論文 / 著書情報
Article / Book Information
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)

論文要旨

Type(English)

Summary

Powered by T2R2 (Tokyo Institute Research Repository)

（博士課程）Doctoral Program論 文 要 旨ＴＨＥＳＩＳ ＳＵＭＭＡＲＹ

系・コース：
Department of, Graduate major in

物理学
物理学

学生氏名：
Student’s Name

養田大騎系
コース

申請学位（専攻分野）：

博士

Academic Degree Requested

Doctor of

指導教員（主）：Academic Supervisor(main)

指導教員（副）：Academic Supervisor(sub)

（理学）

納富雅也
村上修一

要旨（英文 800 語程度）
Thesis Summary （approx.800 English Words ）Photonic crystals are periodic dielectric structures with periodic modulation of the refractive index. Theperiodicity ensures that the dispersion of photons in photonic crystals is described by the photonic bandstructure. The photonic band offers many attractive optical phenomena, and thus photonic crystals areversatile platforms for controlling light. Because the photonic band structure is an optical analog of theelectronic band structure, photons in photonic crystals sometimes display phenomena similar to electrons inelectronic crystals. In this thesis, we mainly deal with two topics: valley-dependent optical physics andtopological 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. 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 states at the K andK’ points split, and it has been known that the gapped states display valley-dependent optical phenomena.
All of the previous works rely on this mechanism because this scheme is just analogous to graphene with astaggered sublattice potential. However, the Berry curvature and angular momentum are general properties
in systems without inversion symmetry, and thus it is not clear whether the presence of Dirac cones isessential. In this thesis, we propose another scheme to create valley photonic crystals. 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 theK and K’ points. Here we focus on the lowest band. We numerically demonstrate that the lowest band
exhibits valley-dependent phenomena such as angular momentum, Berry curvature, and interface states bybreaking 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 K and K’ points due to the time-reversal symmetry. We also find that thelocalized interface states appear at the interfaces between two inverted valley photonic crystals. We
numerically confirm that some of these interface states are robust against the backscattering at corners of a
sharp bend.
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. We start with a photonic
crystal with six-fold rotational symmetry because it can carry at-Γ BICs with charge -2. We numericallyconfirm that the at-Γ BIC with charge -2 splits into two off-Γ BICs with charge -1 by perturbations
breaking six-fold rotational symmetry but preserving two-fold rotational symmetry. The mechanism of thisscheme relies on charge conservation and crystalline symmetry. These results suggest that we candeterministically generate off-Γ BICs by an infinitesimal perturbation without fine-tuning of systemparameters.
We also demonstrate a wide variety of pair-creation and annihilation processes of circularly-polarizedstates with opposite charge and same handedness. Two circularly-polarized states with opposite charge andsame handedness are annihilated by the collision between them. To fully describe the topological nature of
BICs and circularly-polarized states, we introduce the handedness-wise topological charge. The
handedness-wise topological charge consistently explains the creation and annihilation ofcircularly-polarized states, and guarantees the topological protection of these polarization singularities.
Finally, we experimentally confirm the splitting of an at-Γ BIC with charge -2 into two off-Γ BICs withcharge -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 perturbed photonic crystals without
six-fold rotational symmetry. We perform two angle-resolved reflection measurements to characterize theband structure, quality factor, and far-field polarization vector of the fabricated photonic crystals. In thefirst measurement, we measure the reflection spectra of the fabricated photonic crystals, and determine theband structure and quality factor of the modes from the reflection spectra. We observe that the perturbation
destroys the at-Γ BIC and that resonant peaks vanish at finite wavevectors in the perturbed photoniccrystals. These results show the splitting of the at-Γ BIC into two off-Γ BICs by the perturbation. In thesecond measurement, we measure isofrequency contours of the photonic crystals by using two orthogonalpolarizers. We first confirm that the measured isofrequency contours are good agreement with thenumerical results. Next, we determine the charge of the BICs by rotating the two polarizers. When theperturbation is absent, the reflected signals vanish at the Γ point. When the perturbation is introduced, thedisappearance of the reflected signal shifts to finite wavevectors. Combining the two reflection
measurements, we experimentally confirm the splitting from an at-Γ BIC with charge -2 into two off-Γ BICwith charge -1.

備考 : 論文要旨は、和文 2000 字と英文 300 語を 1 部ずつ提出するか、もしくは英文 800 語を 1 部提出してください。
Note : Thesis Summary should be submitted in either a copy of 2000 Japanese Characters and 300 Words (Engｌish) or 1copy of 800
Words (English).
注意：論文要旨は、東工大リサーチリポジトリ（T2R2）にてインターネット公表されますので、公表可能な範囲の内容で作成してください。
Attention: Thesis Summary will be published on Tokyo Tech Research Repository Website (T2R2).