PHYC/ECE 463 Advanced Optics I F. Elohim Becerra Chavez

PHYC/ECE 463 Advanced Optics IF. Elohim Becerra ChavezEmail:fbecerra@unm.eduOffice: PAÍS 2514Phone: 505 277-2616Lectures: Tuesday and Thursday, 2:00-3:15 pmPAIS 1140.Textbook: Many good ones (See webpage)Lectures: many based on Introduction to Optics (3rd Edition):Frank L. Pedrotti Leno M. Pedrotti Leno S. Pedrotti. (Ch 1-28)More good books in websiteAdditional resourcesOptics, 4th Edition: E. Hecht.Fundamentals of Photonics, 2nd Edition: B. E. A. Saleh, Malvin Carl Teich.Optics, 2nd Edition, M. Klein and T. FurtakHomework: Problem sets including problems from book(s) and additional ones about one set per week.They are posted one week before they are due. HW must be turned in to the TA's mailbox before 5:00 pm on the due date.Office hours: Tuesday 12-13 pm. You may also arrange a meeting for another time via email.TA: Ahmed Alhassan. office hrs: Monday 1-2:30 pm in lobby. You may also arrange a meeting for another time via email.Grading1. Homework 20%1. Report and presentation 20%2. Midterm exam: 25%3. Final: 35%Tentative Exam Dates (subject to change): Midterm, October 19. Final Tuesday, Dec. 7 10am-12pm (TBD ).

PHYC/ECE 463 Advanced Optics ISyllabus TopicsBelow is a tentative list of topics that will be covered. You can find the calendar for the course in theTentative Schedule1. Introduction to optics- Overview and fundamentals of light; Fermat principle; reflection and refraction;ray and eikonal equations.2. Geometrical optics- Image formation and ray tracing; Paraxial optics and basic optical elements (lens,mirrors, etc.); Matrix methods in paraxial optics; Stops and apertures; Aberration theory3. Physical optics- Maxwell Equations, E&M waves and Gaussian beams; Dispersion and group and phasevelocity; Fresnel equations of reflection and refraction though dielectric interface4. Interference- Superposition of fields; Interference of multiple fields; Interference in multi-layer thin films(matrix formalism); Interferometers5. Diffraction theory- Fraunhofer (far field) diffraction; Diffraction grating; Fresnel (near-field) diffraction;Fresnel plates6. Polarization- polarization of light; Jones matrix formalism; Polarizers and waveplates; Stokes vectors7. Modern and quantum optics- If time allows, we will discuss some special topics such as Fundamentals;Field quantization and Dirac notation; Quantum properties of light, laser cooling,

PHYC/ECE 463 Advanced Optics IClass Website: 1/index.htmTentative Schedule

Projects for the article and presentationsSuggested topics in classical, modern or quantum optics. You may want to choose another topic, andyou should discuss with the instructor about the suitability.Classical and nonlinear optics and applications1. LIGO, gravitational wave detection.2. Nonlinear crystals for the generation of light, entanglement and squeezing3. Frequency combs and optical clocks4. Super-resolution microscopy and fundamental limits, and optical tweezersModern Optics1. Superconducting technologies for single photon and photon number resolving detection2. Wave-particle duality of light and matter foundations and applications: TEM, atom interferometers,and other applications.3. Laser cooling and trapping of atoms4. Plasmons and plasmonicsQuantum Optics1. Entanglement, Bell Inequality, entanglement verification.2. Quantum properties of light, quantum coherence and correlations: bunching, antibunching, andHong–Ou–Mandel interference.3. Squeezing: generation, characterization, verification, and applications4. Applications: Quantum metrology, quantum communications, quantum sensing,

What is light? Wave?Light can behave as a particle and as a wave Particle?Fresnel Equations(Polarization and Amplitude)Huygens principle(wiki)(1678)Young double slit(1801)(1821)Maxwell Equations(1861)

Historical notes of light Quantum mechanics is born: Planck (1900), Bohr (1913) Wave? Light can behave as a particle and as a wave Particle?(1900)(1913)

A Brief History of Laser Einstein postulated the principle of the “stimulated emission” (1917)𝐾𝐸𝑒 hν Φ(1906)(1917)𝐾𝐸𝑒Φhν

Optics: properties of light: Special Relativity Photons: quanta of light Relativistic particleE 2 m2c 4p chhc pE 2 m2c 4pc 2m2c 4v c 1 2EEPhoton: m 0p 𝑉𝑙𝑖𝑔ℎ𝑡 CEch hc p Epc 2v cEm: rest massp: momentumE: total energyv: velocityh: Planck constantRelativistic massm1 v2vc

Wave Particle DualityAny particle has a wave-like behavior de (Broglie 1924)h pPlanck constant 6.6x10-34 J.sMomentum 34mBaseball ball ball 1x10An electorn in an atom electron 0.1x10 m 9What is important about λ? If λ 1, The wavelike properties of the body are not evident in theinteraction with atoms/matter. if λ datom 1 Å, wave properties are important in the interaction.Electron microscope: electron as wave: (electron diffraction λ 0.1nm)

What is light?E instantanous electric fieldE0 amplitudeeˆ polarization vector Electromagnetic radiation:ˆ 0 cos( t kz )E eE E0êŝ-E0 Propagation is governed by Maxwell’s equations 2 2 c / frequency2 k sˆ sˆ wavevector c wavelength phase

Maxwell EquationsWave EquationME: No charge or current sourcesTransverse fields221 𝐄1 𝐏 2 𝐄 2 2 𝑐 𝑡 𝜖0 𝑐 2 2 𝑡Propagation in a dielectricAtomic Polarization PPhysicsE(𝐫, 𝑡) ℜe ℰ(𝐫, 𝜔)𝑒 𝑖𝜔𝑡𝐃 𝜖0 𝐄 𝐏𝐏 𝜖0 𝝌𝐄EngineeringE(𝐫, 𝑡) ℜe ℰ(𝐫, 𝜔)𝑒 𝑗𝜔𝑡

Models of light 𝑳𝒊𝒎{Physical Optics} {Geometrical Optics}𝝀 𝟎Geometrical OpticsPhysical (Wave) Opticsλ dimensions of optical systemsλ dimensions of optical systemsLight as wavesWave opticsGaussian opticsMatrix methodsLight as raysRay tracingMatrix methods ImagingImaging systemslens designSome Optical DevicesOther Wave propertiesInterferenceDiffractionCoherence (Quant and Class)Etc

Huygens PrincipleEach point on the surface of a wave disturbance (wavefront) may be a source ofspherical waves, which themselves progress with the speed of light in themedium (𝒗 𝒄Τ𝒏) and whose envelope at a later time t constitutes the newwavefront.Each point on the surface of the wavefront may act as a source of sphericalwaves (wavelets), which themselves propagating with 𝒗 in the medium, andwhose envelope at a later time t constitutes the new wavefront.Plane WaveSpherical WaveWavefront after Aperture

Fermat PrincipleLight travels between two points along the path that requiresthe least time, as compared to other nearby paths. This corresponds to a straight line in a homogeneous mediumAlso this principle applies to inhomogeneous mediaModern version:A light ray, in going between two points, must traverse a trajectory withoptical path length which is stationary with respect to variations of the path.The optical path length of a ray from a point A to a point B:BBAAn ( x, y , z )S nds n( x, y, z )dsAn extremum in the light travel time between A and B is an extremum of the optical path length between those points.The optical length of the path followed by light between A and B, is an extremum.B S nds 0AEuler–Lagrange equationB F ( y, y ', x)dx 0As s ( x, y ) 𝐹 𝑦 𝑑 𝐹 0𝑑𝑥 𝑦′

Fermat PrincipleLaw of Reflection

Fermat PrincipleLaw of ReflectionCalculate time t that takes light to travel from pointA to point BOpticalPath AP PBFind the extremum of the optical path length between those pointsIn this case, that corresponds to minimize the time of travel tsin opposite side / hypotenuse

Fermat PrincipleLaw of Refraction

Fermat PrincipleLaw of RefractionCalculate time t that takes light to travel from pointA to point BOpticalPath AP n1 PB n2Find the extremum of the optical path length between those pointsIn this case, that corresponds to minimize the time of travel tsin opposite side / hypotenuse

Formal ReportsFormal reports are based on a topic related to optics, modern optics or quantum optics.Should follow the style of a scientific journal (Typed, one or two columns) Main sections (see guide in class website for specific details)–Abstract: concise description of methods and results.–Introduction: motivation, background and summary of the field/work andexperiments–Methods: description of experimental methods and–Data: present the data, use plots or/and tables–Results and data analysis: describe how the data analysis was done and presentyour results with errorsPhys. Rev. endix if necessaryPurpose–Gain familiarity with formal writing style of scientific journalsOpt. Lett.

Oral Presentation15-minute Oral Presentation based on an experiment. It will be followed byquestions (about 5 minutes) from students, TA and instructor. Suggested outline–Motivation–Theoretical background–Description of the experiment/field of study–Description of data collection process/methods, theory, etc.–Results and discussion of the work; state-of-the-art in the field–Application of the physics learned in technology /fundamental research–ConclusionPurpose–Strengthen your communication skills–Think how to present your results to a broad audience and defend your ideas

Rode map of courseGeometrical OpticsPhysical (Wave) Opticsλ dimensions of optical systemsλ dimensions of optical systemsIntroduction to opticsPhysical opticsFundamentalsMaxwell EquationsFermat principleE&M waves and Gaussian beamsReflection and refractionray and eikonal equationsGeometrical opticsImage formation and ray tracingParaxial optics and basic opticalelements (lens, mirrors, etc.)dispersion and group/phase velocityFresnel equationsInterferenceSuperposition of fieldsMatrix methodsInterference of multiple fields and (matrixformalism)Stops and aperturesInterferometersAberration theoryDiffraction theoryPolarizationFraunhofer (far field) diffractionPolarization of lightDiffraction gratingJones matrix formalismPolarizers and waveplatesStokes vectorsFresnel (near-field) diffractionModern and Quantum OpticsField quantization

Classical and nonlinear optics and applications 1. LIGO, gravitational wave detection. 2. Nonlinear crystals for the generation of light, entanglement and squeezing . Introduction to optics Fundamentals Fermat principle Reflection and refraction ray and eikonal equations Geometrical optics Image formation and ray tracing Paraxial optics and .