大阪府立大学　学術情報リポジトリ

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Optical Properties of CuCl Microcavities and

Dynamical Interference between Rabi

Oscillation and Coherent Phonon

著者

吉野慎吾

内容記述

学位記番号：論理第106号, 指導教員：溝口幸司

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Optical Properties of CuCl Microcavities

and

Dynamical Interference between

Rabi Oscillation and Coherent Phonon

Shingo Yoshino

Department of Physical Science,

Graduate School of Science

Osaka Prefecture University

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Abstract i

論文要旨

Optical Properties of CuCl Microcavities

and

Dynamical Interference between

Rabi Oscillation and Coherent Phonon

CuCl 微小共振器の光学特性と

Rabi 振動とコヒーレントフォノン間の動的干渉効果

理学系研究科物理科学専攻光物性グループ吉野慎吾本論文は全 4 章で構成され、共振器ポラリトンの光学特性と Rabi 振動－コヒーレントフォノン間の干渉現象に関する研究について報告する。Chapter 1 は Introduction である。背景として、本研究において重要な概念となる量子干渉や共振器ポラリトンについて紹介する。また研究の動機や独自性について先行研究を踏まえて説明する。Chapter 2 の内容は Optical Properties of CuCl Microcavities である。本研究で着目する Rabi 振動を研究するうえで Rabi 分裂エネルギーの制御が重要となる。そこで、まずは定常状態において様々な活性層厚のバルク CuCl 微小共振器に対する光学特性を調べた。定常光学測定によって求めた共振器ポラリトンの分散関係や、Rabi 分裂エネルギーの制御について報告する。また、共振器構造に対して膜厚揺らぎを新たに取り入れた理論計算による、共振器ポラリトンの反射スペクトルの再現について述べる。Chapter 3 では Ultrafast

Dynamics of CuCl Microcavities について述べる。Pump-Probe 法を用いて二つの共振器ポ

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ii Abstract

の格子振動であるコヒーレントフォノンとの間で干渉を生じることを初めて見出した。この Rabi 振動とコヒーレントフォノン間の干渉の特徴は以下のとおりである。(i) Rabi 振動とコヒーレントフォノンは共に不連続準位にも関わらず、連続準位と不連続準位間の干渉である Fano 干渉下におけるスペクトルと同様の非対称な周波数領域スペクトルを発現する。(ii) 共振器ポラリトンの性質を反映して、入射光の角度や偏光によって Rabi 振動とコヒーレントフォノン間の干渉をコヒーレント制御することができる。(i) における非対称なスペクトル形状は結合振動子系の古典運動方程式を用いて再現でき、その起源が Rabi 振動とコヒーレントフォノン間の位相差にあることを見出した。また、 (ii)については一般に過渡的に生じる量子振動と物質固有の振動間の動的干渉のコヒーレント制御について、新たな知見を与えるものである。Chapter 4 では以上の内容についてのまとめを行う。 Chapter 1 Introduction 量子干渉は物理において非常に本質的な現象である。ある二つの状態の重ね合わせ状態が形成されたとき量子干渉を生じる。様々な量子振動間の量子干渉や関係する現象についての報告がなされており、そのうち二つの重要な内容について紹介する。Fano 干渉は連続状態と不連続状態間の干渉であり、非対称なスペクトル形状を生じることで知られている。様々な系において定常的な Fano 干渉の報告がなされてはいるが、時間領域において二つの不連続状態間の動的な干渉を生じさせ、その結果として周波数領域で非対称なスペクトルを生じさせるという報告は無い。また、励起子量子ビートは分極の振動を伴うため、コヒーレントフォノンと結合することが知られている。ここで、量子ビートは二つの状態間の干渉であり、過渡的な量子振動である。しかしながら、このような過渡的な量子振動とコヒーレントフォノン間の結合がどのように生じ、発展していくのか、といった観点を持った研究はほとんどなされていない。以上の現状をまとめると、二つの不連続状態とみなせる量子振動とコヒーレントフォノン間の動的な干渉や結合状態について調べることは、干渉現象についての新たな知見を得るということやそのコヒーレント制御といった観点から非常に意義があるといえる。本研究では上記の量子振動として Rabi 振動に着目する。Rabi 振動は、半導体微小共振器において実現される共振器ポラリトン間の量子ビートである。半導体微小共振器はファブリ－ペロー型の共振器であり、共振器モードと呼ばれる光の閉じ込め状態を実現する。この共振器モードが励起子と強結合することにより共振器ポラリトンを実現する。これまでに半導体微小共振器における Rabi 振動はいくつかの報告例があるにとどまっており、これまであまり注目されてこなかった。しかしながら、量子振動として注目した場合、上記の励起子量子ビートなどとは異なる性質を持つと考えられる。そこで本研究では以上の背景を踏まえて、上記の共振器ポラリトンの特性に基づいた性質を持つ Rabi 振動とコヒーレントフォノン間の動的干渉に着目した。

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Abstract iii

Chapter 2 Optical Properties of CuCl Microcavities

Rabi 振動は二つの共振器ポラリトン間のエネルギー差に対応する振動数で振動する。そのため、強結合によりモード分裂した共振器ポラリトン間の反交差の度合いを表す Rabi 分裂エネルギーを制御することが、Rabi 振動を観測するうえで重要となる。そこで本研究ではまず、大きな振動子強度により共振器ポラリトンの研究に適した CuCl 微小共振器を用いて、Rabi 分裂エネルギーの制御を実現し、さらに共振器ポラリトンの光学特性について調べた。実験は作製した微小共振器に対して角度分解反射もしくは透過スペクトルを測定することによって行った。実験結果の解析を行ったところ、各試料に対して共振器ポラリトンの観測に成功した。また、Rabi 分裂エネルギーは、活性層厚を変化させることにより制御することができ、本研究では活性層厚をλ/16－2λ(λ = λex/nb: λexは励起子共鳴波長、nbは背景屈折率)の範囲で変化させることにより、CuCl の Z3励起子に対する Rabi 分裂エネルギーを約 10－140 meV の範囲で制御することに成功した。このような広範囲にわたる Rabi 分裂エネルギーの制御は他の無機半導体微小共振器では実現しえない。さらに共振器ポラリトンの反射スペクトルを理論計算によって再現した。これまでに CuCl 微小共振器の反射スペクトルに対して非局所応答理論を用いた理論計算は行われていたが、実験結果と計算結果は定量的には一致していなかった。本研究ではこの不一致が共振器構造中の界面における、表面ラフネスなどに起因する膜厚の揺らぎにあると考えた。そこで膜厚揺らぎモデルを提唱し理論計算に組み込んでその効果を調べた。次に膜厚揺らぎを導入して反射スペクトルの理論計算を行ったところ、実験結果に見られる各構造のエネルギー位置や幅、数まで大変良く一致した。このことは本研究で用いたようなバルク半導体微小共振器の光学特性を設計するうえで、Q 値や Rabi 分裂エネルギーに影響を与える膜厚揺らぎの概念が非常に重要で必須であることを意味する。

Chapter 3 Ultrafast Dynamics of CuCl Microcavities

Pump-Probe 法を用いて Rabi 振動とコヒーレントフォノン間の動的干渉を初めて見出した。超短パルスレーザーによって二つの共振器ポラリトンモードを同時に励起すると、時間分解信号において量子ビートである Rabi 振動とコヒーレントフォノンが観測された。この信号をフーリエ変換すると、Rabi 振動に由来する幅の広いバンド構造と、CuCl の縦光学(LO)フォノンの振動数位置ωLOにおける非対称な構造が確認できた。この非対称な形状は典型的な Fano 干渉に見られるスペクトル形状に類似していた。また、Pump 光の入射角を変化させることによって Rabi 振動の振動数を変化させると、Rabi 振動の振動数がωLOを低周波数側から横切る際に、ωLO付近の構造がディップ構造から非対称構造を経てピーク構造に変化することを見出した。この非対称なスペクトル形状の起源を理解するために、Rabi 振動とコヒーレントフォノンを古典振動子とみなし、結合振動

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iv Abstract

子系を形成しているとして系の運動方程式を解いた。その結果、系の時間発展 f(t)は

Pump 光によって駆動された Rabi 振動と、結合を通して Rabi 振動に駆動されるコヒー

レントフォノンの重ね合わせ状態となることが分かった。このときコヒーレントフォノンは Rabi 振動との結合振動モードを形成しているが、Rabi 振動の減衰がコヒーレントフォノンに比べて非常に速いため、駆動後、直ちに Rabi 振動が減衰してしまいコヒーレントフォノンのみが生き残る。これが Rabi 振動とコヒーレントフォノン間の動的干渉の様子である。また、Rabi 振動によって間接的に駆動されたコヒーレントフォノンは、二つの振動の振動数が等しい場合、Pump 光によって直接駆動された Rabi 振動に比べて位相がπ/2 だけ遅れて振動する。この位相差がスペクトル形状における非対称性の起源 となることが考えられ、実際に f(t)をフーリエ変換したスペクトルは実験結果を良く再 現した。最後に Pump 光の偏光を変化させることにより、コヒーレントフォノンに対する Rabi 振動の相対位相を変化させることができることを実験的に示した。コヒーレントフォノンに対する Rabi 振動の相対位相を変化させることにより、フーリエ変換スペクトルにおいてωLO付近の非対称な構造を連続的に変化させることに成功した。このような動的干渉のコヒーレント制御の報告はこれまで全くない。以上の結果から、本研究は Rabi 振動のような過渡的に生じる量子振動と物質固有の振動との間の動的干渉についての新たな知見と、そのコヒーレント制御の方法を提供するものである。 Chapter 4 Conclusion 本章では本研究の成果を総括している。

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Contents

Chapter 1 Introduction

1.1 Background

Optical properties of cavity polariton and dynamical interference between Rabi oscillation (RO) and coherent phonon (CP) are studied in this thesis. There are two key physical concepts: quantum interference and cavity polariton. In this section, we review these concepts.

Quantum interference between states is an essential phenomenon in physics. Many kinds of quantum interference and related phenomena have been studied: Fano interference[1.1-1.8], the exciton quantum beat[9], Bloch oscillation[1.10], electromagnetically-induced transparency (EIT)[1.11] and so on[1.12-1.18]. Superposition of two states causes the quantum interference in the time evolution of the system when two states are excited simultaneously, and it shows the various unique characteristics. For example, Fano interference resulting from the interference between continuum and discrete states shows asymmetric spectral profile. Since creation of the discrete state by external perturbation often accompanies excitation of the background continuum state, the asymmetric profiles are ubiquitously observed in spectroscopic signals. However, although there are a lot of studies for Fano interference consisting of continuum and discrete states, there are few reports for the dynamical interference, which causes the asymmetric profile, for the system consisting of the two discrete states in the time domain.

As another example, the exciton quantum beat is a transient intensity modulation of the transition dipole moments of heavy- and light-hole excitons, observed in a pump-probe measurement. Since the exciton quantum beat in the multiple quantum wells induces the polarization which interacts to the coherent phonon (CP), the amplitude of the CP is enhanced and the coupled modes between the exciton quantum beat and the CP are formed[1.19,1.20]. Thus, the quantum oscillations dynamically couple to the CP. However, there are only several kinds of studies for the dynamical coupling between the quantum oscillation and the CP[1.19-1.22], and, the following points are unclear: how the coupling between the quantum oscillation and the CP is formed and how the coupling collapses while the quantum oscillation transiently exists. Therefore, in summary, we are interested in the dynamical interference and coupling between the two discrete states: the quantum oscillation and the CP.

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2 Chapter 1 Introduction

studies of the solid-state physics, many interesting coupling states consisting of the elemental excitations in matters or nanostructures are reported: cavity polariton[1.23], hybrid states between plasmon polaritons and exciton[1.24,1.25], coherent phonons in coupled mechanical resonators[1.26]. They are characterized by the mode splitting in the eigenmodes, and the eigenmodes can realize the various novel phenomena. The cavity polariton in a semiconductor microcavity is a strong coupling state between the exciton and the photon which is confined in the cavity layer and is called the cavity mode. Since the first demonstration of the cavity polariton in a Quantum well (QW) microcavity with III-V semiconductor[1.23], various optical phenomena which originate in the cavity polariton have reported. One of the major streams for the investigation of the cavity polariton is about the condensation of the cavity polariton such as polariton Bose-Einstein condensation[1.27,1.28] and polariton lasing[1.29]. These phenomena originate from the combination between the characteristics of the cavity photon and the exciton: the peculiar dispersion relationship of the cavity photon and the effect of the collision between each exciton in the high density region of the cavity polariton. Thus, the cavity polaritons have a potential realizing novel nonlinear optical phenomena that bare exciton and photon cannot realize.

However, in the point of view of the ultrafast dynamics of the cavity polariton, the studies in the low density regime which the wave nature of the cavity polaritons is dominant are minor, comparing with the studies focusing on the condensation of the cavity polaritons in the high density region. For example, there are only a few works for the RO in a microcavity which is quantum beat between cavity polaritons created by the simultaneous excitation[1.30,1.31], although a lot of studies of the RO in the semiconductor quantum well and quantum dot are reported[1.32,1.33]. Therefore, all the detailed properties of the RO in a microcavity have not been revealed yet. Here, the RO is a quantum oscillation with a Rabi frequency, and the RO is assumed to be the discrete state. Then, we focus on the dynamical coupling between the RO and the CP. To realize the coupling between the RO and the CP, the frequency of the RO needs to be adjusted to that of the CP. The frequency of the RO can be controlled by changing the active layer thickness of the microcavity. However, the frequency range of the RO of QW microcavities is small. Then, we focus on the bulk semiconductor microcavities because they can realize the large frequency range of the RO.

In this thesis, we demonstrate the dynamical coupling and interference between the RO and the CP which originates from the asymmetric spectral profiles in the ultrafast time region. The essence of the dynamical coupling between the RO and the CP is understood by the coupled oscillator model, and the properties are compared to the

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1.2 Cuprous Chloride 3

typical Fano interference. Moreover, the coherent control of the dynamic interference between the RO and the CP is realized by varying the polarization angle of the pump pulse in a pump-probe measurement.

1.2 Cuprous Chloride

CuCl is one of the I-VII semiconductors and has the large exciton binding energy of 197 meV and the large exciton oscillator strength. These properties enable to be the stable exciton state. The crystal structure of the CuCl crystal is a zinc-blend type. Basic optical parameters of CuCl are listed in Table I[1.34]. In Fig. 1.1(a), band structure near the Γ point in CuCl is shown. There are two kinds of excitons in CuCl crystal: Z3 and Z1,2 excitons. The Z3 exciton consists of a Γ7 hole and a Γ6 electron, and the Z1,2 exciton consists of a Γ8 hole and a Γ6 electron, respectively. The Z3 exciton has a simple system, which reflects the simplicity of its hole and electron, and CuCl is a model material for studies of optical properties of the exciton.

In this study, CuCl is embedded in the microcavity as an active material, and the quality of CuCl embedded in NaF which consists of microcavity structure has been verified by confirming that the full width at half maximum (FWHM) of absorption spectra is narrow enough to form cavity polariton modes. Absorption spectrrum of CuCl thin film embedded in NaF thin film on Al2O3 preparing by using the vacuum deposition method at 10 K is shown in Fig. 1.1(b). The thickness of CuCl and NaF are 20 nm and 300 nm, respectively. The dashed vertical lines indicate the energy of Z3 and Z1,2 excitons at 4 K. The two absorption peaks which originate from the by Z3 and Z1,2 excitons are clearly shown. The peak energies of respective excitons are blue-shifted those to comparing the Z3 and Z1,2 excitons at 4 K because the temperature of the CuCl thin film is higher than 4 K. The FWHMs of the spectra for the respective excitons are 7 meV and 30 meV. The FWHMs are narrow enough to form the cavity polariton modes because the Rabi splitting energies of CuCl microcavities are several tens of meV[1.44], when CuCl is even embedded in NaF. Therefore, microcavities embedding CuCl as an active material are appropriate for studies of the cavity polariton and the RO.

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4

Fig. 1.1 (a)

CuCl thin firm embedded in NaF thin film on Al

nm and 300 nm, respectively. The dashed vertical lines indica 4 K.

Fig. 1.1 (a) band structure and exciton states near the CuCl thin firm embedded in NaF thin film on Al

nm and 300 nm, respectively. The dashed vertical lines indica 4 K.

band structure and exciton states near the CuCl thin firm embedded in NaF thin film on Al

nm and 300 nm, respectively. The dashed vertical lines indica Table I

Z3transverse exciton energy Z₃longitudinal exciton energy

binding energy of

binding energy of exciton molecule Bohr radius

background dielectric constant energy of longitudinal

band structure and exciton states near the CuCl thin firm embedded in NaF thin film on Al

nm and 300 nm, respectively. The dashed vertical lines indica Table I. Basic optical parameters of CuCl

bandgap

transverse exciton energy longitudinal exciton energy

Z_1,2exciton energy binding energy of

binding energy of exciton molecule Bohr radius of

background dielectric constant energy of longitudinal

band structure and exciton states near the

CuCl thin firm embedded in NaF thin film on Al2O3 at 10 K. The thickness of CuCl and NaF are 20 nm and 300 nm, respectively. The dashed vertical lines indica

Basic optical parameters of CuCl

energy transverse exciton energy longitudinal exciton energy

exciton energy binding energy of Z3exciton

binding energy of exciton molecule of Z₃exciton background dielectric constant energy of longitudinal-optical phonon

band structure and exciton states near the Γ point in CuCl. (b) Absorption spectra of at 10 K. The thickness of CuCl and NaF are 20 nm and 300 nm, respectively. The dashed vertical lines indicate the energy of

Basic optical parameters of CuCl

3.3990 eV transverse exciton energy 3.20223 eV longitudinal exciton energy 3.20788 eV 3.268 eV exciton 197 meV binding energy of exciton molecule

exciton background dielectric constant

phonon

Chapter 1 Introduction

point in CuCl. (b) Absorption spectra of at 10 K. The thickness of CuCl and NaF are 20

te the energy of Z3 Basic optical parameters of CuCl[1.34].

3.3990 eV 3.20223 eV 3.20788 eV 3.268 eV 197 meV 34 meV 0.7 nm 5.59 26 meV Chapter 1 Introduction

point in CuCl. (b) Absorption spectra of at 10 K. The thickness of CuCl and NaF are 20 and Z1,2 excitons at Chapter 1 Introduction

point in CuCl. (b) Absorption spectra of at 10 K. The thickness of CuCl and NaF are 20 excitons at

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1.3 Semiconductor Microcavities 5

1.3 Semiconductor Microcavities

1.3.1 Cavity Polariton

Semiconductor microcavities consist of the Fabry-Pérot interferometer and the active layer embedding an optical active semiconductor. Distributed Bragg reflectors (DBRs) which have the multilayer structures consisting of materials with high and low refractive indices are often applied to the parallel mirrors of the Fabry-Pérot interferometer. The wide stop band of the light is formed and the reflectivity of the DBR at the center wavelength of the stop band is over 99%. The electromagnetic field which is confined in the cavity layer is called the cavity mode, and the strong coupling modes which are called cavity polaritons are formed by the interaction between the cavity mode and exciton in the active layer as schematically shown in Fig. 1.2(a). Hamiltonian for the system is written as

) 0 , 1 , 1 , 0 , ( 2 1 , 1 , 0 , 0 , _ph ex e e g g e g g e H =h

ω

+h

ω

+hΩ + _{, (1.1)} where hω_ex _and ph ω

h _{are the energies of the exciton and the cavity photon,} respectively.

e

,

0

and

g

,

1

indicate the state of the exciton and the cavity photon, where

e

and

g

are the excited and ground states of the exciton, and

1

and

0

are the states with and without cavity photon in the cavity, respectively. hΩ _{is the coupling} energy, which is called Rabi splitting energy, between the exciton and the cavity photon. The precise description for the interaction between the exciton and the cavity photon in bulk semiconductor microcavity by using the nonlocal response theory is discussed later. The eigenenergies of the system are shown in Fig. 1.2(b) when h

ω

_ex _{is equals to}

ph

ω

h

and the respective eigenstates are called upper polariton (UP) and lower polariton (LP). These polariton modes are often observed in reflectance spectrum as shown in Fig. 1.2(c), where shows the two modes (UP and LP) splitting with the energy gaphΩ _.

The cavity mode has the energy dispersion relationship depending on the external incident angle

θ

because the wave vector kz perpendicular to the microcavity is quantized and the wave vector k// parallel to the microcavity is varied by changing the incident angle (Fig. 1.3). Relationship between wave vector k in the microcavity and wave vector for perpendicular and parallel to the microcavity is given as

2 // 2

k

=

_z

+

. (1.2)

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6

Using an internal incident angle

k_z =

represented

Fig. 1.2 (a)

microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the cavity photon. (c) Reflectance spectrum of the microcavities with and with

dashed line indicates the exciton energy.

φ

cos

k

= and

represented by using the Snell

Fig. 1.2 (a) Schematic diagram of the interaction between the exciton and the cavity photon in the microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the cavity photon. (c) Reflectance spectrum of the microcavities with and with

Using an internal incident angle and k_// =k

by using the Snell

Schematic diagram of the interaction between the exciton and the cavity photon in the microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the cavity photon. (c) Reflectance spectrum of the microcavities with and with

φ

sin , respectively. by using the Snell’s law as

φ

in the microcavity , respectively.

s law as

microcavity,

, respectively. The internal incident angle

, kz and k//

The internal incident angle

Schematic diagram of the interaction between the exciton and the cavity photon in the microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the cavity photon. (c) Reflectance spectrum of the microcavities with and without the exciton.

// are written as The internal incident angle

Schematic diagram of the interaction between the exciton and the cavity photon in the microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the

out the exciton. Chapter 1 Introduction

are written as The internal incident angle

φ

is

Schematic diagram of the interaction between the exciton and the cavity photon in the microcavity. (b) Energy diagram of the cavity polariton modes consisting of the exciton and the out the exciton. The

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1.3 Semiconductor Microcavities 7

θ

φ

sin sin l c n n = , (1.3) where nc and nl are refractive index at an active layer and the air, respectively. The wave vector kz is quantized because of confinement in the microcavity, and is written as

c

cos

L

m

k

_z

=

φ

=

π

, (1.4) where m is a quantum number and Lc is a cavity layer thickness. Using above equations,

Fig. 1.3 (a) Schematic of wave vector of incident light in the microcavity. (b) Energy dispersion relationship of the cavity polariton in CuCl microcavity only with Z3 exciton for various detuning energies δ. LP and UP mean lower polariton and upper polariton, respectively.

(b)

3.6 3.5 3.4 3.3 3.2 3.1 P h o to n E n e rg y Incident Angle UP LP Photon Exciton Photon Exciton Photon Exciton UP UP LP LP δ<0 δ=0 δ>0 θ=0 θ=0 θ=0 E_Z(3) E_Z(3) E_Z(3)

k

_// DBR DBR

L

_c

θ

φ

k

_z

k

active layer

(a)

n

_c

n

_l

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cavity mode energy Ec is expressed as

k

n

c

k

E

c // c

(

)

h

=

2 1 2 // c c       +       = k L m n c π h , (1.5) and 2 1 2 2 c c c( ) tan       +       =

π

φ

θ

kz L m n c E h 2 1 2 c 2 c sin 1 ) 0 ( −       − = n E

θ

(1.6) c c c

(

0 )

L

m

n

c

E

=

h

π

. (1.7) The incident angle dependences of the cavity polariton modes, the Z3 exciton of CuCl, and the cavity modes for the various detuning energies

δ

between the exciton and the cavity photon at incident angle of 0° are shown in Fig. 1.2(d).

1.3.2 CuCl microcavity

Recently, wide-bandgap semiconductor microcavities, such as those of ZnO and GaN,[1.35-1.38] have been reported. Their large exciton binding energies and oscillator strengths can produce stable polariton states at high temperatures. In addition, large mode splitting called vacuum Rabi splitting can also occur. Moreover, the nonlinear optical response is enhanced in the microcavity system with stable excitons and biexcitons.[1.39]

Notably, the semiconductor CuCl microcavity exhibits large Rabi splitting energies due to the large binding energy and oscillator strength of the excitons.[1.40] The nonlocal optical response theory for the CuCl microcavity predicts a highly efficient generation of the entangled photon pair, which is one of the nonlinear optical properties of this microcavity.[1.41-1.43] In order to achieve the highly efficient generation of the entangled

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1.4 Overview of the thesis 9

photon pair, it is essential to control the Rabi splitting energy and the dispersion relationship of the cavity polariton. Nakayama et al. demonstrated that the Rabi splitting energies could be controlled in the energy range from 22(37) to 71(124) meV for the Z3(Z1,2) exciton by changing the active layer thickness in the region less than a half of the thickness for the resonant wavelength of the Z3 exciton.[1.44]

In the region more than a half of the active layer thickness, Oohata et al. determined the optical properties of the CuCl microcavity by comparing the angle-resolved reflectance with theoretical reflectance spectra.[1.40] The theoretical reflectance spectra have been calculated using the nonlocal response theory. The nonlocal response theory is appropriate to the quantitative analysis of the spectral profiles and the Rabi splitting energies of the microcavities, because this theory accurately utilizes the electric field variation in the coherent region of the exciton wave function. Unfortunately, the calculated and experimental spectra reported in Ref. [1.40] were not in agreement quantitatively and the origin of the disagreement was not revealed. To reveal the origin of the disagreement is one of important subjects to control the Rabi splitting energies and derive novel optical responses in the wide-bandgap semiconductor microcavities. We expect that the disagreement between the calculated and experimental spectra will originate from the imperfections of the spatial structures in the microcavities. The imperfections cause the fluctuations in the refractive index profiles along the cavity structures, and thus the observed optical spectra in the fabricated microcavities will deviate from the expected ones in the ideally designed microcavities. To analyze the spectral profiles and the Rabi splitting energies of the CuCl microcavities quantitatively, it is necessary to clarify the effect of the spatial fluctuations in the refractive index profiles on the microcavity optical properties.

1.4 Overview of the thesis

Our purposes are to demonstrate the dynamical interference between the RO and the CP, and to realize its physics. We have performed the following two subjects for the realization of the purposes. First, we show the optical properties of the CuCl microcavities with fluctuations in their refractive index profiles along cavity structures and the dependence on the Rabi splitting energies of the active layer thickness in Chap. 2. For the demonstration of the interference between the RO and the CP, it is necessary to control the optical properties, especially the Rabi splitting energy, of the CuCl microcavities. This is because the frequency of the RO is governed by the Rabi splitting

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energy and must match with the frequency of the CP. In addition, the deviation between the experimental and calculated spectra based on the nonlocal response theory in Ref. [1.40] is discussed. The key idea to solve the deviation is consideration of the fluctuations in their refractive index profiles along the cavity structures. The beautiful coincidence between the experimental and calculated reflectance spectrum calculated by taking account of the fluctuation is shown. Moreover, the control of the Rabi splitting energy for the Z3 exciton in the wide energy range from about 10 to 140 meV by changing the thickness of the active layer is demonstrated.

Second, we demonstrate the dynamical interference between the RO and the CP by using a pump-probe technique in Chap. 3. The dynamic interference between the RO and the CP causes asymmetric spectral profiles in the Fourier-transformation (FT) spectra which is similar to those observed in Fano interference. The various kinds of the spectral profiles are observed by changing the incident angle of the pump pulse. The coupled oscillator model between the RO and the CP reproduces the asymmetric profiles and gives simple insight for the dynamical coupling. The difference between the dynamic interference of the RO and the CP and the Fano interference is discussed. In addition, the coherent control of the dynamical interference between the RO and the CP is demonstrated by varying the polarization angle of the pump pulse in the pump-probe measurement. These characteristics of the dynamical interference between the RO and the CP are unique, which originates in the optical properties of the cavity polariton.

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Reference 11

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14

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Fig. 2.1.

of the mechanism in the vacuum deposition

partitions, current terminals of the resistance heating and a sample holder, respectively.

Chapter 2 Optical Properties of CuCl Microcavities

2.1

In this study, CuCl method

sources are needed. Therefore, the vacuum deposition deposition sources

the sample hol positions of 3 × 10 eigenfreq

for monitoring and

2.1.1. (a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design of the mechanism in the vacuum deposition

Chapter 2 Optical Properties of CuCl Microcavities

Optical Properties of

from

λ

/2

2.1.1 Sample Structure and Experimental Setup

In this study, CuCl

method. To fabricate the CuCl microcavity consistently, the three sources are needed. Therefore, the vacuum deposition

deposition sources the sample holder positions of the

10-6 Torr. The thickness of the layers is measured by monitoring the variation of the eigenfrequency of the quartz crystal. The system of Q

monitoring and

(a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design of the mechanism in the vacuum deposition

Chapter 2 Optical Properties of CuCl Microcavities

Optical Properties of

/2 to 2

λ

In this study, CuCl microcavities

To fabricate the CuCl microcavity consistently, the three sources are needed. Therefore, the vacuum deposition

deposition sources shown in Figs. 2.1.1(a) and (b) has been assembled. The location of der has been

the deposition source when each layer grows. The degree of vacuum g Torr. The thickness of the layers is measured by monitoring the variation of the

uency of the quartz crystal. The system of Q

monitoring and the variation of the eigenfrequency of the quartz

(a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design of the mechanism in the vacuum deposition

Chapter 2 Optical Properties of CuCl Microcavities

Optical Properties of CuCl microcavities with active layer thickness

microcavities

shown in Figs. 2.1.1(a) and (b) has been assembled. The location of has been controlled by using the stepping motor to

deposition source when each layer grows. The degree of vacuum g Torr. The thickness of the layers is measured by monitoring the variation of the

the variation of the eigenfrequency of the quartz

(a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design of the mechanism in the vacuum deposition equipment. Red, blue and green lines show the stainless partitions, current terminals of the resistance heating and a sample holder, respectively.

Chapter 2 Optical Properties of CuCl Microcavities

CuCl microcavities with active layer thickness

microcavities were prepared by

shown in Figs. 2.1.1(a) and (b) has been assembled. The location of controlled by using the stepping motor to

the variation of the eigenfrequency of the quartz

(a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design equipment. Red, blue and green lines show the stainless partitions, current terminals of the resistance heating and a sample holder, respectively.

Chapter 2 Optical Properties of CuCl Microcavities

CuCl microcavities with active layer thickness

were prepared by using the vacuum deposition To fabricate the CuCl microcavity consistently, the three

sources are needed. Therefore, the vacuum deposition equipment

shown in Figs. 2.1.1(a) and (b) has been assembled. The location of controlled by using the stepping motor to

uency of the quartz crystal. The system of Q-pod (INFICON) the variation of the eigenfrequency of the quartz

Chapter 2 Optical Properties of CuCl Microcavities

CuCl microcavities with active layer thickness

using the vacuum deposition To fabricate the CuCl microcavity consistently, the

three-equipment with the three shown in Figs. 2.1.1(a) and (b) has been assembled. The location of

controlled by using the stepping motor to

pod (INFICON) the variation of the eigenfrequency of the quartz

Chapter 2 Optical Properties of CuCl Microcavities

CuCl microcavities with active layer thickness

using the vacuum deposition -way deposition with the three shown in Figs. 2.1.1(a) and (b) has been assembled. The location of

controlled by using the stepping motor to locate the deposition source when each layer grows. The degree of vacuum g Torr. The thickness of the layers is measured by monitoring the variation of the

pod (INFICON) has been the variation of the eigenfrequency of the quartz crystal

15

(a) Schematic diagram of the chamber of the vacuum deposition equipment. (b) Design equipment. Red, blue and green lines show the stainless

CuCl microcavities with active layer thickness

using the vacuum deposition way deposition with the three-way shown in Figs. 2.1.1(a) and (b) has been assembled. The location of the same deposition source when each layer grows. The degree of vacuum got to Torr. The thickness of the layers is measured by monitoring the variation of the has been used stal and

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16

output

CuCl microcavities with DBRs on (001) Al 2.1.2(a))

because the contrast of the refractive index between PbCl and n

DBRs will show a high the PbCl

transmission spectrum, was approximately PbBr

sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The active layer thickness, called the cavity length

multiples of the effecti resonant wavelength of the Z refractive index, and

= m

λ

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range of about 10 %.

Fig. 2.1. cavity structure

calculated intensity profile of the electric field in the CuCl transfer matrix method

outputting it to a

CuCl microcavities with DBRs on (001) Al 2.1.2(a)). In this work, PbCl

because the contrast of the refractive index between PbCl

nNaF = 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl DBRs will show a high

the PbCl2/NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity transmission spectrum, was approximately

PbBr2/PbF2 DBR

sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The active layer thickness, called the cavity length

multiples of the effecti resonant wavelength of the Z refractive index, and

λ

/2 as “m

λ

/2

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range of about 10 %.

2.1.2. (a) Schematic diagram of the CuCl microcavity. (b) cavity structure in the CuCl

calculated intensity profile of the electric field in the CuCl transfer matrix method

a computer.

CuCl microcavities with DBRs on (001) Al . In this work, PbCl

because the contrast of the refractive index between PbCl

= 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl DBRs will show a high reflectivity and a wide stop band. In an empty cavity containing

/NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity transmission spectrum, was approximately

DBR[2.1]. The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The active layer thickness, called the cavity length

multiples of the effective length resonant wavelength of the Z

refractive index, and m is an integer. Hereafter, we refer to a CuCl microcavity with /2-cavity”. The thickness

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range of about 10 %. The ideal refractive index profile of the

(a) Schematic diagram of the CuCl microcavity. (b) in the CuCl λ

calculated intensity profile of the electric field in the CuCl transfer matrix method (red thick

.

CuCl microcavities with DBRs on (001) Al

. In this work, PbCl2 and NaF were used as the constituent layers of the DBRs because the contrast of the refractive index between PbCl

= 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity transmission spectrum, was approximately

. The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The active layer thickness, called the cavity length

ve length

λ

: Lcav

resonant wavelength of the Z3 exciton in vacuum (

is an integer. Hereafter, we refer to a CuCl microcavity with The thickness

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range

The ideal refractive index profile of the

(a) Schematic diagram of the CuCl microcavity. (b)

λ-cavity embedded in the PbCl calculated intensity profile of the electric field in the CuCl

red thick line). nA indicates the refractive index of

Chapter 2 Optical Properties of CuCl microcavities

CuCl microcavities with DBRs on (001) Al

and NaF were used as the constituent layers of the DBRs because the contrast of the refractive index between PbCl

= 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity transmission spectrum, was approximately 250. This was higher than

. The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The active layer thickness, called the cavity length L

cav = m

λ

/2. exciton in vacuum (

is an integer. Hereafter, we refer to a CuCl microcavity with The thicknesses of the PbCl

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range

The ideal refractive index profile of the

(a) Schematic diagram of the CuCl microcavity. (b) cavity embedded in the PbCl calculated intensity profile of the electric field in the CuCl

indicates the refractive index of

CuCl microcavities with DBRs on (001) Al2O3 substrates were

and NaF were used as the constituent layers of the DBRs because the contrast of the refractive index between PbCl2 and NaF layers (

= 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity

50. This was higher than

. The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The

Lcav, was designed to have half /2.

λ

is given by

exciton in vacuum (

λ

ex = 387 nm),

is an integer. Hereafter, we refer to a CuCl microcavity with of the PbCl2 and NaF

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range The ideal refractive index profile of the

λ

-cavity structure is shown in

(a) Schematic diagram of the CuCl microcavity. (b) Refractive index profile of the ideal cavity embedded in the PbCl2/NaF DBRs (

calculated intensity profile of the electric field in the CuCl λ-cavity at normal incidence, using a indicates the refractive index of

substrates were

and NaF were used as the constituent layers of the DBRs and NaF layers (

= 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity

50. This was higher than

. The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The

, was designed to have half is given by

λ

ex/nb, where

= 387 nm), nb is the background is an integer. Hereafter, we refer to a CuCl microcavity with

and NaF layer are

/4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range cavity structure is shown in

Refractive index profile of the ideal /NaF DBRs (black thin

cavity at normal incidence, using a indicates the refractive index of a layer A.

substrates were fabricated and NaF were used as the constituent layers of the DBRs

and NaF layers (nPbCl2 = 1.3 at 3.2 eV) was sufficiently high. Therefore, we expect that the PbCl2

reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity

50. This was higher than that of . The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The , was designed to have half-integer , where

λ

ex is the is the background is an integer. Hereafter, we refer to a CuCl microcavity with

are designed to be /4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range cavity structure is shown in

Refractive index profile of the ideal black thin line) and the cavity at normal incidence, using a

layer A.

fabricated(Fig. and NaF were used as the constituent layers of the DBRs = 2.4 2/NaF reflectivity and a wide stop band. In an empty cavity containing /NaF DBRs, the quality (Q) factor, which was estimated from an empty cavity that of the . The CuCl microcavity was comprised of a CuCl active layer sandwiched between a top DBR with 6.5 periods and a bottom DBR with 6 periods. The integer is the is the background is an integer. Hereafter, we refer to a CuCl microcavity with Lcav

designed to be /4. The difference on the thickness between the fabricated and designed DBRs with one period, estimated by the ellipsometry measurements, was included within the range cavity structure is shown in

Refractive index profile of the ideal line) and the cavity at normal incidence, using a

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2.1 Optical Properties of CuCl microcavities with active layer thickness from λ/2 to 2λ 17

Fig. 2.1.1(b). The intensity profile of the electric field, |E|2, along the growth direction at normal incidence was calculated for the 387 nm wavelength using the conventional transfer matrix method. In the

λ

-cavity, the electric-field intensity has antinodes at the boundaries between the active layer and the DBRs, which indicates a loop cavity.

The angle-resolved reflectance spectra were observed at 13 K using a 32 cm single monochromator combined with a charge coupled device (CCD) camera, where the spectral resolution was 0.37 nm (Fig. 2.1.3). The probe light source was a Xe lamp. The spectroscopic ellipsometry measurements were carried out in order to characterize the refractive indices of constituent layers and boundary regions between the constituent layers in the microcavities. The pseudo complex dielectric functions were obtained by analyzing the ellipsometric data, measured at room temperature in the spectral range from 0.75 to 3.85 eV with a step of 0.02 eV at the angle of incidence of 65º using a

spectroscopic phase modulated ellipsometer (HORIBA jobin-Ybon,

UVISEL-9017TK).[ 2.2-2.4]

2.1.2 Angle-Resolved Reflectance Spectra

The reflectance spectra of the

λ

-cavity at various incident angles from 0° to 65° are shown in Fig. 2.1.4(a). The dashed vertical lines denote the energies of the Z3 and Z1,2 excitons: EZ(3) = 3.202 and EZ(1,2) = 3.268 eV, respectively. Many dip structures were observed in each reflectance spectrum. The three dips, marked with open circles, clearly

FIG. 2.1.3. Schematic diagram of the measurement system of the angle-resolved reflectance spectra. cryostat sample lens lens Xe Lamp optical fiber Monochromator CCD CCD controller PC optical fiber θ θ Pin hole

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18 Chapter 2 Optical Properties of CuCl microcavities

depend on the incident angle; however, other dips, marked with open triangles, change only slightly with the incident angle. The strong angle-dependent dips originate from the cavity-polariton modes, which are assigned to be the lower polariton branch (LPB), the middle polariton branch (MPB), and the upper polariton branch (UPB) in the order of increasing energy. The other dips are attributed to the weakly-coupled modes that are discussed in Ref. [2.1, 2.5-2.7].

The energy positions of the dips observed in the angle-resolved reflectance spectra were plotted as a function of incident angle as shown in Fig. 2.1.4(b). The open circles and triangles show the cavity-polariton and weakly-coupled modes, respectively. The energy positions of the Z3 and Z1,2 excitons are represented by the horizontal dotted

FIG. 2.1.4. (a) Angle-resolved reflectance spectra of the CuCl λ-cavity at 13 K. Open circles and open triangles indicate the strongly coupled modes and weakly-coupled modes, respectively. The vertical dotted lines show the energy positions of the Z3 and the Z1,2 excitons of CuCl. The dashed lines are guides for the eye. (b) The energy positions of the dip due to the cavity polaritons as a function of incident angle obtained in the angle-resolved reflectance spectra. The open circles and triangles are the energy positions of the strongly coupled modes and weakly-coupled modes, respectively. The solid lines are the dispersion relationships of the cavity-polariton modes of the LPB, MPB, and UPB calculated from Eq. (2.1.2). The dotted lines indicate the Z3 (Z1,2) exciton energies, and the dashed curve shows the dispersion relationship of the cavity photon.

3.6 3.5 3.4 3.3 3.2 3.1 3.0 P h o to n E n e rg y ( e V ) 70 60 50 40 30 20 10 0

Incident Angle (Degree)

UPB Photon MPB LPB EZ(3) EZ(1,2) λ-cavity ΩZ(3) = 110 meV ΩZ(1,2) = 195 meV Ec(0) = 3.222 eV (b) R e fl e c ti v it y ( a rb . u n it s ) 3.5 3.4 3.3 3.2 3.1

Photon Energy (eV)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 13 K

Photon Energy (eV)

EZ(3) EZ(1,2)

λ-cavity (a)

(28)

lines. The dashed curve indicates the dispersion relationship of the cavity photon given by, modifying Eq. (1.6),

2 / 1 2 ff 2 cav cav sin 1 ) 0 ( ) ( −       − = e n E E θ θ , (2.1.1)

where Ecav(0) is the energy of the cavity photon at the incident angle of θ = 0° and neff is

the effective refractive index of the active layer. In order to evaluate the vacuum Rabi splitting energies from the incident-angle dependence of the cavity-polarition modes, the eigenenergies of the cavity polaritons were calculated using the phenomenological

Fig. 2.1.5. (a) Angle-resolved reflectance spectra of the CuCl microcavities with the active layer thicknesses of λ/2,. The open circles and triangles indicate the strongly coupled modes and weakly-coupled modes, respectively. (b) Incident-angle dependence of the cavity polariton energies obtained in the respective CuCl microcavities with the active layer thicknesses of λ/2. The open circles and triangles are the energy positions of the strongly coupled modes and weakly-coupled modes, respectively. The solid lines indicate the dispersion relationships of the cavity-polariton modes of the LPB, MPB, and UPB calculated from Eq. (2). The dotted lines indicate the Z3 and Z1,2 exciton energies, and the dashed curves show the dispersion relationship of the cavity photon.

R e fl e c ti v it y (a rb . u n it ) 3.6 3.5 3.4 3.3 3.2 3.1

Photon Energy (eV)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 13 K

Photon Energy (eV) λ/2-cavity E_Z(3)E_Z(1,2) (a) 3.6 3.5 3.4 3.3 3.2 3.1 3.0 P h o to n E n e rg y ( e V ) 70 60 50 40 30 20 10 0

UPB MPB LPB Photon E_Z(3) EZ(1,2) λ/2-cavity ΩZ(3) =97 meV ΩZ(1,2) = 157 meV E_c(0) = 3.201 eV (b)

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20 Chapter 2 Optical Properties of CuCl microcavities

Hamiltonian. The interaction between the cavity photon and the two states of the Z3 and

Z1,2 excitons is given by the following matrix[2.8],

                  Ω Ω Ω Ω = Z(1,2) Z(1,2) Z(3) Z(3) Z(1,2) Z(3) cav 0 2 0 2 2 2 ) ( E E E H θ (2.1.2)

where ΩZ(3) and ΩZ(1,2) are the coupling constants known as the vacuum Rabi splitting

Fig. 2.1.6 (a) Angle-resolved reflectance spectra of the CuCl microcavities with the active layer thicknesses of 3λ/2,. The open circles and triangles indicate the strongly coupled modes and weakly-coupled modes, respectively. (b) Incident-angle dependence of the cavity polariton energies obtained in the respective CuCl microcavities with the active layer thicknesses of 3λ/2. The open circles and triangles are the energy positions of the strongly coupled modes and weakly-coupled modes, respectively. The solid lines indicate the dispersion relationships of the cavity-polariton modes of the LPB, MPB, and UPB calculated from Eq. (2). The dotted lines indicate the Z3 and Z1,2 exciton energies, and the dashed curves show the dispersion relationship of the cavity photon.

3.6 3.5 3.4 3.3 3.2 3.1 3.0 P h o to n E n e rg y ( e V) 70 60 50 40 30 20 10 0

UPB Photon LPB MPB 3λ/2-cavity EZ(3) EZ(1,2) ΩZ(3) = 132 meV ΩZ(1,2) = 223 meV Ec(0) = 3.099 eV (b) R e fl e c ti v it y ( a rb . u n it s ) 3.5 3.4 3.3 3.2 3.1 3.0

Photon Energy (eV)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 13 K

Photon Energy (eV)

EZ(3) EZ(1,2)

3λ/2-cavity (a)

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energies for the Z3 and Z1,2 excitons, respectively. Three solid curves, shown in Fig.

2.1.4(b), are the dispersion relationships of the cavity polariton fitted to the experimental results using Eq. (2.1.2). The fitted dispersion curves agree with the experimental results. Here, the effective refractive index of the active layer, neff, is adopted as an adjustable

parameter to the incident-angle dependence of the cavity-polariton modes, since the electric field of the cavity photon in the microcavities are penetrated into the DBRs as shown in Fig. 2.1.2(b). The value of neff is estimated to be 2.07 by fitting to the

incident-angle dependence. Moreover, the evaluated Rabi splitting energies ΩZ(3) and

ΩZ(1,2) are 110 and 195 meV, respectively. These Rabi splitting energies are larger than

Fig. 2.1.7. (a) Angle-resolved reflectance spectra of the CuCl microcavities with the active layer thicknesses of 2λ,. The open circles and triangles indicate the strongly coupled modes and weakly-coupled modes, respectively. (b) Incident-angle dependence of the cavity polariton energies obtained in the respective CuCl microcavities with the active layer thicknesses of 2λ. The open circles and triangles are the energy positions of the strongly coupled modes and weakly-coupled modes, respectively. The solid lines indicate the dispersion relationships of the cavity-polariton modes of the LPB, MPB, and UPB calculated from Eq. (2). The dotted lines indicate the Z3 and Z1,2 exciton energies, and the dashed curves show the dispersion relationship of the cavity photon.

R e fl e c ti v it y ( a rb . u n it ) 3.5 3.4 3.3 3.2 3.1 3.0

Photon Energy (eV)

0 5 10 15 20 25 30 35 40 45 50 55 60 13 K EZ(3) EZ(1,2)

Photon Energy (eV)

2λ-cavity (a) 3.6 3.5 3.4 3.3 3.2 3.1 3.0 P h o to n E n e rg y (e V ) 70 60 50 40 30 20 10 0

UPB MPB LPB Photon 2λ-cavity EZ(3) EZ(1,2) ΩZ(3) = 135 meV ΩZ(1,2) = 233 meV Ec(0) = 3.116 eV (b)

大阪府立大学 学術情報リポジトリ

Optical Properties of CuCl Microcavities and

Dynamical Interference between Rabi

Oscillation and Coherent Phonon

著者

吉野 慎吾

内容記述

学位記番号：論理第106号, 指導教員：溝口 幸司

Optical Properties of CuCl Microcavities

and

Dynamical Interference between

Rabi Oscillation and Coherent Phonon

Shingo Yoshino

Department of Physical Science,

Graduate School of Science

Osaka Prefecture University

論文要旨

Optical Properties of CuCl Microcavities

and

Dynamical Interference between

Rabi Oscillation and Coherent Phonon

CuCl 微小共振器の光学特性と

Rabi 振動とコヒーレントフォノン間の動的干渉効果

Contents

Chapter 1 Introduction

1.1 Background

1.2 Cuprous Chloride

1.3 Semiconductor Microcavities

ω

ω

e

,

0

g

,

1

e

g

1

0

ω

ω

h

θ

k

k

k

=

+

φ

φ

φ

φ

φ

θ

φ

cos

L

m

k

k

=

φ

=

π

(b)

k

L

θ

φ

k

k

(a)

n

n

k

n

c

k

E

大阪府立大学　学術情報リポジトリ

吉野慎吾

学位記番号：論理第106号, 指導教員：溝口幸司