A Fast Algorithm for Identifying Hierarchical Clustering Structures using Constraint Graph

Jeong-Hun Kim 충북대학교 대학원 2019 국내석사

OPTICS is a state-of-the-art algorithm for visualizing hierarchical clustering structures of multidimensional objects. However, OPTICS requires iterative distance computations for all objects, and thus is computed in O(n²) time that makes it unsuitable for massive datasets. Existing algorithms are not efficient to overcome the OPTICS issue. In this thesis, we propose a fast algorithm, called C-OPTICS, that alleviates the issue of time complexity using the constraint graph. C-OPTICS identifies the hierarchical clustering structures faster by reducing the number of distance computations while guaranteeing the hierarchical clustering structures identical to OPTICS. Both the qualities of the hierarchical clustering structures identified by C-OPTICS and its computational efficiency are demonstrated with experimental evaluations on synthetic and real datasets. OPTICS는 다차원 객체들의 계층적 클러스터링 구조를 시각화하는 최첨단 알고리즘이다. 하지만 OPTICS는 모든 객체들에 대한 반복적인 거리 계산으로 인해 O(n²) 시간을 요구하기 때문에 대용량 데이터 집합에 부적합하다. 기존의 알고리즘들 또한 최악의 경우에 이차 시간 복잡도를 가진다. 이를 개선하기 위해, 본 논문에서는 제약조건 그래프를 이용하여 OPTICS의 이차 시간 복잡도 문제를 완화하는 알고리즘인 C-OPTICS를 제안한다. C-OPTICS는 OPTICS의 결과와 동일한 계층적 클러스터링 구조를 보장하면서 동시에 거리 계산 횟수를 감소시켜 계산 효율성을 향상시킨다. 또한, C-OPTICS의 클러스터링 품질과 계산 효율성은 합성 및 실제 데이터 집합들에 대한 실험적 평가를 통해 입증된다.

Guided polariton optics: A combined numerical, analytical, and experimental investigation of surface plasmon waveguides

Zia, Rashid Stanford University 2006 해외박사(DDOD)

Metals possess unique optical properties distinct from the dielectric materials used today for integrated optics. The promise of "metal optics" is that these properties may one day be exploited to manipulate light at smaller length scales than feasible with dielectric structures. In this context, surface plasmon-polaritons (SPPs) have received considerable attention for their ability to guide electromagnetic energy at optical frequencies. Prior works on surface plasmon waveguides have highlighted their differences from conventional, diffraction-limited dielectric waveguides. It has been suggested that guided polariton modes are not diffraction limited, and specifically, that the surface plasmon modes supported by finite width metal stripes are inconsistent with a ray-optics interpretation of guided wave phenomena. In contrast to previous studies, the work summarized in this thesis presents a physical interpretation for guided polariton optics that is consistent with conventional guided wave optics. While we demonstrate that the confinement of SPPs normal to a metal surface can produce deeply subwavelength optical modes, we prove that the lateral confinement for a surface plasmon mode along a finite interface is consistent with momentum conservation as described by physical optics. Specifically, we have developed a numerical method to solve for the leaky and bounds modes of arbitrary geometry polariton waveguides. With this method, we demonstrate that published experimental results for the field profiles and propagation lengths of metal stripe waveguides are anticipated by their leaky modal solutions. Although the surface plasmon modes supported by stripes guide electromagnetic energy in three dimensions, we establish that such modes can be approximated by the solutions of two-dimensional dielectric slab waveguides. Leveraging this model, we suggest both an effective basis set for the guided polariton modes and an effective diffraction limit in the lateral dimension. To validate these findings, we have fabricated and characterized a variety of passive plasmonic devices using a photon scanning tunneling microscope. In good agreement with numerical simulations and analytical models, we present empirical evidence of guided polariton propagation, diffraction, and interference to support our physical interpretation.

Configurable adaptive optics for the correction of space-based optical systems

McComas, Brian Keith University of Colorado at Boulder 2002 해외박사(DDOD)

Space-based, high resolution, Earth remote sensing systems, that employ large, flexible, lightweight primary mirrors, will require active wavefront correction, in the form of active and adaptive optics, to correct for thermally and vibrationally induced deformations in the optics. These remote sensing systems typically have a large field-of-view. Unlike the adaptive optics on ground-based astronomical telescopes, which have a negligible field-of-view, the adaptive optics on these space-based remote sensing systems will be required to correct the wavefront over the entire field-of-view, which can be several degrees. The error functions for astronomical adaptive optics have been developed for the narrow field-of-view correction of atmospheric turbulence and do not address the needs of wide field space-based systems. To address these needs, a new wide field adaptive optics theory and a new error function are developed. This new error function, which is a new extension of conventional adaptive optics, leads to the development of three new types of imaging systems: wide field-of-view, selectable field-of-view, and steerable field-of-view. These new systems can have nearly diffraction-limited performance across the entire field-of-view or a narrow movable region of high-resolution imaging. The factors limiting system performance are determined and analyzed. The range of applicability of the wide field adaptive optics theory is shown. The range of applicability is used to avoid limitations in system performance and to estimate the optical systems parameters, which will meet the system's performance requirements. Experimental results demonstrate the wide field adaptive optics theory. Finally, it will be shown that a synthetic guide star stimulated from above the atmosphere can be used as a beacon for the wavefront sensors of space-based systems. These wavefront sensors must be optimized such that error in the reconstructed wavefront is minimized. The key equations that govern the optimization of a Shack-Hartmann wavefront sensor exploiting a synthetic guide are developed. The optimization process also is presented. Using modal reconstruction, the first step in this process is the optimization of the retrieved basis function modes. The second step involves optimizing the number of measurement points (or subapertures) in the pupil. Design examples are presented to demonstrate this process.

Elastic transformation optics devices using smart metamaterials

신동혁 Graduate School, Yonsei University 2015 국내박사

Transformation optics and artificial metamaterials can make possible to design and realize new phenomena such as negative refraction and optical cloaking. As invariance of Maxwell’s equations in coordinate transformation, transformation optics can not only control the behavior of electromagnetic wave but also be the theoretical basis for optical cloak which bend the light around an object to conceal. Metamaterials are artificial periodic structure represented by physical properties designed by transformation optics. The metamaterials are satisfied effective medium theory and regard as effective medium not each components because the period of the metamaterials is much smaller than operating wavelength. In this dissertation, I suggest a theoretical approach to elastic transformation optics as a design tool of smart metamaterials that overcome the limit of the conventional metamaterials, then demonstrate these concepts as an electromagnetic cloak which is the most popular transformation optics device. Smart metamaterials have changeable property distribution from altered internal composition of medium by external elastic deformation. So far existing metamaterials with rigid shape and fixed property distribution are fragile to external deformation and impact and hard to fabricate when complicated material properties are required. Smart metamaterials are self-adjustable to the external stimulus, while the distribution of the internal structural compositions and physical properties satisfy the transformation optics during elastic deformation. To design smart metamaterials, it is required that elastic transformation optics integrating elastics and conventional transformation optics. Based on quasi-conformal mapping for isotropic dielectric materials, elastic transformation optics is proved that deformation of linear elastic solid with negative Poisson’s ratio satisfies transformation optics. Then one versatile elastic transformation optics device consist of smart metamaterials with negative Poisson’s ratio is fabricated and experimentally demonstrated in microwave regime(X-band) as a self-adjustable smart cloak for any deformable shape to conceal and a bendable smart waveguide maintaining phase of internal wave. This smart metamaterials with negative Poisson’s ratio and high dielectric constant called auxetic smart metamaterials. Negative Poisson’s ratio and high dielectric component in smart metamaterials make it possible to satisfy transformation optics. However negative Poisson’s ratio requires complex structures that are hard to fabricate and high dielectric constant cannot support broad operating band. Therefore I present another smart metamaterials whose composite structure has ordinary Poisson’s ratio and dielectric constant of silicone rubber. This non-auxetic smart metamaterials without negative Poisson’s ratio satisfy transformation optics only after elastic deformation, not during deformation. However, it is easy to fabricate initial periodic structure then simple deformation complete a transformation optics device. So that non-auxetic smart metamaterial scheme is amenable to easier fabrication of large area metamaterial device. Carpet cloak of non-auxetic smart metamaterials is fabricated and verified in microwave regime, then it is confirmed that the cloak’s broadband performance maintains regardless of incident angles.

Three-dimensional Gradient Index Optics Fabricated in Diffusive Photopolymers

Ye, Chunfang University of Colorado at Boulder 2012 해외박사(DDOD)

This thesis demonstrates three-dimensional gradient index (GRIN) optics fabricated in two diffusive photopolymers. These polymer optical components have localized gradient index structures, which are self-developed in diffusive photopolymers by introducing localized illuminations. Based on the sizes of the formed index structures, the photopolymer optics studied in this thesis fall into two categories: GRIN lens based optics and waveguide based optics. GRIN lenses and lens arrays with parabolic index profiles are created through Gaussian beam exposure, while GRIN lenses with arbitrary index profiles are created through a dual-axis galvo scanning system. Waveguide based optics, which include uniform waveguides, waveguide tapers, waveguides through thin optics and 90<super>0</super> sharp waveguide bends, are fabricated through direct-write lithography. Several quantitative characterization methods for the fabricated polymer optics are described. The index profiles of the GRIN lens based optics are quantitatively measured by a modified scanning transmission phase microscope and a Shack-Hartmann wavefront sensor. Three-dimensional mode profile characterization of the polymer waveguides is carried out through a novel polymer sample preparation procedure and an active mode imaging system. A single mode performance is confirmed for the fabricated waveguides. A loss measurement for the waveguides is also accomplished. An index formation model is developed for a diffusive polymer developed by Dr. McLeod's group, which provides a fundamental guidance for fabricating custom-design index structures in the polymer. A hybrid GRIN axicon lens is fabricated to significantly extend the depth of focus in an endoscopy OCT application. Potential applications of the fabricated polymer optics include hybrid integrated optical circuits. The diffusive photopolymer with self-development characteristics provides a platform to integrate various optoelectronic subcomponents in integrated optical circuits.

Properties of air-silica structured optical waveguide : from ray to electromagnetic optics regime

박민규 Graduate School, Yonsei University 2013 국내박사

Air-silica structured optical waveguides have three different characteristics from conventional silica-structured optical waveguides: High contrast of refractive index, Free-space propagation with no phase delay, and available of arbitrary structures in periodic patterns. In order to analyze air-silica structured optical waveguides exactly, scale of air structure and optical waveguides with respect to wavelength is important. If the scale is larger than wavelength, its governing theory is characterized by ray optics regime. When the structural size is almost same as wavelength, it is explained by wave optics regime. And if the size is smaller than wavelength, optical waveguide can be fully described by Maxwell's equation of electromagnetic optics regime. In this dissertation, air-silica structured optical waveguides and their applications were fully analyzed by exact theories under each optics regime and precisely demonstrated by experiments. In ray optics regime, a novel tapered dielectric waveguide solar concentrator was proposed for compound semiconductor solar cells utilizing optical fiber preform. The concentrator in millimeter scale is enormously bigger than wavelength and its optical mechanism was analyzed by non-imaging optics. Light collecting capability was numerically simulated by ray-tracing method and experimentally demonstrated for feasibility and potential assessments. Utilizing tapered shape of an optical fiber preform with a step-index profile, low loss guidance was enhanced and the limitation in the acceptance angle of solar radiation was alleviated by an order of magnitude. Using a solar simulator the device performances were experimentally investigated and discussed in terms of the photocurrent improvements. Total acceptance angle exceeding ± 6° was experimentally achieved sustaining a high solar flux. In wave optics regime, a compact intrinsic fiber Mach?Zehnder interferometer (MZI) was proposed and experimentally demonstrated by incorporating a micro air-cavity ablated by femtosecond laser irradiation. A short cavity of length ~10 um along the single-mode fiber core provided two optical paths: one propagating through the air and the other guided along the ring-shaped silica cladding. Its exact optical behavior was analyzed by beam-propagation method and a spectral analysis confirmed MZI in a good agreement with experimental results. Temperature-dependent spectral shifts were also measured and analyzed. In electromagnetic optics regime, two different photonic crystal fibers were utilized to study optical properties. One is a new type of birefringent index guiding photonic crystal fiber (PCF) with two hollow GeO2-doped silica ring defects imbedded in a hexagonal hole arrays. Air-holes of photonic crystal are smaller than wavelength, and rigorous finite element method (FEM) using the perfectly matched layer (PML) was applied to calculate complex propagation constant and analyze optical transmission characteristics. Birefringence was flexibly controlled independent of chromatic dispersion, and improvement in confinement loss was achieved by optimizing hollow ring defect parameters. Another is characterizing optical nonlinearity of a Ge-doped core photonic crystal fiber (PCF) in the spectral domain, C-band, by using a cross-phase modulation (XPM) method with a pulsed pump laser and a continuous wave signal laser. A nonlinear phase shift accumulated along the PCF was directly measured in the spectral domain by a high-resolution optical spectrum analyzer. The proposed technique was validated for a conventional step-index high nonlinear optical fiber with a known nonlinear parameter, to confirm its potential in efficiently characterizing the optical nonlinearity of an arbitrary PCF overcoming dispersion and insertion loss penalties.

컴퓨터 적응광학을 이용한 안과영상 광학수차 보정에 대한 연구

정성훈 인하대학교 대학원 2021 국내석사

본 논문에서는 컴퓨터 적응광학(Computaional Adaptive Optics ;CAO)을 알고리즘을 통해 이미지에서 수차를 보정하는 시뮬레이션을 진행하고 평가지표를 통해 결과를 평가하였다. CAO는 하드웨어 기반의 적응광학(Hardware based Adaptibe Optics ;HAO)의 개념에서 시작되었다. HAO는 광학계의 수차 측정 및 보정을 통하여 고해상도 이미지를 얻는 기법으로 HAO 메커니즘을 이해하고 안과영상에 대한 적용은 많은 연구가 이루어지고 있다. HAO는 광학계가 가지고 있는 물리적인 한계인 회절한계까지 이미지의 해상도를 높이는 결과를 보여주었다. 하지만 HAO의 몇 가지 한계점이 제시되고 있어 이를 해결하고 장점을 유지하는 방법에 대한 연구가 진행되고 있다. HAO의 한계점은 먼저 HAO의 주요 요소가 값비싼 광학 장비로 구성되어있으며 장비의 사용에 있어 전문가의 정교한 조작이 필요하다. 이는 HAO 시스템을 작동시키기 위해 광학장비의 정교한 배치(align)가 필요하며 광학계 자체의 수차를 제거하기 위한 최적화 과정에 사용되는 소프트웨어 구동이 복잡한 단점이 있다. 또한 정교한 배치를 통한 작동은 구불구불한 인체 내로 들어가는 내시경처럼 생체 내의 이미지를 얻기 위해 외적인 변형이 필요한 광학장비와 결합하기 어렵게 한다. HAO의 한계점 해결하기 위해 CAO는 정교한 광학계의 배치 없이 이미지로부터 수차를 구성하고 보정하였으며 이미지로부터 수차의 보정을 진행하기 때문에 생체내 이미지를 얻기위한 장비와의 결합 가능성을 제시한다. 본 논문에서는 수차가 생긴 이미지로부터 수차를 보정하는 알고리즘을 제시하고 이미지 시뮬레이션 결과를 제시한다. 또한 이미지 시뮬레이션 결과를 평가지표를 통해 이미지의 품질 개선을 확인하였다. In this paper, we propose a Computational Adaptive Optics(CAO) algorithm for compensating aberrations of an image taken through an optical system. The simulation of compensating aberration in the image through the CAO algorithm was conducted and was evaluated by the least square error(LSE) as the evaluation index. The CAO originated from the concept of Hardware based Adaptive Optics (HAO). The HAO mechanism is a technique for obtaining high-resolution images through aberration compensating. The HAO showed the result of improving the resolution of the image to the diffraction limit that the physical limitations of optics. Many studies on the application of HAO to ophthalmic images have been conducted. However, the HAO has some limitations. First, the HAO consists of expensive optical devices and requires sophisticated manipulation by experts in the use of the devices. This requires the sophisticated alignment of optical devices to operate the HAO system. Second, the HAO has complicated software used in the optimization process to eliminate the aberration in the optics. Operation through sophisticated alignment also makes it difficult to combine with optical devices that require external deformation to obtain an image in vivo, for example, an endoscope entering the stomach or intestine. To address the limitations of HAO, the CAO algorithm has constructed and measured the aberration from the images without the alignment of sophisticated optics. Since the CAO proceeds with the measure of the aberration from the images, it presents the potential for coupling with devices to obtain the in vivo image. In this paper, we propose an algorithm to compensate the aberration from image. The results of the image simulation were demonstrated to improve the quality of the image thorough the least square error(LSE) as the evaluation index. keyword: Aberration correction, adaptive optics, fourier optics, image processing, computational adaptive optics

PO/GO 연계기법을 이용한 RCS 해석코드 개발

장민욱 경상대학교 대학원 2014 국내석사

In the recent years, the combat survivability that measures the capability of performing a mission in hostile environment becomes a critical issue in the development of flying vehicles. An enhancement of survivability in the preliminary design can be achieved by the radar frequency (RF) stealth technique which intends to avoid an enemy’s radar. The level of the RF stealth is measured by introducing the so-called radar cross section(RCS). There are several methods to compute radar cross section(RCS) such as geometrical optics (GO), physical optics (PO), method of moments (MM), and full equation method. In principle, the full Maxwell equations can be solved by the method of moments, finite element method (FEM), and finite volume time domain (FVTD) method. On the other hand, for the high frequency there exist various approximate methods; for example, physical optics and geometrical optics. Since the physical optics and the geometrical optics are dealt with a limited part of scattering and diffraction, these methods are very efficient in calculating the RCS of complicated shapes like an aircraft. In this study, a hybrid method of physical optics and geometrical optics was employed in order to predict the RCS of flying vehicles for proper RCS reduction schemes. An in-house code using MATLAB was developed and validated with a simple model of cylinder, wing section and plate. In addition, RCS analysis of a flying vehicle was performed using a hybrid high-frequency electromagnetic scattering method based on physical optics and geometrical optics theories. In cavity return, the rays are assumed to bounce from the inlet cavity based on the laws of geometrical optics and to exit the cavity via the aperture. In other parts of a flying vehicle, the physical optics method is applied to compute the back-scattered field from the solid surface.

Design and analysis of high resolution solid immersion lens based near field optics with annular aperture

윤용중 Graduate School, Yonsei University 2009 국내박사

To achieve high resolution for the optical imaging systems such as fluorescent imaging microscopy, optical data storage and lithography have been required continuously. These demands can be met by means of solid immersion lens (SIL)-based near-field optics which is one of the strongest candidates to satisfy high resolution optics. By introducing SIL-based near-field optics, a numerical aperture (NA), a factor that defines optical resolution in an inversely proportional relation, can be increased to more than unity, which is the diffraction limit in free space. However, to realize SIL-based near-field optics for applying to high resolution advanced imaging optics, there are several critical problems should be solved. Moreover, higher resolution and longer focal depth than conventional SIL-based near-optics are continuously required to improve the optical performances in near-field optical systems. Therefore, it is inevitably required to solve the current status critical problems of conventional SIL-based near-field optics as well as to improve the optical performances by increasing resolution and focal depth. In this thesis, I will introduce the possible solutions for the dominant problems related to the SIL optical head tolerances among the several problems which conventional SIL-based optics has. One of the critical problems is the fabrication of SIL itself, especially super-hemispherical SIL and the other problem is the assembly of a SIL optical head composed of an objective lens and a SIL. As the final end, I will show the improvement of the optical performances in SIL-based near-field optics by applying an aperture technique which is well known to optimize the intensity distribution of focused beam spot by modulating amplitude and phase. Therefore, first, I will present the general diffraction integral formula for calculating the electric field structure in a focal region composed of a multilayered medium as well as at the exit pupil plane with an arbitrary NA for a finite number of annular aperture zones considering various polarized illumination. Based on the derived formula, it is possible to understand the electric field behavior in the focal region and at the exit pupil plane for the various optical conditions. The analysis based on the derived formula will be effectively used to verify proposed solutions and to design improved SIL-based near-field optics with an annular aperture through this thesis. Second, I will introduce the hybrid SIL optical head design results as well as the conventional SIL optical heads of the hemispherical and super-hemispherical SIL. In the hybrid SIL optical head design, replicated surface is added on the top surface of a SIL to generate aspherical surface. Through the proposed design concept, the thickness tolerance of SIL, which is one of the critical technical barriers, can be increased by 30μm. In addition, through the vector field analysis I will show that the proposed hybrid SIL optical head has good optical performances to apply it to SIL-based near-field optics. Third, I will show the assembly and evaluation results of SIL optical head for surface recording and cover-layer-protected recording types by means of Twyman-Green Interferometer. Interferometer system should be used when assembling and evaluating SIL optical head in order to confirm its optical performances repeatedly due to the severe distance tolerance between an objective lens and SIL. The evaluation results will be also compared with simulation ones. Further, to simplify the assembly and evaluation procedure for cover-layer-protected SIL optical head, I will propose the assembly and evaluation method without contact process between the SIL and the medium that was considered as essential requirement. Finally, I will show high resolution SIL optical head for various polarization illuminations by introducing an annular aperture technique which can optimize interference between propagation and evanescent wave effectively to reduce focused beam spot size and to increase focal depth. By applying an optimized annular aperture to convention SIL optical head resolution can be increased by approximately 20%. This novel SIL-based near-field optics will be verified through experiments such as measuring focused beam spot profiles and observing the topology of a measurement sample. The studied SIL-based near-field optics can be applicable to not only next generation optical storage device but also high resolution microscopy and pattering technologies.

Active FDTD simulation on gradient-refractive-index microcavity semiconductor laser diodes based on transformation optics : 변환광학에 기반한 점진적으로 굴절율이 변화하는 마이크로 캐비티 레이저 다이오드에서 FDTD 시뮬레이션

이용훈 경북대학교 대학원 2019 국내석사

마이크로 디스크 또는 마이크로 토로이드와 같은 원형 대칭성이 있는 마이크로 공진기에서 존재하는 속삭임의 회랑 모드 (whispering gallery modes, WGMs)는 빛이 전반사를 통해 공진기 내부에서 매우 오랫동안 머무르는 공진 모드이다. 이러한 원형 마이크로 공진기를 기반으로 하는 레이저는 매우 낮은 임계전압과 높은 주파수 분해능을 가지기 때문에 초고속/초소형 통신용 광소자와 고분해능 바이오 센서 등 여러 응용분야를 가진다. 그러나 원형 공진기는 많은 장점을 가짐에도 불구하고, 모든 방향으로 일정하게 빛이 방사되어 외부와의 효율적인 광 결합에 한계를 지니게 되므로 응용에 많은 제한이 있다. 많은 연구자들은 공진기가 특정 방향으로 방출특성을 가지도록, 공진기의 외형을 변형시키거나 공진기 내부에 산란체가 추가된 다양한 변형 공진기에 대한 연구를 수행해왔다. 그러나 공진기의 외형을 변형 시키거나 구멍과 같은 산란체를 추가하면 공진기가 가지는 원형 대칭성이 깨지기 때문에 Q 인자가 크게 감소하게 된다.(Q 인자(Q-factor)는 공진기에 빛이 몇 주기 정도를 머무르는지 정량화한 공진 모드 특성 지표이다.) 따라서 방향성 있는 빛의 방출 특성과 높은 Q 인자를 동시에 가지는 공진기의 구현은 오랫동안 불가능한 것으로 여겨져 왔다. 변환광학은 공간이 팽창하거나 수축할 때 빛의 경로가 휘는 일반상대론적 효과를 공간의 왜곡이 아닌 물질의 유전율과 투자율 공간제어를 통해 일반적인 현실 환경에서 구현하는 광학 원리이다. 최근에 이러한 변환광학을 공진기 설계에 적용한 변환광학 공진기 연구가 새롭게 제시되었다. 변환광학을 적용한 변형 공진기는 외형이 변형됐음에도 불구하고 속삭임의 회랑 모드를 유지할 수 있기 때문에 높은 Q 인자를 유지하고 원형 공진기와는 달리 방출 방향성 또한 가진다. 이러한 독특하면서도 뛰어난 광특성을 지닌 변환광학 공진기를 레이저 광원에 응용하고자 하는 연구는 차세대 나노포토닉스 광원 개발이라는 잠재력으로 인하여 크게 주목 받고 있다. 변환광학 공진기와 레이징 게인 물질이 결합한 변환광학 공진기 레이저를 설계하기 위해서는 광/능동물질의 상호작용을 고려한 시간영역 수치계산이 필수적이다. 하지만 변환광학 공진기 레이저의 경우에는 그 짧은 개발 역사로 인하여 관련된 연구가 거의 전무한 실정이다. 이 논문에서는 수동 공진기 계산으로는 예측하기 어려운 게인 물질이 결합한 변환광학 공진기 레이저에서 레이징 모드를 FDTD 방법을 통해서 계산하였다. 이를 통해 뛰어난 주파수 특성과 발진 방향성 및 편광 특성을 가진 최적화된 변환광학 공진기 레이저 구조를 설계하였다. In symmetric micro cavities like micro disk or micro toroid, whispering gallery modes (WGMs) are extremely long lived modes through the total internal reflection [1,2]. Such a circular micro cavity based laser has a very low threshold voltage and high frequency resolution, and thus has many applications such as a high-speed/small-sized communication optical device and a high-resolution biosensor [3-6]. However, although the circular resonator has a number of advantages, there are limitations in the application because the light is uniformly emitted in all directions and has a limitation in efficient optical coupling with the outside. Many researchers have studied a variety of resonant cavity in which the shape of a cavity is transformed or a scatterer is added inside the cavity so that the cavity has emission characteristics in a specific direction [7 8]. However, if the outer shape of the cavity is deformed or a scatterer is added, the Q factor is greatly reduced because the circular symmetry of the cavity is broken [9]. (The Q factor is a resonance mode characteristic index that quantifies the number of cycles of light staying in the resonator.) Therefore, it has long been considered impossible to realize a resonator having directional light emission characteristics and high Q factor simultaneously. Transformation optics is an optical principle that realizes the general relativity of a path of light when a space expands or contracts, not in space distortion but in the real world through spatial control of permittivity and permeability of material. Recently, a transformation optics resonator research has been newly proposed in which the transformation optics are applied to the resonator design [10]. The transformed resonator using the transformation optics maintains a high Q factor because it can maintain the WGMs even though the outer shape is deformed, and it has a directionality unlike the circular resonator. Research to apply such a unique optical characteristic to a transformation optics resonator has attracted much attention due to its potential to develop a next generation nanophotonics light source. In order to design a transformation optics resonator laser that combines a transformation optics cavity and a lasing gain material, time domain numerical calculations that consider the interaction of the optical / active materials are essential. However, in the case of a transformation optics resonator laser, there is almost no related research due to its short development history. In this paper, the lasing mode is calculated by the FDTD method in the transformation optics resonator lasers coupled with gain materials which are difficult to predict with passive resonator calculation. We have designed an optimized optical resonator laser structure with excellent frequency characteristics, oscillation direction and polarization characteristics.