Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov Equations

Quantum Mechanics and ApplicationsQuantum mechanics is a fundamental branch of physics that deals with the behavior of matter and energy at the atomic and subatomic levels. It is a framework for describing the behavior of particles that are too small to be observed directly and for predicting their interactions with one another and with their environment. As a field, quantum mechanics has led to many groundbreaking discoveries and has revolutionized our understanding of the physical world.In this article, we will explore some of the key concepts of quantum mechanics and their applications in modern technology.Wave-Particle DualityOne of the fundamental concepts of quantum mechanics is wave-particle duality. Simply put, this means that particles like electrons and photons can exhibit both wave-like and particle-like behavior, depending on how they are observed. This concept was first proposed by Louis de Broglie in 1924 and has since been confirmed through numerous experiments.One of the most famous experiments that demonstrates wave-particle duality is the double-slit experiment. In this experiment, a beam of electrons or photons is fired at a screen with two slits. Behind the screen, a detector records the pattern of interference that is created by the particles passing through the slits and interfering with each other. This pattern is characteristic of waves rather than particles and demonstrates the wave-like nature of the particles.Quantum SuperpositionAnother fundamental concept of quantum mechanics is quantum superposition. This refers to the ability of particles to exist in multiple states or locations simultaneously. This idea is often illustrated using the famous thought experiment of Schrödinger's cat, in which a cat is placed in a box with a vial of poison that will be released if a particular radioactive atom decays. According to the principles of quantum mechanics, until the boxis opened and the cat is observed, it is in a state of superposition, in which it is both alive and dead at the same time.Quantum superposition is key to the field of quantum computing, which is a new method of processing information that promises to be much faster than classical computing. In a quantum computer, data is stored in quantum bits, or qubits, which can exist in multiple states simultaneously. This allows quantum computers to perform certain calculations much more quickly than classical computers.Quantum EntanglementAnother key concept of quantum mechanics is quantum entanglement. This refers to the phenomenon in which two particles become correlated in such a way that the properties of one particle are dependent on the properties of the other, even when the particles are separated by large distances.Quantum entanglement is a key component of quantum cryptography, which is a method of secure communication that relies on the principles of quantum mechanics. In quantum cryptography, information is encoded using qubits, which are then transmitted over long distances. Because the qubits are entangled, any attempt to intercept or measure them will cause them to become disturbed, alerting the receiver to the presence of an eavesdropper.Applications of Quantum MechanicsThe concepts of quantum mechanics have led to many practical applications in modern technology. One of the most well-known applications is the laser, which uses the principles of quantum mechanics to produce a beam of coherent light.Another important application of quantum mechanics is in the field of medicine. For example, magnetic resonance imaging (MRI) uses the principles of quantum mechanics to produce detailed images of the inside of the body. In an MRI machine, the patient is exposed to a strong magnetic field, which causes the protons in their body to become aligned with the field. When a radio wave is then applied to the patient, the protons release energy, which is detected by the MRI machine and used to produce an image.ConclusionIn conclusion, quantum mechanics is a fundamental branch of physics that has revolutionized our understanding of the physical world. Its concepts of wave-particle duality, quantum superposition, and quantum entanglement have led to many practical applications in modern technology, from lasers to medicine. As our understanding of quantum mechanics continues to develop, it is likely that we will see even more exciting applications in the years to come.。

量子光电器件及应用英文Quantum photonic devices and applications.Quantum photonic devices refer to devices that utilize the principles of quantum mechanics to manipulate and control light at the quantum level. These devices often involve the generation, manipulation, and detection of single photons, as well as the entanglement of photons for applications in quantum computing, quantum communication, and quantum cryptography.One important example of a quantum photonic device is the single-photon source, which is crucial for many quantum technologies. These sources are used in quantum key distribution systems, quantum metrology, and quantum information processing. They can be based on various physical platforms such as semiconductor quantum dots, trapped ions, or nonlinear optical processes.Another key area of research and development in quantumphotonic devices is quantum photodetectors, which are capable of detecting individual photons with highefficiency and low noise. These detectors are essential for applications such as quantum communication and quantum imaging.In addition to these foundational devices, there is ongoing research into more advanced quantum photonic devices, including quantum gates, quantum memories, and quantum repeaters. These devices are essential for the realization of large-scale quantum networks and quantum information processing systems.The applications of quantum photonic devices are wide-ranging. In quantum computing, for example, quantum photonic devices are used for the manipulation and storage of quantum information in the form of photons. In quantum communication, quantum photonic devices enable secure transmission of information through the quantum key distribution and quantum teleportation. Quantum photonic devices also have potential applications in high-precision sensing and metrology, as well as in the development ofquantum-enhanced imaging techniques.Overall, quantum photonic devices and their applications represent a rapidly growing and highly interdisciplinary field, with implications for both fundamental science and advanced technologies. As research in this area continues to advance, we can expect to see even more innovative quantum photonic devices and novel applications in the near future.。

量子力学专业英语词汇1、microscopic world 微观世界2、macroscopic world 宏观世界3、quantum theory 量子[理]论4、quantum mechanics 量子力学5、wave mechanics 波动力学6、matrix mechanics 矩阵力学7、Planck constant 普朗克常数8、wave-particle duality 波粒二象性9、state 态10、state function 态函数11、state vector 态矢量12、superposition principle of state 态叠加原理13、orthogonal states 正交态14、antisymmetrical state 正交定理15、stationary state 对称态16、antisymmetrical state 反对称态17、stationary state 定态18、ground state 基态19、excited state 受激态20、binding state 束缚态21、unbound state 非束缚态22、degenerate state 简并态23、degenerate system 简并系24、non-deenerate state 非简并态25、non-degenerate system 非简并系26、de Broglie wave 德布罗意波27、wave function 波函数28、time-dependent wave function 含时波函数29、wave packet 波包30、probability 几率31、probability amplitude 几率幅32、probability density 几率密度33、quantum ensemble 量子系综34、wave equation 波动方程35、Schrodinger equation 薛定谔方程36、Potential well 势阱37、Potential barrien 势垒38、potential barrier penetration 势垒贯穿39、tunnel effect 隧道效应40、linear harmonic oscillator 线性谐振子41、zero proint energy 零点能42、central field 辏力场43、Coulomb field 库仑场44、δ-function δ-函数45、operator 算符46、commuting operators 对易算符47、anticommuting operators 反对易算符48、complex conjugate operator 复共轭算符49、Hermitian conjugate operator 厄米共轭算符50、Hermitian operator 厄米算符51、momentum operator 动量算符52、energy operator 能量算符53、Hamiltonian operator 哈密顿算符54、angular momentum operator 角动量算符55、spin operator 自旋算符56、eigen value 本征值57、secular equation 久期方程58、observable 可观察量59、orthogonality 正交性60、completeness 完全性61、closure property 封闭性62、normalization 归一化63、orthonormalized functions 正交归一化函数64、quantum number 量子数65、principal quantum number 主量子数66、radial quantum number 径向量子数67、angular quantum number 角量子数68、magnetic quantum number 磁量子数69、uncertainty relation 测不准关系70、principle of complementarity 并协原理71、quantum Poisson bracket 量子泊松括号72、representation 表象73、coordinate representation 坐标表象74、momentum representation 动量表象75、energy representation 能量表象76、Schrodinger representation 薛定谔表象77、Heisenberg representation 海森伯表象78、interaction representation 相互作用表象79、occupation number representation 粒子数表象80、Dirac symbol 狄拉克符号81、ket vector 右矢量82、bra vector 左矢量83、basis vector 基矢量84、basis ket 基右矢85、basis bra 基左矢86、orthogonal kets 正交右矢87、orthogonal bras 正交左矢88、symmetrical kets 对称右矢89、antisymmetrical kets 反对称右矢90、Hilbert space 希耳伯空间91、perturbation theory 微扰理论92、stationary perturbation theory 定态微扰论93、time-dependent perturbation theory 含时微扰论94、Wentzel-Kramers-Brillouin method W. K. B.近似法95、elastic scattering 弹性散射96、inelastic scattering 非弹性散射97、scattering cross-section 散射截面98、partial wave method 分波法99、Born approximation 玻恩近似法100、centre-of-mass coordinates 质心坐标系101、laboratory coordinates 实验室坐标系102、transition 跃迁103、dipole transition 偶极子跃迁104、selection rule 选择定则105、spin 自旋106、electron spin 电子自旋107、spin quantum number 自旋量子数108、spin wave function 自旋波函数109、coupling 耦合110、vector-coupling coefficient 矢量耦合系数111、many-particle system 多子体系112、exchange forece 交换力113、exchange energy 交换能114、Heitler-London approximation 海特勒-伦敦近似法115、Hartree-Fock equation 哈特里-福克方程116、self-consistent field 自洽场117、Thomas-Fermi equation 托马斯-费米方程118、second quantization 二次量子化119、identical particles 全同粒子120、Pauli matrices 泡利矩阵121、Pauli equation 泡利方程122、Pauli’s exclusion principle泡利不相容原理123、Relativistic wave equation 相对论性波动方程124、Klein-Gordon equation 克莱因-戈登方程125、Dirac equation 狄拉克方程126、Dirac hole theory 狄拉克空穴理论127、negative energy state 负能态128、negative probability 负几率129、microscopic causality 微观因果性。

关于量子的英文作文英文：Quantum physics is a fascinating and complex field that has revolutionized our understanding of the universe. Atits core, quantum mechanics is the study of the behavior of matter and energy at the atomic and subatomic level. The principles of quantum mechanics are fundamentally different from those of classical physics, and they have led to some truly mind-bending discoveries.One of the most famous examples of quantum mechanics is the concept of superposition. This refers to the idea that a particle can exist in multiple states simultaneouslyuntil it is observed, at which point it collapses into a single state. This can be difficult to wrap your head around, but it has been experimentally verified time and time again.Another important concept in quantum mechanics isentanglement. This occurs when two particles become linkedin such a way that the state of one particle affects the state of the other, regardless of the distance between them. This has led to the development of technologies like quantum cryptography, which uses the principles of entanglement to create secure communication channels.Despite its many successes, quantum mechanics is still not fully understood. There are many mysteries and paradoxes that continue to baffle scientists, such as the famous Schrödinger's cat thought experiment. However, researchers are making progress every day, and thepotential applications of quantum mechanics are truly exciting.中文：量子物理学是一个令人着迷而复杂的领域，它彻底改变了我们对宇宙的理解。

第1篇Introduction:Quantum entanglement, one of the most intriguing and challenging concepts in quantum mechanics, has puzzled scientists for over a century. This phenomenon, where particles become interconnected regardless of the distance separating them, has far-reaching implications for our understanding of the universe and potential technological advancements. In this interview question, we will delve into the scientific principles of quantum entanglement, its experimental validations, and the potential applications it may offer in the future.Section 1: Introduction to Quantum Entanglement1.1 Definition of Quantum Entanglement:Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles become linked in such a way that the quantum stateof each particle cannot be described independently of the state of the others, even when the particles are separated by large distances.1.2 Historical Background:The concept of quantum entanglement was first introduced by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935 in their famous paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" This paper, often referred to as the EPR paradox, sparked a debate on the completeness and interpretation of quantum mechanics.1.3 Quantum Mechanics and Classical Mechanics:Quantum entanglement is a quintessential feature of quantum mechanics, which fundamentally differs from classical mechanics. In classical mechanics, the state of a system is determined by the positions and velocities of its particles, while in quantum mechanics, particles exist in a probabilistic state until measured.Section 2: The Principles of Quantum Entanglement2.1 Superposition:Superposition is a fundamental principle of quantum mechanics, which states that a quantum system can exist in multiple states simultaneously. This principle allows particles to be entangled, as their combined state cannot be described by the state of each particle individually.2.2 Non-locality:Non-locality is the idea that quantum entangled particles can instantaneously affect each other's states, regardless of the distance separating them. This concept challenges the principle of locality in classical physics, which dictates that no physical influence can travel faster than the speed of light.2.3 Bell's Inequality:John Bell proposed an inequality in 1964 that sets a limit on the amount of non-local correlations that can exist between particles in classical physics. Quantum entanglement violates Bell's inequality, providing experimental evidence for the non-local nature of quantum mechanics.Section 3: Experimental Validations of Quantum Entanglement3.1 Alain Aspect's Experiment:In 1982, Alain Aspect conducted a groundbreaking experiment that confirmed the violation of Bell's inequality, providing strong evidence for quantum entanglement and non-locality. His experiment involved measuring the polarizations of photons emitted from a source and showed that the correlations between the photons exceeded the limits set byBell's inequality.3.2 Quantum Key Distribution (QKD):Quantum key distribution is a secure communication protocol that leverages the principles of quantum entanglement. It allows two parties to share a secret key with the guarantee that any eavesdropping can be detected. QKD has been experimentally demonstrated over long distances, such as satellite-based communication links.3.3 Quantum Computing:Quantum entanglement is a crucial resource for quantum computing, which aims to solve complex problems much faster than classical computers. Quantum computers use qubits, which are entangled particles, to perform calculations by exploiting superposition and interference.Section 4: Implications for Future Technologies4.1 Quantum Communication:Quantum entanglement has the potential to revolutionize communication by enabling secure, long-distance communication using QKD. This technology could be crucial for establishing secure networks and protecting sensitive information.4.2 Quantum Computing:Quantum entanglement is essential for the development of quantum computers, which have the potential to solve complex problems in cryptography, material science, and optimization. Quantum computers could also simulate quantum systems, leading to new discoveries in chemistry, physics, and biology.4.3 Quantum Sensing:Quantum entanglement can be used to enhance the sensitivity of quantum sensors, which have applications in various fields, including gravitational wave detection, quantum metrology, and precision measurement.Conclusion:Quantum entanglement, with its fascinating principles and experimental validations, has the potential to reshape our understanding of the universe and enable groundbreaking technological advancements. From secure communication to powerful quantum computers, the implications of quantum entanglement are vast and far-reaching. As scientists continue to explore this intriguing phenomenon, we can expect even more exciting developments in the field of quantum physics and its applications.第2篇Introduction:Quantum entanglement, one of the most fascinating and enigmatic phenomena in the realm of physics, has intrigued scientists and philosophers alike for decades. This interview delves into the depths of quantum entanglement, exploring its origins, implications, and potential applications. Dr. Emily Newton, a renowned quantum physicist, shares her insights and experiences in this field.Part 1: The Basics of Quantum EntanglementQuestion 1: Can you explain what quantum entanglement is and how it differs from classical entanglement?Dr. Newton:Quantum entanglement is a phenomenon in which two or more particles become interconnected, such that the quantum state of one particle instantaneously correlates with the state of another, regardless of the distance separating them. This correlation persists even when the particles are separated by vast distances, which defies the principles of classical physics.In classical entanglement, such as the entanglement of a pair of dice, the outcome of one die is independent of the other. If you roll a six on one die, it does not affect the outcome of the other die. However, in quantum entanglement, the particles are not independent; their quantum states are correlated in such a way that measuring one particle's state instantly determines the state of the other particle, regardless of the distance between them.Question 2: How was quantum entanglement discovered, and what were the early reactions to this phenomenon?Dr. Newton:Quantum entanglement was first predicted by Albert Einstein, Boris Podolsky, and Nathan Rosen in their famous EPR paradox paper in 1935.They proposed a thought experiment involving two entangled particlesthat seemed to violate the principle of locality, which states that no information can travel faster than the speed of light.The initial reaction to the EPR paradox was skepticism, with Einstein famously dismissing quantum entanglement as "spooky action at a distance." However, subsequent experiments, such as those conducted by John Bell in the 1960s, provided strong evidence in favor of quantum entanglement, leading to a paradigm shift in our understanding of the quantum world.Part 2: The Mechanics of Quantum EntanglementQuestion 3: What are the key factors that contribute to the formation of entangled particles?Dr. Newton:The formation of entangled particles is a result of their interaction during the process of measurement or preparation. For example, when two particles are created together in an entangled state, their quantum states become correlated due to their shared history. This correlationis a fundamental aspect of quantum mechanics and cannot be explained by classical physics.Another way to create entangled particles is through a process called entanglement swapping, where two particles are initially entangled with a third particle, and then the third particle is separated from thefirst two. This results in the first two particles becoming entangled with each other, even though they have never interacted directly.Question 4: Can you explain the concept of quantum superposition and how it relates to entanglement?Dr. Newton:Quantum superposition is the principle that a quantum system can existin multiple states simultaneously until it is measured. This is analogous to a coin spinning in the air, which can be either heads or tails until it lands on one side.In the context of entanglement, superposition plays a crucial role. When two particles are entangled, their combined quantum state is a superposition of the individual states of each particle. This means that the particles can exhibit non-local correlations that are not determined until a measurement is made.Part 3: The Implications of Quantum EntanglementQuestion 5: How does quantum entanglement challenge our understanding of the universe?Dr. Newton:Quantum entanglement challenges our classical understanding of the universe in several ways. Firstly, it defies the principle of locality, which has been a cornerstone of physics for centuries. The idea that particles can instantaneously influence each other across vast distances suggests that the fabric of space-time may not be as fixed as we once thought.Secondly, quantum entanglement raises questions about the nature of reality itself. If particles can be correlated in such a way that their states are instantaneously connected, it challenges the idea that objects have definite properties independent of observation.Question 6: Are there any practical applications of quantum entanglement?Dr. Newton:Yes, there are several potential applications of quantum entanglement. One of the most promising is in quantum computing, where entangled particles can be used to perform complex calculations at speeds unattainable by classical computers. Quantum entanglement is also essential for quantum cryptography, which can be used to create unbreakable encryption methods.Moreover, entanglement has been used in quantum teleportation, where the state of a particle can be transmitted instantaneously from one location to another, potentially leading to new communication technologies.Conclusion:Quantum entanglement remains one of the most intriguing and challenging phenomena in physics. Dr. Emily Newton's insights into the mechanics and implications of this phenomenon provide a deeper understanding of the quantum world and its potential applications. As we continue to explore the mysteries of quantum entanglement, we may uncover new ways to harness its power and reshape our understanding of the universe.第3篇IntroductionQuantum entanglement, one of the most intriguing and mysterious phenomena in the field of quantum mechanics, has captured the imagination of scientists and the public alike. This question invites candidates to delve into the concept of quantum entanglement, its underlying principles, experimental demonstrations, and the potential implications it holds for future technology.Part 1: Introduction to Quantum Entanglement1.1 Definition and Basic PrinciplesQuantum entanglement refers to a phenomenon where two or more particles become interconnected in such a way that the quantum state of each particle cannot be described independently of the state of the others, even when they are separated by large distances. This correlation persists regardless of the distance between the particles, which challenges our classical understanding of locality and separability.1.2 Historical ContextThe concept of quantum entanglement was first introduced by Albert Einstein, Boris Podolsky, and Nathan Rosen in their famous EPR paradox paper in 1935. They described entanglement as "spooky action at a distance," suggesting that it defied the principles of local realism. However, subsequent experiments and theoretical developments have confirmed the reality of entanglement.Part 2: Theoretical Underpinnings of Quantum Entanglement2.1 Quantum SuperpositionQuantum superposition is a fundamental principle of quantum mechanics that allows particles to exist in multiple states simultaneously. This principle is crucial for understanding entanglement, as it enables particles to become correlated in a way that is not possible inclassical physics.2.2 Quantum Correlation and EntanglementQuantum entanglement arises from the non-classical correlations between particles. When particles become entangled, their quantum states become linked, and the state of one particle instantaneously influences the state of the other, regardless of the distance separating them.2.3 Bell's TheoremJohn Bell formulated a theorem in 1964 that demonstrated the incompatibility of quantum mechanics with local realism. Experimentsthat violate Bell's inequalities have confirmed the existence of quantum entanglement and its non-local nature.Part 3: Experimental Demonstrations of Quantum Entanglement3.1 Bell Test ExperimentsBell test experiments have been conducted to test the predictions of quantum mechanics and to demonstrate the non-local nature of entanglement. These experiments involve measuring the properties of entangled particles and analyzing the correlations between them.3.2 Quantum Key Distribution (QKD)Quantum Key Distribution is a protocol that uses quantum entanglement to securely transmit cryptographic keys. It takes advantage of theprinciple that any attempt to intercept the entangled particles will disturb their quantum state, alerting the communicating parties to the presence of an eavesdropper.3.3 Quantum TeleportationQuantum teleportation is the process of transmitting the quantum state of a particle from one location to another, without the particle itself traveling through the space between them. This phenomenon has been experimentally demonstrated and has implications for quantum computing and communication.Part 4: Implications for Future Technology4.1 Quantum ComputingQuantum computing, which relies on the principles of quantum mechanics, has the potential to revolutionize computing by solving certain problems much faster than classical computers. Quantum entanglement plays a crucial role in quantum computing, as it allows for the creation of qubits that can exist in multiple states simultaneously, enabling parallel processing.4.2 Quantum CommunicationQuantum communication utilizes the principles of quantum entanglement and superposition to achieve secure communication and distributed computing. Technologies like QKD and quantum teleportation are expected to transform the field of secure communication and enable new forms of data transmission.4.3 Quantum Sensors and MetrologyQuantum sensors and metrology techniques leverage the precision and sensitivity of quantum entanglement to measure physical quantities with unprecedented accuracy. This has applications in fields such as precision navigation, gravitational wave detection, and quantum simulation.ConclusionQuantum entanglement, with its counterintuitive nature and profound implications, remains a captivating and challenging subject in the field of quantum mechanics. As scientists continue to explore and harness thepower of entanglement, we can expect to see significant advancements in technology, leading to new possibilities in computing, communication, and metrology. This question has provided an opportunity to delve into the fascinating world of quantum entanglement and its potential future impact on society.。

凝聚态物理材料物理专业考博量子物理领域英文高频词汇1. Quantum Mechanics - 量子力学2. Wavefunction - 波函数3. Hamiltonian - 哈密顿量4. Schrödinger Equation - 薛定谔方程5. Quantum Field Theory - 量子场论6. Quantum Entanglement - 量子纠缠7. Uncertainty Principle - 不确定性原理8. Quantum Tunneling - 量子隧穿9. Quantum Superposition - 量子叠加10. Quantum Decoherence - 量子退相干11. Spin - 自旋12. Quantum Computing - 量子计算13. Quantum Teleportation - 量子纠缠传输14. Quantum Interference - 量子干涉15. Quantum Information - 量子信息16. Quantum Optics - 量子光学17. Quantum Dots - 量子点18. Quantum Hall Effect - 量子霍尔效应19. Bose-Einstein Condensate - 玻色-爱因斯坦凝聚态20. Fermi-Dirac Statistics - 费米-狄拉克统计中文翻译：1. Quantum Mechanics - 量子力学2. Wavefunction - 波函数3. Hamiltonian - 哈密顿量4. Schrödinger Equation - 薛定谔方程5. Quantum Field Theory - 量子场论6. Quantum Entanglement - 量子纠缠7. Uncertainty Principle - 不确定性原理8. Quantum Tunneling - 量子隧穿9. Quantum Superposition - 量子叠加10. Quantum Decoherence - 量子退相干11. Spin - 自旋12. Quantum Computing - 量子计算13. Quantum Teleportation - 量子纠缠传输14. Quantum Interference - 量子干涉15. Quantum Information - 量子信息16. Quantum Optics - 量子光学17. Quantum Dots - 量子点18. Quantum Hall Effect - 量子霍尔效应19. Bose-Einstein Condensate - 玻色-爱因斯坦凝聚态20. Fermi-Dirac Statistics - 费米-狄拉克统计。

More informationFundamentals of Photonic Crystal GuidingIf you’re looking to understand photonic crystals,this systematic,rigorous,and peda-gogical introduction is a must.Here you’llfind intuitive analytical and semi-analyticalmodels applied to complex and practically relevant photonic crystal structures.Y ou willalso be shown how to use various analytical methods borrowed from quantum mechanics,such as perturbation theory,asymptotic analysis,and group theory,to investigate manyof the limiting properties of photonic crystals,which are otherwise difficult to rationalizeusing only numerical simulations.An introductory review of nonlinear guiding in photonic lattices is also presented,as are the fabrication and application of photonic crystals.In addition,end-of-chapterexercise problems with detailed analytical and numerical solutions allow you to monitoryour understanding of the material presented.This accessible text is ideal for researchersand graduate students studying photonic crystals in departments of electrical engineering,physics,applied physics,and mathematics.Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals atthe Department of Engineering Physics in´Ecole Polytechnique de Montr´e al,Canada.In2005he was awarded a fellowship from the Japanese Society for Promotion of Science,and he is a member of the Optical Society of America.Jianke Yang is Professor of Applied Mathematics at the University of Vermont,USA.Heis a member of the Optical Society of America and the Society of Industrial and AppliedMathematics.Fundamentals of Photonic Crystal GuidingMAKSIM SKOROBOGATIY 1JIANKE YANG 2´Ecole Polytechnique de Montr ´e al,Canada 1University of Vermont,USA2More informationMore informationcambridge university pressCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521513289C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryLibrary of Congress Cataloging in Publication dataSkorobogatiy,Maksim,1974–Fundamentals of photonic crystal guiding/by Maksim Skorobogatiy and Jianke Y ang.p.cm.Includes index.ISBN978-0-521-51328-91.Photonic crystals.I.Y ang,Jianke.II.Title.QD924.S562008621.36–dc222008033576ISBN978-0-521-51328-9hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationM.Skorobogatiy dedicates this book to his family.He thanks his parentsAlexander and Tetyana for never-ceasing support,encouragement,andparticipation in all his endeavors.He also thanks his wife Olga,his children,Alexander junior and Anastasia,andhis parents for their unconditional love.J.Yang dedicates this book to his family.More informationContentsPreface page xiAcknowledgements xii1Introduction11.1Fabrication of photonic crystals21.2Application of photonic crystals41.2.1Photonic crystals as low-loss mirrors:photonicbandgap effects41.2.2Photonic crystals for out-of-bandgap operation10References112Hamiltonian formulation of Maxwell’s equations(frequency consideration)142.1Plane-wave solution for uniform dielectrics162.2Methods of quantum mechanics in electromagnetism182.2.1Orthogonality of eigenstates192.2.2Variational principle202.2.3Equivalence between the eigenstates of twocommuting Hamiltonians222.2.4Eigenstates of the operators of continuous anddiscrete translations and rotations232.3Properties of the harmonic modes of Maxwell’s equations302.3.1Orthogonality of electromagnetic modes322.3.2Eigenvalues and the variational principle322.3.3Absence of the fundamental length scale in Maxwell’sequations342.4Symmetries of electromagnetic eigenmodes352.4.1Time-reversal symmetry352.4.2Definition of the operators of translation and rotation352.4.3Continuous translational and rotational symmetries382.4.4Band diagrams432.4.5Discrete translational and rotational symmetries44More informationviii Contents2.4.6Discrete translational symmetry and discreterotational symmetry522.4.7Inversion symmetry,mirror symmetry,and other symmetries532.5Problems553One-dimensional photonic crystals–multilayer stacks593.1Transfer matrix technique593.1.1Multilayer stack,TE polarization593.1.2Multilayer stack,TM polarization613.1.3Boundary conditions623.2Reflection from afinite multilayer(dielectric mirror)633.3Reflection from a semi-infinite multilayer(dielectricphotonic crystal mirror)643.3.1Omnidirectional reflectors I683.4Guiding in afinite multilayer(planar dielectric waveguide)693.5Guiding in the interior of an infinitely periodic multilayer703.5.1Omnidirectional reflectors II803.6Defect states in a perturbed periodic multilayer:planarphotonic crystal waveguides823.7Problems864Bandgap guidance in planar photonic crystal waveguides934.1Design considerations of waveguides with infinitelyperiodic reflectors934.2Fundamental TE mode of a waveguide with infinitelyperiodic reflector964.3Infinitely periodic reflectors,field distribution in TM modes984.3.1Case of the core dielectric constantεc<εhεl/(εh+εl)984.3.2Case of the core dielectric constantεl≥εc>εhεl/(εh+εl)1014.4Perturbation theory for Maxwell’s equations,frequencyformulation1034.4.1Accounting for the absorption losses of the waveguidematerials:calculation of the modal lifetime and decay length1044.5Perturbative calculation of the modal radiation loss in aphotonic bandgap waveguide with afinite reflector1064.5.1Physical approach1064.5.2Mathematical approach1085Hamiltonian formulation of Maxwell’s equations for waveguides(propagation-constant consideration)1105.1Eigenstates of a waveguide in Hamiltonian formulation1105.1.1Orthogonality relation between the modes of a waveguide madeof lossless dielectrics111More informationContents ix5.1.2Expressions for the modal phase velocity1145.1.3Expressions for the modal group velocity1145.1.4Orthogonality relation between the modes of a waveguide madeof lossy dielectrics1155.2Perturbation theory for uniform variations in a waveguide dielectric profile1165.2.1Perturbation theory for the nondegenerate modes:example ofmaterial absorption1185.2.2Perturbation theory for the degenerate modes coupled byperturbation:example of polarization-mode dispersion1205.2.3Perturbations that change the positions of dielectric interfaces1235.3Problems126References127 6Two-dimensional photonic crystals1296.1T wo-dimensional photonic crystals with diminishingly smallindex contrast1296.2Plane-wave expansion method1326.2.1Calculation of the modal group velocity1346.2.2Plane-wave method in2D1346.2.3Calculation of the group velocity in the case of2Dphotonic crystals1356.2.4Perturbative formulation for the photonic crystallattices with small refractive index contrast1386.2.5Photonic crystal lattices with high-refractive-index contrast1426.3Comparison between various projected band diagrams1426.4Dispersion relation at a band edge,density of states andVan Hove singularities1446.5Refraction from photonic crystals1476.6Defects in a2D photonic crystal lattice1486.6.1Line defects1486.6.2Point defects1586.7Problems167References171 7Quasi-2D photonic crystals1727.1Photonic crystalfibers1727.1.1Plane-wave expansion method1727.1.2Band diagram of modes of a photonic crystalfiber1767.2Optically induced photonic lattices1777.2.1Light propagation in low-index-contrast periodicphotonic lattices1787.2.2Defect modes in2D photonic lattices with localized defects1817.2.3Bandgap structure and diffraction relation for the modes of auniform lattice182More informationx Contents7.2.4Bifurcations of the defect modes from Bloch band edges forlocalized weak defects1857.2.5Dependence of the defect modes on the strength oflocalized defects1887.2.6Defect modes in2D photonic lattices with nonlocalized defects1927.3Photonic-crystal slabs1957.3.1Geometry of a photonic-crystal slab1957.3.2Eigenmodes of a photonic-crystal slab1977.3.3Analogy between the modes of a photonic-crystal slab and themodes of a corresponding2D photonic crystal2007.3.4Modes of a photonic-crystal slab waveguide2047.4Problems207References208 8Nonlinear effects and gap–soliton formation in periodic media2108.1Solitons bifurcated from Bloch bands in1D periodic media2118.1.1Bloch bands and bandgaps2118.1.2Envelope equations of Bloch modes2128.1.3Locations of envelope solitons2158.1.4Soliton families bifurcated from band edges2168.2Solitons bifurcated from Bloch bands in2D periodic media2188.2.1T wo-dimensional Bloch bands and bandgaps of linearperiodic systems2198.2.2Envelope equations of2D Bloch modes2208.2.3Families of solitons bifurcated from2D band edges2238.3Soliton families not bifurcated from Bloch bands2268.4Problems227References228Problem solutions230Chapter2230Chapter3236Chapter5244Chapter6246Chapter7257Chapter8260 Index263More informationPrefaceThefield of photonic crystals(aka periodic photonic structures)is experiencing anunprecedented growth due to the dramatic ways in which such structures can control,modify,and harvest theflow of light.The idea of writing this book came to M.Skorobogatiy when he was developingan introductory course on photonic crystals at the Ecole Polytechnique de Montr´e al/University of Montr´e al.Thefield of photonic crystals,being heavily dependent onnumerical simulations,is somewhat challenging to introduce without sacrificing thequalitative understanding of the underlying physics.On the other hand,exactly solvablemodels,where the relation between physics and quantitative results is most transpar-ent,only exist for photonic crystals of trivial geometries.The challenge,therefore,wasto develop a presentational approach that would maximally use intuitive analytical andsemi-analytical models,while applying them to complex and practically relevant pho-tonic crystal structures.We would like to note that the main purpose of this book is not to present the latestadvancements in thefield of photonic crystals,but rather to give a systematic,logical,andpedagogical introduction to this vibrantfield.The text is largely aimed at students andresearchers who want to acquire a rigorous,while intuitive,mathematical introductioninto the subject of guided modes in photonic crystals and photonic crystal waveguides.The text,therefore,favors analysis of analytically or semi-analytically solvable problemsover pure numerical modeling.We believe that this is a more didactical approach whentrying to introduce a novice into a newfield.To further stimulate understanding of thebook content,we suggest many exercise problems of physical relevance that can besolved analytically.In the course of the book we extensively use the analogy between the Hamiltonian for-mulation of Maxwell’s equations and the Hamiltonian formulation of quantum mechan-ics.We present both frequency and propagation-constant based Hamiltonian formula-tions of Maxwell’s equations.The latter is particularly useful for analyzing photoniccrystal-based linear and nonlinear waveguides andfibers.This approach allows us touse a well-developed machinery of quantum mechanical semi-analytical methods,suchas perturbation theory,asymptotic analysis,and group theory,to investigate many ofthe limiting properties of photonic crystals,which are otherwise difficult to investigatebased only on numerical simulations.M.Skorobogatiy has contributed Chapters2,3,4,5,and6of this book,and J.Y anghas contributed Chapter8.Chapters1and7were co-authored by both authors.More informationAcknowledgementsM.Skorobogatiy would like to thank his graduate and postgraduate program mentors,Professor J.D.Joannopoulos and Professor Y.Fink from MIT,for introducing him intothefield of photonic crystals.He is grateful to Professor M.Koshiba and ProfessorK.Saitoh for hosting him at Hokkaido University in2005and for having many excitingdiscussions in the area of photonic crystalfibers.M.Skorobogatiy acknowledges theCanada Research Chair program for making this book possible by reducing his teachingload.J.Y ang thanks the funding support of the US Air Force Office of Scientific Research,which made many results of this book possible.He also thanks the Zhou Pei-Yuan Centerfor Applied Mathematics at Tsinghua University(China)for hospitality during his visit,where portions of this book were written.Both authors are grateful to their graduate andpostgraduate students for their comments and help,while this book was in preparation.Especially,J.Y ang likes to thank Dr.Jiandong Wang,whose help was essential for hisbook writing.。

光学专业英语部分refraction [rɪˈfrækʃn]n.衍射reflection [rɪˈflekʃn]n.反射monolayer['mɒnəleɪə]n.单层adj.单层的ellipsoid[ɪ'lɪpsɒɪd]n.椭圆体anisotropic[,ænaɪsə(ʊ)'trɒpɪk]adj.非均质的opaque[ə(ʊ)'peɪk]adj.不透明的；不传热的；迟钝的asymmetric[,æsɪ'metrɪk]adj.不对称的；非对称的intrinsic[ɪn'trɪnsɪk]adj.本质的，固有的homogeneous[,hɒmə(ʊ)'dʒiːnɪəs;-'dʒen-] adj.均匀的；齐次的；同种的；同类的，同质的incidentlight入射光permittivity[,pɜːmɪ'tɪvɪtɪ]n.电容率symmetric[sɪ'metrɪk]adj.对称的；匀称的emergentlight出射光；应急灯.ultrafast[,ʌltrə'fɑ:st,-'fæst]adj.超快的；超速的uniaxial[,juːnɪ'æksɪəl]adj.单轴的paraxial[pə'ræksɪəl]adj.旁轴的；近轴的periodicity[,pɪərɪə'dɪsɪtɪ]n.[数]周期性；频率；定期性soliton['sɔlitɔn]n.孤子，光孤子；孤立子；孤波discrete[dɪ'skriːt]adj.离散的，不连续的convolution[,kɒnvə'luːʃ(ə)n]n.卷积；回旋；盘旋；卷绕spontaneously:[spɒn'teɪnɪəslɪ] adv.自发地；自然地；不由自主地instantaneously:[,instən'teinjəsli]adv.即刻；突如其来地dielectricconstant[ˌdaiiˈlektrikˈkɔnstənt]介电常数，电容率chromatic[krə'mætɪk]adj.彩色的；色品的；易染色的aperture['æpətʃə;-tj(ʊ)ə]n.孔，穴；（照相机，望远镜等的）光圈，孔径；缝隙birefringence[,baɪrɪ'frɪndʒəns]n.[光]双折射radiant['reɪdɪənt]adj.辐射的；容光焕发的；光芒四射的; photomultiplier[,fəʊtəʊ'mʌltɪplaɪə]n.[电子]光电倍增管prism['prɪz(ə)m]n.棱镜；[晶体][数]棱柱theorem['θɪərəm]n.[数]定理；原理convex['kɒnveks]n.凸面体；凸状concave['kɒnkeɪv]n.凹面spin[spɪn]n.旋转；crystal['krɪst(ə)l]n.结晶，晶体；biconical[bai'kɔnik,bai'kɔnikəl] adj.双锥形的illumination[ɪ,ljuːmɪ'neɪʃən] n.照明；[光]照度；approximate[ə'prɒksɪmət] adj.[数]近似的；大概的clockwise['klɒkwaɪz]adj.顺时针方向的exponent[ɪk'spəʊnənt；ek-] n.[数]指数；even['iːv(ə)n]adj.[数]偶数的；平坦的；相等的eigenmoden.固有模式；eigenvalue['aɪgən,væljuː]n.[数]特征值cavity['kævɪtɪ]n.腔；洞，凹处groove[gruːv]n.[建]凹槽，槽；最佳状态；惯例；reciprocal[rɪ'sɪprək(ə)l]adj.互惠的；相互的；倒数的，彼此相反的essential[ɪ'senʃ(ə)l]adj.基本的；必要的；本质的；精华的isotropic[,aɪsə'trɑpɪk]adj,各向同性的；等方性的phonon['fəʊnɒn]n.[声]声子cone[kəʊn]n.圆锥体，圆锥形counter['kaʊntə]n.柜台；对立面；计数器；cutoff['kʌt,ɔːf]n.切掉；中断；捷径adj.截止的；中断的cladding['klædɪŋ]n.包层；interference[ɪntə'fɪər(ə)ns]n.干扰，冲突；干涉borderline['bɔːdəlaɪn]n.边界线，边界；界线quartz[kwɔːts]n.石英droplet['drɒplɪt]n.小滴，微滴precision[prɪ'sɪʒ(ə)n]n.精度，[数]精密度；精确inherently[ɪnˈhɪərəntlɪ]adv.内在地；固有地；holographic[,hɒlə'ɡræfɪk]adj.全息的；magnitude['mægnɪtjuːd]n.大小；量级；reciprocal[rɪ'sɪprək(ə)l]adj.互惠的；相互的；倒数的，彼此相反的stimulated['stimjə,letid]v.刺激（stimulate的过去式和过去分词）cylindrical[sɪ'lɪndrɪkəl]adj.圆柱形的；圆柱体的coordinates[kəu'ɔ:dineits]n.[数]坐标；external[ɪk'stɜːn(ə)l;ek-]n.外部；外观；scalar['skeɪlə]n.[数]标量；discretization[dɪs'kriːtaɪ'zeɪʃən]n.[数]离散化synthesize['sɪnθəsaɪz]vt.合成；综合isotropy[aɪ'sɑtrəpi]n.[物]各向同性；[物]无向性；[矿业]均质性pixel['pɪks(ə)l;-sel]n.（显示器或电视机图象的）像素（passive['pæsɪv]adj.被动的spiral['spaɪr(ə)l]n.螺旋；旋涡；equivalent[ɪ'kwɪv(ə)l(ə)nt]adj.等价的，相等的；同意义的; transverse[trænz'vɜːs;trɑːnz-;-ns-]adj.横向的；横断的；贯轴的;dielectric[,daɪɪ'lektrɪk]adj.非传导性的；诱电性的;n.电介质；绝缘体integral[ˈɪntɪɡrəl]adj.积分的；完整的criteria[kraɪ'tɪərɪə]n.标准，条件（criterion的复数）Dispersion:分散|光的色散spectroscopy[spek'trɒskəpɪ]n.[光]光谱学photovoltaic[,fəʊtəʊvɒl'teɪɪk]adj.[电子]光电伏打的，光电的polar['pəʊlə]adj.极地的；两极的；正好相反的transmittance[trænz'mɪt(ə)ns;trɑːnz-;-ns-] n.[光]透射比；透明度dichroic[daɪ'krəʊɪk]adj.二色性的；两向色性的confocal[kɒn'fəʊk(ə)l]adj.[数]共焦的；同焦点的rotation[rə(ʊ)'teɪʃ(ə)n]n.旋转；循环，轮流photoacoustic[,fəutəuə'ku:stik]adj.光声的exponential[,ekspə'nenʃ(ə)l]adj.指数的;fermion['fɜːmɪɒn]n.费密子（费密系统的粒子）semiconductor[,semɪkən'dʌktə]n.[电子][物]半导体calibration[kælɪ'breɪʃ(ə)n]n.校准；刻度；标度photodetector['fəʊtəʊdɪ,tektə]n.[电子]光电探测器interferometer[,ɪntəfə'rɒmɪtə]n.[光]干涉仪；干涉计static['stætɪk]adj.静态的；静电的；静力的;inverse相反的，反向的，逆的amplified['æmplifai]adj.放大的；扩充的horizontal[hɒrɪ'zɒnt(ə)l]n.水平线，水平面；水平位置longitudinal[,lɒn(d)ʒɪ'tjuːdɪn(ə)l;,lɒŋgɪ-] adj.长度的，纵向的；propagate['prɒpəgeɪt]vt.传播；传送；wavefront['weivfrʌnt]n.波前；波阵面scattering['skætərɪŋ]n.散射；分散telecommunication[,telɪkəmjuːnɪ'keɪʃ(ə)n] n.电讯；[通信]远程通信quantum['kwɒntəm]n.量子论mid-infrared中红外eigenvector['aɪgən,vektə]n.[数]特征向量；本征矢量numerical[njuː'merɪk(ə)l]adj.数值的；数字的ultraviolet[ʌltrə'vaɪələt]adj.紫外的；紫外线的harmonic[hɑː'mɒnɪk]n.[物]谐波。

关于quantum的雅思阅读理解引言概述：Quantum physics, also known as quantum mechanics, is a branch of physics that deals with the behavior of matter and energy at the smallest scales. Understanding quantum concepts is crucial for advancements in various fields, including technology, medicine, and communication. In this article, we will delve into the topic of quantum physics and its significance in IELTS reading comprehension.正文内容：1. Quantum Theory and Its Principles1.1 Wave-Particle Duality: Quantum theory proposes that particles, such as electrons and photons, exhibit both wave-like and particle-like behavior. This principle challenges classical physics, where particles were considered solely as particles or waves.1.2 Superposition: According to quantum theory, particles can exist in multiple states simultaneously. This concept is known as superposition, and it allows for the potential of quantum computing and cryptography.1.3 Quantum Entanglement: Quantum entanglement refers to the phenomenon where two or more particles become correlated in such a way that the state of one particle is instantly linked to the state of another, regardless of the distance between them. This principle has implications for secure communication and quantum teleportation.2. Applications of Quantum Physics2.1 Quantum Computing: Quantum computers utilize the principles of superposition and entanglement to perform complex calculations at an exponential speed compared to classical computers. This technology has the potential to revolutionize fields such as cryptography, optimization problems, and drug discovery.2.2 Quantum Communication: Quantum communication involves the transmission of information using quantum states. Quantum encryption ensures secure communication by exploiting the principles of entanglement and uncertainty. This technology has the potential to protect sensitive information from hacking.2.3 Quantum Sensing: Quantum sensors utilize the unique properties of quantum particles to measure physical quantities with unprecedented precision. This has applications in fields such as navigation, medical imaging, and environmental monitoring.3. Challenges in Quantum Physics3.1 Measurement Problem: The act of measuring a quantum system can disturb its state, leading to the collapse of the superposition. This measurement problem raises questions about the nature of reality and the role of the observer in quantum physics.3.2 Quantum Decoherence: Quantum systems are highly sensitive to their surroundings, which can cause decoherence. This phenomenon disrupts the delicate quantum states and poses challenges for maintaining coherence in quantum technologies.3.3 Quantum Interpretations: The interpretation of quantum mechanics is still a subject of debate among physicists. Different interpretations, such as the Copenhagen interpretation and the Many-Worlds interpretation, offer different explanations for the behavior of quantum systems.4. Quantum Physics in IELTS Reading Comprehension4.1 Vocabulary: Familiarity with quantum-related terms and concepts is essential for understanding reading passages that discuss quantum physics. Being well-versed in terms like superposition, entanglement, and decoherence will aid in comprehending the content.4.2 Inference: IELTS reading passages often require candidates to make inferences based on the information provided. Understanding the principles and applications of quantum physics will enable candidates to make accurate inferences when encountering quantum-related texts.4.3 Critical Analysis: IELTS reading tests candidates' ability to critically analyze information. Being knowledgeable about the challenges and interpretations in quantum physics will help candidates evaluate the validity and implications of the given information.总结：In conclusion, quantum physics plays a crucial role in various scientific and technological advancements. Understanding the principles of quantum theory, its applications, and the challenges it poses is essential for comprehending quantum-related passages in IELTS reading comprehension. By familiarizing oneself with quantum vocabulary, making accurate inferences, and critically analyzing information, candidates can enhance their performance in this aspect of the IELTS examination.。