Theory of Extreme Optical Concentration in All-Dielectric Waveguides

Dielectric waveguides are the solution to the ultra-fast optical communication. In all-dielectric waveguide systems, the boundary condition of Maxwell’s electromagnetic equation can be exploited. Crucially dielectric materials have very low optical losses compared to metal hence the plasmonic structures. Due to very high losses, plasmonic structures are not suitable for practical usage. Achieving small mode dimensions has become an important factor in modern devices since smaller mode dimensions fosters high device density, efficiency, and or performance in a wide array of photonic systems. Keeping these criteria in focus, a transversely structured all-dielectric waveguide has been introduced in this thesis which exploits the vectorial nature of light to achieve extreme sub-wavelength confinement in high index dielectrics, enabling characteristic mode dimensions below λ_0^2/1,000 without metals or plasmonics. A new metric of performance measurement for waveguide structures has been introduced – “optical concentration”. This metric of optical concentration has been derived and illustrated for its convenient usage in characterizing enhanced linear and nonlinear interactions at the nanoscale. This work expands the toolbox of nanophotonics and opens the door to new types of ultra-efficient and record performing linear and nonlinear devices with broad applications spanning classical and quantum optics

Modelling and Characterization of Guiding Micro-structured Devices for Integrated Optics

In this thesis we show several modelling tools which are used to study nonlinear photonic band-gap structures and microcavities. First of all a nonlinear CMT and BPM were implemented to test the propagation of spatial solitons in a periodic device, composed by an array of parallel straight waveguides. In addition to noteworthy theoretical considerations, active functionalities are possible by exploiting these nonlinear regimes. Another algorithm was developed for the three-dimensional modelling of photonic cavities with cylindrical symmetry, such as microdisks. This method is validated by comparison with FDTD. We also show the opportunity to confine a field in a region of low refractive index lying in the centre of a silicon microdisk. High Q-factor and small mode volumes are achieved. Finally the characterization of microdisks in SOI with Q-factor larger than 50000 is presente

복소, 무질서 및 광학적 비선형 퍼텐셜에서의 대칭성 붕괴를 통한 빛의 흐름 제어

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 박남규.매질 내 빛의 흐름은 통상적으로 거시적 맥스웰 방정식에 의해 정의된다. 동질성 및 등방성을 가지고, 선형적이며, 시간에 대해 일정한 광학 매질 변수를 갖는 이상적인 매질에서는 광파의 양상이 페르마의 원리의 직접적인 예인 진동하는 전자기장의 직진 형태로, 간단하며 직관적이다. 이러한 평면파적 특성은 기하 광학의 바탕이며, 슈뢰딩거 방정식 형태의 파동 방정식이 갖는 다양한 대칭성 (병진 대칭, 키랄 대칭, 에르미트 대칭, 로렌츠 대칭 및 시간 반전 대칭)의 보존에서 그 원리을 찾을 수 있다. 렌즈, 거울 및 프리즘과 같은 고전적인 방식에서조차, 빛의 흐름을 조절키 위해서는 일부 광학적 대칭성의 붕괴를 필요로 한다. 비균질 매질에서의 병진 대칭의 붕괴는 굴절, 반사, 회절과 같은 산란 기반 빛 제어를 위한 고전적인 방법이다. 전파 시의 빛 에너지의 소모 또는 증폭은 파동 방정식의 비에르미트 헤밀토니안에 의해 정량화된다. 키랄 분자로 이루어진 매질은 광학 활성, 즉 빛의 편광을 돌릴 수 있도록 한다. 천문학에서 별 및 은하 움직임의 관찰에 이용되는 광학적 도플러 효과는 로렌츠 대칭성을 붕괴시키는 광원의 시간에 따른 변화에 기반한다. 비직관적인 이론적 결과물 및 향상된 공정 기술을 포함하는 광학 분야의 최근 성과들은 이제 비고전적인 빛의 흐름을 이끌어내기 위한 광학적 퍼텐셜 제어의 새로운 영역을 개척하고 있다. 메타 물질 개념과 연계된 나노 스케일 기술은 단방향 빛 전파, 변형된 스넬의 법칙, 음굴절율, 투명 망토, 완전 흡수체와 같은 특이한 빛의 흐름을 지원하는, 이론적으로 증명된 인조 매질의 설계를 가능케 한다. 광 증폭 기술의 발전은 양자역학적 개념인 패리티-시간 대칭성의 구현에 적용되어, 복소 퍼텐셜에서의 새로운 종류의 광학을 탄생시켰다. 이러한 성취물들은 맥스웰 방정식에서의 더 넓고 급격한 형태의 대칭성 붕괴에 기반하기 때문에, 의도된 빛의 흐름 조절을 위해서는 다양한 대칭성 붕괴에 관한 심도있는 연구가 필요하다. 본 학위 논문에서는 복소, 불규칙, 비선형 광학 퍼텐셜과 같은 다양한 플랫폼에서의 대칭성 붕괴에 대하여 살펴보고자 한다. 본 연구는 패리티-시간 대칭성, 키랄 특성, 인과율, 초대칭, 생물 모방 기술, 모드 경계 광학 및 느린 빛 원리와 연계된 빛의 특이한 흐름에 집중한다. 본 연구진이 이끌어낸 비직관적인 개념 및 광소자의 새로운 설계 기법 관련 결과들은 비고전적인 빛의 흐름에 기반한 미래 광학 발전에 도움이 될 것이다.The flow of light in matters is usually defined by macroscopic Maxwells equations. In ideal media with homogeneous, isotropic, linear, and time-invariant optical material parameters, the aspect of light wave dynamics is simple and intuitive: propagating straight with oscillated electromagnetic fields, as the direct example of Fermats principle. This planewave dynamics, the basis of geometric optics, originates from the conservation of various symmetries of the Schrodinger-like wave equation, including translational and chiral symmetry, Hermitian symmetry, Lorentz reciprocity, and time-reversal symmetry. To control the flow of light even in a classical manner such as lens, mirror, and prism, some parts of the symmetries in optics should be broken. Breaking the translational symmetry with inhomogeneous materials is the traditional method of controlling light by scattering such as refraction, reflection, and diffraction. The dissipation or amplification of optical energy during the propagation is quantified by the non-Hermitian Hamiltonian of the wave equation. The materials composed of chiral molecules allow the rotation of the polarization of light, i.e. optical activity. The optical Doppler effect, which has been employed in astronomy for the observation of the motion of stars and galaxies, is based on the time-varying position of light sources, breaking Lorentz reciprocity. Recent achievements in optics, including counterintuitive theoretical results and improved fabrication technologies, have now been pioneering unprecedented regimes of controlling optical potentials which derive non-classical flow of light. Nano-scale technologies linked with the concept of metamaterials have opened a path to the design of theoretically-demonstrated artificial media supporting extraordinary light flows: such as unidirectional light flow, modified Snells law, negative index, cloaking, and perfect absorption. The development of optical amplification techniques has been applied to the realization of the quantum-mechanical notion of parity-time symmetry: stimulating a new class of optics in complex potentials. Because these achievements have been based on broader and drastic forms of symmetry breaking in Maxwells equations, in-depth investigation of various symmetry breakings is now imperative to realize designer manipulation of light flow. In this dissertation, we explore symmetry breakings in various platforms: complex, disordered, and nonlinear optical potentials. The investigation is focused on unconventional flows of light linked with the notions of parity-time symmetry, chirality, causality, supersymmetry, biomimetics, mode junction photonics, and slow-light. We believe that our results including counterintuitive concepts and novel design methods for optical devices will be the foundation of future development in optics based on non-classical flow of light.Table of Contents Abstract i Table of Contents iv List of Figures viii Chapter 1 Introduction １ 1.1 Why should we break the symmetry of light? １ 1.2 Outline of the dissertation ２ Chapter 2 Parity-Time Symmetric Optics ４ 2.1 Introduction to PT-symmetric optics ５ 2.2 PT-symmetric waves in the spatial domain １１ 2.2.1 2-level chirped system １１ 2.2.2 N-level photonic molecule ２４ 2.3 PT-symmetric waves in momentum domains ４３ 2.3.1 Optical chirality in low-dimensional eigensystems ４４ 2.3.2 Interpretation of PT-symmetry in k-space ６３ 2.4 Conclusion ７５ Chapter 3 Disordered Optics ７６ 3.1 Introduction to disordered optics ７７ 3.2 Supersymmetric bandgap in disorder ７８ 3.2.1 Wave dynamics in random-walk potentials ７９ 3.2.2 Supersymmetric transformation for isospectrality ８３ 3.2.3 Bloch-wave family with tunable disorder ８６ 3.3 Biomimetic disordered surface ９１ 3.4 Conclusion ９８ Chapter 4 All-Optical Devices with Nonlinearity ９９ 4.1 Introduction to all-optical devices １００ 4.2 Mode junction photonics １０１ 4.2.1 Photonic Junction Diode １０５ 4.2.2 Multi-Junction Half Adder １１３ 4.3 Slow-light enhanced optical functionalities １１５ 4.3.1 Multiband slow light １１６ 4.3.2 Optical A/D converter １２６ 4.3.3 All-optical A/D converter １３７ 4.3.4 Travelling-wave all-optical isolator １４３ 4.4 Conclusion １４９ Chapter 5 Conclusion １５０ Appendix A Eigenvalues in PT-Meta-molecules １５２ Appendix B Supplements for Section 2.3.1 １５７ B.1 Planewave solution of a PT-symmetric optical material １５７ B.2 Density of optical chirality for complex eigenmodes １５８ B.3 Effect of imperfect PT symmetry on the modal chirality １５９ B.3.1 Broken symmetry in the real part of permittivity １５９ B.3.2 Broken anti-symmetry in the imaginary part of the permittivity １６１ B.4 Transfer between RCP and LCP modes in the PT-symmetric chiral material １６２ B.4.1 Propagation of complex eigenmodes １６２ B.4.2 Strength of chiral conversion CCS before the EP １６３ B.5 The state of polarization (SOP) at the EP: Optical spin black hole １６４ B.6 Giant chiral conversion in the resonant structure １６５ B.7 Detailed information of fabrication and experiment in THz chiral polar metamaterials １６６ B.7.1 Fabrication process of THz chiral polar metamaterials １６６ B.7.2 THz-TDS system for the measurement of intermodal chirality １６７ B.8 Realization of PT-symmetric permittivity in metamaterial platforms １６７ B.9 Design parameters of chiral waveguides １７１ B.10 Low-dimensional linear polarization １７１ Appendix C Detailed Derivation for Section 2.3.2 １７３ C.1 Detailed derivation of Eq. (2.20) １７３ C.2 Serial calculation of discretized coupled mode equations １７５ Appendix D Analytical Methods for Section 3.2 １７７ D.1 Details of the FDM and FGH method １７７ D.2 Calculation of the Hurst exponent １７７ Appendix E Supplements for Section 4.2 １７９ E.1 Details of the device structures and numerical method used in the study １７９ E.2 Coupled mode theory for the di-atomic photonic junction diode １８１ E.2.1 Analytical model and coupled mode equations １８１ E.2.2. Solution of resonator field (a1, a2, a3) １８３ E.2.3 Implementation of Kerr nonlinearity and calculation of diode throughput １８５ Bibliography １８７ Abstract in Korean ２０３Docto

Mode dynamics in coupled disk optical microresonators

Die vorliegende Dissertation beschäftigt sich mit gekoppelten optischen Flüstergalerieresonatoren in Form von Mikrodiskresonatoren und deren kollektiven resonanten Anregungen, den sogenannten Flüstergaleriemoden. Im Mittelpunkt der Arbeit stehen die umfassende theoretische und experimentelle Charakterisierung gekoppelter Mikrodiskresonatoren, wobei gezeigt wird, dass durch die Kopplung mehrerer Resonatoren deren herausragende Eigenschaften, wie etwa die hohe optische Güte, nur geringfügig beeinflusst werden. Der Nachweis der optischen Kopplung der Moden in den vorliegenden Strukturen wird anhand der charakteristischen spektralen Resonanzaufspaltung erbracht, die von der Anzahl als auch der Anordnung der einzelnen Mikroresonatoren abhängt. Es wird eine Methode vorgestellt, mit welcher erstmals die Intensitätsverteilung der kollektiven Anregungen in gekoppelten Scheibenresonatoren mit einer räumlichen Auflösung im Nanometerbereich gemessen werden kann. Aufbauend auf der Realisierung gekoppelter Mikroresonatoren erfolgt die Untersuchung des Einflusses thermischer nichtlinearer Effekte auf die Resonatormoden. Diese dynamische Licht-Materie-Wechselwirkung wird durch Absorption des Lichts in den Mikroresonatoren und der thermischen Relaxationszeit des Resonatorsystems bestimmt. In diesem Zusammenhang wird eine anregungsleistungsabhängige Resonanzverschiebungen und optische Bistabilität in gekoppelten Mikrodiskresonatoren untersucht. Durch Kombination der thermischen Nichtlinearität und der charakteristischen Intensitätsverteilung der einzelnen Moden kann somit in gekoppelten Mikrodiskresonatoren eine differentielle opto-optische Resonanzverstimmung realisiert werden. Des Weiteren erlaubt die detaillierte Kenntnis der thermo-optischen Eigenschaften der Mikrodiskresonatoren die Realisierung einer Methode zur Kompensation der thermisch induzierten Resonanzverstimmungen, wodurch die Resonanzwellenlänge für einen großen Bereich der Anregungsleistung stabilisiert werden kann

Markov-Airy method for electromagnetic fields in layered structures and microsphere-stabilized planar resonators

In this work, a new technique to calculate the behavior of electromagnetic fields in layered structures is presented. Based upon keeping track of reflections throughout the structure, this technique is a special case of the method of moments. Analysis of layered scatterers, waveguides, and resonators is presented for structures possessing rectangular, cylindrical, and spherical symmetry. In rectangular coordinates, exact formulas are presented for calculating the group delay, group delay dispersion, and third-order dispersion upon reflection or transmission. For the first time, exact formulas are derived for calculating the dispersion of a planar waveguide up to third order. The algorithm has been implemented and subsequently validated by testing it against analytic solutions. In the second section of the thesis, a new method of constructing a cavity is demonstrated. A microsphere is placed in between two high-reflecting mirrors. Depending on the separation of the mirrors, the spheres were observed to either lower or raise the lasing threshold. Models of the cavity were developed and agree with observed data. By self-assembling spheres, a laser array is demonstrated

A rigorous analysis of cascaded step discontinuities in open waveguides

SIGLEAvailable from British Library Document Supply Centre- DSC:DX174172 / BLDSC - British Library Document Supply CentreGBUnited Kingdo