OPTI 553

Nonlinear Photonics (3 units). Enables students to use advanced optical waveguide analysis with knowledge of physics of nonlinear optics to understand, design and test nonlinear photonics devices. Balances treatment of advanced topics in optical waveguide theory. Introduces nonlinear optics, with emphasis being placed on technologically significant nonlinear photonics phenomena and devices. Prerequisite: OPTI 510R.

Meeting Times:
W & F 12:30-1:45

Instructor:
Professor Robert A. Norwood
Meinel Building, Room 533, Lab 456
Contact: 626-0936 or rnorwood@optics.arizona.edu

Office Hours: By appointment

Required Textbook:
Boyd, Robert W. (2008). Nonlinear Optics (3rd. ed.). Elsevier/Academic Press. ISBN: 9780123694706. Available: ScienceDirect eBook.

Additional readings and notes will be provided from a variety of sources.

Grading:

  • Homework Assignments - 40%
  • Midterm Exam - 30%
  • Final Exam - 30%


    • The course grade will be determined according to the cumulative percentage earned such that 90-100% = A, 80-89% = B, 70-79% = C, 60-69% = D, below 60% = E.
Course Overview:
This course will start with a review of key concepts from 510R Photonics including the generalized constitutive relationship between polarization and electric field and the optical physics of waveguides. Key optical waveguide building blocks such as directional couplers, Y-splitters, and Mach-Zehnder interferometers will be studied both analytically and with waveguide modeling software. Second-order nonlinear optical phenomena such as second harmonic generation, the Pockels effect, sum and difference frequency mixing, and optical rectification will be introduced through the conventional nonlinear optical susceptibility framework, and specific second NLO devices of significant technological impact such as integrated electro-optic modulators, and quasiphasematched waveguide frequency doublers will be discussed, analyzed and modeled. Careful consideration of the NLO materials requirements and state-of-the-art materials choices will be integrated directly into the development of second-order nonlinear photonics. The course will then move on to similarly treat third order NLO, focusing on the nonlinear photonics of optical fiber and high index contrast optical waveguides.

Learning Objectives:
  • Provide a thorough foundation in the optical physics of both second order and third order nonlinear optical phenomena, including an understanding of material requirements, approaches to solving Maxwell's equations in the presence of nonlinear polarization, and quantum mechanical descriptions of NLO phenomena.
  • Provide students with an understanding of optical waveguide physics and integrated optical device building blocks sufficient to perform the design of nonlinear photonic devices, either using analytical approaches or waveguide modeling software.
  • Comprehensively discuss several technologically significant nonlinear photonics devices/ phenomena including quasiphasematched frequency doublers, electro optic modulators, parametric frequency converters, microresonators, and all-optical switches among other topics.
Course Outline
  1. Brief Review of Electromagnetic Theory and Guided Waves
    1. Maxwell’s equations
    2. Reflection and refraction at boundaries
    3. Guided waves

  2. Step-Index and Graded Index Thin-film Waveguides
    1. Dispersion
    2. Generalized parameters
    3. Fields of step-index waveguides
    4. Linearly graded dielectric waveguides
    5. Exponentially graded dielectric waveguides + WKB method

  3. Three-Dimensional Waveguides
    1. Rectangular waveguide modes
    2. Marcatili method
    3. Effective index method

  4. Optical Directional Couplers
    1. Coupled-mode description
    2. Improved coupled-mode description
    3. Δβ couplers

  5. High Index Contrast Waveguides
    1. Materials candidates
    2. Microring resonators
    3. Slot waveguides

  6. Nonlinear Optical Susceptibility
    1. Introduction to nonlinear optics (NLO)
    2. Formal definition of nonlinear susceptibility
    3. General properties
    4. Time domain description
    5. Macroscopic and microscopic quantities
    6. Units

  7. Second Order NLO −χ(2)
    1. χ(2) wave equation
    2. χ(2) tensor
    3. Symmetry considerations
    4. Second harmonic generation (SHG)
    5. Phasematching and quasiphasematching (QPM)
    6. Sum frequency generation (SFG)
    7. Difference frequency generation (DFG)
    8. Optical rectification −THz generation
    9. Optical parametric amplification and oscillation
    10. Electro-optic (Pockels) effect

  8. χ(2) Materials
    1. Perovskite crystals (lithium niobate, tantalate, etc.)
    2. Other crystals (quartz, BBO, organic,…)
    3. Poled polymers

  9. χ(2) Devices
    1. Quasiphasematched (QPM) waveguide frequency doublers
    2. Optical parametric waveguide devices
    3. Terahertz frequency generators
    4. Integrated electro-optic Mach-Zehnder modulators
    5. Integrated electro-optic directional coupler switches

  10. Third Order NLO −χ(3)
    1. χ(3) wave equation
    2. χ(3) tensor
    3. χ(3) symmetry considerations
    4. Origin of χ(3)
    5. Electronic χ(3)
    6. Orientational χ(3)
    7. Thermal χ(3)
    8. Band filling and population dependent χ(3)
    9. Intensity dependent refractive index − n2

  11. χ(3) Effects
    1. Third harmonic generation (THG)
    2. Degenerate four-wave mixing (DFWM)
    3. Nondegenerate four-wave mixing (NDFWM)
    4. Self-focusing
    5. Self-phase modulation (SPM)
    6. Cross phase modulation (XPM)
    7. Optical Kerr effect (OKE)
    8. D.C. Kerr effect
    9. Stimulated Raman scattering (SRS)
    10. Stimulated Brillouin scattering (SBS)
    11. Nonlinear absorption (NLA)

  12. χ(3) Materials
    1. Glasses
    2. Semiconductors
    3. Organic/Polymeric

  13. Nonlinear Photonics in Single-mode Optical Fibers
    1. Review of LP modes
    2. Phase velocity, group velocity and dispersion
    3. Propagation of pulses in single-mode fibers
    4. Effects of first order and second order group velocity dispersion
    5. Nonlinear envelope equation
    6. Self-phase modulation
    7. Soliton basics
    8. Microstructured fibers for nonlinear photonics

  14. χ(3) Devices
    1. Kerr lens mode locker
    2. Optical bistable switch
    3. All-optical directional coupler switch
    4. Ultrafast Kerr gate
    5. Parametric wavelength generator
    6. Supercontinuum generator
    7. Microresonator and slot waveguide devices