## Courses

## nanoHUB-U: Nanophotonic Modeling

A free self-paced course exploring the next generation of optical and opto-electronic systems.

Classic ray optics played a crucial role in the development of early photonic technology, where components such as glass spheres, thin lenses, and conventional mirrors control the propagation of light. Over time, limitations of these components in terms of size, flexibility, and cost have become increasingly clear. This has impeded solutions to many problems, such as improving thin-film solar cells and enabling higher-speed optical communications.

Fortunately, new optical and opto-electronic systems utilizing components whose size is at the wavelength scale (nanophotonics) or smaller (plasmonics, metamaterials) stand ready to enable these new applications. However, their small component size also subjects them to strong interference effects that are sensitive to the wavelength of light. Thus, these systems often require a full-wave analysis at each wavelength, based directly on Maxwell's equations. These equations generally cannot be solved analytically, necessitating numerical techniques to find their solutions. This course will cover advanced methods of simulating nanophotonic, plasmonic, and metamaterial structures. Related applications in thermal radiation will also be discussed.

## Scientific Overview

## Course Objectives

In this course, we will study advanced methods for simulating nanophotonic, plasmonic and metamaterial systems, including photonic bandstructure solvers, transfer matrix analysis, rigorous coupled wave analysis (RCWA), finite-difference time domain (FDTD), and finite-element methods (FEM). These methods will enable one to explain, predict and design the properties and capabilities of next-generation optical waveguides, lasers, detectors, and solar cells.

## Who Should Take the Course

Anyone seeking an understanding of optical and opto-electronic systems structured at the wavelength scale. Generally these systems will be characterized as having critical dimensions at the nanometer scale. These can include nanophotonic, plasmonic, and metamaterial components and systems. This course may be useful for advanced undergraduates with the prerequisites listed below; graduate students interested in incorporating these techniques into their thesis research; and practicing scientists and engineers developing new experiments or products based on these ideas.

## Prerequisites

This course is intended for audiences with background in the physical sciences or engineering. Basic familiarity with the principles of Maxwell’s equations, covered in a first year class on physics is needed. Some working knowledge of integral and vector calculus, as well as basic linear algebra, is assumed. Prior experience with basic programming techniques and algorithms is useful but not strictly required; pointers to web-based resources covering these background topics will be available.

## Course Outline

Unit 1: Bandstructures and Bandgaps

Unit 2: Solving Multilayered Photonic Systems

Unit 3: Direct Simulation of Maxwell’s Equations in Time

Unit 4: Advanced Time-Domain Simulations

Unit 5: Simulating Multiscale Systems with Finite-Element Methods

## Course Resources

- A free nanoHUB.org account is required to access some course components.
- Homework exercises with solutions.
- Online quizzes to quickly assess understanding of material after most video lectures.
- An online forum, hosted by nanoHUB. Students enrolled in the course will be able to interact with one another.
- Practice exams for each module.

## Licensing

## Registration

This self-paced course is available at no cost.

**nanoHUB-U is powered by nanoHUB.org, the home for computational nanoscience and nanotechnology research, education, and collaboration.**