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Transformations of Functions III

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Updated: Jun 1, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

Transformation optics using graphene.

Ashkan Vakil¹, Nader Engheta

¹Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.

Science (New York, N.Y.)

|June 11, 2011

Summary

This summary is machine-generated.

Graphene can be engineered into a one-atom-thick platform for infrared metamaterials and transformation optics. By controlling conductivity patterns with electric fields, researchers can tune terahertz and infrared frequencies for novel photonic devices.

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Area of Science:

Optical science and engineering
Condensed matter physics
Materials science

Background:

Metamaterials and transformation optics enable precise control of electromagnetic fields.
Graphene's unique electronic properties offer potential for advanced optical applications.

Purpose of the Study:

To theoretically investigate graphene as a platform for infrared metamaterials and transformation optical devices.
To explore methods for tailoring electromagnetic fields using patterned graphene conductivity.

Main Methods:

Theoretical modeling of spatially inhomogeneous, nonuniform conductivity patterns in graphene.
Utilizing static electric fields to tune graphene's chemical potential and conductivity.
Analyzing the behavior of electromagnetic fields interacting with patterned graphene.

Main Results:

Demonstrated that patterned graphene can function as a one-atom-thick platform for infrared metamaterials.
Showcased the ability to tune graphene conductivity across terahertz and infrared frequencies.
Identified the potential for creating "patches" with distinct conductivities on a single graphene flake.

Conclusions:

Spatially engineered graphene offers a versatile platform for developing novel infrared metamaterials and transformation optical devices.
Tunable conductivity via electric fields provides a powerful mechanism for controlling optical properties.
This approach opens avenues for numerous photonic functions and advanced metamaterial concepts.