice photonic crystals with circular and triangular holes. In
triangular-lattice photonic crystals with circular holes, the first band is not degenerate, and the second
and third band form Dirac cones at the K and K’ points. Here we focus on the lowest band. We
numerically demonstrate that the lowest band exhibits valley-dependent phenomena such as angularmomentum, Berry curvature, and interface states by breaking the inversion symmetry. We introduce
the inversion asymmetry by deforming circular holes into triangular holes. The structural asymmetry
induces the asymmetry of the mode profiles at the K and K’ points, which generates the finite angularmomentum and the Berry curvature at the K and K’ points. They are opposite for the modes at the Kand K’ points due to the time-reversal symmetry. We also find that the localized interface states appear
at the interfaces between two inverted valley photonic crystals. We numerically confirm that some ofthese interface states are robust against the backscattering at corners of a sharp bend. These results
show that triangular-lattice photonic crystals with triangular holes are new platforms for theexperimental realization of valley-dependent optical physics.
Second, we investigate far-field polarization vectors radiated from photonic crystals with or without
two-fold rotational symmetry. We first propose a new scheme to generate off-Γ bound states in thecontinuum (BICs) by using an at-Γ BIC with higher-order topological charges. Although off-Γ BICs
recently have attracted much interest, a systematic way to generate off-Γ BICs is still lacking. To
generate off-Γ BICs, we must tune system parameters carefully. In this thesis, we show that at-Γ BICs
with higher-order charges split into multiple off-Γ BICs by breaking the symmetry of photonic crystals.
We start with a photonic crystal with six-fold rotational symmetry because it can carry at-Γ BICs withcharge -2. We numerically confirm that the at-Γ BIC with charge -2 splits into two off-Γ BICs withcharge -1 by perturbations breaking six-fold rotational symmetry but preserving two-fold rotational
symmetry. The mechanism of this scheme relies on charge conservation and crystalline symmetry.
These results suggest that we can deterministically generate off-Γ BICs by an infinitesimal
perturbation without fine-tuning of system parameters. We also demonstrate a wide variety of paircreation and annihilation processes of circularly-polarized states with opposite charge and same
handedness. Two circularly-polarized states with opposite charge and same handedness are annihilatedby the collision between them. To fully describe the topological nature of BICs and circularlypolarized states, we introduce the handedness-wise topological charge. The handedness-wise
topological charge consistently explains the creation and annihilation of circularly-polarized states,and guarantees the topological protection of these polarization singularities. Our results pave the way
for the application of BICs with higher-order charges to far-field topological photonics.
Finally, we experimentally confirm the splitting of an at-Γ BIC with charge -2 into two off-Γ BICs
with charge -1. To demonstrate the splitting of an at-Γ BIC, we fabricate three types of photonic
crystals: one is a photonic crystal with six-fold rotational symmetry, and the others are perturbedphotonic crystals without six-fold rotational symmetry. We perform two angle-resolved reflection
measurements to characterize the band structure, quality factor, and far-field polarization vector of thefabricated photonic crystals. In the first measurement, we measure the reflection spectra of thefabricated photonic crystals, and determine the band structure and quality factor of the modes fromthe reflection spectra. For the photonic crystal with six-fold rotational symmetry, the resonant peakvanishes at the Γ point, indicating the existence of an at-Γ BIC. On the other hand, the resonant peakappears at the Γ point in the perturbed photonic crystal and that resonant peaks vanish at finite
wavevectors in the perturbed photonic crystals. These results show the splitting of the at-Γ BIC into

two off-Γ BICs by the perturbation. In the second measurement, we measure isofrequency contours of
the photonic crystals by using two orthogonal polarizers. We first confirm that the measured
isofrequency contours are good agreement with the numerical results. Next, we determine the chargeof the BICs by rotating the two polarizers. When the perturbation is absent, the reflected signal
vanishes at the Γ point. When the perturbation is introduced, the disappearance of the reflected signal
shifts to finite wavevectors. By comparing the experimental results with the simulated results, wedetermine the charge of the off-Γ BICs. Combining the two reflection measurements, weexperimentally confirm the splitting from an at-Γ BIC with charge -2 into two off-Γ BIC with charge-1.